a rectangular room is 14 feet by 20 feet. the ceiling is 8 feet high. a. find the length and width of the smaller wall. 14 by 8 (express your answer in feet) b. find the area of the smaller wall. 112 (express your answer in square feet) c. find the area of the larger wall. 160 (express your answer in square feet) d. find the total area of the four walls in the room. 544 (express your answer in square feet) e. if a gallon of paint costs $36.50 and it covers 350 square feet on average, what is the cost of painting the room walls with two coats of paint? $73.00 f. this room is well-insulated and is on the north side of the house. how large an air conditioner would this room require? round to the nearest thousand btus. 6,000
Answers
a) The length and width of the smaller rectangle wall (in blue colour) are 14 feet and 8 feet respectively.
b) Area of smaller wall of room is 112 ft².
c) Area of larger wall of room is 160 ft².
d)The total area of the four walls in the room is 544 ft².
e) Total cost of painting the room walls with two coats of paint is $ 146.
f) In thousand btus, 6000 btus sized air conditioner would this room require.
We have, a rectangular room 14 feet by 20 feet, ceiling is 8 feet high. See the above figure,
a) The blue is smaller wall (rectangle ) and brown is the largest wall.
Length of smaller wall ( in blue colour)
= 14 feet
Width of smaller wall = 8 feet
b) Area of rectangle is product of length and width of rectangle. So, Area of smaller wall(in blue colour) = 8 × 14
= 112 ft²
c) For Larger wall (in brown colour)
length = 20 feet and width = 8 feet
So, Area of larger wall = 8× 20 = 160 ft².
d) Total area of the four walls in the room = 2 ( area of smaller wall ) + 2 ( area of larger wall) = 2( 112) + 2( 160) = 224 + 320 = 544 ft².
e) The cost of one gallon of paint
= $36.50
One gallon paint covered approx. 350 square feet. Also, it is said that painting the room walls with two coats of paint that is painting become double = 2× 544 = 1088 ft²
Now, how many 350 ft² area are formed in 1088 ft² = 1088/350 = 3.108 ~ 4 ( because we can only buy a full gallon of paint not 0.1 gallons etc.).
Cost of painting the 350 ft² area = $36.50
Total cost of painting the room walls with two coats of paint i.e., 1088 ft² = 4× $36.50 = $ 146..
f) Now, we have this room is well-insulated and is on the north side of the house. To determine the size of air conditioner we need some parameters of room. If the room is well-insulated, then the level of insulation is 10 and if the room is poorly insulated, then the level of insulation is 18. In this case the level of insulation is 10, i = 10. If the room faces north, then the exposure is 16. In this case, the room faces north and thus the e = 16. We can then determine the BTU rating. BTU rating = (w×h×i×l×e)/60
= (14 x 8 x 10 x 20 × 16)/60
= 358, 400/60
= 17,920/e = 17,920/16
≈ 5,973 ~ 6000
Hence, required air conditioner size is 6,000.
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Related Questions
please help I have tried to Do this problem like 8 times alr
Answers
Answer:
B and C I think.....
Step-by-step explanation:
it makes sense cuz if u make a line it'll kinda go through.
a table is 180 inches long. a bench is 23% shorter than the table. how long is the bench?
Answers
Answer: the bench is 138.6 inches long
Equation with variable on both sides
I need help today and I need it now just today
Answers
The solution to the equations are as follows:
x = 0
r = -4
b = -8
n = -3
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
The equation can be solved by find the values of the variables as follows:
Hence,
5.
1 - 3x = 3x + 1
-3x - 3x = 1 - 1
-6x = 0
x = 0
6.
4r + 8 + 5 = -15 - 3r
4r + 13 = -15 -3r
13 + 15 = -3r - 4r
28 = -7r
r = 28 / -7
r = -4
7.
-12 - 4b = 4 - 2b
-12 - 4 = -2b + 4b
-16 = 2b
b = -8
8.
3n - 15 = 7n + n
3n - 7n - n = 15
-5n = 15
n = -3
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Hello! I'm taking geometry and any help would be appreciated!
Answers
Answer: [tex]4\sqrt{26}[/tex]
Step-by-step explanation:
This is a rather tricky question at first, but it's easy when you figure out the trick.
The key here is using the Pythagorean theorem twice.
We see that the big triangle is divided by its height into two smaller ones.
First, use the Pythagorean theorem on the triangle on the left to find the height.
height = [tex]\sqrt{80-64}=\sqrt{16} =4[/tex]
Now that we know the height is 4, we can use the Pythagorean theorem on the triangle on the right to find x.
x = [tex]\sqrt{20^{2}+4^{2} } =\sqrt{416} = 4\sqrt{26}[/tex]
And there we have our final answer.
You went to Sweet Spot to get ome candy. The cot i $5. 00 per pound. You have a coupon that give you a dicount of $0. 20 off per pound. If you buy $4 pound of candy, what will your total cot be, excluding tax?
Answers
The total cost of the candy excluding tax is $19.2
How to find the total cost of the candy excluding taxFrom the question we have that
The cost of the candy per pound is $5.00
And a coupon that gives a discount of $0..20 per pound
hence 4 pounds of candy without discount is
= 4 * 5
= $20
the discount is solved to be
= 4 * 0.2
= 0.8
subtracting the discount
= 20 - 0.8
= $19.2
So the amount to be paid for the candy is $19.2
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How do you convert vertex form to factored form?
Answers
The way to convert the vertex form to factored form is explained below.
The term vertex is defined as a special point of a mathematical object, and is usually a location where two or more lines or edges meet.
Here we have to write down the steps to convert the vertex form to factored form.
The very first steps is to expand the vertex form into standard quadratic form and then use the quadratic root formula to determine the roots.
Here as we all know that factored term is the product of a constant and two linear terms and they are the roots of the function.
So, now we have to use the quadratic formula to convert them into factor form.
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What does the factored form of a quadratic function tell you about the function's graph?
Answers
The factored form of the quadratic function is f(x) = a(bx + c) (dx + e)
The term quadratic function is defined as a polynomial function with one or more variables in which the highest exponent of the variable is two and the graph of the quadratic equation is always forms the parabola.
Here we have given that we have to find the the factored form of a quadratic function
As we all know that the general form of the quadratic function is written as,
=> f(x) = ax² + bx + c
While we factorize the general form then it can be expanded like the following,
=> f(x) = a(bx + c) (dx + e)
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This diagram was constructed with a straightedge and compass. A is the center of one circle, and C is the center of the other. Select all true statements.
Answers
The correct answers are 1, 2, and 5 AB=BC,AD=2AC and BD=CD.
What is circle?Circle is a two-dimensional shape made up of points that are all the same distance from the center point. This distance is called the radius. Circles are one of the most fundamental shapes in geometry, and can be found in nature in many places, from the sun to the rings of Saturn. Circles can also be used to create other shapes such as ellipses, sectors and arcs.
1. The two circles have the same radius.
2. The two circles intersect at two distinct points.
3. The line segment connecting A and C is the diameter of the larger circle.
4. The line segment connecting A and C is the radius of the smaller circle.
5. The two circles have different radii.
6. The two circles have the same circumference.
The correct answers are 1, 2, and 5.
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supplementary angles.
If the measure of
measure of
m
Answers
The additional angles are P and Q. The measure of angle P = 116 if the measure of angle Q is 64º
What is angle?A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms. An angle is formed when two straight lines or rays meet at a single terminal.The place where two points converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which meaning "corner."When two lines come together at a common point, an angle is created. They are expressed as a number of degrees, denoted by the symbol °. Acute, right, obtuse, and reflex angles are the other three significant types of angles. 360 degrees make up a circle.Additional angles add up to 180.
P+Q = 180
P +64 = 180
Subtract 64 from each side
P = 180-64
P =116
The complete question is:
Angle P and angle Q are supplementary angles. If the measure of angle Q is 64º, find the measure of angle P.
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San Francisco's population has been declining since the "dot com" bubble burst. In 2002, the population was 776,000. The population P of San Francisco is P=776000e^-0. 015, where
t = 0 represents the year 2002. According to this model, when will the population reach 700,000?
Answers
The population will reach 700,000 in the year 2044. The equation to calculate this is t = ln(700000/776000)/(-0.015), which gives t = 42.
1. We are given the population of San Francisco in 2002, which is 776,000.
2. We are also given the equation P=776000e^-0.015, which is a model for the population of San Francisco over time.
3. We need to figure out when the population will reach 700,000.
4. To do this, we need to rearrange the equation to solve for t, the number of years since 2002.
5. Rearranging the equation gives us t = ln(700000/776000)/(-0.015).
6. Plugging in our values gives us t = 42.
7. This means that the population of San Francisco will reach 700,000 in the year 2044 (i.e. 42 years since 2002).
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how to find the domain and range of a piecewise function
Answers
To find the domain and range of a piecewise function, you will need to consider each piece separately and then combine the results. First Identify the domain of each piece, then Identify the range of each piece and Combine the domains and ranges
Identify the domain of each piece: The domain of a piecewise function is the set of all input values (x-values) for which the function is defined. For example, if a piece of the function is defined for x > 2, then the domain for that piece would be all real numbers greater than 2.Identify the range of each piece: The range of a piecewise function is the set of all output values (y-values) that the function can produce. For example, if a piece of the function is defined as y = x^2, then the range for that piece would be all non-negative real numbers.Combine the domains and ranges: Once you have identified the domains and ranges for each piece, you can combine them to find the overall domain and range of the piecewise function. The overall domain is the set of all input values for which any piece of the function is defined, and the overall range is the set of all output values that any piece of the function can produce.Note: Sometimes you may find that domain or range of a certain piece is not mentioned in the function, in that case, you can assume it to be the default domain or range of real numbers.
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7) Write an expression for the following situation: Francine saves money in two separate bank accounts. She deposited $200 in one account and then adds $50 monthly. In her second account she deposited $100 and puts in $75 monthly. Write an expression to show her balance after m months.
Answers
Take the example of a $10,000 savings account earning 2% interest annually. Since the interest rate is 0.02, expressed as a decimal, the following formula would be appropriate: Interest equals $10,000 divided by 0.02 times one to equal $200.
How to calculate simple interest in a savings account?By dividing the account value by the interest rate and the length of time the money has been in the account, you can figure out how much simple interest you'll receive in a savings account. A savings account's interest is money you earn, not money you pay, so keep that in mind.Interest = P x R x T is the formula for calculating interest.
P is Principal amount
R is the interest rate
T is the quantity of time periods.
Take the example of a $10,000 savings account earning 2% interest annually. Since the interest rate is 0.02, expressed as a decimal, the following formula would be appropriate:Interest equals $10,000 divided by 0.02 times one to equal $200.The finest savings accounts pay interest rates of more than 2%. However, some accounts provide far lower earnings. The average savings rate across the country is actually 0.33%. The savings calculator on NerdWallet allows you to calculate the amount of interest you could earn using various rates and timeframes.The interest rate would be stated as 0.0015 for a deposit of $10,000 in a bank account that only pays 0.15% interest annually. For this situation, the computation would be:Interest is calculated as $10,000 divided by 0.0015 times one.
Interest equals $15.
In terms of practicality, this method works well for approximating the amount of interest that money in a savings account can earn.The Complete Question is interest rate.
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The expression that shows Francine balance after 'm' months is
First bank : 200 + 50m
Second Bank : 100 + 75m
How to calculate simple interest in a savings account?By dividing the account value by the interest rate and the length of time the money has been in the account, you can figure out how much simple interest you'll receive in a savings account. A savings account's interest is money you earn, not money you pay, so keep that in mind.
Simple interest is calculated based on a loan's principle or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principle sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
Interest = P x R x T is the formula for calculating interest.
P is Principal amount
R is the interest rate
T is the quantity of time periods.
For this situation, the computation would be:
In the first bank she deposited $ 200 initially and $50 every month so
The equation will be 200 + 50*m
'm' is the number of months
In the second bank she deposited $ 100 initially and $70 every month so
The equation will be 100 + 75*m
'm' is the number of months
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Nathan wants to work at most 50 hours per week. Write an inequality representing that additional constraint. Then, graph it on the same coordinate plane above.
Answers
Answer:
250
Step-by-step explanation:
Which line on the coordinate plane has a zero slope?
Answers
Answer:
Line 1
Step-by-step explanation:
Slope = (y₂ - y₁)/(x₂ - x₁)
Now, in line 1, all the y coordinates are equal, meaning, that y₂ - y₁ = 0 no matter what. Hence, line 1 is the answer.
Cheers!
6. 0.3k - 4m
k = 20 and m = -2
Please help me and show the work please giving 20 points need in 20mins
Answers
The equation evaluates to -2 when k = 20 and m = -2
What is a linear equation in 2 variables?
A linear equation in two variables is an equation that can be written in the form of
ax + by = c
where a, b, and c are constants and x and y are the variables. This equation represents a straight line in a two-dimensional coordinate system where x and y are the coordinates. The values of x and y that satisfy the equation form the set of solutions of the equation.
0.3k - 4m = 0.3(20) - 4(-2) = 6 - 8 = -2
Explanation:
First substitute the given values of k and m into the equation: 0.3k - 4m = 0.3(20) - 4(-2)
Next, simplify the multiplication: 0.3(20) = 6
Now we can simplify the subtraction of a negative number: 4(-2) = 8
So we have: 6 - 8 = -2
As you can see, the equation evaluates to -2 when k = 20 and m = -2
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A 2.8 cm object is placed 35mm in front of a converging lens. The magnification of the lens is 2.5.
a) What is the distance of the image created?
b) What is the height of the image?
c) Describe the S.A.L.T. of the image.
Answers
The image will be formed 23.31 cm along the +x direction of the lens. The height of the image is h{i} = 7 cm.
What is magnification of lens?The magnification produced by a lens is defined as ratio of the height of the image to the height of the object. It is denoted by 'm'.
Given is that a 2.8 cm object is placed 35mm in front of a converging lens. The magnification of the lens is 2.5.
Given is that -
m = h{i}/h{o}
h{i} = 2.8 x 2.5
h{i} = 7 cm
f = {object distance} / {(1 / Magnification) + 1)} × 1000
f = {3.5} / {(1/2.5) + 1} x 1000
f = 2.5 cm
Using the lens formula -
1/d(o) + 1/d(i) = 1/(f)
1/d(i) = 1/2.5 - 1/2.8
1/d(i) = 0.0429
d(i) = 1/0.0429
d(i) = + 23.31 cm
Therefore, the image will be formed 23.31 cm along the +x direction of the lens. The height of the image is h{i} = 7 cm.
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Please reduce each fraction, and give an explanation. Thanks so much!
Answers
Answer:
Step-by-step explanation:
Given that
a
= 10 cm and
b
= 13 cm, work out the height of the triangle.
I want the response only
Answers
The height of the triangle will be equal to 16.4 cm.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that the two sides of the right-angle triangle are a = 10 cm and b = 13 cm.
The height of the triangle will be calculated as,
c² = a² + b²
c² = 13² + 10²
c² = 169 + 100
c = √( 269 )
c = 16.4 cm
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Solve for X, Leave in simplest radical form.
Answers
In mathematics, a radical is a number or expression that represents the principal value of the square root, cube root, or any other higher-order root of a given number or expression.
What is radical form?In mathematics, radical form refers to the expression of a radical in which the number or variable under the radical sign is a product of factors, and any factor that is a perfect power has been removed and is represented as a power outside the radical sign.The radical symbol (√) is used to indicate that the quantity inside the symbol is a radical. An example of a radical in its simplest form is √9, which is equal to 3, the square root of 9. A radical can also be in "radical form" where the number or variable under the radical sign is a product of factors, and any factor that is a perfect power (such as a square or cube) has been removed and is represented as a power outside the radical sign. For example √(36x^6) = 6x^3.If one angle in a right-angled triangle is 30 degrees, and one side has a length of 16 units, then the length of the side opposite the 30 degree angle can be found using the sine function.sin(30) = opposite/hypotenuse
so, the length of the opposite side = sin(30) * hypotenuse
The hypotenuse is the side opposite the right angle, and has a length of 16 units, so we can substitute this into the equation:
sin(30) = opposite/16
To find the length of the opposite side, we can multiply both sides of the equation by 16:
opposite = (sin(30))*16
opposite = 8
So the length of the other side of the triangle is 8 units.
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there will be 45 people on the guest list. 13 of the people will be Musicians, and the rest will be fashion professionals. what is the ratio of the musicians to fashion professionals?
Answers
The ratio of the musicians to fashion professionals is 13 : 32
what is the ratio of the musicians to fashion professionals?Total number of people on the guest list= 45
Number of musicians= 13
Number of fashion professionals = Total number of people on the guest list - Number of musicians
= 45 - 13
= 32 people
The ratio of the musicians to fashion professionals = 13 : 32
Ultimately, based on the given situation the ratio of musicians to fashion professionals = 13 : 32
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Theorem 6.1C states that if a quadrilateral is a parallelogram, then its consecutive _____ are supplementary.
Answers
According to Theorem 6.1C, a quadrilateral's subsequent angles are supplementary if it is a parallelogram.
One of the most fundamental geometric shapes is the square. This particular parallelogram contains four sides that are identical to one another and four right angles. Due to its two sets of parallel sides and four right angles, a square is also a rectangle.
A parallelogram's consecutive angles are congruent. A parallelogram's diagonals cut each other in half. A rhombus has four right-angled angles. A rhombus has consecutive sides that are congruent. Conclusion 6.3C. A parallelogram becomes a rectangle if one of its angles is a right angle.
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a sample of midterm grades for five students showed the following results: 69, 62, 79, 87, 73. which of the following statements are correct, and which should be challenged as being too generalized? (a) the average midterm grade for the sample of five students is 74. (b) the average midterm grade for all students who took the exam is 74. (c) an estimate of the average midterm grade for all students who took the exam is 74. (d) more than half of the students who take this exam will score between 67 and 82. (e) if five other students are included in the sample, their grades will be between 62 and 87. which of the above statements are correct? (select all that apply.) the average midterm grade for the sample of five students is 74. the average midterm grade for all students who took the exam is 74. an estimate of the average midterm grade for all students who took the exam is 74. more than half of the students who take this exam will score between 67 and 82. if five other students are included in the sample, their grades will be between 62 and 87. which of the above statements should be challenged as being too generalized? (select all that apply.) the average midterm grade for the sample of five students is 74. the average midterm grade for all students who took the exam is 74. an estimate of the average midterm grade for all students who took the exam is 74. more than half of the students who take this exam will score between 67 and 82. if five other students are included in the sample, their grades will be between 62 and 87
Answers
The (a) and (c) statements are correct out of five statements are (a) and (c) and other statments i.e., (b), (d) and (e) are too generalised statements.
We have a sample of midterm grades for five students are following 69, 62, 79, 87, 73. Average Formula : It is also called the arithmetic mean, which is calculated by dividing the sum of all given observations to the total number of observations.
Average = (a₁+ a₂+ a₃+ ---+ aₙ )/n
where, a₁, a₂,a₃,--,aₙ --> Obersvations
n --> number of observations
So, Average midgrade is written as
= (69+62+79+87+73)/5 = 370/5 = 74
a) Average of midgrade for the sample of five students is equals to 74, so it is a correct statement.
b) Statement (b) is too generalised because the average 74 is base only on a sample of five students not for all students.
c) A sample five students is selected from population (all students), so the average misgrade 74 of five students referred as estimate for all students who took the exam. Thus, it is correct statement.
d) This statement is too generalised because it is possible that the population deviates from this sample of five students.
e) This statement is too generalised because it is possible that the newly added five students could have different grades which may be lower than 62 and greater than 87.
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Complete question:
A sample of midterm grades for five students showed the following results: 69, 62, 79, 87, 73. which of the following statements are correct, and which should be challenged as being too generalized?
(a) the average midterm grade for the sample of five students is 74.
(b) the average midterm grade for all students who took the exam is 74.
(c) an estimate of the average midterm grade for all students who took the exam is 74.
(d) more than half of the students who take this exam will score between 67 and 82.
(e) if five other students are included in the sample, their grades will be between 62 and 87.
What is the remainder when 2x² − 5x − 1 divided by X − 3?
Answers
The remainder when 2x² - 5x - 1 divided by x - 3 is (2x + 1)
Let p(x) represents a polynomial 2x² − 5x − 1 and m(x) represents a polynomial x - 3
i.e., p(x) = 2x² − 5x − 1
and m(x) = x - 3
we need to find the remainder when 2x² − 5x − 1 divided by x − 3
If we divide a polynomial p(x) = 2x² − 5x − 1 by m(x) = x - 3 using polynomial long division method, the result is:
p(x) / m(x)
= ( 2x² - 5x - 1 ) ÷ (x - 3)
= [ ( 2x² - 5x - 1 ) × ( 2x + 1)] + 2
This means, the quotient is ( 2x + 1) and the remainder is 2
(see in attachment)
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6.
The area of a triangle is 120 m². If the base is
12 m, what is the height of the triangle?
Answers
Therefore , the solution of the given problem of triangle comes out to be height x is 20 m.
What does a triangle signify exactly?Polygons include triangles since they have four sides or more. It has a simple, geometric shape. The letters ABC make up a triangle, which is a square angle. Euclidean geometry results in a single rectangle or square so when sides remain not coincident. Because they have 3 components and three corners, triangles are polygons. A triangle's corners are where its three sides meet. The total of the angles in a triangle is 180 degrees.
Here,
Given :
Area of triangle is 120 m².
the base length is 12m
To find the height = x,
=>Area = 1/2 * base * height
=> 120 = 1/2 * 12 * x
=> 120 = 6 *x
=> x = 120/6
=> x =20
Therefore , the solution of the given problem of triangle comes out to be
height x is 20 m.
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The area of a rectangle is [tex]12x^6y^7[/tex] . If the width of the rectangle is [tex]3x^2z[/tex] , what is the length of the rectangle? A = lw
Answers
Answer:
[tex]l = \dfrac{4x^4y^7}{z}[/tex]
Step-by-step explanation:
[tex]A = l\cdot w[/tex]
We can divide both sides of this formula by width to solve for length.
[tex]\dfrac{A}{w} = l[/tex]
Then, we can plug in the given values for width and area.
[tex]\dfrac{12x^6y^7}{3x^2z} = l[/tex]
Finally, we can solve for length by applying the quotient exponent rule.
[tex]\dfrac{x^a}{x^b} = x^{(a-b)}[/tex]
[tex]\dfrac{12x^6y^7}{3x^2z} = l[/tex]
[tex]4\cdot x^{(6-2)} \cdot \dfrac{y^7}{z} = l[/tex]
[tex]l = \dfrac{4x^4y^7}{z}[/tex]
The students at Benson Middle School were asked to choose a favorite Friday activity. The table shows the survey results for 200 students.
Favorite Percentage of
Activity Students
Bowling 10%
Movies
30%
Dance
50%
10%
Games
How many students chose movies as a favorite activity?
O A 10
OB. 30
C. 60
D. 100
Answers
Answer:c60
Step-by-step explanation:
Which of the following is not a polynomial ?
a: √3x^2-2√3x+3 ,
b: 3x^3/2-5x^2-1/√2x-1 ,
c: x+1/x ,
d: 5x^2-3x+ √2
Answers
The answer is c: x+1/x, which is not a polynomial because it contains a fraction (1/x).
This is not a polynomial because it contains a fraction (1/x). A polynomial is an expression consisting of variables, constants, and exponents. It can be of any degree, but it must not contain any fractions. The other three options (a, b, and d) are all polynomials because they only contain variables, constants, and exponents.
For example, option a: √3x^2-2√3x+3, can be written as 3x2-2x+3, which is the standard form of a polynomial. Similarly, option b: 3x3/2-5x2-1/√2x-1, can be written as 3x2-5x+1, and option d: 5x2-3x+√2, can be written as 5x2-3x+2, which are both in the standard form of a polynomial.
Therefore, the answer is c: x+1/x, which is not a polynomial because it contains a fraction (1/x).
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Jake spent d dollars to go on vacation. He bought a plane ticket for $250 and stayed in a hotel for 5 nights. If the cost of the hotel room was the same each night, what expression can be used to find how much Jake paid each night for the hotel?
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The expression can be used Jake paid each night for the hotel is:
x = d/5 - $50
Now, According to the question:
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
The given data is:
He bought a plane ticket for $250 and stayed in a hotel for 5 nights.
The price d is equal to $250 + 5 prices of staying in a hotel for a night.
If we let "x" be the price per night then we can get the following:
The expression will be:
d = $250 + 5x
5x = d - $250
[tex]x = \frac{d - 250}{5}[/tex]
x = d/5 - $50
Hence, The expression can be used Jake paid each night for the hotel is:
x = d/5 - $50.
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What is AX² in quadratic equation?
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AX² is the standard form of a quadratic equation, where A is a coefficient and X is a variable.
In mathematics, a quadratic equation is a polynomial equation of the form ax2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to zero. A quadratic equation can have either one, two, or no real solutions, depending on the value of the discriminant, b2 - 4ac. The discriminant determines the nature of the roots of the equation: if it is positive, the equation has two distinct real solutions; if it is zero, the equation has one repeated real solution; and if it is negative, the equation has two complex conjugate solutions.
The standard form of a quadratic equation is ax2 + bx + c = 0, where a is the coefficient of the x2 term, b is the coefficient of the x term, and c is the constant or free term. AX2 is the standard form of the equation, where A is the coefficient of the x2 term and X is the variable. If the coefficient A is not equal to 1, the equation can be simplified by dividing both sides of the equation by A. Solving a quadratic equation requires the use of the quadratic formula, which is used to find the roots of the equation. The quadratic formula states that the roots of the equation are x = [-b ± √(b2 - 4ac)]/2a.
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Point B is between A and C if A , B , and C are collinear and the equation AB + BC = AC is true, where AB , BC , and AC are the distances between points A and B , B and C , and A and C , respectively.
Answers
The statement AB + BC = AC is true according to the segment addition postulate.
What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.
The smaller segments in this problem are given as follows:
AB and BC.
The large segment is given as follows:
AC.
Hence the equation is given as follows:
AB + BC = AC.
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