The initial 4 gallons and the fractions of [tex]\frac{1}{2}[/tex] and [tex]1\frac{1}{4}[/tex] gallons of paint used on the first day indicates;
The number of gallons of paint left when they completed the first day of painting is [tex]2\frac{1}{4}[/tex] gallonsWhat is a fraction in mathematics?A fraction is the representation of a number in quotient form such that the value of the number is obtained by dividing the numerator by the denominator.
The amount of paint Lyle and Ming started painting the room with = 4 gallons
Amount of paint Lyle used on the first day = [tex]\dfrac{1}{2}[/tex] gallons of paint
The amount of paint Ming used on the first day = [tex]1\frac{1}{4}[/tex] gallons of paint
Required; The amount of paint remaining after the first day of painting
The paint left after the first day of painting, V, is the difference between the amount of paint with which the painting was started and the amount used by Lyle and Ming on the first day
Therefore; [tex]V = 4 - \left(\dfrac{1}{2} + 1\dfrac{1}{4} \right) = 4 - \left(\dfrac{1}{2} +\dfrac{5}{4} \right) = 4 - \dfrac{7}{4}[/tex]
[tex]V = 4 - \dfrac{7}{4} = \dfrac{16-7}{4} = \dfrac{9}{4} = 2\dfrac{1}{4}[/tex]
The amount of paint left after the first day is [tex]2\frac{1}{4}[/tex] gallonsLearn more about fractions here:
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According to the fundamental theorem of algebra, how many zeros does the function f(x) = 5x - 9 have?
The algebraic fundamental theorem states that there are 12 zeros in the function f(x) = 15x12 + 41x9 + 13x2 10.
What is fundamental theorem?Theorem that connects the ideas of differentiating a function (calculating the gradient) and integrating a function is known as the fundamental theorem of calculus (calculating the area under the curve). With the exception of a constant value that depends on where one starts to compute area, the two procedures are inverses of one another.One of the antiderivatives (also known as an indefinite integral), let's say F, of some function f, may be derived as the integral of f with a variable bound of integration, according to the first section of the theorem, which is frequently referred to as the first fundamental theorem of calculus. This indicates that continuous function antiderivatives existacc to our question-
The degree that we need to identify in a polynomial is the largest exponent used in the equation. In this case, 15x¹², has the largest exponent. It is the degree of n used to determine the number of zeros.Thus, n = 12 so number of zero is also 12.hence,there are 12 zeros
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Tickets for the school play sell for $4 each. Which graph shows the relationship between the number of tickets s
(x) and the total income from the tickets (y)?
14-
12
Dollars
10
8
6
4
2
14
42
12
SH
4 6
8 10 12 14 X
Tickets
The graph of (y = 4x), which depicts the relationship between the quantity of tickets sold (x) and the sum of the proceeds from the sales (y), can be drawn by first formulating the linear equation and then using the transformation.
Which is the function's graph?
We have a piecewise function right here:
If x > 6, f(x) = 0.5*x - 2.
If x > 6, f(x) = -x - 1
Given:
Each ticket for the school play is $4.
There have been 'x' tickets sold in total.
The tickets generated 'y' in total revenue.
The graph showing the relationship between the quantity of tickets sold (x) and the sum of the ticket sales (y) can be drawn using the procedures below:
Form the linear equation in two variables as a first step.
y = 4x
The total revenue from the tickets is shown in the equation above.
Draw the graph of (y = x) in step two.
Step 3: In the graph of (y = x), multiply the x-axis by 4 units. The graph that is produced is (y = 4x).
You may find the graph for (y = 4x) below.
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X+3y+z=-8
2x+y-6z+20
x-2y+z=-13
The solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
We have the following set of equations -
x+3y+z=-8 ..[1]
2x+y-6z=20 ..[2]
x-2y+z=-13 ..[3]
We can write eq [3] as -
z = - 13 - x + 2y
So, eq [1] and [2], will become -
x + 3y + (-13 - x + 2y) = -8
x + 3y - 13 - x + 2y = -8
5y = - 8 + 13
5y = 5
y = 1 ..Eq[4]
AND
2x + y - 6z = 20
2x + y - 6(- 13 - x + 2y) = 20
2x + y + 78 + 6x - 12y = 20
2x + 1 + 78 + 6x - 12 = 20
8x = 47
x = 5.875 ..Eq[5]
Now -
x - 2y + z = -13
5.875 - 2 + z = - 13
z = 16.875
Therefore, the solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875.
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A carpet installer measures three rectangular bedrooms for new carpeting how much carpet is needed for the three bedrooms bedroom a 3.1 m x 3.1 m bedroom be 2.9 m x 3.2 m bedroom c2.5 m x 3.4 m
The 27.4 m² of carpet is needed for three bedrooms.
Firstly we will calculate the area of each room.
Area of bedroom a = 3.1 × 3.1
Area of bedroom a = 9.61 m²
Area of bedroom b = 2.9 × 3.2
Performing multiplication on Right Hand Side of the equation
Area of bedroom b = 9.29 m²
Area of bedroom c = 2.5 × 3.4
Area of bedroom c = 8.5 m²
Total area of all the rooms = 9.61 + 9.29 + 8.5
Performing addition on Right Hand Side of the equation
Total area of all the rooms = 27.4 m²
Hence, 27.4 m² carpet is required for three bedrooms.
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Which values of aand b make the following equation true?
(5x²y²){-4xªy³) =−20xªy°
O
a = 11, b = 7
O a = 11, b = 10
O a=28, b = 7
O a= 28, b = 10
The value a = 2 and b = 5 is makes the expression (5x²y²){-4xªy³) =−20xªyᵇ as true.
Expression:
An expression is set of numbers or variables combined using the operations +, -, * and /.
Given,
Here we have the expression (5x²y²){-4xªy³) =−20xªy°.
Now, we have to the value of a and b which make both equation as equal.
In order to get the value a and b, first, we have to solve the expression in the left hand side,
To solve this type of equation, the first step is to combine the like terms, then we get,
=> (5x²y²){-4xªy³)
=> (5 x -4) (x² xᵃ) (y² y³)
Now, we have to do the multiplication on it, then we get,
=> -20 xᵃ⁺² y²⁺³
=> -20xᵃ⁺²y⁵
Now, we have to equate both LHS and RHS, then we get,
=> -20xᵃ⁺²y⁵ = -20xᵃyᵇ
While we looking into the equation, we have identified that the value of a is 2 and the value of b is 5.
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The table shows the side
lengths and perimeters of
regular hexagons. Is the
relationship between the
perimeter and the side
length of the hexagons
proportional? Explain.
The relationship between the perimeter and the side length of the hexagons is proportional.
What is a proportional relationship?A proportional relationship is one that illustrates the constant between the data that are given.
In this case, when the side length is 2, the perimeter is 12. The constant is:
= Perimeter / Length
= 12 / 2
= 6
Also, when the length is 3, the perimeter is 18. The constant will be:
= 18 / 3
= 6
Since they have 6 as constant, it's a proportional relationship.
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Which triangle congruence postulate or theorem proves that these triangles are
congruent?
The angle-side-angle (ASA) Congruence theorem proves that
ΔABC and ΔPQR are congruent triangles.
We know that the angle-side-angle ASA Congruence theorem states that if two angles and the side between these angles of one triangle are equal to two angles and the side between then of another triangle then those two triangles are congruent.
In given triangles ABC and PQR,
∠ABC ≅ ∠PQR
BC ≅ QR
∠BCA ≅ ∠QRA
so, by ASA Congruence theorem ΔABC ≅ ΔPQR
Therefore, the angle-side-angle (ASA) Congruence theorem proves that
ΔABC and ΔPQR are congruent triangles.
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There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, what is the probability that everyone in the group is a girl
There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, then the probability that everyone in the group is a girl is 1/30
It is given that,
Total number of students = 10
Number of boys = 6
Number of girls = 4
Total number of ways to select 3 students from 10 students.
10C3= 10!/ 3!7!= 120
Total number of ways to select 3 students from 4 girls
4C3 = 4!/ 3!=4
The probability that everyone in the group is a girls is
P = 4/120
= 1/30
Hence , the probability that everyone in the group is a girl is 1/30
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Work out the length of x if one of the lengths is 9.7cm.Give your answer rounded to 3 significant figures.
Tysm if u can work this out correctly.
Considering the figure of a right angle triangle, the given length is the hypotenuse,. The unknown side x is calculated to be 6.86 cm
How to find xinformation given in the question
hypotenuse = 9.7 cm
opposite = x
adjacent = x
The problem is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = opposite² + adjacent²
opposite = adjacent
plugging the values as in the problem
let x be the required distance
9.7² = x² + x²
94.09 = 2x²
47.045 = x²
x² = 47.045
x = √47.045
x = 6.8589
x = 6.86 to 3 significant figures
side x is 6.86 cm
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Select the ordered pair that is NOT marked on the coordinate plane below.
Answer: C. (2, 1)
Step-by-step explanation:
The numbers labeled are
(-5, -8)
(-2, 1)
(4, 0)
(2, 9)
Find coordinates by looking at each line. (x, y)
The x-axis is the horizontal line in the middle.
The y-axis is the vertical line going across.
The x-axis always goes first when plotting down coordinates, and y goes second.
So, the one NOT labeled is C (2, 1)
the area of a rectangle shown is 44m2
3 2/3 m
x?
work out the missing length x
which shape has a larger area: a rectangle that is 7 inches by 3/4 inch, or a square length 2 1/2 inches? Show your reasoning
The area of the of the rectangle is 5.25square inch and the area of the square is 6.25square inch. Therefore the square has larger area.
What is area of plane shape?The area of a shape is the “space enclosed within the perimeter or the boundary” of the given shape. We calculate the area for different shapes using formulas.
Area formula in rectangle is L× W and in square is L^2. This happened in square becos square has all it's sides equal. Where L and W are length and Width respectively
The area of rectangle with dimension 7inches by 3/4 inch is 7×3/4= 5.25 square inches
The area of the square with dimension 2 1/2 inches is( 5/2)^2= 25/4= 6.25m
Therefore the square has larger area
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Select the correct answer. Amy types at an average speed of 38 words per minute. She has already typed 1,450 words of her final paper, which will be more than 4,000 words. Which inequality can be used to solve for x, the number of minutes it will take Amy to finish typing her paper? A. 38x − 1,450 > 76 B. 38(x + 1,450) > 4,000 C. 38x > 4,000 D. 38x + 1,450 > 4,000
The inequality that can be used to solve for x, the number of minutes it will take Amy to finish typing her paper is D. 38x + 1,450 > 4,000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Since Amy types at an average speed of 38 words per minute and has already typed 1,450 words of her final paper, which will be more than 4,000 words.
Let the number of minutes be x.
This will be:
1450 + 38(x) > 400
1450 + 38x > 4000
In conclusion, the correct option is D.
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Felipe received a $25.00 gift card for a photo center. He used it to buy prints that cost 5 cents each. The remaining balance, B (in dollars), on the card after
buying x prints is given by the following function.
B(x)=25.00-0.05x
What is the remaining balance on the card if Felipe bought 20 prints?
Answer:
24
Step-by-step explanation:
lets set up the equation
x=25-(0.05x20) this is
x=25-1
x=24
PLEASE ANSWER
there are no choises
The relation between angle 1 and angle 2 is they are equal and corresponding angle.
What are parallel lines?
Two lines are said to be parallel when they do not intersect each other. We can also say that two lines that run along and meet at infinity are called parallel lines.
What are corresponding angles?
Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines and the transversal.
Given, m and l are parallel line.
Hence, m and l satisfy the condition of parallel lines.
Therefore, the angle 1 and angle 3 are equal.
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A solution that is 20% acid and 80% water is mixed with a solution that is 50% acid and water. If twice as much 50% acid solution is used as 20% solution, then what is the ratio of acid to water in the mixture of the solutions?
Answer:
The ratio of acid to water is 2 to 3 in the mixture of the two solutions
This can be thought of as a chemistry problem or a math problem, but both use practically the same process to find the final answer.
So, let's say 2 liters of 50% acid and 1 liter of 20% acid is mixed.
In total, there is 2*(50%) + 1*(20%) of acid, so there is 1 liter of pure acid in 2 liters of 50% acid, and 0.2 liters of pure acid in 1 liter of 20% acid. This in total is 1.2 liters of acid. The total volume is 2 + 1 liters, which is 3 liters. the percentage can be found by dividing the amount of pure acid by the total volume, so 1.2/3, which equals 0.4, or 40%. The ratio would be 40% to 100-40%, or 40% to 60%, or 2 to 3
Which of the following shows an example of two irrational numbers being multiplied to get a rational number?
Answer:
[tex]\sqrt{2}[/tex] × [tex]\sqrt{8}[/tex] And [tex]\sqrt{2}[/tex] ×[tex]\sqrt{3}[/tex]
Step-by-step explanation:
3x9 are both whole numbers and 0x[tex]\sqrt{5}[/tex] has only one irrational number
Answer:
C) √2 × √8---------------------------
Option A3 × 9 = 27No, all three numbers are rationalOption B0 × √5 = 0No, one irrational number multipliedOption C√2 × √8 = √16 = 4Yes, two irrational numbers multiplied to get a rational numberOption D√2 × √3 = √6No, √6 is still irrational numbercan someone answer this question really quick
c = 2.97r is the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost
How to write an equation that describes proportional relationships?Two variables have a proportional relationship if all the ratios of the variables are equivalent
In order to write an equation that describes the proportional relationship r, the number of reams purchased and c, the total cost, we need to write a proportional equation using the variables:
c α r (Note: α is the proportion symbol)
c = kr
k = c/r
Where k is the constant of proportionality
As shown in the image, you can see that 4 reams cost $11.88 and 6 reams cost $17.82
k = c/r
k = 11.88/4 = 2.97 or 17.82/6 = 2.97
c = kr
c = 2.97r
Therefore, the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost is c = 2.97r. Enter c = 2.97r in the box
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can someone solve this?
Find the values of the variables and the measures of the angles.
Answer:
x = 52°
y = 25°
z = 90°
Step-by-step explanation:
We know there are 180 degrees in a triangle. The box represents 90 degrees.
90° + x + 38° = 180°
x + 128° = 180°
x = 52°
Next, we know that a straight line is equal to 180 degrees. Again, the box represents 90 degrees.
90° + z = 180°
z = 90°
Lastly, we will use the same process for angle x, but for angle y.
y + z + 65° = 180°
y + 90° + 65° = 180°
y + 155° = 180°
y = 25°
Please, can someone help me with this math? I would greatly appreciate it!
The proof that shows that lines DC and AB are parallel is shown below.
What is the SSS Congruence Theorem?The SSS congruence theorem states that two triangles that have three corresponding congruent sides are congruent to each other.
When two triangles are proven to be congruent triangles, invariably, we can state that the corresponding parts of both triangles are also equal to each other by CPCTC.
The following proof shows lines DC and AB are parallel lines:
Statement Reasons
1. AB = CD 1. Given
AD = CB
2. Line AC = Line AC 2. Reflexive property
3. Triangle ADC ≅ Triangle ABC 3. SSS
4. Angle 1 ≅ Angle 4 4. CPCTC
5. DC║AB 5. Converse of alternate interior ∠s theorem
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Write an equation in slope-intercept form for the line that passes through the given point
and is parallel to the graph of the equation.
(1,-3); y=-2r+5
Answer:
equation: y= -2x-1
Step-by-step explanation:
y= -2x+b
-3= -2(1)+b
-3= -2+b
b= -1
equation: y= -2x-1
please help me I’m really stuck on this
Answer:
x < 1 and x > -4 (more down below)
Step-by-step explanation:
First we have to solve the algebra
|-2x - 3| + 2 < 7
|-2x - 3| < 5
1. -2x - 3 < -5 2. -2x -3 < 5
-2x < -2 -2x < 8
x < 1 x > -4 (switch the expression)
Now... The two answers are x < 1 and x > -4
The interval notation is a number line with circles on the two points (answers)
Sorry I can't exactly explain what that is you might have to search it up, but you need a number line like this, and you need to draw another line above the -5 and 1 with an open circle on -5 and 1
O-----------------------O
<---5, -4, -3, -2, -1, 0, 1, 2-->
For graphing, make a graph with 5 points on each side with 4 quadrants or whatever reasonable size, and draw a vertical line that extends all the way above and below your graph above 1 on line x and a vertical line all the way above and below your graph above above -5 on x, then shade everything in between those two lines.
This helps you to know what value you plug in for X makes the inequality true (shaded region)
Eddie is on holiday in Italy
Eddie has €150 to spend on gifts. He buys 1 pair of sunglasses for €70
3 pairs of shorts for €15 each
He also wants to buy a pair of trainers costing €40
Has Eddie got enough money to buy the trainers?
Answer:
No
Step-by-step explanation:
Total money = €150
1 pair of sunglasses = €70
3 pairs of shorts = €15 × 3 = €45
then, Total = €70 + €45 + x
€150 = €115 + x
x = €150 - €115
x = €35
Which means Eddie got only €35 left on him which is not enough for him to buy the trainers
domain of "-x^4-x^3+3x^2+2x+6"
The domain of the given function is -∞ < x < ∞.
What is a domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.So, the function is:
-x⁴-x³+3x²+2x+6Now, the domain of the given function is:
The set of input or argument values for which the function is actual and defined is known as the function's domain.Neither the function's domain constraints nor its undefined points exist.The domain will therefore be -∞ < x < ∞.
Therefore, the domain of the given function is -∞ < x < ∞.
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50 points look at picture (if u troll i will get u banned)
The measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.
According to the question,
We have the following information:
We have a figure where angle MCJ is 130°.
Now, we can extend the two given lines as imaginary lines. After extending the lines, we will find that these lines are parallel and the lines are being cut by another line.
We know that in this case the alternate interior opposite angles are equal and the sum of consecutive alternate interior angles is 180°.
Now, ∠MCJ and ∠CMB are alternate interior opposite angles and thus they are equal.
Hence, the measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.
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HELP ASAP !!!! Use the equation one fourth plus s equals 18 over 20 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
a. The two numbers between which the solution to the equation lies are 0 and 1.
b. The value of the variable "s" is 13/20.
How to solve Algebra Word Problems?The equation given to us is one fourth plus s equals 18 over 20. This can be expressed as;
¹/₄ + s = ¹⁸/₂₀
s = ¹⁸/₂₀ - ¹/₄
s = (18/20) - (5/20)
s = (18 - 5)/20
s = 13/20
The solution is a rational number. A rational number is defined in mathematics as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
We can determine two rational numbers such that the solution is in between them. A rational number smaller than the solution is 0. A rational number larger than the solution is 1. Hence, the solution lies between 0 and 1.
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“Find the requested information based on the given facts.
Total sales is $55,000
The commission is 3.5%
Determine the commission.”
Can someone please help?
Answer:
$1925
Step-by-step explanation:
So your problem is $55,000 x 3.5%
You can rewrite this as:
55,000 x 3.5/100 or 55,000 x 35/1000
Now multiply. I will remove the /1000 for now.
55,000x35=1925000
Now, divide 1925000 by 1000.
1925/1000=$1,925
write down the value of 9 and a half?
The value of 9 and a half will be 9 1/2.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Here, we want to find the value of 9 and half. This will be:
= 9 + 1/2
= 9 1/2
The value is 9 1/2.
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will give you brainliest!! ASAP
Answer:
686 cm^2
Step-by-step explanation:
4(7)=28
7(7)=49
49 x 28= 1372
1372/2=686
hopes this helps
402 students were surveyed about their preferences of sports. 140 students like football, 144 students like baseball, and 42 students like both sports. how many students like exactly one of the two sports? a) 200 b) 140 c) 284 d) 98 e) 102 f) none of the above.
The students that will like exactly one of the two sports out of football and baseball is 200.
What is set theory?These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).
Here,
F=140
B=144
F∩B=42
F-B=n(F)-n(F∩B)
=140-42
F-B=98
B-F=n(B)-n(F∩B)
=144-42
=102
So, the students that will like exactly one of the two sports,
=102+98
=200
There are 200 students who will only enjoy one of the two sports—football or baseball.
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