The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)
Given equation y = 3x + a / 2x - 5
= y(2x - 5) = 3x + a
= 2xy - 5y = 3x + a
= 2xy - 3x = a - 5y
= x(2y-3) = a - 5y
Hence, x = (a - 5y) / (2y - 3)
First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).
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Caleb solved this equation and recorded his work.
7.4x + 4.1(2x − 4) = −2.3(x − 6) − 21.6
1. 7.4x + 8.2x − 16.4 = −2.3x + 13.8 − 21.6
2. 15.6x − 16.4 = −2.3x + 35.4
3. 17.9x − 16.4 = 35.4
4. 17.9x = 51.8
5. x ≈ 2.89
When Caleb verified his solution, it didn’t work. What mistake did he make?
In step 1, the distributive property was not used properly on the right side of the equation.
In step 2, the like terms were not combined properly on the right side of the equation.
In step 3, the addition property of equality was not used properly to isolate the variable term.
In step 5, the division property of equality was not used properly to solve for x.
hurry pls :,)
Answer:
the mistake was in subtracting 21.6 from 13.8
Step-by-step explanation:
the answer was suppose to be -7.8 and not 35.4
Answer:
the mistake was in subtracting 21.6 from 13.8
Step-by-step explanation
the answer was suppose to be -7.8 and not 35.4
As the diameter (d) of a circle increases in size, the circumference (C)
increases Likewise, as the diameter decreases in size, so does the circumference,
The constant of variation between Cand dist. Describe the kind of variation
between eireumference and diameter Write the equation.
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
The equation of the parabola
f(x) = [tex]7x^2[/tex]
The standard vertex form of a parabola is
y = [tex]a(x-h)^2[/tex] + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) = [tex]7x^2[/tex]
The value of a = 7
Substitute the values in the vertex form of a parabola
y = [tex]7(x-3)^2[/tex] + 5
Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
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Need help
The equation of the line L1 is y = 3x - 2
The equation of the line L2 is 3y - 9x + 5 = 0
Show that these two lines are parallel
Which pairs of triangles are similar? check all that apply. â–³abc ~ â–³def â–³def ~ â–³ghi â–³ghi ~ â–³abc â–³ghi ~ â–³jkl â–³jkl ~ â–³abc
The similar pairs of triangles are given as follows:
DEF and HGI.JKL and ABC:What are similar triangles?Similar triangles are two triangles that have the same angle measures.
For these triangles, considering the relations between angles such as sine/cosine/tangent, or the law of sines, the side lengths have to be proportional.
Considering the need for proportional side lengths, the similar triangles in this problem are given as follows:
DEG and HGI: as the proportion between the side lengths of each triangle is of 1.5.JKL and ABC: as the proportion between the side lengths of each triangle is of 0.5.The other triangles are not similar as there are no proportional relationships that can be established from the side lengths of these triangles.
Missing InformationThe problem is given by the image at the end of the answer.
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degree and real roots of (x-3)(x+1)(x-1)=0
Step-by-step explanation:
at first multiply the factors
[tex] ({x}^{2 } + x \: - 3x \: - 3)(x - 1) = 0[/tex]
[tex] {x}^{3} - {x}^{2} - 3 {x}^{2} - \: 3x - {x}^{2} - x \: + 3x + 3 = 0[/tex]
[tex] {x}^{3} - 5 {x}^{2} - x + 3 = 0[/tex]
Here we see the highest power is 3 so the degree of the equation is 3
As for the real roots, the factors each as in (x-1), (x-3) & (x+1) can be considered zero each to find the real roots because for the value of x to be zero any of the multiplied factors must be zero.
either, x-1=0
=> x = 1
or, x+1=0
=> x = -1
or, x-3=0
=> x = 3
real roots of x are: 1, -1 and 3
Write an absolute value equation representing all numbers x whose distance from 5 is 5 units
The absolute value equation representing all numbers x whose distance from 5 is equal to 5 units is written as:
|x - 5| = 5
How to write the absolute value equation?An absolute value equation where the variable is x can be written as:
|x - a| = b
This means that the distance between x and a is equal to b.
So if we want to write an equation where the distance between x and 5 is equal to 5, then we can replace:
a = 5
b = 5
And the absolute value equation will be:
|x - 5| = 5
This is what we wanted to get.
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Omar is hiring a painting company to paint the interior of his house. The table represents prices the painting company quoted Omar.
Write a two-variable linear equation to represent the total cost, c, given the square feet, s, of the house.
A: c=2.25s+1347.85
B: c=2.25s+2847.85
C: c=2.25s+4047.85
D: c=2.25s+7654.60
The linear equation to represent the total cost c = 2.25s + 1,347.85.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
Using slope
slope= ( 5847. 75 - 4074 . 85)/( 2000- 1200)
slope= 1800 - 800
slope= 2.25
and, slope- intercept form
c - 4047.85 = 2.25 ( s- 1200)
c - 4047.85 = 2.25s - 2700
c = 2.25s - 2700 + 4047.85
c = 2.25s + 1,347.85
Hence, linear equation to represent the total cost c = 2.25s + 1,347.85.
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Three friends go grocery shopping together and buy apples. Logan buys 4
pays $7.00. Lin buys 6 lb and pays $10.50. Chita buys 2 lb
pounds (lb) and
and pays
$3.50.
Identify the graph and unit price that represent the cost of the apples.
The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.
What is the slope of a line?
The slope of a line is the tangent of the angle that the line makes with the positive direction of the x-axis. It signifies the rise in the y-variable for a unit change in the x-variable.
If the line passes through the points (x, y) and (x, y), then the slope of the line, m = (y - y)/(x - x).
(2, 3) representing the purchase by Logan,
(5, 7.5) representing the purchase by Lin,
(3, 4.5) representing the purchase by Chita.
The unit price can be calculated by the slope of the line;
m = (7.5 - 4.5)/(5 - 3) = 3/2 = 1.5.
Hence, The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.
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a positive integer divisor of 12! is chosen at random. the probability that the di-visor chosen is a perfect square can be expressed asmn, wheremandnare relativelyprime positive integers. what ism n?
The probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
What exactly is meant by probability?Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring.Given: Randomly, a positive integer divisor of 12! is selected.
Prime factorization of 12! = 2¹⁰ × 3⁵ × 5² × 7¹ × 11
Total divisors of 12! = 11 × 6 × 3 × 2 × 2
Each number in the prime factorization must have an even exponent in order to construct a perfect square divisor. In the prime factorization, the divisor cannot have any factors of 7 and 11 because there is only one of each in 12!. There are 6 × 3 × 2 perfect squares as a result.The probability that the divisor chosen is a perfect square is given as:
(6 × 3 × 2)/(11 × 6 × 3 × 2 × 2)
= 1/22
=m/n
Therefore, the probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
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Explain c-a, when c = 7 and a=6
Answer:
1
Step-by-step explanation:
7-6=1
Answer:
c-a
replace x with 7 and a with 6
rewrite: 7-6
7-6 = 1
Answer: 1
A train leaves a station heading east. after traveling east for 33 miles, the train leaves 56 miles south. How far is the train from the station?
Answer
23
45
65
89
If a train leaves a station heading east. after traveling east for 33 miles, the train leaves 56 miles south. The distance of the train from the station is C. 65.
How to find the distance?Using Pythagoreans theorem formula to find the distance
d² = a² + b²
Where:
d = distance =?
a= east for 33 miles
b = 56 miles south
Let plug in the formula
d = √33² + 56²
d = √ 1089 + 3136
d = √4225
d = 65 miles
Therefore the correct option is C.
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Write 22 as a percentage of 58
Give your answer correct to the nearest whole number.
Answer:
38%
Step-by-step explanation:
22 ÷ 58 = 0.3793...
Ans × 100 = 37.93%
As a whole number = 38%
write a function that will standardize a multivariate normal sample for arbitrary n and d. that is, transform the sample so that the sample mean vector is zero and sample covariance is the identity matrix. to check your results, generate multivariate normal samples and print the sample mean vector and covariance matrix before and after standardization.
The function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
According to a multivariate normal distribution with mean vector m and variance-covariance matrix M, then this random vector, X , will have the joint density function as shown:
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
where, |M| denotes the determinant of the variance-covariance matrix M and M^(-1) is just the inverse of the variance-covariance matrix M.
Hence, the function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
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0.25 in standard form
Answer:
2.5 × 10^-1
step-by-step explanation:
To get to standard form, you must move the decimal to the right one place so the number before it is not a 0. Because you move the decimal, you must add the second part of the equation so that the value does not change.
Answer:
02.5 but the 0 at the beginning isn't significant so 2.5
Step-by-step explanation:
because to find the standard form you move the decimal point so that there is only one non-zero digit in front of the decimal point.
The ratio 20mins to 1 hour can be written in the form 1:n find the value of n.
Answer:
1:3
n=3
Step-by-step explanation:
1 hour = 60 minutes
20:60
20÷20=1
60÷20=3
1:3
Does the diagram contain enough information to prove that line segment JK is parallel to line segment ML? Explain your answer.
I think so ya is does you just need to tell your teacher if you don't understand
At 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.
If he continues at this rate, at what time will he reach `10000` steps?
To cover 10000 steps the time taken will be 115 minutes and he will cover at 9:55 AM.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.
The time will be calculated as,
2000 steps ⇒ 23 minutes
1 Step ⇒ 23 / 2000 minutes
10000 steps ⇒ ( 23 x 10000) / 2000 minutes
10000 steps ⇒ 115 minutes
The time of covering 10000 steps will be at 9:55.
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Find the measures of each numbered angle:
She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 41 seconds at a speed of 4.9 feet per second.
She then ascends for 49 seconds at a speed of 3.2 feet per second.
After this 90-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at 3.6 feet per second?
The scientist will take 23 seconds to get back to the sea level.
Let us calculate the distance covered by the scientist at the given speeds and at the specified times.
She travels down for 41 seconds at speed of 4.9 feet per second.
Distance travelled = 41 × 4.9 = 200.9 feet
Elevation = -200.9 feet
She then goes up for 49 seconds at speed of 3.2 feet per second.
Distance travelled = 49 × 3.2 = 156.8 feet
Elevation = -222.9 + 156.8 = -44.1
So she is at a depth of 44.1 feet below the sea level.
Time taken = 44.1 / 3.6 = 12.25 seconds
Therefore it will take her about 12.25 seconds to go back to the sea level.
The average surface level of one or more of the Earth's coastal bodies of water is known as mean sea level (MSL), which can be used to calculate heights like elevation.
There are several terminologies that describe the ebb and flow of the relationship between sea level and dry land.
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Write the equation of a line in point slope form that has a slope of 2 and passes through the point (-2,5)
Answer:
y=2x+9
Step-by-step explanation:
Fill in the equation
5=2(-2)+b
Solve for b
5 = -4+b
9 = b
Put the original equation
y=2x+9
Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 28.45°. What is the measure of ∠P?
28.45°
75.775°
121.55°
151.55°
Step-by-step explanation:
the sum of all angles in a triangle is ALWAYS 180°.
and by using the word "congruent" : for angles that only means they are equally large.
we know the third angle.
so,
180 = P + Q + R = 2×P + 28.45
(because P = Q)
2×P = 151.55
P = Q = 151.55 / 2 = 75.775°
∠A=5x−12 ∘ start color #11accd, angle, A, equals, 5, x, minus, 12, degrees, end color #11accd \qquad \green{\angle B=2x + 24^\circ}∠B=2x+24 ∘
The solution to the variable x is 12 and the measure of ∠B is 48°.
How to solve congruent angles?∠A = 5x−12°
∠B = 2x+24°
Angle A and Angle B are congruent angles.
Congruent angles are angles with the same or equal measures.
So,
∠A = ∠B
5x - 12 = 2x + 24
collect like terms5x - 2x = 24 + 12
3x = 36
divide both sides by 3
x = 36/3
x = 12
So therefore,
∠A = 5x−12°
= 5(12) - 12
= 60 - 12
= 48°
∠B = 2x+24°
= 2(12) + 24
= 24 + 24
= 48°
Therefore, since ∠A and ∠B are congruent, the measure of ∠A and ∠B is 48° respectively.
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(b) Expand and simplify.
(2x - 5) (x - 3)
help me pls
[tex] = 2x(x - 3) - 5(x - 3) \\ = 2 {x}^{2} - 6x - 5x + 15 \\ = 2 {x}^{2} - 11x + 15 [/tex]
ATTACHED IS THE SOLUTION
a javalina rancher wants to enclose a rectangular area and then divide it into 5 pens with fencing parallel to one side of the rectangle. there are 580 feet of fencing available to complete the job. what is the largest possible total area of the 5 pens?
When there is 580 feet of fencing available to complete the job, the largest possible total area of the 5 pens is 7008.33 feet.
What is an area?The quantity area expresses the extent of a region on a plane or curved surface.
STEP 1: We know that,
A=x y
The perimeter equals 580feet.
The equation is,
580=6x+2y
Step 2: Solving y terns with x,
y=-3x+290
This information will assist us in obtaining our Area equation in terms of a single variable (just in terms of x).
Step 3: Using the x-y relationship discovered in Step 2, write your Area equation in terms of x only. You should obtain
A=x y
A=x(-3x+290)
A=-3x²+290x
Step 4: Derive the area equation, A' = -6x+290
Step 5: Set A' = 0
-6x+290=0
x=290/6
x=48.33
Step 6: Find y by substituting 48.33 in x in the perimeter equation then,
y=-3(48.33)+290
y=145.01
Step 7: A=x y
A=(48.33)(145.01)
A=7008.33 feet
The largest possible total area of the 5 pens is 7008.33 feet
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clint's cowboy shop buys horse feed for $\$10$ per cubic meter ($\text{m}^3$). clint's customers don't like the metric system, so they'll only buy horse feed by the cubic foot. how many cents should clint charge for a cubic foot ($\text{ft}^3$), if he wants to sell the horse feed for twice the price he bought it at?
In linear equation, 57 cents per cubic foot should clint charge for a cubic foot .
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18.cubic meter = [3.28 ft ]^3 ≈ 35.29 cubic feet
So,
price [ in cents] / 35.29 cubic feet = 2000 / 35.29 ≈ 57 cents per cubic foot
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what is the unit rate for $44 in 4 days
Answer:11
Step-by-step explanation: 44 divided into 4 is 11.
Answer:
The answer would be 11
Step-by-step explanation:
Because, 44 divided by 4 = 11
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 24 grams. The jeweler made a total of 16 bracelets and necklaces using 258 grams of gold. Determine the number of bracelets made and the number of necklaces made.
Answer:
Bracelets: 7 Necklaces: 9
Step-by-step explanation:
b+n=16
6n+24n=258
b=-n+16
6(-n+16)+24n=258
-6n+96+24n=258
18n=162
n=9
6n+24(9)=258
6n+216=258
6n=42
n=7
B stands for bracelets
N stands for necklaces
i count in equal steps my first number is -2 my fifth number is 26 whats my third number
The required third number will be 12 when numbers are in the A.P.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The given data as
first number = - 2
fifth number = 26
Assume that the given numbers are in the A.P.
The formula to find the general term of an arithmetic sequence is,
Tₙ = a₁ + (n-1)d ...(i)
Substitute the value of n = 5 and a₁ = -2 in the above formula
T₅ = a₁ + (5-1)d
26 = -2 + 4d
4d = 28
d = 7
For finding the third term (number):
T₃ = -2 + (3-1)7
T₃ = -2 + (2)7
T₃ = -2 + 14
T₃ = 12
Therefore, the required third number will be 12 when numbers are in the A.P.
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Pls help me I need to submit this
(5) All snow geese can eat for 11.5 days before the research and rescue center runs out of supplies.
What is snow geese?
Despite having a reputation for having white feathers, many snow geese are actually blue geese, which are darker, gray-brown birds. These birds were formerly believed to be two distinct species, however it has recently been discovered that they are actually just two color variants of the same bird. The variation in color is controlled by a single gene.
9 snow geese are housed in the research and rescue center.
Each geese consumed 16 ounces of seeds, therefore that's how much.
Therefore, the amount of seeds consumed by 9 snow geese is equal to (16*9) ounces.
144 ounces of seeds were consumed by 9 snow geese.
There are currently 1,656 ounces of seeds.
Thus, the number of days before the center runs out of food is equal to the sum of the ounces of seeds eaten by the nine snow geese divided by the total ounces of seeds.
Days till the food center runs out of supplies = 1656/144
11.5 days are required until the center runs out of food.
Hence, all snow geese can eat for 11.5 days before the research and rescue center runs out of supplies.
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