The value of y varies directly with x.

When y = 3 , x =1 .

What is the value of y when x is 4 ?

Question 2 options:

12


4 1/3


8


3/4

Answer:

Add decimals the same way as whole numbers, taking care to align the decimal points. Equivalently, align the ones because every number has ones.

Step-by-step explanation:

Answer:

A) \(6x^8y^5\)

B) \(4x^5z^8\)

C) \(12a^9b^7\)

D) \(6t^3s^9\)

Step-by-step explanation:

A) \(3x^2y^4\) ×\(2x^6y\)

Multiply the numbers

\(6x^2y^4x^6y\)

Combine exponents

\(6x^8y^4y\)

Combine exponents

\(6x^8y^5\)

===================================================================

B) \(xz^3x 4x^4z^5\)

Step-by-step explanation:

\(xz^3\) ×\(4x^4z^5\)

\(4x^1^+^4z^3^+^5\)

\(4x^5z^8\)

===================================================================

C) \(4a^3b^2 X 3a^6b^5\)

Multiply the numbers

\(12a^3b^2a^6b^5\)

Combine exponents

\(12a^9b^2b^5\)

Combine exponents

\(12a^9b^7\)

===================================================================

D)

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

\(6s^9tt^2\)

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

\(6s^9t^3\)

Answer:  

x = 4

Step-by-step explanation:

See attachment.

The toll charged for driving on a certain stretch of a toll road is $3, except during rush hours when the toll is $5. Here's a step-by-step explanation:
1. The regular toll for driving on the toll road is $3. This means that outside of rush hours, you will need to pay $3 to use the road.
2. Rush hours are between 7 a.m. and 10 a.m. and between 4 p.m. and 7 p.m. During these times, the toll increases to $5. This means that if you drive on the toll road between 7 a.m. and 10 a.m. or between 4 p.m. and 7 p.m., you will need to pay $5 instead of the regular $3.
To summarize, the toll for driving on a certain stretch of a toll road is $3, but during rush hours (between 7 a.m. and 10 a.m. and between 4 p.m. and 7 p.m.), the toll increases to $5.

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The variable x represents the cost of the skateboard shop to install the wheels, which was $15.

The variable x in the equation 132.49 + 15x = 192.49 represents the cost of the skateboard shop to install the wheels that Sam purchased. The equation can be read as "the cost of the wheels plus the cost of the skateboard shop to install them equal the total cost". The cost of the wheels that Sam purchased was $132.49, and the cost of the skateboard shop to install them was $15 - this is represented by the variable x. Therefore, when the equation is solved, the value of x will be the cost of the skateboard shop to install the wheels, which is $15. Therefore, Sam's total cost ended up being $192.49, which is the result of the equation when x is equal to 15.

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

answer: 1/2 bh

Step-by-step explanation

Answer:  The answer that I got was J.

Answer:

70 and 2.91 days

hope this helped

The sum of the denominators of the two fractions is -28.

The sum of the denominators of the two fractions can be found by first finding the equivalent fractions for 2/3 and 5/11 that fit the given conditions, and then adding the denominators together.

To find the equivalent fraction for 2/3 with a sum of 45 for the numerator and denominator, we can use the equation:

x + y = 45, where x is the numerator and y is the denominator.

Since the fraction is equivalent to 2/3, we can also use the equation 2/3 = x/y.

Solving for x in the first equation gives us x = 45 - y, and substituting this into the second equation gives us 2/3 = (45 - y)/y.

Multiplying both sides by 3y gives us 2y = 135 - 3y, and solving for y gives us y = 27.

This means that the denominator of the equivalent fraction for 2/3 is 27.

To find the equivalent fraction for 5/11 with a difference of 30 between the numerator and denominator, we can use the equation:

x - y = 30, where x is the numerator and y is the denominator.

Since the fraction is equivalent to 5/11, we can also use the equation 5/11 = x/y.

Solving for x in the first equation gives us x = 30 + y, and substituting this into the second equation gives us 5/11 = (30 + y)/y.

Multiplying both sides by 11y gives us 5y = 330 + 11y, and solving for y gives us y = -55.

This means that the denominator of the equivalent fraction for 5/11 is -55.

Therefore, the sum of the denominators of the two fractions is 27 + (-55) = -28.

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Step-by-step explanation:

the correct answer is option a 6a-7

We will use the method of undetermined coefficients to solve the given differential equation: y' + 8y = e^(-8t)cos(t), with the initial condition y(0) = 9. Therefore, the complete solution to the given differential equation is: y(t) = y_c(t) + y_p(t) = (9 + 1/65)*e^(-8t) + (-1/65)*e^(-8t)cos(t) + (-8/65)*e^(-8t)sin(t)

In the method of undetermined coefficients, we assume a particular solution in the form of y_p(t) = Ae^(-8t)cos(t) + Be^(-8t)sin(t), where A and B are constants to be determined.

We take the derivatives of y_p(t):

y_p'(t) = -8Ae^(-8t)cos(t) - Ae^(-8t)sin(t) - 8Be^(-8t)sin(t) + Be^(-8t)cos(t)

Plugging y_p(t) and y_p'(t) into the differential equation, we have:

(-8Ae^(-8t)cos(t) - Ae^(-8t)sin(t) - 8Be^(-8t)sin(t) + Be^(-8t)cos(t)) + 8*(Ae^(-8t)cos(t) + Be^(-8t)sin(t)) = e^(-8t)cos(t)

Simplifying and matching the coefficients of the exponential terms and trigonometric terms on both sides, we obtain the following equations:

-8A + B = 1

-A - 8B = 0

Solving these equations, we find A = -1/65 and B = -8/65.

Therefore, the particular solution is y_p(t) = (-1/65)*e^(-8t)cos(t) + (-8/65)*e^(-8t)sin(t).

To find the complete solution, we add the complementary solution, which is the solution to the homogeneous equation y' + 8y = 0. The homogeneous solution is y_c(t) = C*e^(-8t), where C is a constant.

Using the initial condition y(0) = 9, we substitute t = 0 into the complete solution and solve for C:

9 = y_c(0) + y_p(0) = C + (-1/65)*1 + (-8/65)*0

C = 9 + 1/65

Therefore, the complete solution to the given differential equation is:

y(t) = y_c(t) + y_p(t) = (9 + 1/65)*e^(-8t) + (-1/65)*e^(-8t)cos(t) + (-8/65)*e^(-8t)sin(t).

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Answer:

m=37

Step-by-step explanation:

180-35=145

4m-3=145

4m=148

m=37

Answer:

=5/2 - 17/4

=10/4 - 17/4

= -7/4

........................

Option (b) $11004.70 is correct answer. The amount of the Gentrys' annual transportation and taxes budgets combined is approx $11004.70 .

Given,

Total yearly income of the family = $29,742.42

% Expenses for Transportation = 9%

% Expenses for Taxes = 28%

We know that ,

Percentage is from total income of the family,

Expenses for transportation in $ = 9% of $29742.42

                                                      =  0.09 * 29742.42

                                                      =  $2676.8178

Expenses for taxes in $ = 28% of $29742.42

                                       =  0.28 * 29742.42

                                       =  $8327.8776

Total expense Transportation + Taxes =  $2676.8178 + $8327.8776

                                                                = $11004.694

                                                                ≈ $11004.70

Hence, amount of the Gentrys' annual transportation and taxes budgets combined is approximately $11004.70 .

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The complete question is :

What is the dollar amount of the Gentrys' annual transportation and taxes budgets combined?

(a)$2,676. 82

(b) $11,004. 70

(c) $8,327. 88

(d) $18,737.

Gentry Family

Three Children Yearly Budget; Yearly Income - $29,742.42

Item                                      Percentage          

Tithe                                         10%

Taxes                                        28%

Food                                          20%

Housing                                     30%

Clothing                                     6%

Transportation                           9%

Doctor, Medicine, etc.               8%

True, if you use the vertical line test there is never two points on the same vertical line.

Answer:

8 plates

Step-by-step explanation:

The reason for this is because 15 and 9 are both divisible by 3. 15 divided by 3 is 5 and 9 divided by 3 is 3. 5+3= 8. Therefore, you will need 8 plates.

Answer: $790.74

Step-by-step explanation:

0.054

X 790.74

——————-

42.7

By doing reverse you can see that 42.7 pesos=790.74 USD, so $790.74 is the answer.

Answer:

-2.8

Step-by-step explanation:

\( \frac{ - 3.5}{1.25} = - 2.8\)

Answer:

top l) -4\(\frac{4}{5}\)

top r)-7.5

bottom l) 1.5

bottom r)-2\(\frac{2}{5}\)

Step-by-step explanation:

Answer:

I have no answers.

Step-by-step explanation:

Answer: Choice C

x/w and z/(y+v)

======================================================

Explanation:

All answer choices have that first fraction with a denominator of w. This implies that AB = w is the hypotenuse. This only applies to triangle ABD.

Focus on triangle ABD. It has an opposite leg of AD = x, when the reference angle is ABD (or angle B for short).

So we can say sin(ABD) = opposite/hypotenuse = AD/AB = x/w

x/w is one of the answers

-----------

Also note how y+v is the same for each denominator in the second fraction. y+v is the hypotenuse of triangle ABC. When the reference angle is ABD (aka angle ABC), the opposite side of this same triangle is AX = z

Therefore,

sin(ABD) = sin(ABC) = opp/hyp = AC/BC = z/(y+v)

z/(y+v) is the other answer

Side note: triangle ACD is not used at all.

Answer:

\(\frac{x}{w}, \: \frac{z}{y+v}\)

Step-by-step explanation:

sin θ = \(\frac{opposite}{hypotenuse}\)

Let’s take triangle ABD, where w is the hypotenuse.

sin ∠ABD = \(\frac{x}{w}\)

Let’s take triangle ABC (whole triangle), where y + v is the hypotenuse.

sin ∠ABD = \(\frac{z}{y+v}\)

Hi,

Answer is $0.19

Step-by-step explanation:-

We know that:-

15 dimes = $1.50

20 nickels = $1.00

8 quarters = $2.00

half dollar = $0.50

19 pennies = $0.19

Total = $5.19

Since Billy spended $5, so,

$5.19 - $5 = $0.19

Hope it helps you...

In 1940, John Atanasoff, a physicist from Iowa State University, wanted to solve a 29 x 29 linear system of equations. To solve this system using Gaussian elimination, it would have required approximately 29^3/3 = 24389 arithmetic operations.

In 1940, John Atanasoff developed the Atanasoff-Berry Computer (ABC), which was the first electronic computer. Atanasoff wanted to use the ABC to solve a 29 x 29 linear system of equations.

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Answer:

I believe it's 27.

Step-by-step explanation:

I tried the math and ended up with 27.

The solution of the quadratic equation 8x² – 5x – 4 = 0 will be 1.085 and negative 0.460.

The solution of the equation means the value of the unknown or variable.

The quadratic equation is given below.

8x² – 5x – 4 = 0

Then we have

a = 8, b = -5, c = -4

Then the solutions will be

\(\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}\\\\\\\rm x = \dfrac{-(-5)\pm \sqrt{(-5)^2 - 4 * 8 * (-4)}}{2 * 8 }\\\\\\x = \dfrac{5 \pm 12.37}{16}\\\\\\x = \dfrac{5- 12.37}{16}, \dfrac{5 +12.37}{16}\)

On further solving, we have

x = 1.085, -0.460

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The linear function for this problem is given as follows:

y = 15x + 5.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 5, hence the intercept b is given as follows:

b = 5.

When x increases by 1, y increases by 15, hence the slope m is given as follows:

m = 15.

Thus the function is given as follows:

y = 15x + 5.

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