-3x + y = 10

solve the equation for Y

Correct answer is B. The zeros of the function g will be ( -6 and 7.)

(x-7) and (x + 6) are factors in a function g.

To locate: The function g's zeros.

Because x-a=0 x = a, we know that if (x-a) is a function's factor, then x-a is the function's zero.

The fact that (x - 7) and (x + 6) are factors in the function g is a given.

x-7=0

x = 7

Likewise, x+6=0

x = -6

As a result, the function g's two zeros are -6 and 7.

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Answer:

18x

Step-by-step explanation:

2(3x+6x)

Answer:

A higher number.

Step-by-step explanation:

You don't want your credit to be low, and a higher number beats all of them.

You want high credit.

Not low.

Answer:

definately you want a higher number

Translation

We are given two figures ABCD and A'B'C'D' with coordinates:

A(2, 3) B(1, 2) C(2, 1) D(3, 2)

A'(5, 4) B'(4, 3) C'(5, 2) D'(6, 3)

Figure ABCD maps to A'B'C'D' after a translation. It's required to find the rule of the translation.

The same rule should be applied to each one of the vertices, so we can find it by subtracting any pair of corresponding points, for example:

A'(5, 4) - A(2, 3) = (3, 1)

B'(4, 3) - B(1, 2) = (3, 1)

If we continue to test each pair of points, we would get the same difference, thus the rule of the translation is:

Figure ABCD is translated 3 units right and 1 unit up

The equivalent exponential equations are given as follows:

\(2^{4x} = 2^{3(x - 3)}\)

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Answer:

X = 6

Step-by-step explanation:

X + 8 = 14          * Subtract 8 from both sides so that

    -8   -8              the 8 is cancelled out

_________

X + 0 = 6

Hence, 440 cupcakes were sold on that day.

The bakery sold a total of 400 cupcakes that day, with 224 of them being chocolate cupcakes, representing 56 precent of the total.

Use the concept of percentage defined as:

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred.

Given that,

A bakery sold 224 chocolate cupcakes in a day.

The 224 chocolate cupcakes represent 56% of the total number of cupcakes sold that day.

To find the total number of cupcakes sold,

Use the percentage given and some simple math.

If 56% of the cupcakes sold were chocolate cupcakes and that amounts to 224 cupcakes,

Set up the following equation:

0.56 x Total number of cupcakes = 224 cupcakes

To find the total number of cupcakes,

Divide both sides of the equation by 0.56:

Total number of cupcakes = 224 cupcakes / 0.56

Calculating this,

The bakery sold a total of 400 cupcakes that day.

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The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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\(\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}\)

Answer:10 Safety razors

Step-by-step explanation:

27-12=15

15/1.50=10

Answer:

x-4303

Step-by-step explanation:

Answer:

The correct answer is -

1. 2 whole pizza

2. each boy pay for his pizza slices are -

Aaron - $2.80

Glenn - $1.40

James - $2.10,

Matt - $2.80 and

Trevor - $2.10

Step-by-step explanation:

According to the question, Aaron, Glenn, James, Matt, and Trevor are boys who ordered pizza as per their requirements.

Total slices ordered are -1/2 of pizza or 4 for Aaron, 2 for Glenn, 3 slices for James, 4 slices for Matt and 3 for Trevor,

= 4+2+3+4+3 = 16 slices

2 pizza means = 16 slices

total price = 70 cents*16

= $11.20

each boy pay for his pizza slices are -

Aaron - $2.80 - 4 slice

Glenn - $1.40 - 2

James - $2.10, -3

Matt - $2.80 - 4

Trevor - $2.10 -3

Answer:

Step-by-step explanation:

Given  f(x)=√x+1 and g(x)=3+√x, to calculate for  (f∘g)(4), first we need to get the function  (f∘g)(x).

(f∘g)(x). = f{g(x)}

since g(x) =3+√x, then;

f{g(x)} = f(3+√x)

If f(x) = √x+1

f(3+√x) can be gotten by simply replacing x with 3+√x in f(x)

f(3+√x) = √(3+√x)+1

f{g(x)} = √(3+√x)+1

f{g(4)} can be gotten by substituting x = 4 into the resulting function above.

f{g(4)} = √(3+√4)+1

f{g(4)} = √(3+2)+1

f{g(4)} = √5+1

f{g(4)} = √6

f{g(4)}  = 2.449 ≈ 2.45 to two decimal places.

Hence,  (f∘g)(4) for the functions to two decimal places is 2.45

The acceleration of the car is 8 m/s^2.

The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.

Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.

(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m

(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2

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Answer:

Therefore, z = 1 + i.

Step-by-step explanation:

Given that the argument of z + 1 is pi/6 and the argument of z - 1 is 2*pi/3, we can use the fact that the argument of a complex number is equal to the angle between the positive x-axis and the line connecting the origin to the complex number in the complex plane.

Let's call the complex number z = a + bi. Then, z + 1 = a + (b + 1), and z - 1 = a - (b - 1).

Using the argument values given, we have:

arg(z + 1) = pi/6, so the line connecting the origin to z + 1 makes an angle of pi/6 with the positive x-axis.

arg(z - 1) = 2pi/3, so the line connecting the origin to z - 1 makes an angle of 2pi/3 with the positive x-axis.

From the above information, we can sketch the complex plane and find the location of the complex number z. We then have two equations for a and b in terms of the argument of the complex numbers:

a = (z + 1 + z - 1)/2 = 1

b = (z + 1 - z - 1)/2 = 1

Therefore, z = 1 + i.

Answer:

i would belive c i might be wrong

Step-by-step explanation:

Answer:

D: x=10,000

Step-by-step explanation:

The 6 number of muffins in each box if they all contain the same amount of muffins.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Jill made 20 muffins.

She put them into 3 boxes and has 2 muffins left.

That means,

muffins in the boxes =20 -2

                              = 18 muffins are in the boxes.

To find the number of muffins in each box if they all contain the same amount of muffins:

Divide the rest of the muffins to 3.

Number of muffins in the boxes / 3

= 18 / 3

= 6

Therefore, six muffins are in each box.

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Answer:

13525

Step-by-step explanation:

Given the equation :

y=25,450(0.81)^t

where (t) is the number of years since the truck was new ;

The value of y when t = 3 ;

Replace, t with 3 in the equation. And simplify

y=25,450(0.81)^3

Y = 25450 * 0.531441

y = 13525.17345

Worth after 3 years = 13525

Answer:

Amadi: 20 years old

Chima : 4 years old

The equation that describes the graphed function is Option C: g(x) = -f(x) + 2.

The given function is f(x) = √x, which represents the square root function. To determine which equation describes the graphed function, we need to analyze the transformations applied to the original function.

Option A, g(x) = f(-x) + 2:

This equation represents reflecting the graph of f(x) across the y-axis (due to the negative sign in front of x) and then shifting it vertically upward by 2 units. However, this transformation does not match the graph of f(x) = √x.

Option B, g(x) = -f(x + 2):

This equation represents taking the negative of the original function f(x) and shifting it horizontally left by 2 units. This transformation does not match the graph of f(x) = √x.

Option C, g(x) = -f(x) + 2:

This equation represents taking the negative of the original function f(x) and shifting it vertically upward by 2 units. This transformation matches the graph of f(x) = √x.

Option D, g(x) = f(-x + 2)

This equation represents reflecting the graph of f(x) across the y-axis (due to the negative sign in front of x) and shifting it horizontally right by 2 units. This transformation does not match the graph of f(x) = √x.

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Answer:

37x4

4x30=120

4x7=28

120+28=148

this is how i show my work. it has never failed me

Step-by-step explanation:

37×4

4×30

4×7=28

120+28=148

Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Answer:

D

Step-by-step explanation:

The value of tan (A-pi/4) is  (-√(15)- 1) / 1 -√(15).

One of the trigonometric identities for compound angles is the tan(a-b) identity. When the angle for which the tangent function value is to be determined is supplied in the form of the difference of any two angles, it is used. The compound angle is denoted by the angle (a-b) in the formula for tan(a-b).

Given:

tanA = -square root 15

tanA = -√(15)

To find the value of tan (A-pi/4):

Use the formula,

Tan(a - b) Identity

tan(A-B) = (tanA - tanB) / 1 + (tanAtanB)

Substituting the values,

tan(A-π/4) = (tanA - tanπ/4) / 1 + (tanAtanπ/4)

tan(A-π/4) = (-√(15)- 1) / 1 + (-√(15)

tan(A-π/4) = (-√(15)- 1) / 1 + (-√(15)

tan(A-π/4) = (-√(15)- 1) / 1 -√(15)

Therefore, the value is tan(A-π/4) = (-√(15)- 1) / 1 -√(15)

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The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = \(96t - 16t^{2}\)

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

\(\frac{dh(t)}{dt} = 96 - 32t = 0\)

⇒ \(t = 3\)

So, time taken to reach its max height is 3 seconds.

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Answer:

A.

Step-by-step explanation:

She would receive $11.67

A is the correct math

We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D

We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.

If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.

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the best way to solve this is using a system. let's pretend the two numbers we have are notated using the variables x and y.

our first equation is this:

x + y = -46. the sum of the two numbers x and y is -46.

our first equation is this:

x + 13 = y. here, the variable doesn't really matter. so, what this says is that y is 13 greater than x.

now, you know how to represent y in terms of x. plug the second equation into the first and you get this:

x + ( x + 13) = -46.

solve this:

2x + 13 = -46

2x = -59

x = -29.5

now, we know what x equals. using the second equation we created,

x + 13 = y, we can figure out what y equals. so, let's plug x in.

-29.5 + 13 = y

y = -16.5

you've got x and y now! i hope i helped you.

xoxo

Answer:

20 for both

Step-by-step explanation:

hope this helps