I need help figuring out this question. Please help

Explanation:

Plug x = -2 into h(x)

h(x) = x+4

h(-2) = -2+4

h(-2) = 2

This means g[ h(-2) ] = g(2) after replacing h(-2) with 2.

g(x) = 5x

g(2) = 5*2

g(2) = 10

Therefore, g[ h(-2) ] = 10

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of [tex]f(x)=(x-1)(x+7)[/tex] has clear zeroes at [tex]x=1[/tex] and [tex]x=-7[/tex], showing that [tex]f(x) > 0[/tex] when [tex]x < -7[/tex] and [tex]x > 1[/tex]. To determine where the vertex is, we can complete the square:

[tex]f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16[/tex]

So, we can see the vertex is (-3,-16), meaning that where [tex]x > -3[/tex], the function will be increasing on that interval

Both triangles in the image are similar based on the AAA similarity theorem. The radius of the circle B is therefore calculated as: AB = 12.

Similar triangles are geometric figures that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are in proportion to each other.

Since AD serves as a common tangent, angle BAE is equal to 90 degrees, which is also equal to angle CDE due to being opposite angles.

By the Angle-Angle-Angle (AAA) similarity criterion, triangles ABE and DCE are similar.

Therefore:

AB/EA = DC/ED

Substitute:

AB/18 = 4/6

Cross multiply:

AB = 18 * 4/6

AB = 12

Therefore, the radius of the circle B is: 12.

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Answer:

a=55°

b=123°

c=55°

d=123°

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

[tex]{\implies 0.5x + 0.1(70) = 0.4(70 + x)}[/tex]

Simplifying the equation:

[tex]\qquad\implies 0.5x + 7 = 28 + 0.4x[/tex]

[tex]\qquad\quad\implies 0.1x = 21[/tex]

[tex]\qquad\qquad\implies \bold{x = 210}[/tex]

[tex]\therefore[/tex] We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

The appropriate shape to model each section of the tower are the cone and the cylinder.

The approximate surface area of each shape would be =

For cone = 1,041.27m²

For cylinder = 3,543.72m².

The first shape is a cone and the formula for the surface area = A = πr(r+√h²+r²)

where;

Radius = 24/2 = 12

height = 10m

Area = 1,041.27m²

For cylinder:

A = 2πrh+2πr²

where:

r = 12m

h = 35m

A = 3,543.72m²

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Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

The correct range for the piecewise graph is [-4, 2].

We need to find the minimum and maximum values of the y-coordinates.

The first segment goes from (-3, 2) to (0, 1), so the range for this segment is from 1 to 2.

The second segment goes from (0, 1) to (5, -4), so the range for this segment is from -4 to 1.

We must take into account the minimum and maximum values from each segments in order to determine the overall range. The minimum and highest values are -4 and 2, respectively.

Therefore, the correct range for the piecewise graph is [-4, 2].

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Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

[tex]y = ab^x[/tex]

We have :

[tex]y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}[/tex]

Given points : (4, 9) and (5, 34.2)

We have:

[tex]\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b[/tex]

Writing the equation with x, y and b:

[tex]y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043[/tex]

a = 0.043

b = 3.8

When x = 6, y will be:

[tex]y = (0.043)(3.8^6)\\\\y = 128.47[/tex]

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

If Anita and Miguel do not take any money from their accounts, Anita's account will grow faster than Miguel's.

This is because the interest rate for Anita's account is 6%, while Miguel's is 5%.

The interest rate is the percentage of the principal that a bank or other financial institution pays for the use of money.

It can be thought of as a fee charged for borrowing money.

The higher the interest rate, the more money a person can earn on their investment.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

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a. The initial velocity of the marble is 0 cm/s.

b. The marble is rolling at a speed of 80 cm/s at 4 seconds.

c. The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.

d. The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point at t = 9 seconds.

e. lim s(t) as t approaches infinity is 100 cm and lim v(t) as t approaches infinity is 0 cm/s; the model may not be valid for large values of t as it assumes the marble is rolling up an inclined plane without considering other factors such as friction.

a. To find the initial velocity of the marble, we need to calculate the limit of the function s(t) as t approaches 0:

lim (t->0) s(t) = lim (t->0) (100t / (t + 1))

By substituting 0 into the expression, we get:

lim (t->0) (0 / (0 + 1)) = 0 / 1 = 0.

Therefore, the initial velocity of the marble is 0 cm/s.

b. To find the speed of the marble at time 4 seconds, we substitute t = 4 into the expression for s(t):

s(4) = 100(4) / (4 + 1) = 400 / 5 = 80 cm/s

The marble is rolling at a speed of 80 cm/s at 4 seconds.

c. To find the time at which the velocity is 50 cm/s, we set s'(t) (the derivative of s(t)) equal to 50 and solve for t:

s'(t) = 50

[tex](100 / (t + 1))^2 = 50[/tex]

100 / (t + 1) = ±√50

100 = ±√50(t + 1)

±√50(t + 1) = 100

t + 1 = 100 / ±√50

t + 1 = ±2√2

Since time cannot be negative, we take t + 1 = 2√2:

t = 2√2 - 1

The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.

d. To find the speed of the marble when it is 90 cm from its starting point, we need to solve the equation s(t) = 90 for t:

100t / (t + 1) = 90

100t = 90(t + 1)

100t = 90t + 90

10t = 90

t = 9

The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point, which occurs at t = 9 seconds.

e. The limit of s(t) as t approaches infinity (lim s(t) as t->∞) is calculated by considering the dominant term in the numerator and denominator:

lim (t->∞) (100t / (t + 1))

≈ lim (t->∞) (100t / t)

= lim (t->∞) 100

= 100

Therefore, lim s(t) as t approaches infinity is 100 cm.

Similarly, the limit of v(t) (velocity) as t approaches infinity (lim v(t) as t->∞) can be found by taking the derivative of s(t) and evaluating the limit:

[tex]v(t) = s'(t) = 100 / (t + 1)^2[/tex]

lim (t->∞) v(t) = lim (t->∞) (100 / [tex](t + 1)^2)[/tex]

≈ lim (t->∞)[tex](100 / t^2)[/tex]

= lim (t->∞) [tex](100 / t^2)[/tex]

= 0.

The limit of v(t) as t approaches infinity is 0 cm/s.

As for the validity of the model for large values of t, it is important to note that the given model assumes that the marble is rolling up an inclined plane.

However, without further information about the nature of the inclined plane (e.g., its slope, frictional forces), it is difficult to determine the accuracy.

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i. The payback period for the project is 6 years.

ii. The accounting rate of return (ARR) using the average investment method is 21.18%.

iii. The net present value (NPV) of the project is -165,143.

iv. The internal rate of return (IRR) of the project is approximately 19.61%.

i. The payback period for the project:

To calculate the payback period, we need to determine how long it takes for the cumulative net cash flows to equal or exceed the initial investment of 350 million + 150 million.

Year 1: 70,000, Year 2: 70,000, Year 3: 80,000, Year 4: 100,000, Year 5: 100,000, Year 6: 120,000.

Cumulative Cash Flow:

Year 1: 70,000

Year 2: 70,000 + 70,000 = 140,000

Year 3: 140,000 + 80,000 = 220,000

Year 4: 220,000 + 100,000 = 320,000

Year 5: 320,000 + 100,000 = 420,000

Year 6: 420,000 + 120,000 = 540,000.

The cumulative cash flows exceed the initial investment of 500 million (350 million + 150 million) in Year 6.

So, the payback period for the project is 6 years.

ii. The accounting rate of return (ARR) using the average investment method:

ARR = Average Annual Profit / Average Investment

Average Annual Profit = Sum of Net Cash Flows / Number of Years

Average Annual Profit = (70,000 + 70,000 + 80,000 + 100,000 + 100,000 + 120,000) / 6

Average Annual Profit = 540,000 / 6

Average Annual Profit = 90,000

Average Investment = (Initial Investment + Residual Value) / 2

Average Investment = (500 million + 350 million) / 2

Average Investment = 425 million.

ARR = 90,000 / 425,000 = 0.2118 or 21.18%

iii. The net present value (NPV) of the project:

To calculate NPV, we discount each cash flow to its present value using the cost of capital of 12%.

NPV = (Net Cash Flow1 / [tex](1 + r)^1)[/tex]  + (Net Cash Flow2 / [tex](1 + r)^2)[/tex] + ... + (Net Cash Flow6 / (1 + r)^6) - Initial Investment.

[tex]NPV = (70,000 / (1 + 0.12)^1) + (70,000 / (1 + 0.12)^2) + (80,000 / (1 + 0.12)^3) + (100,000 / (1 + 0.12)^4) + (100,000 / (1 + 0.12)^5) + (120,000 / (1 + 0.12)^6) -[/tex] (350 million + 150 million)

Calculating each term and summing them up:

NPV = 54,017 + 48,234 + 54,497 + 62,313 + 55,631 + 60,165 - 500 million

NPV = -165,143

Therefore, the net present value (NPV) of the project is -165,143.

iv. The internal rate of return (IRR) of the project:

To calculate the IRR, we find the discount rate that makes the NPV equal to zero. Using a financial calculator or Excel, we can determine that the IRR for this project is approximately 19.61%.

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Answer:

1. 9 2/7 = (63+2)/7 = 65/7

2. 2 4/5 = (10+4)/5 = 14/5

3. 65/7 * 14/5 = 910/35 = 26

The correct matches are:

-1: 0

-2: 0

X: 14/3

0: 0

6: Not used

= 2² + 2x - 5: Not used

To match the representations with their respective average rates of change, we need to calculate the average rate of change for each function over the interval (0, 3) and compare it to the given values.

Let's calculate the average rate of change for each function:

Function: 2² + 2x - 5

To find the average rate of change, we need to calculate the difference in function values divided by the difference in x-values:

Average rate of change = (f(3) - f(0)) / (3 - 0)

Average rate of change = ((2² + 2(3) - 5) - (2² + 2(0) - 5)) / 3

Average rate of change = (13 - (-1)) / 3

Average rate of change = 14 / 3

Match: X = 14/3

Function: -1

Since the function is constant, the average rate of change is 0.

Match: 0

Function: 2

Since the function is constant, the average rate of change is 0.

Match: 0

Function: 3

Since the function is constant, the average rate of change is 0.

Match: 0

Function: -2

Since the function is constant, the average rate of change is 0.

Match: 0

Function: -3

Since the function is constant, the average rate of change is 0.

Match: 0

Therefore, the correct matches are:

-1: 0

-2: 0

X: 14/3

0: 0

6: Not used

= 2² + 2x - 5: Not used

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Answer: Step-by-step work:

40,328

77

3,105 (Carry the 3)

27,468

302,976

1,609,432

Add the numbers horizontally:

2,943,941

So, 40,328 * 77 = 2,943,941

The remainder when divided by 10 is:

2,943,941 % 10 = 1

Therefore, the remainder is 1.

More concisely:

40,328 * 77 = 2,943,941

2,943,941 % 10 = 1

So the remainder when 2,943,941 is divided by 10 is 1.

Hope this helps! Let me know if you have any other questions

Step-by-step explanation:

a. The exact volume is V = π(9.5 ft)²(50 ft) = 225π ft³.

b. Rounding the answer to the nearest hundredth, the approximate volume of the silo is 706.50 ft³.

(a) The exact volume of the silo can be found using the formula for the volume of a cylinder, which is V = πr²h,

where r is the radius and h is the height.

Since the diameter is given, we can divide it by 2 to find the radius.

The radius of the silo is 19 ft / 2 = 9.5 ft.

The height of the silo is 50 ft.

Using these values, the exact volume of the silo is:

V = π(9.5 ft)²(50 ft) = 225π ft³.

The approximate volume can be found using the ALEKS calculator, which is not available in this text-based interface.

However, you can use the exact volume calculated above to manually approximate the volume to the nearest hundredth by evaluating the expression using the value of π as approximately 3.14 or 22/7.

(b) Approximate volume using the ALEKS calculator: [Please use an online calculator or a scientific calculator to approximate the value to the nearest hundredth].

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This means that she made a 20% return on the money she invested in the property. For every dollar she invested, she earned 20 cents in profit.

To calculate Jennifer Aniston's return on investment (ROI), we can use the formula:

ROI = (Net Profit / Initial Investment) * 100

First, let's calculate the net profit. The net profit is the selling price minus the initial investment:

Net Profit = Selling Price - Initial Investment

Net Profit = $2,200,000 - $2,000,000

Net Profit = $200,000

Next, we calculate the ROI:

ROI = (Net Profit / Initial Investment) * 100

ROI = ($200,000 / $1,000,000) * 100

ROI = 0.2 * 100

ROI = 20%

Jennifer Aniston's return on investment for this property is 20%.

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The area of the parallelogram is  189 square units

First, we have the determine the length of the base and height.

The distance between the lines x = 9 and f(x) = 9 + 2x is the height

We have that the line parallel to f(x) passes through (4, 11)

The equation in point-slope form is;

y - 11 = 2(x - 4

y = 2x + 3

Substitute x = 9 in the equation,  y = 2x + 3.

y = 2(9) + 3 = 21

The  points are then (9, 21) and (9, 0).

The distance between the y-axis and the line x = 9 is the base.

Base = 9 units.

The formula for calculating area of a parallelogram is given by ;

= base × height

= 9 × 21

= 189 square units.

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The domain for the time in this context is (0, 7.4)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let h represent the height of the ball after spending t seconds. A ball is thrown straight up from the top of a building that is 168 ft high with an initial velocity of 96 ft/s.

Given the equation:

h(t) = -16t² + 96t + 168

The reasonable domain restriction for t, is when  the height of the rocket is above the ground. Hence the domain for the time in this context is (0, 7.4)

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Answer:

The total surface area is given by: base area + 4 * triangular face area

Substituting the values we calculated: 52441 + 4 * 10424.4 ≈ 91588.4 square meters.

Therefore, the surface area of the square pyramid is approximately 91588.4 square meters.

Answer:

7

Step-by-step explanation:

V looking shape has ends at 1 & 8

8 - 1 = 7

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Answer: - 27

Step-by-step explanation:

Plug in for x = 3 and y = -6

I'll start with x to make it easier.

Plugging in x =3

[tex]\sqrt{x^4}[/tex]

Means that first we find x^4, and take the square root of that result.

1. Find x^4

x = 3

3^4 = 3 * 3 * 3 *3  = 81

2. Take the square root of x^4

Square root of 81 = 9

So [tex]\sqrt{x^4}[/tex]  = 9

Plugging in y = -6

Let's move onto plugging in y, which appears in the expression  as y²

y = -6

so y²  = -6 * -6 = 36

Putting this together into the expression

[tex]\sqrt{x^4}[/tex] - y²

9 - 36 = -27

The calculated percentage error with the assumed answer of 10%

To find the percentage error in actual weights, we can use the formula:

Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%

In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:

Measured Value = Expected Value + (10% of Expected Value)

              = 4 ounces + (10/100) * 4 ounces

              = 4 ounces + 0.4 ounces

              = 4.4 ounces

Now we can calculate the percentage error:

Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%

               = [(0.4 ounces) / 4 ounces] * 100%

               = (0.4/4) * 100%

               = 0.1 * 100%

               = 10%

Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.

The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%

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,Alice, Raul, and Maria can make 1 whole batch of a dozen cookies together using the ingredients they brought.

To determine how many whole batches of a dozen cookies they can make, we need to compare the amount of flour and butter they have with the required amounts for each batch of cookies.

Let's calculate the total amount of flour and butter each student brought:

Alice:

Flour: 2 cups

Butter: 1/4 cup

Maria:

Flour: 1 1/4 cups

Butter: 3/4 cup

Now let's compare the amounts with the required ingredients for a batch of cookies:

Required amount per batch:

Flour: 3/4 cup

Butter: 1/3 cup

First, let's see how many batches of cookies Alice can make:

Flour: Alice has 2 cups, and each batch requires 3/4 cup. So she can make 2 cups / (3/4 cup) = 8/3 = 2 and 2/3 batches of cookies.

Butter: Alice has 1/4 cup, and each batch requires 1/3 cup. Since she doesn't have enough butter for a full batch, she can't make any batches of cookies with the butter she brought.

Next, let's see how many batches of cookies Maria can make:

Flour: Maria has 1 1/4 cups, and each batch requires 3/4 cup. So she canmake (5/4 cups) / (3/4 cup) = 5/3 = 1 and 2/3 batches of cookies.

Butter: Maria has 3/4 cup, and each batch requires 1/3 cup. So she can make (3/4 cup) / (1/3 cup) = 9/4 = 2 and 1/4 batches of cookies.

Now, to find the maximum number of whole batches they can make together, we take the minimum of the number of batches each student can make:

Alice: 2 and 2/3 batches

Maria: 1 and 2/3 batches

Raul: Not mentioned, so we assume he brought the required ingredients.

The minimum value is 1 and 2/3 batches, which means they can make 1 whole batch of a dozen cookies together.

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No, the expression 3x + 5y - 2200 is not a quadratic expression.

A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.

It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.

"3x + 5y - 2" is a linear expression, not a quadratic expression.

In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.

The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.

It is a first-degree polynomial, meaning that the highest power of the variable is 1.

Linear expressions often have a graph that is a straight line.

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No. The expression, 3x + 5y - 2, is not quadratic.

The expression "3x+5y-2" is a linear expression, not quadratic.

Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.

The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.

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Answer:

Step-by-step explanation:

144*33/

Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%