Mathematics College

## Answers

**Answer 1**

The answer is a donut.

A donut or Toroid is formed when you rotate an circle by a rotation axis displaced of the center of the circle.

**Answer 2**

**Answer:**

**Step-by-step explanation:**

donut

## Related Questions

a quadrilateral has vertices S (0,0) T (4,0) U (5,4) V (1,4). what is the most precise name for the quadrilateral

### Answers

First, plot the points on a coordinate plane:

Notice that ST is parallel to VU, as well as SV is parallel to TU.

A quadrilateral whose opposite sides are parallel, is called a **parallelogram.**

**Therefore, the most precise name for the quadrilateral is: ****parallelogram****.**

Which relations are functions?Select Function or Not a function for each graph. FunctionNot a functionGraph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through the origin and the points begin ordered pair negative 2 comma negative 4 end ordered pair and begin ordered pair 2 comma 4 end ordered pair.Function –Not a function –The graph of a parabola on a coordinate plane. The x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. The vertex is located at begin ordered pair 1 comma 0 end ordered pair. The parabola opens upward. It passes through the vertical axis at begin ordered pair 0 comma 1 end ordered pair. It passes through begin ordered pair 2 comma 1 end ordered pair.Function –Not a function –An absolute value function graphed on a coordinate plane. The x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. The vertex is at the origin. The V-shaped graph passes through the points begin ordered pair 1 comma 1 end ordered pair and begin ordered pair 1 comma negative 1 end ordered pair.Function –Not a function –A circle on a coordinate plane centered at the origin, begin ordered pair 0 comma 0 end ordered pair. The circle passes through points begin ordered pair negative 2 comma 0 end ordered pair, begin ordered pair 0 comma negative 2 end ordered pair, begin ordered pair 2 comma 0 end ordered pair, and begin ordered pair 0 comma 2 end ordered pair.Function –Not a function –

### Answers

**SOLUTION**

**To identify or determine which relation in the graph is a function, we use the vertical line test.**

The vertical line test explains that If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x-value has more than one output. A function has only one output value for each input value.

Hence, from the explanation above, we cam see that

**Graph 1 is a Function**

**Graph 2 is a Function**

Using similar approach

**Graph 3 is not a function **

**Graph 4 is not a function**

The quadratic equation y = - 16t² +40t+2 represents the height of aprojectile, y, in feet, at a particular time, t, in seconds.For what interval or intervals of time will the projectile be above 18 feet?

### Answers

The given equation is:

[tex]y=-16t^2+40t+2[/tex]

It is required to find which interval or intervals of time will the projectile be above 18 feet.

To do this, solve the inequality:

[tex]\begin{gathered} y>18 \\ \Rightarrow-16t^2+40t+2>18 \end{gathered}[/tex]

First, find the** critical points** of the inequality by solving the equation:

[tex]\begin{gathered} −16t^2+40t+2=18 \\ \text{ Subtract 18 from both sides:} \\ \Rightarrow-16t^2+40t+2-18=18-18 \\ \Rightarrow−16t^2+40t-16=0 \\ \text{ Factor the left-hand side of the equation:} \\ \Rightarrow−8\left(2t−1\right)\left(t−2\right)=0 \\ \text{ Equate the factors to 0 to find the t-values:} \\ \Rightarrow(2t-1)=0\text{ or }(t-2)=0 \\ \Rightarrow2t=1\text{ or }t=2 \\ \Rightarrow t=\frac{1}{2}=0.5\text{ or }t=2 \end{gathered}[/tex]

The possible interval of solutions are:

[tex]t<0.5,\;0.52[/tex]

Use test values in the intervals to check which interval whose set of values satisfies the given inequality.

*The only interval that satisfies it is 0.5.*

Hence, the answer is **between 0.5 second and 2 seconds**.

**The answer is option (c).**

fing the probability of .14 .73 .03 is

### Answers

The probabilities are:

*0.14 -> 14%.

*0.73 -> 73%.

*0.03 -> 3%.

A triangle has vertices on a coordinate grid at D(-5, -2), E(-5,4), andF(-1,4). What is the length, in units, of DE?

### Answers

To find the length of DE,

Here D = (-5,-2) and E = (-5,4).

Hence the distance is given by

[tex]DE=\sqrt[]{(-5+5)^2+(4+2)^2}[/tex]

On simplifying,

[tex]\begin{gathered} DE=\sqrt[]{6^2} \\ DE=6 \end{gathered}[/tex]

Hence the length of DE is 6 units

Answer this question

### Answers

Okay, in this case the statement talks about **the sum, **according with this we need to find the sum of the number blue bikes (b) and 9 red bikes.

So, in this case the correct option is A. b+9 because it says sum

During World War I, mortars were fired from trenches 3 feet below ground level. The mortars had a velocity of150 ft/sec. Determine how long it will take for the mortar shell to strike its target.• What is the initial height of the rocket? -3 ft.• What is the maximum height of the rocket? 348.56 ft• How long does it take the rocket to reach the maximum height ? 4.68750 sec.• How long does it take the rocket to hit the ground (ground level)? 9.35 sec.• How long does it take the rocket to hit a one hundred feet tall building that is in it's downward path?[ Select]• What is the equation that represents the path of the rocket? Select]

### Answers

[tex]\begin{gathered} y=-\frac{g}{2}t^2+v_0t+y_0 \\ g\text{ in feets per seconds is 32} \end{gathered}[/tex][tex]\begin{gathered} \text{Now the height of the bilding is 100 hence y must be 100, i.e., y=100, hence one has} \\ 100=-16t^2+150t-3 \\ or \\ -16t^2+150t-103=0 \\ \text{the solutions are given by:} \end{gathered}[/tex][tex]\begin{gathered} t_1=\frac{-150+\sqrt[]{150^2-4(-16)(-103)}}{2(-16)} \\ t_2=\frac{-150-\sqrt[]{150^2-4(-16)(-103)}}{2(-16)} \end{gathered}[/tex][tex]\begin{gathered} t_1=\frac{-150+\sqrt[]{22500-6592}}{-32} \\ t_1=\frac{-150+\sqrt[]{15908}}{-32} \\ t_1=\frac{-150+126}{-32} \\ t_1=\frac{24}{-32}\text{ This solution is negative, it doesnt work. Let us s}ee\text{ the other solution:} \end{gathered}[/tex][tex]\begin{gathered} t_2=\frac{-150-\sqrt[]{150^2-4(-16)(-103)}}{2(-16)} \\ t_2=\frac{-150-\sqrt[]{22500^{}-6592}}{-32} \\ t_2=\frac{-150-\sqrt[]{15908}}{-32} \\ t_2=\frac{-150-126}{-32} \\ t_2=\frac{-276}{-32} \\ t=\frac{276}{32} \\ t=8.6\text{seg} \\ It\text{ takes 8.6 second to hit the bilding} \end{gathered}[/tex][tex]\begin{gathered} \text{the general equation of the parabolic motion is }y=-\frac{g}{2}t^2+v_0t+y_0\text{. In this case, this is} \\ y=-16t^2+150t-3 \end{gathered}[/tex]

Question 1 of 10 The graphs below have the same shape. What is the equation of the red graph? w GE? F%= 3 - 74 G(X)

### Answers

The** equation** of the red graph (Parabola) is** g(x) = 1 – x²**.

The given graph is the graph of the **parabolas**.

We are given;

The equation of the **blue** graph (Parabola) is f(x) = 4 – x².

We need to find the equation of the **red **graph g(x).

Let's **observe** the graph;

All of the lines in the blue graph** pass **through point 4 on the graph. The same is **true** for the red line, **except** that they all pass through 1. As a **result**, we should **alter** the 4 in the blue line **equation** to a 1 to** represent **the red line.

The **equation** of the blue graph is:

f(x) = 4 – x²

Substitute 4 by 1;

p(x) = 1 – x² = g(x)

This is our **required** equation.

Thus, the** equation** of the red graph (Parabola) is** g(x) = 1 – x²**.

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A new car worth $27,000 is depreciating in value by $3,000 per year. After how many years will the car's value be $3,000?

### Answers

The equation for the worth of car after x number of years is,

[tex]\begin{gathered} y=27000-3000\cdot x \\ =27000-3000x \end{gathered}[/tex]

Substitute 3000 for y in the equation to obtain the value of x.

[tex]\begin{gathered} 3000=27000-3000x \\ 3000x=27000-3000 \\ x=\frac{24000}{3000} \\ =8 \end{gathered}[/tex]

So after 8 years the worth of car is $3000.

Find the simple interest earned, to the nearest cent, for the principal, interest rate, and time.

$650, 5%, 1 year

### Answers

The **daily interest rate**, the principal, and the number of days between payments are multiplied to calculate simple interest.

The **simple interest **exists 32.5.

What is meant by simple interest?

Simple interest is a quick and **simple formula** for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.

Simple interest is calculated based on a **loan's principal** or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only **charge interest** on the principal sum, and a borrower will never be required to pay additional interest on the interest that has already accrued.

Let the equation be I = Prt

where, P be the **principal amount** = $650

r be the interest rate = 5%

t be the time = 1 year

substitute the values in the above **equation**, we get

I = 650 × 0.05 × 1

I = 32.5

Therefore, the **simple interest** rate exists 32.5.

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A skating rink attendant monitored the number of injuries at the rink over the past year. He tracked the ages of those injured and the kinds of skates worn during injury. In-line skates Roller skates Age 8 11 10 Age 10 4 9 Age 12 3 16 What is the probability that a randomly selected injured skater was not age 12 and was not wearing roller skates? Simplify any fractions.

### Answers

Given data:

The given table is shown.

The expression for the probability of that a randomly selected injured skater was not age 12 and was not wearing roller skates is,

[tex]undefined[/tex]

The half-life is blank years. Round to one decimal place as needed

### Answers

**SOLUTION **

The formula to apply is

[tex]\begin{gathered} A=A_oe^{-\lambda t} \\ Where\text{ A = amount of substance remaining = 0.5, after half decayed} \\ A_o=1 \\ \lambda=0.051 \\ t=\text{ time in years } \end{gathered}[/tex]

Putting in the values into the formula, we have

[tex]\begin{gathered} 0.5=1\times e^{-0.051t} \\ 0.5=e^{-0.051t} \\ Taking\text{ ln of both sides, we have} \\ ln0.5=-0.05t \\ t=\frac{ln0.5}{-0.051} \\ t=13.59112 \end{gathered}[/tex]

**Hence the answer is 13.6 years to 1 d.p**

After 3 hours, they are ____ miles apart. (Round to the nearest mile as needed.)

### Answers

Since Mike drove at 65 mph for 3 hours, we have that he traveled:

[tex]3\cdot65=195\text{ miles}[/tex]

for Sandra, we have the following:

[tex]3\cdot70=210\text{ miles}[/tex]

notice that both trajectories with the distance apart segment form a right triangle, then, using the pythagoren theorem, we get:

[tex]x=\sqrt[]{(210)^2+(195)^2}=\sqrt[]{44100+38025}=\sqrt[]{82125}\approx287\text{ miles}[/tex]

therefore, Sandra and Mike are approximately 287 miles apart after 3 hours

If AABC is similar to ARST, find the value of x.

### Answers

Given that

[tex]\begin{gathered} \Delta ABC\text{ is similar to }\Delta RST \\ \text{Therefore, the ratio of the corresponding sides is equal.} \\ \text{That is,} \\ \frac{AB}{RS}=\frac{BC}{ST}=\frac{AC}{RT} \end{gathered}[/tex]

Given that AB = 12, BC =18, AC =24 and RS =16, RT=x

We now use the ratio of the corresponding sides to find side RT( the value of x).

Hence,

[tex]\begin{gathered} \frac{AB}{RS}=\frac{AC}{RT} \\ \frac{12}{16}=\frac{24}{x} \\ x=\frac{24\times16}{12} \\ x=32 \end{gathered}[/tex]

Therefore, the value of x (RT) is** 32**

Please give me the correct answer.Please decide if these 4 statements is a function or not a function.

### Answers

As according to given statement:

1). Each school has one principal so as there is a relation between school and principal so it is a function.

2). Each student has a unique student ID number: so as there are so many students and they allhave different unique student ID's so there is a function.

3). Shoe manufacturers make different type of shoes : so as there is relation but we can't describe a function between them.

4). Each month of the year has a total amount of rainfall measured in inches:

So it is a function between month and the rainfall measured in inches.

We start with triangle ABC and seethatangleZAB is anexterior anglecreated by the extension of side AC.AnglesZAB and CAB are a linear pair by definition.We knowthat m∠ZAB + m∠CAB = 180° by the .Wealsoknowm∠CAB + m∠ACB + m∠CBA = 180° because .

### Answers

The first answer is: definition of complementary angles.

The second is: of the triangle sum theorem.

The third one is: substraction property

Find the area of the shaded sector of the circle. Leave your answers in terms of pi

### Answers

**Answer:**

**D. 8pi yd^2**

**Explanation:**

Area of a sector is expressed as;

[tex]A\text{ = }\frac{\theta}{360}\times\pi r^2[/tex]

r is the radius of the circle

theta is the angle substended at the centre

Given the following

r = 9yd

theta = 360-200

theta = 160degrees

Substitute

A = 160/360 * pi(9)^2

A = 4/9*18pi

A = 72pi/9

A = 8pi yd2

**Hence the area of the shaded sector is 8pi yd2**

Find the value of x. Assume that segments that appear to be tangent are tangent. 12, x , 6

### Answers

The** value **of x is 16.64.

Given that 14 is **tangent** to the circle and 9 is a radius, this is a right triangle.

From the **figure**, we have

Using the **Pythagoras theorem,**

a^2 +b^2 =c^2

9^2+14^2 =x^2

81+196 = x^2

277 = x^2

By taking the square root of each side, we get

sqrt(277) = sqrt(x^2)

sqrt(277) =x

**x = 16.64**

**Pythagoras theorem:**

The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the **sides** of a **right-angled triangle** relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem.In essence, the Pythagorean theorem is used to determine a triangle's **angle** and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas.

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Please I need help on this ASAP

### Answers

The value of the **function** h(x) in part (a) is equal to h(x) = 2x.

The value of the **function** h(x) in part (b) is equal to h(x) = 5x/2 - 2.

How to determine the function h(x)?

In this exercise, you are required to calculate the value of the **function** h(x), which is a product of the addition of function f(x) and function g(x). This ultimately implies that, the value of **function** h(x) can be calculated by adding function f(x) and **function** g(x) together.

For the first part (a), the value of **function** h(x) would be calculated as follows:

**Function** h(x) = Function f(x) + Function g(x)

Substituting the given parameters into the formula, we have;

Function h(x) = (x + 4) + (x - 4)

Function h(x) = x + 4 + x - 4

**Function** h(x) = 2x

For the second part (b), the value of **function** h(x) would be calculated as follows:

**Function** h(x) = Function f(x) + Function g(x)

Substituting the given parameters into the formula, we have;

Function h(x) = (2x - 4) + (x/2 + 2)

Function h(x) = 2x - 4 + x/2 + 2

**Function** h(x) = 5x/2 - 2.

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Solve algebraicallyX+4=-2

### Answers

SOLUTION:

Step 1:

In this question, we are given the following:

Solve algebraically

[tex]x\text{ + 4 = -2}[/tex]

**Step 2:**

**The details of the solutio are as follows:**

[tex]\begin{gathered} x\text{ + 4 = -2} \\ collecting\text{ like terms, we have that:} \\ x\text{ = - 2 - 4} \\ x\text{ = - 6} \end{gathered}[/tex]

**CONCLUSION:**

**The final answer is:**

[tex]x\text{ = - 6}[/tex]

1000C The formula that relates the wattage of an appliance to the cost to run the appliance is W = 1000/tcwhere W is the wattage of appliance, C is the cost to use the appliance per month, t is the time in hours per month, and c is the cost of electricity per kilowatt hour. Use $0.15 per kilowatt-hour for the cost of electricity. How much does it cost to run a 60-watt light bulb 720 hours a month? A. $0.15 B.$6.48 C.$12.32 D.$288

### Answers

[tex]\begin{gathered} p=\frac{w}{t} \\ \text{cross}-m\text{ultiply} \\ pt=w \\ \text{divide both sides by p} \\ t=\frac{w}{p} \end{gathered}[/tex]

**Hence, the correct option is Option C**

if FE measures 20 centimeters, the approximate area of circle B is what

### Answers

If FE **measures **20 cm, then the **area **is 314 cm², if BE **measure **3.5 cm, then the **area **is 38.5 cm², if AB **measures **11 cm, then the **area **is 380 cm² and is EF **measures **12 cm, then the **area **is 113 cm².

**Area **of a **circle**:

A = π r²

r = 1 /2 of **diameter**.

FE is the **diameter**

r = 20 / 2

r = 10 cm

**Area **of **circle **using FE:

A = π ( 10 )² = π × 100 = 314 cm²

BE is a **radius**:

**Area **= π × 3.5² = π × 12.25 = 38.465

A = 38.5 cm²

AB is a **radius**:

**Area **= π × 11²

A = π × 121

A = 379.94 = 380 cm²

EF is a **diameter**:

r = 12 / 2 = 6 cm

**Area **= π × 6²

A = π × 36

A = 113.04 = 113 cm²

Therefore, if FE **measures **20 cm, then the **area **is 314 cm², if BE **measure **3.5 cm, then the **area **is 38.5 cm², if AB **measures **11 cm, then the **area **is 380 cm² and is EF **measures **12 cm, then the **area **is 113 cm².

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**Your question was incomplete, Please refer the content below:**

1) if FE measures 20 centimeters, the approximate area of circle B is what?

2) if BE measures 3.5 centimeters, the approximate area of circle B is what?

3) if AB measures eleven centimeters, the approximate area of circle B is what

4) If EF measures twelve centimeters, the approximate area of circle B is what?

What is the area of the figure? Round to the nearest tenth if necessary. Include units in your answer.

### Answers

We can think of a hexagon in the next way:

This is, a shape made of 6 smaller triangles. So, we only need to calculate the area of one of those triangles and multiply it by 6

There is something interesting, each of the angles of every one of the triangles is 60°, those are equilateral triangles. So, let's focus on one triangle:

Notice that the blue line is the height of the triangle, that's what we need to find it's are using the formula:

[tex]A(triangle)=\frac{hb}{2}[/tex]

So, to calculate the height we use the Pythagoras Theorem

[tex]H^2-O^2=b^2\Rightarrow(20\operatorname{cm})^2-10\operatorname{cm}=b^2\Rightarrow b^2=300\operatorname{cm}\Rightarrow b=10\sqrt[]{3}[/tex]

Finally, the area of one of the triangles is:

[tex]A(triangle)=\frac{1}{2}(20cm)(10\sqrt[]{3}cm)=173.2cm^2[/tex]

And, by multiplying the previous result by 6, we get the area

[tex]A(hexagon)=6\cdot A(triangle)=6(173.2cm^2)=1039.2\operatorname{cm}[/tex]

What is thX= ら*e coefficient of the term x³y5 in the expansion of the binomial expression (2x − y)³?

### Answers

The **coefficient **of the term x²y in the **binomial expansion** of (2x − y)³ is -12.

The **expression **(2x − y)³ can be simplified as

8x³−12x²y+6xy²−y³ .

Thus the coefficient of the binomial expansion is -12.

Of the use of the binomial theorem, it is possible to determine the expanded value of either formula with the form (x + y)ⁿ.

The values of (x + y)², (x + y)³, and (a + b + c)² can be easily determined by adding the integers algebraically in accordance with the **exponent **value.

The binomial **theorem **was first mentioned by a well-known Greek mathematician by the name of Euclid in the fourth century BC.

According to the binomial theorem, which represents it as a sum of terms using distinct exponents of the variables x and y, the algebraic statement (x + y)ⁿ can be expanded. A coefficient, or numerical value, is assigned to each word in a binomial **expansion**.

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Determine which if any of given ordered pairs satisfy the system of linear equations

### Answers

**Solution:**

The equations are given below as

[tex]\begin{gathered} x+3y-z=-11-----(1) \\ 2x-y+2z=11------(2) \\ 3x+2y+3z=6------(3) \end{gathered}[/tex]

**Step 1:**

Make x the subject of the formula from equation (1)

[tex]\begin{gathered} x+3y-z=-11 \\ x=-11-3y+z-----(4) \end{gathered}[/tex]

**Step 2:**

Substitute equation (4) in equations (2) and (3)

[tex]\begin{gathered} 2x-y+2z=11 \\ 2(-11-3y+z)-y+2z=11 \\ -22-6y+2z-y+2z=11 \\ -7y+4z=11+22 \\ -7y+4z=33-----(5) \\ \\ 3x+2y+3z=6 \\ 3(-11-3y+z)+2y+3z=6 \\ -33-9y+3z+2y+3z=6 \\ -7y+6z=6+33 \\ -7y+6z=39------(6) \end{gathered}[/tex]

**Step 3:**

Substract equation 5 from 6

[tex]\begin{gathered} -7y-(-7y)+4z-6z=33-39 \\ -2z=-6 \\ z=3 \end{gathered}[/tex]

**Step 4:**

**Substitute the value of z=3 in equation (4)**

[tex]\begin{gathered} -7y+4z=33 \\ -7y+4(3)=33 \\ -7y+12=33 \\ -7y=33-12 \\ -7y=21 \\ y=-3 \end{gathered}[/tex]

**Step 4:**

Substitute y=-3, z= 3 in equation (4)

[tex]\begin{gathered} \begin{equation*} x=-11-3y+z \end{equation*} \\ x=-11-3(-3)+3 \\ x=-11+9+3 \\ x=1 \end{gathered}[/tex]

**Hence,**

**The final answer is**

[tex]\Rightarrow(1,-3,3)[/tex]

**ONLY THE ORDERED PAIR ( 1, -3, 3) satisfies the system of linear equations**

**OPTION B is the right answer**

fresh flowers charges $1.50 per flower and a $10 delivery fee. beautiful bouquets does not change a delivery fee but charges $4.00 per flower. which equation would allow you to find the number of flowers that would make the cost the same.1.50+ 10x=41.50x+10=41.50x + 10=4x1.50+ 10x=4

### Answers

**Step 1 **: Let's review the information provided to us to answer the question correctly:

Fresh flower price = $ 1.50

Delivery = $ 10

Bouquets per flower = $ 4.00

**Step 2**:

Let x to represent the number of flowers, either fresh or in bouquet

A triangle with side lengths 8, 15, and 17 is a right triangle by theconverse of thePythagorean Theorem. What are the measures of the other 2 angles?Round your answers to the nearest whole number.HINT: Draw a diagram of this problem and label your triangle.The méasure of the smaller acute angle is ____degreesand the larger acute angle measures_______degrees.

### Answers

We are given a right-angle triangle with side lengths 8, 15, and 17.

Since it is a right triangle, one angle must be 90°

Let us find the other two angles of this right triangle.

With respect to angle **x**, the** opposite** side is **15** and the **hypotenuse** side is **17**.

Recall from the trigonometric ratios,

[tex]\begin{gathered} \sin (x)=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin (x)=\frac{15}{17} \\ x=\sin ^{-1}(\frac{15}{17}) \\ x=61.9\degree \end{gathered}[/tex]

So, the second angle is **61.9°**

Recall that the sum of angles inside a triangle must be equal to **180°**

So, the third angle can be found as

[tex]\begin{gathered} y+61.9\degree+90\degree=180\degree \\ y=180\degree-90\degree-61.9\degree \\ y=28.1\degree \end{gathered}[/tex]

So, the third angle is** 28.1°**

The measure of the smaller acute angle is **28.1** degrees and the larger acute angle measures** 61.9** degrees.

I need help with question 4, I've included the prior answers from questions 1, 2 and 3 to help you. I've also included what the previous questions were so you have some context of the situation. Although, I think you only need the answers from part C ( which is the graph I've including) to answer question 4

### Answers

**We are asked to determine the equation of the midline for the periodic function. This can be seen below.**

**Explanation**

**Using the parameters from the graph, the function can be expressed as;**

[tex]y=(100sinx)+150[/tex]

The graph that contains the equation of the midline can be seen below.

Therefore, the equation of the midline is

**Answer:**

[tex]y=150[/tex]

Determine the equation of the line that passes through the point (-1, 2) and isperpendicular to the line y = -2.

### Answers

[tex]y=-\frac{1}{2}x+\frac{3}{2}[/tex]

**1) ** In this question, let's find the equation, using the point-slope formula:

[tex](y-y_0)=m(x-x_0)[/tex]

**2) **Notice that since we want a perpendicular line we can write a perpendicular line to y=2, as x=-1/2 for -1/2 is the opposite and reciprocal to 2 (the necessary condition to get a perpendicular line).

So, the slope of that perpendicular line is **-1/2**

**3) **Let's plug into that Point-Slope formula, the slope m= -1/2 and the point:

[tex]\begin{gathered} (y-2)=-\frac{1}{2}(x+1) \\ y-2=-\frac{1}{2}x-\frac{1}{2} \\ y=-\frac{1}{2}x-\frac{1}{2}+2 \\ y=-\frac{1}{2}x+\frac{3}{2} \end{gathered}[/tex]

**4) Thus, the answer is:**

[tex]y=-\frac{1}{2}x+\frac{3}{2}[/tex]

second blank has the option of , the same verticle asymptote as function h, vertical asymptote at x=-7, vertical asymptote at x=-5, and vertical asymptote at x=3

### Answers

Given:

The graph is g(x) is given and the function h(x) is,

[tex]h(x)=g(x+5)[/tex]

To classify the asymptotes:

Since the translated transformation of 5 units left,

There are no changes in the horizontal asymptote.

But, the vertical asymptote is,

[tex]\begin{gathered} x=-2-5 \\ =-7 \end{gathered}[/tex]

Thus, the graph h(x)=g(x+5) has the same horizontal asymptote as the function g