Mathematics High School

## Answers

**Answer 1**

Assume uniformly accelerated motion

Vf = Vo - at => a= [Vo - Vf] / t

Vf = 0, t = 20 s => a = Vo / 20

x = Vot - at^2 / 2

x = Vot - (Vo / 20) * t^2 /2

x = 1775 feet * [1 mile / 5280 feet] = 0.336 mile

t = 20 s

=> 0.336 = 20Vo - Vo(20)^2 /(40) = 20Vo - 10 Vo = 10 Vo

=> Vo = 0.336 /10 = 0.0336 mile /s

Vo = 0.0336 mile/s * 3600 s/h = 120.96 mile / h

Therefore, the car was way over the speed limit.

## Related Questions

The equation y = 35.25x + 40 gives the labor cost y of repairing a car if it takes x hours to repair the car. Which statement is true? For every hour of labor, the cost decreases by $40.

For every hour of labor, the cost decreases by $35.25.

For every hour of labor, the cost increases by $40.

For every hour of labor, the cost increases by $35.25.

### Answers

Repari cost (x) = y = 35.25 x + 40

x = number of hours to repair the car.

Every hour the cost will increase 35.25, becasue 40 is a fixed cost.

if x = 1, repair cost(1) = 35.25 + 40

if x = 2, repair cost (2) = 35.25*2 + 40

if you subtract repair cost (1) from repair cost (2) you get 35.25*2 - 35.25 = 35.25

The same thing every time the repair time increases one hour.

Answer: the last option of the list, for every hour of labor, the cost increases by $35.25

Answer:

For every hour of labor, the cost increases by $35.25.

Step-by-step explanation:

Got it right on the test.

Person A opens an IRA at age 25, contributes $2000/yr for 10 years, but makes no additional contributions thereafter. Person B waits until age 35 to open an IRA and contributes $2000/yr for 30 years. There is no initial investment in either case, and the contributions are made continuously. Determine the return rate r for which the two IRA's have equal value at age 65.

### Answers

For Person 1: IRA = (P((1 + r)^n1 - 1)/r)(1 + r)^n2; where P = 2000, n1 = 10, n2 = 30

For Person 2: IRA = P((1 + r)^n - 1)/r; where P = 2000, n = 30

(2000((1 + r)^10 - 1)/r)(1 + r)^30 = 2000((1 + r)^30 - 1)/r

log(2000((1 + r)^10 - 1)/r)(1 + r)^30 = log(2000((1 + r)^30 - 1)/r)

log 2000 + log((1 + r)^10 - 1) - log r + log(1 + r)^30 = log 2000 + log((1 + r)^30 - 1) - log r

log((1 + r)^30 - 1) - log((1 + r)^10 - 1) = log(1 + r)^30

log(((1 + r)^30 - 1) / ((1 + r)^10 - 1)) = log(1 + r)^30

log((1 + r)^20 + (1 + r)^10 + 1) = log(1 + r)^30

(1 + r)^20 + (1 + r)^10 + 1) = (1 + r)^30

(1 + r)^30 - (1 + r)^20 - (1 + r)^10 - 1 = 0

let (1 + r)^10 be x, then

x^3 - x^2 - x - 1 = 0

x = 1.839286755

(1 + r)^10 = 1.839286755

1 + r = 10th root of 1.839286755 = 1.063

r = 1.063 - 1 = 0.063

Therefore, the required rate is 6.3%.

At 3:00 p.m., Jamie leaves her house and drives north to the beach. She arrives at 5:30 p.m. Also leaving at 3:00 p.m., her brother Raul leaves her house and drives south to a state park. He arrives at 4:30 p.m. The driving distance from the beach to the state park is 240 mi. Jamie and Raul drove at the same speed. What was their speed?

### Answers

Distance from the beach to the park = 240 mi

Distance between beach and her house: x

Time from her house to the beach: 2.5 h

Her speed: x / 2.5

Distance between park and her house: 240 - x

Time from her house to the park: 1.5 h

Raul's speed = (240 - x) / 1.5

Same speed =>

x / 2.5 = (240 - x) 1.5

=> 1.5x = 2.5(240) - 2.5x

3.5x = 600

x = 171 m/h

Answer: 171 m/h .... really fast!

Answer:

the answer is 60 mph

Step-by-step explanation:

A jet ski company charges a flat fee of $24.00 plus $2.25 per hour to rent a jet ski. Another company charges a fee of $23.00 plus $2.75 per hour to rent the same jet ski. Using a graphing calculator, find the number of hours for which the costs are the same. Round your answer to the nearest whole hour.

A) 2

B) 3

C) 4

D) 8

### Answers

The advantage of the graphing calculator is that you just have to find two independent equations, introduce them in the calculator and it will find the intersection point ot the two graphs.

The equations that you have to introduce are:

1) y = 2.25x + 24

2) y = 2.75x + 23

The algebraic solution, which will give you the same coordinates of the intersection point of the graphs is

2.25x + 24 = 2.75x + 23

2.75x - 2.25x = 24 - 23

0.5x = 1 => x 1 /0.5 = 2.

Answer: 2

Two metal spheres (one with radius x cm and the other with radius x+2 cm) will be melted together to create a new single sphere. Express the radius, R, of the new sphere as a function of x.

### Answers

The volume of the new sphere will be the sum of the volume of the two original spheres.

Volume of sphere with radius x:

V = [4 / 3] π (x^3)

Volume of the spher with radius [4/3] π (x +2)^3

Volume of the new sphere =

[4/3]πR^3 = [4/3]πx^3 + [/3]π(x+2)^3

R^3 = x^3 + (x+2)^3 = x^3 + x^3 + 3(x^2)(2) + 3x(2^2) + 2^3

R^3 = 2x^3 + 6x^2 + 12x + 8

Answer: R^3 = 2x^3 + 6x^2 + 12x + 8

The line defined by the equation 2y+3=-(2/3)(x-3) is tangent to the graph of g(x) at x=-3. What is the value of the limit as x approaches -3 of [g(x)-g(-3)]over(x+3)?

### Answers

The limit as x approaches -3 of [g(x) - g(-3)] / [x -(-3)] is, by definition of limit, g '(x) at x = -3.

And g '(x) at x = -3 is the slope of the line tangent to it.

2y + 3 = -(2/3) (x-3)

2y = -2x/3 + 2 - 3

y = -x/3 - 1/2 => slope = -1/3

Then the limit is -1/3

Answer: - 1/3

Livvi invests $19,430 in a savings account at her local bank which pays 1.8% simple annual interest. She also deposits $16,470 in an online savings account which pays 2.7% simple annual interest. After six years, which account will yield more interest, and approximately how much more interest will it yield?

### Answers

Simple interests means that interests are not compounded.

1) $19430 * 1.8 % = $349.74 per year

6 years => $349.74*6 = $2098.44

2) $ 16470 * 2.7% = $ 444.69 per year

6 years => $444.69 * 6 = $2668.14

3) Find the difference: $2668.14 - $2098.44 = $569.7

Then the second account will yield $569.7 more interest than the first one.

Answer:

b

Step-by-step explanation:

Francine and Cheryl received equal scores on a test made up of multiple choice questions and an essay. Francine got 34 multiple choice questions correct and received 14 points for her essay. Cheryl got 30 multiple choice questions correct and received 22 points for her essay. How many points was each multiple choice question worth?

### Answers

Francine's score: 34x + 14

Cheryl's score: 30x + 22

Equal scores => 34x + 14 = 30x + 22

34x - 30x = 22 - 14

4x = 8

x = 8 /4 = 2.

Answer: 2

Devon knows that there are 3 teaspoons (tsp) in 1 tablespoon (tbsp). His cookie recipe calls for 6 tbsp of honey. Which expressions can be used to find the number of tsp in 6 tbsp?

A-3tbps x 1 tsp/3 tbps

B-6tbps x 3 tsp 1 tbsp

C-3 tsp x 1 tsp/ 6 tbsp

D-3 tsp x 6 tbsp/ 1 tsp

### Answers

The answer isB-6tbps x 3 tsp 1 tbsp

there are 3 teaspoons (tsp) in 1 tablespoon (tbsp): 3 tsp - 1 tbsp

find the number of tsp in 6 tbsp: x tsp - 6 tbsp

3 tsp - 1 tbsp

x tsp - 6 tbsp

The proportion is:

3 tsp : 1 tbsp = x : 6tbsp

x = 3 tsp× 6 tbsp / 1 tbsp

which is the choice B.

Answer:

B

Step-by-step explanation:

just took the test on Edge 2020.

A hardware store makes a mixed bag of 42 items using screws, bolts, and washers. The cost of screws are $3.00 each, bolts cost $2.00 each, and washers are $1.50 each. The mixture calls for four times as many screws than bolts. The total cost of the mixture is $102.00. How much of each item did the store use.

### Answers

The answer is 24 screws, 6 bolts, and 12 washers.

s - the number of screws

b - the number of bolts

w - the number of washes

The cost of screws are $3.00 each: 3s

The cost of bolts are $2.00 each: 2b

The cost of washers are $1.0 each: 1.5w

A hardware store makes a mixed bag of 42 items using screws, bolts, and washers: s + b + w = 42

The mixture calls for four times as many screws than bolts: s = 4b

The total cost of the mixture is $102.00: 3s + 2b + 1.5w = 102

The system of three equations:

(i) s + b + w = 42

(ii) s = 4b

(iii) 3s + 2b + 1.5w = 102

Substitute s from (ii) equation into (i) equation and express it in the term of w:

4b + b + w = 42

5b + w = 42

w = 42 - 5b

Substitute s from (ii) equation and w from (i) equation into(iii)equation:

3 * 4b + 2b + 1.5(42 - 5b) = 102

12b + 2b + 63 - 7.5b = 102

6.5b + 63 = 102

6.5b = 102 - 63

6.5b = 39

b = 39 : 6.5

b = 6

s = 4b = 4 * 6 = 24

w = 42 - 5b = 42 - 5 * 6 = 42 - 30 = 12

If (x – 2k) is a factor of f(x), what must be true?

### Answers

If (x – 2k) is a factor of f(x), thenf(2k) = 0 is true.

Answer:

f at 2k will be zero.

Step-by-step explanation:

We have been given the factor of function which is (x-2k)

Whenever we say (x+2) is a factor of some polynomial that means x=-2 is the value where the particular polynomial will give the value zero.

Here, the given factor (x-2k) means x=2k will give the value of f(x) zero that is

f at 2k will be zero.

Rewrite each of the following as an expression of x which does not involve any logs. (a) log_{10} (1000^x) =

### Answers

Answer: 3 x

F(x) = x^-1, x=.9.

Use linear approximation to estimate answer

### Answers

L(x) = f'(a)(x - a)

f(x) = x^(-1), f'(x) = -x^(-2)

Let a = 1, f'(a) = -(1)^(-2) = -1

L(0.9) = f'(1)(0.9 - 1) = -1(-0.1) = 0.1

Therefore, linear approximation of f(x) = x^(-1) for x = 0.9 is 0.1

What number should be added to both sides of the equation to complete the square? x2 – 6x = 5

### Answers

The equation x^2 - 6x = 5 is a quadratic function, and we add 9 to both sides of the equation to complete the square

What is the completing the square?

The completing the square method of solving a quadratic function is a way of expressing the quadratic function as a perfect square

The equation is given as:

x^2 - 6x = 5

Take the coefficient of x

k = -6

Divide by 2

k/2 = -3

Square both sides

(k/2)^2 = 9

This means that we add 9 to both sides of the equation

Read more about completing the square at:

brainly.com/question/13981588

X²- 6x + __= 5 + __

to complete the square, you take your "middle" value, divide it by 2, then square it. in this case:

-6/2 = -3

(-3)² = 9

9 is the number you'd add to both sides to complete the square.

x²- 6x + 9 = 5 + 9

Luis can spend up to $240 buying men’s and women’s shirts for his club. Men’s shirts cost $8 each and women’s shirts cost $12 each. He needs to buy at least 3 of each type of shirt. Also, the women’s shirts must be at least twice the number of men’s shirts. Which combinations of men’s and women’s shirts can Luis buy?

Choose all answers that are correct.

A. 4 men’s shirts and 9 women’s shirts

B. 5 men’s shirts and 8 women’s shirts

C. 6 men’s shirts and 15 women’s shirts

D. 7 men’s shirts and 17 women’s shirts

### Answers

To find all the combinations you need to solve this system of inequations:

8m + 12w ≤ 240

m ≥ 3

w ≥ 3

w ≥ 2m

The way to solve that system is by graphing each inequation in the same system of coordinates (m,w).

From the combinations listed, 6 men's shirts and 15 women's shirts is the only valid one.

8*6 + 12*15 = 228 ≤ 240

6 ≥ 3

15 ≥ 3

15 ≥ 2(6)

Then, the answer is option C. 6 men's shirts and 15 women's shirts

1. Which value is a solution of the equation 3-2x=-5? A. 2

B. 4

C. -2

D. 1/5

2. Which ordered pair is a solution of the equation y=x-3?

A. (-2,5)

B. (-5,2)

C. (2,5)

D. (5,2)

3. Which ordered pair is a solution of the equation y=5x?

A. (-2,10)

B. (-5,25)

C. (-3,15)

D. (-2,-10)

### Answers

Answers:

1) B: 4

________________

2) D: (5,2) .

___________________________________

3) D: (-2, -10).

1. Jamar draws three pairs of parallel lines that are each intersected by a third line. In each figure, he measures a pair of angles. What is a reasonable conjecture for Jamar to make by recognizing a pattern and using inductive reasoning?

When a pair of parallel lines are intersected by a third line, all of the angles formed are supplementary.

When a pair of parallel lines are intersected by a third line, the same-side interior angles are supplementary.

When a pair of parallel lines are intersected by a third line, all of the angles formed are acute.

2. Timothy draws three isosceles triangles. In each figure, he measures a pair of angles.

What is a reasonable conjecture for Timothy to make by recognizing a pattern and using inductive reasoning?

In an isosceles triangle, two of the angles are obtuse.

In an isosceles triangle, one angle is always obtuse.

In an isosceles triangle, all of the angles are congruent.

In an isosceles triangle, two of the angles are congruent.

### Answers

It would be easier if you provided illustration to your problems. Anyway, I think, I can solve theese tasks without pictures, as I've seen it before. Here are my answers, check it out:

1.When a pair of parallel lines are intersected by a third line, the same-side interior angles are supplementary.

2.In an isosceles triangle, two of the angles are congruent.

Hope it's helpful for you

The correct answers are:

#1) When a pair of parallel lines are intersected by a third line, the same-side interior angles are supplementary.

#2) In an isosceles triangle, two of the angles are congruent.

Explanation:

#1) When a pair of parallel lines is intersected by a third line (called a transversal), certain angles are congruent and certain angles are supplementary.

Some of the angles will be acute and some will be obtuse.

However, one thing that is always true is that same-side interior angles are supplementary.

#2) An isosceles triangle is defined as a triangle in which two sides are congruent. The angles formed by each of those two sides and the third side will be congruent as well, due to them being the same length.

Susan makes 5 fruit cups for the picnic. In each cup she has 5 strawberries and 3 kiwi. Joanna uses the same number of total fruits to make her strawberry and kiwi cups. But she makes 4 cups. In each cup she uses 8 strawberries. How many kiwis are in each fruit cup that Joanna makes?

### Answers

The answer is 2 kiwis.

1 cup: 5 strawberries and 3 kiwi 5 + 3 = 8

5 cups: 5 * (5 strawberries and 3 kiwi) 5 * 8 = 40

She makes 4 cups. In each cup she uses 8 strawberries: 4 * 8 = 32 strawberries.

The total number of fruits is 40. So the number of kiwi in 4 cups is: 40 - 32 = 8

If 8 kiwi is in 4 cups, x kiwi is in 1 cup:

8 : 4 = x : 1

x = 8 * 1 / 4 = 2

She would use 4.8 kiwis per cup. so round it up to 5

The equation y = 35.25x + 40 gives the labor cost y of repairing a car if takes x hours to repair the car. According to the model, what is the best estimate of the labor cost if it takes 6 hours to repair a car?

$251.50

$211.50

$81.25

$41.25

### Answers

Y = 32.25 x + 40

If it takes 6 hours to repair a car:

y = 32.25 * 6 + 40 = 193.5 + 40 = $233.50

The closest are $251.50 and $211.50.

$251.50 - $233.50 = $18

$233.50 - $211.50 = $22

$18 < $22

Answer:

The closest estimate is A ) $251.50

The answer is 251.50

Which biconditional is NOT a good definition? a. An angle is a right angle if and only if its measure is 90°

b. An angle is acute if and only if its measure is less than 90°

c. Two angles are congruent if and only if its measure are the same.

d. An angle is obtuse if and only if its measure is greater than 180°

### Answers

Two angles are congruent if and only if its measure are the same is not a good definition because congruent angles sometimes does not has the same measures.

The answer is d because an obtuse angle can be anything over 90°

## FAQs

### What is the first step to take if you are in a crash? ›

Make sure everyone is safe, then **call the police**

If injuries are serious, dial 911 for an ambulance. Regardless, move the vehicles out of traffic to avoid another accident. Experts advise always calling the police after an accident.

**What are the follow up steps you should take after a collision? ›**

**What to do after a car accident: a step-by-step guide**

- Check yourself for injuries. If you're injured, call 911 or ask someone else to do so. ...
- Check on the well-being of your passengers. ...
- Get to safety. ...
- Call 911. ...
- Wait for help. ...
- Exchange information. ...
- Document the accident. ...
- Notify your insurer and start the claims process.

**What are the six correct steps to take after you have an accident? ›**

**Six Steps to Take Following a Car Accident**

- Maintain An Accident Essentials Kit In Your Glove Compartment Or Trunk. ...
- Position Your Vehicle In A Safe Spot. ...
- Be Thorough And Exchange All Necessary Information With The Other Driver. ...
- Always Complete An Accident Report. ...
- Be Familiar With Your Insurance Policy Coverage.