If f(x) = 2(x - 5), find f(8).
4
6
8
16

Answer:

The ball will be the 7 ft high at 2 different times.

Step-by-step explanation:

The height in meters of the ball is given by the following equation:

\(h(t) = -16t^2 + 25t\)

7 feet high

The height, by the equation, is given in meters, so we have to work in meters. Since each feet has 0,3048 meters, 7 feet have have 2.1336 meters. So, we have to solve the following equation

\(2,1336 = -16t^2 + 25t\)

\(16t^2 - 25t + 2,1336 = 0\)

At how many different times will the ball be 7 ft. High?

We have to find the number of solutions for the equation above.

It is given according to the value of \(\Delta = b^2 - 4ac\). If it is positive, there are two solutions, zero one solution and negative no solutions.

In this equation \(a = 16, b = -25, c = 2.1336\). So

\(\Delta = b^2 - 4ac = (-25)^2 - 4*16*2.1336 = 488\)

Since the coefficient is positive, the ball will be the 7 ft high at 2 different times.

Answer:

Jelly beans are $2.50 per pound

Almonds are $1.75 per pound

Step-by-step explanation:

3j + 2a = $11

5j + 6a = $23

Multiply equation 1 by 3

9j + 6a = $33

Subtract

9j + 6a = $33

-(5j + 6a = $23)

=(4j + 0a = $10)

4j = $10

j = $2.50

Plug j into any equation.

3(2.5) + 2a = $11

7.5 + 2a = $11

2a = 3.5

a = $1.75

Jelly beans are $2.50 per pound

Almonds are $1.75 per pound

Answer:

c

Step-by-step explanation:

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

  d = 23 1/3

Step-by-step explanation:

You want to solve the proportion (0.3d -1)/(3 1/3) = (0.84)/(7/15).

  \(\dfrac{0.3d-1}{3\dfrac{1}{3}}=\dfrac{0.84}{\dfrac{7}{15}}\qquad\text{given}\\\\\\\dfrac{3(0.3d-1)}{10}=\dfrac{15(0.84)}{7}\qquad\text{invert and multiply}\\\\0.09d -0.3=1.8\qquad\text{simplify}\\\\0.09d = 2.1\qquad\text{add 0.1}\\\\d=\dfrac{2.10}{0.09}=\dfrac{70}{3}\qquad\text{divide by 0.09}\\\\\boxed{d=23\dfrac{1}{3}}\)

__

Check

  (0.3·(70/3) -1)/(3 1/3) = 0.84/(7/15)

  (7 -1)/(10/3) = 1.8

  6(3/10) = 1.8 . . . . . . true

Answer: 23 1/3

Step-by-step explanation:

They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

Answer:

m = 7

Step-by-step explanation:

to solve this equation first divide both sides by -2

m - 5 = 2

now add 5 to both sides

m = 7

that is your answer

Answer:

m = 7

Step-by-step explanation:

This problem can be solved with basic algebra:

Step 1 is to divide by -2:

m - 5 = 2

Step 2 add 5 to each side:
m = 7

Hope that helps!

Answer:

$25000 * 40% = 100.000

Step-by-step explanation:

The distance between point P and line L is 16/9√(13).

To find the distance between point P and line L, we can use the formula for the distance between a point and a line in two-dimensional space. The formula is as follows:

Let P = (x1, y1) be the point and L be the line ax + by + c = 0. Then the distance between P and L is:

|ax1 + by1 + c|/√(a² + b²)

To find a, b, and c for the given line, we need to put it in slope-intercept form y = mx + b by solving for y.

2x - 3y = 12=> 2x - 12 = 3y=> (2/3)x - 4 = y

The slope of the line, m, is the coefficient of x, which is 2/3. Therefore, the line is:

y = (2/3)x - 4The values of a, b, and c are: a = 2/3b = -1c = -4

Now we can substitute the coordinates of P and the values of a, b, and c into the formula for the distance between a point and a line.

Let P = (3, 5).|a(3) + b(5) + c|/√(a² + b²)= |(2/3)(3) - 1(5) - 4|/√[(2/3)² + (-1)²]= |-4/3 - 4|/√(4/9 + 1)= 16/9√(13).

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Using the future value formula, it is found that the value of the account after the tenth deposit is of $26,361.59.

The future value formula is given by:

\(V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right]\)

In which:

For this problem, the parameters are given as follows:

P = 2000, r = 0.06, n = 10.

Hence the value of the account will be of:

\(V(10) = 2000\left[\frac{(1 + 0.06)^{10} - 1}{0.06}\right]\)

V(10) = $26,361.59.

The complete problem is:

"Suppose that there is an account that pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).

What will be the value of the account after the tenth deposit if no withdrawals or additional deposits are made?"

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Answer:

\(-\frac{1}{\sqrt{2} }\).

Step-by-step explanation:

Check images below.

On image 1, we started applying the L'Hôpital's rule for the limit. This rule consist on taking the derivative of the numerator and the denominator, individually and with respect to the variable of interest (in this case is x).

On image 1 we started taking the derivative with respect to x for the numerator.

Then, on image 2 we we started taking the derivative with respect to x for the denominator.

Finally, on image 3 we substituted the result of the derivatives and simplified the result.

Answer:

196.88 euros

Step-by-step explanation:

Divide 252 by 1.28

252/1.28

= 196.88 euros

Answer:

22707

Step-by-step explanation:

Answer: (iii) Profit The marked price of an article is 15% above its selling price and the cost price is 25% less tha its marked price. Find the discount percent and gain percent.​

Step-by-step explanation:

The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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The he expected value of the raffle is $2.50

What is the expected value of a raffle ticket?

The expected value is the sum of the winnings multiplied by their probabilities of persons participating

One person out of 400 would win $300, we have 1/400*$300

2 persons would win $200 each out of 400, we have 2/400*$200

3 persons would win $100, we have 3/400*$100

expected value=( 1/400*$300)+(2/400*$200)+(3/400*$100)

expected value=$2.50

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Answer:

The expected value of the raffle is -$1.50.

Step-by-step explanation:

Answer:

  1/12

Step-by-step explanation:

  blue = (3/8)collection

  blue&pocket = (2/9)blue = (2/9)(3/8)collection

  blue&pocket = (6/72)collection = (1/12)collection

1/12 of Noah's collection is blue and has a pocket.

The two students that mix the same ratio of juice to water is given as follows:

A. Luca.

D. Micah.

The ratio between two amounts a and b is given as follows:

a to b.

Which is also the division of the two amounts.

Hence the ratio of juice to water for each person is given as follows:

Hence Luca and Micah used the same ratio, meaning that options A and D are correct.

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To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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Answer: 1,000

Step-by-step explanation: if you multiply the 900 in 157,900 by a 1,000 you get the 900,000 in 901,532.

Answer:

(5,100)

Step-by-step explanation:

Answer:

-0.28

Step-by-step explanation:

(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28

Answer:

\(-7/25\)

Step-by-step explanation:

\(1/5 \div -5/7\)

Do the reciprocal of the second fraction.

\(1/5 \times 7/-5\)

Multiply the first fraction by the reciprocal of the second fraction.

\(7/-25=-0.28\)

The answer in decimal form is -0.28.

Answer:x intercept: (-16/3 ,0) y intercept: (0,8). bascially: (-16/3,8)

Step-by-step explanation:

The value of the missing side lengths x and y are 5√2 and 5 respectively.

The figure in the image is a right triangle.

Angle θ = 45 degree

Hypotenuse = x

Opposite to angle θ = y

Adjacent to angle θ = 5

To solve for side x and side y, we use the trigonometric ratio.

Note that:

Cosine = adjacent / hypotenuse

tangent = opposite / adjacent

Solving for x:

Cosine = adjacent / hypotenuse

Plug in the values

cos( 45 ) = 5/x

x = 5 / cos( 45 )

x = 5√2

Solving for side y:

tangent = opposite / adjacent

Plug in the values

tan( 45 ) = y/5

y = tan( 45 ) × 5

y = 5

Therefore, the value of side length x is 5 units.

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The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.

A general exponential decay is:

f(x) = A*(b)^x

Where A is the initial value, b is the rate of decay, x is the variable.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

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The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.

After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.

However, Caesar, true to his word, had the pirates crucified on his own authority.

This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

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