A small rectangular prism has a length of 5 inches, a width of 4 inches, and a volume of 100 cubic inches. A large rectangular prism also has a length of 5 inches and a width of 4 inches, but its volume is 200 cubic inches.
How much taller is the large prism than the small prism?

True, the slope measures the rate of change in the y-values with respect to the x-values. In other words, it indicates how much the y-value changes when the x-value changes by a certain amount. When referring to a linear equation in the form y = mx + b, the slope is represented by the coefficient m.

If the slope is positive, it means that as the x-value increases by a certain amount, the y-value also increases. Conversely, if the slope is negative, it means that as the x-value increases, the y-value decreases. The slope can be calculated using the formula (change in y) / (change in x), which can be written as (y2 - y1) / (x2 - x1) for any two points (x1, y1) and (x2, y2) on the line.In your specific question, the slope would indeed represent how much the y-value changes when the x-value changes by 2 units of the variable being measured. Therefore, if you know the slope and you have a starting point, you can calculate the corresponding y-value after the x-value has changed by 2 units. This concept is important in various fields, such as mathematics, physics, and economics, where the relationships between variables are often represented using linear equations with slopes.

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Answer:

x = 4

Step-by-step explanation:

(7x - 2) + (3x + 9) = 10x + 7

(10x + 7) + (8x - 6) = 18x + 1

18x + 1 = 73

18x = 72

72/18 = x

x = 4

It takes a train going 50 mph approximately 11/2 miles to stop safely.

The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.

In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.

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Answer:

A

Step-by-step explanation:

A linear function is a straight line when graphed so is not B.

For confirmation of A note how for each increase of 3 in x we get the same increase of 5 in y.

Answer:

704

Step-by-step explanation:

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer:

200 pairs of sandals

Step-by-step explanation:

Represent the sandals with x and the running shoes with y.

In a typical month:

\(Total = 2500\)

In April

\(Total = 3000\)

Required

The number of sandals in a typical month

In a typical month:

If 1 sandal costs 2.50, then x costs 2.50x

If 1 running shoe costs 4, then y costs 4y

The total is:

\(2.50x + 4y = 2500\)

In April:

If 1 sandal costs 2.50, then 2x costs 5x ---- we used 2x because the pairs is doubled

If 1 running shoe costs 4, then y costs 4y

The total is:

\(5x + 4y = 3000\)

The equations are:

\(5x + 4y = 3000\)

\(2.50x + 4y = 2500\)

Subtract

\(5x - 2.50x + 4y - 4y = 3000 - 2500\)

\(2.50x = 500\)

\(x = \frac{500}{2.50}\)

\(x = 200\)

Answer:

500 sandals and 300 running shoes

Step-by-step explanation:

9514 1404 393

Answer:

  (1, 7)

Step-by-step explanation:

Fill in x=1 and do the arithmetic.

  h(1) = 4(1) +3 = 7

The coordinate pair is ...

  (x, h(x)) = (1, h(1)) = (1, 7)

Answer:

5

Step-by-step explanation:

Answer:

the answer is 5

Step-by-step explanation:

Answer:

1 : 6

Step-by-step explanation:

3 : 18

3 ÷ 3 : 18 ÷ 3

1 : 18 ÷ 3

1 : 6

Answer:

n=6

Step-by-step explanation:

3:18

1:6

3/1=3

18/3=6

Answer:

c. 44

Step-by-step explanation:

½m - ¾n = 16

½m - (¾×8) = 16

½m - 6 = 16

½m = 16 + 6

½m = 22

m = 44

Answer:

c 44

Step-by-step explanation:

its on edge

The rate of change of the radius when the radius is 2 is approximately 4 / (π³ * 2⁵).

         V = (1/6) * π³ * r⁶

         dV/dt = (1/6) * π³ * 6 * r⁵ * dr/dt

          dV/dt = 4

       4 = (1/6) * π³ * 6 * 2⁵ * dr/dt

       dr/dt = 4 / ((1/6) * π³ * 6 * 2⁵) = 4 / (π³ * 2⁵)

So the rate of change of the radius when the radius is 2 is approximately  with this one: dr/dt = 4 / (π³ * 2⁵).

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The length CT of the line segment is 38 units

From the question, we have the following parameters

CJ = 9x + 1

JT = 2x + 15

Also, we understand that:

Point J is the midpoint of segment CT.

This means that

CJ = CT

So, we have

9x + 1 = 2x + 15

Evaluate the like terms

7x = 14

So, we have

x = 2

Length CT is calculated as

CT = 9x + 1 + 2x + 15

So, we have

CT = 9 x 2 + 1 + 2 x 2 + 15

Evaluate

CT = 38

Hence, the length is 38 units

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The line that is perpendicular to the equation of a line given is y = -2x + 3

The equation of a perpendicular line can be found using the slope of the line first and then applying the points through which the line passes through.

For the given question, the equation of the line is y = 1/2x + 11 and the point is (6, -9).

To find an equation of a line;

The equation of the line can be modified into y - y₁ = m(x - x₁)

substituting the values into the equation above gives y = -2x + 3

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Answer:

The graph is not a function

Step-by-step explanation:

Since the vertical line will pass through more than one point, the graph passes the vertical line test. Therefore, the relation Is Not a function

Answer:

l = Square root of 10

The given function is a piecewise function and we are asked to evaluate f(0). To do this, we need to find the expression that corresponds to x = 0. We can see that x < 2, so the expression we need to use is 1 + x.

Plugging in x = 0 into this expression gives us:

f(0) = 1 + 0 = 1

Therefore, the answer is 1.

In HTML format, the answer would be:

The given function is a piecewise function and we are asked to evaluate f(0). To do this, we need to find the expression that corresponds to x = 0. We can see that x < 2, so the expression we need to use is 1 + x.

Plugging in x = 0 into this expression gives us:

f(0) = 1 + 0 = 1

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Given:

A card is selected randomly from a standard deck of 52 cards.

To find:

The probability of each outcome.

a. a king of heart

b. a queen of spades

c. an ace of flower

d. an ace of diamond​

Solution:

In a standard deck of 52 cards.

Total number of cards = 52

13 cards of each suit (heart, diamond, club, spade).

13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

a. We need to find the probability of getting a king of heart.

Number of king of heart = 1

\(P(\text{a king of heart})=\dfrac{\text{Number of king of heart}}{\text{Total cards}}\)

\(P(\text{a king of heart})=\dfrac{1}{52}\)

b. We need to find the probability of getting a queen of spades.

Number of queen of spades = 1

\(P(\text{a queen of spades})=\dfrac{\text{Number of queen of spades}}{\text{Total cards}}\)

\(P(\text{a queen of spades})=\dfrac{1}{52}\)

c. We need to find the probability of getting an ace of flower (spades).

Number of ace of flower = 1

\(P(\text{an ace of flower})=\dfrac{\text{Number of ace of flower}}{\text{Total cards}}\)

\(P(\text{an ace of flower})=\dfrac{1}{52}\)

d. We need to find the probability of getting an ace of diamond​.

Number of ace of diamond​ = 1

\(P(\text{an ace of diamond​})=\dfrac{\text{Number of ace of diamond​}}{\text{Total cards}}\)

\(P(\text{an ace of diamond​})=\dfrac{1}{52}\)

Therefore, the required probabilities for each parts are:

(a) \(\dfrac{1}{52}\)

(b) \(\dfrac{1}{52}\)

(c) \(\dfrac{1}{52}\)

(d) \(\dfrac{1}{52}\)

The probabilities for each of the given selections are;

A) 1/52

B) 1/52

C) 1/52

D) 1/52

A) Since total number of cards in the deck is 52 and there is only one king of heart, then;

Probability of selecting a king of heart = 1/52

B) Since total number of cards in the deck is 52 and there is only one queen of spades, then;

Probability of selecting a queen of spade = 1/52

C) Since total number of cards in the deck is 52 and there is only one ace of flower, then;

Probability of selecting an ace flower = 1/52

D) Since total number of cards in the deck is 52 and there is only one ace of diamond, then;

Probability of selecting am ace of diamond = 1/52

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a) f'(0) = 1/2 and f(17) (0)= 1/18 b) the series converges for all values of x  c) The three nonzero terms are x, x^2/2!, and x^3/3!, and the general term is x^(n+1)/(n+1)!.   d) f(x) in terms of the same familiar function is e^x

The Maclaurin series for f(x) is given by 1 + (x)/2! + x^2/3! + x^3/4! + ... + x^n/(n + 1)! + ...
a) To find f'(0), we take the derivative of the Maclaurin series and plug in x = 0:
f'(x) = 1/2! + 2x/3! + 3x^2/4! + ... + n*x^(n-1)/(n+1)! + ...
f'(0) = 1/2! = 1/2
To find f(17)(0), we take the 17th derivative of the Maclaurin series and plug in x = 0:
f(17)(x) = 17!/(n+1)! + ...
f(17)(0) = 17!/(17+1)! = 1/18

b) The given series converges for all values of x. This can be shown using the ratio test:
lim (n -> infinity) |(x^(n+1)/(n+2)!)/(x^n/(n+1)!)| = lim (n -> infinity) |x/(n+2)| = 0

Since the limit is less than 1, the series converges for all values of x.

c) To find the Maclaurin series for g(x), we multiply the Maclaurin series for f(x) by x:
g(x) = x*f(x) = x*(1 + (x)/2! + x^2/3! + ... + x^n/(n+1)! + ...)
= x + x^2/2! + x^3/3! + ... + x^(n+1)/(n+1)! + ...

The first three nonzero terms are x, x^2/2!, and x^3/3!, and the general term is x^(n+1)/(n+1)!.

d) To write g(x) in terms of a familiar function without using series, we can use the fact that the Maclaurin series for e^x is 1 + x/1! + x^2/2! + x^3/3! + ...:
g(x) = x + x^2/2! + x^3/3! + ... = x*(1 + x/1! + x^2/2! + x^3/3! + ...) = x*e^x

Then, we can write f(x) in terms of the same familiar function by dividing both sides of the equation by x:
f(x) = g(x)/x = (x*e^x)/x = e^x

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Answer:

1.we know the perimeter of the triangle=x-3+x+6+x=3x+3

so,answer is (b)3x+3

2.area of the triangle=1/2*b*h

=1/2*x+2*2x+6=x+2*2x+6/2=2x^2+6x+4x+12/2=2x^2+10x+12/2=2(x^2+5x+6)/2=x^2+5x+6

so,answer is(b)x^2+5x+6

Answer:

answer is 12

Step-by-step explanation:

because 5×4=20

so u have to multiply 4 and three

3×4=12

and u can reduce it to

6/10 and reduce it again to

3/5

Answer: \(76.1222\)

Step-by-step explanation:

\(Simplify\) \(the\) \(expression\)\(.\)

\(14.53.48 + 12.12.42 + 13.53.48 + 13.28.6 + 20.17.3 + 19.43.8 + 28\)

The degree is the largest exponent on the variable.

\(0\)

Solve the rational equation by combining expressions and isolating the variable.

No solution

A rock that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge is a(n)  ventifact:

A rock refers to the solid portion of the earth crust which contains minerals. There are three types of rocks; The sedimentary rock: They are formed from dead plants, dead animals, sand etc.

The metamorphic rock: They are formed from previously existing rocks. The igneous rock: They are formed from the solidification of the molten magma.

Hence, ventifact are rock  that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge.

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Based on the amount of the loan, and the number of periods as well as the APR, the total amount of the monthly payment would be $6,423.

The monthly payments for the loan would be constant so they can be considered to be annuities.

The value of these annuities would be:

Present value of annuity = Annuity x ( 1 - (1 + rate)^-number of periods) / rate

6,100 = Annuity x (1 - (1 + 5%/12)⁻⁽²ˣ¹²⁾ / 0.05/12)

Annuity = 6,100 / 22.793898393955992921598741250451

= $267.62

The total monthly payment is:

= 267.62 x 12 x 2 years

= $6,423

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Given the following number:

Let's write it in a fraction or mixed number in the lowest terms.

Since the decimal is 0.14, putting it into fraction will be:

Simplifying,

258 is a whole number, thus, it will become a mixed number, we just add 258 and 7/50.

The answer is, therefore:

Your equation would be 7-3x=40. Subtract 7, divide by -3, and your answer is -11

The correct option is A, equilibrium price increases from $6 to $8.

In economics, equilibrium is a state in which the supply and demand for a product or service are balanced, resulting in a stable price. This can occur in a free market, where the price of a good or service is determined by the interaction of buyers and sellers.

Overall, equilibrium is a fundamental concept in many different fields, representing a state of balance or stability in a system or situation.

If the demand schedule changes from D2 to D1, then the demand curve shifts to the left. As a result, the new equilibrium point will be where the new demand curve (D1) intersects with the supply curve (S1).

From the table, we can see that the new equilibrium point is at a price of $8 and a quantity of 15. Therefore, the equilibrium price increases from $6 to $8, but the equilibrium quantity decreases from 15 to 13.

So the correct answer is: equilibrium price increases from $6 to $8.

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