Write a word phrase for the algebraic expression 3x - 7.

100 = 10^2

 so 10^9 * 10^2 = 10^11 kilometers in 100 years

To find the length of the curve, use the formula for arc length and integrate over the given interval. The integrals can be calculated using the derivatives of the curve's components.

To find the length of the curve, we need to calculate the arc length. The formula for arc length is given by:

L = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

In this case, dx/dt = -15sin(3t), dy/dt = -15cos(3t), and dz/dt = 3. We can use these formulas to calculate the integrals over the interval [3, 7] and find the length of the curve.

do order of operations:

60 / 5*(7-5)=

 do parenthesis first: 7-5=2

60 / 5*2 =

 now do division: 60/5 =12

12*2 =

now multiply: 12 *2 = 24

answer is 24

Answer:

She need to put on 6 underpants

Step-by-step explanation:

She has learned from experience that she stays warm about 20 minutes for every undershirt she wears.

Time warmed by 1 undershirt = 20 minutes.

Total time she wants to stay out = 120 minutes

Number of underpants required [tex]=\frac{120}{20}=6\texttt{ underpants}[/tex]

So she need to put on 6 underpants

Answer:

Sloose intercept or a strait line

Step-by-step explanation:

Final answer:

The volume of the new pyramid, after a 50% increase in base side length, is expressed as V = 0.75b²h. This comes from applying the formula for the volume of a square pyramid and substituting the new base length of 1.5b into the formula.

Explanation:

The student is asked to write a simplified expression for the volume of a new pyramid after the side lengths of the base increase by 50%. The formula for the volume of a square pyramid with a base side length b and height h is V = (1/3)b²h.

When the side lengths of the base increase by 50%, the new base side length becomes 1.5b. Plugging this into the volume formula, we have:
V' = (1/3)(1.5b)²h
 = (1/3)(2.25b²)h
 = (2.25/3)b²h
 = 0.75b²h

This is the simplified expression for the volume of the pyramid after the increase in base side length.

The volume of the new pyramid is [tex]\(0.75b^2h\), where \(b\)[/tex] is the base side length and [tex]\(h\)[/tex] is the height.

To find the volume of a square pyramid, we use the formula:

[tex]\[ V = \frac{1}{3} \times (\text{area of base}) \times \text{height} \][/tex]

For a square pyramid, the area of the base is [tex]\( b^2 \), where \( b \)[/tex] is the side length of the base.

So, the volume [tex]\( V \)[/tex] of the original pyramid can be written as:

[tex]\[ V = \frac{1}{3} \times b^2 \times h \][/tex]

Now, if the side lengths of the base increase by 50%, the new side length of the base becomes [tex]\( 1.5b \)[/tex] (since increasing by 50% is the same as multiplying by [tex]\( 1.5 \))[/tex].

Therefore, the new area of the base is [tex]\( (1.5b)^2 = 2.25b^2 \).[/tex]

So, the volume \( V' \) of the new pyramid can be written as:

[tex]\[ V' = \frac{1}{3} \times (2.25b^2) \times h \][/tex]

[tex]\[ V' = \frac{2.25}{3} \times b^2 \times h \][/tex]

[tex]\[ V' = 0.75 \times b^2 \times h \][/tex]

So, the simplified expression representing the volume of the new pyramid in terms of [tex]\( b \) and \( h \) is \( 0.75b^2h \)[/tex].

The 24-inch pizza is a better deal because it costs slightly less per square inch compared to the 12-inch pizza.

To determine which pizza is a better deal, we need to compare their prices per square inch. First, let's find the area of the 12-inch pizza. The formula to find the area of a square is side length squared, so the area of the 12-inch pizza is 12 x 12 = 144 square inches. Now, we can divide the price of the 12-inch pizza by its area to find the price per square inch: $3.95 / 144 = $0.0274 per square inch.

Next, let's find the area of the 24-inch pizza. The area of the 24-inch pizza is 24 x 24 = 576 square inches. Now, we can divide the price of the 24-inch pizza by its area to find the price per square inch: $14.95 / 576 = $0.0259 per square inch.

Comparing the prices per square inch, we can see that the 24-inch pizza is a better deal, as it costs slightly less per square inch compared to the 12-inch pizza.

A traditional barbershop quartet has 8 legs since it consists of four people. Female quartets exist alongside male quartets, with popular female groups like The Sweet Adelines International and The Chordettes. The scenario of a quartet having 16 legs is hypothetical and humorous, similar to a comedic tale from 'Only Fools and Horses' regarding a constantly replaced broom.

The question "When does a barbershop quartet have 16 legs?" seems to contain a riddle rather than a direct inquiry into the makeup of a barbershop quartet. Traditionally, a barbershop quartet comprises four individuals, each with two legs, totaling eight legs. This would shift to 16 legs if the quartet consisted of eight people. However, if we're speaking about the traditional four-person quartet, they would only have 16 legs if each member had four legs, which is not characteristic of human anatomy.

It is important to clarify that despite the common misconception that barbershop quartets are exclusively male, there are female quartets as well, such as those associated with The Sweet Adelines International or popular groups like The Chordettes. Neither of these situations normally results in 16 legs unless for comedic or hypothetical scenarios, akin to the tale shared in the comedy "Only Fools and Horses" where Trigger's broom maintains the same identity despite numerous replacements of its parts.

Examples in Pop Culture and Misconceptions

A blend of humor and play on the concept of identity similar to the aforestated barbershop quartet conundrum is seen in the television sitcom "Only Fools and Horses," where a character humorously remarks on the extensive replacement of broom parts, posing a philosophical question of identity and perception.

Answer:

4m+8n -4p

Step-by-step explanation:

hello

you can just sum like a normal addition, just put  similar terms on each other

       5m   + 3n    +p

                +3n    -5p  (second expression)

        -m    +2n            ( third expression)

    _____________

 (5-1)m  (3+3+2)n+(1-5)p = 4m+8n -4p

I hope it helps you

Have a great day

To find the zeros of the polynomial f(x) = x^4 + 6x^3 - 3x^2 -52x - 60, we can test different values and find that x = 2, -2, -5, -3 are the four real zeros.

To find the zeros of the polynomial f(x) = x^4 + 6x^3 - 3x^2 -52x - 60, we need to solve the equation f(x) = 0. We can do this by factoring or using synthetic division. By testing different values, we find that x = 2, -2, -5, -3 are the four real zeros of the polynomial. Therefore, the correct answer is A. 2, -2, -5, -3.

Number of ways it can happen is 5832.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

We have eighteen-sided die is rolled three times.

When the die is first rolled, there are 18 possibilities of outcomes.

Again when the die is rolled, again there are 18 possibilities.

In the third rolling also, there are 18 possibilities.

Each die has 18 possibilities of numbers for a number for the other die.

Total number of sets = 18 × 18 × 18

                                   = 5832

Hence the total number of ways that the numbers can be formed is 5832.

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You would need approximately 75.7 liters of lemonade for your event. This is calculated by using the conversion factor of 3.78541 liters per gallon.

To calculate how many liters of lemonade you need for 20 gallons, we first need to know the conversion rate. There are about 3.78541 liters in 1 gallon. Thus, if you need 20 gallons, we can use multiplication to find this.

So, if we multiply 20 (gallons) by 3.78541 (liters per gallon), the result is approximately 75.7 liters. You would therefore need about 75.7 liters of lemonade for your event. This is a simple application of conversion factors, where the given quantity (gallons) is multiplied by a conversion factor (liters per gallon) to obtain the desired quantity (liters).

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The zero of the function y = -7x + 8 is 8/7.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y = -7x + 8

y = 0 to find the zeroes.

0 = -7x + 8

7x = 8

x = 8/7

Thus,

The zero of the function is 8/7.

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Answer:A. One graph uses an open circle, but the other graph uses a closed circle. Also, the rays use arrows that point in opposite directions, but they have the same endpoint.