Surface area of this trapezoid prism

In golf, lower scores are better, so a score of 70 is considered to be a good score for a round of golf, especially on a challenging course.

An integer is a whole number that can be either positive, negative or zero, and does not have a fractional or decimal part. Integers can be represented on a number line, with positive integers located to the right of zero and negative integers located to the left of zero.

an integer is a whole number that does not have a fractional or decimal part. In golf, a player's score for a round is determined by counting the number of strokes they took to complete the course.

So, if a golfer took 70 shots to finish his or her round on a golf course, the integer that represents this score is simply 70. This is because 70 is a whole number and there are no fractional or decimal parts involved in the score.

In golf, lower scores are better, so a score of 70 is considered to be a good score for a round of golf, especially on a challenging course.

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Based on the information provided, the polygon can be classified as a trapezoid.

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Answer:

answer is

c. y = 2x - 4

Step-by-step explanation:

y=mx+b is standard, b is also correct but not in standard form, hope this helps

Answer:

The relationship between m number of songs downloaded  and the total cost of $20 Mariana receives will be represented by inequality .

Given,

The value of gift card which Mariana have .

The costs of each downloaded song is .

Since m represents the number of songs downloaded and she has in total , so the inequality represents the given situation is,

.

Hence the required inequality is .

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Step-by-step explanation:

Answer:

The answer should be C

The population will be approximately 29,628 people 5 years from now. (Rounded to the nearest whole number)

To calculate the future population, we need to take into account the growth rate over time.

In this case, we know that the population doubled in size over 26 months and the current population is 20,000.

Let's break down the problem step by step:

Calculate the monthly growth rate:

Since the population doubled in size over 26 months, the monthly growth rate can be calculated as the 26th root of 2.

This is because if the population doubles in size over 26 months, each month the population grows by the 26th root of 2.

Monthly growth rate  [tex]= 2^{(1/26) } \approx 1.027[/tex]

Calculate the number of months in 5 years:  

Since there are 12 months in a year, the number of months in 5 years is [tex]5 \times 12 = 60[/tex] months.

Calculate the future population:

We start with the current population of 20,000 and apply the monthly growth rate for 60 months.

Future population  = Current population [tex]\times[/tex]  (Monthly growth rate)^{(Number of months)

Future population [tex]= 20,000 \times (1.027)^60 \approx 29,628.12[/tex]

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Step-by-step explanation:

Physically, integrating f(x)dx means finding the a. area to the right of point b. b. area to the left of point a . area under the curve and bounded by the lines x= a and x = d. d. area above the curve and bounded by the lines x = a and x = c. b. b.

Answer:

Step-by-step explanation:

means finding the area under the curve from a to b area t0 the left of point area t0 the right of point area above the curve from a to b CelecGne The exact value of xe ' dx is most nearly (A 7.8036 B) 11.807 14.034 19.614 CelecGne

Answer:

Step-by-step explanation:

For creating a budget for your business, you must include 4 main things.

These are as follows:

1. Transportation and vehicle cost.

2. Your estimated revenue plan

3. Profit margin

4. Spending goals

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Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

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Answer:

7

Let's call the width = x

width : x

so (x + 2x-4)2 = 34 (perime formula of a rectangle) x+2x-4 = 7

3x = 21

x = 7

so x is 7

G. y = 37/24x

Direct variation means that the number of inches of rain (y) is directly proportional to the number of hours (x). In this case, 37 inches of rain fell in a 24-hour period. To find the constant of proportionality, divide the total inches of rain by the total hours:

k = 37 inches / 24 hours

Now, we can write the equation of direct variation:

y = kx

Substitute the value of k:

y = (37/24)x

Answer:

To find the factored form of the polynomial function, we start by using the zeros to write out the factors of the polynomial. If the zeros are a, b, c, d, then the factors are (x-a), (x-b), (x-c), and (x-d).

In this case, the zeros are -1, -3, 3, and 1, so the factors are (x+1), (x+3), (x-3), and (x-1). Multiplying these factors together gives the polynomial function:

f(x) = (x+1)(x+3)(x-3)(x-1)

To simplify this expression, we can use the distributive property to expand the factors:

f(x) = (x+1)(x^2 - 9)(x-1)

Next, we can multiply the remaining factors using the distributive property and combining like terms:

f(x) = (x^3 - 8x - 9)(x-1)

Finally, we can use the distributive property again to expand the remaining factor:

f(x) = x^4 - 9x^2 + 8x + 9x^3 - 8x - 9

Simplifying this expression gives the factored form of the polynomial function:

f(x) = (x+1)(x+3)(x-3)(x-1) = x^4 - 9x^2 + 8x - 9x^3 - 8x - 9.

Answer:

1 pound of jelly beans cost $1.75 , 1 pound of trail mix cost $3.75

Step-by-step explanation:

let j represent 1 pound of jelly beans and t represent 1 pound of trail mix , then

5j + 3t = 20 → (1)

7j + 9t = 46 → (2)

multiplying (1) by - 3 and adding to (2) will eliminate t

- 15j - 9t = - 60 → (3)

add (2) and (3) term by term to eliminate t

(7j - 15j) + (9t - 9t) = 46 - 60

- 8j + 0 = - 14

- 8j = - 14 ( divide both sides by - 8 )

j = [tex]\frac{-14}{-8}[/tex] = 1.75

substitute j = 1.75 into either of the 2 equations and solve for t

substituting into (1)

5(1.75) + 3t = 20

8.75 + 3t = 20 ( subtract 8.75 from both sides )

3t = 11.25 ( divide both sides by 3 )

t = 3.75

then

cost of 1 pound of jelly beans = $1.75

cost of 1 pound of trail mix = $3.75

Answer:

Cost for each pound of jelly beans:  $1.75

Cost for each pound of trail mix:  $3.75

Step-by-step explanation:

Define the variables:

Using the given information and defined variables, create a system of equations:

[tex]\begin{cases}5J+3T=20\\7J+9T=46\end{cases}[/tex]

To solve the system of equations, multiply the first equation by 3 to create a third equation:

[tex]5J \cdot 3+3T \cdot 3=20\cdot 3[/tex]

[tex]15J+9T=60[/tex]

Subtract the second equation from the third equation to eliminate the term in T:

[tex]\begin{array}{crcrcl}&15J & + & 9T & = & 60\\\vphantom{\dfrac12}- & (7J & + & 9T & = & 46)\\\cline{2-6}\vphantom{\dfrac12} &8J&&&=&14\end{array}[/tex]

Solve the equation for J by dividing both sides by 8:

[tex]\dfrac{8J}{8}=\dfrac{14}{8}[/tex]

[tex]J=1.75[/tex]

Therefore, the cost of each pound of jelly beans is $1.75.

To find the cost of one pound of trail mix, substitute the found value of J into one of the original equations and solve for T.

Using the second equation:

[tex]7(1.75)+9T=46[/tex]

[tex]12.25+9T=46[/tex]

[tex]12.25+9T-12.25=46-12.25[/tex]

[tex]9T=33.75[/tex]

[tex]\dfrac{9T}{9}=\dfrac{33.75}{9}[/tex]

[tex]T=3.75[/tex]

Therefore, the cost of each pound of jelly beans is $3.75.

Suppose you are driving a car with the velocity function represented by the following equation: f(x)= 2x^3-3x^2-12x+1. The derivative would be: f'(x) = 6x^2 - 6x - 12

To find the acceleration of the car at a particular moment, we would need to calculate the derivative of the velocity function f(x). In this case, the derivative would be:

f'(x) = 6x^2 - 6x - 12

The result of this calculation would give us the instantaneous acceleration of the car at a given time x.

In terms of the car's motion, a positive value for f'(x) would indicate that the car is accelerating, while a negative value would indicate that the car is decelerating. The magnitude of the value would indicate the rate of change of the car's velocity, with larger values indicating a more rapid change.

Translated question "A derivative problem from everyday life using the following function: f(x)= 2x^3-3x^2-12x+1"

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The statement "The capital letter N produces the same capital letter after being rotated 180°" is true.

If you rotate the capital letter N 180°, it will produce the same capital letter, as it has rotational symmetry.

The letter N has a vertical line of symmetry in the center, which means that if you rotate it 180°, it will overlap perfectly with its original position, producing the same letter.

So, the statement "The capital letter N produces the same capital letter after being rotated 180°" is true.

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Answer:

[tex]x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm i\sqrt{\frac{2}{7}}[/tex]

(real solution)       (imaginary solution)

Step-by-step explanation:

For these type of questions, where the exponent is even, it helps to try to rewrite the equation into a quadratic equation as we have a closed formula (quadratic formula) to solve for the zeroes, and it's also just easier to deal with in general.

Let's say that: [tex]u=x^2[/tex], now if we square both sides, [tex]u^2=x^4[/tex], so from here we can substitute in u squared as x to the power of four.

This results in our following equation: [tex]49u^2-4[/tex], from here we could use the quadratic formula, but you may notice a pattern here. We have a difference of squares: [tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]49u^2[/tex] can be written as [tex](7u)^2[/tex] and [tex]4[/tex] can be written as [tex]2^2[/tex], this gives us our equation: [tex](7u)^2-2^2\implies (7u-2)(7u+2)[/tex]. If we use this definition of the equation on the left side, it gives us: [tex](7u-2)(7u+2)=0[/tex] and this is very convenient as we can solve both of them individually.

Whenever we multiply any number (assuming it's defined) by zero, we should get.... zero. This intuitively makes sense as no matter how many times we add zero up (multiplication is repeated addition), we're always just going to have zero.

So when we have the equation: [tex]a*b=0[/tex], if "a" is zero then regardless of what "b" is (assuming it's defined), then the product will be zero. If "b" is zero then regardless of what "a" is (assuming it's defined), then the product will be zero.

Now if we look back at our equation: [tex](7u-2)(7u+2)=0[/tex], if [tex]7u-2=0[/tex], then regardless of what [tex]7u+2[/tex] is equal to, the product will be zero. Likewise, if [tex]7u+2=0[/tex] then regardless of what [tex]7u-2[/tex] is equal to, the product will be zero, thus making the equation true.

So to find the solutions to this, we find what makes [tex]7u-2=0 \text{ and }7u+2=0[/tex] true. If we work them both out individually we

get:

[tex]7u-2=0\\7u=2\\u=\frac{2}{7}\\\\7u+2=0\\7u=-2\\u=-\frac{2}{7}[/tex]

So now we have our two solutions right? Well remember we started off with a "x" variable, and the "u" is merely a substitution. If you recall, the "u" value is set equal to "x^2", so we can just plug that back in, so we can find the solutions in terms of x.

[tex]x^2=\frac{2}{7} \text{ and } x^2=-\frac{2}{7}[/tex]

If we take the square root of both sides, we get:

[tex]x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm\sqrt{-\frac{2}{7}}[/tex]

you'll notice in one of them, we're taking the square root of a negative number. This will result in imaginary solutions, if we factor out a "-1" and take the square root of that, we'll just get an "i" infront, giving us the solutions of: [tex]x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm i\sqrt{\frac{2}{7}}[/tex].

Yellow to red hence has a 4 to 1 ratio. Solution: B. 4 to 1 as 2 red times 5 purple (Instead of purple).

A percent is a claim that two factors are equal in mathematics. When two quantities are compared by dividing them, the result is expressed as a ratio as a fraction. For instance, the number of girls to boys in a class can be expressed as "girls: boys" or "girls/boys." One way to express a percentage is as follows: a/b = c/d in which a, b, c, and d were four values that prevent b and d from being equal to zero. As a result, the ratio of a to b is the same as the ratio of c to d. The first term (a) is therefore equal to the reelection campaign (b), and the τ (c) is equal to the fourth term.

given

The given equalities can be used to calculate the proportion of yellow to red:

5 green times 6 yellow (Subtract both sides by 5)

(6/5) Yellow is equivalent to green.

3 purple + 4 green (substitute for green)

4 (6/5) Purple x 3 yellow

(24/5) Purple x 3 yellow (divide both sides by 4)

(8/5) Purple x yellow

2 red times 5 purple (Instead of purple)

(5/8) yellow Equals 2 red.

2 red x 8 yellow (divide both sides by 5)

Red + 4 yellows

Yellow to red hence has a 4 to 1 ratio. Solution: B. 4 to 1 as 2 red times 5 purple (Instead of purple).

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Answer:

88

Step-by-step explanation:

y=2cm h=7cm

CSA=22/7×4×7

the sevens get crossed out and then 22/1 ×4=88.

The calculated base area of the paperweight is 9.6 square cm.

To calculate the base area of the paperweight, we can use the formula for the volume of a three-dimensional object:

Volume = Base area x Height

In this case, we know that the height of the paperweight is 4cm and the volume is 38.4 cubic cm.

So we can rearrange the formula and solve for the base area:

Base area = Volume / Height

Substituting the values we have:

Base area = 38.4 cubic cm / 4cm

Base area = 9.6 square cm

Therefore, the base area of the paperweight is 9.6 square cm.

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Answer: The two numbers are 5 and 12

Step-by-step explanation:

As the least common multiple of two numbers is

60

, the two numbers are factors of

60

.

Factors of

60

are

{

1

,

2

,

3

,

4

,

5

,

6

,

10

,

12

,

15

,

20

,

30

,

60

}

As one of the numbers is

7

less than the other, the difference of two numbers is

7

Among

{

1

,

2

,

3

,

4

,

5

,

6

,

10

,

12

,

15

,

20

,

30

,

60

}

,

3

&

10

and

5

&

12

are the only two pair of numbers whose difference is

7

. But Least common multiple of

3

and

10

is

30

.

Hence, the two numbers are

5

and

12

.

A. not continuous

Continuous functions have no jumps or vertical asymptotes.

Continuity

For a function to be continuous, each point on the function must be defined. This means that there cannot be points on the graph where there is no value or coordinate point. Additionally, all points must be connected by the graph. Sudden jumps in the graph that are not connected by anything are not continuous.

Determining Continuity

The graph above is not continuous. We know this for 2 reasons. Firstly, the graph is not defined at x = -3. Since there is an open circle at x = -3, the value is not defined. Thus, the function cannot be considered continuous. Additionally, there are multiple jumps. At x = -3, the function suddenly jumps to x = -2 without the points being connected. The same thing happens again at x = 1. This also shows that the graph is not continuous.

a) [tex]f(x) + xg(x) = x^{3} + 7x^{2} + x - 4.[/tex]

b) [tex][f(x)]² = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]

c) [tex]f^{2}(x) = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]

d) [tex]gf(x) = 2x^{4} + 8x^{3} - 13x^{2} - 3x - 8.[/tex]

what is expression ?

It is possible to do mathematical operations like addition, subtraction, division, and multiplication. An expression is put together as follows: Number, expression, and mathematical operator.

a) f(x) + xg(x)

First, we need to find xg(x), which is x multiplied by g(x):

[tex]xg(x) = x(x^{2} + 5x + 2) = x^{3} + 5x^{2} + 2x\\\\f(x) + xg(x) = 2x^{2} - x - 4 + x^{3} + 5x^{2} + 2x\\\\f(x) + xg(x) = x^{3} + 7x^{2} + x - 4[/tex]

Therefore, [tex]f(x) + xg(x) = x^{3} + 7x^{2} + x - 4.[/tex]

b) [f(x)]²

To square f(x), we can simply multiply it by itself:

[f(x)]² = (2x² - x - 4)(2x² - x - 4)

[tex][f(x)]² = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]

c) f²(x)

Since f²(x) means f(x) times f(x), we can use the distributive property of multiplication:

[tex]f^{2} (x) = f(x) * f(x)\\\\f^{2}(x) = (2x^{2} - x - 4)(2x^{2} - x - 4)[/tex]

[tex]f^{2}(x) = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]

d) gf(x)

To find gf(x), we need to multiply g(x) by f(x):

[tex]gf(x) = (x^{2} + 5x + 2)(2x^{2} - x - 4)[/tex]

Multiplying each term of g(x) by each term of f(x), and simplifying:

gf(x) = 2x⁴ + 8x³ - 13x² - 3x - 8

Therefore, [tex]gf(x) = 2x^{4} + 8x^{3} - 13x^{2} - 3x - 8.[/tex]

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a. The exponential model representing the situation is S (t) = 6.26 * [tex]1.04^{t}[/tex]. The number of subscribers in 2016 is 7.32 billion.

b. In the year 2015, the number of cell phone subscribers were about 7 billion.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." In mathematics, operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference.

a. Since, during next 5 years there is increase by 4% so, we get the base using the addition operation as:

1 + 4% = 1.04

The exponential model comes out to be

y = 6.26 * [tex]1.04^{t}[/tex]

Now, the number of cell phone subscribers in 2016 is:

y = 6.26 * [tex]1.04^{4}[/tex]      (This is because t = 4)

y = 7.32 billion

b. We are given y = 7 billion.

So, we get

⇒ 7 = 6.26 * [tex]1.04^{t}[/tex]

⇒ 1.12 = [tex]1.04^{t}[/tex]                           (Using the division operation)

⇒ t = 2.8

So, in 2015, the number of cell phone subscribers were about 7 billion.

Hence, the required solutions have been obtained.

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Answer:

- 2/1

Step-by-step explanation:

if u look at the graph/line it's going up by 2 then across 1

The general common factor (GCF) of the polynomial equation [tex]24x^9 + 21x^6 = 0[/tex] is 3x6, which, after factoring, is the common factor of the coefficients and the terms enclosed in brackets.

We must factor out the common terms from both the coefficients and the exponents in order to determine the GCF (Greatest Common Factor) for the polynomial equation 24x9 + 21x6 = 0.

The first step is to determine the coefficients' common factor, which is 3. The equation can be changed to read:

3(8x^9 + 7x^6) = 0

We now need to determine which term the parenthesized terms have in common the most. Since x is raised to a power in both terms, we may factor out x^6 to obtain:

3x^6(8x^3 + 7) = 0

The greatest common factor of the polynomial equation 24x^9 + 21x^6 = 0 is 3x^6.

We can verify this by dividing both terms in the equation by 3x^6. Doing so gives us:

(8x^3 + 7) = 0

This equation has no common factors, and we cannot factor it further. Thus, the GCF of the original polynomial equation 24x^9 + 21x^6 = 0 is 3x^6

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The formula and the differences are shown below

The formula to calculate weighted average is:

weighted average = (w1x1 + w2x2 + ... + wnxn) / (w1 + w2 + ... + wn)

Where x1, x2, ..., xn are the values being averaged, and w1, w2, ..., wn are their corresponding weights.

The weighted average gives more importance or weight to certain values than others.

The weights can represent the relative importance, significance, or contribution of each value to the final average.

The main difference between ROR and weighted return is that ROR measures the return of a single investment, while weighted return measures the return of a portfolio or investment that is composed of multiple assets with different weights.

Weighted return takes into account the relative importance of each asset or security in the portfolio, while ROR does not consider the impact of other investments.

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Answer:

26π

Step-by-step explanation:

radius=13

double radius to find diameter

diameter=26

equation for circumference= π×d

circumference= 26π

The value of x is 21.75.

We need to convert from mixed number to decimal number. To do this you can follow the steps shown below:

We must divide the numerator of the fraction by the denominator of the fraction.

Now we must add the quotient obtained to the Whole number part.

So, we get:

7 1/4 = 7.25

Then, the scale image that maps "Figure a" onto "Figure b" is: 1 : 7.25.

Finally, in order to find the value of "x", you need to multiply the given length of the corresponding side of "Figure a" by 7.25,

Therefore, you get that the result is:

x = 3(7.25)

x = 21.75

Hence the value of x is 21.75.

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The complete question is ;

Figure a is a scale image of figure b the scale that maps figure a onto figure b is 1:7 1/4 enter the value of x

Both figures are triangles

Figure a is smaller than figure b

Figure a to the right has a 3

Figure b to the right has a x