I need help on functions 50 points

The equivalent expressions \($\frac{21^x}{7^x}\) is \($3^{x}$$\).

Equivalent expressions exist as expressions that work exactly even though they look different. If two algebraic expressions exist as equivalent, then the two expressions contain the exact value when we plug in the same values for the variables.

Given: \($\frac{21^x}{7^x}\)

Factor \($21^{x} = 7^{x} \cdot 3^{x}$\)

\($=\frac{7^{x} \cdot 3^{x}}{7^{x}}$$\)

Cancel the common factor: \($7^{x}$\)

\($=3^{x}$$\)

Therefore, the correct answer is option B. \($3^{x}$$\).

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An equation is formed of two equal expressions. The value of x and y is 17 and 20, respectively. Thus, the correct option is D.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Solving the first equation for y,

4x - 3y = 8

-3y = 8 - 4x

y = (8-4x)/(-3)

Solving the second equation for y,

5x - 4y = 5

-4y = 5 - 5x

y = (5 - 5x)/(-4)

Equate the value of y,

y = y

(8-4x)/(-3) = (5 - 5x)/(-4)

-32 + 16x = -15 + 15x

16x - 15x = -15 + 32

x = 17

Substitute the value of x in any one of the equation,

4x - 3y = 8

4(17) - 3y = 8

68 - 3y = 8

-3y = -60

y = 20

Hence, the value of x and y is 17 and 20, respectively. Thus, the correct option is D.

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Answer:

answer is 100 pages per hour

We have that the equation to find the volume of a hexagonal prism is the following:

where h is the height of the prism and B is the base area. In this case, we have:

then, the volume is:

• therefore, the volume of the hexagonal prism is 198.25 cm^3

Answer:

21 divided by 2 and 2/3 = 11.1666667

Step-by-step explanation:

Answer:

I hoped that helped

Answer:

Solution given:

<3+90=180[co interior angle ]

<3=180-90=90°

is your answer

The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².

Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.

The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.

So, 1/2 * ( 9+5) * 3

   = 1/2 * 14 * 3

   =  1/2 * 42

   =  21 cm²

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The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  

w + l ≥ 17.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

Mackenzie is working two summer jobs, washing cars and landscaping. She must work at least 17 hours altogether between both jobs in a given week.

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

w + l ≥ 17

Hence, the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  w + l ≥ 17.

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Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!

tinyurl.com/wpazsebu

Answer:

Gretta's Contribution = $52,500

Interest = $125,588.79

Step-by-step explanation:

Gretta contributes $125 each month, for 35 years. Therefore, to find the amount she contributed, we multiply those pieces together (12 months in each year).

125 x 12 x 35 = $52,500

Therefore, over the 35 years, Gretta contributed $52,500.

If there was $178,088.79 in her account, and she contributed $52,500, then the rest is interest.

$178,088.79 − $52,500 = $125,588.79

There was $125,588.79 in interest earned on Gretta's account.

Answer:

36 green marbles

Step-by-step explanation:

If 60% of the 60 marbles in the bag are green, then the number of green marbles can be calculated as:

Green marbles = 60% x 60 marbles

To simplify this calculation, we can convert 60% to a decimal by dividing by 100:

Green marbles = 0.60 x 60 marbles

Green marbles = 36 marbles

Therefore, Rudy received 36 green marbles.

Answer: 36

Step-by-step explanation:

60 is 6/10 of 100 so if you are taking a percent of 60 just multiply the percentage by 6/10. 6/10 of 60 is 36

The volume of the tank of water is 653.12 cubic meters.

For a cylinder of height H and diameter D, the total volume is given by:

\(V = 3.14*(D/2)^2*H\)

In this case, we know that:

D = 8m

H = 13m

Replacing that in the above equation:

\(V = 3.14*(8m/2)^2*13m = 653.12 m^3\)

So the volume of the tank of water is 653.12 cubic meters.

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Answer:

29

Step by step explanation.

You add them together then you minus the 8 then you get 29 .

The total amounts paid are displayed in the image below:

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.

The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

How to calculate interest rates

Using S.I:

Simple Interest: The formula for simple interest is I = P x R x T, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.

For example, if you borrow $1,000 at a simple interest rate of 5% per year for 3 years, the interest would be calculated as follows: I = $1,000 x 5% x 3 = $150.

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The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

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The answer of given expression \(343c^3+d^3\) will be \((7c + d)(49c^2-7cd+d^2)\)

We have given an expression \(343c^3+d^3\) which can be written as \((7c)^3+(d)^3\)

Using identity \(a^3 + b^3 = (a + b) (a^2 - ab + b^2)\).   ...(1)

Put a = 7c and b = d in equation (1) , we get

  \((7c)^3 + (d)^3 = (7c + d) ((7c)^2 - 7cd + (d)^2)\\\\(7c)^3 + (d)^3 =(7c + d)(49c^2-7cd+d^2)\)

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Answer:

x=16+√736/16

x=4+√46/4...

Step-by-step explanation:

Answer:

Could you finish the question???

Step-by-step explanation:

The mixed fraction and fraction expression  1 ⁵/₆ - 3/4 in the simplest form will be 13/12.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 1 ⁵/₆ - 3/4

Convert the mixed fraction number into a fraction number. Then we have

⇒ 1 ⁵/₆ - 3/4

⇒ 11/6 - 3/4

⇒ (22 - 9) / 12

⇒ 13 / 12

The mixed fraction and fraction expression  1 ⁵/₆ - 3/4 in the simplest form will be 13/12.

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The total surface area of the cylinder is 157 square feet.

Given the radius of the cylinder = 4 inches

height of the cylinder = 9 inches

Total surface area is calculated by the formula:

A = 2πr² + 2πh

A = 2 × 3.14 × 4² + 2 × 3.14 × 9

or, A = 157 square feet.

Therefore the total surface area of the cylinder is 157 square feet.

The surface area of a solid item is a measurement of the total volume that the surface of the thing occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more complicated than the definition of arc length for one-dimensional curves.

The definition of surface area for polyhedral (i.e., particles with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces. When smooth surfaces, like spheres, are represented as parametric surfaces, their surface area can be calculated.

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In the polynomial function, the number of roots of the graph is 3

Polynomial function:

In math, polynomial function refers a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Given,

Here we need to identify the number of roots of the graph.

If we have the graph like the following,

Then to identify the roots, we have to look at the graph start from negative infinity and end at positive infinity.

While we looking into the given graph, we have identified that, the degree of polynomial must be odd.

And in graph, we can see it cuts at three points

=> (-6,0)    (-2,0)    (-1,0)

This are the points on the graph has three x-intercept.

We know that, the number of x-intercept is equivalent to real roots of the polynomial.

Therefore, graph is cubic polynomial because it has three x-intercept.

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The required it will take 2 hours for the friends to put 7 km between them.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let's call the number of hours it takes the friends to be "x". During that time, Rae will have traveled 2x km. And Dana will have traveled 3(x-1) km (since she left an hour later).

We can now set up an equation:

2x + 3(x-1) = 7

Expanding the second term:

2x + 3x - 3 = 7

Combining like terms:

5x - 3 = 7

Adding 3 to both sides:

5x = 10

Finally, dividing both sides by 5:

x = 2

So it will take 2 hours for the friends to put 7 km between them.

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Answer:

The answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Step-by-step explanation:

We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

The key will equal 2|1 means 21

Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.

Quartile:

Median, Minimum, Maximum, & Range:

Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Answer:

The area is 155 ft.

Step-by-step explanation:

To find the area if a trapezoid, you have to add the number on top( in this case 13 ft) and then add that with the bottom number(18 ft.) Then, you take that answer and divide it by 2. After that, multiply it with the height(10.) Thus, the answer is 155 ft.

The set of values that corresponds to the circle with a radius of three units and the center lying on the Y axis is:

A = 1, B = 1, C = 0, D = 3, E = 0.

The general equation of a circle is given by:

x^2 + y^2 + 2gx + 2fy + c = 0

In this case, since the circle has a radius of three units and the center lies on the Y axis, we can deduce the following information:

The center of the circle lies on the Y axis, which means the x-coordinate of the center is zero.

The radius of the circle is three units, which means the distance from the center to any point on the circle is three units.

Using the information above, we can substitute the values into the general equation to solve for the corresponding values:

Substituting the x-coordinate of the center (zero) into the equation, we have:

0^2 + y^2 + 2g(0) + 2fy + c = 0

y^2 + 2fy + c = 0

Since the center lies on the Y axis, the x-coordinate is zero, so the term with x (2gx) becomes zero.

Substituting the radius of the circle (three) into the equation, we have:

(3)^2 = 9

Therefore, the equation becomes:

y^2 + 2fy + c = 9

Comparing this equation with the general form of the circle equation, we can deduce the values of A, B, C, D, and E as follows:

A = 1 (coefficient of x^2)

B = 1 (coefficient of y^2)

C = 0 (constant term)

D = 3 (coefficient of x)

E = 0 (coefficient of y)

Hence, the set of values that corresponds to the circle is A = 1, B = 1, C = 0, D = 3, and E = 0.

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Answer: its A

Step-by-step explanation: