the prime factorization is 3 to the power of 2 times 5 to the power of 2 what is the number

Answer:

[tex] \huge{ \boxed{gof(3) = 9}}[/tex]

Step-by-step explanation:

In order to find gof(3), we first have to find gof(x). To find gof(x) substitute the f(x) into g(x). That is, for every x found in g(x) substitute it by f(x).

From the question

[tex]f(x) = 2 {x}^{2} - x - 15 \\ g(x) = - 5x + 9 \\ \\ gof(x) = - 5(2 {x}^{2} - x - 15) + 9 \\ gof(x) = - {10x}^{2} + 5x + 75 + 9 \\ \\ gof(x) = - {10x}^{2} + 5x + 84[/tex]

To find gof(3), substitute the value of x that is 3 into gof(x). For every x found in gof(x), replace it by 3 and solve.

[tex]gof(3) = - 10( {3})^{2} + 5(3) + 84 \\ \quad \: \: \: \: \: = - 10(9) + 15 + 84 \\ \: \: \: = - 90 + 15 + 84 \\ = 9[/tex]

We have the final answer as

Answer:

C. C and E

Step-by-step explanation:

The solutions for a system of equations is the point of intersection of the two graphs of those equations. Here, there are two points of intersection, that is, two points where the graphs cross. The graphs cross at point C and point E.

C and E are the solutions to this system.

20 ÷ 1 + 4 on the board is 36 ÷ 3 • 2 + 1 36 ÷ 3 • 2 + 1.According to the order of operations, you should execute addition and subtraction last and multiply and division first, proceeding from left to right

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GCF = 14

LCM = 168

let x and y be the numbers

if X = 56

The other number (y) can be obtained using the formula:

=> (GCF x LCM) / X

=> (14 X 168)/ 56

=> 2352/56

=>42

Option B is correct

The ratio that is equivalent to 25:80 is 5:16 , the correct option is (d) .

In the question ,

it is given that ,

the ratio is 25:18 , we need an equivalent ratio .

the ratio is 25:80 which can be written in fraction as 25/80 .

writing the factors of 25 and 80 .

= (5×5)/(5×16)

we can see that 5 is the common factor in both the numerator and the denominator .

= 5/16

which can be written as

= 5:16

the equivalent ratio is 5:16  .

Therefore , The ratio that is equivalent to 25:80 is 5:16 , the correct option is (d) .

The given question is incomplete , the complete question is

Which of the following ratio is equivalent to  25:80 ?

(a) 2:5

(b) 8:5

(c) 16:5

(d) 5:16

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &6\\ \end{cases} \\\\\\ A=20000(1 + 0.04)^{6} \implies A=2000(1.04)^6\implies A \approx 25306[/tex]

The value of x from the given equations is 0.6.

The given equations are y=4x and y=-x+3.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Here, 4x=-x+3

⇒ 4x+x=3

⇒ 5x=3

⇒ x=3/5

⇒ x=0.6

Hence, the value of x from the given equations is 0.6.

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Answer:45212176

Step-by-step explanation:calculator

Answer:

82x82x82x82, or 82 squared to the 4th power, is 45212176.

answer:

-29

step-by-step explanation:

you need a graphing calculator.

so, let's start by setting up a table (for my sake because that text is confusing)

x       f(x)      g(x)      h(x)

-3      12        39          -14

0       0         3           1

1        0         7           -2

3       6        39         -20

okay, that's out of the way. now, your equation is 2 * f(3) - 3 * g(1) + h(3).

for f(3), we look at the chart to see which f(x) value matches x=3.

f(3) = 6

same with g(1) and h(3)

g(1) = 7

h(3) = -20

now, replacing the functions(x) with their numbers is the next step.

2 * 6 - 3 *7 + (-20)

(2*6) - (3*7) - 20

(12) - (21) - 20 = -29

In solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).

So, the wrong step will be:

Then, the next step should be:

But, the steps it is given as:

Which makes the error.

Therefore, in solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).

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Answer: it would be about 1:30pm

Step-by-step explanation:

Let's check each inequality if the value x = 5 is part of the solution:

a. x < 2

5 is a value greater than 2, so it isn't part of the solution of this inequation.

b. x > 9

5 is lesser than 9, so it isn't part of the solution of this inequation.

c. x < 18

5 is lesser than

Answer:

X / 4 + 22

Step-by-step explanation:

22 more means we add 22. Then, we take x as our variable, in this case, it is "a number". We divide x by 4, and then we add 22. x / 4 + 22.

Answer:

D

Step-by-step explanation:

Answer: B 10.6

Explanation:

We would assume that the stock tank is cylindrical. We would calculate the volume by applying the formula,

Volume = πr^h

where

π = 3.14

r is the radius of the cylinder

h is the height of the cylinder

From the information given,

diameter = 3

radius = diameter/2 = 3/2

r = 1.5

h = 1.5

Volume = 3.14 x 1.5^2 x 1.5 = 10.5975 cubic meters

By rounding to the nearest tenth,

Volume = 10.6 cubic meters

Answer:

b, d

Step-by-step explanation:

20/-4 = -5

20 x (-1/4) = -5

Answer:

===========================

We know parallel lines have equal slopes, so line r has the slope of - 1.

Line r is:

Substitute the coordinates of the point into this equation and find the value of b:

The equation of line r is:

Answer:

No

Explanation:

To determine if the lengths form the side of a right triangle, use the Pythagorean Theorem:

Substitute 15,11 and 4 into the formula:

Since the Pythagorean Theorem does not hold, the side lengths(15,11,4) do not represent the lengths of the sides of a right triangle.

[tex]\fbox{20.25}[/tex]

To find her miles per hour, we need to divide the total miles by the total hours to find how many miles she drives in each hour.

[tex]162\div8[/tex]

[tex]=20.25[/tex]

The proper sampling technique used when the number of samples is less than 100 is saturated sampling where the entire population will be the research sample.

What is saturated sampling ?

According to Arikunto if the population is less than 100 people so the researcher need to take all the samples namely saturated sampling.

What is stratified sampling ?

Stratified sampling is a sampling technique which used when we do a research on a heterogenous population. How to use this technique is to divide the population into several stratum and then take random samples from each stratum an then all the samples that have been taken are collected into one sample.

In conclusion, if the population has fewer than 100 people , the expert suggested to use saturated sampling.

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Answer: Location of T' on the coordinate axis will be (16,7).

T (6,4) → T' (16,7).

Step-by-step explanation:

coordinate vertices of points in rectangle JKLM are:

J (-8,-8)

K (-4,-8)

L (-4,-5)

M (-8,-5)

and coordinate vertices of points in rectangle J'K'L'M' are:

J' (2,-5)

K' (6,-5)

L' (6,-2)

M' (2,-2)

coordinate vertices of points in Quadrilateral STUV are:

S (1,4)

T (6,4)

U (4,6)

V (2,6)

transformation in coordinate vertices from rectangle JKLM to rectangle J'K'L'M' is:

J (-8,-8) → J' (2,-5)

⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.

and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.

similarly for

K (-4,-8) → K' (6,-5)

⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.

and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.

L (-4,-5) → L' (6,-2)

⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.

and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.

M (-8,-5) → M' (2,-2)

⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.

and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.

So, the location of T' of the Quadrilateral S'T'U'V' on the coordinate plane will be:

along x axis the Quadrilateral will shift towards right by 10 units

So, 6 → 6+10=16

and along y axis the Quadrilateral will shift upwards by 3 units

So, 4 → 4+3=7

⇒ T (6,4) → T' (16,7).

Step-by-step explanation:

We want to identify the domain and range of the following function

Recall that the domain of a function is the set of values for the variable x, for which the function is defined. Note that we can see this function as the product of two different functions

and

Note that the first part (1/6) does not depend on x, so this means that it is always defined. Also, note that 8^x is always defined for any value of x. That is, if you replace x by any number, you will get another number.

So, this means that the the original function is defined for every value of x. So the domain of this function is the set of all real numbers.

If we define the equation

the range is the set of all possible values that y can take. Taking a look at the functions we already identified (1/6, and 8^x) we can see that 1/6 is always a positive number, and we can also see that for every value of x, the number

8^x is always positive.

That means that the product

is always a positive number. So, this means that the range of the function is all positive real numbers. That is the set of y such that y>0

The unit price of the oranges bought by the three friends is $3.50 per pound.

Lamar bought 2 pounds for $7 , unit price = 7 / 2 = $ 3.5 per pound

Enrico bought 5 pounds for $17.50 , unit price = 17.50 / 5 = $ 3.5 per pound

Anna bought 3 pounds for $10.50 , unit price = 10.5/ 2 = $3.5 per pound

Hence we can see that the unit price rate for the oranges is $3.50 .

The average price of a product is calculated by dividing the total sales income by the number of units sold. Managers must supply "similar" units when a single product is given in many variations, such as different bottle sizes.

By weighting different unit selling prices higher by unit sales mix (%) for each single variant, the determination of average pricing is made practicable. We obtain pricing per statistical unit when we employ a standard rather than a genuine range of sizes and product types.

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Answer:

2

Step-by-step explanation:

40 x 5 ÷ 100

2 x 5 ÷ 5 = 2

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

Let x be the number of miles the family travel in 4 days

620 miles = 2 days

x = 4 days

cross-multiply

2x = 2480

Divide both-side of the equation by 2

x = 1240 miles

By using combination, it can be obtained that

Number of simple random samples of size 3 that can be selected from a population of size 7 = 35

What is combination?

Combination determines the number of arrangements that can be made from a collection of objects when the order of arrangement is not taken into account.

Here, concept of combination is used

Number of simple random samples of size 3 that can be selected from a population of size 7 = [tex]{7 \choose 3}[/tex] = 35

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EXPLANATION

If the measure of ∠2= x+78 and the other ∠=40 degrees, by definition we know that sum of interior angles of a triangle is equal to 180 degrees.

Furthermore, we have two congruent legs, so this is an Isosceles triangle with two congruent angles (with the same measure).

Thus,

180 = 40 + 2* m∠2

Substituting m∠2 by the equation as follows:

180 = 40 + 2(x + 78)

Subtracting -40 to both sides:

180 - 40 = 2(x+78)

Simplifying:

140 = 2(x+78)

Dividing both sides by 2:

140/2 = x + 78

Simplifying:

70 = x + 78

Subtracting -78 to both sides:

70 - 78 = x

Simplifying:

-8 = x

Switching:

x = -8

Answer: The value of x is -8.