**Given:**

a logarithm is given as

[tex]log(z^5x)[/tex]**Find:**

we have to expand the given logarithm expressionusing properties of logarithm.

**Explanation:**

we know from the properties of logarithm that

[tex]\begin{gathered} log(m^n)=nlog(m) \\ and \\ log(mn)=log(m)+log(n) \end{gathered}[/tex]we will use above properties to expand the given logarithm expression as follows

[tex]log(z^5x)=logz^5+logx=5logz+logx[/tex]**Therefore, the expansion of the given logarithm is 5 log(z)+ log(x)**

Please show work as if you didn’t have a calculator

**SOLUTION**

Given the question in the image, the following are the solution steps to answer the question.

**STEP 1: Write the given function.**

**STEP 2: Explain the means to use to find the required values**

Since we were given a graph and can not use a caculator, we will be using the graph to get the values.

**STEP 3: Plot the given function on a graph**

**STEP 4: Get the domain of the function**

**Domain: The domain is all x-values or inputs of a function. The domain of a graph consists of all the input values shown on the x-axis.**

**STEP 5: Get the Range of the function**

**The range is all y-values or outputs of a function.**

**STEP 6: Get the value on which the function is increasing on**

**STEP 7: Get the value on which the function is decreasing on**

**STEP 8: Get the values of the asymptotes**

**An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.**

five friends earn a total of $33.75 shovellimg snow. How much does each friend earn

Given:

Number of friends = 5

Total amount they earn = $33.75

Let's find how much each friend earn.

To find the amount each friend earn, take the formula below:

[tex]\text{ Amount each friend earn = }\frac{Total\text{ amount they earn}}{\text{Number of friends}}[/tex]Substitute values into the equation above and evaluate:

[tex]\text{ Amount each friend earn = }\frac{33.75}{5}=6.75[/tex]Therefore, each friend earns $6.75

**ANSWER:**

**$6.75**

**Answer: $6.75**

**Step-by-step explanation: Divided 33.75 by 5 which is equal to $6.75**

Aaliyah needs to bake 42 servings of treats. She has cooked 20 servings of treats already. She has bars left to

make and each bar is 2 servings. How many bars does she need to make?

**Answer:**

she needs to make *11** **bars** *

**Step-by-step explanation:**

42-20

22

each bar is 2 servings so

22÷2

11 bars

6 singles, 7 fives, 3 twenties, and 2 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?

**Fair price to play this game is $16.72**

To find the fair price, we divide the total amount by the number of bill denominations given

[tex]\text{fair price = }\frac{total\text{ amount in the hat}}{nu\text{mber of bills in the hat}}[/tex][tex]\begin{gathered} nu\text{mber of bills = }6\text{ + 7 + 3 + 2 = 18} \\ \\ \text{singles = 1} \\ 6\text{ singles = 6 }\times\text{ 1} \\ 7\text{ fives = 7}\times\text{ 5} \\ 3\text{ twenties = 3}\times20 \\ 2\text{ hundred = 2 }\times\text{ 100} \\ \\ \text{Total amount in the hat = 6 }\times\text{ 1 + 7}\times\text{ 5 + 3}\times20\text{ + 2 }\times\text{ 100} \\ \text{Total amount = 6 + 35 + 60 + 200 = 301} \end{gathered}[/tex][tex]\begin{gathered} \text{fair price = }\frac{301}{18} \\ \text{fair price = 16.72} \end{gathered}[/tex]**Fair price to play this game is $16.72**

can someone help please.(the part cut out says" Slope intercept form)

we have that

the equation of the line in slope intercept form is

y-=mx+b

we have

m=2

b=3/2

substitute

y=2x+3/2

answer is option C

14 more than greg’s savings is 58

translate into equation

**Answer:**

1-4<58

**Step-by-step explanation:**

poor Greg is broke and yea

5 MATH QUESTIONS WILL MARK BRAINLIEST PLS HELP

The correct options regarding the **functions **are given as follows:

**1. C. **y = -2x - 7/9, m = -2, b = -7/9.

**2. A. **y = 1400x + 5000, 10,600 lbs.

**3.** **A. **t = 0.75m + 12, $23.25.

**4. A. **y = (x - 2) - 3.

**5.** **B. **302.5 miles.

In **slope-intercept** formula, a linear function is given as follows:

y = mx + b.

In which:

m is the slope.b is the y-intercept.For this problem, the **equation **is:

-18x - 9y = 7.

Then:

9y = -18x - 7

y = -2x - 7/9, which slope -2 and intercept -7/9.

Thus **option C** is correct.

The table represents a** linear function**, in which:

Thus the **function **is:

y = 1400x + 5000.

In **four **weeks, x = 4, hence the amount is of:

y = 1400(4) + 5000 = 10600.

Which means that **option A** is correct.

Also a** linear function**, in which:

Hence the **function **is:

t = 0.75m + 12.

For 15 miles, the **cost **is given as follows:

t = 0.75(15) + 12 = $23.25.

Which means that **option A **is correct.

In this graph, we have a concave up parabola with **vertex **at (2,-3), hence the rule is:

y = (x - 2) - 3.

Which means that **option A** is correct.

The distance function after **t hours **is given by:

d = 45t + 100.

Hence, after 4.5 hours, as 1/2 = 0.5, the distance is of:

d = 45(4.5) + 100 = 302.5 miles.

Which means that** option B** is correct.

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hii i have a question on the question below . in the photo

**Solution**

For this case we need to sort the values and we have:

Studied

79, 83, 84, 88, 89, 89, 91, 92, 93, 94, 95, 95, 96, 99, 100, 100, 100, 100

Q3= 98.25

Q1= 89

**Therefore IQR = 98.25-89= 9.25**

Not Studied

45, 58, 65, 72, 73, 77, 82, 83, 87, 89, 90, 91

Q3= 87.5

Q1= 70.25

**Therefore IQR = 87.5-70.25= 17.25**

From the results obtained we can conclude that the students who not studied havve larger variability compared to those who studied

A chord of a circle is 56cm long. The distance of the chord to the centre of the circle is 20cm. a) calculate the radius of the circle b) calculate the length of a chord which is 24cm from the center of the circle.

**Answer:**

**Step-by-step explanation:**

The distance from the center to the chord is the **perpendicular bisector** of the chord.

The three **segments form a right** **triangle**:

a) Use Pythagorean to **find the radius:**

b) Let the half-chord is x cm long. Use Pythagorean to** find the missing leg**:

The **length of the chord** is:

Find the surface area for the triangular prism below if AB = 16 m, AC = 33 m, AD = 12 m, and DP = 9 m. (Note: the bases are isosceles triangles.)

**INFORMATION:**

We have the following figure

And we must find its surface area

**STEP BY STEP EXPLANATION:**

To find the surface area of the triangular prism, we can divide the figure in:

- The two triangle bases:

We have the next triangle in the two bases:

We can calculate the area of the triangle

[tex]A=\frac{16\times9}{2}=72m^2[/tex]Since we have the same triangle in the two bases, the total area of the two triangles would be

[tex]72m^2\cdot2=144m^2[/tex]-

NEED ASAP PLS QUESTION IS IN THE PICTURE IF CORRECT ILL GIVE BRAINLIEST

The **vertex **and **range** of y = (x + 2) - 3 is ** **[tex]$(0,-1) ;-3 \leq y < \infty[/tex]

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In 2016, there were 34,602 burger restaurants worldwide, with 12,994 of them located in a country. Determine the percent of burger restaurants in that country in 2016Approximately % of the burger restaurants worldwide were in that country in 2016.

% of the burger restaurants worldwide were in that country in 2016 =

= 12994/ 34602 X 100

= 37.55 %

Name the number of degrees in the monomial.8abcd

Given: 8abcd

The number of degrees is the sum of the exponent of each variable in the monomial

**The answer is 4**

What is 3m+n evaluate the expression. I’m confused on how to solve this this is what my teacher gave me that’s it

**Explanation:**

The expression is given below as

[tex]3m+n[/tex]**Concept:**

The sum of two or more like terms is a single like term;** but the two unlike terms cannot be added together to get a single term. **Suppose, to find the sum of two unlike terms **x and y**, we need to connect both the terms by using an addition symbol and express the result in the form of **x + y.**

**In this case, **

The terms given ( **3m and n** ) are unlike terms and as such the expression cannot be simplified further

**Hence,**

**The final answer is **

such

find the length of the base if the area of the trapezoid is 198 M2.

The area of a trapezoid is given by:

[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]where b1 and b2 are the bases of the trapezois and h is the height. In this case we have that A=198, b1=15 and h=12, plugging this values into the equation above and solving for b2 we have:

[tex]\begin{gathered} 198=\frac{1}{2}(b_2+15)12 \\ 2\cdot198=12(b_2+15) \\ 396=12(b_2+15) \\ \frac{396}{12}=b_2+15 \\ 33=b_2+15 \\ b_2=33-15 \\ b_2=18 \end{gathered}[/tex]**Therefore b2 is equal to 18 m**

Mr. Coffey bought a house for $195,000. He made a 20% down payment. The interest rate is 5.25% for 30 years. How much does he need to borrow? What is his monthly payment?

**Explanation:**

**Mr. Coffey bought a house for $195,000 with a 20% down payment.**

A 20% down payment, would be 0.20, so $195,000 times 0.20 equals $39,000. Then $195,000 - $39,000 = $156,000.

**He bought the bouse for $156,000.**

5.25% is 0.525, because you move the decimals back. Understanding the total cost of the house is $156,000 now, we can do $156,000 times 5.25% (0.0525) which equals $8,190.

**He would pay $8,190 every 30 years. (if this was the interest rate.)**

Assuming if the cost was 20% down payment with the 5.25% interest rate then it would have been: $39,000 times 5.25% = 2047.5.

**He would pay $2,047.50 every 30 years. (if this was the interest rate.)**

*There was no context between the interest rate, so let's assume the obvious which is $2,047.50 every 30 years. *

A cell of some bacteria divides into two cells every 30 minutes. The initial population is 3 bacteria.

(a) Find the size of the population after t hours

y(t)

(function of t)

=

(b) Find the size of the population after 7 hours.

y(7)=

=

(c) When will the population reach 21?

T =

After t hours, the population is **3(2^2t)**.

After 7 hours, the population is **3(2^14)**.

In **2.33 minutes**, the population would be 21.

The following formula is used to calculate the bacteria population:

The formula for calculating future value is as follows:

**FV = P (1 + r)^n**

Where:

FV stands for **Future Value**.

P = **Present **value of three

R = **growth rate** = 100%

(hours x 60 minutes) / 30 = 2t = time

**3(2^2t)** = population in t hours

**3(2 ^14)** = population in 7 hours

The population of time would be 21 =[( FV /PV) / r] X 30.

**2.33 minutes** = ( 21 / 3) / 3.

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Tina's kitchen has an area of 54 square feet the kitchen is 9 times as many square feet does Tina's pantry if the pantry is 2 feet wide what is the length of the Pantry in feet

From the information given, the area of the kitchen is 54 square feet and it is 9 times as many square feet as does Tina's pantry. This means that the area of Tina's pantry is

54/9 = 6 square feet

If the pantry is 2 feet wide, we would determine its length by applying the formula for determining the area of a rectangle which is expressed as length * width

Therefore,

2 * length = 6

length = 6/2 = 3 feet

**Length of the pantry is 3 feet**

Which statement is true regarding the functions on the graph? 6 9) O f2) = g(2) O fO) = g(0) O f2) = g(0) Of(0) = g(2) 2 5 6 -421

F(x) is blue and G(x) is red

Have to find at which point both functions have the same value, or the same in which point both lines intercept

and looking at the graph ,theres only one point where both are equal. Its the point x= 2 y=0.

so the correct answer is f(2) = g(2)

3x+7x-28+31-8x for x=2043

The value of the **function **when x is equivalent to 2043 is **4089.**

Linear equations are **equation** that has a leading degree of 1. Given the linear equation;

3x+7x-28+31-8x

Collect the **like terms**

3x+7x-28+31-8x

3x+7x-8x-28+31

10x-8x-28+31

2x+3

If the **value of x** is 2043, substitute;

2x+3 = 2(2043) + 3

2x + 3 = 4086 + 3

2x + 3 = 4089

Hence the value of the **function **when x is equivalent to 2043 is **4089.**

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Determine the slope given two points (-2,3) (6,-7)

**Answer: m = -3/5**

**Step-by-step explanation:**

A. 8 + 8 + 8 + 8B. 2 + 4C. 4 + 4 + 8 + 8 + 1 + 1D. 8 + 8 + 4 + 4 + 2 + 2These Are The Choices

The surface area of a rectangular prism can be represented below

[tex]\begin{gathered} A=2(lw+wh+lh) \\ l=4 \\ w=2 \\ h=1 \end{gathered}[/tex]Therefore,

[tex]\begin{gathered} A=2(8+2+4) \\ A=8+8+4+4+2+2 \end{gathered}[/tex]A basketball player had scored 879 points in 34 games. a) At this rate, how many games will it take him to score 1500 points? b) There are 82 games in an entire season. At this rate, how many points would he score in the entire season? a) It will take him approximately games to score 1500 points . (Round up to the next whole number of games.) b) At this rate, he would score approximately (Round to the nearest one if necessary.) points in the entire season. Enter your answer in each of the answer boxes.

We know that he scored 879 points in 34 games, so we can calculate the average rate as:

[tex]r=\frac{879\text{ points}}{34\text{ games}}=25.85\text{ points/game}\approx26\text{ points/game}[/tex]At this rate, we can calculate the total points P by multiplying the rate r by the number of games n:

[tex]P=r\cdot n=25.85\cdot n[/tex]We can calculate how many games are needed for P=1500 as:

[tex]\begin{gathered} P=26\cdot n=1500 \\ n=\frac{1500}{25.85}\approx58.02\approx58\text{ games} \end{gathered}[/tex]For n=82 games, the expected number of points P is:

[tex]P=25.85\cdot n=25.85\cdot82=2119.7\approx2120\text{ points}[/tex]**Answer:**

**a) It will take him approximately 58 games to score 1500 points.**

**b) At this rate, he would score approximately 2120 points in the the entire season.**

Round your answer to two

decimal places.

7X = 77

**Answer:**

x = 11

**Step-by-step explanation:**

**7X = 77**

**divide both sides by 7 **

**x = 11**

NEEEEEEEEDDDDDD HELPPPPP ASAPPPPPPP

Matching the specific **Polygons** with their descriptions, we have;

15-gon → An exterior angle measures 24°

16-gon → The Sum of interior angles is 2520°

12-gon → An interior angle measures 150°

18-gon → An interior angle measures 160°

What is the sum of interior angles of a Polygon?The formula for **sum **of** interior angles** of a Polygon is;

S = (n - 2) * 180

where n is **number** of **sides** of **polygon**. Thus;

1) For a 15 sided polygon;

Sum = (15 - 2) * 180

Sum = 13 * 180

Sum = 2340

Sum of exterior angles of a polygon is; 360°

Thus, **external angles **= 360/15 = 24°

2) For a 16 sided polygon;

Sum of interior angles = (16 - 2) * 180 = 2520°

3) The value of the** interior angles** of a polygon with 12 sides is;

(12 -2) * 180/12 = 150°

4) The value of the** interior angles** of a polygon with 18 sides is;

(18 - 2) * 180/18 = 160°

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Graph the line with slope 1/3

and y-intercept -2.

The equation of a **straight line **is y = mx + b where m is the **slope **and b is the y-intercept then the two points exist (0, -2) and (6, 0).

A straight line's **general equation **is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with **gradient **m and intercept c on the y-axis.

The equation of a **straight line **is:

y = mx + b where m is the **slope **and b is the y-intercept.

Therefore, the equation for this line is:

y = (1/3)x - 2

To graph it we can identify two points on the line and connect them.

If x = 0, then y = -2 this is the **y-intercept **given in the problem.

If x = 6, then y = 0 this is the** x-intercept**

Therefore, the two points exist (0, -2) and (6, 0).

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3 1 1 1 Evaluate 2 when n = 10 5 1 3 3 2 10 10 1 3 3 + + 2 10 10 (Type integers or fractions.)

The given expression is

[tex]\frac{1}{2}n+\frac{3}{10}[/tex]Where n = 1/5.

Let's replace the variable for its value.

[tex]\frac{1}{2}(\frac{1}{5})+\frac{3}{10}[/tex]First, we solve the product.

[tex]\frac{1}{10}+\frac{3}{10}[/tex]Then, we sum fractions. Notice that we just have to sum numerators because the denominators are equal.

[tex]\frac{1+3}{10}=\frac{4}{10}=\frac{2}{5}[/tex]Therefore, the answer is 2/5.a certain linear function can be described by the equation below

We are given the information that the equation of the line is of the form:

y = a x + b

where a is a negative number and b is a positive number.

And we are asked to select among a number of options that represent the situation.

SInce b is a positive number (being "b" what is understood as the y-intercept) the line DOESN'T pass through the origing of coordinates. So the first option is discarded.

SInce "a"is a negative number (this is the so called "slope' of the line) the line must be slanted, and **dropping** from left to right Therefore option b is also discarded because that represents a line going up from left to right.

Option c is also discarded, because a is a negative number (not a zero) and lines parallel to the x axis have slope zero.

The last option is the correct one, since the intercept oo the y-axis is at a positive value for y, the line must be going down due to the negative slope, and therefore going across the II, I and IV quadrant as shown below: (give me a few minutes to draw a line with this characteristics)

Then, please mark the **last option (d) **as the correct answer.

A local hamburger shop sold a combined total of 632 hamburgers and cheeseburgers on Saturday. There were 68 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?

The number of **hamburger** is 350 and the number of **cheeseburger** is 282.

It should be noted that an **expression** is simply used to show the relationship between the variables.

In this case, the local hamburger shop sold a combined total of 632 **hamburgers** and cheeseburgers on Saturday and there were 68 fewer cheeseburgers sold than hamburgers.

Let **Cheeseburger** = x

Hamburger = x + 68

This will be:

x + x + 68 = 632

2x + 68 = 632

2x = 632 - 68

2x = 564

x = 564/2

x = 282

Cheeseburger = 282

**Hamburger** = x + 68 = 282 + 68 = 350

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8x^2+8x-22 In (x-p)^2=q

The given function 8x^2+8x-22 rewritten using the **completing the square** method is (x+1/2)^2 = 3

By altering the equation's form so that the left side is a perfect square trinomial, a **quadratic equation** can be solved using the "Completing the Square" approach.

Given the quadratic equation below;

8x^2+8x-22 = 0

This can be **simplified** into the equation below;

8x^2+8x-22 = 0

4x^2+4x-11 = 0

**Add 11 to both sides** of the equation

4x^2+4x-11 + 11= 0 + 11

4x^2+4x = 11

**Factor out 4x** from the expression;

4(x^2+1) = 11

(x+1/2)^2 = 11/4 + 1/4

(x+1/2)^2 = 12/4

**(x+1/2)^2 = 3**

Hence the **expressio**n in the form of (x-p)^2=q is (x+1/2)^2 = 3

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Shanika is thinking of a rational number, but tells you its opposite. What is true about the number she is thinking of?a- it is located at zero on the number lineb-it is to the right of zero on the number linec- it is twice as far from zero as the number she tells youd-it is the same distance from zero as the number she tells you
A Ferris wheel is designed in such a way that the height (h), in feet, of theseat above the ground at any time, t, is modeled by the function h(t) = 49cos(/15+T) + 50. What is the maximum height of the wheel?
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