**Step-by-step explanation:**

loga(x) calculates simply the exponent of a needed to get x as result.

so, 5 "to the power of the exponent of 5 needed to get 7" is 7 (we give 5 the exponent that it needs to create 7, so it creates 7).

the same thing with 2, where we give 2 the exponent it needs to create 1/49. so, it creates 1/49.

we get therefore

7 × 1/49 = 7/49 = 1/7

A rancher is filling a trough for her horses. The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. How long will it take for the trough to have 80 gallons of water?

The time for the **trough** to have 80 gallons of water is 5 minutes.

A mathematical **equation** is the statement that illustrates that the **variables** given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of **minutes** be represented as m.

The **trough** already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. This will be:

25 + 11m =80

Collect like **terms**

11m = 80 - 25

11m = 55

**Divide**

m = 55 / 11

m = 5

Therefore, there will be 5 **minutes**.

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The highest temperature recorded in the town of Westgate this summer was 95°F. Last winter, the lowest temperature recorded was −5°F. Find the difference between these extremes.

100° because since it’s subract you minus and since the value is negative you take it as well 95-(-5) = 95+5 = 100

Max is designing a hot tub for a local spa.

He wants the hot tub to have a diameter of 90 inches, what is the approximate area required for the installation of the hot tub? (Use 3.14 for.)

Max is designing a hot tub for a local spa, he wants the hot tub to have a diameter of 90 inches, the approximate **area **required for the installation of the hot tub is [tex]6358.5in^{2}[/tex]

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The **radius **of a **circle **is separation between any point on the **circle **and its center. The radius must typically be a positive integer. A degenerate case is a circle with r=0. Except when otherwise specified, this article discusses circles in **Euclidean geometry**, namely the Euclidean plane.

A **circle**, specifically, is a straightforward closed curve that separates the plane into its inner and exterior. In common parlance, the word "circle" can apply to either the figure's boundary or its entirety, including its inside; in rigorous technical parlance, the circle only refers to the boundary and the entire shape is referred to as a **disc**.

A circle can also be described as a particular type of ellipse where the semi-major and semi-minor axes are equal, the **eccentricity **is 0, and the two foci are coincident, or as the two-dimensional shape with the greatest **area per unit perimeter squared **when applying calculus of variations.

if, diameter= 90 inches

radius = 90/2= 45inches

area= [tex]\pi r^{2}[/tex]

= 3.14* 45* 45

= 6358.5[tex]in^{2}[/tex]

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is 5,521 a reasonable answer for 218x12

**Answer:**

No

**Step-by-step explanation:**

Without even answering 218*12 it is obvious this is the wrong answer

the last digit of each number determines the last digit in the answer

218 has 8 as the last number and 12 has 2

multiply them together

2*8 is 16

the last digit is 6 and not 1

**Answer:**

No- 218 * 12 = 2616.

Multiply with an algorithm and add the partial products up to check. You don't get 5,521 when you multiply 218 * 12.

Write an equation for the line parallel to the given line that contains C.

C(4,6); y=x+7

The equation of the parallel line is….

The **equation **of the** parallel line** is y = x + 2.

**What is Equation of line?**

The **equation of line** with slope m and y intercept at point b is given as;

y = mx + b

Given that;

The **point **= C(4, 6)

And, equation of **line **is y = x + 7

Since, **Slope **of** Parallel lines** are always **same**.

So, The slope of the given line is calculated as;

y = x + 7

m = dy/dx = 1

Thus, **Slope **of parallel **lines **is 1.

Since, The **equation **of **line **is passes through point C (4, 6).

So, The equation of line with **slope**(m) 1 and **point **C(4, 6) is;

y - 6 = 1 (x - 4)

y - 6 = x - 4

y = x - 4 + 6

y = x + 2

Thus, The **equation **of the** parallel line** is y = x + 2.

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A theater manager is planning an upcoming concert. Regular tickets will cost $12 and student tickets will cost $8. The theater can

seat at most 200 people The manager wants to collect at least $1000 from ticket sales.

Let x represent the number of regular tickets sold. Let y represent the number of student tickets sold.

Which inequalities are among the constraints lor this situation?

Select each correct answer.

0 z t y ≥ 1000

O 12z + 8y ≥ 1000

O 12 + 8y ≤ 1000

O zty 2 200

O z+ yS 200

D 12z + 8y ≤ 200

The **inequalities** that are the **constraints** for the situation are 12x + 8y ≥ 1000 and x + y ≤ 200 options **(B) **and **(D) **are **correct**.

It is defined as the** expression **in mathematics in which both sides are not **equal** they have **mathematical **signs either less than or **greater **than known as **inequality**.

It is given that:

A theater manager is planning an upcoming concert. Regular tickets will cost $12 and student tickets will cost $8.

Let x represent the **number **of regular tickets sold. Let y represent the number of **student **tickets sold.

Total **collection **= 12x + 8y

12x + 8y ≥ 1000

x + y ≤ 200

Thus, the **inequalities** that are the **constraints** for the situation are 12x + 8y ≥ 1000, and x + y ≤ 200 options **(B) **and **(D) **are **correct**.

The missing options are:

12x+8y≤100012x+8y≥1000x+y≥1000x+y≤200x+y≥20012x+8y≤200Learn more about **inequality** here:

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What is the least common denominator of 1/2x+1=1/4x-6

**Answer:**

The least common denominator for 1/2 and 1/4 is 4.

1/2 --> 2/4

**Step-by-step explanation:**

Hope this helps!

Pls brainliest, tysm!

Marsha used a graphing calculator to graph an expense and a revenue function for her family’s printing business. The graph looked like the one below.

**Answer:**

a

**Step-by-step explanation:**

Estimation Solve the equation. First estimate using the perfect square closest to 85. Then use a calculator.

72 = 85

Estimate.

Z~ 9, -9"

(Use a comma to separate answers as needed.)

Use a calculator.

zan

(Round to the nearest tenth as needed. Use a comma to separate answers as needed.)

**Answer: z aprox = 9.2**

**Step-by-step explanation:**

**1) Square root 85 to get the answer**

sqrt(z^2)=sqrt(85)

z = sqrt(85)

z = 9.2195

**z aprox = 9.2**

is it right? but there isn't a square root for 3. And also I need an answer for the other one.. I need a great explanation quickly help!

**Answer:**

[tex]x=0, \quad x=3[/tex]

**Step-by-step explanation:**

Given equation:

[tex]9x^2-27x=0[/tex]

**Factor **out the **common term** 9x:

[tex]\implies 9x(x-3)=0[/tex]

Zero Product Property: If a⋅b = 0 then either a = 0 or b = 0 (or both).

Using the **Zero Product Property**, set each factor equal to **zero **and **solve for x**:

[tex]\begin{aligned}\underline{\sf Case\; 1} & & \underline{\sf Case \;2}\\9x&=0 & x-3&=0\\\dfrac{9x}{9} & =\dfrac{0}{9} & \quad \quad x-3+3 & =0+3\\x&=0 & x&=3\end{aligned}[/tex]

Therefore, the **solutions **to the given equation are:

[tex]x=0, \quad x=3[/tex]

Question 14 (5 points) Find the distance between (6, -2) and (1, -2). 7 units 5 units 6 units 4 units

**Answer:**

5 units

**Step-by-step explanation:**

PLEASE HELP THIS MAKES NO SENSE AND WOULD BE VERY MUCH HELPFUL IF YOU CAN JUST ANSWER THEM GRADES ARE DUE TOMORROW, please help.

**Distance** between M(6,-7) and a **line** that contains the points C(-6,-2) and H(-1,10) is **7.846**

First we will find the equation of the **line **containing the points C(-6,-2) and H(-1,10).

Take (x₁, y₁) =** (-6,-2)** and (x₂, y₂) =** (-1,10).**

Then the slope of the** line**, m = y₂-y₁/x₂-x₁

= 10- -2/-1- -6

= -12/7

So the equation of the** line **is

y-y₁ = m(x-x₁)

⇒ y- -2 = -12/7(x- -6)

⇒ y+2 = -12/7(x+6)

⇒7(y+2) = -12(x+6)

⇒ 7y +14 = -12x -72

⇒ 12x+7y +14+72 = 0

⇒ 12x+7y+86 = 0

This is in the form ax+ by+ c = 0

Also given the point (x, y) = (6, -7).

**Distance** between a point (x, y) and a **line** ax+ by+ c = 0 is,

[tex]\frac{|ax+by+c|}{\sqrt{a^2+b^2} }[/tex].

So **Distance** between **M(6,-7)** and the line 12x+7y+86 = 0 is

[tex]\frac{|12.6+7.-7+86|}{\sqrt{12^2+7^2} }[/tex] = |72-49+86|/√(144+49)

= 109/√193

=** 7.846**

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If f(x) = kx^3+ x^2 − kx + 2, find a number k such that the graph of f contains the point (k, -10)

If we write [tex]k[/tex] where we see [tex]x[/tex] in the equation and set the result equal to [tex]-10[/tex], we get the result.

[tex]f(k)=k(k)^3+k^2-k(k)+2[/tex][tex]=k^4+k^2-k^2+2[/tex][tex]=k^4+2=-10[/tex][tex]k^4=-12[/tex][tex]k_{1}=\sqrt[4]{3}(-1-i)[/tex][tex]k_{2}=\sqrt[4]{3}(-1+i)[/tex][tex]k_{3}=\sqrt[4]{3}(1-i)[/tex][tex]k_{4}=\sqrt[4]{3}(1+i)[/tex]PLEASE HELP ME I NEED HELP

The ordered pairs are **(0,-7).**

Any equation's **ordered pair** can be calculated by substituting any integer or the rational number for one of the variables, then solving for the remaining variable.

Consequently, we obtain values for both variables that meet the stated equation.

**Solution:**

5x - y = 7

Lets take,** x = 0**

Then,

5(0) - y = 7

**y = -7**

Then,

The ordered pair is **(0,-7).**

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-(1.67+ 1.67 +26.6) x 10-24

-29.94 x 10-24

-2.994 x 10-23

The mass of a water molecule is about 2.994 x 10-23 g.

Look at the Example. A hydrogen peroxide molecule has two oxygen atoms and

two hydrogen atoms. What is the mass of one molecule of hydrogen peroxide?

Write your answer using scientific notation.

2 a. Use the information from the Example. Complete the steps to find how

many grams as great the mass of one oxygen atom is than the mass of one

hydrogen atom.

(2.66 x 10-23) - (1.67 x 10-24) =(

The mass of an oxygen atom is

=

x 10-24) (1.67 x 10-24)

-) X 10-24

X 10-24

X 10-23

**Answer:**

is it not 10 minus 23 I think that would be the answer

**Answer:**

**Step-by-step explanation:**

1.9×10−221.99×10−231.99×10−231.9×10−221.91.99×10−2210−231.991.9×10−2310−22Divide numbers and 10's separately0.954774...×1010.954774...×101Subtract exponents9.54774...9.54774...Convert to standard notation9.59.5

wander 9.5

Anya plays one round of her favorite online game every day. One week, she played 7 rounds and scored between 120 and 300 points each round. She calculated the mean and median of those scores.

Then, Anya found out that the day she scored 300 points was a special "double points" day, so she actually earned 600 points, not 300.

How will this amount increasing affect the mean and median?

**Answer:**

**D: The mean will increase, and the median will stay the same.**

**Step-by-step explanation:**

**Strategy**

The mean and median are two ways to describe the center of a data set.

When a data set is almost symmetrical, the mean and median are close together.

When a data set is not symmetrical, the mean is usually closer to the outliers or tail than the median.

Let's reason conceptually about the measures of the center since we do not know the exact values.

**Reasoning about the median**

There are 7 scores. When the scores are in order from least to greatest, the median is the 4th score.

The day when Anya scored 300 points was the largest score both before and after that score was increased. So that is the 7th score when we order them from least to greatest.

Changing the 7th score does not change the 4th score, so the median stays the same.

**Reasoning about the mean**

Let's remember how to calculate the mean:

mean = total points/number of rounds

The largest score increasing from 300 to 600 points increases the total number of points. However, it does not change the number of rounds. So the mean increases.

**Conclusion**

**D: The mean will increase, and the median will stay the same.**

Jacob has 7 marbles. Darren has 17 marbles.

How many more marbles does Darren have

than Jacob?

Darren has ten more marbles

Starting from the origin, what movements do you need to plot the ordered pair (2, -3)?

Here, x **coordinate **is 2 and y **coordinate **is -3, so we have to first move two units on right thereafter we will move three units downward.(for better understanding please see the attached graph).

A **coordinate plane** is formed by the intersection of a **horizontal number** **line **and a **vertical number line**. The number lines intersect at the origin and separate the **coordinate plane** into four regions called quadrants.

An ordered pair is used to locate a point in a coordinate plane.

**ordered pair**(P) = (2,-3).

Hence, x **coordinate **is 2 and y **coordinate **is -3. we have to first move two units on right thereafter we will move three units downward.

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Mary Beth collected 8 pounds of aluminum cans to recycle to start. She plans on collecting 3 more pounds each week.

How many total pounds of aluminum cans will she have collected after 3 weeks?

**Answer:**

She will have a total of 17 pounds.

**Step-by-step explanation:**

You could simply put the question is slop intercept form to figure it out from there.

y = m(x) + b

y = 3(x) + 8

y = 3(3) + 8

y = 9 + 8

y = 17

Pls mark Brainliest with the crown

There are 4 consecutive integers with a sum of –278. What is the greatest of the 4 integers?

The **greatest **of the 4 **consecutive integers** with a **sum **of -278 is -68

Let n, n + 1, n + 2 and n + 3 be four **consecutive integers**.

The **sum **of four** consecutive integers** is -278.

⇒ n + (n + 1) + (n + 2) + (n + 3) = -278

⇒ n + n + n + n + 1 + 2 + 3 = -278

⇒ 4n + 6 = -278

⇒ 4n = -278 - 6

⇒ 4n = -284

⇒ n = -284/4

⇒ n = -71

So, the **consecutive integers** would would be:

n = -71

n + 1 = -70

n + 2 = -69

n + 3 = -68

here, the **greatest **of the 4 integers is -68

Therefore, the **greatest **of the 4 **consecutive integers** with a **sum **of -278 is -68

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DONT IGNORE HELP PLEASE

**Answer:**

y = - [tex]\frac{3}{2}[/tex] x + 3

**Step-by-step explanation:**

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0-3}{2-0}[/tex] = [tex]\frac{-3}{2}[/tex] = - [tex]\frac{3}{2}[/tex]

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - [tex]\frac{3}{2}[/tex] x + 3 ← equation of line

pete's pizza sells 12 inch pizzas. if pizza diameter has a mean of 12 inches and a standard deviation of .25 inches, what percent of pizzas are less than 12.04 inches? (z value of .16 is equal to a cumulative standardized normal distribution of .5636). 56.36% 43.64% 6.36% cannot be determined with the information given

The **percent** of pizzas that are **less** than 12.04 inches is 56.36%

Given the following:

Mean, μ=12

Standard deviation, σ=0.25

Percent of pizzas less than 12.04:

Let P(X<12.04) be percent of pizzas less than 12.04

P(X<12.04)=P(Z<(x-μ)/σ)

=P(Z<(12.04-12)/0.25)

=P(Z<0.16)

**Z-value** of 0.16 from cumulative standardized normal **distribution** is 0.5636

Given that P(X<12.04)=P(Z<0.16), and P(Z<0.16) from normal distribution table is 0.5636,

P(X<12.04)=P(Z<0.16)=0.5636

P(X<12.04)=0.5636

=56.36%

Hence, the correct choice is 56.36%

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At a store, shirts are regularly priced $9.95 each. The store is having a sale in which if a customer buys two shirts, he or she will get the third shirt at half-price. Sales tax is 7%. About how much will a customer spend on three shirts? *

.

.

A. $16

B. $25

C. $27

D. $32

**Answer:**

C. $27

**Step-by-step explanation:**

9.95÷2=4.975

9.95+9.95+4.975=24.875 or 24.88

24.88×7%+24.88=26.62

Pentagon A’B’C’D’E’ is the image of pentagon ABCDE under a dilation with a scale factor of 3/4.

What is the length of segment AE?

The **length** of segment A'E' under a dilation with a scale factor of 3/4 is; 3/2 units.

How to Interpret Scale of Dilation?

From the included graph the **coordinates** of the points A and E, in the pentagon ABCDE with **reference** to point A are;

A: (0, 0)

E: (0, 2)

The** length** of the **segment** AE = √((2 - 0)² + (0 - 0)²) = √(2²) = 2

When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a **scale factor** of 3/4, we have;

Length of segment A'E' = 3/4 × Length of segment AE

Therefore;

**Length** of segment A'E' = 3/4 × 2 = 3/2 units.

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I need the blank angles answers with the reason of justification please

**Answer:**

We had this question last week let me check my book real quick.

PLEASE HELP

FAST ;)

Pleaseeeee

The left side of the two-column **proof** should be filled as follows:

Statements Reasons_______________

k||i Given

m∠4 = m∠5 **Alternate Interior Angles **Theorem

**Parallel lines** can be defined as two (2) **lines** that are always the same (equal) distance apart and never meet.

The **Alternate Interior Angles **Theorem states that when two (2) **parallel lines** are cut through by a transversal, the alternate interior angles that are formed are congruent. Also, these **angles** are generally referred to as **alternate interior angles**.

Additionally, there are four (4) special **angle** relationships that are typically formed when two **parallel lines** are intersected by a transversal and these include the following:

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Just the bottom part that’s all :)

To **transform **is to alter. So, changing any given geometric shape would be considered a **geometric transformation**.

What does one** transformation** mean?

A 180° rotation about the origin characterizes the sole transformation. Translation, rotation, reflection, and dilation are the four primary categories of **transformation**.

The term "**Geometric" transformation** refers to a group of picture transformations where the geometry of the image is modified without changing the actual pixel values. In general, various actions can be performed on it, but the actual pixel values will not change.

Students get the opportunity to consider fundamental mathematical concepts in novel ways thanks to **geometric transformations** (e.g., functions whose domain and range are R2). Students can view mathematics as a connected field by using geometric transformations as a framework.

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NEED HELP ASAP - 100 POINTS (Algebra 2)

When solving quadratic equations, there are benefits to utilizing one method over the other. In your own words, explain what the advantages may be of using the method of completing the square to solve quadratic equations.

**Answer:**

**Step-by-step explanation:**

Comment

That's an awful lot of points to give away. Ten or 15 should be enough.

Completing the square.

1. First of all you can find the minimum or maximum immediately.

2. Second it cuts out the need to use the givens (a, b, c) in the quadratic formula which can at times be very cumbersome.

3. It gives you the opportunity to estimate the x and y roots without calculating them. Estimating on a test is a very valuable asset.

1.

Find the perimeter of the figure below.

7 cm

2 cm

4 cm

2 cm

4 cm

4 cm

**Answer:**

42 cm

**Step-by-step explanation:**

7+4+2+4+2+4+7+12

Rewrite the power as a product of powers (2ax)^3

The** power** can be re written as a **product **of (2ax)^3 as (2ax *2ax* 2ax ).

Product can be described as the **multiplication operation** of two or more terms so that another term can be gotten just like the one that is been given in the question that we were asked to rewrite.

Power serves as the **degree **that is been found on the terms , the degree that can be on the term is 3, then this can be expressed in three terms which will be done below.

Therefore, the given expression (2ax)^3 can be rewritten as (2ax *2ax* 2ax )

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the amount of water a washing machine uses varies directly with the number of loads of laundry washed. if a machine uses 65 gallons of water to wash 5 loads, how much water will be used to was 8 loads?
Please help me out with questions 20.-24.
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