**Answer: 129 inches**

**Step-by-step explanation:**

172 inches x 3/4 original with = 129 inches

Which graph represents the solution set of the system of inequalities-2x+y<_4 y>x+2

The **graph **of the **solution set **of the system of **inequalities **y > x + 2 and

- 2x + y ≤ 4 is shown in **figure**.

**What is mean by Inequality?**

A **relation **by which we can compare two or more mathematical expression is called an **inequality**.

Given that;

The **inequalities **is,

⇒ y > x + 2

And, - 2x + y ≤ 4

Now,

The **inequality **is,

⇒ - 2x + y ≤ 4

**Add **2x both side, we get;

⇒ - 2x + y + 2x ≤ 4 + 2x

⇒ y ≤ 2x + 4

And, The second **inequality **is;

⇒ y > x + 2

So, Plot the **graph **of the **inequalities **y ≤ 2x + 4 and y > x + 2.

We get the **solution set **of the system of inequalities.

Which is shown in figure.

Thus, The **graph **of the **solution set **of the system of **inequalities **y > x + 2 and - 2x + y ≤ 4 is shown in **figure**.

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Use the sketch tool to mark the picture with the given information. Then choose what postulate proves the triangles congruent.

We choose **ASA Postulate** to prove this triangle **congruent**.

In the given question given that

[tex]\overline{AC}[/tex] **bisects** [tex]\angle BAD[/tex].

[tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].

Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].

So [tex]m\angle BAC\cong m\angle DAC[/tex]

Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].

So [tex]m\angle BCA\cong m\angle DCA[/tex]

Then [tex]AC\cong AC[/tex]

Then [tex]\triangle BAC\cong \triangle DAC[/tex]

There given **postulate** are AAS, ASA, SSS, SAS.

We have proved using the ASA postulate.

Now describing the ASA postulate.

**ASA** means **Angle-Side-Angle Postulate**.

According to ASA Postulate, two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

Hence, we choose **ASA** Postulate to **prove** this **triangle congruent**.

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The country of Latveria has a population of 11.2 million at the start of 1988, which grows at 4.4% per year.A) Write a recursive equation for the population of Latveria.B) Write an explicit equation for the population of Latveria.C) To the nearest tenth of a million, what is the population of Latveria at the start of 1994.

A) The recursive formula takes into account the previous term. For each term, the next term is expressed in respect to it

Looking at the given scenario, the popularion is increasing by 4.4%. This means that the common ratio is

1 + 4.4/100 = 1.044

Given that the initial population is 11200000, the recaursive formula or equation would be

[tex]\begin{gathered} f_n=\text{ 1.044}f_{n\text{ - 1}} \\ \text{where f}_1=\text{ 11200000} \end{gathered}[/tex]B) For the explicit formula, the general formula for a geometric sequence is

an = a1 * r^(n - 1)

a1 = first term = 11200000

r = common ratio = 1.044

The explicit equation would be

an = 11200000 * 1.044^(n - 1)

C) At the start of 1994, the number of terms, n = 7

We would find a7 by substituting n = 7 into the explicit equation. We have

a7 = 11200000 * 1.044^(7 - 1)

a7 = 11200000 * 1.044^6 = 14501770

Find the total surface area of the cone. Use the r button on your calculator. altitude = 13 cm, diameter = 11 cm, slant height = 15 cm

In general, the area of a cone is given by the formula below

[tex]\begin{gathered} A=\pi r^2+\pi rl \\ r\rightarrow\text{ radius} \\ l\rightarrow\text{ slant height} \end{gathered}[/tex]Therefore, in our case,

[tex]\begin{gathered} r=\frac{11}{2}=5.5 \\ l=15 \\ \Rightarrow A=\pi *5.5^2+\pi *5.5*15 \\ \Rightarrow A=112.75\pi \end{gathered}[/tex]Rounding to two decimal places,

[tex]\Rightarrow A\approx354.22[/tex]The answer is approximately 354.22 cm^, option D.HELP PLSSSSSSSSSSSSSS

**Answer: 64**

**Step-by-step explanation:**

Length x width x higth= volume

4 x 8 x 2 = 64

**Answer:**

4 cm

**Step-by-step explanation:**

First, find the volume of the rectangular prism.

4*8*2=32*2=64 cm^-3

Now, the formula for the volume of the cube is:

Volume = side ^ 3

We know the volume is 64 cm^3, so plug it in to the equation:

64 = side ^ 3

take the cube root of both sides

4 = side

Don buys a shirt for $24.85. His friend Daryl spends $3.15 more for his shirt. Sean paid the same price as Daryl for his shirt but bought 2. How much did Sean spend for his 2 shirts?

**Solution**

- Don buys a shirt for $24.85.

- Daryl spends $3.15 more for his shirt. This means that Daryl spends

[tex]\$24.85+\$3.15=\$28[/tex]- Thus, Daryl spends $28 on his shirt.

- Sean paid the same price as Daryl, that is, he paid $28 for each shirt.

- Sean bought two shirts, thus, Sean spends:

[tex]\$28+\$28=\$56[/tex]**Final Answer**

**Sean spends $56 on his 2 shirts**

(1/5) -1 as the exponent

**Answer:**

1/5

**Step-by-step explanation:**

Write the following sentence using mathematical symbols:

n is greater than or equal to 0.

The sentence using **mathematical symbols **would form an **inequality **as; n ≥ 0.

**Inequality **is defined as the relation which makes a non-equal comparison between two given **functions**. If the equation or inequality contains **variable **terms, then there might be some values of those variables for which that equation or inequality might be **true**. Such values are called **solutions **to that equation or inequality. The Set of such values is; called the solution set to the **considered equation **or inequality.

We need to write a **sentence **using mathematical **symbols**:

Given that "n is **greater **than or **equal **to 0"

The **inequality **form as;

n ≥ 0

Therefore, the sentence using **mathematical symbols **would form an **inequality **as; n ≥ 0.

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a1 = 1; d = 3a1 = 1; d = −3a1 = 17; d = 3a1 = 17; d = −3

**Given:**

A graph is given and the points on the graph are as:

(1, 17), (2, 14), (3, 11), (4, 8), (5, 5), (6, 2)

**Required:**

To determine the value of

[tex]a_1[/tex]and d for the given sequence.

**Explanation:**

We can observe from the graph that the given sequence is an arithmetic sequence.

Here

[tex]a_1[/tex]represent the first value and d represent the common ratio.

So the values are as:

[tex]\begin{gathered} a_1=1 \\ d=14-17=\text{ -3} \end{gathered}[/tex]**Final Answer:**

The second option is the correct answer.

(04.01 LC)The graph shows a system of equations:y = x + 433y = -2x + 2-3-4-5What is the solution to the system of equations?0 1-2, 2)(2, 2)(2,-2)O(-2,-2)

Explanation:

We have two equation of line. Both lines intersect at a point.

The point of intersection of two graphs, is the solution of the graph.

At this point, both will have same x and y values

Tracing the graph:

The point of intersection occurs at x = -2, y = 2

Hence, the solution is at (-2, 2)

please help! what are the x and y values

**Answer: **

**1, -2**

**0, -4**

**-1,-6**

**-2,-8**

HELP ASAP WILL GIVE BRAINLEST

How many times larger is (1.064 x 10^1) than (7 x 10^−1)?

0.152

15.2

6.58

7.448

1.064 x 10¹ is 15.2 **times **larger than the 7 x 10⁻¹. It is obtaining the taking **ratio** of the given number. Option B is correct.

It is defined as the **operation **in which we do the **addition **of **numbers**, subtraction, **multiplication**, and **division**. It has basic four operators that are +, -, ×, and ÷.

We'll apply division by splitting into equal **halves **or groups, the **division **may be used to decide how to **distribute** a dish of cookies evenly among a **group**.

Let 7 x 10⁻¹ be x times the number 1.064 x 10¹.

The value of x is obtained by taking the **ratio **of 1.064 x 10¹ and 7 x 10⁻¹.

x = 1.064 x 10¹ / 7 x 10⁻¹

x = 15.2

Thus,1.064 x 10¹ is 15.2 **times **larger than the 7 x 10⁻¹. It is obtaining the taking **ratio **of the given number. Option B is correct.

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solve the equations and verify the answer

**Answer:**

See below

**Step-by-step explanation:**

I THINK what you wrote is:

2(x-2) - 3(x-3) = (5x-5) - 4(x-8)

2x -4 -3x+9 = 5x-5 -4x+ 32

2x-3x-5x+4x = 4 -9 -5 +32

-2x = 22 ** *** EDITED *****

**x = - 11 **

Your friend has a coln that is not fair. It comes up heads 70% of the time and talls 30% of the time. You flip it twice. Let Xbe the number of heads that come up. Find the probability distribution for X

Let X be the number of heads that come up

[tex]\begin{gathered} \text{Probability of head = 70\% = }\frac{70}{100} \\ \text{Probability of tail = 30\% = }\frac{30}{100} \end{gathered}[/tex]Step 1: Write out the formula for the binomial probability distribution

[tex]P_x=^nC_xp^xq^{n-x}[/tex][tex]undefined[/tex]Find the suma1 = -26/5 , d = -5/3 , n = 10

The sum of the arithmentic series is** -127**

**Step - by - Step Explanation**

What to find? *The sum of the arithmetic series.*

**Parameter Given**:

a₁ = -26/5 , d=-5/3 , n=10

To find the sum of the arithmetic series we will use the formula below:

[tex]S=\frac{n}{2}\mleft\lbrace2a+(n-1)d\mright\rbrace[/tex]Substitute the values and evaluate.

[tex]S=\frac{10}{2}\mleft\lbrace2(\frac{-26}{5}_{})+(10-1)(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace2(\frac{-26}{5})+9(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace-\frac{52}{5}-15\mright\rbrace[/tex][tex]=-52-75[/tex]=-127

Trevor's bonus last year with $6720 and this was 12% of his base salary. what is his base salary?

**Answer:**

$56,000.

**Explanation:**

Let his base salary = s

12% of his base salary = $6720

Thus, we have:

[tex]12\%\text{ of s=6720}[/tex]Next, solve for s:

[tex]\begin{gathered} \frac{12}{100}\times s=6720 \\ 12s=6720\times100 \\ s=\frac{6720\times100}{12} \\ s=56,000 \end{gathered}[/tex]**His base salary is $56,000.**

X Consider lines L and M on the graph below. Which of the following BEST describes the slope of these two lines? y L М. 10 9 8 7 6 5 3 2 1 X 0 1 2 3 4 5 6 7 8 9 10 L has a greater slope than M. Land M have the same slope. M has a greater slope than L.

since they are parellel lines, we conclude that **they have the same slope**, the second option is the correct one.

A shopper pushes a grocery cart with a force F of 50 N downward and to the right, as shown in the figure below. The anglethe handle makes with the horizontal is 37°, and the cart is moved 14 m. Find the work W done, in joules (1).Ed

**Solution**

For this case we can create the following plot:

We want to find the work so we can use this formula:

[tex]W=Fd\cos \theta[/tex]Replacing we got:

[tex]W=50\cdot14m\cdot\cos 37=559.04J[/tex]The data represents the number of cars that the sales staff at Templeton Motors sold this week.

4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3

Which line plot correctly displays the data?

OA.

Formula Sheet

3.

Number of Cars Sold

X X

X X X

X X X X X X

+++

AHH

+

0 1 2 3 4 5 6 7 8 9 10

X

Number of Cars Sold

X X X X X X X

H

0 1 2 3 4 5 6 7 8 9 10

OC.

OD.

←

Number of Cars Sold

X X

X X X

X X X X X X X

++

0 1 2 3 4 5 6 7 8 9 10

X X

Number of Cars Sold

X X

X X X

H11

0 1 2 3 4 5 6 7 8 9 10

The **line plot** that correctly displays the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, is: A.

A **line plot** is a graphical representation of a data whereby the frequency of each data point is represented by a dot on the **line plot**.

The dots on each data point on the **line plot** corresponds to the frequency of a data point in a data distribution.

Given the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, the frequency for each data point is:

2 - 1 dot

3 - 3 dots

4 - 3 dots

5 - 2 dots

6 - 1 dot

7 - 1 dot

8 - 1 dots

Thus, the **line plot** that correctly represents these data points alongside their frequencies is: A.

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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.

slope: 0, ordered pair: (−3,−8)

The **equation** (in **slope-intercept** form) of the line as described whose **slope** is; 0 and passes through the point given is; y = -8.

It follows from the task content that the equation of the line whose **slope** is; 0 and passes through the point; (-3, -8) is to be determined.

Hence, from the **slope** formula;

slope, m = ∆y/∆x

Therefore; 0 = ∆y/∆x

By cross-multiplication; we have;

∆y = 0

Recall, ∆y = y - y1 = y - (-8)

y - (-8) = 0

y + 8 = 0

y = -8.

Therefore, it follows that the **equation** of the** line** described is; y = -8.

Consequently, the **line **in discuss is a **horizontal line.**

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HELP ASAP

Solve z3 = 27.

z = 9

z = −9

z = 3

z = ±3

If z3=27

Z*3=27

Z=27/3

Z=+9

Z*3=27

Z=27/3

Z=+9

**Answer:**

the answer is 3

**Step-by-step explanation:**

Someone please help me with this!

The **width **of the** chest **is 14.7 **inches.**

Given:

The volume of rectangular prism = 10368 **cubic inches** or 6 **cubic feet**

Height of rectangular prism = 24 inches

It is mentioned that the chest will be twice as long as it is wide.

Let the **width** of the chest be x inches, so its** length** is 2x inches.

The volume of the chest = length × width × height

Substituting the values,

10368 = 2x × x × 24

10368 = 2x²× 24

x² = 10368/48

x = √216

x ≅ 14.7 inches ( to the nearest tenth of an inch)

Therefore, the width of the chest is 14.7 inches.

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The difference of seven times a number and five is one hundred find the number

Let the number be x

seven times the number = 7x

The difference of seven times a number and five is one hundred. It means that

7x - 5 = 100

7x = 100 + 5

7x = 105

x = 105/7

x = 15

**The number is 15**

a cylinder had a radius of 3 and height of 2 need answer quick

To find the volume of a cylinder with radius 3 and height 3

we will use the formular below:

[tex]V=\pi r^2h[/tex]where r is the radius and h is the height

From the question, r=3 and h = 2

substitute the value into the formula

[tex]V=\pi(3)^2\times2[/tex][tex]V=18\pi[/tex]If we substitute the value of pie = 22/7

Then,

[tex]V=18\times\frac{22}{7}[/tex][tex]V\approx56.57\text{ cubic unit}[/tex]Please solve for x using steps 1/3x= 1/3+6/x

You have the following algebraic equation:

**1/3x = 1/3 + 6/x**

In order to solve the previous equation you first multiply both sides of the equation by **x, **thus, you can quit x denominators in the equation. Proceed as follow:

**1/3x = 1/3 + 6/x **multiply by x both sides

**1/3 = x/3 + 6 ** multiply by 3 both sides

**1 = x + 18** subtract 18 both sides

**1 - 18 = x + 18 - 18**

**-17 = x**

-17 = x is the same as x = -17.** The solution to the given equation is x = -17.**

write down in terms of n, an expression for the nth term of the following sequences

-7,-12,-17,-22,-27

The expression for the **nth term of the sequence** -7, -12, -17, -22, -27... is -5n-2

The sequence is -7, -12, -17, -22, -27...

The first term = -7

The **common difference** = The second term - The first term

= -12 - (-7)

= -12+7

= -5

The nth term of the sequence = a+(n-1)d

Where a is the** first term**

d is the common difference

n is the n terms

Substitute the values in the equation

The nth term of the sequence = -7+(n-1)-5

= -7-5n+5

= -5n-2

Hence, the expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2

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razy GolfmathsdivThe current value of a baseball card is 60 times its original value v (in dollars). The baseball card is worth$15. Write and solve an equation to find the original value of the baseball card.Equation:= 15Original value: $

**Answer:**

Equation: 60v = 15

Original value: $0.25.

**Step-by-step explanation:**

Current value: $15

Original value: v

The current value is 60 times the original value.

So, the equation is:

Equation: 60v = 15

Now we solve the equation to find the original value.

60v = 15

v = 15/60

v = 0.25

Original value: $0.25.

Jose invests $8,216 in a savings account with a fixed annual interest rate of 7% compounded 12 times per year. What will the account balance be after 11 years?

After 11 years, the **account balance **is **$17,704.987. **(approx.)

The **principle **of the first loan is multiplied by the annual interest rate multiplied by the number of compound periods minus one to calculate **compound interest.**

The **principal **of the loan plus **compound interest **will then be what is left.

Given,

**P = $8,216 **for the principal value.

Interest rate**, r = 7% or 0.07.**

Period, with** t = 11.**

Interest applied** n times** every time period, or** 12 times.**

As far as we are aware, **A = P(1 + r/n) n*t**

where** A** is the whole **sum**.

Fill out the **formula **with the values,

=> **A = 8216(1 + 0.07/12) ^ 11*12**

= 8216((12 + 0.07)/12) ^ 132

Upon calculation, we obtain,

≅ $17,704.987

As a result, after 11 years, the account will have a balance of** $17,704.987 **(about).

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Mrs. Smith wants to buy floor covering for her master bedroom. The dimensions of the master bedroom are 11yd by 7yd. The floor covering is sold in square meters. How many square meters of floor covering will she need?

She will need ____ square meters.

Round answer to the nearest hundredth as needed.

Mrs. Smith will need 64m² of floor** covering** for her master bedroom.

The **length L **of the bedroom is 11 yards,

The **breadth B **of the bedroom is 7 yards.

The floor covering is available only in square meters.

As we know,

**One yard **= 0.9144 meters.

the length of the bedroom in meter is,

Length L = 0.091144 x 11

Length L = 10.02 meters.

the breadth of the bedroom in meters is,

Breadth B = 0.91144 x 7

Breadth = 6.38 meters.

the** Area of Rectangular** master bedroom in Meter square is,

**Area = Length x Breadth**

Area of the bedroom = 10.02 x 6.38

Area of the bedroom = 63.92 m²

Area of floor covering required = Area of the master bedroom.

Area of the floor covering required = 63.92 m².

Rounding off to nearest hundredth = 64m²

Mrs. Smith will need 64m² of floor covering.

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If Y (-7, -4) and Z (5, 2), find the slope of a line perpendicular to YZ

**Answer:**

slope of perpendicular line = - 2

**Step-by-step explanation:**

calculate the slope of YZ using the slope formula

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

with (x₁, y₁ ) = Y (- 7, - 4 ) and (x₂, y₂ ) = Z (5, 2 )

[tex]m_{YZ}[/tex] = [tex]\frac{2-(-4)}{5-(-7)}[/tex] = [tex]\frac{2+4}{5+7}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2

Landon had 56 playing cards. He kept 12 for himself anddealt the rest evenly to his 4 friends. Which expression bestrepresents the number of cards each friend received?
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