8. In the following diagram, the diameter of the circle is 15m. What is the distance between the chord and the edge of the circle?​

The amount his account will have after 3 months be $ 759.38.

Given, Angel Garcia deposited his $750 federal income tax refund check into his savings account. The account pays 5% and he made no other deposits or withdrawals.

we have to find the amount in the account after 3 months,

So, the amount he made is,

Amount = 750(1 + 5/100)^0.25

Amount = 759.38

So, the amount his account will have after 3 months be $ 759.38.

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The percent increase in the median monthly rent prices is 14.3%

From the information, the median monthly rent in 2005 was $694 and $810 in 2010.

The increase in the amount will be:

= $810 - $694.

= $116

The percent increase in the median monthly rent prices from 2005 to 2010 will be:

= Increase in amount / Old rent × 100

= 116/810 × 100

= 14.3%

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The equvalent fractions of 5/7 using 35 as a common denominator is 25/35.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, it should be noted that the fraction given is 5/7.

The equivalent fraction will be:

= 5/7 × 5/5

= 25/35

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Complete question

Write the equvalent fraction of 2/5 using 35 as a common denominater

The sales tax rate of the cocktail table is 0.055

A sales tax is a consumption tax imposed by the government on the sale of goods and services

The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:

Sales tax = list price * sales tax rate

Therefore,

sale tax rate = sales tax / list price

sales tax = $13.75

list price = $250

sale tax rate = 13.75 / 250

sales tax rate = 0.055

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Answer: School is 10 blocks north and 2 blocks west of Megan's house. A straight line from Megan's house to school is 10.2 blocks long, Northwest

Step-by-step explanation:

5 blocks north, then 4 east, then 5 north is a total of 10 blocks north.  The last turn is 6 blocks west. So she walks 4 blocks west to get her back to due north of her house then an additional 2 more blocks west.

Use the pythagorean theorem to calculate the straight line if Megan were able to take a straight path there:

According to the volume of cylinder formula, an aluminum can with a 2 3/5 diameter and 5 1/4 in height are in 27.86 cubic inches.

Volume of Cylinder

The formula to calculate the volume of the cylinder is

Volume of a cylinder = πr²h cubic units.

where

r refers the radius

h refers the height.

Given,

Here we have an aluminum can with a 2 3/5 diameter and 5 1/4 in height and now we have to find the volume in cubic inches.

While we looking into the given question, we know the following values,

Diameter = 2 3/5

When we simplify it, then we get the value of diameter as

d = 13/5 or 2.6

Similarly, the value of height is rewritten as,

h = 5.25

So, based on the formula of volume of cylinder,

We get the value as,

=> V = π x (2.6/2)² x 5.25

Apply the value of π as 3.14, then we get,

=> V = 3.14 x (1.3)² x 5.25

=> V = 16.485 x 1.69

Therefore, the volume in cubic inches is 27.86 cubic inches.

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Applying the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.

There are 4 different pairs of lines given to us.

We have to find out the pair of lines that are perpendicular to each other.

We know that the general equation of a line in slope-intercept form is represented as -

y = mx + c --- (1)

where

(x, y) = coordinates of the lines

m = slope of the line

c = y-intercept

It is also known to us that for two lines to be perpendicular the product of their slope must be equal to -1.

A. y = -8 and y = 2

Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.

So, these two pair of lines are not perpendicular.

B. x = 4 and y = -1

Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.

So, these two pair of lines are not perpendicular.

C. x - y = 7 and y = x + 3

Now, x - y = 7

=> -y = 7 - x

=> y = x - 7

Comparing this to the equation (1), we have slope of the line, m = 1.

Also, y = x + 3

Comparing this to the equation (1), we have slope of the line, m = 1.

We see that the product of the slope of these pair of lines is not equal to -1.

So, these two pair of lines are not perpendicular.

D. y = -4x + 1 and 8x + 2y = -10

Now, y = -4x +1

Comparing this to the equation (1), we have slope of the line, m = -4.

Also, 8x + 2y = -10

=> 2y = -8x - 10

=> y = -4x - 10

Comparing this to the equation (1), we have slope of the line, m = -4.

We see that the product of the slope of these pair of lines is not equal to -1.

So, these two pair of lines are not perpendicular.

Thus, according to the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.

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Answer:

NOT CONGRUENT

Step-by-step explanation:

There are several types of congruence:

ASA - Angle Side Angle

AAS - Angle Angle Side

HL - Hypotenuse Leg

This image shows two triangles which have 2 congruent sides and one congruent angle.

Is it ASA?

There is only one congruent angle, so this cannot be congruent by ASA

Is it AAS?

By the same reasoning, it cannot be congruent by AAS.

Is it HL?

Although there are 2 congruent sides, neither one is the hypotenuse. Is is not congruent by HL.

There is no such thing as SSA congruence, because it is actually possible to have 2 non-congruent triangles who have 2 congruent sides and 1 congruent angle. Therefore, these are NOT CONGRUENT

Answer:

[tex] \huge{ \bold{y = - 43x - 25}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is given by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = - 43

In order to find c we substitute the point (0,−25) into the equation y = mx + c

That's

[tex] - 25 = - 43(0) + c \\ - 25 = 0 + c \\ c = - 25[/tex]

We now substitute m and c into the equation

We have the final answer as

[tex] \bold{y = - 43x - 25}[/tex]

Hope this helps you

For give expression Ben's work is correct.

In this question, Ben and Jerry both simplified the expression √24x⁵y³

where x > 0, y > 0

We need to determine which student is correct.

First we simplify given expression.

√24x⁵y³

= √(2)(2)(2)(3)(x)(x)(x)(x)(x)(y)(y)(y)

= √(2²)(2)(3)(x²)(x²)(x)(y²)(y)

= √(2²) * √(2) * √(3) * √(x²) * √(x²) * √(x) * √(y²) * √(y)    ...(seperate the radical symbol)

= 2 * √(2) * √(3) * x * x * √(x) * y * √(y)            ...........exponent rule

= 2x²y√(2)(3)(x)(y)                     ........(combine terms with same powers)

= 2x²y √6xy

So, Ben's work is correct.

We observe that by rule of exponents, the fourth step in Jerry's work is incorrect.

Therefore, Ben's work is correct.

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Answer:

slope = (1/3)

Step-by-step explanation:

(-8, 2), (-11, 3)

(x₁, y₁)   (x₂, y₂)

m = slope

        y₂ - y₁          3 - 2              1              1

m = ------------ = -------------- = ----------- = -------

        x₂ - x₁         -11 - (-8)       -11 + 8        3

I hope this helps!

Answer:

Step-by-step explanation:

Point- slope form:

Given:

Substitute into equation to get the line:

Answer:

x^25

Step-by-step explanation:

The simplified expression is x²⁵.

Given is an expression (x⁵)⁵, we need to simplify the expression.

To simplify the expression (x⁵)⁵, we need to apply the exponentiation rules.

The exponent outside the parentheses should be distributed to each term inside the parentheses.

In this case, the exponent outside is 5, and the term inside the parentheses is x⁵.

To distribute the exponent, we multiply the exponents together.

Applying the rule, we get:

(x⁵)⁵ = x⁵⁽⁵⁾ = x²⁵

Therefore, the simplified expression is x²⁵.

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The number of highway routes from A to D is 560

Number of highway routes from A to B = 7 highways

Number of highways routes from B to C = 8 highways

Number of highways routes from C to D = 10 highways

Number of routes from A to D = Number of highway routes from A to B × Number of highways routes from B to C × Number of highways routes from C to D

Here we have to use multiplication

Substitute the values in the equation

Number of routes from A to D = 7 × 8 × 10

= 560 highways

Hence, the number of highway routes from A to D is 560

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Answer:

Below

Step-by-step explanation:

x^2 + 32 + 116 = 12x         1st intermediate step: put everything on one side

x^2 -12x + 148 = 0      2nd intermediate step : re-arrange with constant on R

x^2 -12x = -148            3 rd intermediate step : take 1/2 of the 'x' coefficient

                                            square it and add to both sides

x^2 -12x + 36 = -148 + 36    4th intermediate step :   simplify

(x-6)^2  = -112

Answer:

46.9

Step-by-step explanation:

sin54=x/58

58sin54=46.922

The selling price of the two washing machies are

I will buy the first because it has a lower selling price

The question is a percentage problem

The first washing machine has a mark down by ​40%

= 40 percent

= 40 / 100

= 0.4

marked down factor = 1 - 0.4 = 0.6

selling price of the first machine = 550 * 0.6 = 330

the second washing machine has mark down of 30%

30% = 0.3

marked down factor = 1 - 0.3 = 0.7

selling price of the second washing machine at first mark down

= 550 * 0.7 = 385

marked down again

10% = 0.1

the  factor here is = 1 - 0.1 = 0.9

selling price of the second washing machine at second mark down

= 385 * 0.9 = 346.5

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Answer: 5 is the ancer

Step-by-step explanation:!

Answer:

A. (10x^2) / (5x + 4y)

B. (8xy) / (4y + 5x)

Step-by-step explanation:

A. Factor the numerator and denominator, then cancel out like terms

(10x^2(2a + 3b)) / (2a(5x + 4y) + 3b(5x + 4y))

(10x^2(2a + 3b)) / ((2a + 3b)(5x + 4y))

(10x^2) / (5x + 4y)

B. Factor the numerator and denominator, then cancel out like terms.

(8xy(3p - 4q)) / (3p(5x + 4y) - 4q(4y + 5x))

(8xy(3p - 4q)) / ((3p - 4q)(4y + 5x))

(8xy) / (4y + 5x)

slope= -3/2, y-intercept=8

y=mx+b m is the slope while b is the y-inteecept

Answer:

y-intercept (0,-3)

x-intercept (3,0)

Step-by-step explanation:

Let x = 0

-y =3

y = -3

(0,-3)

Let y = 0

x = 3

(3,0)

The value of f(x+h)-f(x)  = h.

Given function:

f(x) = x + 7

difference quotient = f(x+h) - f(x)

= (x+h) - 7 - (x - 7)

= x + h - 7 - x + 7

= x - x + 7 - 7 + h

= 0 + 0 + h

= h

Therefore the value of f(x+h)-f(x)  = h.

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The earnings of Rayan per hour is $5 per hour

The first point = (1, 5)

The second point = (2, 10)

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the function

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The slope of the line m = (10-5) / (2-1)

Subtract the terms

= 5 / 1

= $5 per hour

Hence, the earnings of Rayan per hour is $5 per hour

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77 is 0.7% of 11000

this number is a lot greater than 77.

Let 77 is 0.7% of m

0.7 percent of m = 77

(0.7/100) * m = 77

m = 77 * (100/0.7)

m = 11000

Therefore, 77 is 0.7% of 11000

this number is a lot greater than 77.

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Answer:

$205.6

Step-by-step explanation:

20.56hours × $10/hour = $205.6

The center of gravity of the distribution center is located at (14.84, 12.84)

The center of gravity is a point at which the total weight of a body can be thought to be located for calculation purposes.

The coordinates of the five distribution centers using the x and y coordinates are;

A(20, 15) 75, B(10, 12) 50, C(15, 10) 60, D(15, 20) 80, E(12, 12) 50

The center of gravity is found using the formula;

[tex]x = \dfrac{m_1\cdot g\cdot x_1+ m_2\cdot g\cdot x_2 + m_3\cdot g\cdot x_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]

[tex]y = \dfrac{m_1\cdot g\cdot y_1+ m_2\cdot g\cdot y_2 + m_3\cdot g\cdot y_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]

Coordinates of the center of gravity of the distribution center is therefore;

[tex]x = \dfrac{75\times 20+ 50\times 10+ 60\times 15+80\times 15+50\times 12}{75+50+60+80+50} \approx 14.92[/tex]

[tex]y = \dfrac{75\times 15+ 50\times 12+ 60\times 10+80\times 20+50\times 12}{75+50+60+80+50} \approx 12.84[/tex]

The coordinates of the center of gravity of the distribution center is; (14.92, 12.840

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Answer:

z=38

Step-by-step explanation:

Using the fact that angles on a straight line add to 180°, the interior angles of the triangle are 86°, (180-3z)°, and (180-4z)°.

Angles in a triangle add to 180°, so:

[tex]86+180-3z+180-4z=180 \\ \\ 86-3z+180-4z=0 \\ \\ 266-7z=0 \\ \\ 7z=266 \\ \\ z=38[/tex]

Answer:

150

Step-by-step explanation:

I had this on one of my quizzes, hope this helps :D

The slope for the following question is = 4.

acc to our question-

hence the value of slope=4

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The simple interest owned for the use of the money is $2625.

What is Simple Interest?

Simple interest is a quick and simple way to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of many forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest. A loan is a sum of money that someone borrows from a bank or other financial institution to cover expenses. Home loans, auto loans, student loans, and personal loans are a few instances of loans.

In the given question we have:

Principal amount  = ​7000$​,

Rate of interest r​ = ​7.5%,

Time t​ =  15 months;

So, applying the formula to calculate simple Interest:

S.I = [tex]\frac{PRT}{100}[/tex]

S.I = [tex]\frac{7000 \times 7.5 \times 15}{ 12 \times 100}[/tex]

S. I =  $2625;

Hence, The Simple Interest owed for the use of the money.  is $ 2625.

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