Simplify the expression

Answer:

y = -1/2x + 19/2

Step-by-step explanation:

Hi there!

We are given the points (9,5) and (7,6)

We want to write an equation of the line that contains these two points, in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope of the line

The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything we need to find the slope, but let's label the values of the points to avoid any confusion.

[tex]x_1=9\\y_1=5\\x_2=7\\y_2=6[/tex]

Now substitute these values into the formula to find the slope

m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{6-5}{7-9}[/tex]

Subtract

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

m=-1/2

The slope of the line is -1/2

We can substitute this as m into the formula for slope-intercept form:

y = -1/2x + b

Now we need to find b

As the equation passes through (9, 5) and (7, 6), we can use either one to solve for b

Taking (7, 6) for example:
Substitute 7 as x and 6 as y into the equation

6 = -1/2(7) + b

Multiply

6 = -7/2 + b

Add 7/2 to both sides

19/2 = b

substitute 19/2 as b:

y = -1/2x + 19/2

Hope this helps!

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Answer:

this is the unit area of: 24

Step-by-step explanation: hope this helps

The question is an illustration of arrangements, and the number of possibilities of the password is 65000

The length of the password is:

Length = 4

If the password begins and ends with a letter and cannot be repeated, then the possibilities are:

First = 26

Last = 25

If the password contains numbers that can be repeated, then the possibilities are:

Number 1 = 10

Number 2 = 10

So, the number of possibilities is:

Possibilities = 26 * 10 * 10 * 25

Evaluate the product

Possibilities = 65000

Hence, there are 65000 possibilities of a 4 character password

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The fraction 6/10 and 4/10 can be represented by using the objects laid together to form a square.

An equation is an expression that shows the relationship between two or more variables and numbers.

The fraction 6/10 and 4/10 can be represented by using the objects laid together to form a square.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

-11

Step-by-step explanation:

The | | around a number means the absolute value of that number. The absolute value is the positive value of the number given.

Answer:

1.) men: 1800, women: 3000

2.)2275/65 = 35 mins

3.)P 2,175,000

4.) 5400 in 6 mins

5.) Probably 5?

6.) P 120 000

Step-by-step explanation:

Answer:

Pool 1:  2(3)*3*3= 54 ft^3

pool 2: 2(4)*4*4= 128 ft^3

Pool 3: 2(5)*5*5= 250 ft^3

pool 4:  2(6)*6*6= 432 ft^3

Step-by-step explanation:

length can be modeled by twice the width or twice the depth which means that deapth=width,

both the width and the depth are equal, hence

L= 2x

W=X

x=3,4,5,6 (which are values for depth as well as width)

susbtitute values:

Pool 1:  2(3)*3*3= 54 ft^3

pool 2: 2(4)*4*4= 128 ft^3

Pool 3: 2(5)*5*5= 250 ft^3

pool 4:  2(6)*6*6= 432 ft^3

Answer:

Diameter = 14 cm

Circumference = 44 cm

Step-by-step explanation:

[tex]\pi {r}^{2} = 154 \\ {r}^{2} = \frac{154}{\pi} \\ r = \sqrt{ \frac{154}{\pi} } \: cm[/tex]

[tex]Diameter = 2r \\ = 2 \sqrt{ \frac{154}{3.142} } \\ ≈ 14 \: cm[/tex]

[tex]Circumference = πd \\ = 14\pi \\ = 14 \times 3.142 \\ = 43.988 \\ ≈ 44 \: cm[/tex]

Answer:

The factored form of the equation is f(x) = (x - 2)(x + 10), which makes the zeros of the function x = -10 and x = 2.

In order to factor a quadratic like this, you must find factors of the constant (in this case -20). The pairs of factors are listed below.

1 and -20

-1 and 20

2 and -10

-2 and 10

4 and -5

-4 and 5

Now we must pick out the pair that add to the coefficient of x.

1 and -20

-1 and 20

2 and -10

-2 and 10

4 and -5

-4 and 5

Once you've picked out those numbers, you can place each in a parenthesis with x.

f(x) = (x - 2)(x + 10)

Then to find the zeros to the equation, set each parenthesis equal to 0 and solve.

x - 2 = 0

x = 2

x + 10 = 0

x = -10

Step-by-step explanation:

hope this helps:)

Answer:

a: 13 + t = 17

Step-by-step explanation:

the top is equal to the bottom

the top is 13 and t together but you are not multiplying

thus the answer is 13 + t = 17

Answer:

A, 13+t=17

Step-by-step explanation:

Since you are trying to find the missing part of the diagram and both rows add up to 17, the answer would be A. This is the case because you aren't multiplying 13 over and over to get 17, rather instead you are adding a number to get 17.

Answer:

x= 89°

Step-by-step explanation:

Let's use the rule of corresponding angles.

x+ 32°= 121° (corr. ∠s)

x= 121° -32°

x= 89°

Answer: The dimensions of the builder's scale drawing is 40 x 32 inches.

Step-by-step explanation:

The scale factor of Karl = 1:12

Dimensions = 10 x 8 inches

Area = 80 square inches

1:12 = 1/12

1/12 = 80/a

a = 80 x 12

a = 960 square inches

So dimensions are 120 x 96 inches

Builders scale factor = 1:3

Actual Length = 120inches

Actual width = 96 inches

Builders drawing length = 120/3

= 40 inches

Builders drawing width = 96/3

= 32 inches

Answer:

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Step-by-step explanation:

The situation that best represents the equation y = 25x is David earned y amount of money at a rate of $25 per x hours.

Rate of payment is the amount of money a worker receives after each hour, day or week.

David receives the amount of y as his payment every hour.

He is paid at the rate of $25 every X hours.

Therefore the amount he will receive which is represented as y would be $25 * X hours.

Learn more about rates here:

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Answer:

Scale faction is 4

Step-by-step explanation:

You want to step this up as new/old this is because the shape is increasing in size. 18 times 4 is 72.

Answer: 7.2

Step-by-step explanation:

Using proportions, it is found that she needs 4 consecutive hits to raise her batting average to .400.

A proportion is a fraction of a total amount.

Hence, the batting average is given by the number of hits divided by the number of at-bats.

If she gets x consecutive hits, she will have 8 + x hits in 25 + x at-bats, for an average of 0.400, hence:

[tex]0.4 = \frac{8 + x}{25 + x}[/tex]

8 + x = 10 + 0.4x

0.6x = 2

x = 3.33

Rounding up, she needs 4 consecutive hits to raise her batting average to .400.

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the answer of the year is 20%

Answer:

427

Step-by-step explanation:

i could be wrong i used surface area calculator

[tex]3v^2-10v+3=0\\\\\implies 3v^2 - 9v-v +3=0\\ \\\implies 3v(v-3)-(v-3)=0\\\\\implies (v-3)(3v-1)=0\\\\\implies v = 3,~~v=\dfrac 13[/tex]

Answer:

The numbers are 12 and 4

Step-by-step explanation:

12÷4=3

4÷4=1

12×4=48

Answer:

Disagree

radius = 7 m

diameter = 14 m

Step-by-step explanation:

Formula

[tex]\sf Area\:of\:a\:circle=\pi r^2[/tex]

Given:

Substitute given value into the formula and solve for r:

[tex]\sf \implies \pi r^2=153.88[/tex]

[tex]\sf \implies r^2=\dfrac{153.88}{\pi}[/tex]

[tex]\sf \implies r=\sqrt{\dfrac{153.88}{\pi}}[/tex]

[tex]\sf \implies r=6.998680253[/tex]

Therefore r ≈ 7 m

So I disagree with Nysean, as from my calculations, the approximate radius of the merry-go-round is 7 m.

Diameter = 2r

⇒ diameter of merry-go-round = 2 x 7 = 14m

So Nysean has actually given the approximate measure of the diameter rather than the radius.

Answer:

30.67 inches

Step-by-step explanation:

Area of a triangle: 1/2 x b x h

115 = 1/2 x b x 7.5

115 = 3.75b

115/3.75 = b

30.66666 = b

30.67 = b

Answer:

D i think a number represents x. not sure

Answer:

8x+5

Assume x is the unknown number.

8x+5 means

8*x = a number multiplied by eight

8x+5 = a number multiplied by eight eight then added to five.

Therefore, the correct option is D.

Answer:

f(n+1) = f(n)+5

Step-by-step explanation:

So lets say

f(1)=5

f(2)=10

1+1=2 so

f(2)=f(1+1)

therefor

f(n+1)=f(n)+5 since the difference of the functions is 5

the answer is A f(n+1)=f(n)+5

we know that

An arithmetic sequence is a sequence of numbers which increases or decreases by a constant amount each term

In this problem

the sequence of numbers increase by a constant amount equal to

5

each term

so

f(2)=f(1)+5

f(3)=f(2)+5

f(4)=f(3)+5

.

.

f(n+1) = f (n) + 5

therefore

the answer is the option

f(n + 1) = f(n) + 5

Answer:

A

Step-by-step explanation:

Answer:

[tex]y = \frac{5}{3} x - 5[/tex]

Step-by-step explanation:

To write an equation in the slope-intercept form, we need the slope (which can also be calculated) and at least a coordinate.

What is slope-intercept form?

x- intercept occurs at y= 0 while y-intercept occurs at x= 0. With this information, let's write out the two coordinates given.

With two coordinates, we can calculate the slope using the equation below.

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

[tex]slope = \frac{ - 5 - 0}{0 - 3} [/tex]

[tex]slope = \frac{ - 5}{ - 3} [/tex]

[tex]slope = \frac{5}{3} [/tex]

Substitute the value of the slope into m in the equation.

[tex]y = \frac{5}{3} x + c[/tex]

Given that the y-intercept is -5, c= -5.

[tex]y = \frac{5}{3} x - 5[/tex]

Answer:

Answer is G 1.5

Step-by-step explanation:

1. Distribute the 5 to x and 2 by multiplying. and the 7 to the 4 and -x by multiplying

2. carry over the 7x by adding it to 5x. to get x to one side.

3. subtract 10 from both side

4. Divide both side by 12

5. simplify and convert to decimal

The equation that is true for x = -6 and x= 2 is given by: Option B: 2x^2 +8x -24 = 0

Suppose there is an equation given, involving some variables.

Then, those values of the involved variable, for which the equation is true, are called solution of the equation.

For single variable equations, specially for polynomials, these solutions are called the roots of the equation.

Suppose that the given quadratic equation is

[tex]ax^2 + bx + c = 0[/tex]

Then its roots are given as:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

For this case, the options are all quadratic equations, so we can check all the options to find the roots to see if they match to x = -6 and  = 2

Then its roots are given as:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{-(-16) \pm \sqrt{(-16)^2 - 4(2)(12)}}{2(2)}\\\\x = \dfrac{16 \pm \sqrt{196 - 96}}{4} = \dfrac{16 \pm 10}{4}\\\\x = 26/4, x = 6/4[/tex]

Thus, this equation isn't true for both x = -6 and x= 2

Then its roots are given as:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{-8 \pm \sqrt{(8)^2 - 4(2)(-24)}}{2(2)}\\\\x = \dfrac{-8 \pm \sqrt{64 +192}}{4} = \dfrac{-8 \pm 16}{4}\\\\x = -6, x = 2[/tex]

Thus, this equation is true for both x = -6 and x= 2

Since the question says "Which equation is true", so that means only one option is true.

Thus, the equation that is true for x = -6 and x= 2 is given by: Option B: [tex]2x^2 +8x -24 = 0[/tex]

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Answer:

b

Step-by-step explanation:

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