what is the equation of the line through the points (3,2),(8,5),(13,8), and (18,11)

Answer:

( x-7) ( x-5)

Step-by-step explanation:

x^2 -12x + 35

To factor this problem, we want to know that two numbers multiply to 35 and add to -12

-7 * -5 = 35

-7 + -5 = -12

( x-7) ( x-5)

Answer:

The answer is (x-7)( x-5)

Step-by-step explanation:

We need to find two numbers that add up to −12 and those same two numbers should have a product of 35

Here the common factors are -7 and -5 because when added they give -12 and when multiplied they give 35.

Therefore we write the answer as (x-7)(x-5)

The number that completes the System of Linear Inequalities represented by the Graph y >= 2x – 2 and x + 4y > =  is -12. Hence, x + 4y [tex]\geq[/tex] -12

A collection of linear inequalities in the same variables is referred to as a system of linear inequalities. Any ordered pair that fulfills all of the inequalities is the solution.

Recall that:

y = mx + c

m = (y2 - y1)/(x2 - x1)

Given that

The orange line intersects y-axis at (0,-2), therefore the y-intercept is -2.

The orange line intersect the points that are (1,0)  and (0, -2).

The slope of the line can be obtained as follows:

m = (-2-0)/(0-1)

= -2/-1

= 2

The slope of the line is m = 2.

Therefore, the orange line is y [tex]\geq[/tex] 2x -2

The blue line intersects y-axis at (0,-3), therefore the y-intercept is -3.

The blue line intersect the points that are (-4, -2) and  (0, -3)

The slope of the line can be obtained as follows.

m = (-3-(-2))/(0-(-4))

= (-3 + 2)/4

= - (1/4)

The slope of the line is:
m = -(1/4)

The inequalities is x + 4y [tex]\geq[/tex] b passes through the point (0, -3)

(0) + 4 (-3) = b

-12 =b

Thus, -12 in is the number that completes the system. Hence, x + 4y [tex]\geq[/tex] -12

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3x + 6 = 48 (alternate angles are equal)

- 6

3x. = 42

÷3

x = 14 degrees

180-48 - 2y + 5y-9 =180

123 + 3y = 180

-123

3y = 57

÷3

y = 19 degrees

Explanation:

To find the last angle on the top straight line, do:

180 - (the 2 given angles).

So, 180 - (3x + 16, which is 48 due to alternate angles being equal). Then, minus the 2y.

(180 - 48 - 2y) & simplify => 132 - 2y

This gives you the equation for the missing angle on our top straight line.

Thus, co-interior angles add to 180. So, we add the new equation (132 - 2y) to 5y - 9.

Simplify

=> 123 + 3y (because - 2+5 =3)

and put it equal to 180. Solve for y

Hope this helps!

Answer:

3/500

Step-by-step explanation:

.6%   = .006   =    6/1000  = 3/500

Answer:

x = 41* & y = 90.

Step-by-step explanation:

Since we know that the figure is a right triangle, we can solve for y easily, as 90+y = 180

y = 90

to solve for x, we have 49+90+x, since the angle that makes up the left side is perpendicular to the triangle,

so 139+x = 180

x = 180-139

x = 41

Answer:

y = 4x + 11

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 )

y = 4x - 2 ← is in slope- intercept form

with slope m = 4

• Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation

to find c substitute (- 2, 3 ) into the partial equation

3 = - 8 + c ⇒ c = 3 + 8 = 11

y = 4x + 11 ← equation of line

Explanation:

The first step is to add up all the values given:

11.01 + 10.50 + 5.70 + 14.67 + 9.50 + 12.54 + 8.90 + 13.56 + 11.23 + 6.80 + 3.00 + 10.55 = 117.96

Then we divide this sum over n = 12 since this is the sample size given (i.e. the number of customers)

117.96/n = 117.96/12 = 9.83

Answer: D

Step-by-step explanation:

Answer: Choice D

Open hole at -3 with shading to the left.

==========================================================

Explanation:

The inequality [tex]-3 > \text{x}[/tex] is the same as [tex]\text{x} < -3[/tex]

When swapping both sides, the inequality sign flips as well.

Since we're looking for numbers smaller than -3, this includes things like -4, -5, -6, -7, and so on. Therefore we shade to the left of -3 on the number line.

We have an open hole at -3 to indicate it's not included as part of the solution set. We would include it if there as an "or equal to" as part of the inequality sign.

Answer:

Step-by-step explanation:

If 2u-6=4, let's solve for u.

Add 6 to both sides

2u-6+6 = 4+6

Simplify

2u = 10

Divide both sides by 2

u = 5

Now, we can solve u-5

5-5 = 0

The formula of P(x) = -0.7 (x-2)²(x+4)

A root of a polynomial is defined as the point or value at which the overall value of the polynomial = 0

It is given that

for a polynomial of degree 3

root x=2, multiplicity 2:  (x-2)²

root x= - 4, multiplicity 1:  (x+4)                  ³ ²

P(x) = a(x-2)²(x+4)

here a is constant

y-intercept =  -11.2

P(0) = -11.2

a(0-2)²(0+4) = -11.2

a * 4 * 4  = -11.2

16a = -11.2

a = -11.2/(16)

a= -11.2/16

P(x) = -(11.2/16)(x-2)²(x+4)

P(x) = -0.7 (x-2)²(x+4)

Therefore the formula of P(x) = -0.7 (x-2)²(x+4)

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Answer:

25 hours.

Step-by-step explanation:

Let the hours worked be x

2/5x = 10

2x = 50

x = 25

She has to work 25 hours to spend 10 hours doing paperwork.

Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

The parameters for this problem are given as follows:

A = 144, r = 0.06, n = (68 - 24) x 12 = 528.

Then:

r/12 = 0.06/12 = 0.005.

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}[/tex]

[tex]P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}[/tex]

P = $26,731.23.

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Answer:

-x + 7 / x + 1

Step-by-step explanation:

6 -(x - 1)/ x + 1

Apply distributive law: -(x - 1) = -x + 1

= 6 - x + 1 / x +1

Group like terms:

= -x + 7/ x + 1

Answer:  its 5x+7/x+1

Step-by-step explanation:

Answer:

4x

Step-by-step explanation:

[tex]\frac{500x^{4} }{(5x)^{3} }[/tex] = [tex]\frac{500x^{4} }{125x^{3} }[/tex] = [tex]4x[/tex]

The value of this car is decreasing at a rate of 6% per year.

The function V(t) = 38000 (0.94)^t represents the value (in dollars) of a car "t" years after its purchase

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,

V(t) = 38000 (0.94)^t
Cleary, above function is an exponential function
while putting certain values in equation we have certain outcomes.
for,
V(1) = 35720;    V(2) =33576.8;      V(3) = 31562.192

Now, the rate of change is given by = [V(2)-V(1)/ V(1)] x 100
= [(33576.8-35720)/35720]*100
= 6%

now V(2) x 6% = V(3)
33576.8 x 6% = 31562.192 = V(3)

Thus, The required rate of decreasing care price is 6%.

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Answer:

it should be fine, but it can also depend on the quality of the wig

Step-by-step explanation:

The formula for simple interest is the following:

[tex]S=Prt[/tex]

In this formula, [tex]S[/tex] is the amount of interest, [tex]P[/tex] is the principal (or initial) amount, [tex]r[/tex] is the interest rate, and [tex]t[/tex] is the length f time, typically in years.

First, let's make a couple of changes to how we wrote down the variables.

Substitute in the values and solve with a calculator.

[tex]\begin{aligned}S&=16,500\cdot0.06\cdot0.5\\&=\boxed{495}\end{aligned}[/tex]

Answer:

1/9m. just take 2/9- 1/9 then you'll get the material remaining good day.

Using the concept of subtraction of fractions, Jillian have 1/9m of cloth left.

Fractions are a way to represent numbers that are not whole numbers. They represent parts of a whole or divisions of a quantity. A fraction consists of two parts: a numerator and a denominator.

The numerator is the number on the top of the fraction and represents the number of parts being considered or counted. The denominator is the number on the bottom of the fraction and represents the total number of equal parts into which the whole is divided.

In this problem, we can easily determine the amount of cloth she have left.

Since she used 1/9 of it, we can proceed as;

2/9 - 1/9 = 1/9m

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The results of the expression 9 and 1/9 subtracted by 1 and 4/5 is 7 14/45

9 and 1/9 subtracted by 1 and 4/5

= 9 1/9 - 1 4/5

= 82/9 - 9/5

= (410-81) / 45

= 329/45

= 7 14/45

Therefore, 9 and 1/9 subtracted by 1 and 4/5 is 7 14/45

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The equivalent expression of [tex]6^\frac 25[/tex] is [tex](\sqrt[5]{6})^2[/tex]

The expression is given as:

[tex]6^\frac 25[/tex]

The law of indices states that:

[tex]a^\frac mn = (\sqrt[n]{a})^m[/tex]

Using the above as a guide, we have:

[tex]6^\frac 25 = (\sqrt[5]{6})^2[/tex]

Hence, the equivalent expression of [tex]6^\frac 25[/tex] is [tex](\sqrt[5]{6})^2[/tex]

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The slope of the line will be – 1/5. Then the correct option is B.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

Take two point from the graph.

(0, 2) and (1, –3)

Then the slope will be

m = (2 – (–3)) / (0 – 1)

m = 5 / (–1)

m = – 1/5

Then the correct option is B.

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Answer:

Center: (-4, 1)

Radius: √2

Explanation:

Circle general equation is represented by (x - h)² + (y - k)² = r²

where (h, k) is the center and "r" resembles radius

To write in general equation form, start completing square:

x² + y² + 8x -2y + 15 = 0

x² + 8x + y² - 2y + 15 = 0

(x + 4)² - 4² + (y - 1)² - (-1)² + 15 = 0

(x + 4)² + (y - 1)² - 16 - 1 + 15 = 0

(x + 4)² + (y - 1)² - 2 = 0

General equation form:

(x - (-4))² + (y - 1)² = (√2)²

From here, comparing with the formula equation.

It is determined: center: (-4, 1) and radius: √2

Answer:

center = (-4, 1)

radius = √2

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given equation:

[tex]x^2+y^2+8x-2y+15=0[/tex]

Subtract 15 from both sides to move the constant to the right side of the equation:

[tex]\implies x^2+y^2+8x-2y=-15[/tex]

Rearrange the left side to collect like variables:

[tex]\implies x^2+8x+y^2-2y=-15[/tex]

Add the square of half the coefficients of the variables x and y to both sides:

[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2+y^2-2y+\left(\dfrac{-2}{2}\right)^2=-15+\left(\dfrac{8}{2}\right)^2+\left(\dfrac{-2}{2}\right)^2[/tex]

[tex]\implies x^2+8x+16+y^2-2y+1=2[/tex]

Factor the two perfect square trinomials on the left side:

[tex]\implies (x+4)^2+(y-1)^2=2[/tex]

Compare the found equation with the general form to find the center and radius of the circle:

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Answer:

[tex] {x}^{2} - 16 = 0 \: is \: the \: equation[/tex]

Step-by-step explanation:

[tex]x = - 4 \\ or \: x = 4[/tex]

[tex](x + 4) = 0 \: or \: (x - 4) = 0 \\ (x + 4)(x - 4) = 0 \\ open \: the \: bracket[/tex]

[tex]x(x - 4) + 4(x - 4) = 0[/tex]

[tex] {x}^{2} - 4x + 4x - 16 = 0 \\ {x}^{2} - 16 = 0[/tex]

The value of line AL is 21. 51cm

Let's start by finding line AB using

Sin α = opposite/ hypotenuse

Sin 90 = x/ 24

1 = x/24

Then, cross multiply

We have line AB = 24cm

Now, let's find line AC

Sin angle B = line AC/24

Let's find angle B

We know that angle A + angle B + angle C = 180

But angle B = 2 Angle A

x + 2x + 90 = 180

3x + 90 = 180

3x = 180-90

x = 30°

Then Angle B = 2 × x = 2 × 30 = 60°

Sin 60 = x/ 24

0. 8660 = x/24

Cross multiply

x = 24 × 0. 8660

x = 20. 78cm

From the diagram, we have the angle of A  in the given triangle to be divide into two by the bisector, angle A = 15°

To find line AL, let's use

Cos α = adjacent/ line AL

Cos 15 = 20. 78/ line AL

Line AL = 20. 78/ cos 15

Line AL = 20. 78 / 0. 9659

Line AL = 21. 51 cm

Thus, the value of line AL is 21. 51cm

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Answer:

y-2=2(x-5), y=2x-8, y+16=2(x+4)

Step-by-step explanation

Round

8724 to the nearest whole number is 8720

Answer:

1,483

Step-by-step explanation:

The equation that models this set of data is y=17.2x^2-226.3x+2184.5. Since x=0 represents 6:00 a.m, x=5 represents 11:00 a.m. Substitute 5 for x in the model, and solve for y.

Based on the number of registered users who log into the social media app during weekdays and weekends, the following are true:

The given model for the users in the week is:

y = 17.2x² - 226.3x + 2,184.5

x is 5 because 11 am is 5 hours after 6 am:
= 17.2(5)² - 226.3(5) + 2,184.5

= 1,483 users

The company should post when there are the most people online and on weekdays that's 14 hours after 6 am which is:
=14 + 6

= 20:00

= 8 pm

On weekends this is 6 hours after 6 am:

= 6 + 6

= 12 pm

Missing information from question:

Model for calculating weekday users y = 17.2x² - 226.3x + 2,184.5.

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Answer:

7/12 or 0.5833

Step-by-step explanation:

So you're going to have 36 combinations, because for each number 1-6 which may be rolled for the first roll, you're going to also have 6 other possible numbers for the second roll. This gives you 6 * 6 or 36. So you could define the entire sample space, but you could also just list the sample space with all the sums less than 7 that way you don't have to list all of the sample space, since you already know how many combinations there are going to be

Let's start with the case that you roll a 1, for the first roll:

1+1 = 2

1+2 = 3

1+3=4

1+4=5

1+5=6

These are the only combinations that will be less than 7 so stop here

Now do the case where you roll a 2, for the first roll

2+1 = 3

2+2= 4

2+3 = 5

2+4 = 6

The next roll will result in a roll greater than 6. This time there were only 4 combinations which is one less than the previous. This makes sense, since you're still increasing in intervals of 1, except the starting number is increasing by 1, meaning as the first roll increases, the amount of combinations with that starting roll that are below 7, will decrease by 1. So this means that:

1: 5 combinations

2: 4 combinations

3: 3 combinations

4: 2 combinations

5: 1 combination

6: 0 combination

This means there are going to be a total of 15 combinations which are less than 7, that means there are 36-15 combinations which are greater than or equal to 7. This simplifies to 21/36 which simplifies to 7/12. This can also be expressed as: 0.5833