Find the slope of the line. Write your answer in simplest form.

Slope = change in y / change in x

Slope = (10 - -2) / (-11 - 19)

Slope = 12/-30

Simplify to get:

Slope = -2/5

Answer:

1) There are four roots, with two real and two imaginary roots

The roots are x ±2, ±5·i

2) Therefore, there are 2 roots

The roots are real

The roots are x = -5 and x = 5

3) The possible factored form is therefore; (x + 5)²×(x + 1)×(x - 4)³×(x + 7)

4) Please see the attached graph of the function drawn with Microsoft Excel

Step-by-step explanation:

1) The given equations is as follows;

f(x) = x⁴ + 21·x² - 100

Let a = x², we have;

f(x) = a² + 21·a - 100

a = (-21 ± √(21² - 4 × 1 ×(-100))/(2 × 1)

a = -25 or 4

Therefore, x = √4 = ±2 or x = √(-25) = ±5·i

There are four roots, with two real and two imaginary roots

2) For f(x) = x³ - 5·x² - 25·x + 125

We have;

f(x) = x³ - 5·x² - 25·x + 125

From the equation, we see that x = 5 is a solution of the equation, therefore;

f(5) = 5³ - 5·5² - 25·5 + 125 = 0

Which gives, (x - 5) is a factor of the equation,

Dividing x³ - 5·x² - 25·x + 125 by (x - 5) gives;

x² - 25

(x³ - 5·x² - 25·x + 125)/(x - 5)

x³ - 5·x²

             [tex]{}[/tex]- 25·x

[tex]{}[/tex]                -25·x + 125

[tex]{}[/tex]                0          +  0

Therefore, by long division, (x³ - 5·x² - 25·x + 125)/(x - 5) = x² - 25

(x - 5)×(x² - 25) = (x - 5) × (x - 5) × (x + 5)

Therefore, there are 2 roots

The roots are real

The roots are x = -5 and x = 5

3) From the polynomial zeros, we have x = -5, x = -1, x = 4, and x = 7

At x = -5 the polynomial touches the x-axis given two real roots with (x + 5)² being a factor

With the root at x = -1, a factor is (x - 1)

With the root at x = 4 which has the shape of a cubic function, we have a factor of (x - 4)³

For the root at x = 1, the factor is taken as (x + 7)

The possible factored form is therefore; (x + 5)²×(x + 1)×(x - 4)³×(x + 7)

4) The given function is therefore;

f(x) = (x + 8)³(x + 6)²(x + 2)(x - 1)³(x - 3)⁴(x - 6)

(x + 8)³(x + 6)²(x + 2)(x - 1)³(x - 3)⁴(x - 6)

Please see the attached graph of the function drawn with Microsoft Excel

Answer:

6.60$ dollars per movie

Step-by-step explanation:

99/15=6.6

Answer:

$6.60

Step-by-step explanation:

[tex]\frac{99}{15}[/tex] = 6.60

Answer:

x≥6.43

Step-by-step explanation:

Let's solve your inequality step-by-step.

x+13.8≥20.23

Step 1: Subtract 13.8 from both sides.

x+13.8−13.8≥20.23−13.8

x≥6.43

490909/200000 is the answer

Have a great day!

Stay safe and healthy!

Happy holiday seasons!

May I please have brainliest?

Answer:

(1,2)

Step-by-step explanation:

The solution is the point where the two lines intersect at.

In other words the point where the two lines make an x.

Hope this helps ya!!

Answer: (2,1)

Step-by-step explanation:

Answer:

$12,656.25

Step-by-step explanation:

year 1: 30,000-25%=22,500

year 2: 25,000-25%=16,875

year 3: 16,875-25%=12,656.25

Answer:

(x+9)(x+9)=25

Step-by-step explanation:

x^2+18x+81=25

or x^2+(9x+9x)+81=25

or x^2+9x+9x+81=25

or x(x+9)+9(x+9)=25

:: (x+9) (x+9) =25

Answer:

[tex]B = 38[/tex]

Step-by-step explanation:

This question can be illustrated using the attachment and the required bearing will be calculated using cosine theorem;

[tex]b^2 = a^2 + c^2 - 2ac\ CosB[/tex]

In this case:

[tex]b = 5[/tex]

[tex]a = 7[/tex]

[tex]c = 8[/tex]

[tex]<B = ??[/tex]

Substitute these values in [tex]b^2 = a^2 + c^2 - 2ac\ CosB[/tex]

[tex]5^2 = 7^2 + 8^2 - 2 * 7 * 8\ CosB[/tex]

[tex]25 = 49 + 64 - 112\ CosB[/tex]

[tex]25 = 113- 112\ CosB[/tex]

Collect Like Terms

[tex]25 -113=- 112\ CosB[/tex]

[tex]-88=- 112\ CosB[/tex]

Divide through by -112

[tex]\frac{-88}{-112}= \frac{- 112\ CosB}{-112}[/tex]

[tex]\frac{-88}{-112}= CosB[/tex]

Reorder

[tex]Cos\ B = \frac{-88}{-112}[/tex]

[tex]Cos\ B = 0.7857[/tex]

Take arccos of both sides

[tex]B = cos^{-1}(0.7857)[/tex]

[tex]B = cos^{-1}(0.7857)[/tex]

[tex]B = 38[/tex] --- (approximated)

Hence, the bearing is approximately 38 degrees

Answer: -y=7

Explanation:

Think of your problem as subtraction:

2x-3y+15

-2x+3y=-1

Answer:

Step-by-step explanation:

P = [tex]\left[\begin{array}{ccc}2&7\\3&0\\5&4\\-1&-3\end{array}\right][/tex]

Q = [tex]\left[\begin{array}{ccc}-4\\-3\end{array}\right][/tex]

PQ = [tex]\left[\begin{array}{ccc}2(-4)+7(-3)\\3(-4)+0(-3)\\5(-4)+4(-3)\\-1(-4)+(-3)(-3)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-29\\-12\\-32\\13\end{array}\right][/tex]

600 mL corresponds to 15 teaspoons of sugar

That gives the ratio 600:15

Divide both parts of that ratio by 3 so we get to 200:5

Then multiply both parts by 10 to get 2000:50

This says 2000 mL, aka 2 liters, of soda has an estimated 50 teaspoons of sugar.

To convert from teaspoons to grams, we multiply by 4. This is directly from the equation of 1 teaspoon = 4 grams of sugar

So 50 teaspoons = 50*4 = 200 grams of sugar.

To go from grams to teaspoons, we divide by 4.

-----------------

To find the actual amount of sugar, you'll need to find a 2 liter bottle of soft drink and look at the nutrition facts label. You can search for the nutrition facts label online if you don't have a bottle near you. Keep in mind you're looking for the 2 liter plastic bottle version and NOT the 12 fluid-ounce can version.

Also, keep in mind that the nutrition facts label will list the amount of sugar per serving. This isn't the total sugar since it's just a small portion. Multiply the number of servings by the amount of sugar per serving.

Example: If there are 7 servings and 20 grams of sugar per serving, then that's a total of 7*20 = 140 grams of sugar total.

Side note: the amount of sugar will vary from brand to brand. However, they should all be in the same basic ballpark.

Answer:

There is a total of 100 stamps, or 10² stamps.

Explanation:

10•10=100 (standard form)

100 can be written as 10² in scientific notation (power)

Answer:

x = 36°

Step-by-step explanation:

m<RST + m<TSV = m<RSV

m<RST = 5x + 5

m<TSV = 46

RSV = 232

Plug in these values

5x + 5 + 46 = 232

5x + 51 = 232

5x = 181

x = 36.2, if rounding down;

x = 36°

Answer:

20 Cups of peanut butter

Step-by-step explanation:

Answer:

20 cups

Step-by-step explanation:

80 cookies are made by 4 cups

which means 1 cookie is made by

[tex] \frac{4}{80} cups[/tex]

Therefore 400 cookies would require

[tex]400 \times \frac{4}{80} cups = 20cups[/tex]

Please mark me brainliest

Answer:

[tex] \sf \: 104.4[/tex]

Step-by-step explanation:

(7.36)(10)(9)−(6.2)(10)(9)

=(73.6)(9)−(6.2)(10)(9)

=662.4−(6.2)(10)(9)

=662.4−(62)(9)

=662.4−558

=104.4

Answer:

Step-by-step explanation:

Let required amount be x

Using the ratio to find x:

Answer:

p(5) = 30

Step-by-step explanation:

p(t) and if t=5 then p(5)

p(5) = 3(2)(5)

p(5) = 6(5)

p(5) = 30

Hope this helps and I hope u have an Amazing day!!

Answer:

its 1

Step-by-step explanation:

Answer:

15625

Step-by-step explanation:

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

Calculate 5 to the power of 6 and get 15625.

Answer:

1.66666666667

Step-by-step explanation:

4/2.4 = 1.66666666667

All you do is choose two lenghts and divide to see what factor was used for the dilation.

Answer: 41%

Step-by-step explanation:

15 girls prefer biology.

Find the boys who prefer biology;

There are 36 girls in total so;

= 100 - 36

= 64 boys interviewed

14 boys prefer Physics

= 64 - 14

= 50 boys prefer Biology and Chemistry

7 out of the 31 who prefer chemistry are girls so the boys who prefer chemistry are;

= 31 - 7

= 24 boys

Boys who prefer Biology;

= 50 - 24

= 26 boys

Total who prefer biology;

= 15 girls + 26 boys

= 41 students

Percentage = 41/100 = 41%

The total number of students is equal to 16 students.

We are given that the accompanying histogram shows the heights of the students in Kyra's health class.

A histogram is a graph that shows the frequency of numerical data with the help of rectangular bars.

The height of a rectangle (the vertical axis) represents the distribution frequency of a variable ( amount).

We need to calculate the total number of students in the class.

We can see that for the first interval, the frequency is given as:

F1 = 2

For the 2nd interval, the frequency is given as:

F2 = 4

For the 3rd interval, the frequency is given as:

F3 = 5

For the 4th interval, the frequency is given as:

F4 = 4

For the 5th interval, the frequency is given as:

F5 = 1

The total students = 2 + 4 + 5 + 4 + 1

Total number of students = 16 students.

Therefore, the total number of students is equal to 16 students.

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Answer:

2/3

Step-by-step explanation:

6/9=8/12=2/3

........

Answer:

y=mx+b is the slope intercept form.

Step-by-step explanation:

m is the slope (how the line is moving across the graph)

b is y-intercept (where the line crosses the y axis)

Hope this helps!

Answer:

125

Step-by-step explanation:

C : F

10: 25

×5: ×5

50: ?

No. of fish in the tank = 25 × 5

                                    = 125

Answer:

Slope is rate of change, so define your values.

-$100 is the initial fee

-$70 is charged per month

per month is the constant rate of change

70 is the slope

The slope (rate of change) of the function is 70.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

Verizon charges a $100 initial contract fee,

then $70 a month for a basic cell phone plan.

Let the x be the number of months.

So, the equation,

y = 70x + 100

By comparing with the slope-intercept form,

y = mx + b, where m is the slope.

So, m = 70.

Therefore, 70 is the slope.

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Answer:

Step-by-step explanation: The equation of the line passing through the points (2, –1) and (5, –10) is y = -3x + 5 .Jun 9, 2017

Answer:12.5 times out of 50

Step-by-step explanation:think about it add tails and 2

The numbers is 44/3 and 22/3 are that numbers.

Given that

The sum of two numbers is 22.

One of the numbers is two times the other.

To find

What are the numbers ?

So, according to the question

Let's assume that numbers are x and y, where x is greater then y.

So, we can say that

The sum of that numbers,

x+y = 22,  -------------(1)

And

One of the numbers is two times the other.

x = 2y ---------------(2)

Now, put the value of eq(1) in eq(2)

So, we will get

x+y = 22,  -------------(1)

2y+y = 22

3y = 22

y = 22/3

Now, put the value of y in eq(2)

So, we will get

 x = 2y ---------------(2)

x = 2 (22/3)

x = 2 ×[tex]\frac{22}{3}[/tex]

x = 44/3

That numbers are 44/3 and 22/3.

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