(06.04 MC)



What is the approximate equation of this line of best fit in slope-intercept form?

Answer:

[tex]\large\boxed{y=6x+9}[/tex]

Step-by-step explanation:

The slope-intercept form of the equation of a line:

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

m - slope

b - y-intercept

The formula of a slope:

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

We have the points E(-1, 3) and F(-2, -3). Substitute:

[tex]m=\dfrac{-3-3}{-2-(-1)}=\dfrac{-6}{-2+1}=\dfrac{-6}{-1}=6[/tex]

Therefore the equation of a line is:

[tex]y=6x+b[/tex]

Put the coordinates of the point E(-1, 3) to the equation and solve it for b:

[tex]3=6(-1)+b[/tex]

[tex]3=-6+b[/tex]             add 6 to both sides

[tex]9=b\to b=9[/tex]

Finally we have:

[tex]y=6x+9[/tex]

her resolution is incorrect because it's 6 times x=48. so to get rid of of the six you have to divide it on both sides, so x can be alone. and that's will only have one solution which is x=8

the answer is C because it is the right answer

Answer:

The answer is D/trust me

Step-by-step explanation:

the other answer is wrong

Answer:

$21

Step-by-step explanation:

She bought the book for $15.

15 x 40% = 6

Since she rised the price just add 6 to 15

Hope it was helpful ^^ <3

Good Luck

Answer:

See possible solutions below.

Step-by-step explanation:

The equation x^2 = 36 is a polynomial equation.

It can be solved by using a radical on both sides. The solution is x = +/- 6.

The equation has two solutions. x = -6, 6.

While this is a polynomial equation, it is specifically called a quadratic since the exponent is 2.

The equation x^2 = 36 has two real number solutions: x = 6 and x = -6. Statements that acknowledge both of these solutions as possible would be true.

The equation in question is x^2 = 36. To solve this equation, one must realize that there are two real number solutions since squaring either a positive or negative number will result in a positive number. Taking the square root of both sides of the equation gives us two solutions: x = 6 and x = -6.

Therefore, any statement claiming that there is only one solution is incorrect. The true statements would acknowledge the existence of two solutions, one positive and one negative.

Answer:

A. 7560

Step-by-step explanation:

There are nine letters in the word SEVENTEEN:

1 S

4 Es

1 V

2 Ns

1 T

Possible positions:

For the S, any one of the nine positions. That's ⁹C₁ positions.

For the Es, any four of the remaining eight positions. That's ⁸C₄ positions.

For the V, any one of the remaining four positions. That's ⁴C₁ positions.

For the N, any two of the remaining three positions. That's ³C₂ positions.

For the T, only one way  to fill the last position. That's ¹C₁ position.

Total number of positions

= ⁹C₁ × ⁸C₄ × ⁴C₁ × ³C₂ × ¹C₁ = 9 × 70 × 4 × 3 × 1

= 7560

There are 7560 permutations of the letters in the word SEVENTEEN.

13 - 6 is 7

7 + 6 = 13

Just subtract the 2 numbers and you get your answer.

Final answer:

The equation 13 = 6 + y is solved by subtracting 6 from both sides, yielding y = 7.

Explanation:

To solve for y in the equation 13 = 6 + y, we need to isolate y on one side of the equation. We can do this by subtracting 6 from both sides of the equation.

Here is how you can solve the equation step by step:

Start with the original equation: 13 = 6 + y.

Subtract 6 from both sides: 13 - 6 = 6 + y - 6.

This simplifies to: 7 = y.

So, the value of y is 7.

ok did you get what I solved I hope it's fine by you, if you have a problem with the way I solved it still ask questions ok

Answer:

(0,-9)

Step-by-step explanation:

You simply solve the equation and you get the y value. And since the x value is zero...

TA DA!!!!

Answer:

Its -2, I took the test and got it right i dont think this person ^ knows what you meant i might even be wrong with what you want but if its mulitiple choices its -2

First we have to find 25% of 900 pounds (i hope that's the right currency). so 900 x .25 = 225

so we subtract 225 from 900 and get 675 pounds.

to find sales tax we have to find 6% of 675, so 675 x .06 = 40.50

675 + 40.50 = 715.5 pounds

Quick Anwser:

Numbers 3-4, you already have the name, BUT you have to classify if the sides are equal. So, for 3-4 ALSO put, “ top and bottom are equal “ or “sides are the same” so for the rhombus, as an example, say, “all sides are the same”..understand?

Answer: OPTION D.

Step-by-step explanation:

The symbol of the inequality ">" means "greater than". Then, -5 is greater than -6.

If a negative number -a is greater than other negative number -b , then the distance between -a and zero is shorter than the distance between -b and zero.

You can see in the number line attached that -5 is closer to 0 than -6. Therefore, -5 is located to the right of -6.

Answer:

D

Step-by-step explanation:

Answer:

y=-3/2x-1

explanation:

Answer:

Option D

Step-by-step explanation:

The domain of h(x) cannot include 0

h(0) = sqrt (-3) = i sqrt(3)

Which is an imaginary number, and doesn't make sense for the equation to represent imaginary numbers if we are talking about the production of hammers.

The same reasoning can be applied for the second statement.

The domain of the graph should not include zero, beacuse zero people cannot produce any wrenches.

Option D.

Answer:

180 feet

Step-by-step explanation:

√2000 = 44.8

44.8 x 4 =  179.2 = 180 feet

The amount of fencing that would be needed to enclose this square field is  178.88 feet.

A square field would have both the length and the width being equal both of them could be represented as x.

Area of a square = Length x Width

2,000 = x × x

x² = 2,000

x = √2,000

x = 44.72 feet

The fencing needs to go around the field which means it needs to go around the field's perimeter.

Perimeter of Square = Length x 4

= 44.72 x 4

= 178.88 feet

In conclusion, 178.88 feet of fencing would be needed.

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Answer:

x=-25

Step-by-step explanation:

Inverse variation

xy =k

We know x and y

20*5 =k

100 =k

So the formula is

x y = 100

We know y = -4

x (-4) = 100

Divide each side by -4

-4x/-4 = 100/-4

x = -25

Step-by-step explanation:

[tex]1.\ \dfrac{x}{16}=\dfrac{45}{40}\qquad\text{cross multiply}\\\\40x=(16)(45)\\\\40x=720\qquad\text{divide both sides by 40}\\\\\boxed{x=18}\\\\======================[/tex]

[tex]2.\ \dfrac{x}{5}=\dfrac{1}{4}\qquad\text{cross multiply}\\\\4x=(1)(5)\\\\4x=5\qquad\text{divide both sides by 5}\\\\\boxed{x=\dfrac{4}{5}}\\\\======================[/tex]

[tex]3.\ \dfrac{2.5}{10}=\dfrac{x}{50}\qquad\text{cross multiply}\\\\10x=(2.5)(50)\\\\10x=75\qquad\text{divide both sides by 10}\\\\\boxed{x=7.5}\\\\======================[/tex]

[tex]4.\ \dfrac{x}{6}=\dfrac{2}{9}\qquad\text{cross multiply}\\\\9x=(6)(2)\\\\9x=12\qquad\text{divide both sides by 9}\\\\x=\dfrac{12}{9}\\\\x=\dfrac{12:3}{9:3}\\\\\boxed{x=\dfrac{4}{3}}[/tex]

Answer:

36 inches

Step-by-step explanation:

P= 2l + 2w

P= 2(10) + 2(8)

P= 20 + 16

P= 36

Answer:

The answer is 36inches

Step-by-step explanation:

to find out a perimeter of something you need to add the the with and length so basically all you had to do was

10+10+8+8 = 36 inches

hope this helps bye

As the x-values go to positive infinity, the function's values go to positive infinity.

Answer: D, As the x values go to positive infinity, the functions values go to positive infinity.

Step-by-step explanation:

This is true for just about any [tex]y=x^{3}[/tex] graph. As the value of the input (x) get larger, the value of the output (y) will get exponentially larger.

[tex]\bf \textit{Amount of Population Decay} \\\\ A=Pe^{-rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &40000\\ r=rate\to 3.1\%\to \frac{3.1}{100}\dotfill &0.031\\ t=\textit{elapsed time}\dotfill &4\\ \end{cases} \\\\\\ A=4000e^{-0.031(4)}\implies A=40000e^{-0.124}\implies A=\cfrac{4000}{e^{0.124}} \\\\\\ A\approx 35335.194\implies \stackrel{\textit{rounded up}}{A\approx 35335}[/tex]

Amount of population Decay A= Pe^-re

A= accumulated amount

P= initial amount =40000

r=rate ⇒3.1% ⇒ 3.1/100. ⇒0.031

t = elapsed time ⇒ 4

A=40000e ^0.031(4) ⇒A=40000 ^0.124⇒A=40000/e^0.124

A  ≈35335.194 ⇒ A ≈ 35335.(rounded up

The population means is nothing but the average of this group of items. It is basically arithmetic mean of the group and can be calculated by taking a sum of all the data points and then dividing it by the number of items we have in the group.

A population is defined as a group of individuals of the same species living and interbreeding within a given area. Members of a population often rely on the same resources, are subject to similar environmental constraints, and depend on the availability of other members to persist over time.

Population is the number of people or animals in a particular place. An example of population is over eight million people living in New York City.

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Answer:

The perimeter is equal to [tex](y+39)\ units[/tex]

Step-by-step explanation:

we know that

The perimeter of the triangle is equal to the sum of the length of its sides.

so

[tex]P=AB+BC+AC[/tex]

substitute the values

[tex]P=(y+7)+18+14[/tex]

[tex]P=(y+39)\ units[/tex]

Answer:

Step-by-step explanation:

Pete played 18 tennis matches in a week.

P = 18

Jack played 6 fewer matches than Pete.

J = P - 6

J = 18 - 6

J = 12

How many times the number of matches pete played is the number of matches jack played?

18 / 12 = 1.5

Pete played 1.5 times the number of matches that Jack played.

Answer:

Pete played 1.5 times the amount of matches Jack did.

Step-by-step explanation:

In order to find this, first find the number that Jack played. Since he played 6 fewer than Pete we can solve by subtracting 6 from Pete's number.

18 - 6 = 12

Now to find how many more times higher it is, divide the number Pete does by Jack's number. 18/12 = 1.5

Answer:

Yes it is the correct "mean" for that

Answer:

5.32255

Step-by-step explanation:

if the circle's surface area is 89 square feet. The circle's radius will then be 5.32 feet.

It is the closely curving line drawn from the center to an equally distant point. The distance separating a circle's center and perimeter is its radius.

Let r be the radius of the circle. Then the area of the circle is written as,

A = πr² square units

The area of the circle is 89 square feet. Then the radius of the circle will be given as,

89 = πr²

Simplify the equation, then the radius is written as,

πr² = 89

r² = 28.34

r = 5.32 feet

if the circle's surface area is 89 square feet. The circle's radius will then be 5.32 feet.

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There are no tanks with less than 30 fish, so the first two groups ( 20-24) and (25-29) aren't used.

There are 3 tanks with 30-34 fish.

There are 3 tanks with 35-39 fish.

There are 3 tanks with 40-44 fish.

There are 1 tanks with 45-49 fish.

Now drag the bars for each group to the number of tanks.

See attached picture:

Answer:

There are no tanks with less than 30 fish, so the first two groups ( 20-24) and (25-29) aren't used.

There are 3 tanks with 30-34 fish.

There are 3 tanks with 35-39 fish.

There are 3 tanks with 40-44 fish.

There are 1 tanks with 45-49 fish.

Now drag the bars for each group to the number of tanks.

Step-by-step explanation:

Answer:

x1 = - 4

x2 = 2/3

Step-by-step explanation:

Divide the equation by 3 to give

x^2 + 10x/3 + c/3 = 0

The sum of the two roots = - 10/3

So

x1 + x2 = -10/3

x1 - x2 = 4 2/3                Add these two equations.

2x1 = -10/3 + 4 2/3         Change 4 2/3 to an improper fraction

2x1 = -10/3 + 14/3            Combine the right

2x1 = 4/3                         Divide by 2

2x1/2 =4/3//2        

x1 = 2/3

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

x1 + x2 = - 10/3

2/3 + x2 = - 10/3

x2 = - 10/3 - 2/3

x2= -12/3

x2 = - 4

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

(x - 2/3)(x +4) = 0              Multiply through by 3

(3x - 2)(x + 4) =0

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

Check

(3x - 2)(x + 4) = 0

3x^2 + 12x - 2x - 8 =0

3x^2 + 10x - 8 = 0

Answer:

$15,500

Step-by-step explanation:

Let s represent the initial salary.  That salary, plus a 5% raise, comes out to 1.05s = $16,275.

Solve for s by dividing both sides by 1.05:

s = $16,275 / 1.05 = $15,500.

The original salary was $15,500.

Final answer:

The original salary before a 5% raise resulting in a new salary of $16,275 was $15,500. We found this by dividing the new salary by 1.05.

Explanation:

The question asks us to determine an employee's original salary before a 5% raise. To solve this, we assume that the new salary ($16,275) is 105% of the original salary (100% + 5% raise). Therefore, we can set up the following equation: Original Salary × 1.05 = $16,275. Now, we want to find the Original Salary, so we divide $16,275 by 1.05.

Original Salary = $16,275 ÷ 1.05

When we divide $16,275 by 1.05, we get the Original Salary = $15,500.

Therefore, before the increase in pay, the employee's salary was $15,500.

Carlo can use 3 triangles to make a square if the triangles are the correct size and type, such as right-angled triangles, whose hypotenuses can form one side of the square.

Alternatively, he could arrange the triangles to cover half the square's area; however, this would require six triangles, not three.

It is theoretically possible for Carlo to use 3 triangles to make a square, but it requires the right types and sizes of triangles.

A square is a geometrical shape with four equal sides and four right angles.

Triangles, on the other hand, have three sides and can have various angles.

If Carlo is using right-angled triangles, he might arrange them in such a way that the hypotenuses form one side of the square and the other sides of the triangles complete the remaining sides of the square.

However, this would need a bit of creative thinking and specific side lengths for the triangles to ensure the sides of the resulting square are equal.

Another way to approach this is by considering the area of the shapes.

By dissecting the square into smaller squares, and further into triangles, if three triangles can be arranged to form a larger triangle that covers exactly half the area of the square, then two sets of such triangles would be required to form the entire square.

Answer:

c)11√2

Step-by-step explanation:

Given that two of the angles are equal ,each measuring 45 degrees then two legs will be equal as well each measuring 11 units. We have a right angled triangle with two sides given and we are required to determine the hypotenuse. We use Pythagoras theorem;

hypotenuse^2 = 11^2 + 11^2

hypotenuse ^2 = 242

hypotenuse = [tex]\sqrt{242}[/tex]

hypotenuse = [tex]11\sqrt{2}[/tex]

Answer:

a) 11

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

if you simplify it all then you have to flip creating 50 = 49

The variable got eliminated. Then inequality –7(3x – 7) + 21x ≥ 50 has no solution.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

–7(3x – 7) + 21x ≥ 50

Simplify the inequality, then we have

–7(3x – 7) + 21x ≥ 50

–21x + 49 + 21x ≥ 50

–21x + 49 + 21x ≥ 50

–21x + 21 ≥ 1

The variable got eliminated. Then inequality –7(3x – 7) + 21x ≥ 50 has no solution.

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