Need Help on Both of these, Will give 50 Points to answerer:

Part A:
After grading the most recent chapter test, a science teacher asks twelve of his 10th-grade summer school students how long they studied for the test. Their answers, as well as their corresponding test grades, were recorded on a table and placed on a scatter plot.


(Scatter plot values: 0,25 1,53 2,50 2,80 3,58 4,92 6,74 6,89 8,100 10,60 10,90 12,100)


Use the line of best fit shown (not provided) in the scatter plot to make a conjecture about the number of hours studied versus the resulting test grade. Answer in complete sentences.

Part B: Algebraically write the equation of the best fit line in slope-intercept form. Include all of your calculations in your final answer.

Answer:

80

Step-by-step explanation:

The measure of a triangle is 180.

Answer: The answer to your question is 80

Step-by-step explanation: The first thing you do is set up your problem to find the side measure of bac, which is an angle they are looking for. The problem would look like this:

180-50+50

180-100

=80 degrees

Answer:

D

Step-by-step explanation:

Use the formula for the volume of a cylinder.

[tex]V=\pi r^2h[/tex]

Plug in the values we know.

[tex]V=\pi6^2*9 \\ \\ V=36\pi*9 \\ \\ V=324\pi[/tex]

The volume of the cylinder given will be 324π.

The volume of a cylinder is calculated by using the formula:

Volume = πr²h

where,

r = radius = 6 inches.

h = height = 9 inches

Volume = πr²h

Volume = π × 6² × 9

Volume = π × 36 × 9.

Volume = 324π

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Answer:

(2,-2)

(10,-10)

(2,-9)

(7,-10)

Step-by-step explanation:

The given point is (2,-10)

This point is in the fourth quadrant.

To be able to use the number line to find the distance between this point , (2,-10) and another point in the fourth quadrant, the second point must have the same x-coordinate with this point or the same y-coordinate with this point.

Answer:

A

B

D

E

Step-by-step explanation:

simple stuff i know

Answer:

Option A

Step-by-step explanation:

The parent function [tex]y=x^2[/tex] has a minimum [tex](0,0)[/tex].

If we map [tex]x\mapsto x-1[/tex] we get [tex]y=(x-1)^2[/tex]. This is a horizontally translated copy of the parent function, so the minimum is still 0.

Then if we map [tex]f(x)\mapsto f(x)-4[/tex] we have [tex]y=(x-1)^2-4[/tex]

This is a vertical translation 4 units down, so now the minimum is -4, which appears in the equation.

The required equation which includes the minimum or maximum of f is given as f(x) = (x - 1)² - 4. Option A is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,

First of all, all the function mentioned does not have a maximum,  but have the same minimum, at (1, -4).
But, as of the appearance equation f(x) = (x - 1)² - 4 includes the minimum. because when terminating x it gives minimum y and when terminating it gives x minimum.

Thus, The required equation which includes the minimum or maximum of f is given as f(x) = (x - 1)² - 4. Option A is correct.

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Answer:

Part A) The diameter of the rug is [tex]10\ ft[/tex]

Part B) The radius of the rug is [tex]r=5\ ft[/tex]

Part C) The area of the rug is [tex]78.5\ ft^{2}[/tex]

Step-by-step explanation:

Part A) Find the diameter of the rug

we know that

The circumference of a circle (circular rug) is equal to

[tex]C=\pi D[/tex]

where

D is the diameter

we have

[tex]C=31.4\ ft[/tex]

[tex]\pi=3.14[/tex]

substitute the values and solve for D

[tex]31.4=(3.14)D[/tex]

[tex]D=31.4/(3.14)=10\ ft[/tex]

Part B) Find the radius of the rug

we know that

The radius of a circle (circular rug) is half the diameter

we have

[tex]D=10\ ft[/tex]

[tex]r=D/2[/tex]

substitute

[tex]r=10/2=5\ ft[/tex]

part C) What is the area the rug is covering?

The area of the circle (circular rug) is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=5\ ft[/tex]

[tex]\pi=3.14[/tex]

substitute

[tex]A=(3.14)(5)^{2}[/tex]

[tex]A=78.5\ ft^{2}[/tex]

Answer:

[tex]\frac{463}{3}[/tex]

Step-by-step explanation:

The given geometric series is:

243-162+108.....+64/3

The first term is [tex]a=243[/tex].

The common ratio is:

[tex]r=\frac{-162}{243}=-\frac{2}{3}[/tex]

The sequence is finite, so we can generate all the terms by repeatedly multiplying by the common ratio until we get to the last term.

The complete series is

243-162+108-72+48-32+64/3

The sum is:

[tex]243+108+48+64/3-162-72-32=\frac{463}{3}[/tex]

Answer:

the answer is A.

Step-by-step explanation:

that is a good good question

Answer:

C. 43.72

Step-by-step explanation:

just took it on edge

Answer:

The solution was solved correctly by Keith

The solutions of the equation are x=-5,x=-12

Step-by-step explanation:

we have

[tex]x^{2}+17x+72=12[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}+17x=12-72[/tex]

[tex]x^{2}+17x=-60[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]x^{2}+17x+8.5^{2} =-60+8.5^{2}[/tex]

[tex]x^{2}+17x+72.25 =12.25[/tex]

Rewrite as perfect squares

[tex](x+8.5)^{2}=12.25[/tex]

square root both sides

[tex](x+8.5)=(+/-)3.5[/tex]

[tex]x=-8.5(+/-)3.5[/tex]

[tex]x=-8.5(+)3.5=-5[/tex]

[tex]x=-8.5(-)3.5=-12[/tex]

The solution was solved correctly by Keith

The solutions of the equation are x=-5,x=-12

Answer:

The first box is Keith and the second box is -5,-12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Givens

d = 20 for the bike

d1 = 3 for the person

rate of person = r

rate of bike = r + 5

Formula

d = r*t;  t = d/r

Solution

t is the same for both

20/(r + 5) = 3/r                  Cross multiply

20*r = 3*(r + 5)                  Remove the brackets.

20*r = 3r + 15                    Subtract 3r from both sides.

20r - 3r = 3r - 3r + 15        Combine

17r = 15                               Divide by 17

r = 15/17

r = 0.8824 miles per hour running

Area is calculated by multiplication of dimensions:

length×width= Area

both are lesser than 1, let's say 0.5 and 0.9 as examples.

0.5×0.5=0.25

0.9×0.9=0.81

you see the area is less than one and area can never be negative so first answer is the right answer.

The correct statement is option a. The area is between 0 square units and 1 square units

Any 2-diamensional figure bounded by 4 sides in which opposite sides are equal and parallel and all the 4 angles are right angled.

Now,   0 unit<length<1 unit

           0 unit<width<1 unit

∴ Area of the rectangle = (length x width)

⇒ 0 square units <Area of the rectangle <1 square units

∴ The area  of the rectangle is between 0 square units and 1 square units

The first option matches with the answer.

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Final answer:

The equation y = -x² - 2x + 3 can be expressed in vertex form as y = -(x + 1)² + 4.

Explanation:

The equation y = -x² - 2x + 3 can be expressed in vertex form as:

y = -(x + 1)² + 4

To convert the equation to vertex form, we need to complete the square. Here are the steps:

Factor out a common negative from the first two terms: y = -1(x² + 2x) + 3

Take half the coefficient of x (-2/2 = -1) and square it: (-1)² = 1

Add the squared value inside the parentheses and subtract it outside: y = -(x² + 2x + 1) + 3 - 1

Simplify: y = -(x + 1)² + 2

The vertex form of the equation is y = -(x + 1)² + 4.

Answer:

Final answer is [tex]c=12t[/tex].

Step-by-step explanation:

Given that the amount c of energy you burn and the time t you spend exercising, if you burn calories at a rate of 12 Cal/min.

Now we need to write a function rule for the relationship between c and t.

given that cal/min=12

or [tex]cal/min=12/1[/tex]

or [tex]c/t=12[/tex]

or [tex]c=12t[/tex]

Hence final answer is [tex]c=12t[/tex].

Range is the biggest number minus the smallest from the list.

R = 16 - 4

R = 12

The range is 12.

[tex]3(2 + x) \\ = 6 + 3x \\ = 3x + 6[/tex]

Yes it is because three times two is six and three times x is three x hope this helps

To solve for the vertical angles, we set up the equation 2y = y + 130. Solving for y gives us 130, and substituting back, we get each angle measures 260 degrees, which is reasonable since vertical angles are equal.

Two angles are vertical angles, which means they are opposite each other when two lines intersect and they are equal in measure. The problem states that one angle is 2y and the other is y + 130. Since vertical angles are equal, we can set up the equation 2y = y + 130.

Now, we solve for y:

To check if the answer is reasonable, we can note that vertical angles must be equal, and both our calculated angles are 260 degrees, confirming they are equal and thus reasonable.

Answer:

x=-1 or x=7

Step-by-step explanation:

|x−3|=4

x-3=-4 or x-3=4

x=-1 or x=7

Answer:

1 1/3

Step-by-step explanation:

(5/6 x 1/1) + (1/2 x 2/3) + ?

the answers to that are 5/6 and 3/6 so

5/6 + 3/6 = ???

5 + 3/ 6 = 8/6

8 divided by 2/ 6 divided by 2 = 4/3

so divide the numerator and denominator 4 divided by 3

then convert that to a mixed number

1 1/3

Answer:

13/16.

Step-by-step explanation:

1/2 = 8/16 so:

5/16 + 1/2

= 5/16 + 8/16

= 13/16 (answer).

Answer:

(3,-3)

Step-by-step explanation:

An ordered pair is written with X first, then Y (X,Y).

X is the left and right axis Y is the up and down axis.

The dot is at X = 3 and Y = -3

It would be written as (3,-3)

Answer:

Could be C) or D) None of these, 29688.05cm^2

Step-by-step explanation:

Did the question to round off to any numbers?

Formula for cylinder's T.S.A: 2 π r h + 2 π r^2

Diameter= 2 x radius

Radius = 70cm / 2 = 35cm

Height -> need to convert m to cm -> 100cm

Substitute these values into the formula:

2 x π  x 35 x 100 + 2 x π x (35)^2 = 29688.05cm^2

Answer:

7

Step-by-step explanation:

Since the triangle is right we can use the cosine ratio to find IR

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{IR}{TR}[/tex] = [tex]\frac{IR}{14}[/tex]

Cross- multiply

IR = 14 × cos60° = 14 × 0.5 = 7

Answer:

y = -1/2 x + 1

Step-by-step explanation:

Lines that are perpendicular to each other have slopes that are negative reciprocals. You get the negative reciprocal of a number by flipping the fraction for the slope, then changing the positive/negative.

The lines are written in slope-intercept form, y = mx + b.

"x" and "y" are points on the line.

"m" is the slope.

"b" is the y-intercept.

In y = 2x + 8, the slope is 2. Find its negative reciprocal.

Write the slope as a fraction.

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

Flip the fraction.

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

Change the negative/positive.

[tex]m=-\frac{1}{2}[/tex]    This is the slope of the perpendicular line.

Now we need to find the y-intercept, "b", for our line. We know m = -1/2, and we know a random point (6, -2). Points are written (x, y), which mean x = 6 and y = -2. Substitute the values of the point and the slope into y = mx + b.

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

[tex]-2 = -\frac{1}{2}*6 + b[/tex]      Multiply (-1/2)(6) by combining into the numerator

[tex]-2 = -\frac{6*1}{2} + b[/tex]      Simplify numerator

[tex]-2 = -\frac{6}{2} + b[/tex]       Reduce fraction

[tex]-2 = -3 + b[/tex]         Isolate "b" now

[tex]-2 + 3 = -3 + b + 3[/tex]      Add 3 to both sides

[tex]1 = b[/tex]        Solved for "b"

[tex]b=1[/tex]         Write the variable on the left side for standard formatting

b = 1 and m = -1/2

Substitute them into slope-intercept form for the final answer.

y = -1/2 x + 1

To find the equation of a line perpendicular to a given line and passing through a specific point, use the negative reciprocal of the original line's slope. Applying this to the point-slope form of the line equation gives y = -(1/2)x + 1, which is the correct answer as per the given options.

The subject of the question is about writing the equation of a line that is perpendicular to another line, specifically y = 2x + 8, and passes through a specific point (6, -2). The concept involved here is the slope of the lines. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. Since the slope of our given line is 2, the slope of the line that is perpendicular to this would be -1/2.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point through which the line passes, we can substitute m = -1/2 and (x1, y1) = (6, -2). Therefore, the equation of the line is y = -(1/2)x + 1.

The correct answer from the given options is (D) y = -(1/2)x + 1.

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Answer:

see explanation

Step-by-step explanation:

Given

T= 2π[tex]\sqrt{\frac{L}{g} }[/tex]

Square both sides

T² = 4π² [tex]\frac{L}{g}[/tex] ( divide both sides by 4π²

[tex]\frac{T^2}{4\pi ^2}[/tex] = [tex]\frac{L}{g}[/tex]

Multiply both sides by g

L = [tex]\frac{gT^2}{4\pi^2 }[/tex]

Answer:

Radius = 2.

Step-by-step explanation:

We have been given equation of the circle which is [tex]x^2 + y^2 = 4[/tex].

Now we need to find the radius of the given circle [tex]x^2 + y^2 = 4[/tex].

To find that let's compare with the formula of the circle with standard equation of the circle  [tex]x^2 + y^2 = r^2[/tex], where r is the radius.

We get [tex]r^2 = 4[/tex]

take square root of both sides.

[tex]r=2[/tex]

Hence radius of the given circle is r = 2.

A scale factor of 2 means the dimensions are multiplied by 2.

15 x 2 = 30

8 x 2 = 16

1)5sqrt17,2sqrt157,8sqrt2

2)sqrt7

3)-3(3sqrt3+2sqrt5)

4)18sqrt6,12sqrt3-9sqrt15

Hello There!

First, we are give the problem which is 2,624/4

 0 6 5 6

4 2 6 2 4

− 0      

 2 6    

− 2 4    

   2 2  

 − 2 0  

     2 4

   − 2 4

       0

ANSWER IS 656

Answer: 170

Step-by-step explanation:

Based on the problem, you know that this corporation listed their sales in 100s as 1,700. This means that, to calculate their actual volume in thousands, you need to multiply 1,700 by 100 and divide the product by 1,000.

Let be "x" their actual volume in thousands.

Therefore, applying the corresponding procedure, you get that the value of "x" is the following:

[tex]x=\frac{(1,700)(100)}{(1,000)}\\\\x=\frac{170,000}{1,000}\\\\x=170[/tex]

Final answer:

To find the corporation's sales volume in thousands from a base of '100s', one needs to multiply 1,700 by 100 and then divide by 1,000, resulting in a sales volume of 170 thousand shares.

Explanation:

The question asks us to convert a corporation's sales figure from 100s to thousands. The listed sales are 1,700 in 100s, which means the sales are 1,700 × 100 shares. To convert this number into thousands, we divide by 1,000 because there are 1,000 units in one thousand.

Thus, the calculation would be:

Multiply 1,700 by 100 to get the total sales in shares.

Divide the result by 1,000 to convert it into thousands.

(1,700 × 100) / 1,000 = 170,000 / 1,000 = 170.

Therefore, the actual volume of sales in thousands is 170.

Answer:

x = 11

Step-by-step explanation:

Given the 2 equations

y = [tex]\frac{1}{4}[/tex] x → (1)

5x - 8y = 33 → (2)

Substitute y = [tex]\frac{1}{4}[/tex] x into (2)

5x - 8( [tex]\frac{1}{4}[/tex]x ) = 33

5x - 2x = 33

3x = 33 ( divide both sides by 3 )

x = 11

Answer:

11

Step-by-step explanation:

Given that ,

⇒ y = 1/4x and

⇒ 5x - 8y = 33

We can write 1st equation as ,

⇒ 4y = x

Put x = 4y in 2nd Equation ,

⇒ 5*4y - 8y = 33

⇒ 20y - 8y = 33

⇒ 12y = 33

⇒ y = 33/12

Put this in 1st ,

⇒ 33/12 = 1/4 x

⇒ x = 33/12 × 4

⇒ x = 33/3

⇒ x = 11 .

The answer is (-3,2) because when it’s present in the graph the graph would not pass the vertical line test.

Another way to think about it is that -3 (input) has more than one output.

Answer:

The answer is (-3, 2)

Step-by-step explanation:

Let's define the two sets

A = {4, -3, 3, 1} and B = {-2, 2, 4, 1 -3}, so that the set of ordered pairs is a function , we should have that to every element from the first set (in this case A) corresponds (or is associate to) an element (and only one element) from the second set (in this case B). But we have that the element -3 in the set A (the domain) is related to the elements 2 and -3 which belong to the set B (the codomain), this in not allowed by the definition of function. So in order to the set of ordered pairs is a function we should remove the pair (-3, 2).

To find an equivalent ratio, multiply both the numerator and denominator of the given ratio by the same number. In this case, multiplying both 1 and 26 by 2 gives us an equivalent ratio of 2:52.

To find an equivalent ratio, we can multiply or divide both the numerator and denominator of the given ratio by the same number. In this case, we can multiply both the numerator and denominator of the ratio 1:26 by 2 to get an equivalent ratio. Therefore, the equivalent ratio is 2:52.