Michaels test scores for this semester were 83,80,91,74,66,99,87,72,95,98. What was the median of his scores

Answer:

[tex]x = \frac{3}{2} [/tex]

Step-by-step explanation:

first distribute

[tex] \frac{36x - 9}{2x} = 15[/tex]

next multiply both sides by 2x

[tex]36x - 9 = 15(2x) \\ 36x - 9 = 30x[/tex]

simplify

[tex] - 9 = - 6x[/tex]

divide both sides by -6

[tex] \frac{ - 9}{ - 6} = x \\ \frac{3}{2} = x[/tex]

In order to use the Pythagorean Theorem to find out if a triangle has a right angle, you have to determine If the squares of the two shorter sides add up to the square of the hypotenuse, then you know the triangle contains a right angle.

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

How to get that answer:

The slope is the rate of change for any linear function.

Apply the slope formula for any two points on the diagonal line.

I'll use the points (-4, -3) and (0, 4)

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{4-(-3)}{0-(-4)}\\\\m = \frac{4+3}{0+4}\\\\m = \frac{7}{4}\\\\[/tex]

The slope is m = 7/4

This indicates that each time we go up 7 (rise), we also go to the right 4 units (run)

slope = rise/run = 7/4

rise = 7, run = 4

The fraction 7/4 converts to the decimal form 1.75

Step-by-step explanation:

2 similar triangles (the angles are the same, and the lengths of the corresponding sides have the same multiplication factor from one triangle to the other) :

1. support post (14ft), post to back (b), the long roof line

2. front to post (f), support post (14ft), dotted line

so, because the multiplication factor is the same for the sides, the ratio

"support post" / f

must be the same as

b / "support post"

14 / f = b / 14

b = 14²/f = 196/f

and then we know that

f + b = 53

by putting the first into the second equation we get

f + 196/f = 53

f² + 196 = 53f

f² - 53f + 196 = 0

the solution of such a quadratic equation in general is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = f

a = 1

b = -53

c = 196

f = (53 ± sqrt(53² - 4×1×196))/(2×1) =

= (53 ± sqrt(2809 - 784))/2 = (53 ± sqrt(2025))/2 =

= (53 ± 45)/2

f1 = (53 + 45)/2 = 98/2 = 49

f2 = (53 - 45)/2 = 8/2 = 4

as the distance "front to post" is shorter than "back to post", f2 = 4 must be or solution.

therefore, the support post is positioned 4ft from the front of the house.

Answer:

12.5% and 60%

Step-by-step explanation:

0.125 x 80 = 10

160-64 = 96

96/160 = 0.6

0.6 x 100 = 60%

Step-by-step explanation:

I think you mean that 10 cm³ of air are escaping every second.

and we start with a volume of 500 cm³.

V = 500 - 10t 0 <= t <= 50

because negative t (seconds) don't make any sense, and neither does a negative volume (for t > 50).

Answer:

A multiplicative inverse or reciprocal for a number x, is denoted by 1/x or x‾¹.

So, the answer to your question is B.  a × (1/a) = 1.

Hope this helps!! :)

Answer:

126

Step-by-step explanation:

Answer:

First one :

Function? Yes

Domain : { -1 , -2 , -3 }

Range { 10 , 13 , 16 }

Second one:

Function? No

Domain : { 2 , 3 }

Range : { 10 , 13 , 16 }

Third one :

Function ? No

Domain : { 33 , 35 , 36 }

Range : { 8 , 10 }

Step-by-step explanation:

A function is a relation where each input has its own output. In other words a function is a relation where each x value has its own y value. If an x value repeats the relation is not a function.

The domain is the set of x values in a relation whereas the range is the set of y values in a relation

For the first one. No x value repeats, each input has its own output therefore this is a function.

Domain : { -1 , -2 , -3 }

Range { 10 , 13 , 16 }

The second one : The x value 2 repeats therefore the relation is not a function.

Domain : { 2 , 3 }

Range : { 10 , 13 , 16 }

The third one : Each x value has its own y value therefore this relation is a function. ( Note that y values are allowed to repeat )

Domain : { 33 , 35 , 36 }

Range : { 8 , 10 }

Answer:

(m+8) - 2

Step-by-step explanation:

Answer:

2^2n = 4n

hope it helps you :)

Answer:

4n

Step-by-step explanation:

2^2n = 4n

hope u liked this answer :)

Blake has 5 dimes and 10 nickels.

Let x represent the number of dimes and y represent the number of nickels.

Each dime is worth 10 cent ($0.1) and each nickel is worth 5 cents ($0.05).

Since he has a minimum of 13 coins, hence:

x + y ≥ 13     (1)

It is worth at most $1 combined, hence:

0.1x + 0.05y ≤ 1     (2)

From the graph, a possible solution is (5, 10).

Blake has 5 dimes and 10 nickels.

Find out more about inequalities at: https://brainly.com/question/241541

Answer:

12 apples

Step-by-step explanation:

32/8=4 Then you multiply it by 3 to get 12.

Answer:

41:9

Step-by-step explanation:

You have 32 red apples.

And a ratio of red apples to green.

The ratio is 8:3.

This ratio is a simplified veiw of it.

You need to do,

32 ÷ 8

which equals 3.

So then multiply both sides of the ratio by 3.

8 × 3 is 32

3 × 3 is 9.

Your new ratio is,

32:9

Red apples to green apples.

Now since you need the total amount of apples to green apples.

Add 32 and 9.

Which is 41 total apples.

Your new ratio is,

41:9

Answer:

8

Step-by-step explanation:

Answer:

check online for more information

Answer:

292 acres.

Step-by-step explanation:

OK so if there are 73,000 acres of trees in total and 0.4% are old we would simply calculate what 0.4% of 73,000 which is 292. So of those 73,000 acres of trees 292 acres of them would be "old-growth trees".

Answer:

its c

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

8 + 27 would give us 35

We add the negative since it starts from there and works it's way up.

Answer:

y=-5/2x+2

y+3= -5/2. (x-2)

Step-by-step explanation:

Answer:

y=-5/2x+2

Step-by-step explanation:

y=mx+b, where m is slope, b is y-int and y and x are variables.

Step 1: plot your points

Step 2: draw a line thru them

Step 3: find the slope. -5/2. And your y-int. +2

Hope that helps! Brainliest is appreciated :)

Answer:

3. x=14° y=7

4. x=29° y=3

Step-by-step explanation:

3. this is a 45 - 45- 90 triangle

so the side is a-a-a√2 ( two sides are the same)

4y-3=10+2y+1 -- collect like terms

4y-2y=10+1+3

2y=14

y=7

find the angle of the inside triangle

180-59-90 =

31°

we know the big triangle was a 45-45-90 angle

so x+31=45

x=45-31

x=14°

4. this is a square, all sides are same

5y+3y=24

8y=24

y=3

angle is 90°

x+x+9y+5=90

we know y=3 --substitute

x+x+9(3)+5=90

2x+27+5=90

2x=90-27-5

2x=58

x=58/2

x=29

Answer:

dimes: 5

quarters:8

Step-by-step explanation:

she has 2$ in quarters and $0.25 in dimes

Answer:

10 Dimes and 5 Quarter

Step-by-step explanation:

Important info:

18 Coins worth a total of $2.25

Note:

Dimes = .10

Quarter = .25

10 Dimes = 1.00

4 Quarter = 1.00

Question to Answer:

How many each type of Coin does she have?

Solution:

Lets get rid of .25 in $2.25 :)

So that 1 Quarter..

2.00

Takes away 1.00 = 10 Dimes

Now we have 1 Quarter and 10 Dimes.

1.00 Left..

4 Quarter = 1.00

So now we have 5 Quarter and 10 Dimes..

Check Work:

5 Quarter = 1.25 and 10 Dimes = 1.00

1.25+1.00=

$2.25

Hence. Loria has 5 Quarter and 10 Dimes.

{ Couldn't figure out 18 Coins worth a total of $2.25 the closest I could get was 15 Coins worth a total of $2.25}

~[ RevyBreeze]~

Answer: Perpendicular

Step-by-step explanation: If you graph these points you will get two lines that from at a right angle and cross through each other. This means they are perpindicular.

Answer:

Perpendicular

Step-by-step explanation:

Lines that are parallel have the same slope, and lines that are perpendicular have an negative reciprocal slope.

To clarify, the reciprocal of 2 would be 1/2, and the negative reciprocal of 2 would be -1/2.

Calculate the slope of the lines by dividing the difference in y by the difference in x:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{4-0}{7-1}=\frac{4}{6}=\frac{2}{3}\\\\m_2=\frac{6-0}{3-7}=\frac{6}{-4}=-\frac{3}{2}[/tex]

m₂ is the negative reciprocal of m₁, so these lines are perpendicular.

Showing the graph in the image as an example, though the equations only have the slope and not the y-intercept so the points wont be on the lines.

Answer:

B

Step-by-step explanation:

21 inches to 7 inches

The width of the original image is B)  [tex]7\frac{7}{8}[/tex] inches.

Given that: The width of the large poster is 21 inches.

Given that: The original image has dimensions that are 3/8 of the dimensions of the image in the poster.

So the width of the original image is = [tex]\frac{3}{8}\cdot21=\frac{63}{8}=7\frac{7}{8}[/tex]

Learn more: https://brainly.com/question/16596053

Answer:

C(C^3 + 8C^2 -3C -7)

Step-by-step explanation:

(-3C^4-5C^2-7C)+(4C^4+8C^3+2C^2)  

(-3C^4 +4C^4)+8C^3 + ( -5C^2 +2C^2)  -7C  [Combine like terms]

C^4 + 8C^3 -3C^2 -7C                                     [Simplify]

C(C^3 + 8C^2 -3C -7)                                   [Isolate 1C from the rest]