prove, using algebra, that the difference between the squares of consecutive odd numbers is always a multiple of 8.
lets 2n+1 be the smaller of the two odd numbers

Answer: 90

Step-by-step explanation:

Let the sides have lengths 2n, 11n, and 15n.

Since the perimeter is 168, 2n+11n+15n=168, meaning that n=6.

So, the longest side is 15(6)=90 inches.

Answer:

1/5

Step-by-step explanation:

Arrange the numbers from smallest to largest...the median is the one in the middle of the list

-12/4   - 2.5    1/5    18/5    10       the middle is 1/5

Answer:

Explanation:

False statements:

Answer:

By examining the table of ordered pairs, notice that the function f(x) is the cube of [tex]x[/tex].  Therefore,  [tex]f(x)=x^3[/tex]

By examining the table of ordered pairs, notice that as [tex]x[/tex] increases by a constant value, the value of the function g(x) increases by the common ratio of 3. Therefore, [tex]g(x)=3^x[/tex]

From the table, both functions equal 27 when [tex]x=3[/tex], therefore, the point of intersection of the two functions is (3, 27).

As x increases past [tex]x=3[/tex], g(x) increases quicker than f(x) since g(x) is an exponential function and f(x) is a cubic polynomial.

So the following statements are true:

Please refer to the attached graph of both functions with plotted ordered pairs.

Answer:

A) x = 4, y = 3.

B. x = 0, y = -4.

Step-by-step explanation:

A) 2x+ 3y =11 .........(a)

x+ y = 4.......(b)

Multiply equation (b) by 2:

2x + 2y = 8

Subtract this from equation (a):

y = 11-8 = 3.

Substitute y = 3 into equation (a):

2x + 3*1 = 11

2x = 11 - 3 = 8

x = 4.

B) 4x+ 3y = -12

   2x - y= 4

Multiply second equation by 2:

4x - 2y = 8

Subtract this from first equation:

3y - (-2y) = -12 - 8

5y = -20.

y = -4.

Substitute y = -4 into equation 1:

4x + 3*(-4) = -12

4x = -12 + 12 = 0

x = 0.

Answer:

9%

Step-by-step explanation:

Answer:

yes it is less then a right angle

Step-by-step explanation:

Answer:

40 degrees

Step-by-step explanation:

(to find coterminal angles to a given angle, we add 360 degrees to the given angle or subject 360 degrees from the given angle any angle any number of time).

-1400 degrees is negative angl, so to get the coterminal angle between 0 degrees and 360 degrees ( the smallest positive coterminal angle), we must add multiples of 360 degrees until we get a possitive coterminal angle:

-1400 degrees+(360 degrees*4)

=-1400 degrees+1440

=40 degrees

so the answer is 40 degrees

The glide translation and the reflection over x-axis are illustrations of transformation

The new ordered pairs for P'and S'are (x - 2, -y)

The given parameters are:

Glide translation (x-2, y)

Reflection over x axis

Assume the coordinates of point P and S are (x,y)

When translated, the new points would be:

(x-2, y)

The rule of reflection over the x-axis is:

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex](x - 2,y) \to (x - 2,-y)[/tex]

Hence, the new ordered pairs for P'and S'are (x - 2, -y)

Read more about transformation at:

https://brainly.com/question/4289712

Answer: 99%

Step-by-step explanation:

Answer:

its blury

Step-by-step explanation:

Answer:

Mode=8

This is because it occurs the most

Median

=8+8/2

=16/2

=8

Therefore, the median is 8

Mean= £x/n

=6+7+7+8+8+8+8+8/8

=60/8

=15/2

=7.5

Step-by-step explanation:

Please mark me brainliest if correct

The mean, median, mode, and range of the data set will be 7.5, 8, 8, and 2, respectively.

Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.

The quantities of hours mary works over a time of 8 days are 8, 7, 8, 8, 8, 7, 6, and 8.

Arrange the data in increasing order, then we have

6, 7, 7, 8, 8, 8, 8, 8

The mean of the data is given as,

Mean = (6 + 7 + 7 + 8 + 8 + 8 + 8 + 8) / 8

Mean = 60 / 8

Mean = 7.5

The median of the data is given as,

Median = {[8 / 2 + (8 + 2)/ 2] / 2}

Median = (4th + 5th) / 2

Median = (8 + 8) / 2

Median = 16 / 2

Median = 8

The mode of the data is given as,

Mode = Frequency of the number

Mode = 8

The range of the data set is given as,

Range = 8 - 6

Range = 2

The mean, median, mode, and range of the data set will be 7.5, 8, 8, and 2, respectively.

More about the statistics link is given below.

https://brainly.com/question/10951564

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Answer:  Dilated and then translated

Step-by-step explanation:

Answer:

dilated and then translated

Step-by-step explanation:

Rectangle A has been enlarged (dilated) and then translated up and to the right.

Answer:

The answer would be B. c ÷ 158.14

Step-by-step explanation:

i just took this test :) the question was:

The space shuttle carries c pounds of cargo, and each piece of cargo weighs 158.14 pounds. Which of the following expressions represents the number of pieces of cargo The space shuttle carries c pounds of cargo, and each piece of cargo weighs 158.14 pounds? Which of the following expressions represents the number of pieces of cargo?

A. c × 158.14

B. c ÷ 158.14

C. c - 158.14

D. c + 158.14

Answer:

[tex]\boxed{\sf{4(5x+3y-7)}}[/tex]

Step-by-step explanation:

It is necessary to find the factors and solve them using their expressions in order to solve this problem.

7*4=28

3*4=12

5*4=20

Rewrite the problem down.

5*4x+3*4y+7*4

Solve.

Common term of 4.

4(5x+3y-7)

I hope this helps you! Let me know if my answer is wrong or not.

[tex]========================================[/tex]

In order to factor this expression, we should factor out the common term (divide all terms in the polynomial by the common term)

In this case, the common term is

4

Note:- Usually, we factor out the G.C.F. (Greatest Common Factor)

So here, the G.C.F. is 4.

Why 4? Because in this trinomial (a polynomial with 3 terms) all 3 terms are divisible by 4.

So divide all the terms

5x

3y

-7

Put 4 outside the parentheses:

4(5x+3y-7)

Is the trinomial in its simplest form? Sure!

Hence, we are done! :)

[tex]================================[/tex]

Hope everything is clear; if you need any more clarification/explanation, kindly let me know, and I will comment and/or edit my answer. :)

Answer:

34.38 (rounding to the nearest hundredth)

Step-by-step explanation:

I have my work linked below, but I used to arc length formula and plugged in all known numbers. Then solved for x which will be the angle you are looking for. Hope this helps!

On a circle of radius 10 feet,  34.37° angle would subtend an arc of length 6 feet.

The length of an arc formula is represented as follows

The length of arc = Ф / 360 × 2πr

where

Ф = angle, r = radius

It is given that circle of a radius of 10 feet,

The length of arc = 6 ft

Therefore,

6 = Ф / 360 × 2 × 3.14159 × 10

6 = 62.8318Ф / 360

360 x 6 =  62.8318Ф

Ф = 360 x 6 / 62.8318

Ф = 34.3784

Ф ≈ 34.37°

Learn more about the length of the arc ;

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Answer:

  y = x

Step-by-step explanation:

Any equation that describes a different line will be part of a system with exactly one solution. There are an infinite number of possible equations.

Perhaps one of the simplest is ...

  y = x

_____

Together with the given equation, this has the solution ...

  x = y = 1/15

Hey there!

Let's make an equation

=> 9h = 144

{ Make h the subject of formula}

=> 9h = 144

=> 9h/9 = 144/9

=> h = 144/9

=> h = 16

Answer:

Step-by-step explanation:

Remark

You are given the diameter but the formula uses the radius. So your first job is find the radius. Then you use this value in the formula to find the volume. Substitute

Givens

pi = 3.14

d = 3.8

r = d/2

r = 3.8/2 = 1.9

Formula

V = (4/3) * pi * r^3

Solution

V = (4/3) * 3.14 * 1.9^3

V = 4/3 * 3.14 * 6.859

V = 28.7163

Answer:

For the 1st row:

6.38 - 6 19/50 - 638%

Step-by-step explanation:

I would suggest using MathPapa if you are trying to do it quick. MathPapa will only really help with finding fractions and percentages, though. To get the decimal, need to find percentages then move decimal to the left 2 times.

ex. 125% -> 1.25

I hope this helps! Have a blessed rest of your night!

Answer:

Step-by-step explanation:

Given,

Let's assume, width of rectangle x feet and length of the Rectangle be 12 + 2x respectively. To Calculate the length and width of rectangle we'll use the formula of area of rectangle:

[tex] \\ \star \: { \underline{ \boxed { \pmb{ \sf{ \purple{Area _{(rectangle)}= Length \times width}}}}}} \\ \\ [/tex]

Substituting the required values:

[tex]\dashrightarrow \sf \: \: \: \: (12 +2x) (x) = 320 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 12x + 2x^2 = 320 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 12x + 2x^2- 320 = 0 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 2x^2 + 12 - 320 = 0 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 2(x^2 + 6x - 160) = 0 \\ [/tex]

[tex] \dashrightarrow \sf \: \: \: \: 2(x^2 + 16x - 10x - 160) = 0 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 2(x - 10)(x + 16) = 0 \\ [/tex]

[tex]\dashrightarrow \: \: \: \: \underline{ \boxed{ \purple{ \pmb{ \rm{ x = 10 \: or \: -16}}}}} \\ [/tex]

Hence,

[tex]~[/tex]

[tex] \underline{\therefore{ \pmb { \frak{Length \: and \: width \: of \: rectangle \: is \: 32 \: and \: 10 \:ft}}}}[/tex]

Answer:

Your answer is C and D

Step-by-step explanation:

Answer:

D. y = -x - 1

Step-by-step explanation:

   We are using slope-intercept form for this problem.

   Since this line is going from upper left to bottom right we know it will have a negative slope.

   The line intersects the y-axis at -1, so the b value is -1.

             The equation for this line is D. y = -x - 1

Answer:

$1493.49

Step-by-step explanation:

The original cost was doubled initially.

$995.66 x 2 = 1991.32

1991.32 x 0.75 (25% discount) = $1493.49

Answer:

60 feet

Step-by-step explanation:

The easiest way to do this is to go answer by answer with the triangle area formula :)

Formula: A=hb/2

H = height

B: base

Now lets solve this :)

Choice 1: 50 feet

50 x 20 = 1000

1000/2 = 500

Choice 2: 40 feet

Since 40 feet is smaller than the 50, we know this will not be correct :)

Choice 3: 120 feet

120 x 20 = 2400

2400/2 = 1200

Choice 4: 60 feet

60 x 20 = 1200

1200/2 = 600

The correct answer is 4, 60 feet :)

Have an amazing day!!

Please rate and mark brainliest!!

10y⁵ + 30y³ - 15y =

5y * 2y⁴ + 5y * 6y² + 5y * (-3) =

5y (2y⁴ + 6y² - 3)

Answer:

13.93

Step-by-step explanation:

find the mean
11.60 + 16.25 ÷ 2 = 13.93