What two consecutive perfect squares does 10 lie between

The solutions of the system of equations are:

x = -2, y = 4, z = -2

Here we have the system of equations:

4x - y - 2z = -8

-2x + 4z = -4

x + 2y = 6

To eliminate one variable, we can add the second equation and two times the third equation, we will get:

(-2x + 4z) + 2*(x + 2y) = -4 + 2*6

Now we can simplify that so we get:

4z + 4y = -4 + 12

4*(z + y) = 8

z + y = 8/4  =2

z + y = 2

With that we can write z in terms of y.

z = 2 - y

And with the third equation we can write x in terms of y.

x = 6 - 2y

Replacing that in the first equation we get:

4*(6 - 2y) - y - 2*(2 - y) = -8

Now we can solve this for y.

24 - 8y - y +2y - 4 = -8

20 - 11y = -8

-7y = -28

y = 28/7  = 4

Now that we know the value of y we can find the values of x and z.

x = 6 - 2y = 6 - 2*4 = -2

z = 2 - y = 2 - 4 = -2

The solutions of the system of equations are:

x = -2, y = 4, z = -2

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According to the plot, it looks like [tex]y=3.5[/tex] when [tex]x=4[/tex], and [tex]y=7[/tex] when [tex]x=5[/tex]. Then the average rate of change from [tex]x=4[/tex] to [tex]x=5[/tex] is

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{7 - 3.5}{5 - 4} = 3.5[/tex]

Kelvin score 29 points in All-State Basketball team more than Brandon.

We are given that

Brandon averaged 21.25 points per game in 16 games which means that the mean of points made by Brandon in All-State Basketball team of 16 matches is 21.25

So, the total points made by Brandon is

21.25 × 16 = 340

Kelvin averaged 20.5 points per game in 18 games which means that the mean of points made by Kelvin in All-State Basketball team of 18 matches is 20.5

So, the total points made by Kelvin is

20.5 × 18 = 369

we can see that total score made by kelvin is more

The difference is 369- 340 = 29

Hence, Kelvin score 29 points in All-State Basketball team more  than Brandon.

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passive income

dividends, real estate, interest income

active income

salary, business income,  

-1/2 = 3/8y
Answer:

y = -4/3

answer is y= -4/3

step by step

-1/2 = 3/8y

divide both sides by 3/8 to solve for y

-1/2 divided by 3/8 = 3/8 divided by 3/8y

when you divide fractions you flip the divisor and multiply

-1/2 x 8/3 = y

-8/6 or simplified to -4/3

you can check your work by substituting your y value of -4/3 into your original equation

-1/2= 3/8y

-1/2 = (3/8) (-4/3)

-1/2 = -12/24

-1/2 = -1/2

They equal so problem solved!

[tex]\cfrac{1}{2}(4x-2)\leqslant 9+7x\implies 2x-1\leqslant 9+7x\implies -1\leqslant 9+5x \\\\\\ -10\leqslant 5x\implies \cfrac{-10}{5}\leqslant x\implies {\LARGE \begin{array}{llll} -2\leqslant x \end{array}}[/tex]

le's notice that, we divided by a positive number, thus the inequality sign didn't flip.

Answer:

x ≤-4 or x> 2

Step-by-step explanation:

x+1 ≤-3 or-4x<-8

First solve the inequality on the left

x+1 ≤-3

Subtract 1 from each side

x+1-1 ≤-3-1

x ≤-4

Then solve the inequality on the right

-4x<-8

Divide each side by -4, remembering to flip the inequality

-4x/4 > -8/-4

x > 2

Put them back together

x ≤-4 or x> 2

Closed circle at -4 and line going to the left and open circle at 2 and line going to the right

Answer:

Step-by-step explanation:

a Whar grsde are u even in >:/

Answer:

I think the answer is B

Step-by-step explanation:

Hope this helps

Sorry if I'm wrong

Answer:

f'(x) = 0

Step-by-step explanation:

the derivative of a constant is zero , that is

f(x) = 5 ( a constant ) , then

f'(x) = 0

Answer: 17/18=34/36

11/12=33/36

Step-by-step explanation:

17/18 and 11/12

First find the LCM, least common multiple, of the denominators 18 and 12.

In order to do that, list the factors of 18 and 12 and find the least common factors of them excluding 1.

18: 1, 2, 3, 6, 9, 18

12: 1, 2, 3, 4, 6, 12

Notice any common small factors? Yes they are 2 and 3. Now, multiply them with 18 and 12.

18*2=36

12*3=36

Hence, LCM is 36.

17/18=(17*2)/(18*2)=34/36

11/12=(11*3)/(12*3)=33/36

The sun's diameter as described in the task content is; ; 1.09 × 10⁵ times the earth's diameter.

This follows from the given premise that; the diameter of the sun is approximately 1.4x10⁹ Km and the diameter of Earth is approximately 1.28x10⁴ Km

According to the task content; The diameter of the sun is approximately 1.4x10^9 Km and the diameter of Earth is approximately 1.28x10^4 Km.

The number of times by which the sun's diameter is greater than the earth's diameter can be evaluated as follows;

= 1.4 × 10⁹/1.28 × 10⁴

= 1.09 × 10⁵

Ultimately, The sun's diameter as described in the task content is; 1.09 × 10⁵ times the earth's diameter.

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Answer:

  15 : 20 : 8

Step-by-step explanation:

Given ratios a:b = 3:4 and b:c = 5:2, you want the ratio a:b:c in simplest form.

The extended ratio you want can be written only when the number of ratio units associated with 'b' is the same in both ratios. Multiplying the first ratio by 5, we get ...

  a:b = 3:4 = 15:20

Multiplying the second ratio by 4 gives ...

  b:c = 5:2 = 20:8

Now, 20 "ratio units" represent 'b' in both ratios, so we can combine them:

  a:b:c = 15:20:8

__

Additional comment

The value we chose to represent 'b' is the least common multiple (LCM) of the values that represent 'b' in the given (reduced) ratios.

Answer:

3x, where x = the price of a football ticket

Answer: the one that cross -7 and -7

Step-by-step explanation:

f(x)= -x-7

y=mx+b m is the slope and the b for y-intercept form

y-intercept  (0,-7)   m= -1

-1 the line go  down from left to right

The coordinates of H are (-9,-1) when H is on FG and divides it such that  FH:GH is 1:2.

It is given that  F(–8,3) and G(–2,–9) and ratio of  FH:GH is 1:2.

The diagram of this question is given below.

Let  coordinates of H be ( x , y) .

By using sections formula , we get

(x , y) = ( 1(-2) + 2(-8) / 1+2 , 1(-9) +2(3) / 1+2 )

(x , y) =  ( -2 -16 / 1 +2 , -9 +6 / 1 +2 )

(x , y) = ( -18 / 3 , -3/3)

(x , y) = ( -9 , -1)

On comparing , we get x = -9 and y = -1.

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The mean is  12.28

The mode is 9.6.

The median is 10.25.

Mean, median, and mode are measures of central tendency. Mean is the average of a set of numbers. Median is the number that is at the center of a dataset when the dataset is arranged in ascending or descending order. Mode is the number that occurs most frequently in a dataset.

Mean = sum of numbers / total number

(11.3 + 9.9 + 9.6 + 11.5 +9.6 + 11.2 + 10.6) / 6

= 73.7 / 6

= 12.28

The number that occurs most frequently is 9.6. It occurs twice in the dataset. 9.6 is the mode.

The median = (total number + 1) / 2

(6 + 1) / 2

= 7/2 = 3.5 digit

9.6, 9.6, 9.9, 10.6, 11.2, 11.3

(9.9 + 10.6) / 2

= 20.5 / 2 = 10.25

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Answer:

28/35

Step-by-step explanation:

4/5 *7/7=28/35

Answer:

pre-test

Step-by-step explanation:

(1) identifity my own strengths

interest and challenges.

Check the picture below.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{(~~ 2- (-4)~~)^2 + (~~ 3- 0~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 6 )^2 + ( 3)^2}\implies \boxed{AB=\sqrt{45}}[/tex]

[tex]B(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{6}~,~\stackrel{y_2}{0}) ~\hfill BC=\sqrt{(~~ 6- 2~~)^2 + (~~ 0- 3 ~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 4)^2 + ( -3)^2}\implies \boxed{BC=5} \\\\\\ C(\stackrel{x_1}{6}~,~\stackrel{y_1}{0})\qquad D(\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) ~\hfill CD=\sqrt{(~~ 0- 6~~)^2 + (~~ -3- 0~~)^2} \\\\\\ ~\hfill CD=\sqrt{( -6)^2 + ( -3)^2}\implies \boxed{CD=\sqrt{45}}[/tex]

[tex]D(\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad A(\stackrel{x_2}{-4}~,~\stackrel{y_2}{0}) ~\hfill DA=\sqrt{(~~ -4- 0~~)^2 + (~~ 0- (-3)~~)^2} \\\\\\ ~\hfill DA=\sqrt{( -4)^2 + ( 3)^2}\implies \boxed{DA=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{\sqrt{45}~~ + ~~5~~ + ~~\sqrt{45}~~ + ~~5 ~~ \approx ~~ \text{\LARGE 23.42}}[/tex]

Answer:

-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using linear functions, it is found that Ginny must attend at least 13 events to make the premier member package cost less.

The complete question is given as follows:

"Ginny wants to join a local dance club that has dance events every week. There are two membership options available: Ginny may become a premier member by paying a fee of $150 per year and attend an unlimited number of dances. Ginny may become a regular member by paying a fee of $50 and then pay $8 per dance she attends. How many dances must Ginny attend such that becoming a premier member will cost less than becoming a regular member? "

A linear function is modeled in slope-intercept form by:

y = mx + b

In which:

For this problem, we have that:

Hence the functions for each option are given as follows:

Being a premier member will cost less when:

P(x) < R(x).

Hence:

150 < 50 + 8x

8x > 100

x > 100/8

x > 12.5 -> at least 13 events.

Ginny must attend at least 13 events to make the premier member package cost less.

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Answer:

3/20

Step-by-step explanation:

when multiplying fractions, you don't have to worry about changing denominators, since they will multiply together, so just multiply the numerators and denominators

2*3/5*8=6/40

Then, simplify

6/2/40/2=3/20

The original length of the square garage is 19.1 ft.

The length of the new garage is 23.4 ft and the percentage increase in length is 81.6 %.

Yossi used to have a square garage with 364ft of floor space.

Recently, built an addition to it.

The garage is still a​ square, but now it has​ 50% more floor space

Therefore,

area of a square = l²

where

Therefore,

364 = l²

l = √364

l = 19.0787840283

l = 19.1 ft

Therefore, the original length of the square garage is 19.1 ft.

After 50% increase in the area,

New area = 50 / 100(364) + 364

New area = 546 ft²

Therefore,

546 = l²

l = √546

l = 23.3666428911

l = 23.4 ft

Hence,

percentage increase in length = 19.1 / 23.4 × 100

percentage increase in length = 1910 / 23.4

percentage increase in length = 81.6239316239

percentage increase in length = 81. 6 %

Therefore, the length of the new garage is 23.4 ft and the percentage increase in length is 81.6 %.

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When the area A of a rectangle is represented by the formula A= lw, the formula for the length will be l = A / w.

It should be noted that the area A of a rectangle is represented by the formula A= lw

where I is the length

W is the width

It should be noted that based on the information, we want to find the formula to solve for the length.

A = lw

Divide through by w

A/w = lw/w

l = A / w

Therefore, when the area A of a rectangle is represented by the formula A= lw, the formula for the length will be l = A / w.

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let me give you a mouthful of something

the domain of f(x) is the range of its inverse, or namely the domain of f(x) is the same set as the range of f⁻¹(x), so for any (a , b) pair on the domain of f(x), there's a (b , a) on the range of f⁻¹(x).

now, that's a bit of of a mumble, but in short it means, if f(x) has a point of (3 , 5), then the graph of f⁻¹(x) has a point which is the same pair but flipped sideways, namely (5 , 3).

that's pretty much true for any function that has an inverse.

Based on the number of hours in the work week, the cost of the laborers and masons, worth of the materials and the profit, the estimated cost of the job can be written as a mathematical statement of A. 3 x $15 x 40 + 4 x $25 x 40 + $3,268 + $700 = $

The total estimated cost is $9,768

The total estimated cost of the job can be found by the formula:

= (Number of laborers needed x Cost of laborers x Number of hours in work week) + (Number of masons x cost of masons x number of hours in work week) + materials worth + Required profit

The total estimated cost is therefore:

= (3 x $15 x 40) + (4 x $25 x 40) + $3,268 + $700

= 1,800 + 4,000 + 3,268 + 700

= $9,768

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Question: Hello: )✨A masonry contractor is preparing an estimate for building a stone wall and gate. He estimates that the job will take a

40-hour work week. He plans to have three laborers at $15 per hour and four masons at $25 per hour. He'll need $3268

worth of materials and wishes to make a profit of $700. Write a mathematical statement that will give the estimated cost of

the job. Then calculate this total.

Select the correct choice below and fill in the answer box to complete your choice.

Answer: Checked to see if this was right* Based on the number of hours in the work week, the cost of the laborers and masons, worth of the materials and the profit, the estimated cost of the job can be written as a mathematical statement of A. 3 x $15 x 40 + 4 x $25 x 40 + $3,268 + $700 = $

The total estimated cost is $9,768

What is the total estimated cost?

The total estimated cost of the job can be found by the formula:

= (Number of laborers needed x Cost of laborers x Number of hours in work week) + (Number of masons x cost of masons x number of hours in work week) + materials worth + Required profit

The total estimated cost is therefore:

= (3 x $15 x 40) + (4 x $25 x 40) + $3,268 + $700

= 1,800 + 4,000 + 3,268 + 700

= $9,768

Have an awesome day/night<3

Answer:

Hello,

Step-by-step explanation:

[tex]x^4+4x^3-64x-256\\=x^3(x+4)-64(x+4)\\=(x+4)(x^3-64)\\-----------\\s(x)=x^4+4x^3-64x-256\\=(x+4)(x^3-4^4)\\=(x+4)(x-4)(x^2+4x+16)\\[/tex]