rewrite the following linear equations in general form

can someone help explain how to do this?​

Answer:

The beam should be placed 8 feet from the center.

Step-by-step explanation:

According to the Question,

The struts are y = √(x + 8) and y = √(x − 4).  The struts are 2 feet apart at the location of the beam:

thus, √(x + 8) − √(x − 4) = 2  

on Solving we get,

√(x + 8) = 2 + √(x − 4)

x + 8 = 4 + 4√(x − 4) + x − 4

8 = 4√(x − 4)

2 = √(x − 4)

x − 4 = 4

x = 8

Answer:

0.97

Step-by-step explanation:

in this case the number 1 signifies 100 percent hence

1-0.03=0.97

:))) enjoy your day

Step-by-step explanation:

1.V=LWH L is the length, W is the width and H is the height.

12×6×3=216

2.V=Ah A is the area of the base, h is the height

18×16=288

3.V=LWH L is the length, W is the width and H is the height

10×14×5=700

Answer:

-2x-11=0

1) Add 11 to both sides

Dividde both sides by - 2

X= _11/2

Drcimal form: - 5.5

Answer:  To find the average rate of change, evaluate the function at the given points.

Evaluate the difference of the function at the given points.

Divide the difference of the function at the given points with the difference of the given points.

Step-by-step explanation:

The Average of rate is -1.

Everytime it goes up by one the y goes down by 1 so it would be -1.

The average rate of change of the function in the table given is: -1.

Average rate of change of a function = change in y / change in x = rise/run.

Given the table representing a function, and using two set of ordered pairs, (-2, 7) and (0, 5):

Average rate of change of the function = (7 - 5)/(-2 - 0)

Average rate of change of the function = 2/-2

Average rate of change of the function = -1.

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Answer:

x=50, y=20

Step-by-step explanation:

50-20=30, 50+20=70

Answer:

Step-by-step explanation:

α + β = -b/a

αβ = c/a

α² + β² = (α + β)² - 2αβ

           [tex]= (\frac{-b}{a})^{2}-2\frac{c}{a}\\\\= \frac{b^{2}}{a^{2}}-\frac{2c}{a}\\\\=\frac{b^{2}}{a^{2}}-\frac{2c*a}{a*a}\\\\=\frac{b^{2}-2ca}{a^{2}}[/tex]

Answer:

Part A;

$79

Part B;

The amount Stella would have saved in 'w' weeks = 15 + 8·w

Step-by-step explanation:

Part A

The amount of money Stella already has = $15

The amount she can save per week = $8

The total amount of money, 'A', Stella would have after 8 weeks is given as follows;

A = The amount Stella already has + The amount she can save per week × The number of weeks of savings

Therefore;

A = 15 + 8 × 8 = 79

The amount Stella would have after 8 weeks, A = $79

Part B

The expression that represents the amount of money Stella would have saved in w weeks is given as follows;

A = The initial amount Stella has + The amount she can save per week × w (number of weeks)

∴ A = 15 + 8·w.

Answer:

9x^2 + 27x + 18

Step-by-step explanation:

(9x + 9)(x + 2)

=9x(x + 2) +9(x + 2)

=9x^2 + 18x + 9x + 18

=9x^2 + 27x + 18

Option C with h and k

see screenshot for an example

general formula is

r² = (x - x-center)² + (y - y-center)²

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

[tex] \huge\underline{\sf{\red{Problem:}}}[/tex]

7.) Detemine the value of [tex] \sf{ {3a}^{2} -b.}[/tex]

[tex] \huge\underline{\sf{\red{Given:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{a = 2}[/tex]

[tex]\quad\quad\quad\quad\sf{b = - 1}[/tex]

[tex]\quad\quad\quad\quad\sf{c = - 3}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{3a}^{2} - b}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶{(3)( 2)}^{2} -( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶3(4)-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12 + 1 }[/tex]

[tex]\quad \quad \quad \quad ⟶ \boxed{ \sf{ 13}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{\:13}}}}[/tex]

8.) Find the value of [tex] \sf{ {a}^{3} {b}^{3} - abc.}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶ {a}^{3} {b}^{3} - abc}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(2)}^{3} {( - 1)}^{3} - (2)( - 1)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(8)}{( - 1)} - ( - 2)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{( - 8)} - ( 6)}[/tex]

[tex]\quad\quad\quad\quad ⟶\boxed{\sf{ - 14}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{-14}}}}[/tex]

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

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[tex]\sf{\red{✍︎ C.Rose❀}}[/tex]

Answer:yes, base = 9. No, the exponent is not variable. yes, base =9/10.

Step-by-step explanation:

Answer:

33 blooms

Step-by-step explanation:

This can be set up by an equation. x represents the number of days and y represents the number of corresponding blooms. y = 3x + 12 is the equation, as 3 is the rate of change and 12 is the initial amount. One week is 7 days, so 7 can be plugged in for x. 21 + 12 = 33, so after one week, Debbie has 33 blooms.

Answer:

84pi

Step-by-step explanation:

Sector Area = (pi x r^2 x *angle*)/ 360

(pi x 12^2 x 210)/ 360

= 84pi

= 263.893

Answer:

∠a=∠b

Step-by-step explanation:

Alternate exterior angles are congruent

The Above triangles are similar, Therefore the corresponding sides would be proportional.

that is : -

[tex]\mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}[/tex]

Answer:

200 vs 230

$30

Step-by-step explanation:

Step-by-step explanation:

the lines on the graph of inequality second option

Answer:

98 m³

Step-by-step explanation:

For similar shapes

The ratio of the cube of the corresponding length of similar shapes is equal to the ratio of their volume.

Applying,

L³/L'³ = V/V'............... Equation 1

Where, L = Length of the smaller prism, L' = Length of the larger prism, V = Volume of the smaller prism, V' = Volume of the larger prism

From the question,

Given: L = 5 m, L' = 7 m, V = 50 m³

Substitute these values into equation 1

5²/7² = 50/V'

25/49 = 50/V'

V' = (50×49)/25

V' = 98 m³

Answer: 137.2

Step-by-step explanation:

I'm just making the correct answer an actual answer instead of a comment so it's easier to see

The equation of the red graph is g(x) = 6 - [tex]x^4[/tex].

Thus, option (B) is correct.

Given:

Function 1 : f(x) = 3 - [tex]x^4[/tex]

As, the y-intercept is the point where a line or curve intersects the y-axis.

It is the value of y when the corresponding x-coordinate is zero. It is the point(s) where the graph crosses the y-axis.

Now, from the graph of function f(x) has the intercept 6.

Also, the graph of function g(x) is 3 unit up from the function f(x).

So, the equation of g(x) will be

= f(x)  + 3

= 3 - [tex]x^4[/tex] + 6

= 6 - [tex]x^4[/tex]

Thus, option (B) is correct.

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Answer:

option alphabet c is the answer

Answer:

x=1

Step-by-step explanation:

7x-1+2x-1=7

7x+2x-1-1=7

9x-2=7

9x=7+2

9x=9

9x/9=9/9

x=1

Answer:

-4 < n ≤ 5

Step-by-step explanation:

________________

Answer:

Yes, I agree

Step-by-step explanation:

See attachments for cone

Cone A

[tex]h = 2r[/tex]

Cone B

R = 2r

[tex]h=r[/tex]

The volume of a cone is

[tex]V = \frac{1}{3}\pi r^2h[/tex]

For cone A, we have:

[tex]V = \frac{1}{3}\pi r^2*2r[/tex]

[tex]V_A = \frac{2}{3}\pi r^3[/tex]

For cone B, we have:

[tex]V = \frac{1}{3}\pi *(2r)^2 * r[/tex]

[tex]V = \frac{1}{3}\pi *4r^2 * r[/tex]

[tex]V_B = \frac{4}{3}\pi r^3[/tex]

So, we have:

[tex]V_B = 2 * \frac{2}{3}\pi r^3[/tex]

Substitute [tex]V_A = \frac{2}{3}\pi r^3[/tex]

[tex]V_B = 2 * V_A[/tex]

Make VA the subject

[tex]V_A = \frac{1}{2}V_B[/tex]

Hence, I agree with Ahmad

Answer:

hundredths

Step-by-step explanation:

Numbers after the decimal start with

tenth

hundredth

Answer:

The absolute maximum and the absolute minimum are (0, 16) and (2, 0).

Step-by-step explanation:

First, we obtain the first and second derivatives of the function by chain rule and derivative for a power function, that is:

First derivative

[tex]f'(x) = -4\cdot (-x+2)^{3}[/tex]

Second derivative

[tex]f''(x) = 12\cdot (-x + 2)^{2}[/tex]

Then, we proceed to do the First and Second Derivative Tests:

First Derivative Test

[tex]-4\cdot (-x+2)^{3} = 0[/tex]

[tex]-x + 2 = 0[/tex]

[tex]x = 2[/tex]

Second Derivative Test

[tex]f''(2) = 12\cdot (-2+2)^{2}[/tex]

[tex]f''(2) = 0[/tex]

The Second Derivative Test is unable to determine the nature of the critical values.

Then, we plot the function with the help of a graphing tool. The absolute maximum and the absolute minimum are (0, 16) and (2, 0).

Answer:

$5.50

Step-by-step explanation:

5+6= 11

11/2

Answer:

See Below.

Step-by-step explanation:

We want to prove that the expression:

[tex](125^2+25^2)(5^2-1)[/tex]

Is divisible by three.

We can simplify the second factor:

[tex]=(125^2+25^2)(25-1)\\\\ = (125^2+25^2)(24) \\\\ = (125^2+25^2)(8\cdot 3)[/tex]

Since the second factor is being multiplied by three, we can conclude that the entire expression is divisible by three.

Answer:

It is divisible by 3.

Step-by-step explanation:

(125² + 25²)(5² - 1) ÷ 3

(15625 + 625)(25 - 1) ÷ 3

(16250)(24) ÷ 3

390000 ÷ 3

130000

Answer:

90 or -270

Step-by-step explanation:

Answer: 7.142857142857143

Step-by-step explanation: all you have to do is divide 28.5 by 3.99

The cost per ounce of shampoo is 7.15 ounce.

Assume that the cost per ounce of shampoo is ${x}.

Total cost of bottle of a dog shampoo is $3.99.

Amount of shampoo in the bottle is 28.5 ounces.

So, we can write the cost per ounce of shampoo as

x = 28.5/3.99

x = 7.15 ounce

The cost per ounce of shampoo is 7.15 ounce.

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