John is solving x^2 + 4x + 8=0 by completing the square. Which step would be part of John's solution.?

(x + 4)^2 = - 4
(x+2)^2 = - 4
(x+4)^2 = - 8
(x + 2)^2 = - 8

Answer:

Volume of a sphere = 4/3 πr³

4/3 * 3.14 * r³ = 4000

4.19 * r³ = 4000

r³ = 4000 / 4.19

r = ∛1058

r = 10.19

Now, surface area = 4πr² = 4 * 3.14 * (10.19)²

S.A. = 12.56 * 104

S.A. = 1307

In short, Your Answer would be Option D) 1307 m²

Hope this helps!

Step-by-step explanation:

#a

H(0)

It refers to y value on graph when x is 0

So here it refers to y intercept

Hence

#b

Observe the graph

y intercept is not 0 so it's not true

#3

Domain is set of x values in graph

#4

Range is set of y values on graph

The consumer will pay $31.91 as an interest.

Initial balance = $2,530.16

Daily interest rate = 0.042%

Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments

So, balance at the end of the first day = 2530*(1.00042)¹

balance at the end of the second day =  2530*(1.00042)²

Similarly, balance at the end of the 30th day =  2530*(1.00042)³⁰

Balance at the end of the 30th day = $2562.07291

So, interest levied =  $2562.07291 -  $2,530.16

Interest levied = $31.91

Therefore, the consumer will pay $31.91 as an interest.

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Answer:

-8, -2, 4, 10

Step-by-step explanation:

Plug the x value into the function.

2(-6)+4 = -8

and so on for all of the values in the table.

Answer:

y = 2(-6) + 4

y = -12 + 4

y = -8

y = 2(-3) + 4

y = -9 + 4

y = -5

y = 2(0) + 4

y = 0 + 4

y = 4

y = 2(3) + 4

y = 6 + 4

y = 10

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Answer:

C)  2808

Step-by-step explanation:

Volume of Triangular Prism = 1/2 x height x length x base

= 1/2 * 9 * 24 * 26

= 2808 mm^3

I hope my answer helps you.

The equation of the blue line is y = 7x - 8 and the equation of the red line is y = -2x + 2

Equations are written as a function of two or more variables with input and output.

The standard linear equation is given in the form y = mx + b

m is the slope

b is the y-intercept

For the red line, the y-intecept is 2

Using the coordinate point on the red line (0,2) and (1, 0)

Slope = -2/1
Slope = -2

Equation of the  red line is y = -2x + 2

For the blue line, we will use the coordinate points (2, 6) and (1, -1)
m = -7/-1

m = 7

-1 = 7(1) + b

-1 - 7 = b

b = -8

Hence the equation of the blue line is y = 7x - 8

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Answer: 95% of the customers have to wait.

Answer: 68%

Step-by-step explanation:

Answer:

8x+7

Explanation:

f(x) = x + 3

g(x) = 7x + 4

==========

Put values

Done!

Answer:

The 63rd Term Is 309

Step-by-step explanation:

Answer:

$27.5

Step-by-step explanation:

Other solution

38.2 X 0.8 = 30.56 (20% off)

30.56 X 0.9 = 27.504 (Another 10% off)

Answer:

x | -3  -2  -1   0  1

y | 0   -3  -4 -3  0

Step-by-step explanation:

f(x) = x² + 2x - 3

x = -3 then y = (-3)² + 2(-3) - 3 = 9 - 6 - 3 = 3 - 3 = 0

x = -2 then y = (-2)² + 2(-2) - 2 = 4 - 4 - 3 = 0 - 3 = -3

x = -1 then y = (-1)² + 2(-1) - 1 = 1 - 2 - 3 = -1 - 3 = -4

x = 0 then y = (0)² + 2(0) - 3 = 0 + 0 - 3 = 0 - 3 = -3

x = 1 then y = (1)² + 2(1) - 3 = 1 + 2 - 3 = 3 - 3 = 0

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{2\sqrt{6}}{ r} \\\\[-0.35em] ~\dotfill\\\\\ [x-3]^2~~ + ~~[y-(-3)]^2~~ = ~~(2\sqrt{6})^2\implies (x-3)^2+(y+3)^2=24[/tex]

Answer: 9

Step-by-step explanation:

So I will be giving you the formula

[tex]a^{2} +b^{2} =c^{2}[/tex]

This [tex]c^{2}[/tex] is the hypothenuse which is opposite to 90 degrees

ill start from B

so [tex]a^{2}[/tex] and [tex]b^{2}[/tex] can be any side except the side opposite to 90 degrees it shouldn't change.

Answer for B with steps:

=> [tex]11^{2} +13^{2} =c^{2}[/tex]

=>simplify [tex]290=c^{2}[/tex]

=> get square root using your calculator [tex]\sqrt{290} =\sqrt{c^{2}[/tex]

=>the answer to B is 17.0 which is just 17

Answer for C

=>[tex]7^{2} +x^{2} =12^{2}[/tex]

=>[tex]49+x^{2} = 144[/tex]

=> subtract 49 on both sides 95 so its [tex]x^{2} = 95[/tex]

=> take square root [tex]\sqrt{x} ^{2} = \sqrt{95}[/tex]

=> Its 9.7

For the rest of the hard questions you have to know whats width is and height and the properties of rectangles they are very easy

As long as you understand the concept-

follow the steps I provided.

Now

[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{22}{H}=sin77[/tex]

[tex]\\ \rm\Rrightarrow H=22/sin77[/tex]

[tex]\\ \rm\Rrightarrow H=22.59ft\approx 23ft[/tex]

The length of the extension ladder that is against the outside wall of the house is 22.58 feet.

When the ladder lies against a house, a right triangle is formed. The length of the ladder is the hypotenuse. The distance from the base of the ladder to the house is the base. The lenfth off the house is the length.

To find the length of the ladder, Sin would be used:

Sin = opposite / hypotenuse

Sin 77 = 22 / h

h = 22 / 0.9743 = 22.58 feet

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#SPJ2

u can add lines to split the figure into a triangle and two rectangles.

Area of the figure

= (12x15)/2 + 6x4 + 2x5

=124 yd^2

Answer:

z = -4

Step-by-step explanation:

Given :

Solving :

Answer:

You can draw a trapezoid

i hope this helps if you know how to draw the trapezoid you can search on website

Answer:

Pierre has  £ 146 and

Alex has  £ 106

Step-by-step explanation:

Let the money with Pierre be = p

Let the money with Alex = a

If Pierre gave Alex £20, they would have the same amount.

So, we should subtract £ 20 from p and add £ 20 to a

p - 20 = a + 20

     p    = a + 20 + 20

 p    = a + 40 ----------------(I)

If Alex gave Pierre £22, then Pierre would have twice as much as Alex.

p + 22 = 2*(a -22)

 p + 22 = 2a - 44      

         p  = 2a - 44 - 22

         p = 2a - 66

p -2a    = - 66   -----------------(II)

Substitute p = a + 40 in equation (II)

a + 40 - 2a = -66

 a - 2a + 40 = -66

     -a            = - 66 - 40

              -a  = - 106

      Multiply both sides by (-1)

[tex]\boxed{a = \£ \ 106}[/tex]

Substitute a = 106 in equation (I)

p = 106 + 40

[tex]\boxed{p = \£ 146}[/tex]

so hmmm from the equation we can see that is in "x terms" so the independent variable is "x", that tells us the parabola is a vertical one, leading term's coefficient is "2", that means it opens upwards like a bowl.

on a vertical parabola the axis of symmetry is the x-coordinate of its vertex, let's find the vertex of this one.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 12}{2(2)}~~~~ ,~~~~ 4-\cfrac{ (12)^2}{4(2)}\right)\implies \left( -3~~,~~4-\cfrac{144}{8} \right) \\\\\\ (-3~~,~~4-18)\implies (\stackrel{x}{-3}~~,~~-14)~\hfill \stackrel{\textit{axis of symmetry}}{x=-3}[/tex]

The Pythagorean Theorem is used to solve for the hypotenuse of a right triangle.

The formula for solving it is [tex]a^2 + b^2 = c^2[/tex], as a represents one side of the triangle, and b represents the other side. C is the hypotenuse as which we are trying to solve for.

Answer:

My answer is The diameter is 24

Answer:

Northside

Median: 36

Range: 32

IQR: 17

Southside:

Median: 39

Range: 38

IQR: 22

Step-by-step explanation:

Northside first

Order the ages from least to greatest

24, 28, 32, 32, 32, 36, 41, 44, 49, 49, 56

Median is 36 since it's in the middle

Subtract the greatest number from the smallest number to find the range (56-24) = 32

To find the IQR you need the ages least to greatest

24, 28, 32, 32, 32, 36, 41, 44, 49, 49, 56

Find the lower quarter = 32

Find the upper quarter = 49

Subtract 49 and 32 (49-32) = 17

Southside

The Median is the line at the middle of the box, in this case its between 38 and 40 which is 39.

The range is 61 - 23 = 38 (Greatest - least)

The IQR is 52 - 30 = 22

Hope this helps!

[tex]\log_{10} (3y+2) - 1 = \log_{10}(y-4)\\\\\implies \log_{10} (3y+2) - \log_{10} 10 = \log_{10} (y-4)\\\\\implies \log_{10} \left( \dfrac{3y+2}{10} \right) = \log_{10} (y-4)\\\\\implies \dfrac{3y+2}{10} = y-4\\\\\implies 3y+2 = 10y-40\\\\\implies 10y-3y = 40+2\\\\\implies 7y = 42\\\\\implies y = \dfrac{42}7\\\\\implies y = 6[/tex]

Approximately 2 gallons will be needed if each gallon of stain and  the project will cost be $73.96 if  each gallon costs $36.98

The formula for calculating the area of a triangle is expressed as:

A = 0.5bh

where

base = 15feet

height = 20feet

Area of the deck = 20 * 15 * 0.5

Area of the deck is  150 square feet

Number of gallons needed  = 350/150 = 2.3

Hence approximately 2 gallons will be needed if each gallon of stain covers a maximum of 350 square feet.

Cost of the two gallons  = 36.98 * 2

Cost of the two gallons  = $73.96

Hence the project will cost be $73.96 if  each gallon costs $36.98

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

Explanation:

For any parallelogram, the opposite sides are parallel and are the same length.

AB = CD

9x+2 = 12x-4

2+4 = 12x-9x

6 = 3x

x = 6/3

x = 2

Which leads to

Side AD is opposite BC, so AD = BC = 9

Answer:

2001-2003

Step-by-step explanation:

This because the trend is almost the same in these yrs

Answer:

146 m²

Area of triangle:

Area of upper rectangle:

Area of bottom rectangle:

Total area:

Answer:

146 m²

Step-by-step explanation:

Divide the figure into a triangle and 2 rectangles (see attached diagram)

Formulae

Triangle 1

⇒ area = 1/2 x 16 x (6 + 9 - 4 - 4)

            = 1/2 x 16 x 7

            = 56 m²

Rectangle 2

⇒ area = 3 x (6 + 9)

            = 3 x 15

            = 45 m²

Rectangle 3

⇒ area = 5 x 9

            = 45 m²

Total area

⇒ Total area = triangle 1 + rectangle 2 + rectangle 3

                      = 56 + 45 + 45

                      = 146 m²