Rewrite the function by completing the square. g(x)= x^2 + 15x +54
(24 POINTS)

Answer:

NUMBER3

Step-by-step explanation:

Table no 3 is representing here a non-linear function.

A nonlinear function, as its name suggests, is a function that is not linear. In other words, the graph of a nonlinear function is not a line, its graph can be anything other than a line

Since a nonlinear function is a function that is not a linear, its equation can be anything that is not of the form f(x) = ax+ b. One examples of nonlinear functions is, f(x) = x2 is nonlinear as it is a quadratic function.

The right answer is option 3.

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Answer:

The statement -11 is greater than -3, so it was colder in Milwaukee is true.

Answer:

-11 is greater than -3, so it was colder in Milwaukee.

Step-by-step explanation:

Answer 1 (-11 is greater than -3, so it was colder in Chicago) is incorrect because it was -3 in Chicago, not -11.

Answer 2 (-3 is greater than -11, so it was colder in Chicago) is incorrect because -3 is not greater than -11.

Answer 3 is correct because -11 is greater than -3 and the cities are labeled correctly.

Answer 4 (-3 is greater than -11, so it was colder in Milwaukee) is incorrect because -3 is not greater than -11. Milwaukee was also -11, not -3.

I hope this helps!

Answer:

Step-by-step explanation:

The equation of a circle in the standard form:

[tex](a-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (-7, -3) and the radius r = 2. Substitute:

[tex](x-(-7))^2+(y-(-3))^2=2^2\\\\(x+7)^2+(y+3)^2=4[/tex]

Probably to get a 4 or 1,3,5,7,8 so is the probability of getting 1,3,4,5,7,8 so answer is 6/10=3/5

Answer:

6/10 or 0.6 or 60%

Step-by-step explanation:

The options for numbers are 1,2,3,4,5,6,7,8,9,and 10. There are 5 odd numbers from 1-10, 1,3,5,7, and 9. This woud be 50/50 odds. If you add four as an option, there would be 6 numbers, 1,3,4,5,7, and 9. the odds would be 6/10 which would be 60%.

well, she knows that the mass of chocolate is 1.8 times that of powered sugar.

it just so happen that powered sugar is 100 grams for one cup, and since chocolate is 1.8 times "that", then in one cup of chocolate there must be 1.8 times 100 grams, or 1.8*100 = 180 grams.

the recipe uses 1/2 cup of chocolate, well, half a cup of chocolate, namely half of 180 grams is just 90 grams.

Answer: [tex]\bold{C)\quad y=2sin(x+\dfrac{3\pi}{4})}[/tex]

Step-by-step explanation:

A sin graph is a cosine graph shifted to the left [tex]\dfrac{\pi}{2}[/tex] units.

[tex]y=2cos(x + \dfrac{\pi}{4})\qquad \implies y=2sin(x+\dfrac{\pi}{4}+\dfrac{\pi}{2})\\\\\\.\qquad \qquad \qquad \qquad \quad \implies \large\boxed{y=2sin(x+\dfrac{3\pi}{4})}[/tex]

I actually don't have enough information to complete this question but if you have a positive slope the line goes either up and right or down and left but when it is negative it goes down left or up right.

Answer:

Since theres no graph i cant really explain it to you. What i do know is that on TTM the answer would be (1,2)

Step-by-step explanation:

Answer:

volume=240

height=9.6

width=3

height=2.5

length=7

Step-by-step explanation:

the formula for colume of prism is area of teh base times the heigth so

the first one is 6*5(8)=240

the next one you wouold solve for height so 4.5 tims 5 times x(height)= 2.6

height equals 9.6

the next one solve for width so 3*x*3=27

width is 3

the next one you solve for height so 2.5*8.4*x=52.5

the height is 2.5

the last one you solve for length so x*7*7=343

length equals 7

Answer:  -2

Step-by-step explanation:

f(-5)  - (-5) - 7

+5 -7

-2

Answer:

-2

Step-by-step explanation:

=-(-5)-7

Answer: B) A = 750(1.04)ⁿ

Step-by-step explanation:

The formula for compounded annually is: A = P(1 + r)ⁿ   where

A = 750(1 + 0.04)ⁿ

  = 750(1.04)ⁿ

Answer:

Juice, Juice, and no association

Step-by-step explanation:

Answer:

y=x+6

Step-by-step explanation:

If you need to find a standard linear equation from two points, you have to first find the slope, then find the y intercept.

To find the slope, you should do the change in y over the change in x.

that would be:

(4-9)/(-2-3)

(-5)/(-5)

the slope is 1

plug that in along with values of x and y taken from known point (3,9) to the standard equation of a linear relationship:

y=mx+b

m=1

y=9

x=3

b=?

9=(1)(3)+b

9=3+b

b=6

The equation of the line would be y=x+6

Answer:

x - y = - 6

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (3, 9)

m = [tex]\frac{9-4}{3+2}[/tex] = [tex]\frac{5}{5}[/tex] = 1, hence

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 9), then

9 = 3 + c ⇒ c = 9 - 3 = 6

y = x + 6 ← equation in slope- intercept form

Subtract y from both sides

0 = x - y + 6 ( subtract 6 from both sides )

- 6 = x - y, thus

x - y = - 6 ← in standard form

Answer:

b.  27,405

Step-by-step explanation:

So, we have a total population of 30 (n) and we sample 4 (r) from it.

Now, is it a combination or a permutation?  Does the order matter?  Is it important that the teacher picked John before Andrew?  No.  So, it's a combination:

C(n,r)=C(30,4)

[tex]C(30,4) = \frac{30!}{4| (30-4)!} = 27405[/tex]

So, the teacher has 27,405 ways to combine groups of 4 students from his 30-student class.

Answer:

A

Step-by-step explanation:

27,405

Answer:

1/4 is the original length

Step-by-step explanation:

The original length of the rectangle is 11/72 square feet. To get the area of a rectangle, you multiply the length x width.

You already know the width in this problem. The width is 1/6 feet. So, divide the area (11/72 feet) by the width (1/6 feet) to get the length, 11/12 feet.

However, the original length was increased by 2/3 feet. So, take our new length (11/12 feet) and subtract the increased length (2/3 feet) from it. When you do that, you get 1/4 feet.

Therefore, the answer is 1/4 feet. Hope this helps! :)

ANSWER

The water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.

EXPLANATION

The water arc is modeled by the function:

[tex]y = - 0.006 {x}^{2} + 1.2x + 10[/tex]

We write this function in vertex form:

[tex]y = - 0.006 ({x}^{2} - 200x )+ 10[/tex]

[tex]y = - 0.006 ({x}^{2} - 200x + ( - 100)^{2} ) - - 0.006( - 100)^{2} + 10[/tex]

[tex]y = - 0.006 ( x- 100)^{2} ) + 60+ 10[/tex]

[tex]y = - 0.006 ( x- 100)^{2} ) +70[/tex]

The vertex of this function is at

(100,70).

This means that the water arc reached a height of 50ft.

We put y=50 and solve for x.

[tex]- 0.006 ( x- 100)^{2}+70 = 50[/tex]

[tex]- 0.006 ( x- 100)^{2} = - 20[/tex]

[tex]( x- 100)^{2} = \frac{10000}{3} [/tex]

[tex]x = 100 \pm \frac{100 \sqrt{3} }{3} [/tex]

x=42.3 or x=157.7

Hence the water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.

The water arc does reach a height of 50 feet, and it is about 42.27 feet and 157.73 feet from the north shore when it is 50 feet above the water.

1.Set up the equation:

[tex]\[ -0.006x^2 + 1.2x + 10 = 50 \][/tex]

2. Simplify the equation:

Subtract 50 from both sides:

[tex]\[ -0.006x^2 + 1.2x + 10 - 50 = 0 \] \[ -0.006x^2 + 1.2x - 40 = 0 \][/tex]

3. Solve the quadratic equation:

We can use the quadratic formula

[tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = -0.006 \), \( b = 1.2 \), and \( c = -40 \).[/tex]

[tex]\[ a = -0.006, \quad b = 1.2, \quad c = -40 \][/tex]

[tex]\[ \Delta = b^2 - 4ac \] \[ \Delta = 1.2^2 - 4(-0.006)(-40) \] \[ \Delta = 1.44 - 0.96 \] \[ \Delta = 0.48 \][/tex]

[tex]\[ x = \frac{-b \pm \sqrt{\Delta}}{2a} \] \[ x = \frac{-1.2 \pm \sqrt{0.48}}{2(-0.006)} \][/tex]

Calculate the square root of 0.48:

[tex]\[ \sqrt{0.48} \approx 0.6928 \][/tex]

  Now, find the two values of x:

[tex]\[ x_1 = \frac{-1.2 + 0.6928}{-0.012} = \frac{-0.5072}{-0.012} \approx 42.27 \] \[ x_2 = \frac{-1.2 - 0.6928}{-0.012} = \frac{-1.8928}{-0.012} \approx 157.73 \][/tex]

Therefore, the water arc reaches a height of 50 feet at approximately [tex]\( x = 42.27 \) feet and \( x = 157.73 \)[/tex] feet from the north shore.

Answer:

5/6

Step-by-step explanation:

Answer:

5/6 i think

hope this helps pls if mine is right make it the brainlest thx

Answer:

It is 0

Step-by-step explanation:

Unlike the positive side of the number line which increases its value as it goes up in numbers, the negative side of a number line increases its value as it goes goes down in numbers as the more closer a negative number is to the positive side of infinity, the greater value it has. In this instance, zero is the greater number than -6 and all other negative numbers.

Josef's error will be Josef confused the range and the interquartile range.

The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.

Given that:-

From the given statement we can conclude that Josef confused the range and the interquartile range.

Therefore Josef's error will be Josef confused the range and the interquartile range.

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I am pretty sure 52 degrees

Answer:

the answer is D

Step-by-step explanation:

because the measurements for CAD is 92

Answer:

Step 2 is incorrect

Step-by-step explanation:

Step 2 is incorrect

step 1: 3x + 15 = 2x + 35

step 2: subtract 2x from both sides

           3x + 15 - 2x = 2x + 35 - 2x

          x + 15 = 35

Answer:

Step 2

Step-by-step explanation:

2x was moved to 3x just to add.

It was supposed to be 3x - 2x = x

Hello, I can give you some help w/ steps below! Hope this helps a lot :D

1.

8x < 48 || divide 8 on both sides of the equal sign

x < 6 || final answer, so your correct

2.

10 + x > 23 || subtract 10 on both sides of the equal sign

x > 13 || final answer, so your correct

3.

x - 14 < 28 || add 14 on both signs of the equal sign

x < 42 || final answer

4.

[tex]\frac{y}{21}[/tex] < 3 || multiply 21 on both sides

y < 63 || final answer

5.

2p < 18 || divide 2 on both sides of the equal signs

p < 9 || final answer

6. i have no idea how to do this one, sorry!

The value of x is B. 8.

Answer:

Graph C on edge

Step-by-step explanation:

I Just did the Assignment

The second graph is the graph of logarithmic function

Logarithmic functions are the inverses of exponential functions. The logarithmic function [tex]y=1og_ax[/tex]is defined to be equivalent to the exponential equation [tex]x=a^y[/tex].

The logarithmic function is similar in shape to the square root function. To graph a logarithmic function it is better to convert the equation to its exponential form.

The second graph is the graph of logarithmic function

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So , at first we should calculate the power because in calculating order we have:

first power or radical

then multiply or division

then + or -

so according to the rules we must do:

1)(x-3)^2=x^2 -6x +9

2)5(x^2 -6x +9)=5x^2 -30x +45

3)then -6 and we have:

Y=5x^2 -30x +39

The last one is the true statement

Correct option: 2. The only true statement is -2 4/9 > -2.6.

To determine which statement is true, let's compare the given pairs of numbers:

The correct statement among the options is option 2. -2 4/9 > -2.6.

Complete Question:

Which statement is true?

Answer:

composite number

Step-by-step explanation:

Answer:

s = ∛2560

Step-by-step explanation:

The volume of a cube is found by V = s³. To solve for the side of a cube with a specific volume, we use inverse operations to find it. s = ∛V. If the volume is 2560 then the s = ∛2560.

Answer:

it's the last one

Step-by-step explanation:

I took the K12 test

1. From the given right-triangle, the side opposite to [tex]\theta[/tex] is 6.8 units.

The adjacent side to [tex]\theta[/tex] is 4 units.

Recall the mnemonics, SOH-CAH-TOA.

We use the tangent ratio to obtain:

[tex]\tan \theta=\frac{Opposite}{Adjacent}[/tex]

[tex]\tan \theta=\frac{4}{6.8}[/tex]

[tex]\tan \theta=\frac{10}{17}[/tex]

[tex]\implies \theta=\tan^{-1}(\frac{10}{17})[/tex]

[tex]\implies \theta=30.5\degree[/tex] to the nearest tenth.

2. This time we were given the hypotenuse to be 15.7 units and the adjacent side is 6 units.

We use the cosine ratio to obtain:

[tex]\cos \theta=\frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos \theta=\frac{6}{15.7}[/tex]

[tex]\cos \theta=\frac{60}{157}[/tex]

[tex]\implies \theta=\cos^{-1}(\frac{60}{157})[/tex]

[tex]\implies \theta=67.5\degree[/tex] to the nearest tenth.

Answer:

25).  55.02°

26).  30.46°

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

To find the answer of question 25

Cos θ = Adjacent side/Hypotenuse

 = 9/15.7 = 0.573

θ = Cos⁻¹(0.573) = 55.02°

To find the answer of question 26

Tan θ = Opposite side/Adjacent side

 = 4/6.8 = 0.588

θ = Tan⁻¹(0.588) = 30.46°

ANSWER

The correct answer is C

EXPLANATION

The given triangle is a right triangle. Since two angles are equal, it is a right isosceles triangle.

This implies that, x=8 units.

Using Pythagoras Theorem,

[tex] {y}^{2} = {8}^{2} + {8}^{2} [/tex]

This implies that:

[tex]{y}^{2} = 64 + 64[/tex]

[tex]{y}^{2} =128[/tex]

Take positive square root,

[tex]{y} = \sqrt{128} [/tex]

[tex]{y} = 8 \sqrt{2} [/tex]

The correct answer is C

Answer:

Correct choice is C. [tex]x=8[/tex], [tex]y=8\sqrt{2}[/tex].

Step-by-step explanation:

Apply formula [tex]\sin\left(\theta\right)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sin\left(45^o\right)=\frac{8}{y}[/tex]

[tex]\frac{1}{\sqrt{2}}=\frac{8}{y}[/tex]

[tex]y=8\sqrt{2}[/tex]

Apply formula [tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]

[tex]\tan\left(45^o\right)=\frac{8}{x}[/tex]

[tex]1=\frac{8}{x}[/tex]

[tex]x=8[/tex]

Hence correct choice is C. [tex]x=8[/tex], [tex]y=8\sqrt{2}[/tex].

do u have the answer