Simplify (4x + 12) - (6x - 18)

Answer:

see explanation

Step-by-step explanation:

The vertex form of f(x) is

f(x) = (x - h)² + k

where (h, k) are the coordinates of the vertex

To obtain this form use the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 14x

f(x) = x² + 2(7)x + 49 - 49 + 36

     = (x + 7)² - 13

The minimum value of f(x) is the y- coordinate of the vertex

vertex = (- 7, - 13), that is minimum value = - 13

The vertex form of the function f(x)=x²+14x+36 is (x + 7)² - 13, with the vertex at (-7, -13). The minimum value of f(x) is -13.

To convert the function f(x) = x²+ 14x + 36 into vertex form, we need to complete the square. First, factor out the coefficient of the x² term if it is not 1 (in this case it is 1, so no factoring is necessary), and then group the x terms.

f(x) = (x²+ 14x) + 36

Add and subtract the square of half of the coefficient in front of x within the parenthesis to complete the square:

f(x) = (x² + 14x + 49) - 49 + 36

Simplify:

f(x) = (x + 7)² - 13

Now the function is in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex. Here, the vertex is at (-7, -13).

The minimum value of the function f(x) occurs at the vertex since the coefficient of the x² term is positive, indicating a parabolic shape opening upwards. Therefore, the minimum value of f(x) is -13.

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For this case we have:

[tex]3 \frac {8} {9} = \frac {27 + 8} {9} = \frac {35} {9} = 3.8888[/tex]

Round the nearest whole, that is, to 4.

[tex]2 \frac {5} {6} = \frac {12 + 5} {6} = \frac {17} {6} = 2.8333[/tex]

Round the nearest whole, that is, to 3.

So, rewriting we have:

[tex]4 + 3 = 7[/tex]

ANswer:

[tex]3 \frac {8} {9} +2 \frac {5} {6} = 7[/tex]

Remember that a complex number has the form a + bi. You need to figure out what a and b need to be. Since −3i is an imaginary number, it is the imaginary part (bi) of the complex number a + bi. This imaginary number has no real parts, so the value of a is 0.

ANSWER

Yes

EXPLANATION

The number

[tex]3i[/tex]

can be rewritten as

[tex]0 + 3i[/tex]This is of ty form

[tex]z = a + bi[/tex]

where 0 is the real part and 3i is the imaginary or complex part.

[tex]3i[/tex]

is therefore a complex number. It is purely imaginary because the real part is zero.

Answer:

the answer is anything less than 24

Step-by-step explanation:

[tex]x - 9 < 15 = x - 9 + 9 < 15 + 9[/tex]

[tex] \times < 24[/tex]

Answer:

Yes, the answer provided is correct.

Step-by-step explanation:

Angles TRV and SRW are vertical angles, so they are the same value.

Answer:

hi so finding the volume you need to do

pi times R² times height

Step-by-step explanation:

hopes this will help u  outttttt

Answer:

y=8x-3

Step-by-step explanation:

Answer:

Not safe

Step-by-step explanation:

Using the sine ratio in the right triangle

let the angle be x, then

sinx° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{16.5}{17}[/tex]

x = [tex]sin^{-1}[/tex] ([tex]\frac{16.5}{17}[/tex] ) ≈ 76.1°

Since 76.1° > 70° then not safe at this height

Answer: OPTION C.

Step-by-step explanation:

Given a function f(x), the range of the inverse of f(x) will be the domain of the function f(x) and the range of the domain of f(x) will be the range of the inverse function.

For example, if the point (2,1) belongs to f(x), then the point (1,2) belongs to the inverse of f(x).

Observe that in the graph of the function f(x) the point (-3,1) belongs to the function, then the point (1,-3) must belong to the inverse function.

Therefore, you need to search the option that shown the graph wich contains the point (1,-3).

Observe that the Domain f(x) is (-∞,0) then the range of the inverse function must be (-∞,0).

This is the graph of the option C.

Answer:

[tex]A=376.99\ units^2[/tex]

Step-by-step explanation:

By definition, the surface area of a cylinder is given by the following formula:

[tex]A = 2\pi r h + 2\pi r ^ 2[/tex]

Where r is the radius and h is the height.

In this case, we have to:

[tex]r = 4\\\\h = 11[/tex]

then the surface area is:

[tex]A = 2\pi(4)(11) + 2\pi(4) ^ 2[/tex]

[tex]A=120\pi[/tex]

[tex]A=376.99\ units^2[/tex]

120pi units^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Look at the picture.

It's a net of right rectangular prism.

We have three pairs of rectangles:

7ft × 8ft

7ft × 18ft

8ft × 18ft

The formula of an area of a rectangle l × w:

A = lw

Calculate the areas:

A₁ = (7)(8) = 56 ft²

A₂ = (7)(18) = 126 ft²

A₃ = (8)(18) = 144 ft²

The Surface Area :

S.A. = 2A₁ + 2A₂ + 2A₃

Substitute:

S.A. = 2(56) + 2(126) + 2(144) = 652 ft²

Answer:

17.4 i believe

Step-by-step explanation:

Answer:

The answer would be B. decrease the temperature by 2 degrees Celsius.

Step-by-step explanation:

Since 2°C - 2°C= 0, then you would obviously have to subtract to find your answer.

Answer:

B

Step-by-step explanation:

The angle of 110° and the angle labelled as 1 form 180°, so we have

[tex]<1> = 180-110=70[/tex]

The same holds for the angle labelled 2 and the 115° angle:

[tex]<2> = 180-115=65[/tex]

Angle 1, 2 and 7 are the interior angles of a triangle, so they sum to 180. We can deduce

[tex]<7> = 180-70-65=45[/tex]

Angles 5 and 7 are corresponding angles, so they have the same measure.

[tex]\bf (\stackrel{x_1}{t}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{-10}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-7}{-10-t}=\stackrel{\stackrel{slope}{\downarrow }}{9}\implies \cfrac{-9}{-10-t}=9 \\\\\\ -9=-90-9t\implies 81=-9t\implies \cfrac{81}{-9}=t\implies -9=t[/tex]

T=-9 and the work is there

If you have any questions about what I did

Hope this helps.if it does please mark brainliest

Answer:

[tex]x=44[/tex]

Step-by-step explanation:

[tex]\frac{x}{4}+4=15 \\ \\ \frac{x}{4}=11 \\ \\ x=44[/tex]

Answer:

C. 0.8125

Step-by-step explanation:

The probability to sell 5 or more DVDs in a day is the complement of the probability of selling less than 5 DVDs in a day, since sales <5 DVDs + sales >= 5 DVDs = 100% of the sales.

So, we know what's the probability of selling less than 5 DVDs in a day is... it's 0.1875

So, to find the possibility of selling 5 or more DVDs in a day, we take 100% of the chances (1.0) and we subtract the probability of selling <5 DVDs in a day:

P = 1.0 - 0.1875 = 0.8125

C. 0.8125 is your answer.

Ok, so equation for this would be 2x-35=9, 2x because its twice a number, x. 35 because it is taking off of 35. 9 because the grand total is 9.

2x-35=9 First add 35 to 9

2x=44 Then divide 44 by 9

x= approximately 4.9 

His sister is 8 and he is 20.

let's say z represents liz. we can make an equation where z+12=4z.

Solve for that and z is equal to 4. Now that was 4 years ago. She should be 8 now?

I hope this is correct because my brain isn't doing so well today.

Answer:

Adam is 20 years old and Liz is 8 years old.

Step-by-step explanation:

Let present age of Adam = x years

Let present age of Liz = y years

Now we will make the equations.

x = y + 12 -------------(1)

For second equation

( x-4) = (y-4) × 4

x-4 = 4y - 16

x = 4y + 4 - 16

x = 4y - 12 -----------------(2)

By substitution method, we  substitute  the value of  x  from equations (1) to equation (2).

y + 12 = 4y - 12

y - 4y + 12 = -12

-3y = -12 -12

3y = 24

y = 8

Now we put the value of y in equation (1)

x = 8 + 12 = 20

Therefore, Adam is 20 years old and Liz is 8 years old.

Answer:

Depends

Step-by-step explanation:

Depends on how many questions you missed. I'm going to assume that you mean you somehow missed every question. So, 86% - 25% would be 46%.

You must use Pythagorean theorem, which is [tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are both legs (the two legs are the sides that form a perpendicular right angle) while c is the hypotenuse (side opposite the right angle)

In this case...

a = y

b = 8

c = 12

^^^Plug these numbers into Pythagorean theorem

[tex]y^{2} +8^{2} =12^{2}[/tex]

Simplify as much as possible

[tex]y^{2}[/tex] + 64 = 144

Isolate y by subtracting 64 to both sides

[tex]y^{2}[/tex] + (64 - 64) = 144 - 64

[tex]y^{2}[/tex] = 80

Further isolate y by taking the square root of both sides. This will take away the square from the left side

y = [tex]\sqrt{80}[/tex]

[tex]\sqrt{80}[/tex] <<< Can be further simplified

4√5 = y

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

C. [tex]f(x)=\sqrt[3]{-x} -1[/tex]

Step-by-step explanation:

Consider graph of the parent function (red curve in attached diagram)

[tex]g(x)=\sqrt[3]{x}[/tex]

First, multiply it by -1 to get function

[tex]h(x)=-\sqrt[3]{x}[/tex]

Then translate the graph of the function h(x) 1 unit down, then you'll get the function

[tex]f(x)=-\sqrt[3]{x} -1\\ \\ \text{or}\\ \\f(x)=\sqrt[3]{-x} -1[/tex]

The graph of the function f(x) is represented by the blue curve in attached diagram

-Hello There-

ANSWER: 10 Is 40% Of 25

EXPLANATION

What is 40% of 25?

Y is 40% of 25

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 40% * 25

Converting percent to decimal:

p = 40%/100 = 0.4

Y = 0.4 * 25

Y = 10

Have A Great Day!

Be Safe,

TheBlueFox

Answer: 15 ounces

Step-by-step explanation:

We need to find the unit rate for each of the prices/ounces,

0.89/10 = 0.089

1.29/15 = 0.086

2.26/18 = 0.125...

3.39/32 = 0.1059375

The answer is:

B. 15 ounces

Because the unit rate(cost per ounce) is 0.086 cents per ounce which is less than:

A. 0.086

C. 0.126

D. 0.106

Answer:

The area of rectangle C is 2

Step-by-step explanation:

Using a scale factor of [tex]\frac{1}{5}[/tex] yields the side lengths of 1 and 2

[tex](1)(2)=2[/tex]

Answer:

2 square units

Step-by-step explanation:

hello

The scale factor or linear scale factor is the ratio between the length of the same side in two similar figures.

in the graph we have  a rectangle with width 5 units and long 10 units, and we know the scale factor is 1/5

[tex]S_{f}=\frac{width(C)}{width(B)}\\ \\Width(B)*S_{f} =width(C)=5 units *\frac{1}{5} \\\\Width(C) =\frac{5}{5} units =1 unit[/tex]

[tex]S_{f} =\frac{length (C)}{length(B)} \\\\\\length(C)=length(B)*S_{f}\\length(C)=(10*\frac{1}{5})[/tex]

[tex]Length(C) =2 units\\\\ the area is A=w*l\\\\A=1 unit * 2 units\\\\\\[/tex]

A=2 square units

I hope it helps

Answer:

22.5 lbs

Step-by-step explanation:

First you find the cubic feet. That is the volume of the object which is length*width*height.

In your example, they are using inches. So you have to convert all units to feet. That would be 0.5 inches, 0.5 inches, and 5/3 inches. The volume would be 0.5*0.5*5/3 which is about 5/12 cubic feet

You then take that 5/12 cubic feet and multiply it by the 54 lbs/cubic foot. The answer would be 22.5 lbs

Answer:

42.5%

Step-by-step explanation:

Answer:

42.5

Step-by-step explanation:

34/80×100/1

=340/8

=42.5

Answer:

Two solutions.

Answer:

Step-by-step explanation: if she runs 1 lap in 6 minutes, divide 66 by 6 to find how many laps she runs. this is 11. 11 is the minimum amount of laps that she runs.

n≥11

Answer:

11 ≤ n

Explanation:

[tex] \frac{66}{6} = 11[/tex]

More than indicates the minimum value, so you use the greater than or equal to.

The above answer is written in reverse, which the exact same result.

I am joyous to assist you anytime.