The function fis defined as follows.
f(x)=2x²+3
If the graph of fis translated vertically downward by 6 units, it becomes the graph of a function g.
Find the expression for g(x).

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 45}}{\left( \cfrac{30}{100} \right)45}\implies 13.5~\hfill \underset{final~cost}{\stackrel{45~~ - ~~13.5}{31.5}}[/tex]

Answer:

f(-2)=4

Step-by-step explanation:

put -2 where x is

f(x)=2x²+x-2

f(-2)=2(-2)²+(-2)-2

f(-2)=(2*4)-4

f(-2)=8-4

f(-2)=4

Answer:

27 Units

Step-by-step explanation:

To find the distance using x and y components, use the Pythagorean theory [tex]a^2 + b^2 = c^2[/tex]. Set a as your x-coordinate and b as your y-coordinate (although you can flip them if you so desire). The result will you the square of your distance, so take the square root.

Alternatively, we can solve for C and find that [tex]c = \sqrt{a^2 + b^2}[/tex] or in this case [tex]distance = \sqrt{-25^2 + 10^2}[/tex].

This shows us that distance = 26.93 which is close enough to 27.

For more information: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem

Answer:

2?

Step-by-step explanation:

2 is the square root of 4 since 2×2=4

Answer:

2

4

Step-by-step explanation:

Because 2 × 2 = 4, we know that 2 is the square root of 4.

√4 = 2

it will print no, because B = 3 and not 2 so it will skip the print yes line.

Answer:

x = 16

Step-by-step explanation:

 SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.

The angles opposite to equal sides are equal.

  ⇒  ∠STR  = ∠R

       ∠STR = 4x - 28

Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair

∠STR + ∠STU = 180°    {linear pair}

4x - 28 + 9x = 180

4x + 9x - 28  = 180      {Combine like terms}

       13x- 28 = 180

Add 28 to both the sides

          13x    = 180 + 28

           13x  = 208

Divide both sides by 13

              x = 208/13

  [tex]\sf \boxed{x = 16}[/tex]

Answer:

x = 16

Step-by-step explanation:

since SR = ST , then Δ RST is isosceles with the 2 base angles congruent.

∠ STR = ∠ SRT = 4x - 28

∠ STR and ∠ STU are a linear pair and sum to 180° , that is

9x + 4x - 28 = 180

13x - 28 = 180 ( add 28 to both sides )

13x = 208 ( divide both sides by 13 )

x = 16

The equivalent expression of 2(3x+5)+4(2x-1) is 2(7x + 3)

The expression is given as:

2(3x+5)+4(2x-1)

Open the brackets

6x + 10 + 8x - 4

Evaluate the like terms

14x + 6

Factor out 2

2(7x + 3)

Hence, the equivalent expression of 2(3x+5)+4(2x-1) is 2(7x + 3)

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     If the question should read as the following, then I hope my answer will help;       -3 +7 _ -10 - 2

Answer: A. >

Step-by-step explanation:

  Given:

-3 + 7 _ -10 - 2

  Simplify both sides by combining like terms:

4 _ -12

  Compare, knowing that 4 is greater than -12:

4 _ -12

4 > -12

             A. >

Answer:

I think it's letter C.

Step-by-step explanation:

not sure correct me if I'm wrong.

We are going to multiply the fraction 1/2, to the power of 3.

This means that:

Therefore:

[tex]\bf{\left(\dfrac{1}{2}\right)^{3}=\dfrac{1\times1\times1}{2\times2\times2}=\dfrac{1}{8} }[/tex]

Therefore, the answer of the fraction (1/2)^3, is equal to 1/8.

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

Answer:y=-7

Step-by-step explanation:

When x=-4 then y=4 and if x=7 then y=-7

Because y=-x

[tex]\begin{array}{r|l}576&2\\288&2\\144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}[/tex]

[tex]576=2^6\cdot3^2[/tex]

Therefore

[tex]4\sqrt{576}=4\sqrt{2^6\cdot3^2}[/tex]

Answer: B

Step-by-step explanation:

The angles add to 90 degrees if they are complementary, so:

[tex]x-2+2x+5=90\\3x+3=90\\3x=87\\x=29[/tex]

So, the angles measure 29-2=27 degrees and 2(29)+5=63 degrees.

The function of the graph is y = 4(3)^x

The graph is an exponential function with the following points

(x,y)= (0,4) and (1,12)

An exponential function is represented as:

y = ab^x

Substitute (0,4) in the equation

4 = a * b^0

a = 4

Substitute a = 4 in y = ab^x

y = 4b^x

Substitute (1,12) in the equation

12 = 4b^1

12 = 4b

Divide by 4

b = 3

Substitute b = 3 in y = 4b^x

y = 4(3)^x

Hence, the function of the graph is y = 4(3)^x

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Answer:

Look at the equations:

y

=

−

9

x

−

21

and

y

=

5

x

+

7

Because both equations equal (y), they both equal the same.

If an equations says "

y

=

−

9

x

−

21

" , that means we can replace (y) with

−

9

x

−

21

.

Therefore when i take the equation:

y

=

5

x

+

7

, we can replace (y) to get:

−

9

x

−

21

=

5

x

+

7

Now isolate (x):

−

9

x

−

21

=

5

x

+

7

⇔

−

21

=

14

x

+

7

⇔

−

28

=

14

x

⇔

x

=

−

2

Answer:

534

Step-by-step explanation:

The length of the arc of the circle will be 19.8 ft.

The arc of the circle is the distance of the circumference of the circle formed sector of the circle at a particular angle.

The formula for the length of the arc of the circle will be given as:-

Arc = Angle x radius

We have Angle = 1.1 radians Radius = 18ft

Arc = 1.1 x 18

Arc = 19.8 ft.

Therefore the length of the arc of the circle will be 19.8 ft.

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The value of y from the given trig expression is pi/3 rad

These identities are expressed in terms of sine, cosine and tangent

Given the expression

[tex]sin(x+y)=\frac{1}{2}sinx+\frac{\sqrt{3}}{2} cosx[/tex]

Expand sin(x+y)

sin(x+y) = sinxcosy + cosxsiny

Compare both equations

cosy = 1/2

y = arccos(1/2)

y = 60 degrees

y = pi/3 rad

Hence the value of y from the given trig expression is pi/3 rad

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Answer:

The answer is pi/4

When you input all the other values into the equation, they aren't true. When you input pi/4 the equation is true.

The angle of depression of the airplane is 39.8°, length of the runway is 45794 ft, and approximate height of the tower is 321 m.

The angle of depression of the airplane is given as follows:

Let the angle of depression be A.

[tex]A= {tan}^{ - 1} ( \frac{15000}{8000} ) = {39.8}^{o} [/tex]

Angle of depression is 39.8°.

If the angle of elevation is 6.8°, the length of the runway l is calculated thus:

horizontal distance of airplane from end of runway = d

length of runway, L = d - 80000 ft

[tex]d = \frac{15000}{tan 6.8°} = 125794 ft[/tex]

L = 125794 - 80000

L = 45794 ft

The length of the runway is 45794 ft

2. Let the height of the tower be H

[tex]H = \tan(69.8) \times 118 = 321m[/tex]

The approximate height of the tower is 321 m

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Answer:

x<_-5

Step-by-step explanation:

-4(x+3)<_-2-2x

-4x-12<_-2-2x

-4x+2x<_-2+12

-2x<_10

-2x/-2<_10/-2

x<_-5

Answer:

D. f(x) = -|x+4| +3

The graph is flipped over the x-axis (facing down) so there's a negative sign in front of the function. It's shifted to the left 4 units so it'll be |x+4|. Finally, it's shifted up 3 units so it'll be +3 outside of the absolute bracket.

NOTE: if there's a change to the x value then it's inside the bracket or parenthesis, if there's a change to the y value then it's outside of the bracket or parenthesis

Answer:

[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 307.7 \: m {}^{3} } ( \rm \: nearest \: tenth )[/tex]

Step-by-step explanation:

Given:

To Find:

Solution:

Use the formulae of the volume of cylinder:

[tex] \boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}[/tex]

where,

According to the question:

Substitute the values onto the formulae in order to find out the volume:

[tex] \rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} (2)[/tex]

[tex] \rm \: Volume_{(Cylinder)} = \pi(49)(2)[/tex]

[tex]\rm \: Volume_{(Cylinder)} = 98\pi[/tex]

[tex]\rm \: Volume_{(Cylinder)} = \: 98 \times 3.14[/tex]

[tex]\rm \: Volume_{(Cylinder)} = 307.72 \: m {}^{3} \: (exact \: form)[/tex]

[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 307.7 \: m {}^{3} } \: ( \rm nearest \: tenth )[/tex]

Hence,we can conclude that:

The volume of the cylinder is approximately

307.7m³.

Answer: 25x^2+15x-4

Step-by-step explanation:

Multply 5x by the other 5x

25x^2

Multiply 5x by 4

20x

Multiply -1 by 5x

-5x

Multiply -1 by 4

-4

Add them together

25x^2+20x-5x-4

Combine like terms

20x-5x=15x

25x^2+15x-4

the length of the bottom side is 17-3 = 10

to be a square all sides need to be 10 units.

A(7,13)

B (17,13)

Answer:

  (a)  The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread

Step-by-step explanation:

The equation for exponential growth can be written in the form ...

  f(t) = a·b^t

where a is the initial value, and b is the growth factor for time period t. The growth factor is related to the growth rate by ...

  b = 1 +r . . . . . where r is the growth rate in time period t

__

The equation for the area of mold on the banana bread is given as ...

  B(t) = 20·1.06^t

Comparing to our generic equation, we see ...

The growth rate of the mold on the banana bread is given as 0.06 = 6% per week.

__

We are given some values of t and area that we can use to find the growth rate of mold on the whole wheat bread.

  W(1) = 40.8 = a·b^1

  W(4) = 43.30 = a·b^4

The ratio is ...

  W(4)/W(1) = (a·b^4)/(a·b^1) = b^3 = 43.30/40.8

Then the value of b can be found to be ...

  b = ∛(43.30/40.8) ≈ 1.02002 ≈ 1 + 0.02

The growth rate of mold on the whole wheat bread is about 0.02 = 2% per week.

__

The mold growth rate on the banana bread compared to that on the whole wheat bread is ...

  (banana bread growth rate)/(whole wheat bread growth rate) = 6%/2% = 3

We can conclude ...

  The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread

Answer:

54 refrigerators

Step-by-step explanation:

In order to find the amount of refrigerators this month, we can do it in one of 2 ways.

The easier way is to multiply 45 by 1.20:

(45)(1.20) = 54

1.20 represents a 120%. This is because 45 refrigerators is 100% of last month, and Simon repaired 20% more, so 100 + 20 = 120.

The next way would be to multiply 45 by 0.20, and then add it to 45.

(45)(0.20) = 9

45 + 9 = 54

Both of the ways result in 54. So, Simon repaired 54 refrigerators this month.

Hope this helps! If you have any questions about my work, please let me know in the comments below!

Answer:

permutation is multiplying numbers from the number given to its last end. so that 9*8*7*6*5*4*3*2*1=is answer. thesame for 12!

Answer:

9! = 362,880

12!=479,001,600

Step-by-step explanation:

the symbol ! simply means factorial

9! = 9×8×7×6×5×4×3×2×1= 362,880

12! = 12×11×10×9×8×7×6×5×4×3×2×1=479,001,600

Answer:

Step-by-step explanation:

D²=290²+2030²

=290²+(290×7)²

=290²+290²×7²

=290²(1+7²)

=290²(1+49)

=290²×50

=290²×25×2

=290²×5²×2

D=290×5×√2

D=1450√2

Answer:

2 points are solutions

Step-by-step explanation:

A solution is a value that makes the equation true, meaning the points fall on the line. For example, the point (0,1) is on the line, which means that for the equation, when x=0, y=1. This also applies for a second point, which is about (-3.5,-1.5).

Hope this helps! :)