What was done to the linear parent function f(X) = x to get the function g(x) = 1/5x

A. Horizontally compressed by a factor of 5
B. Vertically stretched by a factor of 5
C. Shifted 1/5 unit up
D. Vertically compressed by a factor of 5

Answer:

[tex]\boxed{\text{b. \$1845 a month}}[/tex]

Step-by-step explanation:

   Amount if retired at 66 = $2460/mo

Less 25 % = 0.25 × 2460 =    -615

   Amount if retired at 62 = $1845/mo

John would receive [tex]\boxed{\text{\$1845/mo}}[/tex] if he retired at 62.

Answer:

Step-by-step explanation:

A=BH/2

A=9x12/2

A=54

Answer: 54

Step-by-step explanation:

A = base * height ÷ 2

A = 12 * 9 ÷ 2

A = 108 ÷ 2

A = 54

Answer:

60

Step-by-step explanation:

(This is not how teachers usually teach you)

First i divided 36 by 2 to get 30% = 18 then i multiplied 30% by 3.3333etc. to get 100% and i multiplied 18 by the same number (18*3.3333 = 60) and i got 60.

Answer:

Step-by-step explanation:

Givens

To find the regular price for tickets, we can use the rule of three.

If $36 represents 60%, how much would represents 100%?

[tex]x=100\% \frac{\$36}{60\%} = \$60[/tex]

Therefore, the cost of a regular price ticket is $60.

Answer:

x must be 5

Step-by-step explanation:

Recall that the area formula for a trapezoid is

A = (average of base lengths)(width)

Here we have

                                                                   17 cm + x

      (average of base lengths) = 11 cm = ----------------

                                                                           2

So 2(11 cm) = 17 cm + x, or

      22 cm = 17 cm + x

Then x must be 5.

To find the length of the other base of the trapezoid with a midsegment of 11 cm and one base of 17 cm, use the average property of the midsegment. The calculation reveals the other base is 5 cm in length.

The question is about finding the length of the other base of a trapezoid when the length of the midsegment and one of the bases is known. The midsegment of a trapezoid is parallel and equal to the average of the two bases. Therefore, if the midsegment is 11 cm and one base is 17 cm, the other base can be found by setting up the equation:

Midsegment = (Base1 + Base2) / 2

Substitute the known values:

11 = (17 + Base2) / 2

Multiplying both sides by 2 gives:

22 = 17 + Base2

Subtracting 17 from both sides gives:

Base2 = 22 - 17

Base2 = 5

Thus, the length of the other base of the trapezoid is 5 cm.

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Check the picture below.

so, the triangular prism is really 2 triangles and 3 rectangles stacked up to each other at the edges.  Let's simply get the area of each shape and sum them up, and that's the area of the prism.

[tex]\bf \stackrel{\textit{two triangles}}{2\left[ \cfrac{1}{2}(\stackrel{base}{6})(\stackrel{height}{5.2}) \right]}+\stackrel{\textit{right-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{left-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{base rectangle}}{(8\cdot 6)} \\\\\\ 31.2+48+48+48\implies 175.2[/tex]

Answer:

The surface area = 175.2 mm²

Step-by-step explanation:

Formula:-

Area of rectangle = lb

Area of triangle = bh/2

It is given a triangular prism.

To find the surface area

Surface area = 3 Rectangle area + 2 triangle area

Rectangle area = 3 * lb

 = 3 * 8 * 6

 = 144  mm²

Triangle area  = 2 * bh/2 = bh

  = 6 * 5.2 = 31.2²

Total area = 144 + 31.2 = 175.2 mm²

Answer:

Quadrant II

Step-by-step explanation:

I attached an image of the quadrants system.

You'll see that the scenario where we have a point with a negative X value and a positive Y value, it belongs to Quadrant II.

Quadrant I

Degrees: 0-90

X values: positive (+)

Y values: positive (+)

Quadrant II

Degrees: 90-180

X values: negative (-)

Y values: positive (+)

Quadrant III

Degrees: 180-270

X values: negative (-)

Y values: negative (-)

Quadrant IV

Degrees: 270-360

X values: positive (+)

Y values: negative (-)

Answer:

It would be 139$

Step-by-step explanation:

In order to find a percent of a value you first move the decimal place over 2 to the left or divide by 100(percentage is no longer there). In this case it would be .20. You multiply that with the total number(695) and the product is your answer.

Answer:

A

Step-by-step explanation:

Taking the square root of both sides, you get

[tex]\sqrt{x^2} = \pm\sqrt{180}[/tex]

which simplifies to

[tex]x = \pm\sqrt{180}[/tex]

The square root of 180 is approximately 13.42 and since it is the plus or minus square root, the answer is A, -13.42, 13.42.

Final answer:

The equation x²=180 is solved by taking the square root of both sides, yielding two solutions: x = 13.42 and x = -13.42. Thus, option A is corect.

Explanation:

To solve the equation x² = 180 algebraically, we need to take the square root of both sides of the equation. This gives us two solutions, since both a positive and negative number squared will yield 180. The square root of 180 once calculated is approximately 13.42. Therefore, the two solutions are x = 13.42 and x = -13.42.

Answer:

Use the square root function on your calculator

Step-by-step explanation:

Look at the third line down, where is says that 936 = AD^2.  If you hit the 2nd button on your calculator then the x^2 button, you will get the square root function.  After you hit those buttons in that order, you'll get the opportunity to find the square root of 936 by entering it in and hitting "enter" on your calculator.  The square root of 936 is 30.59417

Answer:

A) - 39,991

Step-by-step explanation:

Sum of geometric sequence formula is

[tex]S = a(\frac{1 -r^n}{1-r} )\\a=-1, r=6/(-1)=-6, n=7\\\\S = -1(\frac{1 -(-6)^7}{1-(-6)} )= -\frac{279937}{7} = -39991[/tex]

Answer:

The correct answer option is A) -39,991.

Step-by-step explanation:

We know that the sum of the geometric sequence is given by the formula:

[tex] S _ n = \frac { a _ 1 ( 1 - r ^ n ) } { 1 - r } [/tex]

where [tex]a_1[/tex] is the first term, [tex]r[/tex] is the common ratio and [tex]n[/tex] is the number of terms.

Here,

[tex]a_1 = -1[/tex]

[tex]r = -6[/tex]

[tex]n=7[/tex]

Substituting these values in the above formula to get:

[tex] S _ 7 = \frac { -1 ( 1 - (-6) ^ 7 ) } { 1 - (-6) } [/tex]

S_n = -39,991

Answer:

4046.56 cm3

Step-by-step explanation:

The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of [tex] \frac{360} 5 = 72° [/tex]. Each of the other angle is [tex]\frac{180-72} {2} =54°[/tex]. From there, you can calculate the height of each base triangle as in [tex]\frac {h} 7 = tan54[/tex] or 9.634...cm.

Your volume will be [tex]5 * \frac  {(14 * 9.634)} 2 * 12 = 4046.56 cm^3[/tex]

There was 23.29 inches used on a headband for each player.

And 8.54 inches used on a wristband for each player.

To find out how much fabric for headbands and would beused for each player/person you would do

[tex]total \: fabric \: used \: \div \: total \: amount \: of \: people[/tex]

So, if you substitute the values in it is

[tex]791.86÷34=23.29 \: inches \: for \: 1 \: headband. \: [/tex]

And finally, to find how much fabric is used on a wristband for each player/person you would use the same formula.

[tex]273.28 \: \div 32 = 8.54 \: inches[/tex]

It takes 5 meters per second.

If you divide 250 by 50 you would get his average speed

The average speed of Ahmed is 5 meters per second.

Important information:

We need to find the average speed of Ahmed.

Formula for average speed is:

[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

Using this formula, the average speed of Ahmed is:

[tex]\text{Average Speed}=\dfrac{250}{50}[/tex]

[tex]\text{Average Speed}=5[/tex]

Thus, the average speed of Ahmed is 5 meters per second.

Find out more about 'Average speed' here:

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To find (ƒ + g)(x) for the given functions ƒ(x) = 5x² + 4 and g(x) = 6x² - x, we add the like terms to get

(ƒ + g)(x) = 11x² - x + 4.

To find (ƒ + g)(x) where ƒ(x) = 5x²  + 4, and g(x) = 6x²  – x, we simply add the two functions together. We combine like terms to calculate the sum.

By adding the corresponding terms:

Combining these, we get

(ƒ + g)(x) = f(x) + g(x)

(f + g)(x) = 11x² - x + 4.

Answer:

D. [tex]y=\frac{7}{x}[/tex]

Step-by-step explanation:

Let y varies inversely with x.

Then we can write the variation equation:

[tex]y\propto \frac{1}{x}[/tex]

We introduce the constant of proportionality, k and obtain the inverse variation equation:

[tex]y=\frac{k}{x}[/tex]

From the given options, the only equation in this form is

[tex]y=\frac{7}{x}[/tex]

In this case, k=7 is the constant of proportionality or constant of variation.

Answer:

x= 0 and x=-3/4

Step-by-step explanation:

[tex]4x^2 + 3x =0[/tex]

We need to solve this equation using quadratic formula.

The quadratic formula is:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

for the type of equation

[tex]ax^2 +bx+c=0[/tex]

So, for our given equation:

a= 4

b= 3

c=0

putting values in the formula

[tex]x=\frac{-3\pm\sqrt{9-0}}{8}\\x=\frac{-3\pm3}{8}\\x=\frac{-3+3}{8}\,and\, x=\frac{-3-3}{8}\\x=\frac{0}{8}\,and\, x=\frac{-6}{8}\\x=0\,and\, x=\frac{-3}{4}[/tex][/tex]

so, x= 0 and x=-3/4.

Answer:

7

Step-by-step explanation:

In similar triangles, corresponding elements are proportional. Then we get,

(2x + 1)/(x-1) = 10/4

4(2x +1)       = 10(x-1)

8x + 4         = 10x - 10

8x               = 10x - 14

2x               = 14

x                 = 7

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Answer:

7

both sides are corresponding so triangleABC AB=AC.

ANSWER

B. 13cm

EXPLANATION

The radius of the circle becomes the hypotenuse of the right triangle formed.

We can use the Pythagoras Theorem to obtain,

AC²+CY²=r²

This implies that,

r²=5²+12²

r²=25+144

r²=169

Take positive square root to get;

r=√169

r=13

AB and AC are two equal chord of a circle, therefore the centre of the circle lies on the bisector of ∠BAC.

OA is the bisector of ∠BAC.

Again, the internal bisector of an angle divides the opposite sides in the ratio of the sides containing the angle.

P divides BC in the ratio 6:6=1:1.

P is mid-point of BC.

OP ⊥ BC.

In △ ABP, by pythagoras theorem,

AB2=AP2+BP2

BP2=36−AP2         ....(1)

In △ OBP, we have

OB2=OP2+BP2

52=(5−AP)2+BP2

BP2=25−(5−AP)2      .....(2)

From 1 & 2, we get,

36−AP2=25−(5−AP)2

36=10AP

AP=3.6cm

Substitute in equation 1,

BP2=36−(3.6)2=23.04

BP=4.8cm

BC=2×4.8=9.6cm

Final answer:

After removing one bulb of each type, the probability of the next customer getting an amaryllins bulb is 5/16, which is 31.25%. Thus, the closest answer provided is 31%, option B.

Explanation:

The question asks for the probability of the next customer getting an amaryllins bulb after four bulbs of different types have been removed from a basket containing miscellaneous flower bulbs. Initially, there were 6 amaryllins, 7 daffodils, 4 lilies, and 3 tulips. Since one bulb of each type was bought by the previous customer, we now have 5 amaryllins, 6 daffodils, 3 lilies, and 2 tulips remaining.

To find the probability of selecting an amaryllins bulb, we divide the number of amaryllins bulbs left by the total number of bulbs remaining:

Probability of selecting an amaryllins = Number of amaryllins bulbs remaining / Total number of bulbs remaining

Probability = 5 / (5 + 6 + 3 + 2) = 5 / 16

To convert this to a percentage, we multiply it by 100: (5 / 16) * 100 = 31.25%

Therefore, the probability is closest to 31%, which corresponds to option B.

Answer:

Final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].

Step-by-step explanation:

using given information from the attached picture, we need to find the value of cos(H) so let's apply the formula of cosine.

[tex]\cos\left(\theta\right)=\frac{adjacent}{hypotenuse}[/tex]

[tex]\cos\left(H\right)=\frac{GH}{FH}[/tex]

[tex]\cos\left(H\right)=\frac{36}{85}[/tex]

[tex]\cos\left(H\right)=0.423529411765[/tex]

Hence final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].

Using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.

Cosine ratio is expressed as, cos ∅ = adjacent/hypotenuse of a right triangle.

Given:

Therefore:

Cos H = 36/85

Cos H = 0.4235

Therefore, using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.

Learn more about cosine ratio on:

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Hm, it seems like his answer is off. The image is what I got.

Answers:

X+3

Step-by-step explanation:

I got it right

Answer:

31.4cm

Step-by-step explanation:

C = 2*pi*r

2r = d

2r=10

r=5

C = 2*5*pi

C = 10*3.14

C = 31.4cm

Answer:

Option D. [tex]x=10[/tex]

Step-by-step explanation:

step 1

Find the midpoint of the given line segment

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

[tex]A(5,10),B(15,10)[/tex]

substitute the values

[tex]M=(\frac{5+15}{2},\frac{10+10}{2})[/tex]

[tex]M=(10,10)[/tex]

step 2

Find the equation of the perpendicular bisector

we know that

The equation of a perpendicular bisector is equal to the x-coordinate of the midpoint, because is a vertical line (parallel to the y-axis)

therefore

the equation is equal to

[tex]x=10[/tex]

Answer:

10

Step-by-step explanation:

Answer:

"the addition of a negative constant"

Step-by-step explanation:

Please note the following points of functions regarding transformations:

1. If there is a change in amplitude, the function will be compressed/stretched vertically, keeping other variables constant

2. If there is a phase shift, the function would be horizontally transformed

3. If there is a period change, the function would be horizontally compressed/stretched

4. If there is addition of positive/negative constant, the function would shift vertically upward/downwards, respectively.

We can clearly see from the graph that the new function is a vertical downward shift from the original. Hence, looking at the above points, point #4, addition of a negative constant, is correct.

Answer:

28

Step-by-step explanation:

7*4

Answer:

28

Step-by-step explanation:

7*4

Answer:

Blank 1. Professional engineer

Blank 2. ABET( Accreditation Board for Engineering and Technology)

Answer:

  62 Sunday papers were sold

Step-by-step explanation:

Let x represent the number of Sunday papers sold. Then half that many, or x/2, is the number of Friday papers sold. The total revenue from the sales is the sum of products of quantity and price:

  1.50 · x + 0.75 · (x/2) = 116.25

Multiplying by 2, this becomes ...

  3.00x +0.75x = 232.50

  3.75x = 232.50

Dividing by the coefficient of x gives ...

  232.50/3.75 = x = 62

The number of Sunday newspapers sold is 62.

Answer:

e = 8x + 0.1y

Step-by-step explanation:

If Gustavo makes no sales at all, he still gets $8 per hour worked (x).  We can model this part with this equation:

e = 8x

But then, if he sells something, he makes extra money.. He makes 10% (0.1) of every sale (y).  So the equation becomes:

e = 8x + 0.1y

or you can express it this way:

e = 8x + y/10

which is the same thing just written differently.

For this case we have that the figure shown is composed of a cylinder and a cone.

We have that the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

Substituting the values:

[tex]V = \pi * (5) ^ 2 * 10\\V = \pi * 25 * 10\\V = 250 \pi \ m ^ 3[/tex]

On the other hand, the volume of a cone is given by:

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

Where:

A: It's the radio

h: It's the height

Substituting the values:

[tex]V = \frac {\pi * (5) ^ 2 * 4} {3}\\V = \frac {\pi * 25 * 4} {3}\\V = \frac {100 \pi} {3} \ m ^ 3[/tex]

Then, the total volume is:

[tex]V_ {t} = 250 \pi \ m ^ 3 + \frac {100 \pi} {3} \ m ^ 3[/tex]

Taking [tex]\pi = 3.14[/tex], we have to:

[tex]V_ {t} = 889.67 \ m ^ 3[/tex]

Answer:

Option D