gcf of 80, 16 and 96

Answer:  Range: y = {-7.5, -5, 10, 15}

Step-by-step explanation:

Domain is "x" and range is "y" f(x)

Replace the x's in the equation with each given value:

[tex]f(x)=3x-\dfrac{x}{2}\qquad \qquad \text{when}\ x={-3, -2, 4, 6}\\\\\\\\f(-3)=3(-3)-\bigg(\dfrac{-3}{2}\bigg)\\\\\\.\qquad =-9+\dfrac{3}{2}\\\\\\.\quad =\dfrac{-18}{2}+\dfrac{3}{2}\\\\\\.\quad =\large\boxed{-\dfrac{15}{2}}[/tex]

[tex]f(-2)=3(-2)-\bigg(\dfrac{-2}{2}\bigg)\\\\\\.\qquad =-6+1\\\\\\.\qquad =\large\boxed{-5}[/tex]

[tex]f(4)=3(4)-\bigg(\dfrac{4}{2}\bigg)\\\\\\.\qquad =12-2\\\\\\.\qquad =\large\boxed{10}[/tex]

[tex]f(6)=3(6)-\bigg(\dfrac{6}{2}\bigg)\\\\\\.\qquad =18-3\\\\\\.\qquad =\large\boxed{15}[/tex]

The range of the function with the specified domain of {-3, -2, 4, 6} is {-15/2, -5, 10, 15}.

The student asks: if fx=3x-x/2 find the range if the domain is {-3,-2,4,6}. To find the range of the function f(x) = 3x - x/2, we will evaluate the function for each value in the given domain and record the corresponding outputs. This function simplifies to f(x) = (5/2)x when you combine like terms.

For x = -3, f(-3) = (5/2)(-3) = -15/2.

For x = -2, f(-2) = (5/2)(-2) = -10/2 = -5.

For x = 4, f(4) = (5/2)(4) = 20/2 = 10.

For x = 6, f(6) = (5/2)(6) = 30/2 = 15.

Answer:

7.2 Hours

Step-by-step explanation:

To find the mean which is also known as the average of a set of data, you first have to add all the numbers then divide the sum by the amount of data values. (I remember this by saying the mean teacher averages your grade.)

First, you need to add the numbers. 5+5+5+4+17= 36

Secondly, you need to divide the sum of all the data by the amount of data there is. In this case, there are 5 pieces of data.

Lastly, you divide 36/5

Your final answer should be 7.2

You can check your work by doing 7.2 times 5 which equals 36.

Sorry I couldn't reply sooner, hope this helped!

Answer:

x=75 degrees because it is an isosceles triangle, and both 75 and x are equiangular.

Step-by-step explanation:

Check the picture below.

so we have two twin sides stemming from a common vertex, once they reach the base, they'd make up an angle, however, in an isosceles triangle, the twin sides always make twin angles at the base.

Answer:

27,050

Step-by-step explanation:

Thousand is three zeroes, so we start with 27,000

Hundred is two zeroes, so we add 300

Ones have no zeroes, so we add 5

27,305

but then this is times 10 which adds another zero, so our final result is

27,050

Answer: 600.62

Step-by-step explanation:

1018 x 0.59 = 600.62

Answer:

600.6. to the nearest tenth.

Step-by-step explanation:

59 % = 59/100 = 0.59.

0.59 * 1018

= 600.6.

Answer:

60

Step-by-step explanation:

y+y+60=180

2y =120

therefore,y=60

Answer:

C. 60°

Step-by-step explanation:

To answer this problem we must make use of the sum of the internal angles of a triangle.

For any triangle the sum of its internal angles is equal to 180 °.

So we must add all the angles to find the answer:

[tex]y+y+60=180[/tex]

now we can add the two terms 'y'

[tex]2y+60=180[/tex]

and now we clear for 'y':

[tex]2y=180-60\\2y=120\\y=120/2\\y=60[/tex]

The value of y is 60°

Answer:

b. (-1, 1.5)

d. (0,3)

Step-by-step explanation:

we have

[tex]4y-6x=12[/tex]

we know that

If a ordered pair is on the graph of the linear equation, the the ordered pair must satisfy the linear equation

Verify each case

case a) we have

(-4,3)

substitute the value of x and the value of y in the equation

[tex]4(3)-6(-4)=12[/tex]

[tex]36=12[/tex] ----> is not true

The ordered pair not satisfy the equation

therefore

The ordered pair is not on the graph of the linear equation

case b) we have

(-1,1.5)

substitute the value of x and the value of y in the equation

[tex]4(1.5)-6(-1)=12[/tex]

[tex]12=12[/tex] ----> is true

The ordered pair satisfy the equation

therefore

The ordered pair is  on the graph of the linear equation

case c) we have

(0,-2)

substitute the value of x and the value of y in the equation

[tex]4(-2)-6(0)=12[/tex]

[tex]-8=12[/tex] ----> is not true

The ordered pair not satisfy the equation

therefore

The ordered pair is not on the graph of the linear equation

case d) we have

(0,3)

substitute the value of x and the value of y in the equation

[tex]4(3)-6(0)=12[/tex]

[tex]12=12[/tex] ----> is true

The ordered pair  satisfy the equation

therefore

The ordered pair is on the graph of the linear equation

case e) we have

(3,4)

substitute the value of x and the value of y in the equation

[tex]4(4)-6(3)=12[/tex]

[tex]-6=12[/tex] ----> is not true

The ordered pair not satisfy the equation

therefore

The ordered pair is not on the graph of the linear equation

case f) we have

(6,4)

substitute the value of x and the value of y in the equation

[tex]4(4)-6(6)=12[/tex]

[tex]-12=12[/tex] ----> is not true

The ordered pair not satisfy the equation

therefore

The ordered pair is not on the graph of the linear equation

The only points that a valid points on the graph of 4y - 6x = 12 are;

Option A; (-4,-3)

Option B; (-1, 1.5)

Option D; (0,3)

We are given the equation;

4y - 6x = 12

Let us make y the subject to get;

4y = 12 + 6x

y = (12 + 6x)/4

y = 3 + ³/₂x

Option A; at (-4, -3), let us put -4 for x to see if we will get y as -3;

y = 3 + ³/₂(-4)

y = 3 - 6

y = -3

Thus, (-4, -3) is a valid point

Option B; at (-1, 1.5)

y = 3 + ³/₂(-1)

y = 3 - 1.5

y = 1.5

Thus, (-1, 1.5) is a valid point

Option C; at (0, -2)

y = 3 + ³/₂(0)

y = 3

Thus, (0, -2) is not a valid point

Option D; at (0, 3)

y = 3 + ³/₂(0)

y = 3

Thus, (0, 3) is a valid point

Option E; At (3, 4)

y = 3 + ³/₂(3)

y = 3 + 4.5

y = 7.5

Thus; (3, 4) is not a valid point

Option F; At (6, 4)

y = 3 + ³/₂(6)

y = 3 + 9

y = 12

Thus, (6, 4) is not a valid point

In conclusion the only valid points are; (-4, -3), (-1, 1.5), (0, 3)

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Just divide one by another and you'll get the ratio

4000/15 = 800/3 ≈ 266,67

So 4000 is 266,67 times greater than 15

Answer:

266.666 or 266.67

Step-by-step explanation:

You´d divide 4000 by 15 and you get 266.666, which can be simplified to 266.67.

Final answer:

To find the tax on a $76 automobile tune-up at 8.25%, convert the tax rate to a decimal (0.0825), multiply it by the tune-up cost ($76), resulting in a tax of $6.27. Adding the tax to the original cost gives a total price of $82.27.

Explanation:

To calculate the amount of tax on an automobile tune-up costing $76 with a tax rate of 8.25%, first, you need to convert the percentage to a decimal. The decimal form of 8.25% is 0.0825. Then multiply the cost of the tune-up by this decimal:

The amount of tax to be paid is $6.27. To find the total price of the tune-up with tax, you simply add the tax amount to the original tune-up cost:

Therefore, the total price of the automobile tune-up including tax is $82.27.

Answer:

Figure 4

because they both have same sizes

The figure 4 is translation of figure 1.

Transformation is the process of changing the graph to a new graph by Rotation, Reflection, Translation, and Dilation.

The translation is a transformation in which the x and y coordinates are shifted of the object.

The only figure in which the transformation is translation of figure 1 is Figure 4.

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Answer:

8.5 £

Step-by-step explanation:

1.90 * 35

= 66.5 £

so,

75 - 66.5

= 8.5 £

Answer:

She lost £8.50

Step-by-step explanation:

£1.90 x 35 = £66.50 (how much she earned on Tuesday)

£75.00 - £66.50 = £8.50

Answer:

-$195

Step-by-step explanation:

If she made 3 withdrawals and they are all the same amount then the equation is

65 x 3 or 65+65+65

Which equals 195

Since she is taking money out of her bank account, the total change is negative because she is subtracting it from her current amount

The total change is -$195

Answer:

The last digit of this number is 5

Therefore, it is divisible by 5

It is composite

Step-by-step explanation:

Answer:

B. x^4+2x^2+2

Step-by-step explanation:

(x^2+1)^2+1

=(x^2+1)(x^2+1)+1

=(x^4+x^2+x^2+1)+1

=x^4+2x^2+2

Answer:

The proportional relationships are used by showing ratios that can be simplified into 2:3.

Answer:

hbd

Step-by-step explanation:

fcvhk;mlsdhijksnmc3w

Answer:

52:72

Explanation:

Because it's comparing the men to the TOTAL passengers. Not the women, that's trying to trick you.

Answer:

52:72

Step-by-step explanation:

because it said the male to total passengers

For this case we have that the total minutes spent in yoga classes last week was 165.

Subtracting the 45 minutes of the Saturday day we have:

[tex]165-45 = 120[/tex]

Those 120 minutes were distributed in the weekly yoga classes

where each lasted 30 minutes.

[tex]\frac {120} {30} = 4[/tex]

So, 4 week yoga classes were held

ANswer:

4 week yoga classes were held

Hey!

---------------------------------------

Solution and Answer:

Amy swam 30 laps in 20 minutes.

Rate = [tex]\frac{20 minutes}{30 laps} = \frac{2 minutes}{3 laps}[/tex]

---------------------------------------

Hope This Helped!

Answer:

Each bus could pick up 49 students

Step-by-step explanation:

(449-8):9=49

Answer:

Number of students on each bus = 49

Step-by-step explanation:

On Monday, 449 students went on a trip to the zoo. All 9 buses were filled and 8 students had to travel in cars.

Total number of students = 449.

Number of students traveled in car = 8

Number of students traveled in bus = 449 - Number of students traveled in car = 8

Number of students traveled in bus = 449 - 8 = 441

Number of buses = 9

Number of students traveled in bus = Number of buses x number of students on each bus

441 = 9 x number of students on each bus

Number of students on each bus = 49

Hey!

------------------------------------------------

[tex]\large\boxed{0.65~rotations~per~foot}[/tex]

------------------------------------------------

Solution:

speed = rotations / distance

speed = 65 / 100

speed = 0.65

------------------------------------------------

Hope This Helped! Good Luck!

Answer:

y = 4x - 8

Step-by-step explanation:

x = 1/4y + 2

-1/4y   -1/4y

-1/4y + x = 2

-x              -x

-1/4y= -x + 2

*-4        *-4

y = 4x - 8

Hey!

------------------------------------------------

Solution:

~Subtract x to both sides

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

~Simplify

1/4y = 2 + (-x)

~Multiply 4 to both sides

1/4y * 4 = 2 + (-x) * 4

~Simplify

y = 8 - 4x

~Switch

y = 4x - 8

------------------------------------------------

Answer:

[tex]\large\boxed{y~=~4x~-~8}[/tex]

------------------------------------------------

Hope This Helped! Good Luck!

Answer:

f(x) is greater

Step-by-step explanation:

The function that has a greater value when x = 3 is: A. f(x) is greater.

In Mathematics and Geometry, a linear function refers to a type of function whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.

Based on the information provided, we can logically deduce the following linear functions;

f(x) = 3x + 1

g(x) = 4x - 5

When x is equal to 3, we have:

f(x) = 3x + 1

f(3) = 3(3) + 1

f(3) = 10

g(x) = 4x - 5

g(3) = 4(3) - 5

g(3) = 7.

Therefore, f(x) is greater.

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Answer:

[tex]72[/tex]  [tex]times[/tex]

Step-by-step explanation:

This answer can be found by a very easy method.

72 divided by 1

==> 72

Meaning that if we do 1 * 72, and we get 72, this means that 1 can go into 72, 72 times

Answer:

k = B

px

Step-by-step explanation:

Divide both sides by px

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

given

[tex](1.5 \times {10}^{4} )(8 \times {10}^{8} )[/tex]

in order to make multiplication easier we need to change the 1.5 into a whole number form.

thus

[tex](15 \times {10}^{ - 1} \times {10}^{4} )(8 \times {10}^{8} )[/tex]

[tex] = (15 \times {10}^{4 - 1} )(8 \times {10}^{8} )[/tex]

First law of indices applied there

=(15×10^3)(8×10^8)

=(15×8)(10^3×10^8)

=120×10^3+8 ( first law of indices, which states that , numbers of the same base multiplying each other, take one of the base and add the exponent. and clearly both 15 and 8 are in base 10

=120×10^11

=1.20×10^2 ×10^11

=1.20×10^11+2

=1.20×10^13

so the answer is alt B

(1.5 x 10^4)(8 x 10^8) written in scientific notation will be  1.2×10¹³.

We write standard numbers in scientific form as it can be written in more compact way.Think of writing a billion in copy and writing it in scientific notation.

Given (1.5×10⁴)(8×10⁸) and we have to write it in scientific form.

Let us first multiply the bases which are (8×1.5) = 12 and 10⁴×10⁸ is 10⁴⁺⁸ = 10¹².

∴ (1.5×10⁴)(8×10⁸) = 12×10¹² but is scientific natation base should be less than 10 so we'll a decimal one digit before 12 like dividing it by 10 so to balance it out we also have to multiply by 10 we'll multiply that 10 to the 10¹² which will make it 10¹³.

∴ 12×10¹² = 1.2×10¹³.

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[tex]\bf a_n=\cfrac{20}{3}+\cfrac{1}{3}(n-1) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{89^{th}~term~\hfill }{a_{89}=\cfrac{20}{3}+\cfrac{1}{3}(89-1)}\implies a_{89}=\cfrac{20}{3}+\cfrac{1}{3}(88)\implies a_{89}=\cfrac{20}{3}+\cfrac{88}{3} \\\\\\ a_{89}=\cfrac{20+88}{3}\implies a_{89}=\cfrac{108}{3}\implies a_{89}=36[/tex]

Answer:

B

Step-by-step explanation:

Just did it

Answer:

x different from 2

Step-by-step explanation:

The function is written as the quotient: [tex]\frac{x+3}{x-2}[/tex]

that can give us a real value for any value of x except for x=2 that creates a ZERO in the denominator, making the division undefined.

So the only value for which the function cannot be evaluated is x=2, therefore the function's domain is all the real numbers except for x=2.