F(x) = -3x +20; f(8)

Answer:

2

Step-by-step explanation:

Final answer:

The missing value in the ratio table is 16.

Explanation:

To find the missing value in the ratio table, we can look at the relationship between the given values. In this case, we have the ratios of towels to blankets. We can see that the ratio of towels to blankets is the same for each pair of values. So, we need to find a value that, when divided by 8, gives the same result as when 14 is divided by 7.

Let x be the missing value. We can set up the equation 14/7 = x/8. To solve for x, we can cross multiply: 14 * 8 = 7 * x. This gives us 112 = 7x. Dividing both sides by 7, we find that x = 16.

Therefore, the missing value in the ratio table is 16.

Answer:

p=11 packets were purchased

Step-by-step explanation:

30+11p=151

11p=121

then

121/11

so

p=11

Hope I understood the question :/

Answer:

Step-by-step explanation:

I believe the correct answer is that Andrew's Math Teacher purchased 11 packets of 10 tests each, meaning that the total number of test would be 110. I got this by subtracting the $30 entrance fee from the $151. After doing this we are left with $121. I then divided the $121 by the cost per packet and I was left with 11 packets. Since every packet contains 10 tests I multiplied that by the number of packets to get the final answer... 110 tests purchased.

The inverse is: {(3,5), (4,-2), (-2,7)}

Step-by-step explanation:

In the inverse of a function, the output becomes input and the input becomes output i.e. the functions is reversed.

Given function is:

[(5,3) (-2,4) (7,-2)]

The order of elements in ordered pairs will be reversed. The second elements will be on first place and first element will be on second place.

So,

The inverse is: {(3,5), (4,-2), (-2,7)}

Keywords: Functions, inverse

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The inverse of the given function (5,3), (-2,4), (7,-2) is (3,5), (4,-2), (-2,7).

The inverse of a function is created by swapping each input-output pair.

For the given function with ordered pairs (5,3), (-2,4), and (7,-2), we can find the inverse by switching each pair's coordinates. This yields the inverse ordered pairs (3,5), (4,-2), (-2,7). Remember that the inverse function only exists if the original function is bijective, meaning each output is paired with exactly one input.

Answer:

Part 1) The domain is the interval (-∞,-7) ∪ (-7,0) ∪ (0,∞)

Part 2) The domain is the interval (-∞,0) ∪ (0,2) (2,∞)

Part 3) The domain is the interval (-∞,-6) ∪ (-6,6) ∪ (6,∞)

Step-by-step explanation:

Part 1) we have

[tex]\frac{32}{y}-\frac{y+1}{y+7}[/tex]

we know that

The denominator cannot be equal to zero

so

The value of y cannot be equal to 0 or cannot be equal to -7

The domain for y is all real numbers except the number -7 and the number 0

The domain in interval notation is

(-∞,-7) ∪ (-7,0) ∪ (0,∞)

Part 2) we have

[tex]\frac{y^2+1}{y^2-2y}[/tex]

we know that

The denominator cannot be equal to zero

[tex]y^2-2y=0\\y^2=2y\\y=2[/tex]

so

The value of y cannot be equal to 0 or 2

The domain for y is all real numbers except the number 0 and 2

The domain in interval notation is

(-∞,0) ∪ (0,2) (2,∞)

Part 3) we have

[tex]\frac{y}{y-6}+\frac{15}{y+6}[/tex]

we know that

The denominator cannot be equal to zero

so

The value of y cannot be equal to 6 or cannot be equal to -6

The domain for y is all real numbers except the number -6 and the number 6

The domain in interval notation is

(-∞,-6) ∪ (-6,6) ∪ (6,∞)

Answer:

f(-1) = -6

f(0) = -5

f(1) = -4

f(2) = -3

f(5) = 0

f(8) = 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

[Function] f(x) = x - 5

f(-1) is x = -1 for function f(x)

f(0) is x = 0 for function f(x)

f(1) is x = 1 for function f(x)

f(2) is x = 2 for function f(x)

f(5) is x = 5 for function f(x)

f(8) is x = 8 for function f(x)

Step 2: Evaluate

f(-1)

f(0)

f(1)

f(2)

f(5)

f(8)

Answer:

D. Subtraction property of equality; n = 15

Step-by-step explanation:

Given equation that shows the cost of n basketballs uniforms,

C = 40n + 260

According to the question,

Total cost = $ 860,

⇒ 40n + 260 = 860

Using subtraction property of equality, subtract 260 on both sides,

⇒ 40n = 860 - 260

⇒ 40n = 600

Using division property of equality, divide both sides by 40.

⇒ n = [tex]\frac{600}{40}[/tex] = 15.

Hence, 15 uniforms were purchased.

i.e. Option D is correct.

Answer:

D

Step-by-step explanation:

There are 2 answers: Choice 1, Choice 4

=======================================

Why is this? Because we use the rule

P(A & B) = P(A) * P(B)

which only works if events A and B are independent

----

For the first answer choice,

P(A) * P(B) = 0.6*0.4 = 0.24 = P(A & B)

so that matches.

The same applies to the fourth answer choice as well

P(A) * P(B) = 0.3*0.2= 0.06 = P(A & B)

----

The other answer choices don't match up.

The second answer choice has

P(A) * P(B) = 0.3*0.4 = 0.12 but that doesn't match with the 0.70 given

Similarly for the third answer choice,

P(A) * P(B) = 0.5*0.1 = 0.05 which doesn't match with the 0.60

Answer:

Yes

Step-by-step explanation:

Answer:6.7

Step-by-step explanation:5.2+6.3=11.5 then you do -12 divided by 2.5 and get -4.8 then you add the answers together but that won’t work because different signs subtract and you get positive 6.7

To evaluate the expression (5.2+6.3) - 12 ÷ 2.5, you first perform the division. Then, substitute the result and add the numbers inside the parentheses. Finally, subtract the result from the addition.

To evaluate the expression (5.2+6.3) - 12 ÷ 2.5, we start by performing the division. 12 ÷ 2.5 equals 4.8. Now, we substitute this result into the expression, so the expression becomes (5.2+6.3) - 4.8. Next, we add the numbers inside the parentheses together, giving us 11.5. Finally, we subtract 4.8 from 11.5, resulting in 6.7.

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Multiply the number of hours worked by how much is made per hour:

7 hours x $10.25 per hour = $71.75 total

so it's 71.76  all i did was multiply 7 x 10.25 which equals 71.76

Answer:

5.8m

Step-by-step explanation:

Answer:

17 × 12 = 204 teddy bears

Step-by-step explanation:

17 cases, 12 bears in each case

Answer:

The values are x = 0° or x = 60°

Step-by-step explanation:

Given:

[tex]\cos x + \frac{1}{\sqrt{3} }\times \sin x = 1[/tex]

Let it be in the form of

[tex]a\cos x + b\sin x = 1[/tex] such that

a = 1

[tex]b=\frac{1}{\sqrt{3} }[/tex]

We have

[tex]\sqrt{(a^{2}+b^{2} )}=\sqrt{(1^{2}+(\frac{1}{\sqrt{3} }) ^{2} )}\\=\sqrt{\frac{4}{3}}\\=\frac{2}{\sqrt{3} }[/tex]

Now, Dividing both the side by [tex]\frac{2}{\sqrt{3} }[/tex] we get

[tex]\frac{\sqrt{3} }{2}\cos x + \frac{1}{2}\sin x =\frac{\sqrt{3} }{2}\\[/tex]

We Know

[tex]\sin 60 =\frac{\sqrt{3} }{2}\\and\\\cos 60 = \frac{1}{2}[/tex]

Now by replacing with above values we get

[tex]\sin 60\times \cos x + \cos 60\times \sin x = \frac{\sqrt{3} }{2}\\[/tex]

Also we have formula

[tex]\sin A\times \cos B + \cos A\times \sin B = \sin (A+B)[/tex]

By applying the above Formula we get

[tex]\sin (60+x)=\frac{\sqrt{3} }{2}\\[/tex]

Also ,

[tex]\sin (60)=\frac{\sqrt{3} }{2}\\and\\\sin (120)=\frac{\sqrt{3} }{2}[/tex]

Comparing we get

 60 + x = 60   or  60 + x = 120

∴ x = 0°               ∴ x = 120 - 60 = 60°    

Therefore, the values are x = 0° or x = 60° i.e between 0° to 360°

Answer:

B

Step-by-step explanation:

20% is 20 out of 100

and that's how you find out how much of a tip you should leave.

The proportion that would BEST represent how to find how much tip she should leave is x/15 = 20/100

Let the amount of tip h left be expressed as x

Given the following parameters

To find the amount of tip Jennifer dropped;

Price of tip = 20% of 15

x = 20/100 * 15

x/15 = 20/100

Hence the proportion that would BEST represent how to find how much tip she should leave is x/15 = 20/100

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Answer: A. g+2g =352

Step-by-step explanation:

Let points : g

If molly has half of George then let

Let molly : 1

Let George: 2

Therefore g*1 =g

And g*2 = 2g

So, g+2g = 352

Final answer:

The solution to the given system of equations is x=3 and x=-7. To find the solution, set the expressions for y equal to each other, combine like terms, and solve for x. Substitute the values of x back into one of the original equations to find the corresponding y value.

Explanation:

The solution to the given system of equations is x = 3 and x = -7.

To find the solution, we can set the expressions for y equal to each other:

2x + 3 = -3x + 3

Combine like terms:

5x = 0

Divide both sides by 5:

x = 0/5

x = 0

Substitute x = 0 back into either of the original equations to find the corresponding y value:

y = 2(0) + 3

y = 0 + 3

y = 3

The solution to the system of equations is (0, 3).

Answer:

The average rate of speed of the model airplane, per second is 18 feet.

Step-by-step explanation:

Given:

It took the model airplane 5 seconds to go 90 feet.

Now, to find the average rate of speed in feet per second.

So, in 5 seconds the airplane go to = 90 feet.

In 1 second the airplane go to = 90 ÷ 5 feet.

Therefore, by dividing 90 feet by 5 seconds we get = 18 feet.

Thus, the average rate of speed of the model airplane, per second is 18 feet.

Answer:

The total cost is $95.32.

Step-by-step explanation:

Given:

Total came to $76.75. There is an 8% sales tax and 15% tip.

Now, to find the total cost.

8% sales tax is there so we calculate the amount after adding sales tax:

$76.75 + 8% of $76.75

[tex]76.75+\frac{8}{100}\times 76.75[/tex]

[tex]76.75+0.08\times 76.75[/tex]

[tex]76.75+6.14[/tex]

[tex]82.89[/tex]

The cost after sales tax is $82.89.

Now, the cost after 15% tip:

$82.89 + 15% of $82.89

[tex]82.89+\frac{15}{100}\times 82.89[/tex]

[tex]82.89+0.15\times 82.89[/tex]

[tex]82.89+12.43[/tex]

[tex]95.32[/tex]

The cost after the tip is $95.32.

Therefore, the total cost is $95.32.

Answer:

2114.7 people per square mile

Step-by-step explanation:

Population density can be calculated by dividing the total number of people by the area.

23,896 people ÷ 11.3 square miles

≈ 2114.7 people per square mile    (rounded number)

Your answer is one decimal place off.

Answer:

The cabinet is longer by 1/12 foot.

Step-by-step explanation:

3/4 x 3/3 = 9/12

2/3 x 4/4 = 8/12

Answer:

5 hours  was Aaron at the sitter

Explanation:

Cost of baby sitting for the first hour: 10

Cost of baby sitting for additional hour= 12

Total cost of babysitting= 58

Since the cost of first hour is 10

Hence  the remaining cost after first hour

= 54-10

=48

Which means 1 hour  is consumed in the first hour

Now to calculate the remaining hours for every additional hour

= [tex]\frac{48}{12}[/tex]

=4 hours

Hence the total hour Aaron was with the sitter

= 1 hour + 4 hours

= 5 hours

Answer:

Step-by-step explanation:

a(c + b) = d          // We multiply a by c and b (addition is distributive)

ac  +  ab = d        // We let the c addend in the left

ac = d - ab          // We divide by a

c = (d - ab) / a

Answer: Hi Hi I know this is like a year late but I would like to be able to help future people with this question.

The correct answer is: c=d+ab/a (B)

Isolate the variable by dividing each side by factors that don't contain the variable.

I really hope this helps people, have a happy halloween :D

Answer:

120 gallons per hour.

Step-by-step explanation:

Between 1:30 P.M. and 1:50 P.M., 40 gallons of water leaked into a boat.

We know, the (1: 50 P.M. - 1: 30 P.M.) = 20 minutes.

So, the time span is of 20 minutes and the amount of water leaked into is 40 gallons.

Therefore, the amount of water that will leak into the boat in 60 minutes is [tex]\frac{40 \times 60}{20} = 120[/tex] gallons.

So, the rate in gallons per hour of the leaking water is 120 gallons per hour. (Answer)

The mean absolute deviation is a measure of variation in a dataset, not its center. It helps indicates how spread out the data is from the mean value.

The mean absolute deviation is not a measure of center,instead, it is a measure of variation. The center of a data set is typically represented by measures like the mean, median, or mode. These describe the common, central value in the dataset.

Conversely, the mean absolute deviation is a statistical tool used for understanding the dispersion or variation in a set of values. It gives an average of the absolute differences between each data point and the mean of the data set. This helps identify how spread out the data is from the mean.

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Answer:

The equation of the hyperbola in standard form is [tex]\frac{(x - 4)^2 }{ 9} - \frac{(y +2)^2}{2.25} = 1[/tex]

Step-by-step explanation:

Given:

Centre of the hyperbola=(−2,4)

one vertex of the hyperbola= (−2,7) .

slope of the asymptote = 12

To Find:

The equation of the hyperbola in standard form=?

Solution:

W know that the  standard form of hyper bola is

[tex]\frac{(x - h)^2 }{ a^2} - \frac{(y - k)^2}{  b^2} = 1[/tex]............................(1)

where

(h,k) is the centre

(x,y) is the vertex of the parabola

a is the length between the centre and the vertices of the hyperbola

b is  the distance perpendicular to the transverse axis from the vertex to the asymptotic line

Now the length of a is given by

a=|k-y|

a=|4-7|

a=|-3|

a=3

Also we know that,

Slope =[tex]\frac{a}{b}[/tex]= 2

=>[tex]\frac{3}{b}=2[/tex]

=>[tex]\frac{3}{2}=b[/tex]

=>b=1.5

Now substituting the known values in equation(1)

[tex]\frac{(x - 4)^2 }{ 3^2} - \frac{(y - (-2)^2}{  1.5^2} = 1[/tex]

[tex]\frac{(x - 4)^2 }{ 9} - \frac{(y +2)^2}{2.25} = 1[/tex]

Answer:

[tex]\frac{(x+2)^{2}}{1296} - \frac{(y-4)^{2}}{9} = 1[/tex]

Step-by-step explanation:

The standard form of a hyperbola centered at a point distinct from origin has the following form:

[tex]\frac{(x-h)^{2}}{a^{2}} - \frac{(y-k)^{2}}{b^{2}} = 1[/tex]

The distance between the center and the vertex is:

[tex]b = \sqrt{[(-2)-(-2)]^{2}+(7-4)^{2}}[/tex]

[tex]b = 3[/tex]

The value of the other semiaxis is:

[tex]\frac{a}{b} = 12[/tex]

[tex]a = 12\cdot b[/tex]

[tex]a = 36[/tex]

The standard equation of the hyperbola is:

[tex]\frac{(x+2)^{2}}{1296} - \frac{(y-4)^{2}}{9} = 1[/tex]

Answer:

7.88

Step-by-step explanation:

Answer: 7,88

Explanation

Final answer:

The slope of the line passing through (0, 5) and (-12, 2) is calculated using the slope formula and is found to be 1/4.

Explanation:

The slope of the line passing through the points (0, 5) and (-12, 2) can be calculated using the formula slope (m) = (rise)/(run), where 'rise' is the change in the y-values and 'run' is the change in the x-values. To find the slope, we subtract the y-value of the second point from the y-value of the first point and divide by the subtraction of the x-value of the second point from the x-value of the first point: m = (5 - 2) / (0 - (-12)) = 3 / 12 = 1/4. Therefore, the slope of the line is 1/4.

Answer:

Yes,two planes descending at the same angle

Explanation:

Given the angle of deviation as seen by the pilot is equal to 15 degrees,

i.e the angle made by the line of sight with the ground is 15 degrees also the angle of elevation from a person at ground to the other plane is given to be equal to 15 degrees

which means the angle made by line of sight to plane and ground is equal to 15 degrees hence both of these situations refer to the same angle at a point and hence both planes are descending at the same angle.