you are given that is directly proportional to , and is inversely proportional to . if the value of is when is , what is the value of when is equal to ? express your answer as a common fraction.

Answer:

(1, - 8) and (2, -9)

Step-by-step explanation:

We have the following system of equations

\(\begin {aligned}\\f(x) & = x^2 - 4x - 5\\f(x) & = -x - 7\\\end{aligned}\)

Setting the right side of each of these expressions equal to each other gives us:

\(x^2 - 4x - 5 = -x - 7\\\)

Add x to both sides:
\(x^2 - 4x + x - 5 = -x + x - 7\\\\x^2 -3x -5 = -7\\\)

Add 7 to both sides:
\(x^2 - 3x - 5 + 7 = -7 + 7\\x^2 - 3x + 2 = 0\\\)

This is a quadratic equation which can be easily solved by factoring:

\(x^2 - 3x + 2 = 0 \\\\ (x - 1) (x - 2) = 0\\\\\implies x- 1 = 0 or x - 2= 0\\x - 1 = 0 = > x = 1\\x - 2 = 0 = > x = 2\\\)

So the possible solutions are x = 1 and x = 2

Substituting each of these values for x in the second equation(or the first) will yield the value of f(x) for that value of x

At x = - 1,  -x - 7 ==> -1 - 7 = -8
So one ordered pair is (1, -8)

At x = 2, -x - 7 ==>-2 - 7 = -9
So the other ordered pair is (-2, -9)

Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

The total price of 2 bags of apples and 3 bags of oranges can be calculated by adding 2 times the price of a bag of apples to 3 times the price of a bag of oranges.

To determine the total price of 2 bags of apples and 3 bags of oranges, you need to know the price per bag of apples and the price per bag of oranges. Let's assume the price per bag of apples is $A and the price per bag of oranges is $O.

The total price of 2 bags of apples would be 2 * A, and the total price of 3 bags of oranges would be 3 * O. To find the overall total price, you can simply add these two amounts together:

Total price = (2 * A) + (3 * O)

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Answer:

Mixed number: 1 9/10

Improper fraction: 19/10

Answer:

y=2.89

explanation

square root of 24=square root of (6)^2+(y-8)^2

4.89=6+y-8

4.89-2=y

2.89=y

Answer:

6 laps

Step-by-step explanation:

Each lap Jeffrey needs to run is one tenth of a mile he wants to run threee fifths of a mile how many laps does he need to run

One tenth of a mile = 1/0

Three fifths of a mile = 3/5

From the question:

1/10 mile = 1 lap

3/5 mile = x

Cross Multiply

1/10 mile × x = 3/5 mile × 1 lap

x = 3/5 mile × 1 lap/ 1/10 mile

x = 3/5 ÷ 1/10

x = 3/5 × 10/1

x = 6 laps

Therefore, for there fifths of a mile(3/5) he needs to run 6 laps

Answer:

(-4 ,3)

Step-by-step explanation:

Point a lies on -4

Point B lies in between 2 and 4 so lets call it 3

Answer:

ITS BBBBB

Step-by-step

hope this heLPS

Answer:

y=-2x+8

Step-by-step explanation:

slope formula is y=mx+b

slope(m)=-2, and y-value(b)=8

so ya just plug in what ya know to get y=-2x+8

The equation of the line that passes through point (−3, 8) and has the slope m=−2 is \(y=-2x+2\)

Given, x= -3, y = 8 and m = -2

usiny y =mx+c

we get,

8 = -2*-3+c

8 = 6+c

c = 8-6 = 2

Therefore, The equation of the line that passes through point (−3, 8) and has the slope m=−2 is \(y=-2x+2\)

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Answer:

2502.1

Step-by-step explanation:

4754/1.9

= 2,502.1

Hence the andwer is 2502.1

Answer:

(S-2πr^2)/ 2πr = h

Step-by-step explanation:

S = 2πrh + 2πr^2

Subtract 2 pi r^2 from each side

S-2πr^2  = 2πrh + 2πr^2 -2πr^2

S-2πr^2  = 2πrh

Divide each side by 2 pi r

(S-2πr^2)/ 2πr = 2πrh/2πr

(S-2πr^2)/ 2πr = h

It is given that,

→ S = 2πrh + 2πr²

Now subtract 2πr² from the both sides,

→ S - 2πr² = 2πrh + 2πr² - 2πr²

→ S - 2πr² = 2πrh

Then divide both sides by 2πr,

→ (S-2πr²)/2πr = 2πrh/2πr

→ (S-2πr²)/2πr = h

Hence, (S-2πr²)/2πr = h is the result.

The statements about the graph of function that are true include:

From the information given, f(0) = 4(0) - 15

= 0 - 15

= -15

Therefore, the graph crosses the y-axis at (0,-15) is true.

Also, the graph has a point of discontinuity at x=-2 and the graph is increasing over the interval (4,inf).

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Answer:

can u add a image of the different systems??

Step-by-step explanation:

By using the range, the result obtained is-

Sample average range = 4.33

What is range?

Range is the difference between the highest value and lowest value of the data set.

Measurements from machine 1 = 17, 15, 15, 17

Range for measurements from machine 1 = 17 - 15 = 2

Measurements from machine 2 = 16, 25, 18, 25

Range for measurements from machine 1 = 25 - 16 = 9

Measurements from machine 3 = 23, 24, 23, 22

Range for measurements from machine 1 = 24 - 22 = 2

Sample average range =   \(\frac{2 + 9 + 2}{3}\)

                                      = \(\frac{14}{3}\)

                                      = 4.33

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Answer: Well this is a improper answer but here is it.

186.0714285714286

Step-by-step explanation:

The number of people died from aids in U.S. in 2005 are 2,30,68,96,671

Given, diseases tend to spread according to the exponential growth model.

In the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9.

In 1983, about 1700 people in the U.S. died of aids.

we have to find the number of people died from aids in 2005.

Let the exponential function, be

P(x) = AB^x

where, A is the initial population of people died of aids in U.S.

B is the growth factor of aids in U.S.

as, B = 1.9

In 1983, x = 0

P(0) = AB^0

1700 = A

Now, P(x) = 1700(1.9)^x

and the number of years from 1983 to 2005 are, 22 years

The number of people died from aids in 2005 be,

P(22) = 1700(1.9)^22

P(22) = 2,30,68,96,671

So, 2,30,68,96,671 people died from aids in 2005.

Hence, 2,30,68,96,671 people died from aids in 2005.

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The statue should be 48 inches tall to fit in Jerry's backyard.

Given that Model height is 8 inches, Model width is 15 inches and Actual height is 4 feet.

Since there are 12 inches in a foot, the actual height can be converted to inches as:

Actual height = 4 feet × 12 inches/foot = 48 inches

Now, let's set up the proportion using the height ratios:

Model height / Model width = Actual height / Actual width

8 inches / 15 inches = 48 inches / Actual width

Cross-multiplying:

(8 inches) × (Actual width) = (15 inches) × (48 inches)

8 × Actual width = 15 × 48

Dividing both sides by 8:

Actual width = (15 × 48) / 8 = 90 inches

Now that we have the actual width of the statue (90 inches), we can set up another proportion to find the height of the statue:

Model height / Model width = Actual height / Actual width

Plugging in the values:

8 inches / 15 inches = Actual height / 90 inches

Cross-multiplying:

(8 inches) × (90 inches) = (15 inches) × (Actual height)

720 inches = 15 × Actual height

Dividing both sides by 15:

Actual height = 720 inches / 15 = 48 inches

Therefore, the statue should be 48 inches tall to fit in Jerry's backyard.

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Answer 9 inches

Step-by-step explanation: im not 100% sure but i think its 9 sorry if im wrong

Answer:

536 cm is equal to 53.6 dm

Step-by-step explanation:

Answer:

=

Step-by-step explanation:

The average height for a 15-year-old male in the United States is roughly 5 feet, 7 inches, according to the Centers for Disease Control and Prevention (CDC) growth charts (170 cm). Some 15-year-old guys may be shorter or taller than usual.

Height is a measure of the distance between the base of an object and its highest point. Human height is commonly described as the vertical distance between the bottom of the feet and the top of the head. Height is generally measured in centimetres or feet and inches. Height is an important physical feature that can be influenced by both inherited and environmental factors such as nutrition and physical activity.

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Answer:

0.125 inches per hour

Step-by-step explanation:

2.25/18 = 0.125

0.125in per hour

Answer:

408.41 cm²

is the answer

The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

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Answer:

Step-by-step explanation:

Hope that helps! :)

-Aphrodite

For comparing three treatments using a one-way fixed effects model, the required sample size (n) is 2.5088

we need to consider the desired power level, significance level, effect size (∆), and the variance (σ²). In this scenario, we want at least 80% power at the 5% significance level, with treatment means that differ by 100 - ∆, 100, and 100 + ∆, where ∆ = 5. The variance is given as σ² = 10.

To calculate the sample size, we can use power analysis based on the F-test. The formula for sample size in this case is:

n = 2 * [(Zα/2 + Zβ)² * σ²] / ∆²

where Zα/2 is the critical value for the desired significance level (5% or 0.05), and Zβ is the critical value for the desired power level (80% or 0.80).

Plugging in the values, we get:

n = 2 * [(1.96 + 0.84)² * 10] / 5²

n = 2 * [(2.80)² * 10] / 25

n = 2 * 7.84 * 10 / 25

n = 6.272 * 10 / 25

n = 2.5088

Rounding up to the nearest whole number, the required sample size (n) is 3.

Therefore, the sample size must be at least 3 in order to achieve at least 80% power at the 5% significance level for comparing the three treatments using a one-way fixed effects model.

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Answer:

25 cm^2

24 cm

Step-by-step explanation:

5*5 = 25 cm^2

Make sure not to forget the cm^2, otherwise you will get it wrong

10 + 14 = 24 cm

this is only perimeter so only cm

Answer:

25 cm²

24 cm

Step-by-step explanation:

Area of a Square: A = lw

Since the sides of a square are all the same, we have A = 5(5) = 25 cm²

Perimeter of a Rectangle: 2w + 2l

Simply plug it in:

P = 2(7) + 2(5)

P = 14 + 10

P = 24 cm

Answer:

3

Step-by-step explanation: 15 divided by 3 is 5, 30 divided by 3 is 10

The quotient is 140 and the remainder is 0.

We have,

To divide 4,900 by 35, we perform the division as follows:

Step 1: Find the quotient:

The quotient is obtained by dividing the radicand (4,900) by the divisor (35):

4,900 ÷ 35 = 140

Step 2: Find the remainder:

The remainder is the part that is left over after the division:

Remainder = 4,900 - (Quotient * Divisor)

Remainder = 4,900 - (140 * 35) = 4,900 - 4,900 = 0

Since the remainder is 0, there is no remainder in this division.

Therefore,

The quotient is 140 and the remainder is 0.

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The complete question:

Divide 4,900 by 35, and check the boxes that show the quotient and remainder of the division.

Answer:

1/2 or 0.5

Step-by-step explanation:

Hello!

Pick two points on the graph, I'm picking (0,5) and (2,6)

To solve for the slope, we want the ratio to the rise of the graph, over the run of the graph (Rise/Run).

As the graph Rises 1 unit, it also Runs 2 units.

Hence the fraction 1/2.

We can also use the slope formula, given two points : (\((x_1, y_1) , (x_2, y_2)\)

Formula: \(\frac{y_2 - y_2}{x_2 - x_1}\)

Plug in our points (0,5) and (2,6):

The slope is 1/2, or 0.5

Answer:

A. -(7/5)

B.-41

Lemme know if u need an explanation

Answer: 6

Step-by-step explanation:

The typical way to solve this problem is with the Pythagorean Theorem, which states that a^2 + b^2 = c^2, where a and b are the legs of the right triangle, and c is the hypotenuse.  Unfortunately, due to a lack of a diagram, I am forced to infer.

Because the most famous Pythagorean triplet is 3, 4, 5, and 8 and 10 are multiples of the latter two terms, I can infer that the final side length is 6.

Hope it helps :) and if it is wrong, please let me know, and repost another question with the provided diagram.