3. - 15 x + 30 2 -3
Write the equation in slope-intercept form

Step-by-step explanation:

By Side-Splitter Theorem,

20 / 30 = 36 / (x + 5 + 30).

Therefore (x + 5 + 30) = 54, x = 19.

Answer:

x=59

Step-by-step explanation:

hope this helped

Answer:

70 I think but I'm not sure

Step-by-step explanation:

AC=70

Answer:

\( \frac{1}{2} \times base \times height\)

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The correct value of Jessica's new net salary will be $225.

To calculate Jessica's new net salary after a 5% raise, we need to first determine Sarah's gross salary. We know that Sarah's net salary is $212.50, and 15% of her gross salary is withheld each week.

Let's denote Sarah's gross salary as "G." We can set up the following equation:

G - 15% of G = $212.50

Simplifying the equation, we have:

G - 0.15G = $212.50

0.85G = $212.50

G = $212.50 / 0.85

G ≈ $250

Sarah's gross salary is approximately $250.

Now, to find Jessica's new net salary after a 5% raise, we can calculate 5% of Sarah's gross salary and subtract the withheld amount:

Jessica's net salary = Sarah's gross salary + 5% of Sarah's gross salary - 15% of Sarah's gross salary

Jessica's net salary = $250 + 0.05 * $250 - 0.15 * $250

Jessica's net salary = $250 + $12.50 - $37.50

Jessica's net salary = $225

Therefore, Jessica's new net salary will be $225.

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Answer:

270 items

Step-by-step explanation:

Answer:

270 of them were not jackets dresses or shoes

Step-by-step explanation:

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

y-3 = -4 (x-1)

Step-by-step explanation:

y= -4x - 5

In slope-intercept form, they give us the slope, -4, and the y-intercept, -5 (we don't need for point-slope form).

Use the point (1,3) and substitute it into the equation.

Point-slope form: y-y1 = m(x-x1)

y-3 = -4 (x-1)

Answer:

7.1 miles

Step-by-step explanation:

13.8-6.7=7.1

Answer:

7.1 miles

Step-by-step explanation:

subtract 6.7 from 13.8 (13.8 - 6.7)

Answer:

9/40

Step-by-step explanation:

3/5 - 3/8 =

24/40 - 15/40 =

9/40

Hope that helps!

Answer:

2

Step-by-step explanation:

1+1=2

Answer:

y=2x+6

Step-by-step explanation:

Answer: y = 5x-2

Step-by-step explanation:

The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

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

    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

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Answer:

Graph A

Step-by-step explanation:

A linear association means that the dots form a line

Answer:

The answer is A

Step-by-step explanation:

A linear association is when the dots on the graph create a straight line. A creates a straight line therefore it is a linear association.

To calculate the length of cable needed, we first need to determine the length of the zip line itself. We can use the distance between the trees and the change in height of the cable to calculate the horizontal and vertical distances.

Let's say the distance between the trees is 200 feet and the change in height is 80 feet. To ensure a 6 to 8 feet of vertical change for every 100 feet of horizontal change, we need to limit the horizontal distance to between 750 and 1000 feet.

We can use the Pythagorean theorem to calculate the length of the zip line:

horizontal distance = √(100^2 - 80^2) = 60 feet

total length of zip line = √(200^2 + 60^2) = 208.44 feet

To account for the required 5% slack in the line, we need to add 5% to the total length:

total length with slack = 208.44 + (0.05 * 208.44) = 218.86 feet

To wrap around each tree, we need an additional 6 feet at each end, so we need to add 12 feet to the total length:

total length with slack and extra cable = 218.86 + 12 = 230.86 feet

Therefore, we need a total length of 230.86 feet of cable.

Step-by-step explanation:

To determine the length of cable needed for the zip line, we first need to calculate the horizontal distance between the two trees. Let's assume that the distance between the trees is d feet. We also need to calculate the vertical change in height of the cable between the two trees. Let's assume that the height difference is h feet.

Given the slope constraint, we know that for every 6 to 8 feet of vertical change, we need 100 feet of horizontal change. This means that the slope of the zip line should be between 6/100 and 8/100. We can use this information to set up a proportion:

vertical change / horizontal change = slope

h / d = 6/100 or h / d = 8/100

Solving for d in each of these equations, we get:

d = h / (6/100) = 100h / 6 = 50h / 3 (for the minimum slope of 6/100)

d = h / (8/100) = 100h / 8 = 25h / 2 (for the maximum slope of 8/100)

To account for the required 5% slack in the line, we need to increase the length of the cable by 5%. This means that the actual length of cable needed is:

L = 1.05d + 12

where 12 feet represents the 6 extra feet of cable needed at each end to wrap around each tree.

Substituting the expressions for d that we derived earlier, we get:

L = 1.05(50h/3) + 12 = (175h/6) + 12 (for the minimum slope of 6/100)

L = 1.05(25h/2) + 12 = (131h/40) + 12 (for the maximum slope of 8/100)

Therefore, the total length of cable needed for the zip line depends on the height difference between the trees and the desired slope of the line. For example, if the height difference is h = 50 feet and we want to use the minimum slope of 6/100, then the total length of cable needed would be:

L = (175(50)/6) + 12 = 1462.5 feet

If we want to use the maximum slope of 8/100, then the total length of cable needed would be:

L = (131(50)/40) + 12 = 73.2 + 12 = 85.2 feet

Note that these values are approximations and do not take into account factors such as the weight of the rider or the tension of the cable.

Answer:

hope this helps

Step-by-step explanation:

The value of c by using the mean value theorem is c = 6.25.

The mean value theorem in mathematics says that for any given planar arc between two endpoints, there exists at least one point where the tangent to the arc is parallel to the secant between its endpoints. It is one of the most significant findings in the real-world analysis.

Given that the function is f(x) = 5√x and the interval is (4,9).

Calculate the value of 'c' as below,

f(x) = 5√x

f(4) = 5√4 = 10

f(9) = 5√9 = 15

Calculate the value of f'(c) as below,

f'(c) = ( f(b) - f(a) ) / (b - a)

f'(c) = f(9) - f(4) / ( 9 - 4 )

f'(c) = (15 - 10 )  / ( 9 - 4)

f'(c) = 1

Again the value of f'(x) is,

f'(x) = 5/2/√x

f'(c) = 5 / 2 / (√c)

5 / 2 / (√c) = 1

√c = 5 / 2

c = 25 / 4

c = 6.25

Therefore, the value of c by using the mean value theorem is c = 6.25.

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Answer:

First, we rearrange the equation to isolate the y-term on one side:

dy/dx + ytanx = secx

Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1

Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1

Integrating both sides with respect to x, we get:  y |secx| = x + C

where C is the constant of integration. Solving for y, we have:

y = (x + C)/|secx|

Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined

The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.

The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.

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Answer:

a=54

Step-by-step explanation:

a/9 = 6

(mutliply both sides by 9)

9(a/9) = 6(9)

a = 54

Answer:

54

Step-by-step explanation:

Answer:

Let f(x) be y.

y=2x-4

interchanging the position of x and y,

x=2y+4

or,x-4=2y

or,x-4/2=y

y=x-4/2

F^-1=x-4/2

Answer:

1/2 and 2

Step-by-step explanation:

Just did it

Answer:

If Olivia's H and Sam is five centimenters taller than Olivai, then Sam is H+5.

Answer:

ferfttttttttt

Step-by-step explanation:

hi hihihhhiii

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Answer:

{ - 4, - 1, 2, 5 }

Step-by-step explanation:

the range is the values of y from the ordered pairs in the relation

range = { - 4, - 1, 2, 5 }

Answer: 20 log (2)

Step-by-step explanation:

Answer: Logarithms are mathematical functions that are used to represent the relationship between two quantities that are related by a power law. For example, if we have an exponential equation like 2^x = 8, we can use logarithms to solve for x: log2 8 = x.

In general, logarithms are written in the form logb a, where b is the base of the logarithm and a is the number we want to take the logarithm of. There are several different bases in that logarithms can be written in, including the common logarithm (base 10) and the natural logarithm (base e).

To evaluate a logarithm, we need to use the logarithmic properties and the change of base formula. One important property of logarithms is that logb (xy) = logb x + logb y. Another property is that logb (x/y) = logb x - logb y.

The change of base formula is used when we need to evaluate a logarithm in a different base than the one given. The formula is:

logb a = logc a / logc b

where c is any base other than b or a. By using this formula, we can convert a logarithm from one base to another in order to evaluate it using a calculator.

In the case of log4 25, we can use the common logarithm (base 10) or the natural logarithm (base e) to evaluate the logarithm. Using the change of base formula with the common logarithm, we have:

log4 25 = log(25) / log(4)

Using a calculator, we find that log(25) ≈ 1.39794 and log(4) ≈ 0.60206, so:

log4 25 ≈ 1.39794 / 0.60206

Simplifying this expression, we get:

log4 25 ≈ 2.32193

Rounding to the nearest thousandth, we get:

log4 25 ≈ 2.322

So, the value of log4 25 to the nearest thousandth is 2.322.

Step-by-step explanation:

Answer: A

In looking for solutions in the graph of y=f(x) where f(x) = 0, you're looking for the x-intercepts.  The catch is that you only want the x-value of the intercepts.

The intercepts are (-4,0) and (7,0), so the solutions are -4 and 7.

Answer:

Explanation:

Maia can run 4/5 of a mile in 5/3 of an hour.

Let the mile run in 1 hour = x

We therefore have that:

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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