HELP ME WITH THIS QUESTION AS SOON AS POSSIBLE

The solution of the equation in terms of z will be; z = 2x - 8/y

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given the equation as;

2xy-yz=8

Now we have to solve for z;

2xy-yz=8

-yz = 8 - 2xy

Then divide by y on both sides;

z = 2xy/y - 8 / y

z = 2x - 8/y

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Answer:

See the image for marked congruences.

1. JM ≅ LM                           |      Given

2. △JML is isosceles          |      definition of isosceles

3. ∠MJL ≅ ∠MLJ                  |       isosceles triangle theorem

4. m∠MJL = m∠MLJ             |      definition of ≅

5. JK ≅ LK                            |      Given

6. △JKL is isosceles           |      definition of isosceles

7. m∠KJL = m∠KLJ              |       isosceles triangle theorem

8. m∠MJL + m∠KJM = m∠KJL                         |  adjacent angle theorem

9. m∠MLJ + m∠KMJ = m∠KLJ                         |  adjacent angle theorem

10. m∠MJL + m∠KJM = m∠MLJ + m∠KLM      |   transitive property of =

11. m∠MJL + m∠KJM = m∠MJL + m∠KLM      |   substitution

12. m∠KJM = m∠KMJ          |        subtraction

13. ∠KJM ≅ ∠KLM                |        definition of ≅

14. △KJM ≅ △KLM             |        SAS theorem

15. ∠JKM ≅ ∠LKM                |        CPCTC

16. KM bisects ∠JKL            |        definition of bisector

Positively Skewed: A positively skewed distribution is one that has a long tail in the positive direction (to the right).

The mean is usually greater than the median, and the data points are concentrated on the left side of the graph. To calculate the skewness of a distribution, we use the formula: skewness = (mean – median) / standard deviation. In the case of the histogram, the mean is greater than the median, and the skewness is therefore positive.

Symmetric: A symmetric distribution is one that is perfectly centered around the mean and has equal amounts of data points on either side of the mean. In the histogram, the data points are not perfectly centered around the mean, so this term does not apply.

Uniform: A uniform distribution is one that has all the data points clustered around the same value. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.

Unimodal: A unimodal distribution is one that has a single peak. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.

Bimodal: A bimodal distribution is one that has two peaks. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.

Negatively Skewed: A negatively skewed distribution is one that has a long tail in the negative direction (to the left). The mean is usually less than the median, and the data points are concentrated on the right side of the graph. To calculate the skewness of a distribution, we use the formula: skewness = (mean – median) / standard deviation. In the case of the histogram, the mean is less than the median, and the skewness is therefore negative.

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Answer:

32

Step-by-step explanation:

77 quarters and dimes

q + d = 77

subtract q from both sides

d = 77 - q

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

A collection of  quarters and dimes is worth $12.50 (1250 cents)

25q + 10d = 1250

substitute for d

25q + 10(77 - q) = 1250

distribute

25q + 770 - 10q = 1250

Combine like terms

15q + 770 = 1250

subtract 770 from both sides

15q = 480

divide both sides by 15

q = 32

I got you, buddy!

Let x be the length of the shortest side. Then, the length of the second side is 2x, and the length of the third side is x + y, where y is the additional length.

The perimeter of the triangle is the sum of the three sides, so we have:

x + 2x + (x + y) = 60

Simplifying this equation, we get:

4x + y = 60

We also know that the area of a triangle is given by:

A = (1/2)bh

where b is the length of the base, and h is the height. Since the base of the flower bed is the shortest side of length x, we can choose the height to be y. Therefore, we have:

A = (1/2)xy

Now we need to solve for x and y. We can use the equation for the perimeter to solve for y:

y = 60 - 4x

Substituting this into the equation for the area, we have:

A = (1/2)x(60 - 4x)

Simplifying and expanding, we get:

A = 30x - 2x^2

To maximize the area, we can take the derivative of A with respect to x and set it equal to 0:

dA/dx = 30 - 4x = 0

Solving for x, we get:

x = 7.5

Substituting this back into the equation for y, we get:

y = 60 - 4x = 45

Therefore, the dimensions of the flower bed are:

shortest side = x = 7.5 feet second side = 2x = 15 feet third side = x + y = 52.5 feet

Answer:

Will is 122% of Wandas height.

Step-by-step explanation:

Answer:

x+y=40 and 6x+9y=288

Answer:

Step-by-step explanation:

Mean is the ratio of sum of the dataset to the sample size. Mathematically:

\(\overline x = \frac{\sum Xi}{N}\)

Xi are the individual periods

N is the sample size

\(\sum Xi = 1.06+1.31+1.28+0.99+1.48+1.37+0.98+1.31+1.59+1.55\\\sum Xi = 12.92\)

N = 10

Substitute

\(\overline x = \frac{12.92}{10}\\\overline x = 1.292\)

hence the mean of the samples is 1.292

For the standard deviation:

\(\sigma = \sqrt{\frac{\sum (x-\overline x)^2}{N} } \\\)

\(\sum (x-\overline x)^2 = (1.06-1.292)^2+ (1.31-1.292)^2+ (1.28-1.292)^2+ (10.99-1.292)^2+ (1.48-1.292)^2+ (1.37-1.292)^2+ (0.98-1.292)^2+ (1.31-1.292)^2+ (1.59-1.292)^2+ (1.55-1.292)^2\\\sum (x-\overline x)^2 = 0.43996\)

Substitute into the formula:

\(\sigma = \sqrt{\frac{0.43996}{10} }} \\\sigma = \sqrt{{0.043996}}} \\\sigma = 0.2098\)

Hence the standard deviation is 0.2098

the (ascending) least to greatest of the given numbers are

Answer: (6,-6)

Step-by-step explanation:

To find the coordinates of point B, we can use the midpoint formula:

Midpoint formula: The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

M = ((x1+x2)/2, (y1+y2)/2)

Here, we know that the midpoint M is (4, -2), and one endpoint A is (2, 2). Let B be the other endpoint, so we can use the midpoint formula to find B:

4 = (2+x2)/2 --> 8 = 2+x2 --> x2 = 6

-2 = (2+y2)/2 --> -4 = 2+y2 --> y2 = -6

Therefore, point B has coordinates (6, -6).

As for the second question, without a graph or information about the equation of line t and point P, it is not possible to determine which points lie on the line passing through P and perpendicular to t.

m / n = 4 / 330 in its lowest terms.

Let's first calculate the number of ways to arrange the trees such that no two birch trees are next to each other.

There are 3! (3 factorial) ways to arrange the maple trees, 4! ways to arrange the oak trees, and 5! ways to arrange the birch trees. To arrange all the trees in a row such that no two birch trees are next to each other, we need to arrange the maple and oak trees in between the birch trees.

There are 4 positions where the birch trees can be placed:

The number of ways to arrange the trees such that no two birch trees are next to each other is then 4 * (3! * 4!) * (5!).

Finally, to find the probability that no two birch trees are next to each other, we divide this by the total number of possible arrangements, which is (3 + 4 + 5)!.

m / n = (4 * (3! * 4!) * (5!)) / (3 + 4 + 5)! = (4 * 720 * 120) / (12!) = 4 * 720 / (12 * 11 * 10!) = 4 / 330

So, m / n = 4 / 330 in its lowest terms.

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Answer:

41/5

Step-by-step explanation:

7+5m=48

5m=41

m=41/5

If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and  \(\frac{9K}{8}\)

Spring stiffness is a characteristic that describes the relationship between load and deflection. If k is stiffness, P is load, and x is deflection, P = kx. The smaller the deflection at a constant load, the stiffer the spring, k.

Given that,

If spring A has a spring constant which is 8 times spring B's spring constant,

Let us assume,

A spring is cut into two parts of length La and Lb

Also given that La : Lb

La : Lb = 1 : 8

The total of spring constant is = 1 + 8 = 9

If the length of spring is L , then La

La = \(\frac{L}{9}\)

And length of B , Lb

Lb = \(\frac{8L}{9}\)

We know, for spring force , spring constant or stiffness of spring is inversely proportional to length of spring .

K ∝ 1 / L

If initial spring constant is k then,

kL= KaLa = KbLb

Then,

Ka = \(\frac{K}{\frac{1}{9} }\)

Ka = 9K

And Kb = \(\frac{K}{\frac{8}{9} }\)

Kb = \(\frac{9K}{8}\)

Hence, stiffness of A is given by, 9K

Stiffness of B is given by  \(\frac{9K}{8}\)

Therefore,

If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and  \(\frac{9K}{8}\)

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Answer:

Either B or C but i'll have to say B if I had to choose.

Step-by-step explanation:

\( {0.9}^{0} = 1\)

\( {0.9}^{1} = 0.9\)

\(0.9 ^{2} = 0.81\)

\( {0.9}^{3} = 0.729\)

\( {0.9}^{4} = 0.6561\)

\( {0.9}^{5 } = 0.59049\)

As we can tell it decreases slowly.

The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.

Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.

A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.

According to the given information:

The Capital Asset Pricing Model (CAPM) is expressed as:

R = Rf + beta*(Rm - Rf)

Where:

R = Required rate of return

Rf = Risk-free rate of return

beta = Beta coefficient (systematic risk)

Rm = Expected market return

Using the given values, we can compute the required rate of return for each stock:

Stock with beta of 0.5:

R = 5% + 0.5*(10% - 5%)

R = 7.5%

Stock with beta of 2:

R = 5% + 2*(10% - 5%)

R = 15%

Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.

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The length of the longest side is 90 feet, length of the shortest side is 80 feet and the length of the middle side is 85 feet.

Given, the shortest side of a triangle is 10 feet shorter than the Longest side. The middle side is 5 feet shorter than the longest side.

let the longest side be x feet.

shortest side be x ₋ 10 feet.

middle side be x ₋ 5 feet.

the perimeter of the triangle is 255 feet.

a ₊ b ₊ c = 255

x ₊ x ₋ 10  ₊ x ₋ 5 = 255

3x ₋ 15 = 255

3x = 255 ₊ 15

3x = 270

x = 270/3

x = 90

substitute x value in : x ₋ 10

hence the length of the shortest side is 90 ₋ 10 = 80 feet.

similarly, x ₋ 5 = 90 ₋ 5 = 85 feet is the length of the middle side.

hence we get the desired results.

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Answer:

q = 9

Step-by-step explanation:

Make a ratio equation:

36 : 54 = 6 : q

\(\frac{2}{3} =\frac{6}{q}\)

2q = 18

q = 9

Answer:

q = 9

Step-by-step explanation:

These shapes are similar, so set up a proportion like so:

\(\frac{54}{36} =\frac{9}{q}\)

→Cross multiply:

\(\frac{324}{36q}\)

→Divide 324 by 36:

q = 9

The given histogram is bimodal, which is the last option/ option E, as bimodal distribution means that the data set has two distinct peaks or modes. In a bimodal histogram, the bars are grouped in a way that shows two prominent peaks or modes in the data.

Each bar in the histogram represents a specific range of values, and the height of the bar indicates the frequency or count of data points falling within that range. In a bimodal histogram, there will be two relatively high bars that correspond to the two modes of the data. The bimodal histogram is useful for visualizing and analyzing data sets that exhibit two distinct groups or clusters. It provides a clear visual representation of the two modes and their frequencies, which can help in identifying patterns and understanding the underlying characteristics of the data.

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Answer:

Below

Step-by-step explanation:

(x-10)^2 = 90     sqrt both sides

x-10  =  ± sqrt (90)

x  =   10 ± sqrt (90)

Answer:

Step-by-step explanation:

The kite is approximately 345 feet above the ground.

The height of the kite above the ground is 287 ft

The length of the string, the height of the kite (h) above ground and the perpendicular distance from the end of the kite string to the man forms a right angled triangle.

Trigonometric shows the relationship between the lengths and angles of a right angled triangle.

Therefore using trigonometric ratios:

sin(55) = h / 350

h = 287 ft

Therefore the height of the kite above the ground is 287 ft.

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

The hill makes an angle of approximately 11.98 degrees with the horizontal.

From the information, a force of 5 lb is required to hold a 24-lb crate on a hill and we want to know the angle that the hill make with the horizontal.

F = W * sin(θ)

where sin(θ) is the sine of the angle θ.

Solving for sin(θ), we get:

sin(θ) = F / W

       = 5 lb / 24 lb

       ≈ 0.2083

θ = arcsin(0.2083)

  ≈ 11.98 degrees

Therefore, the hill makes an angle of approximately 11.98 degrees with the horizontal.

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The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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You would pay $3 per mile if the cab travels 6 miles

The graph that completes the question is added as an attachment

On the graph, we can see that

When x = 6, the value of y is at 3

This means that the rate at 6 miles is $3

Hence, you would expect to pay $3 per mile for 6 miles

Also, from the graph

The value of y does not enter the negative axis

This means that will the average cost per mile never go below zero.

What could contribute to this?

Because the cost should not be negative. Also, distance in miles can not be negative.

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The function given is:

We can re-arrange it in the form:

This takes the form:

This is the equation of a line in the slope-intercept form where m is the slope of the line and b is the y-intercept of the line (y-axis cutting point). This is a linear function.

Answer: Base and Height

Step-by-step explanation: You would multiply the base and height. Since it is not a triangle you wouldn't divide it by 2

The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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Answer:

14cm²

Step-by-step explanation:

Add up all the squares and the other bits to get the answer.