The sum of the measures of angle M and angle R is 90°.
• The measure of angle M is (5x + 10)°.
• The measure of angle R is 55°.
What is the value of x?

Answer:

The inverse Laplace transform of 1/(s-1)^2 (s+1) is e^t - te^t + e^(-t)

We start by applying partial fraction decomposition to the given expression:

1/(s-1)^2 (s+1) = A/(s-1) + B/(s-1)^2 + C/(s+1)

Multiplying both sides by the denominator, we get:

1 = A(s-1)(s+1) + B(s+1) + C(s-1)^2

Substituting s=1 gives:

1 = 4C

So, C=1/4.

Substituting s=-1 gives:

1 = -4A

So, A=-1/4.

Substituting s=1 and simplifying gives:

B = 1/2.

Thus, we have:

1/(s-1)^2 (s+1) = (-1/4)/(s-1) + (1/2)/(s-1)^2 + (1/4)/(s+1)

Taking the inverse Laplace transform of each term using the table of Laplace transforms, we get:

L^(-1){(-1/4)/(s-1)} = -e^t

L^(-1){(1/2)/(s-1)^2} = te^t

L^(-1){(1/4)/(s+1)} = (1/2)e^(-t)

Hence, the inverse Laplace transform of 1/(s-1)^2 (s+1) is e^t - te^t + e^(-t).

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since the population standard deviations (σ1 and σ2) are not provided, we cannot calculate the exact test statistic Z.

To test the null hypothesis H0: (μ1 - μ2) = 0 versus the alternative hypothesis Ha: (μ1 - μ2) ≠ 0, we can use a two-sample z-test. The test statistic is calculated as:

Z = (x bar1 - x bar2) / sqrt((σ1^2 / n1) + (σ2^2 / n2))

Where:
X bar1 and x bar2 are the sample means of the two groups,
σ1 and σ2 are the population standard deviations of the two groups,
n1 and n2 are the sample sizes of the two groups.

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Answer: y = -3x + 10

Step-by-step explanation:

Slope-Intercept is written as y = mx + c : m represents the slope and c represents the y-intercept.

On this graph, we see that the line crosses the y-axis when y = 10, meaning we can replace c with positive 10: y = mx + 10.

Now we need to find the slope. In order to this, we need to use a formula:

\(m=\frac{y_2 - y_1}{x_2 - x_1}\)

We will need to choose two coordinates for this, I will be using the coordinates (0, 10) and (1, 7). We can then plug the appropriate values in:

\(m = \frac{7 - 10}{1 - 0} = \frac{-3}{1} = -3\)

Now we can replace the m in the equation with -3, so we will not get:

y = -3x + 10

Hope this helps.

Answer:

i dont really know but im gonna guess that its the first one

Answer:

When y = |x + h|, the graph is shifted (or translated) to the left.

When y = |x - h|, the graph is shifted (or translated) to the right.

Step-by-step explanation:

Part A:

The parent function of vertex graphs are y = |x|, and any transformations done to y = |x| are shown in this format (also known as vertex form): y = a|x - h| + k

(h , k) is the vertex of the graph.

So, for the first part, what y = |x + h| is saying is y = |x -  (-h)|.

The -h is substituted for h, and negatives cancel out, resulting in x + h.

This translates to the left of the graph.

Part B:

For the second part, y = |x - h| looks just like the normal vertex form. In this one, we are just plugging in a positive value for h.

This translates to the right of the graph.

Therefore , the solution of the given problem of function comes out to be Nolan dropped the ball from a height of 12 units at the beginning.

The study of mathematics includes numbers, symbols, and their parts, as well as anatomy, building, and both actual and hypothetical geographic locations. The relationships between different components, each of which has a corresponding result, are described by a function. A function is made up of a variable of distinct components that, when put together, produce specific results for each input.

Here,

Assume that h represents the original height at which Nolan threw the ball. The object bounces once and rises to a height of 4, so after the bounce it has a height of h + 4.

=> h = k f(1) (1)

where k is a constant that denotes how much energy the object retains after each bounce.

=> h = k(4) (4)

The knowledge that the ball returns to a height of 4 on the first bounce must be used to determine the value of k:

=> 4 = k f(1) (1)

=> 4 = k (4/3)

=> k = 3

When we put this number of k back into the equation as a replacement for h, we get:

=> h = k(4) = 3(4) = 12

Nolan dropped the ball from a height of 12 units at the beginning.

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As the sample size increases, the margin of error a. decreases

In a random survey sample, the margin of error is a statistical measure that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.

The number of distinct samples that are measured or observations that are used in a survey or experiment is known as the sample size. For instance, your sample size is 100 if you examine 100 samples of soil for signs of acid rain. If 30,500 completed questionnaires from an online survey were returned, your sample size is 30,500.

Hence, as the sample size increases, the margin of error decreases.

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Answer:

A

Step-by-step explanation:

option A has two linear equations that intersect at one point

option B has two linear equations that are parallel and do not intersect

option C has one linear equation and an absolute value equation that intersect at two points

option D has one linear equation and a quadratic equation that intersect at two points

Answer:

72

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

18 divided by 3/4 equals 24

Answer:

b

Step-by-step explanation:

just add x values and numbers

\((8x^4y^5)^{\frac{2}{3}}\implies (2^3x^4y^5)^{\frac{2}{3}}\implies 2^{3\cdot \frac{2}{3}} x^{4\cdot \frac{2}{3}} y^{5\cdot \frac{2}{3}}\implies 2^2 x^{\frac{8}{3}} y^{\frac{10}{3}}\implies 4x^{\frac{8}{3}} y^{\frac{10}{3}}\)

The simplest radical form of the expression  \((8x^4y^5)^{\frac{2}{3} }\)  is \(\sqrt[3]{(8x^4y^5)^2}\).

What is radical form of the expression?

A radical expression is an expression containing a square root.

We have,

\((8x^4y^5)^{\frac{2}{3} }\)  

To write it in simplest radical form,

We will use this formula \(a^{\frac{x}{n} } =\sqrt[n]{a^{x} }\)

So, using this we get,

\((8x^4y^5)^{\frac{2}{3} }=\sqrt[3]{(8x^4y^5)^2}\)

Hence, we can say that the simplest radical form of the expression  \((8x^4y^5)^{\frac{2}{3} }\)  is \(\sqrt[3]{(8x^4y^5)^2}\).

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Answer:

A. and D.

Step-by-step explanation:

Match the side lengths with each other. For 3), the reflect each other, so RQ would be parallel to RV. For 4), it is upside down, so if you were to flip it around, it would be MK is parallel to RS.

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Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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If 250 bricks are used to build a wall of 15 ft high then, there is total 1250 bricks will be used to build a wall that is 75 ft high.

Proportion:

A proportion is an equation between two ratios or rates that is useful in solving for a single unknown.

We have given that,

It takes 250 bricks to build a 15 ft high wall. Let us consider x bricks , is needed for a 75 ft high wall, use the ratio given for a 15 ft high wall and equate it to the ratio for the unknown number of bricks for a 75-ft high wall.

In making proportions, make sure that the rate on one side has the same units as the rate on the other as shown :

x/75 = 250/15

=> 15 × x = 250 ×75

=> x = 250×75/15

=> x = 1250

Thus, it will take 1250 bricks to build a wall 75 feet high.

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A cone has a diameter of 12 centimeters and a height of 9 centimeters. The volume of the cone would be 2034.72 cubic cm.

Suppose that the radius of considered right circular cone be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

\(V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3\)

The right circular cone is the cone in which the line joining the peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

A cone has a diameter of 12 centimeters and a height of 9 centimeters.

Radius = 12/2 = 6cm

Height h = 9 cm

The volume of the cone

\(V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3\)

\(V = \dfrac{1}{3} \times 3.14 \times 6^3 \times 9\: \rm unit^3\\\\V = 3.14 \times 648\\\\V = 2034.72 cm^{3}\)

Hence, The volume of the cone would be 2034.72 cubic cm.

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Answer:

45 jeweled and 20 enameled music boxes.

Step-by-step explanation:

( j stands for jeweled and e stands for enameled )

j + e = 25        The equation for the original total of music boxes.

3j + 2e = 65    The equation for the current total of music boxes.

15{ j } + 10{e} = 25     Since the total is 25, I know that the variable will be a multiple of 5. (since that's the only way to get a number that ends in 5).

3(15) + 2(10) = 65  

45 + 20 + 65

Answer:

33.88

Step-by-step explanation:when u divide you get it.when you divide the equvelents of the fraction you can get a deciml of that predicament heras ives got 22.33.

a. False; if b is negative, then -b is positive, so

a - b = a + (-b)

is the sum of two positive numbers, which must be positive.

b. True; the sum of two negative numbers is again negative.

c. True; a + b will be positive as long as a > |b|. (For example, if a = 2 and b = -1, then of course 2 > |-1| = 1, and a + b = 2 + (-1) = 1 > 0.)

d. False; this would contradict the result of part (c). b + a is only negative if a ≤ |b|. (For example, if a = 1 and b = -2, then b + a = -2 + 1 = -1 < 0.)

The slope of the line will allow us to determine the resistance of the wire so option (D) will be correct.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

Resistance of a wire is given by

R = V/I

The slope of a linear function is nothing by

Slope = y/x

So,

The slope of the given diagram

Slope = V/I

So,

R  = Slope

Hence to determine the resistance we need to determine the slope of the graph.

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The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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To maximize the area, the fence should be laid out in a square shape, where both sides measure 15 feet. To maximize the area of a rectangular vegetable garden with a given fence length.

it's important to understand that a rectangle with equal side lengths will yield the maximum area.

Let's denote the length of one side of the rectangle as x and the other side as y. According to the problem, the perimeter of the rectangle is given as 60 feet, so we have the equation:

2x + 2y = 60

Simplifying this equation, we get:

x + y = 30

To maximize the area, we need to maximize the product of x and y. Since x + y = 30, we can rewrite the equation as:

y = 30 - x

Substituting this into the area equation A = x * y, we get:

A = x * (30 - x)

To find the maximum area, we can take the derivative of A with respect to x and set it equal to zero:

dA/dx = 30 - 2x = 0

Solving this equation, we find x = 15. Substituting this back into y = 30 - x, we get y = 15 as well.

Therefore, to maximize the area, the fence should be laid out in a square shape, where both sides measure 15 feet.

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Answer:

A.

Step-by-step explanation:

The answer is B.

Each pack costs 2.50, so this means we can add all of our packs brought together, before multiplying. (2+4+3)=7. So our final equation should be 7 x 2.50 ,therefore B is our correct answer.

Hope this helps. & don't forget to drink water !!

Answer:

Step-by-step explanation:

moving the two segments as in the figure I put, the perimeter doesn't change.

P = 2(length + breadth)

2 x (12 + 18) = 60 cm

The required speed in km/hr are 108km/hr and 25.704km/hr

Given the following conversion rate

Given that the speed of cheetah is 30meters per second. Converting to m/s will give:

30m/s = \(\frac{30m}{1s} \times \frac{1km}{1000m} \times \frac{3600s}{1hr} \\\)

30m/s = 30 * 3.6

30m/s = 108km/hr

For the person with speed of 7.14m/s, the value in km/hr is expresssed as:

7.14m/s = 7.14 * 3.6

7.14m/s = 25.704km/hr

Hence the required speed in km/hr are 108km/hr and 25.704km/hr

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Answer: The answer is 226.2 feet.

Step-by-step explanation: The formula to find the total surface area of a cylinder is 2\(\pi\) x radius squared x height. If you use the formula you will get 226.19 feet as your answer and I rounded that to 226.2 feet.

UR MOM

Answer:

3.14ft²

Step-by-step explanation:

Area of a circle= πr²

= 3.14 x 1²

= 3.14 x 1

= 3.14 ft²

Answer:

The answer is 5/6.

Step-by-step explanation:

Lets start with a=1.

a+1=2, which is the denominator. (1/2)

Taking the same number as numerator, now, consider a=2.

a+1=3, denominator.(2/3)

Now, let a=3.

a+1==4, denominator for a=3. (3/4)

If continued a becomes equal to 4.

a+1=5, which is also the denominator. (4/5)

Now, since the denominator is 5, let a=5.

a+1=6, which will become the denominator. (5/6)

Thus the series follows a pattern of a/a+1.

Answer:

5/4

Step-by-step explanation:

Let's put the unknown value as X

To solve this equation, we must solve for x

First we need to isolate x, which means we need to get it by itself.

To do this, we must subtract 3/4 on both sides since it is being added.

This gets rid of 3/4 on the first side and changes the second side to whatever 2+3/4 is

This leaves us with x=5/4

Therefore, your answer is 5/4.

Answer:

1/3

Step-by-step explanation:

there are two numbers greater than 4, 5 and 6

so the probability is 2/6 or 1/3

Answer: There is an 1/3 chance of landing on a number greater than 4.

Step-by-step explanation: Divided into thirds to be made simpler 1/3 is 1-2, 2/3 is 3-4, and 3/3 (or the last third) is 5-6 (the number(s) greater than 4)

Based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

To determine the amount of capital this year based on the given information, we can use the investment and depreciation rates.

Let's denote the amount of capital this year as K1.

According to the information provided:

People invest 55% of income, but we don't have any information about income. Therefore, we cannot determine the exact investment amount.

10% of capital depreciates. Based on this, the capital at the beginning of this year (K1) can be calculated as follows:

K1 = K - 0.1K

= 0.9K

Since we know that the capital last year was equal to 25, we substitute K = 25 into the equation above:

K1 = 0.9 * 25

= 22.5

Therefore, based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

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