What is the slope of the line on the graph

Step-by-step explanation:

A. Each point in the image has the same x-coordinate as the corresponding point

in the figure.

D. Each point in the image moves the same distance and direction from the

figure.

These two statements are true about a figure and an image created by a translation. When a figure is translated, every point in the figure is moved the same distance and direction. This means that each point in the image has moved the same way as its corresponding point in the figure. Additionally, since a translation only involves moving a figure without changing its shape or size, the image and figure are the same shape and size, but just in different positions. As such, statement B and C are not true for figures and images created by translation.

To graph the image G'R'A'M', we need to add 10 to each x-coordinate and subtract 2 from each y-coordinate:

G': (-9+10, -9-2) = (1,-11)

R': (-8+10, -6-2) = (2,-8)

A': (-4+10, -6-2) = (6,-8)

M': (-5+10, -9-2) = (5,-11)

Graphing these points and connecting them gives us parallelogram G'R'A'M'.

The table of values that represents exponential decay is (c)

From the question, we have the following parameters that can be used in our computation:

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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Answer:

\(Given ~that:-\)

\(y=f(u)\\\)

\(and~u=g(x)\)

\(So, dy/dx=f'(g(x))g'(x)\)

\(Now, y=u(u-1)\)

\(So, f(u)=4(4-1)\)

\(u=x^2+x\)

\(so,g(x)=x^2+x\)

\(d/dx=(g(x))=2x+1\)

\(g'(x)=2x+x\)

\(f(x)g'(x)=(x^2+x)(x^2+x-1)\)

\(f(g(x))g'(x)=x^2(x^2+x-1)+x(x^2+x-1)\)

\(=x^4+x^3-x^2+x^3+x^2-x\)

\(f(g(x)g'(x)=x^4+2x^3-x\)

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

\(So, ~ your~ answer~ is~ (B)~f'(g(x))g'(x)=4x^3+6x^2-1\)

Debido a que los amortiguadores, por ellos mismos, no son suficientes para absorber completamente los golpes provocados por las irregularidades del terreno, las suspensiones incorporan muelles interpuestos entre el eje y el chasis.

Los amortiguadores son elementos clave en los sistemas de suspensión de los vehículos, ya que absorben la energía generada por las irregularidades del terreno y evitan que las vibraciones lleguen al chasis y a la carrocería del vehículo. Sin embargo, los amortiguadores por sí solos no son suficientes para proporcionar una conducción suave y cómoda. Por esta razón, se incorporan muelles entre el eje y el chasis para ayudar a absorber los golpes y las vibraciones adicionales. Los muelles están diseñados para comprimirse y expandirse de manera controlada, lo que reduce la transferencia de energía al chasis del vehículo y mejora la estabilidad y el confort de la conducción.

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Answer:

I'm pretty sure A is the correct answer :)

(x-2)(x^4+3) is a polynomial

Answer:

You keep adding 15.

Step-by-step explanation:

5+15=20

20+15=35

35+15=50

50+15=65

To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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Given:

Two brothers are sharing a certain sum of money in the ratio \(\dfrac{2}{3}:\dfrac{3}{5}\).

The largest share was Gh¢500.00.

To find:

The total amount shared between them.

Solution:

It is given that, two brothers are sharing a certain sum of money in the ratio \(\dfrac{2}{3}:\dfrac{3}{5}\).

First we need to make the denominators common.

\(Ratio=\dfrac{2\times 5}{3\times 5}:\dfrac{3\times 3}{5\times 3}\)

\(Ratio=\dfrac{10}{15}:\dfrac{9}{15}\)

\(Ratio=10:9\)

So, the two brothers are sharing a certain sum of money in the ratio 10:9.

Let the shares of two brothers are 10x and 9x respectively. So, the larger share is 10x.

It is given that the largest share was Gh¢500.00.

\(10x=500\)

\(x=\dfrac{500}{10}\)

\(x=50\)

Now, the total amount shared between them is:

\(Total=10x+9x\)

\(Total=19x\)

\(Total=19(50)\)

\(Total=950\)

Therefore, the total amount shared between them is Gh¢950.00.

Answer:

49 mins

Step-by-step explanation:

11.08=15-0.08x

11.08-15=-0.08x

-3.92=-0.08x

x=49

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

In the given statement is:

λ = 2.5 x 10^-2 \(min^{-1}\)is the rate constant of the nucleus

To solve this problem, we use

N(t) = \(N_{0}\)e^-λt

and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set

N(t) = 1/4 \(N_{0}\) = 0.25\(N_{0}\)

We can substitute this in the decay equation:

0.25\(N_{0}\) =\(N_{0}\) e^-λt

Cancel the like terms

0.25 = e ^-λt

Take the natural logarithm of both sides:

㏑(0.25) =㏑(e^-λt)

㏑(0.25)= -λt

Solve for the time t:

t = - ㏑(0.25)/λ

Substitute the given rate constant :

t = ㏑(0.25) / 2.5 x 10^-2 \(min^{-1}\)

t = -1.3863 /2.5 x 10^-2 \(min^{-2}\)

t = 55.452mins

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

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Answer:

The maximum number of  square feet Jasmine can purchase is 12 square feet

Step-by-step explanation:

Given:

Jasmine has a budget of $600.00 to spend  on home renovations.

She will spend $175.00  on a new sink and the remainder on  countertops.

The countertops cost $35 per  square foot.

Now, to get the maximum number of  square feet Jasmine can purchase.

Now, we find the remainder amount to be spend on countertops:

$600 - $175 = $425.

Remainder amount = $425.

Cost of per square foot countertops = $35.

Now, to get the number of square feet which can purchase with $425:

Estimating value = 12 square feet.

Therefore, the maximum number of  square feet Jasmine can purchase is 12 square feet.

Answer:2/25

Step-by-step explanation:

The answer is already there\

Yes, snow and "cold" weather are independent events. The probability of snow and a "cold" day is 15.

Based on the given probabilities, we can determine if snow and "cold" weather are independent events. Independent events occur when the probability of both events happening together is equal to the product of their individual probabilities.

P(snow) = 0.30

P(cold) = 0.50

P(snow and cold) = 0.15

If snow and cold are independent, then P(snow and cold) = P(snow) * P(cold).

0.15 = 0.30 * 0.50

0.15 = 0.15

Since both sides of the equation are equal, snow and "cold" weather are independent events.

Your answer: b. yes

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Answer:

Bond

Step-by-step explanation:

A promissory note or a promise to repay a certain amount of money at some point in the future is basically a bond.

A bond is a debt security that represents a loan made by an investor to a borrower, which is usually a corporation or government agency. It is a fixed-income investment, meaning that the borrower promises to pay a specific amount of interest over a set period of time and return the principal amount of the loan on the date of maturity. Bonds are issued for various purposes, such as raising capital, funding new projects, or refinancing debt.

CD (Certificate of Deposit) is a savings instrument issued by a bank or credit union that generally pays a fixed rate of interest over a set term. Mutual fund is an investment vehicle that pools money from multiple investors to purchase a portfolio of securities, such as stocks, bonds, or both. Stock is an ownership share in a company that represents a claim on part of the company's assets and earnings.

Total distance represented by the simplified expression for which the car was tested equals option c. x² + 2x - 4 .

Total distance drive on flat road = x miles

Total distance drive on downhill =  (x²+ 3) miles

Total distance drive on uphill =  ( x - 7 ) miles

Simplified expression which is equivalent to total distance drive by a car

= Distance drive on ( flat road + downhill + uphill )

= ( x +  x²+ 3 + x - 7 ) miles

= ( x² + 2x - 4 ) miles

Therefore, the simplified expression equivalent to the total distance drive by a tested car is equal to option c.  ( x² + 2x - 4 ) miles.

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The above question is incomplete , the complete question is:

A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road,    (x²+ 3) miles downhill, and (x - 7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested?

a.3x² _ 4

b. 3x² + 10

c. x² + 2x - 4

d. x² + 2x + 10

Achieve a utility level of 2, we substitute the values of x and y into the utility function u(x, y) = √x + √y and set it equal to 2. Then, solve for I to find the required income.

To compute the expenditure function, we need to find the minimum expenditure required to achieve a given level of utility. In this case, the utility function is given as u(x, y) = √x + √y.

Let's denote the expenditure function as e(pₓ, pᵧ, u), where pₓ and pᵧ are the prices of goods x and y, respectively.

To find the expenditure function, we need to solve the utility maximization problem subject to the budget constraint.

The budget constraint equation is given by: pₓx + pᵧy = I, where I is the income.

Since the utility function is increasing in both x and y, the consumer will spend all their income to maximize utility. Therefore, the budget constraint becomes an equality: pₓx + pᵧy = I.

Now, let's solve the utility maximization problem by using the Lagrange multiplier method. We set up the following Lagrangian function:

L(x, y, λ) = √x + √y - λ(pₓx + pᵧy - I)

Taking partial derivatives with respect to x, y, and λ, and setting them equal to zero, we get the following equations:

(1/2√x) - λpₓ = 0 (1)

(1/2√y) - λpᵧ = 0 (2)

pₓx + pᵧy - I = 0 (3)

From equation (1), we have:

√x = 2λpₓ (4)

From equation (2), we have:

√y = 2λpᵧ (5)

Squaring both sides of equations (4) and (5), we get:

x = 4λ²pₓ² (6)

y = 4λ²pᵧ² (7)

Substituting equations (6) and (7) into equation (3), we have:

4λ²pₓ³ + 4λ²pᵧ³ - I = 0

Simplifying, we get:

λ²(pₓ³ + pᵧ³) = I/4

Solving for λ, we have:

λ = √(I / (4(pₓ³ + pᵧ³)))

Substituting the value of λ back into equations (6) and (7), we can find the values of x and y in terms of I.

Finally, to achieve a utility level of 2, we substitute the values of x and y into the utility function u(x, y) = √x + √y and set it equal to 2. Then, solve for I to find the required income.

Note: Due to the complexity of the calculations involved, providing a numerical solution for the income would be more appropriate.

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The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Answer:

203m^2

Step-by-step explanation:

Answer:

I think its 203m^2

Step-by-step explanation:

sorry if its not!

Applying the limit concept, it is found that the limit is 2 for 3 positive values of b.

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

The function given is:

\(f(x) = 0.1x^4 - 0.5x^3 - 3.3x^2 + 7.7x - 1.99\)

The limit of the function as x tends to b is:

\(\lim_{x \rightarrow b} f(x) = 0.1b^4 - 0.5b^3 - 3.3b^2 + 7.7b - 1.99\)

To find when the result of the limit is 2:

\(0.1b^4 - 0.5b^3 - 3.3b^2 + 7.7b - 1.99 = 2\)

Placing into standard polynomial format:

\(0.1b^4 - 0.5b^3 - 3.3b^2 + 7.7b - 3.99 = 0\)

Using a calculator, the solutions are: \(b_1 = -4.9978613719838, b_2 = 0.84536762603715, b_3 = 1.1540644992178, b_4 = 7.9984292467288\)

Of those, 3 are positive, thus the limit is 2 for 3 positive values of b.

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Answer:

The area of a trapezium is computed with the following formula: Area = 1 2 × Sum of parallel sides × Distance between them.

Step-by-step explanation:

Hope it help! :)

1. The solution to the given equation is y = (36/5)x.

In this question, we have been asked to find the solution to the given equation. We can solve the equation by combining like terms. On adding 3y and 2y, we get 5y. Then, we can solve for y by dividing both sides by 5

2. The solution to the given equation is j = 3x2 - y.

In this question, we have been asked to find the solution to the given equation. We can solve the equation for j by subtracting y from both sides.

The solution to the given equation is y = -3e-*.  In this question, we have been asked to find the solution to the given equation. We can solve the equation by combining like terms. On adding 2y and -3y, we get -y. Then, we can solve for y by dividing both sides by -1.Exercise 4: The given equation is û + 2y + 5y = 4e->cos2xSolution: û + 2y + 5y = 4e->cos2x (given equation) 7y = 4e->cos2x y = (4/7)e->cos2xTherefore, the solution to the given equation is y = (4/7)e->cos2x. In this question, we have been asked to find the solution to the given equation. We can solve the equation by combining like terms. On adding 2y and 5y, we get 7y. Then, we can solve for y by dividing both sides by 7.Exercise 5: The given equation is j- 2y + 5y = 4e-*cos2xSolution: j- 2y + 5y = 4e-*cos2x (given equation) j + 3y = 4e-*cos2x j = 4e-*cos2x - 3yTherefore, the solution to the given equation is j = 4e-*cos2x - 3y.  We can solve the equation for j by adding 2y and 5y to get 7y, then subtracting 7y from both sides, and finally, simplifying the equation.

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Answer:

4 square units

Step-by-step explanation:

The formula x = 800 - 400p represents the number of sketch pads sold per week based on the price p. R(p) = (800 - 400p) ˣ p; R(x) = (800 - 400x) ˣ x; The revenue obtained by selling the pads for $1.60 each is $384.

To write the formula for R(p), which represents the revenue obtained based on the price p, we need to multiply the number of sketch pads sold (x) by the price (p).

Therefore, R(p) = x ˣ p.

To write the formula for R(x), which represents the revenue obtained based on the number of sketch pads sold (x), we need to substitute the value of x from the given equation. Since x = 800 - 400p, we can write R(x) = (800 - 400p) ˣ p.

To find the revenue obtained by selling the pads for $1.60 each, we substitute p = 1.60 into R(p) or R(x) and evaluate the expression.

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Answer:

375$

Step-by-step explanation:

25*8 is 200, 575-200 is 375

The platelet count is 652 x 10^3.

Based on the information provided, it seems that the platelet count from a test result is 652, and the normal range for platelet count is 150,000 to 450,000 platelets per microliter of blood. The value "10(3)" likely refers to the measurement being in thousands.

To convert the measurement to the standard unit of platelet count, we need to multiply the given value by 1,000. Thus, 652 * 1,000 = 652,000 platelets per microliter.

It's important to note that platelet counts can vary depending on various factors, and medical professionals typically interpret the results in conjunction with other clinical information. If the obtained value of 652,000 platelets per microliter is accurate, it would be significantly higher than the upper limit of the normal range.

It's crucial to consult a healthcare professional or a qualified medical practitioner for an accurate interpretation of test results and any necessary medical advice or treatment.

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Answer:

x = 7 or x = -7

Step-by-step explanation:

First, divide both sides by 3 so we leave with x^2.

\(\displaystyle \large{x^2 = \frac{147}{3} \longrightarrow x^2 = 49}\)

Now we have x^2 = 49, remember that we are solving a quadratic equation which means x-values and their counterpart aka negative forms give same output value.

Ex.

2^2 is 4 and (-2)^2 is 4 as well.

3^2 is 9 and (-3)^2 is 9 as well.

Since both positive and negative or counterpart form give same output, when we square both sides, write plus or minus (apply plus or minus when the degree of term is even such as x^2, x^4, x^6, etc.)

Hence, \(\displaystyle \large{\sqrt{x^2} = \pm \sqrt{49} \longrightarrow x = \pm 7}\)

Therefore, x = 7 or x = -7 (you can write x = ± 7 instead)

Answer:

w > -16

Step-by-step explanation:

Answer:

72ft^2 is the answer hope it helps

Answer:

Step-by-step explanation:

Answer:

660 g

Step-by-step explanation:

12/4 = 3 large

12-3 = 9 small

3(70g) + 9(50g) = 660 g