The sun of two numbers is 51 and their difference is 13. find the numbers.

Answer:

3

Step-by-step explanation:

The equation has a double root at x = 2, this means the tangent line intersects the curve only at P(2, 10).

Therefore, Q does not exist in this case.

To find the coordinates of Q, we need to determine the equation of the tangent line at point P(2, 10) and then find the point where this tangent line intersects the curve \(y = x^2 + 3x\)  again.
Differentiate y with respect to x to find the slope of the tangent line.
\(y = x^2 + 3x\)
dy/dx = 2x + 3
Find the slope of the tangent line at P(2, 10).
dy/dx at P = 2(2) + 3 = 7
Use the point-slope form to find the equation of the tangent line.
y - y1 = m(x - x1)
y - 10 = 7(x - 2)
Simplify the equation.
y - 10 = 7x - 14
y = 7x - 4
Find the intersection between the tangent line and the curve by setting the equations equal.
\(x^2 + 3x = 7x - 4\)
Solve for x.
\(x^2 - 4x + 4 = 0\)
(x - 2)(x - 2) = 0
We already know P(2, 10) is one of the intersection points.

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Answer:

5.) Associative Law

6.) Commutative Law

7.) Distributive Law

8.) Associative Law

9.) Distributive Law

10.)

Step-by-step explanation:

The associative law means that if all the arithmetic operations in an equation are the same, the position of the brackets do not matter and no matter which variables are associated, the result would still be the same.

The commutative law means that if all the arithmetic operations in an equation are the same, the position of the variables do not matter and no matter what order the variables are placed, the result would still be the same.

The distributive law means that whatever is outside of the bracket has to be multiplied into the variables in the bracket evenly. E.g. 1/4 (8x - 20) involves multiplying both 8x by 1/4 and 20 by 1/4.

A parametrization of the line passing through (-2, 10, -8) and (1, -6, -10) is given by (x, y, z) = (-2 + 3t, 10 - 16t, -8 - 2t), where t is a parameter.

To find a parametrization of the line, we can start by calculating the differences between the corresponding coordinates of the two given points: Δx = 1 - (-2) = 3, Δy = -6 - 10 = -16, and Δz = -10 - (-8) = -2.

We can express the coordinates of any point on the line in terms of a parameter t by adding the differences scaled by t to the coordinates of one of the points. Let's choose the first point (-2, 10, -8) as the starting point.

Therefore, the parametric equations of the line are:

x = -2 + 3t,

y = 10 - 16t,

z = -8 - 2t.

These equations give us a way to generate different points on the line by varying the parameter t.

For example, when t = 0, we obtain the point (-2, 10, -8), and as t varies, we get different points lying on the line.

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Mohr's circle is a graphical method used to determine the principal stresses and shear stresses in a material. Given the stress components σx = 16 ksi, σy = 9 ksi, and τxy = 5 ksi, we can follow several steps to draw and analyze Mohr's circle.

1. To begin, draw a stress element with the x-axis representing normal stress (σ) and the y-axis representing shear stress (τ). Label the x-axis as σ and the y-axis as τ.

2. Find the center of Mohr's circle by calculating the average of the normal stresses: (σx + σy) / 2. In this case, the center is ((16 + 9) / 2, 0) = (12.5 ksi, 0).

3. Determine the radius of Mohr's circle using the formula: R = ((σx - σy) / 2). In this case, the radius is ((16 - 9) / 2) = 3.5 ksi.

4. Draw Mohr's circle with the center at (12.5 ksi, 0) and a radius of 3.5 ksi. The circle represents all possible stress states for the given stress components.

5. To draw the principal stress element, draw a line from the center of the circle to the right edge of the circle. The angle between this line and the x-axis represents the orientation of the principal stress element.

To find the absolute shear stress when σx = σy, we need to identify the point on Mohr's circle where the x-axis intersects. At this point, the shear stress (τ) is zero, since there is no shear stress when σx = σy.

Mohr's circle can be drawn by following the steps outlined above. The circle represents all possible stress states, and the principal stress element can be identified by drawing a line from the center to the right edge of the circle. The absolute shear stress when σx = σy is zero, as indicated by the point where the x-axis intersects Mohr's circle.

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Answer:

slope = 3

Step-by-step explanation:

rise/run = 6/2 = 3

Answer:

3/20

Step-by-step explanation:

-

Answer:

0.15

Step-by-step explanation:

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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The measure of variability that is sensitive to the presence of outliers is the standard deviation.

The standard deviation takes into account the distance between each data point and the mean, which means that extreme values, such as outliers, can have a significant impact on the calculation of the standard deviation.

Standard deviation is a measure of the variability or dispersion of a set of values or data points. It quantifies how much the individual data points in a dataset deviate from the mean (average) value.

Mathematically, the standard deviation is calculated as the square root of the variance. The variance is the average of the squared differences between each data point and the mean. By taking the square root of the variance, we obtain the standard deviation, which is expressed in the same units as the original data.

The standard deviation provides a measure of how spread out the data is around the mean. A small standard deviation indicates that the data points are close to the mean, while a large standard deviation indicates that the data points are more spread out.

In statistical analysis, the standard deviation is often used to assess the variability and to compare the spread of different datasets. It is an important tool for understanding the distribution of data and making inferences about the population based on a sample.

In addition, the standard deviation is a key component in many statistical calculations and hypothesis tests. It is used to calculate confidence intervals, determine the significance of differences between groups, and assess the precision of estimates.

Overall, the standard deviation provides valuable information about the spread and variability of data, helping to summarize and interpret datasets in a meaningful way.

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Answer:

2.94

Step-by-step explanation:

multiply them like normal multiplication

remember that 2 negatives equal positive

The correct response is d) Exponential Decay. The x- intercept(s) of f(x)\(=25 *(0.20)^x\) does not exist.

The x- and y-intercepts of a line are the locations where the x- and y-axes, respectively, cross. When we take intercepts into account, graphing linear equations becomes simpler. the point where the x-axis crosses a surface, curve, or line. The x-intercept of a line on a graph is where the line intersects the x-axis. The value of the y coordinate is zero at that point. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).

f(x)\(=25*(0.20)^x\)

dy/dx=\(25*(0.2)^x\)

Evaluate derivative.

x- intercept(s) does not exist.

The type of function for f(x)\(=25 *(0.2)^x\) is exponential function.

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this is a example of f(x)=25 •(0.20)^x

a) Linear Growth

b) Linear Decay

c) Exponential Growth

d) Exponential Decay

Answer:

the graph has a minimum

Step-by-step explanation:

the minimum is -9

Answer:

the graph has a minimum & the vertex is located at (-1,-9)

Step-by-step explanation:

Minimum is where its like at the bottom opening down. And the vertex is the x value of the minimum point. Maximum is the opposite where the curve is facing upwards and is the highest point where the vertex is the x value of the maximum or highest point.

Answer:

B.2x-5=x+25

Step-by-step explanation:

2x+15=35            x = 10

4/5x=8                x = 10

2x-5=x+25          x = 30

2x+7=27             x = 10

4/3x=x+10/3       x = 10

Answer:

Answer:

D -512

Step-by-step explanation:

All you have to do is just multiply the exponents and you are done.

Step-by-step explanation:

4(5x-9)=-2(x+7)

4*5x-4*9=-2*x-2*7

20x-36=-2x-14

20x+2x=-14+36

22x=22

x=22/22

x=1

Answer: 96

Step-by-step explanation:

A palindrome is a number that is the same when reading in both ways (right to left, and left to right), for example, 121

Then, we have 9 digits, and all the digits need to be even.

the options are: 0, 2, 4, 6, 8.

Now, we can tink a 9 digit number as 9 empty slots, and in each slot, we can put a number.

But because this is a palindrome, the first digit must be equal to the ninth, and the second digit must be equal to the eight, and so on.

So we can tink it as actually only 5 slots, where in each slot, we can put an even number, now let's count the options that we have in each selection.

For the first digit we have 4 options: 2, 4, 6 and 8 (0 is not counted here because if the first digit was a 0, then this would not be a 9 digit number).

for the second digit, we have also 4 options (because we already toked one, but now the 0 can be chosen)

for the third digit, we have 3 options

for the fourth digit, we have 2 options

for the fifth digit, we have only one option.

The total number of combinations is equal to the product of the number of options for each selection:

C = 4*4*3*2*1 = 96

Answer:

96

Step-by-step explanation:

Based on the monthly expenses breakdown, getting a car loan to cut down on monthly car repair cost would be a good move.

Using the parameters given :

Total income : $705.00

Total Expenses : $510.00

Amount saved = $225.00

The amount saved from Last month's income is quite okay. However, looking at the breakdown of her expenses, we can see that she spent quite a lot on car repairs.

It would be advisable of Lianna could get a good car which would allow her to cut down on repair cost because in the long run, it could eat up her savings as well.

Hence, Lianna should opt for a car loan to cut down on repair cost.

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The amount of material is the area of the kite

The amount of material needed for the entire kite is 48 square inches

The given parameters:

Start by calculating the area of the bottom triangle using:

\(Area = 0.5 * base * height\)

So, we have:

\(Area = 0.5 * KI * KT\)

This gives

\(Area = 0.5 * 6* 10\)

\(Area = 30\)

The amount of material used is the sum of both areas

\(Material = 30 + 17\)

\(Material = 47\)

This approximates to 48

Hence, 48 square inches of material is used for the entire kite

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Answer:

c ( 48 )

Step-by-step explanation:

edg

The woman plans to save $1,000,000 by depositing $500 each month into an ordinary annuity with a 4.3% annual interest rate. The explanation will calculate the number of years it will take for her to retire.

To determine the number of years it will take for the woman to retire, we need to calculate the future value of the annuity and find the time it takes to reach or exceed $1,000,000.The future value of an ordinary annuity can be calculated using the formula:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the annuity

P is the monthly deposit ($500)

r is the monthly interest rate (4.3% / 12 = 0.03583)

n is the number of months

We can rearrange the formula to solve for n:

n = log(1 + (FV * r) / P) / log(1 + r)

Substituting the given values, we have:

n = log(1 + (1,000,000 * 0.03583) / 500) / log(1 + 0.03583)

Calculating this expression, we find that the woman will be able to retire in approximately 232.94 months. Since we are looking for the number of years, we divide this value by 12:

n = 232.94 / 12 ≈ 19.41

Therefore, it will take approximately 19.41 years for the woman to save $1,000,000 and retire.

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Answer:

i think its 14.4

Step-by-step explanation:i

Answer:

i think its c (14.4)

Step-by-step explanation:

pls mark brainliest! im tryna get to vituoso :3

If the geometry is Euclidean, then AB is congruent to CD in parallelogram ABCD.

To prove that if the geometry is Euclidean, then AB is congruent to CD in parallelogram ABCD, we can use the properties of parallel lines and Euclidean geometry.

Given: Parallelogram ABCD with AB || CD and AD || BC.

Now, the proof is:

1. Assume the geometry is Euclidean.

2. Since AD || BC and AB || CD, we have two pairs of parallel lines.

3. By the Euclidean Parallel Postulate, parallel lines remain equidistant from each other.

4. Take point A on line AD.

5. Draw a line segment AE parallel to BC from point A.

6. Since AB || CD, line AE is also parallel to CD.

7. By the properties of parallelograms, opposite sides are congruent.

8. Therefore, segment AB is congruent to segment AE.

9. Similarly, we can choose a point on line CD and draw a line segment parallel to AB to obtain a congruent segment.

10. Hence, segment CD is congruent to segment AE.

11. Combining steps 8 and 10, we have AB congruent to CD.

Therefore, if the geometry is Euclidean, then AB is congruent to CD in parallelogram ABCD.

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Probability that the event can happen = 1/2

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes

Given,

Total outcomes of event = 14

Outcomes, event can happen = 7

Probability

= Favorable Outcomes/Total Outcomes

= 7/14 = 1/2

Hence, 1/2 is Probability that the event occurs.

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Answer:

.35

.07

.625

.06625

.0325

Step-by-step explanation:

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Answer:

Yes, it is

Step-by-step explanation:

It is biased because all of the employees have over a decade of experienc, what about the newly hired ones?

Answer:

No it would be -15

Step-by-step explanation:

-3x-5=-15 where did you get that

Answer:

Your answer would be no.

Step-by-step explanation:

Hope I helped!! :)