A is the poin 3,5 and b is the point 0,k if the distance of ab is 5 units find the possible value of k

Answer:

89

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Answer:

104 m²

Step-by-step explanation:

There is a 1 m sidewalk around the garden

Then length = 30 + 1 + 1 = 32 m

and width = 20 + 1 + 1 = 22 m

Area = 32 × 22 = 704 m²

Area of garden = 30 × 20 = 600 m²

Area of sidewalk = 704 - 600 = 104 m²

To determine the number of points on the curve x³ + y³ = 9 in the xy-plane where the curve has a tangent line that is horizontal, we need to analyze the slope of the curve at different points.The answer is (d) 3.

First, we find the derivative of the given equation with respect to x:

d/dx (x³ + y³) = d/dx (9)

3x² + 3y² * dy/dx = 0

To have a horizontal tangent line, the slope dy/dx must be zero. Therefore, we need to find the values of x and y where dy/dx = 0.

From the equation 3x² + 3y² * dy/dx = 0, we see that dy/dx = -x²/y². For dy/dx to be zero, the numerator, x², must be zero. This implies that x = 0.

Substituting x = 0 into the original equation x³ + y³ = 9, we get y³ = 9. Solving for y, we find three possible values for y: y = ∛9, -∛9, and 0.

Therefore, there are three points on the curve x³ + y³ = 9 in the xy-plane where the curve has a tangent line that is horizontal. The answer is (d) Three.

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The value of q is -27.

Recall Vieta's Formulas, which state that for a quadratic equation \(ax^2\) + bx + c = 0 with zeroes alpha and beta, the sum of the zeroes is equal to -b/a, and the product of the zeroes is equal to c/a.

In our equation \(x^2\) - 3x + q, the sum of the zeroes alpha and beta is -(-3)/1 = 3.

We are given that 2 alpha + 3 beta = 15. Substitute alpha = (15 - 3 beta)/2 into the equation.

Replace the value of alpha in the sum of zeroes equation: (15 - 3 beta)/2 + beta = 3.

Simplify the equation by multiplying both sides by 2: 15 - 3 beta + 2 beta = 6.

Combine like terms: 15 - beta = 6.

Subtract 15 from both sides: -beta = -9.

Multiply both sides by -1 to solve for beta: beta = 9.

Substitute the value of beta into the sum of zeroes equation: alpha = (15 - 3 * 9)/2 = -3.

Since we have the values of alpha and beta, we can find q using the product of the zeroes formula: q = alpha * beta = -3 * 9 = -27.

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Step-by-step explanation:

1) To draw triangle ABC, we start by drawing a line segment BC of length 6 cm. Then we draw an angle of 40° at point B, and an angle of 60° at point C. We label the intersection of the two lines as point A. This gives us triangle ABC.

```

C

/ \

/ \

/ \

/ \

/ \

/ \

/ \

/_60° 40°\_

B A

```

2) To find the measure of angle BAC, we can use the fact that the angles in a triangle add up to 180°. Therefore, angle BAC = 180° - 40° - 60° = 80°.

3) To show that ABD is an isosceles triangle, we need to show that AB = AD. Let E be the point where the bisector of angle BAC intersects AB. Then, by the angle bisector theorem, we have:

AB/BE = AC/CE

Substituting the given values, we get:

AB/BE = AC/CE

AB/BE = 6/sin(40°)

AB = 6*sin(80°)/sin(40°)

Similarly, we can use the angle bisector theorem on triangle ACD to get:

AD/BD = AC/BC

AD/BD = 6/sin(60°)

AD = 6*sin(80°)/sin(60°)

Since AB and AD are both equal to 6*sin(80°)/sin(40°), we have shown that ABD is an isosceles triangle.

4) To show that MD is the perpendicular bisector of AB, we need to show that MD is perpendicular to AB and that MD bisects AB.

First, we can show that MD is perpendicular to AB by showing that triangle AMD is a right triangle with DM as its hypotenuse. Since M is the midpoint of AB, we have AM = MB. Also, since ABD is an isosceles triangle, we have AB = AD. Therefore, triangle AMD is isosceles, with AM = AD. Using the fact that the angles in a triangle add up to 180°, we get:

angle AMD = 180° - angle MAD - angle ADM

angle AMD = 180° - angle BAD/2 - angle ABD/2

angle AMD = 180° - 40°/2 - 80°/2

angle AMD = 90°

Therefore, we have shown that MD is perpendicular to AB.

Next, we can show that MD bisects AB by showing that AM = MB = MD. We have already shown that AM = MB. To show that AM = MD, we can use the fact that triangle AMD is isosceles to get:

AM = AD = 6*sin(80°)/sin(60°)

Therefore, we have shown that MD is the perpendicular bisector of AB.

5) Finally, to show that DM = DN, we can use the fact that triangle DNM is a right triangle with DM as its hypotenuse. Since DN is the orthogonal projection of D on AC, we have:

DN = DC*sin(60°) = 3

Using the fact that AD = 6*sin(80°)/sin(60°), we can find the length of AN:

AN = AD*sin(20°) = 6*sin(80°)/(2*sin(60°)*cos(20°)) = 3*sin(80°)/cos(20°)

Using the Pythagorean theorem on triangle AND, we get:

DM^2 = DN^2 + AN^2

DM^2 = 3^2 + (3*sin(80°)/cos(20°))^2

Simplifying, we get:

DM^2 = 9 + 9*(tan(80°))^2

DM^2 = 9 + 9*(cot(10°))^2

DM^2 = 9 + 9*(tan(80°))^2

DM^2 = 9 + 9*(cot(10°))^2

DM^2 = 9 + 9*(1/tan(10°))^2

DM^2= 9 + 9*(1/0.1763)^2

DM^2 = 9 + 228.32

DM^2 = 237.32

DM ≈ 15.4

Similarly, using the Pythagorean theorem on triangle ANC, we get:

DN^2 = AN^2 - AC^2

DN^2 = (3*sin(80°)/cos(20°))^2 - 6^2

DN^2 = 9*(sin(80°)/cos(20°))^2 - 36

DN^2 = 9*(cos(10°)/cos(20°))^2 - 36

Simplifying, we get:

DN^2 = 9*(1/sin(20°))^2 - 36

DN^2 = 9*(csc(20°))^2 - 36

DN^2 = 9*(1.0642)^2 - 36

DN^2 = 3.601

Therefore, we have:

DM^2 - DN^2 = 237.32 - 3.601 = 233.719

Since DM^2 - DN^2 = DM^2 - DM^2 = 0, we have shown that DM = DN.

Answer:

12

Step-by-step explanation:

See attached picture. We have a 3x3x3 cube. If we cut it into 27 cubes, we will end up with a rubik's cube like cube. Each of the small cubes will measure 1x1x1. So if we pay close attention to the cube, we will see that only the cubes on the edges will have two of its faces painted in two colors. We can think of the cube as having three layers. Each of the layers will have 4 edge cubes, so we will have in total:

3x4=12 cubes that will have only two of its faces with paint on them.

Concentric circles are internally tangent circles which is the true statement.

Geometry is the description of figures in a space with a specific number of dimensions and types. Plane geometry is the most prevalent sort of geometry (dealing with objects like the point, lines, circles, triangles, and polygons)

Concentric circles are circles that have the same center but different radii.

When two concentric circles are drawn, it is possible for them to be internally tangent, meaning that they touch each other at exactly one point and the point of tangency is inside both circles.

In this case, one circle is entirely contained within the other circle.

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Answer: -5/3

Step-by-step explanation:

Answer: m = -4/3

Step-by-step explanation:

If you're given two different coordinates, and you want to find the slope, the general rule is that you subtract the first coordinates from the first. The formula for these kinds of problems is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) .

If A(3,-4) and B(13,11), the coordinates of the point 3/5 from A to B is, (9, 5).

The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Section formula for a point which divides line joining points into m:n ratio,

(X,Y) = { (mx₂+nx₁)/m+n , (my₂+ny₁)/m+n }

Given that, two points,

A(3, -4) and B(13, 11),

the coordinates of the point 3/5 from A to B

Difference, in x coordinates

13 - 3 = 10

It is 3/5 from A to B

So,    x coordinate is,3 + 10 × 3/5 = 9

Difference, in y coordinates

11 -(-4) = 15

It is 3/5 from A to B

So,    y coordinate is, -4 + 15 × 3/5 = 5

Hence, the point is (9, 5)

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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Step-by-step explanation:

let the number be x

x+x -4=5

2x- 4=5

2x =5+4

2x =9

divide both sides by 2

x=9/2=4.5

Answer:

B: 20 sq. inches

Step-by-step explanation:

The area of the triangle is calculate by;  A= b. h /2

b= 10 inches

h = 4 inches

10 . 4= 40 sq. inches : 2 = 20 sq.inches

The area of the triangle is 20 sq. inches

Answer:

H0: p= 0.39   vs    Ha: p ≠ 0.39

Step-by-step explanation:

She wants to test whether this holds true for teachers in her state.

The test is the formulated into the hypotheses.

The null hypothesis would be

H0: p= 0.39   against the claim    Ha: p ≠ 0.39

The null hypothesis tells that the the proportion of teachers in her state that are members of a union is equal to the proportion of teachers in the US that are members of the labor union.

against the claim

That the the proportion of teachers in her state that are members of a union is  not equal to the proportion of teachers in the US that are members of the labor union.

The linear equation in two variable form to show the number of cars seen each week at the mechanic is f(x) = −4x + 200.

Detailed explanation:

You know the slope will be negative because the number is going down, ruling out the first two options. The final option can be discarded since its equation does not correspond to the provided data.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Consequently, the formula for the change in y-coordinate with regard to the change in x-coordinate is

m = Δy/Δx = dy/dx = change in y/change in x

In other words, comparing the responses to the provided information is the simplest method to solve this problem.

You must determine the slope if you wish to recreate the equation from scratch. Yes, that is.

=> (Change in Weeks)/(Change in Cars) = (184 -192)/(4 -2) = -8/2 = -4

There is just one solution that this matches, however you may continue by starting with point-slope form to complete the equation:

y -192 = -4(x -2) (x -2)

y = -4x + 8 + 192; remove parenthesis after adding 192;

y = -4x + 200

=>Therefore, The linear equation in two variable form to show the number of cars seen each week at the mechanic is f(x) = −4x + 200.

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Answer:

The equation of the line that represents the reduction in the number of cars each week is:f(x) = -4x + 200The correct option is f(x) = -4x + 200.

Step-by-step explanation:

he problem is asking to write a linear equation that represents the reduction in the number of cars each week. To form an equation for a line we need to know at least two points. We can use the given information to find two points, (2, 192) and (4, 184).Using the slope-intercept form of the equation, we can determine the equation of the line. The slope (m) of the line is the change in the number of cars (y) divided by the change in the number of weeks (x):m = (184 - 192) / (4 - 2) = -4The intercept (b) of the line is the value of y when x = 0. In this case, we assume that the manufacturer fixed 200 cars before starting the recall. 

Therefore, b = 200.The equation of the line that represents the reduction in the number of cars each week is:f(x) = -4x + 200The correct option is f(x) = -4x + 200.

Answer:

when x = -5 y is -48

when x is -1 y is -8

when x is 0 y is 2

when x is 1 y is 12

Step-by-step explanation:

the acosta family went out to dinner. the price of the meal was $79.85. if the tip was 15%.The Acosta family paid $91.83 for the meal, including the 15% tip.

To calculate the total amount paid, we need to add the original price of the meal to the tip amount. The price of the meal was $79.85, and the tip was 15% of that amount. To find the tip, we multiply $79.85 by 0.15 (or 15% expressed as a decimal), which equals $11.98. Adding the tip of $11.98 to the original price, the total amount paid is $91.83.

In more detail, a 15% tip means that 15% of the meal price is added as an extra amount to the bill. To calculate the tip, we multiply the meal price ($79.85) by 0.15 (or 15% as a decimal), resulting in $11.98. This represents the additional amount the Acosta family paid for the tip. To find the total amount paid, we add the tip amount to the original meal price: $79.85 + $11.98 = $91.83. Therefore, the Acosta family paid $91.83 for the meal, including the tip.

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The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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The recursive rule for the sequence in the graph is aₙ = aₙ₊₁ + 4

Recursive rule are the rules that continually takes a previous number and changes it to get to a next number.

It gives first term or terms of sequence and describes how term is related to previous term with an equation.

Looking at the graph ,

taking first two point  ,n = 1 and n = 2

At n = 1 , a(n) = 13

At n = 2 , a(n) = 9

so , 9 = 13 - 4

we can write it as,

a₂ = a₁ - 4

Hence , recursive formula for sequence :

aₙ₊₁ = aₙ - 4

bring aₙ to the left

=>  aₙ = aₙ₊₁ + 4 is required recursive formula

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Answer:

15

Step-by-step explanation:

As we can see, we have the total ratio as;

5 + 2 + 1 = 8

Total of NQ is 24

The ratio accorded to NO is 5

so we have the length of NO as;

5/8 * 24 = 15

The bearing of the oil rig from the port is 28.61° west by north.

What are the trigonometric identities?

All trigonometric identities are based on the six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent are the functions. All of these trigonometric ratios are defined using the sides of a right triangle, specifically the adjacent, opposite, and hypotenuse sides.

We have,

First, the boat travels 55km toward the west,

and then it travels 30km toward the north.

So the boat forms the right triangles, see in the image attached,

tanθ = 33/55

θ = tan⁻¹ (33/55)

θ = 28.61°

28.61° west by north.

Hence, the bearing of the oil rig from the port is 28.61° west by north.

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Given:

Consider the given sides are,

\(BD=21m\)

\(BC=25m\)

\(DE=40m\)

\(AB=xm\)

To find:

The measure of AB.

Solution:

Let x be the measure of AB.

From the given figure it is clear that,

\(\angle ADE \cong \angle ABC\)                 (Right angles)

\(\angle ADE \cong \angle ABC\)                  (Corresponding angles)

Two corresponding angles are congruent. So, by AA property of similarity,

\(\Delta ABC\sim \Delta ADE\)

Corresponding sides of similar triangle are proportional.

\(\dfrac{AB}{BC}=\dfrac{AD}{DE}\)

\(\dfrac{x}{25}=\dfrac{(x+21)}{40}\)

\(40x=25(x+21)\)

\(40x=25x+525\)

Isolating x, we get

\(40x-25x=525\)

\(15x=525\)

\(x=\dfrac{525}{15}\)

\(x=35\)

Therefore, the measure of AB is 35 m.

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer:

2x2x3x5= 60

I hope you like it

Answer:

2 X 2 X 3 X 5

Step-by-step explanation:

We divide 60 by 2 as many times as possible to get 60 = 15 x 2 x 2. 2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2. Now we collect the factors, so our final answer is 60 = 5 x 3 x 22.

The total number of bushels the farmer has for sale at the farmers market is 9.75 bushels.

The given parameters;

The actual amount of the bushel sold in per day;

\(= \frac{15.75}{1 \ day}\)

After 7 days the amount of the bushel sold is calculated as;

\(= \frac{15.75}{1 \ day} \times 7\ days= 110.25 \ bushels\)

The amount of the bushel left after the 7 days;

\(= 120 - 110.25\\\\= 9.75 \ bushels\)

Thus, the total number of bushels the farmer has for sale at the farmers market is 9.75 bushels.

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Answer:

\( \frac{1}{2} \)

Step-by-step explanation:

Given line is passing through the points (8, 0) & (0, - 4)

\(slope \: of \: line = \frac{ - 4 - 0}{0 - 8} = \frac{ - 4}{ - 8} = \frac{1}{2} \\ \)