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slavikrds [6]
4 years ago
14

Point J is located at (2,5)(2,5) and point K is located at (4,19)(4,19).

Mathematics
1 answer:
Anni [7]4 years ago
5 0
We have the coordinates
J (2,5)
K (4,19)

Since we are to find the point that partitions the line segment into 3:2 ratio, we have 5 equal parts of the line segment. So,

Get the horizontal distance:
4 - 2 = 2
Divide by 5
2/5
Multiply by 3
2/5 x 3 = 1.2
Add this to the x coordinate of J
2 + 1.2 = 2.2

Get the vertical distance:
19 - 5 = 14
Divide by 5
14/5
Multiply by 3
14/5 x 3 = 8.4
Add this to the y coordinate of J
5 + 8.4 = 13.4

The coordinates of the point is
(2.2,13.4)
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Suppose that a rectangle has a perimeter of 26 meters. Express the area A(x) of the rectangle in terms of the length x of one of
ch4aika [34]

The area A(x) of the rectangle in terms of the length x of one of its sides. A(x) = x(13-x).

<h3>What is rectangle?</h3>

A rectangle is really a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal & parallel. Because  rectangles is a 2-D form, it has two dimensions: length and width.

Some characteristics of rectangle are-

  • The length of the rectangle is the longer side, while the width would be the shorter side.
  • Because all of the angles in a rectangle are equal, it is also known as an equiangular quadrilateral. The quadrilateral is a closed 4-sided shape.
  • Since a rectangle contains parallel sides, it is also known as a right-angled parallelogram.
  • The parallelogram would be a quadrilateral with equal and parallel opposite sides. Rectangles are a type of parallelogram.

Now, according to the question,

Let 'P' be the perimeter of the rectangle.

Perimeter = 2(Length + Breadth)

P = 2(L + B)

The perimeter is 26 meters.

26 = 2(L + B)

L + B = 13

B = 13 - L

Now, the area of the rectangle is given as;

Area = Length×Breadth

A = L×B

Substitute the value of B in area.

A = L×(13 - L)

Area in terms of length x, Put L =x

A(x) = x(13 - x)

Therefore, the area A(x) of the rectangle in terms of the length x of one of its sides. A(x) = x(13 - x).

To know more about the rectangle, here

brainly.com/question/25292087

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4 0
1 year ago
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 120 months, with a
IrinaK [193]

Answer:

P(X<118.81)=0.0803

Step-by-step explanation:

Assuming the distribution for the mean life is approximately normal, with mean 120 months and variance 64 months^2, we can calculate the parameters for a sampling distribution with sample size = 89 computers.

The sampling distribution mean will be equal to the mean for a single computer:

\mu_{89}=\mu=120

The standard deviation will be adjusted by the sample size as:

\sigma_{89}=\sqrt{\sigma^2/n}=\sqrt{64/89}=\sqrt{0.719}=0.848

With these parameters, we can calculate the z-score for X=118.81.

z=\dfrac{X-\mu}{\sigma}=\dfrac{118.81-120}{0.848}=\dfrac{-1.19}{0.848}=-1.403

Then, the probability that the mean of a sample of 89 computers is less than 118.81 months is:

P(X

7 0
3 years ago
Find the missing side<br><br> 5<br> 1.3<br> 6.2<br> 8.2
zimovet [89]

Answer:

I think it is 1.3

Step-by-step explanation:

8 0
3 years ago
Given csc(A) = 65/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational
andrew11 [14]
<h3>Answer:  65/63</h3>

=================================================

Explanation:

Draw a right triangle in the first quadrant, aka northeast quadrant, as shown in the diagram below.

Cosecant involves the ratio of hypotenuse over opposite. It's the reciprocal of sine

sin(angle) = opposite/hypotenuse

csc(angle) = hypotenuse/opposite

since csc = 1/sin

Use the pythagorean theorem to solve for b in the diagram

a^2+b^2 = c^2

16^2+b^2 = 65^2

256+b^2 = 4225

b^2 = 4225-256

b^2 = 3969

b = sqrt(3969)

b = 63

So this is the adjacent side. The secant ratio involves hypotenuse over adjacent (it's the reciprocal of cosine).

sec(angle) = hypotenuse/adjacent

sec(A) = 65/63

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The distance, y, in miles, traveled by a car for a certain amount of time, x, in hours, is shown in the graph below:
Hoochie [10]

Answer:

It travels for 1 h, then stops for 1 h, and finally travels again for 3 h.  

Step-by-step explanation:

The sloped parts of the graph are where the car is moving.

For example, in the first hour the distance travelled changes from zero to 12 mi.

The horizontal part of the graph is where the car is stopped.

For example, between hours 1 and 2, the distance travelled stays the same at 12 mi.

The car travels for 1 h, then stops for 1 h, and finally travels again for 3 h.

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