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3 years ago

Rectangle has vertices a(1,3) b (1,10) c(5,10) and d(5,3) what is the length of each side of the rectangle?

Mathematics

1 answer:

Taya2010 [7]3 years ago

6 0

Answer:

AB= 7

BC= 4

CD= 7

DA= 4

Step-by-step explanation:

The rectangle has vertices as given. Plot the vertices on a coordinate graph and then count each side length. See picture below.

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To two decimal places, find the value of k that will make the function f(x) continuous everywhere. f of x equals the quantity 3x

Fiesta28 [93]

Given function is

$f(x)=\left\{\begin{matrix}3x+k & x\leq -4 \\ kx^2-5 & x> -4\end{matrix}\right.$

now we need to find the value of k such that function f(x) continuous everywhere.

We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.

So we just need to find both left and right hand limits then set equal to each other to find the value of k

To find the left hand limit (LHD) we plug x=-4 into 3x+k

so LHD= 3(-4)+k

To find the Right hand limit (RHD) we plug x=-4 into

$kx^2-5$

so RHD= $k(-4)^2-5$

Now set both equal

$k(-4)^2-5=3(-4)+k$

$16k-5=-12+k$

$16k-k=-12+5$

$15k=-7$

$k=-\frac{7}{15}$

k=-0.47

<u>Hence final answer is -0.47.</u>

7 0

3 years ago

What is the solution to 18 = 2(2x + 7)?

dusya [7]

Answer:

x= 1 :))

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Select the correct answer. What is the area of the triangle in the diagram? A. B. C. D. Reset Next Previous5 Next Using Coordina

Komok [63]

The area of the triangle can be calculated using the distance formula if the coordinates are given.

<h3>What is the triangle?</h3>

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have a triangle with coordinates on the coordinate plane.

It is required to find the area of the triangle using the coordinate points.

Here the coordinates are not given, so we are assuming the coordinates are (x1, y1), (x2, y2), (0,0)

From the distance formula:

The distance(b) between (0, 0) and (x1, y1):

$\rm b = \sqrt{(x_1-0)^2+(y_1-0)^2} \Rightarrow \sqrt{x_1^2+y_1^2}$

The distance between (0, 0) and (x2, y2):

$\rm h = \sqrt{(x_2-0)^2+(y_2-0)^2} \Rightarrow \sqrt{x_2^2+y_2^2}$

So the area of the triangle:

A = bh/2

$\rm A = \dfrac{1}{2}\times \sqrt{x_1^2+y_1^2} \times \sqrt{x_2^2+y_2^2}$

$\rm A = \dfrac{1}{2} \sqrt{(x_1^2+y_1^2) (x_2^2+y_2^2)}$

Thus, the area of the triangle can be calculated using the distance formula if the coordinates are given.

Learn more about the triangle here:

brainly.com/question/25813512

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6 0

2 years ago

9. A business records its net profits for the week by subtracting the operating costs from the revenue. The function P(x) = (140

guapka [62]

Answer:

Profit Function, P(x) Total Income minus Total Cost. Profit ... The next unit will make this Revenue. Marginal Cost Function, C'(x) The next unit will be this Cost ... A manufacturing company produces and sells tables. The cost function is given by: where x is the number of tables. The tables are sold for $200 each. Find . 1. The total cost of ...

Step-by-step explanation:

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3 years ago

I don't get this one?

Vlad1618 [11]

Answer:

4000

Step-by-step explanation:

V=4/3(3)(10)^3

V= 4/3 (3)(1000)

V=4/3 (3000)

V=4000

7 0

2 years ago