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3 years ago

What is the height of the trapezoid if the Area = 26 un²? un

Mathematics

1 answer:

Artist 52 [7]3 years ago

6 0

Answer:

if i'm right it 676

Step-by-step explanation:

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Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

3 years ago

A cheetah runs 296 feet in 4 seconds. How far could a cheetah run in 10 seconds at this rate?

melomori [17]

Answer:

740 feet

Step-by-step explanation:

The speed of the cheetah is 74 feet per second:

speed = distance ÷ time

= 296 ÷ 4 = 74 feet per second

In 10 seconds:

distance = speed × time

= 74 × 10

= 740 feet

4 0

2 years ago

Read 2 more answers

6|2x+3|=36 need a mini step by step

ELEN [110]

Answer:

x=1.5

Step-by-step explanation:

We are trying to get x by itself to see what it equals.

6(2x+3)=36

So first you want to distribute you proprieties. You do that by multiplying 6 and 2x. Then multiplying 6 and 3.

12x+18=36

Now in equations where you need to find the variable, whatever you do on one side of the equal sign, you have to do on the other side. So now we want to subtract 18 from both sides.

12x+18=36

-18 -18

Then we divide 12 from both sides.

12x=18

÷12 ÷12

Now you have your answer!

x=1.5

6 0

3 years ago

Please help, the question below

Licemer1 [7]

Answer:

$\sf R=\left(3, -\dfrac{5}{4}\right)$

Step-by-step explanation:

Given:

P = (1, 5)
Q = (-2, 3)
R = (a, b)
R lies on line x = 3
PR = QR

If point R lies on the line x = 3, then the x-value of point R is 3.

⇒ a = 3

Distance between two points

$\sf d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

(where (x₁, y₁) and (x₂, y₂) are the two points)

Use the distance formula to derive equations for PR and QR.

Let (x₁, y₁) = P = (1, 5)

Let (x₂, y₂) = R = (3, b)

$\begin{aligned} \sf PR & =\sf \sqrt{(3-1)^2+(b-5)^2}\\ & = \sf \sqrt{4+(b-5)^2} \end{aligned}$

Let (x₁, y₁) = Q = (-2, 3)

Let (x₂, y₂) = R = (3, b)

$\begin{aligned} \sf QR & =\sf \sqrt{(3-(-2))^2+(b-3)^2}\\ & = \sf \sqrt{25+(b-3)^2} \end{aligned}$

As PR = QR, equate the derived equations and solve for b:

$\begin{aligned} \sf PR & = \sf QR \\\sf \sqrt{4+(b-5)^2} & = \sf \sqrt{25+(b-3)^2}\\\sf 4+(b-5)^2 & = \sf 25+(b-3)^2\\\sf 4+b^2-10b+25 & = \sf 25 + b^2-6b+9\\\sf b^2-10b+29 & = \sf b^2 -6b +34\\\sf -10b+29 & = \sf -6b + 34\\\sf -4b & = \sf 5\\\sf b & = -\dfrac{5}{4}\end{aligned}$

Substitute the found values of a and b to find the coordinates of R:

$\sf R=(a,b)=\left(3, -\dfrac{5}{4}\right)$

Learn more about the distance formula here:

brainly.com/question/28144723

8 0

2 years ago

Read 2 more answers

Shelby, Allen, and Denise printed their digital photos. Each requested the same size prints. Shelby paid $2.70 for 5 prints. All

tekilochka [14]

Person: Number of prints Total Cost
Shelby 5 2.70
Allen 11 3.24
Denise 20 4.05

To solve for the variable cost:
11 - 5 = 6
3.24 - 2.70 = 0.54
0.54 / 6 = 0.09 per print

To solve for the fixed cost
0.09 x 5 = 0.45
2.70 - 0.45 = 2.25

y = 2.25 + 0.09x

y = 2.25 + 0.09(5) = 2.25 + 0.45 = 2.70
y = 2.25 + 0.09(11) = 2.25 + 0.99 = 3.24
y = 2.25 + 0.09(20) = 2.25 + 1.8 = 4.05

4 0

3 years ago

Read 2 more answers