42x(raise to 4) - 13x²

likoan [24]

Answer= 22

Explanation
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2l+2w=p

2(8)+2(3)= 22

4 0

4 years ago

find the number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next

zalisa [80]

Answer:

The number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E is 10,080 ways

Step-by-step explanation:

We need to find the number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E.

There are 9 letters in the word WONDERFUL

There is a condition that letter R is always next to E.

So, We have two letters fixed WONDFUL (ER)

We will apply Permutations to find ways of arrangements.

The 7 letters (WONDFUL) can be arranged in ways : ⁷P₇ = 7! = 5040 ways

The 2 letters (ER) can be arranged in ways: ²P₂ =2! = 2 ways

The number of ways 'WONDERFUL' can be arranged is: (5040*2) = 10,080 ways

So, the number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E is 10,080 ways

8 0

3 years ago

What is the area of the trapezoid shown below?

denis-greek [22]

Hello there!

Your answer is 180 units²

Step-by-step explanation:

$\large \boxed{ \mathsf{ \frac{1}{2} \times sum \: of \: two \: parallel \: \times height}}$

The formula in the box is an area of trapezoid formula. We know the sum of two parallel lines which is 15 because 7+4 = 11 + 4 = 15

another 4 comes from parallel side. If both sides are parallel, they have same length.

The only thing that is missing is the height. The height can be found by using Pythagorean Theorem as you notice a right-angle triangle when splitting in half.

$\large \boxed{ {a}^{2} + {b}^{2} = {c}^{2} }$

The formula in the box is Pythagorean Theorem for finding a length of right-angle triangle.

Given where a is opposite, b is adjacent and c is hypotenuse. (Note that c must be hypotenuse.)

Our a is missing

Our b is 7

Our c is 25.

From the formula and given lengths:

$\large{ {a}^{2} + {7}^{2} = {25}^{2} } \\ \large{ {a}^{2} + 49 = 625} \\ \large{ {a}^{2} = 625 - 49} \\ \large{ {a}^{2} = 576} \\ \large{a = 24}$

Therefore, our opposite is 24. Since our opposite equals the height of a trapezoid. We can proceed with the trapezoid formula.

$\large{ \frac{1}{2} \times 15 \times 24 = 15 \times 12 = 180 } \\ \large{180}$

Therefore, the area of trapezoid is 180 units²

We can also use another method to find the area by adding up between area of triangle and area of Rectangle.

Our rectangle formula is length × width. We know width which is 4 and our length is 24 from opposite side of triangle which equal to the length of rectangle.

Length × Width = 24 × 4 = 96

Hence, the area of Rectangle is 96.

Next, we find the area of triangle which is 1/2 × base × height.

Our base is 7 and height is the opposite side of triangle which is 24.

Therefore, the area of triangle is 1/2 × 7 × 24 = 7 × 12 = 84

If we add the area of triangle and rectangle up each other, we will get the area of trapezoid for this problem which is 96 from rectangle and 84 from triangle. Therefore, 96+84 = 180 units²

4 0

3 years ago

The area of a triangle is 140 cm?.<br> Its base is 70 cm. Find its height.<br> !!!!

valentinak56 [21]

Answer:

4

Step-by-step explanation:

70 x 4 = 280 but a triangle's area is halved so 140

6 0

3 years ago

Belle made a scale drawing of a mural where 2 inches of the drawing represents 3 feet on the actual mural (scale 2 in. = 3 ft.).

ehidna [41]

Answer:

<h3>Very sorry if this is wrong but, I think the answer would be 48 inches. </h3>

Step-by-step explanation:

If every 3ft. = 2in. then I believe you would first divide the length and width by 3. So 6 divided by 3 is 2 and 18 divided by 3 is 6. Then you would multiply 2 and 6 by 2 since every 3ft = 2in.

4 0

3 years ago

42x(raise to 4) - 13x² - 40