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sladkih [1.3K]
3 years ago
10

Hannah's school hosted a book donation. There are 150 students at her school, and they donated a total of b books! Hannah donate

d 3 times as many as the average number of books each student donated.
How many books did Hannah donate?
Write your answer as an expression.
Mathematics
1 answer:
svetoff [14.1K]3 years ago
4 0

Answer:

x=3*\dfrac{b}{150}

Step-by-step explanation:

Let x = number of books that Hannah donated

We know that the number of students is 150 and the total number of books is represented by b, we can write that as:

Average number of books donated by each student = \dfrac{b}{150}

Now we know that Hannah donated 3 times as much as the average. We can write that as:

x=3*\dfrac{b}{150}

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yarga [219]
Dy/dx = (4y²)(x⁴/³)

Find ∫(4y²)(x⁴/³) =∫(4y²∛(x⁴)dx = 3∛(x⁴).y² +c or 3x⁴/³.y² + c
4 0
3 years ago
Alex is creating an outdoor structure out of two 12 foot boards. The boards must have an angle of elevation
Whitepunk [10]

Answer:

5.0 ft - 5.6 ft

Step-by-step explanation:

Given that the structure is to be made using two 12 foot boards, then we expect the total perimeter to be equal to (2*12)= 24 ft.

Using the angle of elevation, 40° and the width of 8 ft then you can apply the formula for tangent of a triangle where ;

Tan α = opposite side length/adjacent length

Tan 40°= h/8

h= 8 tan 40° = 6.71 ft

Applying the cosine of an angle formula to find the length of the sliding side

Cosine β = adjacent length /hypotenuse

Cosine 40°= 8/ sliding side length

sliding side length = 8/cosine 40° =10.44 ft

Checking  the perimeter = 10.44 +8+6.71= 25.15 ft

This is more than the total lengths of the boards, so you need to adjust the height as;

24 - 18.44 = 5.56 ft ,thus the height should be less or equal to 5.56 ft

h≤ 5.6 ft

6 0
3 years ago
Help please and thank you
Bingel [31]

Answer:

40° D. is your answer to this question

3 0
3 years ago
Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find
densk [106]

Answer:

x=4

Step-by-step explanation:

<u>Step 1</u>:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

AC^2 = AB^2 + BC^2

<u>step 2:-</u>

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

(a + b)^2 = a^2 +2ab+b^2

289 = 4x^2 +9(x^2+2x+1)

13x^2 +18x-280 = 0

finding factors  70 X 52 = 3640

13x^2 +70x-52x-280 = 0

13x^2 -52x+ 70x-280 = 0

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and 13x =-70

x=4 and x=\frac{-70}{13}

we can not choose negative value so x value is 4

Final answer:- x = 4

<u>verification:-</u>

<u></u>AC^2 = AB^2 + BC^2<u></u>

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

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3 years ago
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