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gtnhenbr [62]
1 year ago
13

(Refer to the attached image)​

Mathematics
1 answer:
gayaneshka [121]1 year ago
8 0

Explanation:

Provided <u>2 length sides</u> and <u>one angle</u> also need to find <u>one missing side</u>.

So, use cosine rule:

a² = b² + c² - 2bc cos(A)

<h3><u>Part 1</u></h3>

c² = 9² + 11² - 2(11)(9) cos(57)

c² = 94.16147

c = √94.16147 = 9.70 cm

<h3><u>Part 2</u></h3>

d² = 5² + 7² - 2(5)(7) cos(48)

d² = 27.16

d = √27.16 = 5.21

<h3><u>Part 3</u></h3>

5² = 7² + 9² - 2(7)(9) cos(H)

-126cos(H) = 25 - 49 - 81

cos(H) = -105/-126

cos(H) = 5/6

H = cos⁻¹(5/6) = 33.56°

<h3><u>Part 4</u></h3>

8² = 4² + 7² - 2(4)(7) cos(J)

-56cos(J) = 64 - 16 - 49

cos(J) = -1/-56

J = cos⁻¹(1/56) = 88.98°

Passcode: 3142

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Alik [6]

Here, we are required to find the equation, in terms of w, that could be used to find the dimensions of the storage unit in feet.

The polynomial is;. 3w³ + 22w + 24w = 5440ft³.

From the question;

  • <em>Let the width = w</em>
  • <em>length,</em><em> </em><em>l</em><em> = 3w + 4</em>
  • <em>height,</em><em> </em><em>h</em><em> = w + 6</em>

<em>The </em><em>volume </em><em>of </em><em>a </em><em>rectangular</em><em> </em><em>prism </em><em>is </em><em>given </em><em>by </em><em>the </em><em>product </em><em>of </em><em>its </em><em>length,</em><em> </em><em>width </em><em>and </em><em>height.</em><em> </em><em>Thus</em><em>;</em>

Volume = l × w × h

Therefore, Volume, V = (3w +4) × w × (w +6)

To obtain the required polynomial, we expand the expression for Volume above;

<em>V = (3w² + 4w) × (w + 6)</em>

<em>V = (3w² + 4w) × (w + 6)V = 3w³ + 22w² + 24w.</em>

However, the volume of the rectangular prism has been given to be 5440 cubic feet.

Therefore, the polynomial is;

3w³ + 22w + 24w = 5440ft³.

Read more:

brainly.com/question/9740998

8 0
1 year ago
Read 2 more answers
WhIich of the following mathematical expressions is equivalent to the verbal expression "A number, x, squared is 39 more than th
MrRa [10]

Answer:

E. x^2 = 39 + 10x

Step-by-step explanation:

It helps to do one piece of the sentence at a time.

"A number, x, squared is 39 more than the product of 10 and x"

x

"A number, x, squared is 39 more than the product of 10 and x"

x^2 =

"A number, x, squared is 39 more than the product of 10 and x"

x^2 = 39 +

"A number, x, squared is 39 more than the product of 10 and x"

x^2 = 39 + 10x

Answer: E. x^2 = 39 + 10x

6 0
2 years ago
Read 2 more answers
3x+2(4x-4)=3 help pls
Vlada [557]

Answer: 1

Step-by-step explanation:

3x + 8x-8= 3

11x-8=3

Then you move the 8 to the other side and change it to a positive.

11x= 11

11x/11 = 11/11

Answer is 1

3 0
2 years ago
6. All angles in the figure below are right angles. What is the area of the figure? (1 point)
lilavasa [31]

Answer:

Option (4)

Step-by-step explanation:

Area of the figure given in the picture = Area of large rectangle - Area of rectangle A

Area of rectangle A = Length × Width

                                 = [9 - (2 + 4)] × 3

                                 = 3 × 3

                                 = 9

Area of the large rectangle = Length × Width

                                             = 9 × 5

                                             = 45

Therefore, area of the given figure = 45 - 9

                                                          = 36

Option (4) will be the correct option.

5 0
2 years ago
Angle pwm is equal to angle pkm
Len [333]
<h3>Answer: 24 (choice C)</h3>

Assuming M is a midpoint of KW, this means that WM and KM are congruent

WM = KM

x+3 = 2(x-3) ... substitution

x+3 = 2x-6

2x-6 = x+3

2x-6-x = x+3-x .... subtract x from both sides

x-6 = 3

x-6+6 = 3+6 ... add 6 to both sides

x = 9

Use x = 9 to find the length of WM

WM = x+3 = 9+3 = 12

Which can be used to find the length of KM as well

KM = 2(x-3) = 2(9-3) = 2(6) = 12

both lengths are the same (12) as expected

This makes WK to be

WK = WM + KM

WK = 12 + 12

WK = 24

3 0
2 years ago
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