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Mars2501 [29]
3 years ago
13

The length of a rectangle is 8 cm greater than its width. Find the dimensions of the rectangle if its area is 105 square centime

ters. (a) Write a polynomial equation that can be solved. (b) Solve the equation by factoring (input equation with binomials in this step). (c) State solution with units *
Mathematics
2 answers:
Nikitich [7]3 years ago
7 0

Answer:

105 = (w+8) *w

w = 7 cm

l = 15 cm

Step-by-step explanation:

Area of a rectangle is

A = l*w

l = w+8

105 = (w+8) *w

Distribute

105 = w^2 +8w

Subtract 105 from each side

105-105 = w^2 +8w -105

0 =w^2 +8w -105

Factor

What 2 number multiply to 105 and add to 8

15*-7 = -105

15-7 = 8

(w+15) (w-7) =0

Using the zero product property

w+15 =0               w-7 =0

w=-15                      w=7

impossible

not negative

w =7

l = 15

BigorU [14]3 years ago
6 0

Answer:

Width: w

Length: w + 8

w(w + 8) = 105

w² + 8w - 105 = 0

w² + 15w - 7w - 105 = 0

w(w + 15) - 7(w + 15) = 0

(w + 15)(w - 7) = 0

w = -15, 7

width = 7cm

length = 7+8 = 15cm

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Through a regular hexagon whose base edge is 8cm and whose height ii 12cma hole in the shape of the right prism with ots end bei
guapka [62]

The total surface area of the remaining solid is 48(4+✓3) centimeters square.

<h3>How to calculate the surface area?</h3>

Through a regular hexagonal prism whose base edge is 8 cm and the height is 12 cm, a hole in the shape of a right prism.

The formula for the total surface area will be:

= Total surface area=2(area of the base)+ parameter of base × height

where,

Height= 8cm

Parameter of base=12(2) = 24

Area of the base= 6×✓3/4×4² = 64✓3/4

The surface area of the remaining solid will be:

= 2(64✓3/4) + 24 × 8

= 2(64✓3/4 + 192

With the hole is a rhombus prism with the following parameters:

diagonal 1 = 6, diagonal 2 = 8, height = 12

The volume is:

V1 =0.5 × d1 × d2 × h

V1 = 0.5 × 6 × 8 × 12

V1 = 96

The dimensions of the hexagonal prism are:

Base edge (a) = 8

Height (h) = 12

The volume is

V2 = (3✓(3)/2)a²h

V2 = (3✓3)/2) × 8² × 12

V2 = 1152✓3

The remaining volume is

V = V2 -V1

V = 1152✓3 - 96

Learn more about the hexagonal prism on:

brainly.com/question/27127032

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4 0
2 years ago
Gieo đồng thời hai con xúc xắc. Tìm xác suất để nhận được:Tổng số chấm là 8.
vampirchik [111]

Answer:

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Step-by-step explanation:

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3 years ago
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Answer: The last option, <u>28</u> minutes

Step-by-step explanation:

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7 0
2 years ago
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True of False:the following polynomial is written in standard form<br> 2x^4-x^3+5x^2+x-7
djyliett [7]
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3 0
3 years ago
What is "A number decreased by 4 is less than 14" written as an inequality?
navik [9.2K]

Answer:

"A number decreased by 4 is less than 14" written as an inequality is x - 4 < 14

Step-by-step explanation:

First: Figure out what a number decreased by 4 is.

Well, a number decreased by 4, how would that look like? To find out, we should look for some key words in the term. So, I will bold out the keywords in the term this time:

A number decreased by 4

That word 'decreased' gives us a hint. Out of the four basic operations (addition, subtraction, multiplication and division), 'decreased' fits into the subtraction category best. So we can replace 'decreased' with a minus sign. Since we don't know the specific value of 'A number', we will assign it a variable, the variable x. 4 is just 4 so we can leave that number alone. So the first term would look like this:

A number decreased by 4 = x - 4

Second: Since we know what the first term is, we need to find out what the second term is and the inequality sign.

This step is quite easy. Let's tackle the inequality sign first:

A number decreased by 4 is less than 14

The only words that would describe an inequality sign are the words: 'less than'. The less than sign looks like this: <

Fourteen [just like four] is just a number so we don't need to change that

So our final product is this: x - 4 < 14

Thank you for reading.

Topic: Inequalities

6 0
3 years ago
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