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Rasek [7]
3 years ago
12

Simplify (x − 4)(2x2 + 3x − 5).

Mathematics
1 answer:
xeze [42]3 years ago
5 0

The simplified form of given expression is 2x^3-5x^2-17x+20

<em><u>Solution:</u></em>

Given that we have to simplify the expression

<em><u>Given expression is:</u></em>

(x-4)(2x^2+3x-5)

We can simplify the expression by multiplying each term in first bracket with each term term in second bracket

\rightarrow (x-4)(2x^2+3x-5)

\rightarrow (x)(2x^2)+(x)(3x)+(x)(-5)-4(2x^2)-4(3x)-4(-5)

Simplify the above expression by multiplying the numbers in each term and adding the coefficients of like variables in each term

\rightarrow 2x^3+3x^2-5x-8x^2-12x+20

Combine the like terms

\rightarrow 2x^3+3x^2-8x^2-5x-12x+20

\rightarrow 2x^3-5x^2-17x+20

Thus the expression is simplified

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The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its
Elodia [21]

Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

<em>Shape: Triangle</em>

<em>Represent the height with h and the base with b</em>

b = 3 + 2h

Area = 22

Required

Find the length of the base

The area of a triangle is calculated as thus;

Area = \frac{1}{2} * b * h

Substitute 22 for Area and 3 + 2h for b

The formula becomes

22 = \frac{1}{2} * (3 + 2h) * h

Multiply both sides by 2

2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h

44 = (3 + 2h) * h

Open the bracket

44 = 3 * h + 2h * h

44 = 3h + 2h^2

Subtract 44 from both sides

44 - 44 = 3h + 2h^2 - 44

0 = 3h + 2h^2 - 44

Rearrange

0 = 2h^2 +3h - 44

2h^2 +3h - 44 = 0

At this point, we have a quadratic equation; which is solved as follows:

2h^2 +3h - 44 = 0

2h^2 + 11h - 8h - 44 = 0

h(2h + 11) - 4(2h + 11) = 0

(h - 4)(2h + 11) = 0

Split the above

(h - 4) = 0\ or\ (2h + 11) = 0

h - 4 = 0\ or\ 2h + 11 = 0

Solve the above linear equations separately

h - 4 = 0

Add 4 to both sides

h - 4 + 4 = 0 + 4

h = 0 + 4

h = 4 ---- <em>First value of h</em>

2h + 11 = 0

Subtract 11 from both sides

2h + 11 - 11 = 0 - 11

2h  = 0 - 11

2h = -11

Divide both sides by 2

\frac{2h}{2} = -\frac{11}{2}

h = -\frac{11}{2}<em> ------ Second value of h</em>

Since height can be negative, we'll discard h = -\frac{11}{2}

Hence, the usable value of height is h = 4

Recall that b = 3 + 2h

Substitute 4 for h

b = 3 + 2(4)

b = 3 + 8

b = 11

Hence, the length of the base is 11 meters

3 0
3 years ago
A GP has 8 terms, it's first and last terms are 0.3 and 38.4/, calculate the common ratio
gladu [14]

Answer: The right  answer is 2

Step-by-step explanation:

  1. Write out the expression

T1; a = 0.3 ------------ (I)

T8; ar^7 = 38.4 ------------ (ii)

Substituting for 'a' in the second equation, we have;

0.3r^7 = 38.4

0.3r^7 = 38.4

Divide both sides by 0.3

r^7 = 38.4/0.3

r^7 = 128

r = (128)^1/7

r = 2

5 0
3 years ago
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