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MakcuM [25]
3 years ago
7

The height of a triangle is 7 ft more than its base. if the area of the triangle is 30 ft^ what is the lentgh of the base

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
6 0
Since the area of a triangle is in the form
area=0.5(base)(height)
height=base+7
let base=x
area=0.5(x)(7+x)
30=3.5x+0.5x^2
multiply the equation by 2
60=7x+x^2
subtract 60 from both sides
x^2+7x-60=0
(x-5)(x+12)=0
thus  x=5 or x=-12 since we are only considering positive answers
x=-12 is rejected
so base=5 and height=5+7=12
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According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x^5
nata0808 [166]

Answer:

The correct option is A.

Step-by-step explanation:

The question is:

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?

A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12

B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x

C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3

D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48

Solution:

The function given to us is:

3x5 – 2x4 + 9x3 – x2 + 12

Find the factors of 12 and consider it as 'p'

The factors of 12 are:

p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6

Now find the factors of 3 and consider it as 'q'

The factors of 3 are:

q = +/- 1 , +/- 3

We know that we write rational terms in p/q form.

Therefore the Rational roots are given by p/q

+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3

Now we will solve the first function given in part A.

f(x) = 3x^5 – 2x^4 - 9x^3 + x^2 - 12

Again find the factors of 12 and consider it as 'p'

The factors are:

p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6

Now find the factors of 3 and consider it as 'q' .

q = +/- 1 , +/- 3

Rational root are given by p/q

+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3

Therefore the rational roots of the given function matches the rational roots of the given equation.

Hence the correct option is A

6 0
3 years ago
What is 3 in a+ b- in C written as a single logarithmn?
Leona [35]

There are a lot of other step that will be in between but the answer will end up being.....

Answer: Log (a^2c/ b^3 d^4)

4 0
3 years ago
What’s the correct answer for this question?
Helen [10]

Answer:

( -1 , 1 )

Step-by-step explanation:

(x1,y1) = (5,9)

(x2,y2) = (-7,-7)

=(-7+5/2 , -7+9/2)

= (-1,1)

3 0
3 years ago
How do you solve 3 1/4- 1 7/8 step by step?
Vilka [71]

Answer:

1 3/8.

Step-by-step explanation:

3 1/4 - 1 7/8

First convert to improper fractions:

3 1/4 = (3*4) + 1 / 4 =  13/4.

1 7/8 = (1 *8)+7 / 8 = 15/8. So we have:

13/4 - 15/8

The Lowest Common Multiple of 4 and 8 is 8 so we convert 13/4 to eighth's

13 / 4 = 13*2 / 4 *2 = 26/8

Finally: we have

26/8 - 15/8 = (26 - 15) /8

= 11 /8

= 1 3/8 (answer)

4 0
3 years ago
Can someone please help me with the answer.
Elza [17]

Answer:

The answer to your question is : f(-2) = 2

Step-by-step explanation:

Just look for -2 in the x- axis and look for some line or point, vertical to number two.

In your example you can find a point two units upward the x-axis.

5 0
3 years ago
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