The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle?

Answers

Answer 1

Answer: x=base
(2x+4)=height
Area of a triangle=(base x height)/2
We can suggest this inequality:

x(2x+4)/2<168
x(2x+4)<336
2x²+4x<336
2x²+4x-336<0
x²+2x-168<0

1) we change the inequality sign of inequality by equality sign.
x²+2x-168=0
x=[-2⁺₋√(4+672)] / 2
x=(-2⁺₋√676)/2
we have two solutions:
x₁=(-2-√676)/2=-14
x₂=(-2⁺√676)/2=12

2) we make intervals with these values.
(-∞, -14 )
(-14,12)
(12, +∞)

3) we check it out if these intervals work
(-∞,-14), For instead; if x=-15⇒ (-15)²+2(-15)-168=27>0. this solution interval don´t work.

(-14,12), For example; if x=1 ⇒(-1)²+2(1)-168=-168<0 this solution interval works.
but the solutions have to be always positive numbers, therefore, the solution is: (0,12).

(12,+∞) , For example, if x=13 ⇒ (13)²+2(13)-168=27>0, this solution interval don´t work.

Answer: the inequality is : x(2x+4)/2<168, and the interval solution is (0,12) for the values of the base.

Answer 2

Answer: Recall that A = 1/2bh. We are given that h = 4+2b So, putting it all together: 168 = 1/2 b(4+2b) 168 = 1/2(4b + 2b^2) 168 = 2b + b^2 b^2 + 2b - 168 = 0. Something that multiplies to -168 and adds to 2? There's a trick to this. Notice 13^2 = 169. So, it's more than likely in the middle of the two numbers we're trying to find. So let's try 12 and 14. Yep. 12 x 14 = 168. So this factors into (b+14)(b-12) So b = -14 or b =12. Is it possible to have a negative length on a base? No. So 12 must be our answer. Let's check this. If 12 is our base, then according to our problem, 2*12 + 4 would be our height... or 28. so what is 12 * 28 /2? 196. Check. Hope this helped!

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Rewrite the equation below so that it does not have fractions

2/3x-5=3/4

Answers

Answer:

Step-by-step explanation:

The best way to do this problem is to find the lowest common denominator.

2/3 : 3*2/(3*3)

3/4 : 3*3 / 3*4

Notice what you have done. You have multiplied both denominators by something that gets rid of the denominators, or will when you multiply by 4 * 3 = 12

So multiply the equation by 12

(2/3 x- 5 = 3/4 ) 12

8x - 60 = 9 Add 60 to both sides

8x - 60 = 9 Combine

8x = 69 Divide by 8

x = 69/8

x = 8 5/8

What is the gcf of 18,54, and 72

Answers

I think its 9 because 9 times 2 is 18 9 times 6 is 54 and 9 times 8 is 72

Oop- help me;-;
please..

Answers

answer:
5c+4=2(c-5)
opening the parentheses we get:
5c+4=2c-10
putting like terms together we get
5c-2c=-10-4
3c=-14
c=-14/3

so the answer would be A. C = - 4 2/3

Write the equation in slope-intercept form. y−2=−4/3(x+6)

Answers

Answer: y = -4/3x - 6

Step-by-step explanation: To write the equation in slope-intercept form, we need to solve for y.

Starting with the given equation: y - 2 = -4/3(x + 6)

First, distribute -4/3 to both terms within the parentheses: y - 2 = -4/3x - 8

Next, isolate y by adding 2 to both sides of the equation: y = -4/3x - 8 + 2

Simplifying further: y = -4/3x - 6

Therefore, the equation in slope-intercept form is y = -4/3x - 6.

What is the area of the figure? A.
256 square inches

B.
288 square inches

C.
320 square inches

D.
384 square inches

Answers

The answer is a. What you need to do is find the area of the shape if it were a perfect rectangle - (20)(16)=320 in^2. Next you make an imaginary square in the corner (it's a square because it's 8in by 8 in) and find the area - 8^2 or (8)(8)=64. Finally you subtract the values - 320 - 64 = 256 in^2 voila.

Find n.
6/9=n/36
n=_____

Answers

multiple 6 with 36 and divide with 9
n = 24

Answer:

its 24 Hope this have a great day!

Step-by-step explanation:

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