Mathematics, 24.11.2019 16:31 kendall984

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?

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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!

Answer from: nickname0097

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.

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

Answer from: Quest

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

)=3(6x−9)−8

7x+(8)(x)+(8)(

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

−37

−3

Answer from: Quest

1. sometimes

2. never

3 .08c = 7.50+.05c 250 pages

step-by-step explanation:

1. sometimes

the theoretical probability of rolling a 1 is 1/6. perhaps you got really lucky and never rolled a 1 in those 60 times. your experimental probability is 0. or perhaps you rolled a 1 20 times. your experimental probability is 20/60 is 1/3. it really just depends on how you rolled in that experiment.

2. never

the probability of the event occurring is 1. that is being 100 % sure it will happen. that is the maximum amount of confidence we have.

3. no customer card cost: .08 times number of pages

customer card cost: 7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250

the cost is the same at 250 pages

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