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Rasek [7]
3 years ago
9

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 inequali

ty can be used to find the possible lengths, x, of the base of the triangle?
Mathematics
2 answers:
Jet001 [13]3 years ago
8 0
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!
den301095 [7]3 years ago
8 0
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<span> )
</span><span>(-14,12)
</span>(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 : <span>x(2x+4)/2<168, and the interval solution is (0,12) for the values of the base. </span>

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Write an equation for the line that is parallel to the given line and passes through the given point Y= 1/2 x -8 (-6 ,-17)
mylen [45]
Parallel to : y = 1/2x - 8

Passes through (-6, -17)

Our given slope is 1/2.

Plug the given coordinates into point-slope form.

y - y₁ = m(x - x₁)

y - (-17) = 1/2(x - (-6))

Simplify.

y + 17 = 1/2(x + 6)  ← Your answer.

However, sometimes teachers want this simplified even further.

So, simplify this.

y + 17 = 1/2x + 3

Subtract 17 from both sides.

y = 1/2x + 3 - 17

Simplify.

y = 1/2x - 14 ← Slope-intercept form.

Standard form → -1/2x + y = -14


~Hope this helped!~
8 0
3 years ago
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lukranit [14]
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6 0
3 years ago
Read 2 more answers
Past the core
Basile [38]

Answer:

Building's shadow length = 180 feet.

Step-by-step explanation:

Given:

A 50-foot flagpole is at the entrance of a building that is 300 feet tall.

Its forms a right angled triangle from both ends,both of them are similar because the angle of the sun is the same at the same time of day.

From similar triangle property we can say that.

⇒ length of the building shadow times height of the flagpole's = length of the flagpole's shadow times height of the building

Or

\frac{length\ of\ the\ building\ shadow}{height\ of\ the\ building} =\frac{length\of\ the\ flagpole's\ shadow}{height\ of\ the\ flagpole's}

Plugging the values in the above equation we have,

Let length of the building shadow ='x' feet

⇒ \frac{x}{300} =\frac{30}{50}

⇒ \frac{x}{300}\times 300 =\frac{30}{50}\times 300

⇒ x=\frac{300\times 30}{50}

⇒ x=\frac{9000}{50}

⇒ x=180 feet.

So the length of the building shadow is 180 feet.

5 0
3 years ago
Please help ASAP!!!!!!
erica [24]

Answer:

300

Step-by-step explanation:

20*30=600

600/2=300

Please mark as Brainliest! :)

Have a nice day.

6 0
3 years ago
Write a polynomial function given the zeros 5, 6+2i, and 6-2i and passes through the point (2, 64)
ivolga24 [154]

Answer:456 thatas the answer

Step-by-step explanation:

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2 years ago
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