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bekas [8.4K]
3 years ago
14

The height of a triangle is 4 m less than its base. The area of the triangle is 48 m2. Find the length of the base.

Mathematics
2 answers:
Hitman42 [59]3 years ago
7 0
If I did the math right, it should be D) 12 m
Finger [1]3 years ago
5 0
The area for a triangle is A= \frac{1}{2}bh.  We have an expression that puts the height in terms of the base.  We are told that the height is 4 m less than the base.  Therefore, h = b - 4.  We are also given a value for the area.  So our formula is 48= \frac{1}{2} b(b-4).  To avoid the confusion of what to do with the 1/2, let's multiply both sides by 2: 96 = b(b-4).  Distributing through the parenthesis, we have 96=b^2-4b.  In order to solve for b, we have to factor.  Bring the 96 over to the other side by subtraction to get b^2-4b-96=0.  Factor that however you are most familiar to get that your b values are 12 and -8.  The two things in math that will never EVER be negative are distance/length and time.  Therefore, -8 cannot be the length of our base.  12 is the answer D.
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strojnjashka [21]

Answer:

<em>95% of confidence interval for the Population</em>

<em>( 6.1386 , 6.8614)</em>

Step-by-step explanation:

<u><em>Step( i ):-</em></u>

<em>Given random sample size 'n' =85</em>

<em>Mean of the sample size x⁻ = 6.5 years</em>

<em>Standard deviation of Population = 1.7 years</em>

<em>Level of significance = 0.95 or 0.05</em>

<u><em>Step(ii):-</em></u>

<em>95% of confidence interval for the Population is determined by</em>

<em></em>(x^{-} - Z_{0.05} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.05} \frac{S.D}{\sqrt{n} })<em></em>

<em></em>(6.5 - 1.96\frac{1.7}{\sqrt{85} } , 6.5 + 1.96 \frac{1.7}{\sqrt{85} })<em></em>

<em>( 6.5 - 0.3614 , 6.5 + 0.3614 )</em>

<em>( 6.1386 , 6.8614)</em>

<u><em>Conclusion</em></u><em>:-</em>

<em>95% of confidence interval for the Population</em>

<em>( 6.1386 , 6.8614)</em>

8 0
3 years ago
No links, will be reported
kirza4 [7]

Answer:

(1,0)

Step-by-step explanation:

This is because a system of equations is when two lines cross to form a point that they share. (1,0) is the point where the two lines cross/intersect.

6 0
2 years ago
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The perimeter of a rectangle is 62 m. The length is four more than two times the width. What is the length?
Travka [436]
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Define length and width
--------------------------------------------------
Let x be the width
width = x
Length = 2x + 4

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Formula
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Perimeter = 2(length + width)

--------------------------------------------------
Find Length and width
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62 = 2(2x + 4 + x)
62 = 2(3x + 4)            <em> ← combine like terms  </em> 
62 = 6x + 8                 <em>← remove bracket </em>  
62 - 8 = 6x                  <em>← minus 8 on both sides </em>
6x = 54                      <em> ← swap sides  </em>
x = 54 ÷ 6                   <em>← divide by 6 on both sides</em>
<em>x = 9 m</em>

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Find Length and Width
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Width = x = 9 m
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Answer: Length = 22m
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3 0
3 years ago
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A triangular course for a canoe race is marked with buoys. The first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg
balu736 [363]
<h2>The race is 1.2 miles long</h2>

Step-by-step explanation:

The first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg is 2/5 mi.

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Now we need to find length of race

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The race is 1.2 miles long

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