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pav-90 [236]
3 years ago
13

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
1 answer:
wlad13 [49]3 years ago
3 0
Let x be the base of the triangle, and
      2x + 4 be the height. 

One of the ways in solving for the area of a triangle is to half the product of its height (h) and base (b). Mathematically,
 
                              A = bh / 2

Substituting the expression for b and h and the given condition for the area,
   
                                    <em>(x)(2x + 4) / 2 ≤ 168</em>
  
                              
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The longer leg of a 30-60-90 trangle is 18
evablogger [386]

Answer:

The longer leg is opposite the 60, so to get the shorter leg you have to divide by  \sqrt{3}  

18 /  \sqrt{3}  = 6 \sqrt{3}



5 0
2 years ago
What is the value of r2 for the following data to three decimal places?
Viktor [21]

Answer:

R² = 0.964

Step-by-step explanation:

y = 1.9694x - 0.6122

R² = 0.964

6 0
2 years ago
you order two tacos and a salad. The salad cost $2.50. You leave a three-dollar tip. Theres is no sales tax. How much does one t
Diano4ka-milaya [45]

Answer:

$5.50

Step-by-step explanation:

2.50+3.00=5.50

4 0
3 years ago
Read 2 more answers
A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, whic
Rainbow [258]

angles formed by these tosses are  79.45, 59.02 and 41.53 degrees to the nearest hundredth.

<u>Step-by-step explanation:</u>

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

c^2 = a^2 + b^2 - 2ab (cosx)

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ c^2 = a^2 + b^2 - 2ab (cosx)

⇒ c^2 -a^2 - b^2 = -2ab (cosx)

⇒ (cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}

⇒ (cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}

⇒ (cosx) =0.18310

⇒ cos^{-1}(cosx) = cos^{-1}(0.18310)

⇒ x = 79.45

The Law of Sines (or Sine Rule) is very useful for solving triangles:

\frac{a}{sin A} = \frac{ b}{sin B} =  \frac{c}{sin C}

We can now find another angle using the sine rule:

⇒\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}

⇒sin Y = \frac{(7.5 (sin 79.45))}{  8.6}

⇒Y = 59.02 degrees

So, the third angle =180 - 79.45 - 59.02 = 41.53 degrees.

Therefore, angles formed by these tosses are  79.45, 59.02 and 41.53 degrees to the nearest hundredth.

4 0
3 years ago
The number of letters in Stephanie's full name is sixteen less than twice the number of letters in Amy's full name. If the numbe
Anestetic [448]

Answer:

19 letters

Step-by-step explanation:

Suppose Number of Amy's full name letters = X

               Number of Stephanie's full name letters = Y

Now, according to given condition that ''number of letters in Stephanie's full name is sixteen less than twice the number of letters in Amy's full name'',

Equation 1 becomes

Y = 2X-16

Now, according to second condition, product of their names' letter is 418. So,

Equation 2 becomes

XY = 418

Deducing value of X from equation 1,

X = (Y+16)/2

Putting this value in equation 2 we get,

{(Y+16)/2}*Y = 418,

By simplifying this equation we get a quadritic equation

(Y^2)+16Y-836=0

By breaking middle term (You can use quadratic formula here as well)

(Y^2)+38Y-22Y-836=0

Y(Y+38)-22(Y+38)=0

(Y-22)(Y+38)=0

At this stage we have two values for Y,

Y=22, or Y=-38

Now considering only positive value since the number of letters in a name can not be in negative number,

Y=22,

So X=(Y+16)/2

X=19

7 0
3 years ago
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