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Paladinen [302]
3 years ago
14

. A triangle has side lengths of 8, 7, and 14. To the nearest tenth of a degree find the measure of the angle opposite the side

of length 8.
Mathematics
1 answer:
4vir4ik [10]3 years ago
7 0

Given:

The measure of three sides of a triangle are 8, 7 and 14.

To find:

The measure of the angle opposite the side of length 8.

Solution:

According to the Law of Cosine:

\cos A=\dfrac{b^2+c^2-a^2}{2bc}

Let a=8, b=7 and c=14, then by using Law of Cosine, we get

\cos A=\dfrac{7^2+14^2-8^2}{2(7)(14)}

\cos A=\dfrac{49+196-64}{196}

\cos A=\dfrac{181}{196}

Taking cos inverse on both sides.

A=\cos^{-1}\dfrac{181}{196}

A=22.561328

A\approx 22.6

Therefore, the measure of the angle opposite the side of length 8 is 22.6 degrees.

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AlladinOne [14]

Answer:

y = -32

Step-by-step explanation:

-6(y+15)=-3y+6

Distribute

-6y - 90 = -3y +6

Add 6y to each side

-6y -90+6y = -3y+6y +6

-90 = 3y+6

Subtract 6 from each side

-90 -6 = 3y +6-6

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7 0
3 years ago
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Choose the model that represents the function
kirill [66]

Answer:

OPTION D

Step-by-step explanation:

We have to determine which option determines the function given above.

To determine the function, just substitute the values and compare LHS and RHS.

we have $ f(4) = 18 $

$ f(-2) = -12 $

$ f(0) = -2 $

$ f(-3) = -17 $

Here, $ x $ is the domain and $ f(x) $ is the co-doamin.

Therefore, $ x = \{4, -2, 0, -3\} $

Now, OPTION A: $ f(x) =  2x - 5 $

Substitute x = 4. We get f(x) = 3 $ \ne $ 18.

So, OPTION A is rejected.

Similarly, OPTION B: $ f(x) = 5x + 2 $

Substitute x = 4. We get f(4) = 22 $ \ne $18.

It is rejected as well.

Now, for OPTION C: $ f(x) = \frac{x}{2} - 5 $

Substitute x = 4. We get f(4) = -3 $ \ne $ 18.

So, OPTION C is also rejected.

OPTION D: $ f(x) =  5x - 2 $

Substitute x = 4. We get f(4) = 18.

Substitute the remaining points in domain as well. We notice that it exactly matches the given function. So, OPTION D is the answer.

8 0
3 years ago
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natta225 [31]

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3 0
2 years ago
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Lori creates the following design for a T-shirt.
kakasveta [241]

<u>Solution-</u>

From the figure,

AE = 2.4

EB = 2.8

BC = 11.7


Area of rectangle 1 = 8.68 sq.in

\Rightarrow FH \times HI=8.68

\Rightarrow EB \times HI=8.68  (∵ sides of the rectangle 2)

\Rightarrow 2.8 \times HI=8.68

\Rightarrow HI=3.1


Area of Triangle 1 = 6.48 sq.in

\Rightarrow \frac{1}{2}\times AE \times EG= 6.48

\Rightarrow \frac{1}{2}\times AE \times (EF+FG)= 6.48

\Rightarrow \frac{1}{2}\times AE \times (EF+HI)= 6.48  (∵ sides of the rectangle 1)

\Rightarrow EF+3.1= 5.4

\Rightarrow EF=2.3

\Rightarrow BH=2.3  (∵ sides of the rectangle 2)


BC = BH+HI+IC

\Rightarrow 11.7= 2.3+3.1+IC

\Rightarrow IC=6.3


The area of Rectangle 2,

=EB\times BH =2.8\times 2.3=6.44\ sq.in


The area of Triangle 2,

\frac{1}{2}\times GI \times IC=\frac{1}{2}\times EB \times IC=\frac{1}{2}\times 2.8 \times 6.3=8.82\ sq.in


The area of the whole figure = Area of Triangle 1 + Area of rectangle 1 + Area of Triangle 2 + Area of rectangle 2

= 6.48+8.68+8.82+6.44=30.42 sq.in


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3 years ago
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kolezko [41]

Answer:

f=−35

Step-by-step explanation:

<em>1.Simplify  4×6.5 to 26</em>

f=-26-9

<em>2. Simplify  -26-9 to  -35</em>

f=-35

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