Find the length of the third side. If necessary, round to the nearest tenth.​

Answer:

11.6

Step-by-step explanation:

The length of f of the triangle is f = 11.7 cm

The Law of Cosines is a mathematical formula used to find an unknown side or angle of a triangle, given the lengths of the other two sides and the angle opposite the unknown side. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite side c, the following equation is true:

c² = a² + b² - 2ab cos(C)

where cos(C) is the cosine of angle C. This formula can be rearranged to solve for any of the variables, depending on which values are known.

Given data ,

Let the triangle be represented as ΔEFG

And , the measures of the sides of the triangle are

g = 4.3 cm

e = 9.1 cm

And , measure of angle ∠F = 116°

where c² = a² + b² - 2ab cos(C)

On simplifying , we get

a² = c² - b² + 2abcos ( C )

78.26 ( cos 116° ) - 4.3² - 9.1² = f²

f² = 135.7344

Taking square roots on both sides , we get

f = 11.7 cm

Hence , the length is f = 11.7 cm

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Answer:

I think it is 5x+2y=41

Step-by-step explanation:

Answer:

volume

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

theres no weight refered, no length and ratio i dont know cause im not english but i think its A

Answer:

I am almost positive it is Complementary.

Step-by-step explanation:

Sorry if i am wrong please let me know if i am.

Answer:

17.5

Step-by-step explanation:

2.5 multiplier

Answer:

$7910.3

Step-by-step explanation:

Given data

P=$3572

n=4

T=16 years

R= 5%

The compound interest is expressed as

A= P(1+r/n)^nt

Substitute

A=3572(1+0.05/4)^16*4

A=3572(1+0.0125)^64

A=3572(1.0125)^64

A=3572*2.21453241061

A=$7910.3

Answer:

160=b  

      14

b: 2240

Answer:

b= 2240

Step-by-step explanation:

Multiply all terms by the same value to eliminate fraction denominators

then you simplify

hope this helps!

Answer:

See screenshot below

Step-by-step explanation:

Yes Bus Column:

No Bus Column:

Total column:

I hope this helps!

Answer:

a

Step-by-step explanation:

6^2+8^2=100

sqrt of 100 = 10

Answer:

A. 10

Step-by-step explanation:

Answer:

products - -3x and 6x^2

factors - 8 and 2x

Step-by-step explanation:

Answer:

-8x would go in the box above -16x and -8 would go in the other box

Answer:The best prediction is 1/6 of the times or one time of the six that you will roll a two..

This is because without any interference, each of the six numbers of the dice will have same theoretical probability (which is the probability or chances that is expected.

The inequality of the statememt is x < 78000

From the question, we have the following parameters that can be used in our computation:

An employee makes less than $78,000 a year in income.

Represent the earnings of the employee with x

So, we have

x is less than $78,000

When represented as an inequality, we have

x < 78000

See attachment for the graph

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Answer:

I would say 45

Step-by-step explanation:

180-90=90

90/2=45

Answer:

26x+5

Step-by-step explanation:

Answer:

$745,460.8

Step-by-step explanation:

2.8/100 × 3827 = $107.16

monthly = 1/12

[tex]p = \frac{100 \times i}{rt} = \frac{100 \times 107.16}{2.8 \times \frac{1}{12} } = \frac{10716}{0.23} \\ = 46591.3[/tex]

$46,591.3 in 1year

16 years; $46,591.3 × 16 = $745,460.8

Answer:

Luis wrote an incorrect expression.

Step-by-step explanation:

As per Terrell, the correct expression is (2x+2x) + (5x+5x) + (1+1) which is equal to 12x + 2

For you who got incorrect answer, the answer if you simplified it must be 12x + 2. Let's check:

Anya     2x+2x+5x+1+5x+1 =

            12x + 2 [CORRECT]

Katrin    2(5x+1) + 2x

             10x+2+2x

             12x + 2 [CORRECT]

Luis       2(2x) + 2(5x+1)

             4x+10x+2

             14x + 2 [INCORRECT]

Steve     1+1+ x(2+2+5+5)

              2+ x(12)

             12x + 2 [CORRECT]

Answer: [tex]\overline{AC}=[/tex] 12.5

Step-by-step explanation: The triangle ABC and its altitude [tex]\overline{BD}[/tex] is represented in the figure below.

Altitude is a segment of line that link a vertex and the opposite side, forming a right angle.

So, because of [tex]\overline{BD}[/tex], now we have two similar triangles, which means that ratios of corresponding sides are equal:

[tex]\frac{\overline{BD}}{\overline{BC}} =\frac{\overline{AD}}{\overline{BD}}[/tex]

[tex]\overline{BD}^{2}=\overline{BC}.\overline{AD}[/tex] (1)

This is always true for a right triangle and a altitude drawn to the hypotenuse.

Triangle BDC is also right triangle. So, we can use Pythagorean theorem to determine the missing side.

[tex]\overline{BC}^{2}=\overline{CD}^{2}+\overline{BD}^{2}[/tex]

[tex]\overline{BD}^{2}=\overline{BC}^{2}-\overline{CD}^{2}[/tex] (2)

Substituting (2) into (1):

[tex]\overline{BC}^{2}-\overline{CD}^{2}=\overline{BC}.\overline{AD}[/tex]

We want to find f, so:

[tex]\overline{AD}=\frac{\overline{BC}^{2}-\overline{CD}^{2}}{\overline{BC}}[/tex]

[tex]f=\frac{10^{2}-5^{2}}{10}[/tex]

f = 7.5

The length of [tex]\overline{AC}[/tex] is

[tex]\overline{AC}=f+5[/tex]

[tex]\overline{AC}=7.5+5[/tex]

[tex]\overline{AC}=12.5[/tex]

The length of the hypotenuse of triangle ABC is 12.5 units.

Answer:

x = 20

Step-by-step explanation:

Answer:

y=0x+(-3)

Step-by-step explanation:

Answer:

6.4

Step-by-step explanation:

Using Pythagorean theorem (a^2+b^2=c^2), 4^2+5^2=41. The square root of 41 is 6.4.

Answer:

4:5

Step-by-step explanation:

You are doing ratios

Answer:

f(-5) = 37

f(-3)= 13

f(-1)= -3

f(1)=  -11

f(3)= -11

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

4x-3=5x-7

-1x-3=-7 Subtract the 5x on both sides

-1x=-4 Add the -3 to the -7

x=4

Answer:

8q7s6271 be ta up dkdieow

Answer:

20²+21² = x²

841= x²

x= 29

nearest tenth = 30

Answer:

[tex] \boxed{x = 29}[/tex]

Step-by-step explanation:

[tex] {x}^{2} = {21}^{2} + {20}^{2} \\ {x}^{2} = 841 \\ x = \sqrt{841} \\ x = 29[/tex]

Answer:

(3x+2)(x+4)

Step-by-step explanation:

(3x+2)(x+4) = (3x)(x) + (3x)(4) + (2)(x) + (2)(4)

= 3x² + 12x + 2x + 8 *****

= 3x² + 14x + 8

You start by figuring it will be in the form of (3x + a)(x + b) because 3 doesn't factor. The two middle terms in the line followed by the stars must add up to 14x. And in (3x + a)(x + b), ab must be equal to the 8 on the end (the constant factor).

For most people, factoring takes a LOT of practice. And somethimes you just have to try a lot of factors before you hit the right combination. But if you do it enough, it really does get easier to 'see' the answer a lot of the time.

Hope this helped!

Answer:

5

Step-by-step explanation:

Perimeter is created by add all sides together

20 / 4 sides = 5