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Answer:

9. x = 31°

10. m∠ABC = 62°

11. m∠BCA = 60°

Step-by-step explanation:

We are given the following values for ΔABC, and its exterior angle, ∠ACD:

In ΔABC, the two nonadjacent interior angles are:  

While the exterior angle, m∠ACD = (5x - 35)°.

In order to solve for questions 9 through 11, we must apply the Exterior Angle Theorem which states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent or remote interior angles.

In order to find the value of x, we can use the Exterior Angle Theorem:

m∠ACD = m∠A + m∠B

(5x - 35)° = 58° + 2x°

5x° - 35° = 58° + 2x°

Subtract 2x from both sides:

5x° - 2x - 35° = 58° + 2x° - 2x

3x - 35° = 58°

Next, add 35° to both sides:

3x° - 35° + 35° = 58° + 35°

3x° = 93°

Divide both sides by 3 to isolate x:

[tex]\displaystyle\mathsf{\frac{3x}{3}\:=\:\frac{93}{3} }[/tex]

x = 31°

Therefore, the value of x = 31°.

In order to find m∠ABC, we must first substitute the value of x into m∠B:

m∠B = 2x° = 2(31)° = 62°

Therefore, m∠ABC = 62°.

In order to find m∠BCA, we must first find the value of its supplement, m∠ACD, by substituting the value of x derived from question 9.

m∠ACD = 5x° - 35° = 5(31)° - 35° = 120°

Next, substitute the value of m∠ACD into the following equation:

m∠BCA + m∠ACD = 180°

m∠BCA + 120° = 180°

Subtract 120° from both sides:

m∠BCA + 120° - 120° = 180° - 120°

m∠BCA = 60°

Therefore, m∠BCA = 60°.

In order to verify whether we have the correct values for each interior angles, we can apply the Triangle Sum Theorem which states that the sum of all interior angles of a triangle is equal to 180°.  In other words:

m∠A + m∠B + m∠C = 180°.

58° + 62° + 60° =  180°

180° =  180° (True statement).

The value of x from the expression is [tex]\frac{ln8-8}{3}[/tex]

Given the exponential function [tex]e^{3x+8}=8[/tex]

Take the natural logarithm of both sides:

[tex]lne^{3x+8}=ln8\\3x +8=ln8[/tex]

Subtract 8 from both sides:

[tex]3x-8+8=ln8-8\\3x=ln8-8[/tex]

Divide both sides by 3:

[tex]\frac{3x}{3} =\frac{ln8-8}{3}\\x= \frac{ln8-8}{3}[/tex]

Hence the value of x from the expression is [tex]\frac{ln8-8}{3}[/tex]

Learn more on exponential functions here: https://brainly.com/question/12940982

Answer:

27/20

Step-by-step explanation:

135% = 135/100 = (27/20 × 5) = 27/20 = 1 7/20 I think

Answer:

Step-by-step explanation:

A = 4πr² = 4π9² = 324π units²

324(3.14) = 1,017.36 units²

Explanation :

________________________________

Factorizes:

⇒ a² + 8a + 16 = 0.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ a² + 4a + 4a + 16 = 0.

⇒ a(a + 4) + 4(a + 4) = 0.

⇒ (a + 4)(a + 4) = 0.

⇒ (a + 4)² = 0.

⇒a=-4.

Hence a=-4.

Using the interpretation of a confidence interval, it is found that the correct option is:

x% confidence interval:

Hence, the correct option is:

You can learn more about the interpretation of a confidence interval at https://brainly.com/question/25822483

Answer:

It is 1 unit to the right of 0.

Step-by-step explanation:

Step-by-step explanation:

The answer im just guessing but teachers like to do false false true true so sorry if im wrong

Answer:

180° - (61° + 61°) = 58°

Step-by-step explanation:

we can see that two sides of the angle are equilateral making it equiangular therefore the other angle is 61° and solve for <FED

Not sure what your asking but i know from 3 1/3 of it is 10 means 3 1/3 equals 1/3rd of 10 but please tell me what your asking in the comment section ty

Answer:

3 dregreess 5 degrees temperature

Answer:

C. PO

Step-by-step explanation:

SURE PO AKO DYAN PA BRAINLEST PO

TAMA PO TALAGA YAN

Answer:

Each chicken wing costs $1.80.

Explanation:

To find the cost for each wings, you need to split the money by 7 which is: 12.60/ 7

this gives us:

1.80

[tex]\\\\\\x^2 -8x +16 = 0\\\\\implies x^2 - 2(4) + 4^2 =0\\\\\implies (x-4)^2 =0\\\\\implies x -4 =0\\\\\implies x =4\\\\\text{This equation has only one solution.}[/tex]

Answer:

114.59155

Step-by-step explanation:

Answer:

Sorry i didn't know that

Answer:

  71.6°

Step-by-step explanation:

The angle can be found from the dot product of PQ and PR.

  PQ·PR = |PQ|×|PR|×cos(α)

where α is the angle between the two segments.

  cos(α) = (Q -P)·(R -P)/(|Q -P|×|R -P|)

  = ((0, 1, 0) -(1, 0, 0))·((0, 0, 2) -(1, 0, 0))/(|Q -P|×|R -P|)

  = (-1, 1, 0)·(-1, 0, 2)/(√(((-1)² +1²)((-1²) +2²)) = (1+0+0)/√10

  α = arccos(1/√10) ≈ 71.6°

The angle at P is about 71.6°.

_____

Additional comment

The side lengths of the triangle are √2, √5, √5. As we have seen, the angle at P is bounded by the sides of length √2 and √5. The law of cosines can also be used to arrive at the angle between these sides.

Answer: y

Step-by-step explanation:

Slope intercept form is written as

Y=mx+b, so you’d solve for the variable y

Answer:

9

Step-by-step explanation:

12/4=3

3*3= 9

Filler and more filler

The area of  the square is 9 [tex]cm^{2}[/tex].

The space occupied by a flat shape or the surface of an object is called area.

[tex]Area = a^{2}[/tex]

Where, a is the length of the side of a square

Perimeter is the total length of the sides of a two-dimensional shape.

Perimeter of a square = 4a

Where, a is the side of a square

According to the given question

Perimeter of a square is 12cm.

Let a be the length of the side of a square.

Therefore,

Perimeter of the square = 4a

⇒ 12 = 4a

⇒ a = 12/4

⇒ a = 3cm

So, the area of square = 3cm × 3cm = 9 square cm

Hence, the area of  the square is 9 [tex]cm^{2}[/tex].

Learn more about  area of square here:

https://brainly.com/question/1658516

#SPJ2

Answer:

Step-by-step explanation:

Parallel lines have identical slopes

y = 3x + b

add in the desired point

10 = 3(2) + b

b = 4

B.  y = 3x + 4

Answer:

30

Step-by-step explanation:

sh well cm to cm et FL to

Answer:

Solve what?

Step-by-step explanation:

You didn't put the question.

Answer:

946 square Inches

Step-by-step explanation:

First, you should split up the shape into parts.

1st part 28x7

2nd part 30x25

We are multplying simply because

Area = Length x Width

Now that we have split up the parts lets multply them and add them togeher.

28 x 7 =  196

30 x 25 = 750

196 +750 = 946

So the area of this figure is 946 square inches.

Answer:

Because if you didn't you would not know anything about the past.

Step-by-step explanation:

Yes

Answer:

Try this on for size

Step-by-step explanation:

Answer:

Slope is 4.8

Step-by-step explanation:

[tex]{ \tt{G(x) = 4.8x - 5}} \\ [/tex]

Answer: The Answer is 4.8

Answer:

for 3, 4 or both?

4. is probably zero

Step-by-step explanation:

Wait is 4 a question?

[tex]cos^2 x + \cos^2 y = \cos(2x + 2y)\\\\\implies \dfrac{d}{dx} (\cos^2 x + \cos^2 y) = \dfrac{d}{dx} \cos(2x+2y)\\\\\implies -2\cos x \sin x -2 \cos y \sin y \dfrac{dy}{dx}=-\sin(2x+2y) \left(2+2\dfrac{dy}{dx} \right) \\\\\implies -2\cos x \sin x -2 \cos y \sin y \dfrac{dy}{dx}=-2\sin(2x+2y) -2\sin(2x+2y)\dfrac{dy}{dx} \right) \\\\\implies 2 \sin(2x+2y) \dfrac{dy}{dx} - 2 \cos y \sin y \dfrac{dy}{dx} = 2 \cos x \sin x-2\sin(2x+2y)[/tex]

[tex]\implies \sin(2x+2y) \dfrac{dy}{dx} - \cos y \sin y \dfrac{dy}{dx} = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} [\sin(2x+2y) - \cos y \sin y] = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} [\sin(2x+2y) - \cos y \sin y] = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} = \dfrac{\cos x \sin x-\sin(2x+2y)}{\sin(2x+2y) - \cos y \sin y}\\\\\implies y'(x) = \dfrac{\cos x \sin x-\sin(2x+2y)}{\sin(2x+2y) - \cos y \sin y}[/tex]

Answer:

2x + y = 26

Step-by-step explanation:

The standard form of a linear equation is   A x + By = C.

Simplify -2(x - 8)

Multiply -2 by -8

y - 10 = -2x + 16

2x + y - 10 = 16

Add 10 to both sides.

Add 16 and 10

Answer= 2x + y = 26

Answer:

Exponents

Step-by-step explanation:

Parentheses

Exponents and roots

Multiplication

Division

Addition

Subtraction

Answer:

0.4

Step-by-step explanation:

2/5 converted into hundredths is 40/100.

40/100 as a decimal is 0.40, or 0.4

-hope it helps