Two angles are ______ if the sum of their measure is 180 degrees.

Answer:

[tex]\sin(\theta)=4/5[/tex]

Step-by-step explanation:

Refer to the graph.

From the graph, we can see that our angle is in QII.

In QII, sine is positive and cosine and tangent are negative.

Since our point is at (-3, 4), this means that our adjacent side to our angle is -3 while our opposite side to our angle is 4.

To find sine, we need to find the hypotenuse c.

So, we can use the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute -3 for a and 4 for b. This yields:

[tex](-3)^2+(4)^2=c^2[/tex]

Square:

[tex]9+16=c^2[/tex]

Add:

[tex]25=c^2[/tex]

Take the square root of both sides:

[tex]c=5[/tex]

So, our hypotenuse is 5.

And our adjacent is -3 and opposite is 4.

Now, remember that:

[tex]\sin(\theta)=\text{opp}/\text{hyp}[/tex]

Substitute 4 for the opposite and 5 for our hypotenuse. This gives us:

[tex]\sin(\theta)=4/5[/tex]

Since sine is positive in QII, we don't need to add any negatives.

And we're done!

Answer:

E: 625

F: 155

G: 625

Step-by-step explanation:

Hi!

E.

A number, reduced by 20% is 500.

Originally, that number was at 100%.

Reduced = subtraction, so that number = 100%-20%, or 80%.

80% of a number = 500.

80% = .8

.8x = 500

Divide both sides by .8

x = 625

F.

A number that is increased by 100% is a number that is doubled (multiplied by 2).

2x=310

x=155

G.

Originally, the money was at 100%. After being reduced by 20%, the money is at 80% (.8).

.8x = 500

Once again, the answer is 625.

H (?)

To change a decimal to a percent, we multiply by a 100.

1.40 * 100 = 140%

As a fraction: 140/100

Answer:

a = 14

Step-by-step explanation:

Step 1: Write out your problem

f (a) = 5a + 14 | f (a) = 0

Step 2: Solve

f (a) = 5 (0) + 14 , Input a.

f (a) = 0 + 14 , 5 x 0 = 0

(a) = 14 , 0 + 14

a = 14

Answer:

440 ≤ x ≤560

Step-by-step explanation:

Answer:

Step-by-step explanation:

A) Find the figure attached. According to the figure, since line PQ is parallel to line RS, then <CBQ = <DCS (corresponding angle)

Also <BCS + <DCS = 180° (sum of angles on a straight line)

Given

<BCS = (5a+14)° and <DCS = <CBQ =(2a-9)°

Substituting this values into the formula to calculate the value of a;

(5a+14)°+(2a-9)° = 180°

5a+2a+14-9 = 180

7a+5 = 180

7a = 180-5

7a = 175

a = 175/7

a = 25°

Hence the value of a is 25°

B) From the diagram <ABQ = <BCS = 5a+14 (corresponding angle)

Substitute a = 25 into the expression

<ABQ = 5(25)+14

<ABQ  = 125+14

<ABQ = 139°

C) To get <BCR, we will use the formula;

<BCR + <BCS = 180

Given <ABQ = <BCS = 139°

<BCR = 180 - <BCS

<BCR = 180 - 139

<BCR = 41°

Answer:

Part A: 25

Part B: 139

Part C: 41

Step-by-step explanation:

5a+14+2a-9

a=25

5(25)+14

=139

2(25)-9

=41

Answer: A, BAC, CAB

Step-by-step explanation: A already says it’s an angle . BAC & CAB are congruent meaning they are equal . Hope this helped !

Answer:

Abram payed $12.50 for the cab ride in all.

Answer:

(fg)(x)= 6x^3-13x^2+8x-3

Step-by-step explanation:

(fg)(x)= f(x).g(x)

(fg)(x)=(3x^2-2x+1).(2x-3)

(fg)(x)= (6x^3-9x^2-4x^2+6x+2x-3)

(fg)(x)= 6x^3-13x^2+8x-3

Answer:

1000 milliliters in a liter, so 325 mL = 0.325 L

Step-by-step explanation:

Answer:

I believe the awnser is 539 total.

Step-by-step explanation:

If you take the 4 and times it by 1 you get 4.

Same with the nine.

But if you times 49 by 11 you get 539.

Hope this helps!

Answer:

C. 1/6

Step-by-step explanation:

negative times a negative is a positive

4 times 3 is 12

9 x 8 is 72

12/72 can be reduced to 1/6 because the top and bottom are both divisible by 12

Answer: 1/6 C

Step-by-step explanation:

Answer:

The Correct Answer is 1/4 .

Step-by-step explanation:

Because, She ran 2 Laps in 8 minutes, So if you split the 8 In half it's four, So she runs 1/4 of a lap per minute.

1/4

Step-by-step explanation:

Respuesta: [tex]\frac{7}{8}[/tex] de taza o 0.875 tazas

Explicación:

Repartir un número total de objetos entre personas implica dividir el total entre el número de personas. Es decir que en este caso las 7 tazas deben dividirse entre los 8 bebes. Esta división o partición puede representarse por medio de una fracción o por medio de una división:

Fracción: Esta situación puede ser representada como una fracción si se incluye el número total de bebés o partes a repartir como denominador (número de abajo) y el número de tazas o cantidad total como numerador.

[tex]\frac{7}{8}[/tex]  de taza

División: Divida el total en la cantidad de partes a repartir

7 tazas ÷ 8 bebes = 0.875 tazas por bebé

Here, we have the expression [tex]\frac{x^2 + 4}{2}[/tex] and we're asked

to evaluate the expression when x = -2.

To evaluate an expression, we simply plug

the value of the variable into the expression and solve.

So here, since x = -2, we have [tex]\frac{(-2)^2 + 4}{2}[/tex].

Notice that I used parentheses around the -2.

This is a good idea when substituting numbers in for variables.

Next, the order of operations tell us that exponent comes first.

So we have (-2)² which is 4.

So we have [tex]\frac{4 + 4}{2}[/tex].

Now when we have a division bar, it's important to understand

that it has the same effect on a problem as a set of parentheses

in that it groups terms together.

So this 4 + 4 can be thought of as being inside a set of parentheses.

So we can also write this as [tex]\frac{(4 + 4)}{2}[/tex].

Now simplify the top to get 8 and we have 8/2 which is 4.

Answer:

$9 in interest for a total of $159

Step-by-step explanation:

Answer:

u have to finish the question ...

Answer:

the answer to the question is 8

Answer:

louis age is 26

Step by step explanation:

their difference = 20

and Louis is 6 times

then 20 + 6 = 26

Louis is [tex]6[/tex] times Mary's age. If the difference in their ages is 20 then Louis is [tex]24[/tex] years old.

Age is defined as the length of time that somebody has lived or that something has existed.

Let,

Mary's age  [tex]=x[/tex] years

So, Louis' age  [tex]= 6x[/tex] years

According to question,

[tex]6x-x=20[/tex]

[tex]5x=20[/tex]

[tex]x=4[/tex]

So, Louis' age  [tex]= 24[/tex] years

Hence, we can say that Louis is [tex]24[/tex] years old.

To learn more about ages click here

https://brainly.com/question/91727

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Answer:

W=-3 because negative divided by a negative equals a positive

Step-by-step explanation:

Hope this helps!!!

Answer:

-20+1 every minute

Step-by-step explanation:

Answer:

[tex]PS=13\text{ units}[/tex]

Step-by-step explanation:

So, we know that PR is 20, SR is 11, and QS is 5.

We also know that PQ is perpendicular to QR, forming the right angle at ∠Q.

We know all the side lengths except for PQ and PS (the one we want to find). Notice that if we find PQ first, we can then use the Pythagorean Theorem to find PS since we already know QS.

So, let's find PQ.

We can see that we can also use the Pythagorean Theorem on PQ. PQ, QR, and PR (the hypotenuse) will be our sides. So:

[tex](PQ)^2+(QR)^2=(PR)^2[/tex]

We know that PR is 20.

QR is the combined length of QS+SR, so QR is 5+11 or 16.

So, substitute:

[tex](PQ)^2+(16)^2=(20)^2[/tex]

Solve for PQ. Square:

[tex](PQ)^2+256=400[/tex]

Subtract 256 from both sides:

[tex](PQ)^2=144[/tex]

Take the square root of both sides:

[tex]PQ=12[/tex]

So, the side length of PQ is 12.

Now, we can use the Pythagorean Theorem again to find PS. Notice that PQ, QS, and PS also form a right triangle, with PS being the hypotenuse. So:

[tex](PQ)^2+(QS)^2=(PS)^2[/tex]

We already know that QS is 5. We also just determined that PQ is 12. Substitute:

[tex](12)^2+(5)^2=(PS)^2[/tex]

Square:

[tex]144+25=(PS)^2[/tex]

Add:

[tex]169=(PS)^2[/tex]

Take the square root of both sides:

[tex]PS=13[/tex]

Therefore, the length of PS is 13 units.

And we're done!

The answer to this is PS=13.

Answer:

x=11

y=-7

z=-6

Step-by-step explanation:

y=11+3z

x-33-5z=8

11+8z=-37

z=-6

x-3=8

y=-7

x=11

Answer: 4 - 5 = 4 + (-5) = -1

Step-by-step explanation:  You have to make the 5 into a negative number using parenthesis and do the math.

Answer:

4+(-5)

Step-by-step explanation:

Here is the number line

The standard form of  [tex]3+2 \cdot \frac{1}{10} +4 \cdot \frac{1}{1000}[/tex] is 3.204

Explanation :

Given : [tex]3+2 \cdot \frac{1}{10} +4 \cdot \frac{1}{1000}[/tex]

Lets convert fractions into decimals

[tex]\frac{1}{10} =0.1\\\frac{1}{1000}=0.001[/tex]

Now 2 times 0.1 becomes 0.2

Also 4 times 0.001 becomes 0.004

So the given expression becomes

[tex]3+2 \cdot \frac{1}{10} +4 \cdot \frac{1}{1000}\\3+2 \cdot 0.1+4 \cdot 0.001\\3+0.2+0.004\\3.204[/tex]

Learn more : brainly.com/question/14426774

Answer:

A 95% confidence interval for the mean credit card debt of all college students in Illinois is [$316.06, $375.94] .

Step-by-step explanation:

We are given that in a sample of 50 college students in Illinois, the mean credit card debt was $346. Suppose that we also have reason to believe that the population standard deviation of credit card debts for this group is $108.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                               P.Q. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean credit card debt = $346

            [tex]\sigma[/tex] = population standard deviation = $108

            n = sample of college students = 50

            [tex]\mu[/tex] = population mean credit card debt

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.

So, a 95% confidence interval for the population mean, [tex]\mu[/tex] is;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

                                                 level of significance are -1.96 & 1.96}    P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}} }[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                       = [ [tex]\$346-1.96 \times {\frac{\$108}{\sqrt{50} } }[/tex] , [tex]\$346+1.96 \times {\frac{\$108}{\sqrt{50} } }[/tex] ]

                                       = [$316.06, $375.94]

Therefore, a 95% confidence interval for the mean credit card debt of all college students in Illinois is [$316.06, $375.94] .

Answer:

2000

Step-by-step explanation: