m∠ABC = (9x + 4)° and m∠DEF = (13x − 22)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle?

Answer:

x = 6.5

Step-by-step explanation:

In order to solve this problem, you need to use trigonometry (sin, cosine, tangent).  

Sin = opposite/hypotenuse

Cosine = adjacent/hypotenuse

Tangent = opposite/adjacent

We need to use tangent in this case because 10 is the opposite side from the 57° angle, and x is right next to it, making it adjacent.  So, our equation would look like this:

tan (57)° = 10/x

Multiply both sides by x

x (tan (57)°) = 10

Divide both sides by tan (57)°

10 / tan (57)° = 6.49408 = 6.5

Step-by-step explanation:

We are given two angles measures and one side. Notice the given angle and the side that is opposite to that given angle is given. We need to find side x. But can we also find the angle opposite of the side we are trying to find. Yes we can

Remeber that triangles interior angles add up to 180.

Remeber that triangles interior angles add up to 180.One angle measure 90 and the other measure is 57 so

[tex]90 + 57 + x = 180[/tex]

[tex]x = 33[/tex]

So the angle opposite of the side we are trying to find is 33.

Since we know two angles and two sides that are opposite of those two angles respectively, we can use what is called Law of Sines

[tex] \frac{b}{ \sin(b) } = \frac{c}{ \sin(c) } [/tex]

where the numerator are the side measures, and the denominator are the angle measures.

Plug in the respectively values. Angle 57 is opposite of 10 and Angle 33 is opposite of x.

[tex] \frac{10}{ \sin(57) } = \frac{x}{ \sin(33) } [/tex]

Multiply both sides by sin 33 to isolate x.

We get

[tex]x = 6.494[/tex]

Round if needed

In other words, apply law of sines when you have two angles and two sides that are opposite of those angles respectively.

Answer:

-8/3x

Step-by-step explanation:

-8 / 3x / 1

-8 / 3x

.....

..

Answer:

B

Step-by-step explanation:

For example, if i gave u 28

The digit two stands for 20, and the digit 8 stands for 8, therefore u call it 28

Each spot has it own name

For example if i gave u the number 12345

5 is in the first spot, therefore 5 x 1 =5

4 is in the tenth spot, therefor 4 x 10 = 40

3 is in the hundred spot, therefore 3 x 100 =300

2 is in the thousand spot, therefore 2 x 1000=2000

1 is in the ten thousand spot, therefore 1 x 10000

=100000

So if u add all these numbers together u will get

12345

OK, so for your question, the 6 in 558672, is in the hundred spot, so 6 x 100 =600

The 3 in 74139 is in the ten spot, so 3 x 10=30

So the product is to multiply them together

600 x 30 =18000

Answer:

c.15+2z/6x-12y

f.7a+b/4a-6b

Step-by-step explanation:

z+1/x-2y - 2x-3/2x-4y + z/3x-6y

z+1/x-2y - 2x-3/2(x-2y) + z/3(x-2y)

6(z+1)-3(2z-3)+2z

15+2z/6x-12y

3a/2a-3b - a+b/2(-3b+2a)

6a+a+b/2(2a-3b)

7a+b/4a-6b

Answer:

10

Step-by-step explanation:

[tex]\\ \rm\longmapsto Speed=\dfrac{Distance}{Time}[/tex]

[tex]\\ \rm\longmapsto Speed=\dfrac{800}{10}[/tex]

[tex]\\ \rm\longmapsto Speed=80km/h[/tex]

[tex]\\ \rm\longmapsto Distance=Speed(Time)[/tex]

[tex]\\ \rm\longmapsto Distance=80(14)[/tex]

[tex]\\ \rm\longmapsto Distance=1120km[/tex]

Answer:

5,12,13

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

Its C.

Step-by-step explanation:

I had this and its C. trust me

Answer:

105

Step-by-step explanation:

219+(-114)=219-114=105

Answer:

girly he probably does and just give subtle signs that you do. if a guy wants to spend more time w u he will try his best to get some time w u if that makes sense.

Step-by-step explanation:

Presumably, the two dice are fair, so that each face has an equal 1/6 probability of being rolled. We roll 2 dice, so there are 6² = 36 possible outcomes, each with 1/36 probability of occurring.

We have

• P(A) = 2/36 = 1/18, because there are only 2 ways to roll a sum of 3 (1+2 and 2+1)

• P(B) = 6/36 = 1/6, because there are 6 ways of rolling a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)

• P(C) = 12/36 = 1/3, because if 1 die shows a 1, then there are 6 possible values for the other die, and vice versa)

(a) By definition of conditional probability,

P(A | C) = P(A and C) / P(C)

A and C only occur together if we had rolled either {1, 2} or {2, 1}, so ultimately

P(A and C) = P(A)

so that

P(A | C) = (1/18) / (1/3) = 3/18 = 1/6

(b) From the definition,

P(B | C) = P(B and C) / P(C)

By the same reasoning as in (a), we have to roll either {1, 6} or {6, 1} to have both B and C occur, so

P(B and C) = (2/36) / (1/3) = 6/36 = 1/6

(c) In order for two events X and Y to be independent, we need to have

P(X and Y) = P(X) P(Y)

or in terms of conditional probability,

P(X | Y) = P(X and Y) / P(Y) = P(X) P(Y) / P(Y) = P(X)

Then it follows that A and C are not independent, while B and C are independent.

Step-by-step explanation:

a)6!+12-3

=6!+9

b)-18+3!+4

=3!-14

=3!+(-14)

both are in the form if (+)!+constant.

Note:if you need to know any question about it please let me know.

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer:

no we cannot add them, though we can multiply or divide them. You cannot add them because they have different variables, we need the same variables to add or subtract those.

Step-by-step explanation:

Hope it helps

keep smiling :)

Conjectures are used to form opinions about a certain subject. The conjecture from the given figure is that:

The number of triangles that can be formed by an n-sided shape is n - 2.

Given that:

[tex]n \to[/tex] number of sides

From the attached figures, we have the following observation.

If this pattern continues, the number of triangles for an n-sided shape will be: n - 2

Hence, the conjecture is:

The number of triangles that can be formed by an n-sided shape is n - 2.

Read more about conjectures at:

https://brainly.com/question/15947300

Step-by-step explanation:

[tex] \sin(x) + \cos(x) \times \tan(x) \\ = \sin(x) + \cos(x) \times \frac{ \sin(x) }{ \cos(x) } \\ = \sin(x) + \sin(x) \\ = 2 \sin(x) [/tex]

Step-by-step explanation:

sin(x) + cos(x) = sin x ÷cos x

sin(x) + cos(x) sin(x) ÷ cos (x)

join cos x and sin x

sin x + sin x

cancel cos x with cos x

The answer is 2 sin x

Answer:

so our x is <

less than

explanation: 3>2x= 1.5<x

x- 4>2 =6<x

Answer:

24 is the answer. Hope it helps you! Stay blessed.

Step-by-step explanation:

[tex] \frac{ - 21}{3} - \frac{11}{2} [/tex]

[tex] \frac{ - 21 \times 2 - 11 \times 3}{6} [/tex]

[tex] \frac{ - 42 - 33}{6} [/tex]

[tex] \frac{ - 75}{6} [/tex]

[tex]12.5[/tex]

Answer:

95kg

Step-by-step explanation:

Mass÷Volume=Density

Therefore, Mass = Volume × Density

Mass = 1500 × 95

Mass = 95,000g

Since we were asked to find the mass in kg:

1000g = 1kg

Therefore, 95,000g = 95kg

Answer:

Small shirts = 12 shirts

Large shirts = 18 shirts

Step-by-step explanation:

Given information

There are plans for ordering 24 medium shirts.

For every 4 medium shirts, there would always be 2 small shirts and 3 large shirts.

STEP ONE: Find how many groups of [4 medium shirts] are ordered.

24 / 4 = 6

There should be 6 groups of 4-medium-shirts orders.

STEP TWO: Find the number of small shirts.

6 × 2 = 12 shirts

STEP THREE: Find the number of large shirts.

6 × 3 = 18 shirts

Hope this helps!! :)

Please let me know if you have any questions or need further explanations

Answer: 8.1 × 10¹⁰

Concept:

When multiplying exponents, add the exponents together.

When dividing exponents, subtract the exponents.

Solve:

Given expression

(3 × 10⁶) × (2.7 × 10⁴)

Put like terms together

=3 × 2.7 × 10⁶ × 10⁴

Combine like terms

=8.1 × 10⁶⁺⁴

=[tex]\boxed{8.1*10^{10}}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

8.1 x 10^10

Step-by-step explanation:

When you do this type of problem you want to combine the like terms together, in this case is this.

3 × 2.7 × 10⁶ × 10⁴. So you will get.        

8.1 x 10⁶⁺⁴

Which is 8.1 x 10^10 simplified

Answer:

4 days

Step-by-step explanation:

Since it is 8 more than 4 times, take 24 because that is how many days away rays birthday is and subtract 8. So now we have 24-8 which is 16. Now divide 16 by 4 to get 4 which is how many days away janes birthday is. So the answer is 4 days.

Answer:

b. The opposite of the number is negative

Step-by-step explanation:

the opposite of -6.7 would be 6.7 not a negative

Hi ;-)

[tex]\frac{v}{6}>11 \ \ /\cdot6\\\\\frac{6v}{6}>66\\\\v>66\\\\\huge\boxed{v\in(66;+\infty)}[/tex]

Answer:

721.

Step-by-step explanation:

The total number must be a multiple of 7

One less than the number is the LCM of 2 3 4 5 6 and 8.

The LCM is worked out as follows

2

3

4 = 2*2

5

6 = 2*3

8 = 2*2*2

LCM = 2*2*2* 3*5 = 120

But 121 is not divisible by 7 so it must be a multiple of 120 + 1 which is divisible by 7.

240 + 1 = 241 - not divisible by 7

480 + 1  = 481 - not divisible by 7

720 + 1 = 721

721/7 = 103

Answer:

Step-by-step explanation:

Let say n the number of pennies in the jar.

n is a multiple of 7 : n=7*k

n-1 is a multiple of 2,3,4,5,6,8 so a multiple of the lcm= 120

n-1=120*t

n-1=120*t

n=7*k

120*t=7k-1

7k=120*t+1

[tex]k=\dfrac{120*t+1}{7}\\k=17*t+\dfrac{t+1}{7}\\t=6+7*a\\k=17*(6+7a)+\frac{6+7*a+1}{7} =102+119*a+1+a=103+120*a\\n=7*k=7*(103+120*a)=721+840a\\\\[/tex]

The least number of pennies is 721 (when a=0)

Proof:

n-1=720

720/2=360

720/3=240

720/4=180

720/5=144

720/8=90

721/7=103

Answer:

f(g(25)) = -5

Step-by-step explanation:

You have to put 25 in place of x in g, and after, you take the result and put in place of x in f:

g(5) = √25 = 5

f(5) = 5^2 -6•5

f(5) = 25 -30

f(5) = -5

Answer:

6

Step-by-step explanation:

The range of the middle 50% is the right side of the box subtracting the left side of the box

14-8

6