50 POINTS! Fully correct and explanatory answers only!


In the figure, ∠4 is an exterior angle to triangle ∠A∠U∠L .



(a) What is the angle measurement of Angle 3? Explain the angle relationship you used.



(b) What is the angle measurement of Angle 4? Explain the angle relationship you used.



(c) What is the angle relationship between angles 1, 2, & 3? What do you notice that is similar and different between the angle relationship between angles 1, 2, & 3 and that between 3 & 4?



(d) The combination of which two angles in the triangle equal angle 4? Use your work from Part C to figure out why this is the case, and explain your conclusion.


ANSWER ALL 4 PARTS FULLY AND EXPLANITORY!

The number of withholding allowances which Mario currently claim for her gross biweekly earnings of $784. 21 is 4.

Federal income tax is the tax which is used to develop and run the city or country and charged on the citizen residing there .

Mario has gross biweekly earnings of $784.21. By claiming 1 more withholding allowance, Mario would have $13 more in his take home pay.

The value $784.21 lies between $780 and $800. Here, in the problem, the Mario can claim $13 more in his take home pay.

Form, the table of Federal income tax, the calculated amount will be,

[tex]n=20-7\\n=13[/tex]

Now, again from the table, Mario still claim 4 withholding allowances currently.

The number of withholding allowances which Mario currently claim for her gross biweekly earnings of $784. 21 is 4.

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Answer:

10.2

Step-by-step explanation:

I stuck it into a calculator the exact number is ~10.295630141

a. The speed of the wind is 30 mph

b. The speed of the plane in still air is 450 mph

Let

Since the plane can travel 480 miles per hour with the wind, we have that

V + v = 480 (1)

Also, the plane travels 420 miles per hour against the​ wind, we have that

V - v = 420 (2)

The speed of the wind is 30 mph

subtracting equations (1) and (2), we have

V + v = 480 (1)

-

V - v = 420 (2)

2v = 60

v = 60/2

v = 30 mph

So, the speed of the wind is 30 mph

The speed of the plane in still air is 450 mph

Substituting v into equation (1), we have

V + v = 480 (1)

V + 30 = 480

V = 480 - 30

V = 450 mph

So, the speed of the plane in still air is 450 mph

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Answer:

No, he incorrectly rounded 1.25 to 2

Step-by-step explanation:

hope this helps :)

Answer:

No, he incorrectly rounded 1.25 to 2

Step-by-step explanation:

To find out how many pages Yutto writes in 1 hour we divide

1.25/2=0.625

Now we multiply

0.625×6=3.75

3.75≠6

So now we know that Yutto was incorrect so we can eliminate the last two options. Now how did he get his original estimate? For option A,

1.25 is rounded to 2

2/2=1

1×6=6

So the answer is A

Answer:

88

Step-by-step explanation:

92 and angle 2 are corresponding and 180-92= 88

Answer:

43

Step-by-step explanation:

Total number of different colors = 7

Probability of spinner landing on blue = 1/7

Probability of spinner landing on green = 1/7

Probability of spinner landing on blue OR green = 1/7 + 1/7 = 2/7

if the spinner is spun 150 times,

Number of times spinner will land on green or blue = Probability of spinner landing on blue OR green x 150

= 2/7 x 150

= 42.85714...

= 43 (rounded to the nearest whole number)

Answer:

Step-by-step explanation:

Number of sections is 7

Probability of each section is 1/7

Probability of blue or green:

Spinner nun 150 times, number of stops on blue or green:

The number of cans that can be recycled in 16 days, written in scientific notation is 2.6 x 10⁹.

The way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5x 10¹².

Given to us

Average 113,204 aluminum cans are recycled in a minute.

Firstly, in order to find the number of cans that can be recycled in 16 days, we need to find the number of minutes in 16 days. we know that 1 day has 24 hours where each hour has 60 minutes. therefore,

Number of minutes in 16 days = 16 x 24 x 60

Number of minutes in 16 days = 23,040 minutes

As it is given that on an average 113,204 number of cans can be recycled in a minute, therefore,

Total number of can that can be recycled = 113,204 x 23,040

                                                                      = 2,608,220,160

                                                                       = 2.6 x 10⁹

Hence, the number of cans that can be recycled in 16 days, written in scientific notation is 2.6 x 10⁹.

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Answer:

6/5

Step-by-step explanation:

rise/run

I hope this is right! :D

Answer:

The slope would be 6/5

Answer:

d. $233.40

Step-by-step explanation:

you solve this by first multiplying Ryan's hourly rate($5.30) by how many hours he worked last week(32 hours)

5.30*32=169.6

then you take that number and subtract it from how much he earned($403) and the resulting number will be what he made in tips

403-169.9=233.40

Answer:

d. $233.40

Step-by-step explanation:

pay for 32 hours

= $5.30 × 32

= $169.60

tips = $403 - $169.60

= $233.40

Answer:

sinθ=√7/4

Step-by-step explanation:

Here,

cosθ=3/4

b/h=3/4

b=3 and h=4

Using Pythagoras theorem,

h²=p²+b²

4²=p²+3²

16-9=p²

p=√7

Now,

sinθ=√7/4

Answer:

Step-by-step explanation:

14 - 5 = 9

9 - 5 = 4

4 - 5 = - 1

................

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 5

Answer:

Triangle = 10

Circle = 5

Two halves of Square = 2

Fourth answer: 20

Step-by-step explanation:

Figuring out the triangle first is easiest because since 3 triangles make 30, then each triangle must be 10.

Now, we have our second equation become 10 + C + C = 20, and we get C=5 after solving for the value of the circle.

Our third equation will be 5 + S + S = 13, which becomes 5+2S=13, 2S=8, and then S=4, so the value of a square is 4

Our fourth equation will be 10 + 5*(1/2)(4) = ?, and we see that half of 4 is 2, so we have 10 + 5(2) = 10 + 10 = 20 as our answer.

The value of the given expression x + yz will be 20.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let 'x' represents an equilateral triangle, 'y' represent a circle, and 'z' represents the right triangle. Then the equations are given as,

x + x + x = 30

3x = 30

x = 10

x + y + y = 20

10 + 2y = 20

y = 5

y + 2z + 2z = 13

5 + 4z = 13

z = 2

Then the value of the expression is calculated as,

x + yz = 10 + 5 × 2

x + yz = 10 + 10

x + yz = 20

The value of the given expression x + yz will be 20.

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Answer:

24 units

Step-by-step explanation:

create a proportion:

15/20 = 6/XY

cross-multiply:

15·XY = 120

XY = 8

15/25 = 6/YZ

cross-multiply:

15·YZ = 150

YZ = 10

Perimeter:

6 + 8 + 10 = 24

Answer:

  12 cm by 14 cm

Step-by-step explanation:

The area is given by ...

  A = LW

The perimeter is given by ...

  P = 2(L +W)

Substituting the given values, we have ...

  168 = LW

  52 = 2(L +W)

The second equation can be used to find an expression for L:

  26 = L +W . . . . . divide by 2

  L = 26 -W . . . . . subtract W

Using this in the first equation, we have ...

  168 = (26 -W)(W)

  W² -26W +168 = 0

Factors of 168 are ...

  168 = (-1)(-168) = (-2)(-84) = (-3)(-56) = (-4)(-42) = (-6)(-28) = (-7)(-24)

     = (-8)(-21) = (-12)(-14)

Only the last factor pair (-12, -14) has a sum of -26, so the equation factors as ...

  (W -12)(W -14) = 0

Solutions are W=12, and W=14. The corresponding values of L are 14 and 12.

The quadrilateral has dimensions of 12 cm and 14 cm.

Answer:

having a sticky surface

Step-by-step explanation:

Just took the tests

Answer:

width = 50 cm

Step-by-step explanation:

The volume (V) of a rectangular box is calculated as

V = lwh ( l is length, w is width and h is height )

Since V is given in cm³ then dimensions must be in cm

l = 1 m = 100 cm , then

100 × w × 75 = 375000

7500w = 375000 ( divide both sides by 7500 )

w = 50

the width of the box is 50 cm

Answer:

7,500 was the attendance before the drop.

Step-by-step explanation:

3750 x 2

The word problem that must be solved with division and includes 2/7 as the dividend and 4 as the divisor is that John wants to buy a 4 yards cloth qnd there are pieces of 2/7 yards each. How many pieces will he buy?

In this case, it should be noted that division is used.to separate into different parts.

Therefore, John wants to buy a 4 yards cloth qnd there are pieces of 2/7 yards each.

The pieces to be bought will be:

= 4 ÷ 2/7

= 4 × 7/2

= 14

He'll buy 14 pieces.

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Answer:

1. 1/5  1/3  4/6

2. 3/5  3/4  7/8

3. 87 nickels

4. 150 minutes

5. 2

6.  3/4

Step-by-step explanation:

1.  least to greatest:  1/5  1/3  4/6

2.  least to greatest:  3/5  3/4  7/8

3. 1 nickel = 5 cents

So 485 ÷ 5 = 87 nickels

4. Total number of minutes = 50 x 2 = 150 minutes

5. A composite number is a whole number that can be made by multiplying other whole numbers.

3 x 3 = 9  ⇒  composite number

3 x 5 = 15  ⇒  composite number

3 x 7 = 21  ⇒  composite number

Therefore 2 is NOT a composite number (it is a prime number)

6. 6/8 = 3/4

Answer:

[tex]a \times b \\ (4y + 12)6x \\ 24xy + 72x \\ = 24x(y + 3)[/tex]

Answer:

5r+4

Step-by-step explanation:

Let's simplify step-by-step.

6r−r+4

=6r+−r+4

Combine Like Terms:

=6r+−r+4

=(6r+−r)+(4)

=5r+4

Answer:

D

Step-by-step explanation:

the odds are less than .24 so it must be 0.12

Answer:

10 A. Quadrent 2

10 B. Quadrent 3

Step-by-step explanation:

Image

Answer:

(4, -3)

Step-by-step explanation:

Rewrite equations:

x−2y=10;6x+3y=15

Step: Solvex−2y=10for x:

x−2y=10

x−2y+2y=10+2y(Add 2y to both sides)

x=2y+10

Step: Substitute2y+10forxin6x+3y=15:

6x+3y=15

6(2y+10)+3y=15

15y+60=15(Simplify both sides of the equation)

15y+60+−60=15+−60(Add -60 to both sides)

15y=−45

15y

15

=

−45

15

(Divide both sides by 15)

y=−3

Step: Substitute−3foryinx=2y+10:

x=2y+10

x=(2)(−3)+10

x=4(Simplify both sides of the equation)

Therefore answer: is

x=4 and y=−3

Hope it helps!