0.4x3.2
Step by step

x = first angle

y = second angle

z = third angle

x + y + z = 180

The sum of the measures of the second and third angles is twice the measure of the first angle.    ---->       y + z = 2x

The third angle is 12 more than the second.  ---->    z = y + 12

Use substitution to find each variable. Since z is already isolated/by itself, plug it into the other equation

y + z = 2x    Plug in (y + 12) for z

y + (y + 12) = 2x      Simplify

2y + 12 = 2x    Divide 2 on both sides

y + 6 = x          Isolate "y"

y = x - 6         Next you could plug this into z = y + 12, so that z has the x variable

z = y + 12

z = x - 6 + 12

z = x + 6

Now that you have y and z, you can do this:

x + y + z = 180

x + (x - 6) + (x + 6) = 180     Simplify

3x = 180    Divide 3 on both sides

x = 60             Now that you found x, plug it into the other equations to find y and z

y = x - 6

y = 60 - 6

y = 54

z = x + 6

z = 60 + 6

z = 66

x = 60°

y = 54°

z = 66°          [sorry if this is confusing]

PROOF

x + y + z = 180

60 + 54 + 66 = 180

180 = 180

The problem can be solved by setting up and solving a system of equations based on the information given in the problem. Using these equations, we are able to establish a relationship between the angles and thus calculate their individual measures.

To solve this problem, we need to set up and solve a system of equations based on the information provided. We know from the problem that:

First, let's substitute z = y + 12 into the other two equations:

We now substitute x = y + 6 into the equation x + 2y = 168 to find the values of x and y and hence z.

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Answer:

c. 2,4

Step-by-step explanation:

Answer:

y = - 4x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute (- 1, 6) into the partial equation

6 = 4 + c ⇒ c = 6 - 4 = 2

y = - 4x + 2 ← equation of line

The trains are 275 km apart when both are at their first stop

Solution:

The tracks make an angle of 130°, with the station as a vertex

Therefore, from given figure in question,

Angle at station = 130 degree

Let "c" be the point at station

The first train  travels 100 km and makes its first stop at point A

Distance between A and station c = 100 km

Let a = 100 km

The second train travels 200 km and makes it first stop at point B

Distance between B and station c = 200 km

Let b = 200 km

We have to find the value of "d"

We can use the law of cosine

The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

From given figure in question,

Side opposite "d" to 130 degree is equal to sum of square of other sides a and b minus twice the product of those sides and the cosine of the angle between them which is 130 degrees

Therefore,

[tex]d^2 = a^2 + b^2 - 2ab\ cos\ d[/tex]

[tex]d^2 = 100^2 + 200^2 - 2(100)(200)cos 130\\\\d^2 = 10000 + 40000 - 40000cos 130\\\\d^2 = 50000 - 40000 \times -0.6427\\\\d^2 = 50000 + 25711.5\\\\d^2 = 75711.5\\\\\text{Take square root on both sides }\\\\d = 275.15 \approx 275[/tex]

Thus trains are 275 km apart when both are at their first stop

Answer:

D. 275 km

Step-by-step explanation:

Total Cost = 250 + 60x is the equation that models the given situation

Solution:

Given that, Linda's start up cost for her online jewelery store was $250

She has to pay an additional $60 per month to keep it running

To find: Equation that models this situation

From given,

Start up cost = $ 250

Let "x" be the number of months she keeps the store running

Additional pay per month = $ 60

Thus, the total cost Linda spend to keep the store running is given as:

Total Cost = Startup cost + (Additional pay per month)(number of months)

[tex]Total\ Cost = 250 + 60x[/tex]

Thus the equation that models the given situation is found

Final answer:

To divide a whole number by a unit fraction using fraction tiles, treat the division as multiplication by the reciprocal of the unit fraction and then split the whole number tiles accordingly.

Explanation:

To use fraction tiles to help divide a whole number by a unit fraction, you can follow these steps:

Answer:

What is n?

Step-by-step explanation:

Answer: 0 on edge

Step-by-step explanation:

got it correct

Answer: C

Step-by-step explanation:

took quiz

Are there any more instructions or information?

Due to requirements such as height and ride capacity, only one friend can go on both the loop and the roller coaster at the same time.

In order to go on the loop and the roller coaster, the friends need to meet certain requirements. For example, they need to be tall enough to ride the roller coaster and meet any age restrictions. Additionally, the roller coaster may have a limited number of seats or ride capacity. Due to these factors, it's possible that only one friend can go on both of these rides at the same time.

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Answer: 3 millions

Explanation: To determine what the digit "3" means in 3,562,185, if we put 3,562,185 into the place value chart, we can see that the 3 appears in the units column of the millions period so in this problem 3 refers to 3 millions.

Answer:

3,300 sec

Step-by-step explanation:

Answer: 90

Step-by-step explanation:

Total number of lunches sold = 450

Number of hamburgers = 40% of the total , that is

number of hamburgers = 40/100 x 450 = 180

number of pizza = 450 - 180 = 270

Therefore , the number of pizza lunches sold more than hamburgers will be

270 - 180 = 90

Therefore : 90 more pizza lunches were sold than hamburgers.

Answer:

i don't know

Step-by-step explanation:

Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

Perimeter of Rectangle is given as

[tex]\textrm{Perimeter of Rectangle}=2(Length+Width)[/tex]

Length = AB

Width = BC

Now By Distance Formula  we have'

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting the values we get

[tex]l(AB) = \sqrt{((-4-(-6))^{2}+(-4-(-4))^{2} )}[/tex]

[tex]l(AB) = \sqrt{((2)^{2}+(0)^{2} )}=2\ unit[/tex]

Similarly

[tex]l(BC) = \sqrt{((-4-(-4))^{2}+(-2-(-4))^{2} )}[/tex]

[tex]l(BC) = \sqrt{((0)^{2}+(2)^{2} )}=2\ unit[/tex]

Therefore now

Length = AB = 2 unit

Width = BC = 2 unit

Substituting the values  in Perimeter we get

[tex]\textrm{Perimeter of Rectangle}=2(2+2)=2(4)=8\ unit[/tex]

Therefore Perimeter of Rectangle ABCD is 4 units

Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

Answer: m = 15

Step-by-step explanation:

45 = 30 + m

subtract 30 , from both sides  , that is , -30 should be added to both sides to find the variable

45 - 30 = 30 + m - 30

15 = m

Therefore : m = 15

Hii!

_________________________________________________________

Answer:

5(x-5)

Step-by-step explanation:

Both terms, 5x and -25, have something in common. This "something" is called the greatest common factor, or g.c.f.

The g.c.f. of 5x and -25 is 5, so we factor 5 out by dividing 5x and -25 by 5. Upon doing this we obtain

x-5

Now we need to put parentheses around x-5.

(x-5)

Next, we put 5 outside the parentheses.

5(x-5)

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Hope that this helped! Best wishes.

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Answer:

Des can run faster than Elizabeth.

Des can run 1 mile in 4.037 minutes while Elizabeth can run 1 Mile in 4.9 minutes

Step-by-step explanation:

If Elizabeth can run 5 miles in 24.5 minutes. Elizabeth will run 1 mile in 24.5/5=4.9 minutes.

If Dez can run 8 miles in 32 1/3 minutes. Then Dez will run 1 mile in 32.3/8=4.037 minutes

Therefore if Dez can run 1 mile in 4.037 minutes and Elizabeth can run 1 mile in 4.9 minutes then Dez can run faster than Elizabeth.

Answer:

Option D: y = 4x + 16

Step-by-step explanation:

Given the line:  y - 1 = 4(x + 3)  ⇒  y = 4x + 13

The slope of the given line = m = 4

The required line is parallel to the given line

So, the slope of the required line = m = 4

So, the general equation of the required line: y = 4x + c

Where c is constant represents y-intercept

To find the value of c, substitute with the point (4,32)

At x = 4 y = 32

∴ 32 = 4 * 4 + c

∴ c = 32 - 16 = 16

∴ y = 4x + 16

The answer is option D: y = 4x + 16

Answer:

f^-1 (x)=-x-1

Step-by-step explanation:

y=-x-1

x=-y-1

-y=x+1

y=-x-1

Answer:

Quadrant 4

Step-by-step explanation:

sinA < 0 in quadrants 3 and 4

cosA > 0 in quadrants 1 and 4

Thus sinA < 0 and cosA > 0 in quadrant 4

Answer: y = 3

Step-by-step explanation:

Two lines are said to be parallel if they have the same slope. All we need to do is to find the slope of each line . The formula for finding slope is given as :

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

For the first line

[tex]x_{1}[/tex] = 11

[tex]x_{2}[/tex] = 2

[tex]y_{1}[/tex] = y

[tex]y_{2}[/tex] = 0

substituting into the formula , we have

m = [tex]\frac{0 - y}{2 - 11}[/tex]

m = [tex]\frac{-y}{-9}[/tex]

m = [tex]\frac{y}{9}[/tex]

Also Finding the slope of the second line we have

[tex]m_{2}[/tex] = [tex]\frac{2-5}{-2 - 7}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{-3}{-9}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{1}{3}[/tex]

Since the two lines are parallel , we will equate their slope , that is

[tex]\frac{y}{9}[/tex] = [tex]\frac{1}{3}[/tex]

3y = 9

y = 3

Answer:

Step-by-step explanation:

Jordan it a bigger number

Answer:

f−1(f(x)) = f(f−1(x)) = x

Step-by-step explanation:

Follow this simple example using the function f(x) = x + 2

f(x) = x + 2

NOw we find the inverse function f^(1)(x).

y = x + 2

x = y + 2

y = x - 2

f^(-1)(x) = x - 2

The inverse function is f^(-1)(x) = x - 2

Now we do the two compositions of functions:

f^(-1)(f(x)) = x + 2 - 2 = x

f(f^(-1)(x)) = x - 2 + 2 = x

Both are equal to x.

Answer: f−1(f(x)) = f(f−1(x)) = x

The expression [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

We are to prove the relationship;

[tex]f^{-1}(f(x)) = f(f^{-1}(x)) = ?[/tex]

To get the unknown, let f(x) = x - 2

Find its inverse:

Let y = x - 2

Replace y with x;

x = y - 2

y = x+2

Hence [tex]f^{-1}x = x+2[/tex]

Next is to get [tex]f(f^{-1}(x))[/tex]

[tex]f(f^{-1}(x))=f(x+2) = (x+2) - 2\\f(f^{-1}(x))= x\\[/tex]

We can conclude that [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

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Answer:

20

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

a) (1, -2)

Step-by-step explanation:

The given inequality is y < -|x|

We substitute the point to see which points satisfy the inequality.

For a) (1, -2), we substitute x=1 and y=-2 to get:

-2 < -|1|---------->-2<-1--------->True

For b) (1, -1), we substitute x=1 and y=-1 to get:

-1 < -|1|---------->-1<-1--------->False

For a) (1, 0), we substitute x=1 and y=0 to get:

0 < -|1|---------->0<-1--------->False

The first choice is correct.

Answer:

15

Step-by-step explanation:

First subtract the remainder from 403 to get 390. then divide 390 by 26 to get 15.

The number used by Justin used to divide 403 to get a quotient of 26 with a remainder of 13 is 15.

Division is theartimetic process used to divide a number into equal parts using another number. The sign used to denote division is ÷.

In order to detemine the number used to divide 403, take the following steps:

Subtract 13 from 403 = 403 - 13 = 390

Now divide 390 by 26: 390 / 26 = 15

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Answer:

10/16

Step-by-step explanation:

Answer:

c= -2

Step-by-step explanation:

Perpendicular lines imply that the product of the gradient of the two lines is -1.

So let's find the gradient of each lines.

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Gradient of 1st line

= 1-(-4)/ -3-2

= 5/-5

= -1

(gradient of 1st line)(gradient if 2nd line)= -1

(-1)(gradient of 2nd line)= -1

gradient of 2nd line= -1 ÷ (-1) =1

Now make use of the gradient formula to find an expression of the gradient of the second line.

Gradient of 2nd line= c-1/ -2-1

subst. gradient of second line and simplify:

1= c-1/-3

c-1= -3 (multiply by -3 on both sides)

c= -3+1 (add 1 on both sides)

c= -2