membership to iron gym cost $40 per month plus $30 registration fee. the monthly cost is deducted automatically from your account. if your starting balance is $350 how many months will you be able to go to the gym before you have to add money to your account?
A. 6
B. 7
C. 8
D. 9

We want to find the measure of x given that we know that m and n are congruent.

The measure of x is 116°.

Two angles are congruent if they have the same measure.

Then we have ∠n = ∠m

We also know that the sum of all interior angles of a triangle is equal to 180°, then if we look at the smaller triangle we have that:

114° + ∠n + ∠m = 180°

∠n + ∠m = 180° - 114° = 66°

Knowing that these measures are equal we can write:

2*∠m = 66°

∠m = 66°/2 = 33°

Now that we know the measure of m, we can do the same thing for the larger triangle:

∠x + ∠m + 31° = 180°

∠x + 33° + 31° = 180°

∠x = 180° - 64° = 116°

The measure of x is 116°.

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Applying the exterior angle theorem and the sum of triangles, the value of x in the figure is: [tex]\mathbf{x = 64^{\circ}}[/tex]

Recall:

Sum of triangles = 180 degrees

Exterior angle = sum of two interior opposite angles

Since we know that angles m and n are congruent, therefore:

[tex]m = \frac{1}{2} (180 - m \angle RTU)[/tex]

[tex]m = \frac{1}{2} (180 - 114)\\\\\mathbf{m = 33^{\circ}}[/tex]

Find x (exterior angle of triangle SUV):

[tex]x = 31 + m[/tex] (exterior angle of a triangle theorem)

[tex]x = 31 + 33\\\\\mathbf{x = 64^{\circ}}[/tex]

Therefore, applying the exterior angle theorem and the sum of triangles, the value of x in the figure is: [tex]\mathbf{x = 64^{\circ}}[/tex]

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Answer:

x = 8, y = 2

Step-by-step explanation:

Multiply the second equation by -2:

x + 6y = 20

-2x - 6y = -28

Add the equations and simplify:

-x = -8

x = 8

Plug x = 8 back into the first equation and solve for y:

8 + 6y = 20

6y = 12

y = 2

Answer:

x=8

Y=2

or

(x,y)=(8,2)

Step-by-step explanation:

x+6y=20

x+3y=14

solve the equation for x

x+6y=20

x=14-3y

substitute the given value of x into the equation

x+6y=20

14-3y+6y=20

14+3y=20

3y=20-14

3y=6

3y/3=6/3

y=2.

substitute the given value of y into the equation

x=14-3y

x=14-3×2

x=14-6

x=8.

the possible solution of the system is the ordered pair (x,y)

(x,y)=(8,2)

or

x=8

Y=2

Proof:

Check if the given ordered pair is the solution of the system of equations

8+6×2=20

8+3×2=14

simply the equalities

20=20

14=14

since all of the equalities are true, the ordered pair is the solution of the system

(x,y)=(8,2)

Answer:

B. The population has increased by 105% each year since 1980.

D. Each year since 1980, the population is 105% of the population of the previous year.

E. Each year since 1980, the population is 1.05 times the population of the previous year.

Step-by-step explanation:

From the question, we are given the exponential function:

The exponential function P(t)=2000(1.05)^t models the population of the town since 1980.

Exponential growth rate =

P(t) = P(1 + r)^t

Where r = growth rate in percentage

P(t) = Size of the population after t years

t = time in years

Hence,

From the formula above, we can say =

1 + r = 1.05

r = 1.05 - 1

r = 0.05

Converting to percentage = 0.05 × 100 = 5%

1.05 can also converted to percentage and this = 1.05 × 100 = 105 %

The population has increased by 105% each year since 1980.

Hence, Options, B, D and E is correct

Answer:

125m^6n^24

Step-by-step explanation:

When exponents are raised by another exponent, they are multiplied

2 x 3 = 6

8 x 3 = 24

5^3 = 5 x 5 x 5 = 125

Answer:

hi! thanks for free points!

Step-by-step explanation:

Answer:

Choice C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

7x - 42 + 5x =  180  {linear pair}

7x + 5x - 42 = 180              {Combine like terms}

      12x - 42 =180

             12x = 180 + 42

            12x = 222

             x = 222/12

x = 18.5

5x = 5*18.5 = 92.5

7x - 42 = 7*18.5 - 42  = 129.5 - 42 = 87.5

Answer:

2/5

Step-by-step explanation:

you have to do slope formulation which is y2 minus y1 over x2 minus y1

Answer:

C:  2/5

Step-by-step explanation:

how because its me i'm always right

Answer:

Step-by-step explanation:

[tex]X + Y \geq 15\\\\10X + 5Y \leq 100[/tex]

we want to put it into terms of Y

[tex]y \geq 15 - x\\and\\5y \leq 100 - 10x\\y \leq 20 - 2x[/tex]

the graph is in the attached image. Any point in the shaded overlap region where x is greater than or equal to 0 (assuming you cannot have negative coins) works, e.g. (2, 14)

The solution of the inequalities is required.

One of the solutions is [tex](5,10)[/tex]

Number of dimes is [tex]x[/tex]

Number of nickels is [tex]y[/tex]

Minimum number of coins is 15.

So, [tex]x+y\geq 15[/tex]

Maximum total value of the coins is $1

So, [tex]0.1x+0.05\leq 1[/tex]

The equations are

[tex]x+y=15[/tex]

[tex]0.1x+0.05y=1[/tex]

Points of the first equation

[tex](0,15)[/tex] and [tex](15,0)[/tex]

Graph the points and draw a line through them.

Points of the second equation

[tex]x=0[/tex]

[tex]y=\dfrac{1}{0.05}=20[/tex]

[tex]y=0[/tex]

[tex]x=\dfrac{1}{0.1}=10[/tex]

[tex](0,20)[/tex] and [tex](10,0)[/tex]

Graph the points and draw a line through them.

The shaded regions can be determined by substituting the point in the equations.

One of the solutions is [tex](5,10)[/tex]

This means there are 5 dimes and 10 nickels.

[tex]5+10=15\geq 15[/tex]

[tex]0.1\times 5+0.05\times 10=1\leq 1[/tex]

Hence, one of the solutions is [tex](5,10)[/tex].

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Answer:

W > -5

Step-by-step explanation:

5×(-1) < 5W + 20

-5 < 5W + 20

-25 < 5W

-5 < W

W > -5

Answer:

1/2

Step-by-step explanation:

1/4 (4x - 8) + 3x =0

distribute the 1/4

x-2+3x=0

combine like terms

-2+4x=0

move -2 to the other side [by ADDing +2 to each side

4x=2

divide [by 4 on both sides]

x=1/2

Answer:

Step-by-step explanation:

Step 1:

2 : 11           Ratio

Having a ratio is the same thing as dividing so if you divide 2 by 11 you get 2/11.

Step 3

2 ÷ 11

Answer:

C. 2/11

Hope This Helps :)

Answer:

shut up b

sorry gad will elp you

Step-by-step explanation:

Answer:

5 hours

Step-by-step explanation:

24miles = 1hour

120miles = x

120*1=120/24

=5hours

I would say -2

Step-by-step explanation:

Answer:

100000

Step-by-step explanation:

 The given expression is;

       Log x = 5

Find x;

 Solution:

The log is to the base of 10;

   Log₁₀x  = 5

     if Logₓ t  = n;

                 t = xₙ

So;

      Log₁₀x  = 5

               x  = 10⁵

               x  = 100000

Answer:

y = - [tex]\frac{28}{5}[/tex]

Step-by-step explanation:

Given y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 7 when x = - 4, then

7 = [tex]\frac{k}{-4}[/tex] ( multiply both sides by - 4 )

- 28 = k

y = [tex]\frac{-28}{x}[/tex] ← equation of variation

When x = 5 , then

y = [tex]\frac{-28}{5}[/tex] = - [tex]\frac{28}{5}[/tex]

Answer:

Step-by-step explanation:

y + 4 = -2(x - 5)

y + 4 = -2x + 10

y = -2x + 6

Answer:1/4+m= 2/3

Step-by-step explanation:

Plz brainliest and extra points!

I’m almost an expert!!

Answer:

4

Step-by-step explanation:

4 1/2 - 1/2

4

You start with 4 + 1/2 but you subtract 1/2 so it just cancel's itself out leaving you with 4.

Hope this helps! If you have any additional questions please don't hesitate to ask me or your teacher to be sure you master the subject. Stay safe and please mark brainliest! :)

Answer:

[tex]3 \frac{7}{12}[/tex]

Step-by-step explanation:

1 - multiply the 1/2 out to make the denominators the same (Ignore the 4 for now)

To make 2 equal 12 you multiply by 6 and what you do to the bottom you do to the top.

[tex]\frac{1}{2}(\frac{6}{6}) = \frac{6}{12}[/tex]

2 - Now solve

Now we need to know what 4 1/12 - 6/12 equals.

1-6 is -5 so we will take out of the whole number to continue this subtraction

3 12/12 - 5/12

After subtracting that out we're left with

3 7/12

Hope this helps :)

Answer:

x = 2

Step-by-step explanation:

B(x) = - 1 means what is the value of x for y = - 1

This is the dot positioned at (2, - 1 )

with x = 2

Answer: its the first one

Step-by-step explanation:

hope thats what your lookinf for

Answer:

b

Step-by-step explanation:

Answer:

The guy above me its right its B.

Step-by-step explanation:

Just did the quiz and got it right

Answer:

36V²+84V+49

Step-by-step explanation:

since it is (7+6V) in two places,therefore

7(7+6v)+6v(7+6v)

49+42v+42v+36v²

36v²+84v+49

Answer:

70kg

Step-by-step explanation:

s = small bag

b = big bag

Equations

s + b = 95

s + 45 = b

plug in

s + s + 45 = 95

2s + 45 = 95

2s = 50

s = 25

plug in to find big bag

25 + 45 = b

70 = b

Answer:

The weight of the pebbles in the large bag is 70kg.

Step-by-step explanation:

This looks like a substitution algebra problem. To do this, I’m going to mark the large bag with (L) and the small bag with the variable, (s). I will make first 2 equations to show the value. The first equation would be L=45+s. The second equation would be 95=L+s. Since L is literally 45+s, add this into the 2nd equation. This would be 95=45+s+s. You should have 95= 45+2s and you would subtract 45 from both sides then. Finally, divide 2s by 2 to get what the small bag weighs, (which is 25kg). To find the large bag’s weight, use the first equation to find the answer. L= 45+s or 25. The answer would bring us to 70 kg.

Answer:

2nd option; y = 1/5x + 12/5

Step-by-step explanation:

Take a look at the attached file for the explanation.

Step-by-step explanation:

answer is 1/7 and 6/8 = 55/76

Answer: option b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

0.4 is 40 percent of something because 100 percent is 1 x something. On the other hand, 0.12 is 12 percent of something because 0.12 x something will get you 12 percent of the value. Therefore, 0.4 is 40 percent of a thing while 0.12 is 12 percent of a thing and 0.4 is bigger than 0.12

Step-by-step explanation:

Answer:

0.4 is 40 percent of a thing while 0.12 is 12 percent of a thing and 0.4 is bigger than 0.12

Step-by-step explanation:

0.4 is 40 percent of something because 100 percent is 1 x something. On the other hand, 0.12 is 12 percent of something because 0.12 x something will get you 12 percent of the value.