The total cost C (in dollars) of playing an online game is given by the literal equation C = 30x + 50, where x is the number of months you play the game. Solve the equation for x. How many months do you play the game when you spend $170? $260?

Answer:

a). y = 0.25x + 15

b). x = 480 cups

Step-by-step explanation:

(a). Let the equation of the linear function passing through a point (x', y') is,

y - y' = m(x - x')

'm' = slope of the line

b = y-intercept

Two points lying on the linear function will be (200, 65) and (250, 77.5).

Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{77.5-65}{250-200}[/tex]

   = [tex]\frac{12.5}{50}[/tex]

   = 0.25

Therefore, equation of the line passing through (200, 65) and slope 0.25 will be,

y - 65 = 0.25(x - 200)

y - 65 = 0.25x - 50

y = 0.25x + 15

(b). For y = $135 we have to calculate the number of cups of coffee produced.

135 = 0.25x + 15

0.25x = 135 - 15

0.25x = 120

x = 480 cups

Therefore, 480 cups of coffee will be produced.

Answer:

CrO₃.

Step-by-step explanation:

We'll begin by calculating the percentage of chromium in the oxide. This can be obtained as follow:

Oxygen (O) = 48%

Chromium (Cr) =?

Oxide of chromium contains only chromium and oxygen. Therefore, the percentage of chromium in the oxide is given by:

Cr = 100 – percentage of oxygen

Cr = 100 – 48

Cr = 52%

Finally, we shall determine the empirical formula of the oxide as follow:

Chromium (Cr) = 52%

Oxygen (O) = 48%

Divide by their molar mass

Cr = 52/52 = 1

O = 48/16 = 3

Divide by the smallest

Cr = 1/1 = 1

O = 3/1 = 3

Therefore, the empirical formula of the oxide is CrO₃.

Answer:

[tex]12.1 < Y < 35.1[/tex]

Step-by-step explanation:

Given

Sides: 11.5 and 23.6

Required

Determine the range of the third side

Let the third side with Y

Two of the following conditions must be satisfied to calculate the range of the third side

[tex]11.5 + Y > 23.6[/tex]

[tex]23.6+ Y > 11.5[/tex]

[tex]11.5 + 23.6 > Y[/tex]

We'll solve one after other

1.    [tex]11.5 + Y > 23.6[/tex]

[tex]Y > 23.6 - 11.5[/tex]

[tex]Y > 12.1[/tex]

2.    [tex]23.6+ Y > 11.5[/tex]

[tex]Y > 11.5- 23.6[/tex]

[tex]Y > -12.1[/tex]

3.    [tex]11.5 + 23.6 > Y[/tex]

[tex]35.1 > Y[/tex]

[tex]Y < 35.1[/tex]

Inequalities with negative can't be used' So, we have

[tex]Y > 12.1[/tex] and [tex]Y < 35.1[/tex]

Rewrite inequality

[tex]12.1 < Y[/tex]   and   [tex]Y < 35.1[/tex]

Combine inequality

[tex]12.1 < Y < 35.1[/tex]

Answer:

Step-by-step explanation:

From the given information, the symmetric equations for the line pass through(4, -5, 2) i.e ([tex]x_o, y_o, z_o[/tex]) and are parallel to [tex]\dfrac{x+5}{1} = \dfrac{y}{2}= \dfrac{z-3}{1}[/tex]

The parallel vector to the line i + zj+k = ai + bj + ck

Hence, the equation for the line is :

[tex]x = x_o + at \\ \\ x = y_o + bt \\ \\ x = z_o + ct[/tex]

x = 4 + t

y = -5 + 2t

z = 2 + t

Thus, x, y, z = ( 4+t, -5+2t, 2+t )

The symmetric equation can now be as follows:

[tex]\begin {vmatrix} x = 4+ t \\ \\ \dfrac{x-4}{1} = t \begin {vmatirx} \end {vmatrix}[/tex][tex]\begin {vmatrix} y = - 5+2t \\ \\ \dfrac{y+5}{2} =t \end {vmatrix}[/tex][tex]\begin {vmatrix} z =2+t \\ \\ \dfrac{z-2}{1} =t \end {vmatrix}[/tex]

∴

[tex]\dfrac{x-4}{1}= \dfrac{y+5}{2}=\dfrac{z-2}{1}[/tex]

Questions 1, 2, and 5 are correct.

Question 3:

To find the common difference, we can subtract the last two numbers.

60 - 47 = 13

So, the common difference is 13

We can add 13 to each term to get the next term.

8 + 13 = 21

21 + 13 = 34

So, 8, 21, 34, 47, 60

Question 4:

To find the common difference, we can subtract the last two numbers.

8/3 - 2 = 2/3

So, the common difference is 2/3

We can add 2/3 to each term to get the next term.

0 + 2/3 = 2/3

2/3 + 2/3 = 4/3

So, 0, 2/3, 4/3, 2, 8/3

Question 4:

Since we are only given the first and last number, we need to find a number we can subtract that we get -13 at the end. The distance between 3 and -13 is 16. We can divide this by 4 since there are 4 numbers before -13.

16 / 4 = 4

Since the number is going down, the common difference is going to be -4.

Subtract find the next terms.

3 - 4 = -1

-1 - 4 = -5

-5 - 4 = -9

-9 - 4 = -13

So, 3, -1, -5, -9, -13

Best of Luck!

I cannot see the statements you are given as options, but if x = y, and y = z, you can write that as x = y = z, which means that x = z also.

I hope this helps!

Answer:

Step-by-step explanation:

If x=y and y=z, then x=z.

Answer:

3.78x10^5

Step-by-step explanation:

Answer:

√45 =6.71

Step-by-step explanation:

[tex]\sqrt{45} = 6.708203932\\\\= 6.71[/tex]

Answer:

110.7 inches

Step-by-step explanation:

Width : Height ( 46:30 )

Width is 46 and Height is 30

So 46 = 170 inches

1 = ?

1 = 170/46

=3.69 inches.

To know the height, multiply that(3.69) with 30. And you will get the inches of the height which is "110.7 inches"

Answer:

no

Step-by-step explanation:

You will have more time to do it, but no, try extra credit

Sorry mate hope this helps<3

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

Based on the clues in the problem wording, we assume the numbers given for C and D are the weights of planes, in pounds. For whatever reason, we seem to be interested in the difference of those weights.

The difference in weights is 22,489 pounds.

The difference in weights is given by the expression 79,473 - 56,984.

We can add 16 to both numbers to make the second number a multiple of 1000. To compensate, we also add 16 to the first number.

Doing this gives the new expression 79,489 - 57,000.

The value of this expression is 22,489.

_____

Additional comments

A number of thinking processes are taught for mental math. In this process, you recognize that 984 is near 1000, so you can add a small number to make all the rightmost digits be zeros. That number will have the digits that "make a ten" working from right to left. 4 needs 6 added to make a 10. Adding 6 to 84 makes it 90. Then the 9 needs 1 added to make a 10. Now, we have 984 with 16 added, which makes 1000. Adding that 16 to 79473 to make 79489 completes the transformation we're looking for: 79489 -57000.

Answer:

B) c=25 +10p +5h

id expect 25 per night with the n variable next to it but i guessed not

, but one night would cost 25 but with the addition of 10 per person and 5 for every hour of a late checkout

Answer:

A

Step-by-step explanation:

C=25

25= How much she was Paid

p=People

1person is 10$

10$Was given in

10+

Late fee 5$

Then by there she gets Her 25

C=25-10p-5h

Answer:

Step-by-step explanation:

this problem is on vector

given the vectors

a = 5i + j, and

b = i − 2j

1. summation of vector a + b

[tex]= (5i+j)+(i-2j)\\\\=5i+j+i-2j\\\\[/tex]

collect like terms

[tex]=5i+i+j-2j\\\\=6i-j\\\\[/tex]

2. 2a + 3b

[tex]= 2(5i+j)+3(i-2j)\\\\=10i+2j+3i-6j\\\\[/tex]

collecting like terms we have

[tex]=10i+2j+3i-6j\\\\=10i+3i+2j-6j\\\\=13i-4j[/tex]

(3) |a|, and |a − b|.

|a|= |5i+j|

[tex]=\sqrt{5^2+1^2} \\\\=\sqrt{25+1} \\\\=\sqrt{26} \\\\= 5.1[/tex]

also,

[tex]|a - b|= |(5i+j) -(i-2j)| \\\\ a-b= 5i+j -i+2j \\\\ a-b=5i-i+j+2j \\\\a-b= 4i+3j\\\\[/tex]

[tex]|a -b|=\sqrt{4^2+3^2} \\\\|a -b|=\sqrt{16+9} \\\\|a -b|=\sqrt{25} \\\\|a -b|=25[/tex]

Answer:

  10 ft

Step-by-step explanation:

The formula for the area of a triangle can be used. Put the known values into the formula and solve for the unknown.

  A = (1/2)bh

  15 = (1/2)(3)h

  h = 15/1.5 = 10

The triangle's height is 10 feet.

Answer:

10

Step-by-step explanation:

A=1/2*b*h

15=1/2*3*h

15=3/2*h

15=3/2h

h=15/(3/2)

h=(15/1)(2/3)

h=30/3

simplify

h=10

Answer

2

Step-by-step explanation:

6+2=8     15/5*2=6       8-6=2

Answer:

0.16

Step-by-step explanation:

The calculation of probability by applying the is shown below:-

It is evident from the pedigree that the mode of inheritance is recessive and the characteristic is recessive that's also phenotype of disease is only seen if the genotype is aa.

The genotype of 1. In pedigree Can be either AA or Aa.

The chance that the offspring of the [tex]3\times 7[/tex] cousin marriage will have the characteristic is

[tex]= \frac{1}{6}[/tex]

which gives results

= 0.16

Answer:

z = 36

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

6 would be the overlined number

Step-by-step explanation:

Answer:

6 will be the overlined number.

Step-by-step explanation:

Hey there! I'm happy to help!

Let's call the hamburgers h and the cheeseburgers c.

h+c=234

c=2h

Let's plug this value of c into the first equation to solve for h.

h+2h=234

3h=234

Divide both sides by 3.

h=78

Therefore, 78 hamburgers were sold on Thursday.

Have a wonderful day! :D

Answer:

y= [tex]\frac{-3}{5}x -2[/tex]

Step-by-step explanation:

find the gradient by rearranging the equation, y= [tex]\frac{-3}{5}x[/tex] +[tex]\frac{18}{5}[/tex]

from here we can see that the slope or gradient is [tex]\frac{-3}{5}x[/tex]

now using the equation y-y2 = f'(x1)(x-1) we find the equation by subbing

= y- (-4) = [tex]\frac{-3}{5}[/tex] (x - [-10])

= y + 4 = [tex]\frac{-3}{5}x -6[/tex]

= y= [tex]\frac{-3}{5}x -2[/tex]

Answer: 24°

Step-by-step explanation:

Given the following :

supplement of an angle is 42 degrees less than 3 times the complement of the angle

Let the angle = θ

Supplement of angle = 180° - θ

Complement of angle = 90° - θ

Supplement of angle is also said to be:

(3 × complement) - 42° = 3(90° - θ) - 42°

= 270° - 3θ - 42° = 228° - 3θ

Hence,

180° - θ = 228° - 3θ

Solve for θ

-θ + 3θ = 228° - 180°

2θ = 48°

θ = 48°/2

θ = 24°

Step-by-step explanation:

a) The distance is the integral of the velocity vs. time graph.  We can approximate the distance using a left hand Riemann sum.  That means for each interval, use the velocity at the beginning of the interval.  Don't forget to convert mi/hr to mi/s.

d₁ = (10 s − 0 s) (183.9 mi/hr × 1 hr / 3600 s) = 0.5108 mi

d₂ = (20 s − 10 s) (169.0 mi/hr × 1 hr / 3600 s) = 0.4694 mi

d₃ = (30 s − 20 s) (105.6 mi/hr × 1 hr / 3600 s) = 0.2933 mi

d₄ = (40 s − 30 s) (99.8 mi/hr × 1 hr / 3600 s) = 0.2772 mi

d₅ = (50 s − 40 s) (124.5 mi/hr × 1 hr / 3600 s) = 0.3458 mi

d₆ = (60 s − 50 s) (177.1 mi/hr × 1 hr / 3600 s) = 0.4936 mi

d = 0.5108 + 0.4694 + 0.2933 + 0.2772 + 0.3458 + 0.4936

d = 2.390 miles

b) Do the same as part a, but this time, use a right hand Riemann sum.  Instead of using the velocity at the beginning of the interval, use the velocity at the end of the interval.

d₁ = (10 s − 0 s) (169.0 mi/hr × 1 hr / 3600 s) = 0.4694 mi

d₂ = (20 s − 10 s) (105.6 mi/hr × 1 hr / 3600 s) = 0.2933 mi

d₃ = (30 s − 20 s) (99.8 mi/hr × 1 hr / 3600 s) = 0.2772 mi

d₄ = (40 s − 30 s) (124.5 mi/hr × 1 hr / 3600 s) = 0.3458 mi

d₅ = (50 s − 40 s) (177.1 mi/hr × 1 hr / 3600 s) = 0.4936 mi

d₆ = (60 s − 50 s) (175.6 mi/hr × 1 hr / 3600 s) = 0.4878 mi

d = 0.4694 + 0.2933 + 0.2772 + 0.3458 + 0.4936 + 0.4878

d = 2.367 miles

c) The velocity decreases from 0 s to 30 s, but then increases from 30 s to 50 s, and then decreases from 50 s to 60 s.

Since the velocity doesn't consistently increase or decrease, these Riemann sums are neither lower nor upper sums.

Steps to solve:

40 + 5x > 95 - 4x

~Subtract 40 to both sides

5x > 55 - 4x

~Add 4x to both sides

9x > 55

~Divide 9 to both sides

x > 55/9

Best of Luck!

Answer:

23+10r= 5+r

Step-by-step explanation:

let r be the number

Answer:

The value of uw is 67

Step-by-step explanation:

Given that,

If uw= 6x-35...(I)

Line segment consists of points u,v,w

u to v is 19

v to w is 4x-20

We need to calculate the value of x

Using given data

[tex]uw=6x-35[/tex]

[tex]uv+vw=6x-35[/tex]

Put the value of u and w

[tex]19+4x-20=6x-35[/tex]

[tex]19+35-20=6x-4x[/tex]

[tex]34=2x[/tex]

[tex]x=\dfrac{34}{2}[/tex]

[tex]x=17[/tex]

We need to calculate the value of uw

Put the value of x in equation (I)

[tex]uw=6\times17-35[/tex]

[tex]uw=67[/tex]

Hence, The value of uw is 67

Answer:

If two angles form a linear pair, they are supplementary.

Step-by-step explanation:

A linear pair is two angles that are adjacent and the non-common sides form a straight line.

Answer:

They are supplementary

Step-by-step explanation:

A linear pair is two angles ajacent. The non - common side forms a straight line. So the angles added together are equal to 180 degrees.

Answer:

The expressión is:

10(a+14) = 9a

and the number is:

-140

Step-by-step explanation:

The expression is:

10(a+14) = 9a

then:

10*a + 10*14 = 9a

10a + 140 = 9a

10a - 9a = -140

a = -140

Check:

10(-140+14) = 9*140

10*-126 = 1260