The fairs train ride covers a distance of 3 miles in 20 minutes what is the speed for the ride in miles per minute​

Answers

Answer 1

Answer:

0.15 miles per minute or 9 miles per hour

Step-by-step explanation:


Related Questions

Suppose two utilites, People's Electric and Muricipal Energy, each produce 900 tons of pollution per year. The government has a goal of eliminating haf the pclution, and, in turn, provides 450 pollution permits to each utlity. A pollution permit is required to legally produce a ton of poliubon. However, the tao utities are allowed to trade permas. Suppose the cost of eliminating one ton of pollution for People's Electric is $400 and the cost of eliminating a ton of polution for Municipal Energy is $350. The total cost of each utility eliminating 450 tons of pollution is $ (Enter your response as a whole number)

Answers

The total cost of each utility eliminating 450 tons of pollution is $180,000.

To calculate the total cost for each utility to eliminate 450 tons of pollution, we need to multiply the cost per ton of pollution elimination by the number of tons each utility needs to eliminate.

For People's Electric, the cost of eliminating one ton of pollution is $400. So, to eliminate 450 tons, the total cost would be 450 tons * $400/ton = $180,000.

For Municipal Energy, the cost of eliminating one ton of pollution is $350. Again, to eliminate 450 tons, the total cost would be 450 tons * $350/ton = $157,500.

Therefore, the total cost for each utility to eliminate 450 tons of pollution is $180,000 for People's Electric and $157,500 for Municipal Energy.

The cost calculation is based on the given information that each utility is provided with 450 pollution permits by the government. These permits allow them to legally produce a ton of pollution. By setting a limit on the number of permits, the government aims to reduce pollution by half. The utilities have the option to trade permits with each other.

In this scenario, People's Electric has a higher cost of eliminating pollution per ton compared to Municipal Energy ($400 vs. $350). It means that People's Electric would find it more expensive to reduce pollution through internal measures like investing in cleaner technology or implementing environmental initiatives. On the other hand, Municipal Energy has a lower cost, indicating that they have relatively more cost-effective methods for pollution reduction.

Given these costs, it is more beneficial for People's Electric to purchase permits from Municipal Energy rather than eliminating the pollution themselves. By purchasing permits, People's Electric can meet the pollution reduction target at a lower cost. Conversely, Municipal Energy can generate additional revenue by selling their permits.

This permit trading mechanism allows for cost efficiency in achieving the government's pollution reduction goal. The total cost for each utility is determined by multiplying the cost per ton of pollution elimination with the number of tons they need to eliminate.

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What’s the sum of 8 and the difference of 2

Answers

Answer:

4

Step-by-step explanation:

The sum of two numbers is 20 and their difference is 12.

Answers

Answer:

16 and 4

Step-by-step explanation:

x + y= 20

x -y =12

(add both equal #'s)

2x =32

x = 16

y=4

Answer:

4 and 16

Step-by-step explanation:

First, let's find first term using sum formula:

\( \displaystyle \large{S_n = \frac{1}{2} n[2a_1 + (n - 1)d]}\)

We know that d or common difference is 12 and only sum of two terms so n = 2.

\( \displaystyle \large{S_2 = \frac{1}{2} (2)[2a_1 + (2- 1)d]} \\ \displaystyle \large{S_2 = 2a_1 +d}\)

Since sum of two numbers equal 20.

\( \displaystyle \large{20 - 12= 2a_1 +12 - 12} \\ \displaystyle \large{8= 2a_1 }\)

From above, subtract both sides by 12, solving for a1.

\( \displaystyle \large{8= 2a_1 } \\ \displaystyle \large{4= a_1 } \)

Therefore our first number is 4.

Finding next number, create an equation:-

\( \displaystyle \large{4 + a_2 = 20 } \\ \displaystyle \large{4 - 4 + a_2 = 20 - 4} \\ \displaystyle \large{ a_2 = 16 } \)

Another number is 16

So 4 and 16 has 12 as difference because 4+12=16 and 16-12 = 4

how do you solve this?? please answer quick!!

how do you solve this?? please answer quick!!

Answers

Answer:

X is 10 Y is 6

Step-by-step explanation:

Ivan and Tanya share £150 in the ratio 4:1
Work how much more Ivan gets compared to Tanya
Any Ideas???????????????
First to answer gets a brainliest and it needs to be correct

Answers

Answer:

£ 90 because

Step-by-step explanation:

4x+x= £ 150

5x =£150

x=£150/5

x=£30

ivan share = 4x=4x£30

=£120

Tanya share =x=£30

difference ,=£120 - £30

=£90

A box of pancake mix containing 2 1/4 pounds costs $3.60. What is the cost per pound?

Answers

Answer:

$1.60

Step-by-step explanation:

$3.60 divided by 2 1/4 is $1.60

2) The representative agent lives for infinite periods (0,1,2,…) and receives exogenous incomes of y0​,y1​,y2​,…, respectively. The lifetime present discounted value of utility is given by: ∑t=0[infinity]​βtln(ct​) with β(<1) being the discount factor and ct​ is consumption at time t. The agent is allowed to save or borrow at the real interest rate r, but she cannot die with debt or wealth. Assume also that the initial wealth is zero. a. Solve the optimization problem of the agent using the period-by-period budget constraints. In particular, show the Euler equation. b. Using the given functional form, write the Euler equation between time 1 and time 3 . In other words, show how c1​ and c3​ are related. c. Write the present discounted value of optimal lifetime consumption as a function of c0​ (and, potentially, other parameters or exogenous variables). d. Write the present discounted value of optimal lifetime utility as a function of c0​ (and, potentially, other parameters or exogenous variables). e. Find the present discounted value of lifetime income as a function of y0​ (and, potentially, other parameters or exogenous variables) when income is growing each period at the rate of γ, where 0<γ0 ? Explain!

Answers

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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Who took tiny pieces of mail across country over a hundred years ago?

Answers

The estimated number of pieces of mail are sent each year worldwide is equal to 425 billion.

Percent of world's total mail US Postal Service handles = 40% .

Let X be the total number of pieces of mail sent worldwide each year.

The US Postal Service handles pieces of mail each year   = 170,000,000,000 .

Which is equal to 40% of X.

Required equation for the estimated data we have,

170,000,000,000 = 0.4X

Solve for X.

Divide both sides of the equation by 0.4 we get,

⇒ X = 170,000,000,000 / 0.4

⇒ X = 425,000,000,000

Therefore, it is estimated that approximately 425 billion pieces of mail are sent each year worldwide.

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The given question is incomplete, I answer the question in general according to my knowledge:

The U.S postal service handles 170,000,000,000 pieces of mail each year. this is 40% of the worlds total. How many pieces of mail are sent each year?

A bag contains all the letters in the word MATHEMATICS. You draw two letters, one at a time. What is the probability of drawing a T, replacing it, then drawing a C?

Answers

2 x 10-7  is the probability of drawing a T, replacing it, then drawing a C.

What is Probability?

Probability is simply the chance that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics

There are 11 letters in MATHEMATICS which consist of 2 each of M, A and T and 1 each of H, E, I, C and S.  

P(M on 1st choice) = 2/11   since there are 2 M's out of 11 letters

P(A on 2nd choice) = 2/10   since there are 2 A's out of 10 remaining letters

P(T on 3rd choice) = 2/9     since there are 2 T's out of 9 remaining letters

At this point there are 8 letters remaining which are all distinct so they must be chosen in the correct order

P(H on 4th choice) = 1/8

P(E on 5th choice) = 1/7

P(M on 6th choice) = 1/6

P(A on 7th choice) = 1/5

P(T on 8th choice) = 1/4

P(I on 9th choice) = 1/3

P(C on 10th choice) = 1/2

P(S on 11th choice) = 1/1  

The probability of spelling the word correctly is the product of all the probabilities

P = 2*2*2 / 11! = 8 / 39916800 = 1 / 4989600 ~ 2 x 10-7

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Linda is training for a half marathon. She ran
3 34 miles Monday, 3 miles Tuesday, and 2 12 miles Wednesday. How many miles did she
run in those three days?

Answers

Answer:

8 14

Step-by-step explanation:

Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below: A. The thickness of the slices will be dx for both methods. B. When using the shell method, we cut the region into small slices perpendicular to the x-axis. C. When using the disk method, we cut the region into small slices perpendicular to the x-axis. D. The volume of the solid of revolution can be interpreted as the limit of Riemann sums. E. When using the shell method, we cut the region into small slices parallel to the x-axis. F. The shell method will always result in a less complicated integral. G. When using the disk method, we cut the region into small slices parallel to the z-axis.

Answers

The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.

(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using shell method, we cut region into small slices parallel to x-axis.

In the question ,

seven statements are given about a solid of revolution obtained by rotating a region R around the x-axis.

we have to find statement which are true .

Option (a)

Thickness of the slide is dx for disk method and

dy for the shell method while rotating about x - axis ,

So , statement of option(a) is false .

Option(b)

In shell method , elementary cylinders are drawn with axis of symmetry same as axis of rotation ,

thus the cylinder elements will be parallel to x axis rather than being perpendicular to the x axis ,

So , statement of option (b) is false .

Option(c)

In disk method , the slices are cut perpendicular to the axis of rotation , since we are rotating the region about x axis ,

Thus , slices are cut perpendicular to the x axis .

statement of option (c) is True .

Option (d)

As in 2D , the  bounded area can be interpreted as a limit of Riemann sums , Similarly in 3D , the volume formed by rotating the bounded region about the x axis can be interpreted as a limit of Riemann sums .

So , statement of option(d) is True .

Option(e)

When using shell method, we cut region into small slices perpendicular  to the x-axis .

So , statement of option(e) is False .

Option(f)

There can be both the kinds of cases , like in some cases disk method is easier than shell method and

in other cases shell method can be easier than disk method .

So , statement of option(f) is False .

Option(g)

When using disk method, we cut region into small slices perpendicular to x-axis .

So , statement of option (g) is False .

Therefore , The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.

(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using shell method, we cut region into small slices parallel to x-axis.

The given question is incomplete , the complete question is

Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below:

(a) The thickness of the slices will be dx for both methods.

(b) When using the shell method, we cut the region into small slices perpendicular to the x-axis.

(c) When using the disk method, we cut the region into small slices perpendicular to the x-axis.

(d) The volume of the solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using the shell method, we cut the region into small slices parallel to the x-axis.

(f) The shell method will always result in a less complicated integral.

(g) When using the disk method, we cut the region into small slices parallel to the z-axis.

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explain? thank youuuu <3 GEOMETRY

explain? thank youuuu &lt;3 GEOMETRY

Answers

Answer:

B

Step-by-step explanation:

I'm assuming the end point is to draw line CG parallel to AB. Question doesn't specify. Student A is drawing the line CG before the point G has even been determined yet

Multiply (3-i) (7+2i)

Multiply (3-i) (7+2i)

Answers

Answer:

23-i

Step-by-step explanation:

Multiply using the FOIL method and after that combine the real and imaginary parts of the expression.

one of the pages help my lil cousin out

one of the pages help my lil cousin out

Answers

Answer:(that was a joke)

1.) acute

2.) right

3.) obtuse

4.) acute

5.) obtuse

6.) right

Step-by-step explanation:

if hes doing advanced stuff like isosceles equilateral and that then im sorry for the answer.

(x+4)(x+4)/2 pls help

Answers

Answer:

x^2/2+4x+8 hope this helps

It’s X^2+8x+8 when evaluating

Find the equation of a line perpendicular to y = 3x - 8 which contains the point (3, -2)

Answers

The equation of a line perpendicular to y = 3x - 8 which contains the point (3, -2) is y=-1/3 x-1.

The given line equation is y = 3x - 8 and the coordinate point is (3, -2).

What is slope of a line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope of a line y = 3x - 8 is m=3.

The slope of a line perpendicular to given line is m1=-1/m2 = -1/3

Now, put m=-1/3 and (3, -2) in y=mx+c, we get

-2=-1/3(3)+c

⇒ -2 = -1+c

⇒ c=-1

Substitute, m=-1/3 and c=-1 in y=mx+c, we get

y=-1/3 x-1

Therefore, the equation of a line perpendicular to y = 3x - 8 which contains the point (3, -2) is y=-1/3 x-1.

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how do you do slope i have no clue and my teacher isnt helping me

Answers

Answer:

Slope. y2 – y1 / x2 – x1 = slope.

Step-by-step explanation:

like  for example find the slope of (6,5) (3,6)

remember (x,y)

(x1,y1)(x2,y2)

x1 which is 6

x2 is 3

y1 is 5

y2 is 6

so 6-5/3-6

6-5=1

3-6=3

so slope is rise/run

so rise = 1

run = 3

so the answer would be 1/3

Step-by-step explanation:

Slope, at its core, can be very simple both graphically or mathematically.

Mathematically:

Lets say we have a random straight line that goes through the points (2, 5),     (6, 15), (4, 10), and (20, 50).

Take any two points on that line.

I will use (2, 5) and (4, 10) for the sake of simplicity.

The slope formula is \(\frac{y_2-y_1}{x_2-x_1}\) where point 1 is (x2,y2), and point 2 is (x1, y1).

Thus, the slope is (4-2)/(10-5), or 2/5

please help
Basic Radicals ​

please help Basic Radicals

Answers

Answer:

B

Step-by-step explanation:

\(( \sqrt{c})^{2}= \sqrt{c}* \sqrt{c}= \sqrt{c*c}= c\\\)

I need help quick 16 mins left and I’m on the last question

I need help quick 16 mins left and Im on the last question

Answers

Answer:

try 2+2 that should work

Write the equation of a line that forms a 45 degree angle with the positive x- axis and passes through the origin?.

Answers

Answer:

y = x

Step-by-step explanation:

an equation that an equation that forms an angle of 45 ° and passes through the origin of the axes is the bisector, and its equation is y = x.

true or false: if you are given a graph with two shiftable lines, the correct answer will always require you to move both lines.

Answers

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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You place two wooden support beams under a shelf, as shown. Find the value of x. (3x-13 ) (x- 3) x=

Answers

Answer:

x = 49

Step-by-step explanation:

Fins the similar diagram attached;

The sum of the angles is 180 degree since they lie on the same straight line. Hence;

3x - 13 + x - 3 = 180

Collect the like terms;

3x+x -13 - 3 = 180

4x - 16 = 180

4x = 180 + 16

4x = 196

x = 196/4

x = 49

Hence the value of x is 49

Note that the values in question is different from that of diagram but the diagram is similar to what we need

You place two wooden support beams under a shelf, as shown. Find the value of x. (3x-13 ) (x- 3) x=

Eunice is a dressmaker. She spent a mean of $15.87 / meter of fabric. She spent a total of $5,554.50. How many meters of fabric did she buy?
Hint: mean ($÷m) = total cost ÷ number of meters of fabric

Answers

Answer:

hope you can understand

Eunice is a dressmaker. She spent a mean of $15.87 / meter of fabric. She spent a total of $5,554.50.
5554.50 divided by 15.87 equals to 350

Graph P=6d and P=5d+15

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The point of intersection is found by equating the expressions for P:

  6d = 5d +15

  d = 15

  p = 6d = 6·15 = 90

The point of intersection of the graphs is (15, 90).

The first equation graphs as a line with slope 6 through the origin.

The second equation graphs as a line with slope 5 through point (0, 15).

It is inconvenient to graph p and d using the same scale, so the attache graph has the vertical scale compressed somewhat.

Graph P=6d and P=5d+15

Given f(x) = 3/4x + 12, find the value of x when f(x) = x.

Answers

Answer:

48 =x

Step-by-step explanation:

3/4x + 12 = x

Subtract 3/4 x from each side

3/4x + 12-3/4x = x-3/4x

12 = 1/4x

Multiply each side by 4

12*4 =1/4x *4

48 =x

Answer:

x=48

Step-by-step explanation:

f(x) is basically just another way to write y.

If f(x)=x, then y=x.

x=3/4x+12 (Original Equation Substituting x for f(x), equal to y)

1/4x=12 (Subtract 3/4 from both sides of the linear equation)

x=48 (Multiply both sides by 4)

Find compound interest on 15,625 at 4% for 3 years.
Help! With steps

Answers

Answer:

P=15,625

Rate=4%

Time=3 years

CI=P(1+R/100)^T

=15,625(1+4/100)^3

=15,625*1.124864

=17576 Ans

Step-by-step explanation:

hope it helps

In a school hall 2/5 of the chairs are red 3/7
are blue and the rest are yellow
If there are 24 yellow chairs, how many chairs are blue?

Answers

Answer:

  60

Step-by-step explanation:

We can use 5·7 = 35 as a common denominator for these fractions. This tells us the fraction of red chairs is 2/5 = 14/35, and the fraction of blue chairs is 3/7 = 15/35. The rest of the (35 -14 -15)/35 = 6/35 chairs are yellow. This means the ratio of chair colors is ...

  red : blue : yellow = 14 : 15 : 6

Multiplying this by 4 will give 24 yellow chairs:

  4·14 : 4·15 : 4·6 = 56 : 60 : 24 . . . . red : blue : yellow chairs.

60 chairs are blue.

It takes a train going 50 mph approximately _____ to stop safely.
A. 100 ft B. 1/2 miles C. 1 1/2 miles D. 5 miles

Answers

It takes a train going 50 mph approximately 11/2 miles to stop safely.

The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.

In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.

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what is the value of b? Help pls!!!

what is the value of b? Help pls!!!

Answers

Answer:

b=24

Step-by-step explanation:

Main concepts

Concept 1. Congruent Triangles

Concept 2. Hypotenuse-Leg Congruence

Concept 3. Congruent Triangles implies congruent parts

Concept 4. Solving a one-variable equation

Concept 1. Congruent Triangles

For two triangles to be congruent, the three angles of one triangle must be congruent to the three angles of the other triangle, AND the three side lengths of one triangle must be congruent to the three side lengths of the other triangle.

Fortunately, through various proofs about different types of triangles, it isn't necessary to prove all six of those things.

The 5 cases of triangle Congruence are

SSS -- Side-Side-SideSAS -- Side-Angle-SideASA -- Angle-Side-AngleAAS -- Angle-Angle-SideHL -- Hypotenuse-Leg (only for Right Triangles, since a Hypotenuse is a part of a Right Triangle)

Concept 2. Hypotenuse-Leg Congruence

Proving they are both right triangles, and that HL congruence can be used

In this situation, we are given that Angle UVT is a right angle.  Under the assumption that US is a line that contains V, then Angle UVT and Angle SVT form a linear pair and are supplementary (their measures add to 180 degrees).

So, Angle SVT is also a right angle.  This means that both Triangle UVT and Triangle SVT are Right Triangles, since they are each a triangle with a right angle.

To prove HL congruence, we need to prove that one leg of each triangle is congruent to the other, and that the hypotenuse of each triangle is congruent to the other.

Proving Hypotenuse congruence

Note that the Hypotenuse (side across from the right angle) of Triangle UVT is side UT with measure 67 units.

The Hypotenuse of Triangle SVT is side ST, also with measure 67 units.

So the Hypotenuses are congruent.

Proving Leg congruence

Note that one leg of the triangles is shared as a common side:  line segment VT is common to both triangles.  Even though we don't know the actual length of VT, the length of VT for the first triangle is the same as the length of VT for the second triangle.

The official reason that VT is congruent to VT is because of the "Reflexive property".  

Since the Hypotenuses and one leg from each triangle are congruent, the two triangle are congruent.  Specifically, Triangle UVT is congruent to Triangle SVT.

Concept 3. Congruent Triangles implies congruent parts

Even though we didn't prove all 6 congruences, we did prove that the triangles ARE congruent.  Therefore, all 6 congruences are true.  This means that any other pair of corresponding parts is also congruent.

Specifically, we're interested in the last pair of sides, because they have measurements that contain "b" the value we're trying to solve for.

Side UV is congruent to Side SV because Corresponding parts of Congruent triangles are Congruent.

This means that their lengths are equal:

\(Length_{UV}=Length_{SV}\)

\(b+24=2b\)

Concept 4. Solving a one-variable equation

For any equation in math where there is only one item that is unknown, (even if it shows up multiple times in the equation), there are two main steps:

Step 1.  Get the variable to show up exactly once

Step 2.  Isolate the variable

Step 1.  Get the variable to show up exactly once

Since we know that in the very end, we want b=__, we know that the b will appear only once (and thus only on one side of the equation, not both), and will be by itself.

In practice, sometimes there are special tricks that have to be employed to make this step happen.  Generally, this means simplify each side of the equation, and try to group like terms together.

For this equation, observe that b appears twice: once on the left side of the equation, and once on the right side of the equation.  

At some point, we'll need to get the "b"s on the same side of the equation, and hopefully combine like terms into a single term with b.

To get the "b"s on one side, we'll subtract b from both sides:

\((b+24)-b=(2b)-b\)

On the left, the positive b and negative b cancel completely, leaving just 24.  On the right, the 2b subtracted by 1b leaves just 1b, or more simply, b.

\(24=b\)

Step 2.  Isolate the variable

While trying to get the variable to show up exactly once, we also incidentally isolated the variable, as the like terms combined.

So, b=24.


Someone please help due tonight
To encourage new customers, a movie theater is offering a different way to pay for a movie.
Members will pay $5 a year plus $2 per movie
Complete the table that shows the number of movies n and the cost for members C. Include values from 0 to 6.
Movies
0
1
2
3
4
5
6
Cost

Answers

0=$5
1=$7
2=$9
3=$11
4=$13
5=$15
6=$17
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