Solve this equation for x in terms of the other pronumerals.

x/a - x/2a = b

Answer: This is a linear pair of angles because they are two adjacent angles that have a common side and whose other sides point in opposite directions.

The area of square is increasing with the rate of 144 cm/s2.

For physics, The term "thermal expansion" refers to a material's change in length, width, height, or volume when its temperature is raised or lowered. Solids exhibit particularly noticeable thermal expansion due to their closely packed atoms. There are numerous uses for thermal expansion of solids in daily life.

A solid's atoms vibrate more quickly around their fixed positions when it is heated. As a result, there is little relative growth in the size of solids during heating. In order to prevent buckling when exposed to heat from the sun, metal train tracks feature tiny gaps.

L = length of a side

A = L2

dA/dt = 2L dL/dt

dL/dt = 8 cm/s

A = 81 cm2 ⇒ L = √A = √81 cm = 9 cm

dA/dt = 2(9cm)(8 cm/s) = 144 cm/s2

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Answer: Your answer would be D

Step-by-step explanation: The reason why is because in the question it said he is already carrying a 20 pound chair. It then say he can carry some boxes that weigh 5 pounds each. The word each is your keyword. With that you can replace the x variable with some single digit numbers. But you also need to make sure your total is less than or equal to 60 pounds. You would pick the less than or equal to sign since he can only carry 60 pounds or less.

Using substitution method, the best initial step in solving the equation is solve the first equation for x.

The equation can be solved by substitution method as follows:

2x + 3y = -12

6x + y = 18

Hence, let's make y the subject of the formula in equation(ii)

6x + y = 18

y = -6x + 18

We have to substitute the value of y in equation(i)

2x + 3y = -12

2x + 3(-6x + 18) = -12

2x - 18x + 54 = -12

- 16x + 54 = -12

-16x = - 12 - 54

- 16x = -66

x = 66 / 16

x = 33 / 8

Therefore,

6(33 / 8) + y = 18

99 / 4 + y = 18

y = 18 - 99 / 4

y = - 27 / 4

From the solving above the best step to solve the equation is solving the first equation for x.

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The number of heartbeat in ten minutes is 420 beats

Unit rates are the rates of a quantity to one of another quantity

From the question, the given parameters are:

The number of heartbeats in these ten minutes is then calculated as

Total heartbeats = Number of heartbeats per minute x Number of minutes

Substitute the known values in the above equation

So, we have

Total heartbeats = 42 x 10

Evaluate

Total heartbeats = 420

Hence, the total heartbeat is 420 beats

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48×35. By using standard algorithm we got 1680.

Given that,

48×35

We have to find the multiplication of the numbers by standard algorithm.

Standard algorithm is nothing but the words "Standard" and "Algorithm" make up the standard algorithm. Standard refers to the standard or standard way of doing anything, such as eating, bathing, or brushing one's teeth. Algorithms are nothing more than a task's sequential execution. As a result, solving a problem step by step is a common algorithm in mathematics. You will discover what a standard algorithm is in this article, along with the addition, subtraction, multiplication, and division standard algorithms.

If you don't use the standard algorithm , your answers will be incorrect.

48×35=1680

Therefore, By using standard algorithm we got 1680.

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Answer: [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]

Step-by-step explanation:

Using the vertex form, the equation is

[tex]y=a \left(x-\frac{1}{2} \right)^2 +1[/tex]

Substituting in the coordinates (2, -8) to solve for a,

[tex]-8=a \left(2-\frac{1}{2} \right)^2 +1\\\\-8=\frac{9}{4}a+1\\\\-9=\frac{9}{4}a\\\\a=-4[/tex]

So, the equation is [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]

Answer:

1

Step-by-step explanation:

Total outcome is 50 [because the number produced by the machine is from 1 to 50]

Question a:

Multiple of 10 are 10, 20, 30, 40, 50

There are five possible outcomes for multiple of 10

P(Multiple of 10) = 5/50 = 1/10

Question b:

Number 1 to 50 will be all the outcomes that are not 100

There are 50 possible outcomes

P(not 100) = 50/50 = 1

Question c:

Multiple of 4 that are less than 50 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

There  are 12 possible outcomes for multiple of 4

We want 'not multiple of 4' so we need to do 50 - 12 = 38 outcomes

P(not a multiple of 4) = 38/50 = 19/25

Question d:

One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9

There are 9 possible outcomes

P(one-digit number) = 9/50

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K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)

Firstly, we needt to identify the coordinates of the vertices of the quadilateral

Afterwards, we then perform the translation

The translation simply means we add 2 to the x-value and add 4 to the y-value

So if we had coordinates of a vertex as (x,y); upon translation, we will have (x + 2, y+ 4)

Let us identify the vertices;

K'

K (-4,-2)

L (-1,-2)

M (-1,-5)

N (-4,-5)

After translation, we have;

K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)

Answer:

define the unknown quantity as =variable. Then use the given info to write down an equation in terms of the unknown quantity. At the end, solve the equation for the unknown.

a.) The Assessed value is $43,830

b.) Annual Tax is $2,848.95

Define marked price

'Marked price' is the general price of the thing without any discount. 'discount' is a percentage of the marked price.

Given,

Assessment rate = 45%

Tax rate is $65 per $ 1000 of assessed value

Marked value = $97,400

a.)

To obtain assessed value,

calculate the 45% of $97,400 like that

45/100 = x/97,400

cross multiply the ratios

100x = 45 * 97,400

x = (45 * 97,400) / 100

x = 45 * 974

x = 43,830

Hence,the Assessed value is $43,830

b.)

Find yearly real estate tax,

Assessed value = $43,830

Tax rate is = 65 / 1000 of assessed value

                 = 0.065 * 43830

                 = 2,848.95

Hence, the  annual tax is $2,848.95

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The expression, for example, x²- 49 may be factored as (x+7)(x-7).  can be factored in using the difference of squares identity.

The difference of the square's identity is shown below:

(a+b)(a-b) = a² -b²

When an expression can be seen as the difference of two perfect squares, i.e. a² -b², we can factor it as (a+b) (a-b).

For example, x²- 49 may be factored as (x+7)(x-7).

This approach is based on the pattern (a+b)(a-b) = a² -b², which may be validated by extending the parenthesis in (a+b)(a-b).

Thus, the expression, for example, x²- 49 may be factored as (x+7)(x-7).  can be factored in using the difference of squares identity.

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The example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because it will not occur.

The probability is the branch of mathematics that shows the occurrence of the random event. The value of the probability varies from 0 to 1.

The equation of the probability is

Probability = Number of favorable outcomes / Total number of outcomes

The probability of getting number number 7 when you throw a die once is zero. Because when you throw a die the possible outcomes are 1, 2, 3, 4, 5 and 6. We wont get number 7. Therefore the probability is zero

Hence, the example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because  it will not occur.

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the probability that a randomly selected student scored less than 82.

Then the value is  P( X< 82)=0.9192

From the question we are told that

The sample size is  n  =  24

The mean is    =75

The standard deviation is  =5

Generally the  probability that a randomly chosen student scored is less than 82 is mathematically represented as

P( X < 82) = P ( Z< 82-75/5)

                =P(Z <1.4)

                =0.9192

From the z table  the area under the normal curve corresponding to  1.4 is  0.9192

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Answer: 54%

Step-by-step explanation:

From the histogram of the distribution, it is found that Zoe is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.

An histogram is a graph that shows the number of times each element of x was observed in the distribution. When the input is an interval of values, as is the case in this problem, it shows the number of observations that is in each interval.

Hence, from the histogram in this distribution, it is found that:

75 is a greater amount than 50, hence Zoe's statement is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.

The complete problem is given by the image at the end of the answer.

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Answer:

6/3=2

30/10=3

Step-by-step explanation:

For simple division like this, you can look and see how many times 3 can go into 6, and 10 into 30.

Answer:

y= -3x + 5

Step-by-step explanation:

m= (y2-y1)/(x2-x1)

m= [8-(-4)]/(-1-3)

m=12/-4

= -3

y= mx + b

-4=(-3)(3) + b

-4=9+b

b=5

therefore, y= -3x+5

Answer:39.2 40.2 444.96

Step-by-step explanation:

Given:

The given function is, f (x) = -4x + 5.

The objective is to reflect the graph across the y - axis and find the new function.

Explanation:

The general transformation formula for reflection over y-axis is,

To find f(-x):

The required transformation can be calculated as,

Hence, the new function is g(x) = 4x + 5.

Answer:

Speed of northbound train = 66

Speed of southbound train = 54

Step-by-step explanation:

First, let's make the variables simpler:

Speed of southbound train = x

Thus:

Speed of northbound train = y = x + 12

Distance = speed · time

240 = 2 ( x + x + 12 ) = 2 ( 2x + 12 ) = 4x + 24

216 = 4x

x = 54

Now, plug in x to find the speed of the northbound train (y):

y = 54 + 12 = 66

For the function f(x) =[tex]\sqrt{8x+10}[/tex] the inverse function [tex]f^{-1}[/tex](x) = [tex]\frac{x^2-10}{8}[/tex] x≥ 0 as can be calculated through the inverse function's formula.

In mathematics, any kind of inverse is a function that serves to “undo” any other function. That is, if f(x) produces y, then while putting y into the inverse off it produces the output x.

To find the inverse of a function, write the function y as a function of x i.e., y = f(x) and then solve for x as a function of y.

Inverse operations are seen as opposite operations that provides undo to each other. For example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse operations.

Every one-to-one function f has an inverse; this inverse is denoted by f−1 and read aloud as 'f inverse'. A function and its inverse 'undo' each other: one function does something, the other undoes it.

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Answer:

Use this relation

Im^2 = 10000cm^2

Answer:

multiply m² by 10000

Step-by-step explanation:

1 m = 100 cm

1 m² = 100² = 10000 cm²

then to change m² to cm² , multiply m² by 10000

Answer:

I would say yes they are

Step-by-step explanation:

because you multiply the small one's numbers by 2 and get the big triangle

Answer:

they are similar! :)

Step-by-step explanation:

the best way to figure this out is just by looking to see if they have anything in common. in this case, the larger figure is just two times more on each side than the smaller figure.

Answer:

348 ft

Step-by-step explanation:

First split the sidewalk into two rectangles. then multiply the LxWxH (length times width times height) of both rectangles. 8 times 6 times 6 = 288 ft. then 10 times 2 times 2 = 60. then add the two volumes of the rectangles to result in 348 cubic ft

The probabilities from the venn diagram are:

Let A be the event that the Mechanic is AC repairman and T be the event that he does tune ups.

The probability that he does tune ups is:

Hence the required probability is given by:

Hence the probability is 2/3.

Answer: I think the width is 7.

Step by step explanation:

So let's say the length is 12. This means I need to subtract 5 from it, since the width is 5 inches less than the length. Now that we know this, that means the width is 7, which is the area.

I hope this helps.