Select equivalent or not equivalent for each pair of expressions

Step-by-step explanation:

[tex] \frac{1}{a + b} \times ( \frac{a + b}{ab}) = \frac{1}{ab} [/tex]

Answer with step-by-step explanation:

[tex](a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1[/tex]

First, convert these into positive indices.

[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})=\frac{1}{ab}[/tex]

And now, let us solve the left side.

[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\[/tex]

First, solve the brackets. That is add the fractions inside the brackets.

[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\\frac{1}{(a+b)}*(\frac{1*b}{a*b} +\frac{1*a}{b*a})\\\\\frac{1}{(a+b)}*(\frac{b}{ab} +\frac{a}{ab})\\\\\frac{1}{(a+b)}*\frac{(a+b)}{ab}[/tex]

Now multiply the fractions.

[tex]\frac{1}{ab}[/tex]

So, it's clear that the left side equals the right side.

Left side = Right side

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

∴ [tex](a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1[/tex]

The boat is moving at 2  miles per hour and current is 4 miles per hour.

In calm water, the boat travels at a 2 mph pace.

4 miles per hour is the current's speed.

One such computation is as follows.

Let a be a representation of the boat's speed.

Allow b to be the current's speed.

20(a + b) = 240, according to equation 1.

Equation 2: 60(a + b)

Equation 3: a + b = 12

Equation 4: a - b Equals 4.

Equation 3 and equation 4 combined

(a + b) + (a - b)= 12+4

2x = 16

a= 16/2

a= 8

Calculate equation 4 minus equation 3

(a + b) - (a-b)= 12-4

2b= 8

b= 8/2

b= 4

As a result, the boat is moving at 2 miles per hour, while the current is moving at 4 miles per hour.

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Answer:

Step-by-step explanation:

"D" would be the correct answer. "f(x-10)" means that the "10" would be moving right-- the positive direction. Therefore, h(x) would be located 10 units RIGHT of f(x), which passes through the origin, (0,0). Statement A is correct because, on a graph, you'd have line f(x) passing through the origin, and towards the right, 10 units, (positive) you would have h(x) making them identical. So yes, same slope. Statement B is also correct, they're obviously parallel if they're beside each other. Statement C is correct as well. Although they're parallel, they don't share the same X-intercept. f(x)'s x-intercept would be (0,0), origin. h(x)'s x-intercept would be (10,0). These three statements, A,B, & C are correct statements therefore they're not our answers since we're looking for the incorrect statement....... STATEMENT D!

Answer:

lower bound for area = 140.25 square cm

upper bound for perimeter = 54 cm

======================================================

Explanation:

L = length

W = width

The unknown length L is rounded to the nearest cm to get to 17

This means it's in the interval [tex]16.5 \le L < 17.5[/tex]

The smallest it can get is L = 16.5 since that rounds to 17

It doesn't reach 17.5 since that would round to 18. But it could be L = 17.49 or L = 17.499 or L = 17.4999 and so on.

Similarly, if the unknown width W rounds to 9 cm, then its unrounded value is somewhere in the interval [tex]8.5 \le W < 9.5[/tex]

------------------------

Select the lower bounds of L and W to compute the lower bound of the area

length*width = L*W = 16.5*8.5 = 140.25

The smallest area possible is 140.25 square cm.

--------------------------

Use the upper bounds of each L and W to find the upper bound of the perimeter.

P = 2(L+W)

P = 2(17.5 + 9.5)

P = 54

In the previous example, we could have a true area of 140.25 square cm. However in this case, there's no way to reach this upper bound 54 itself. This is the so called "ceiling" which we can think of as an electric fence or asymptote value.

We could have the following example perimeter values that approach 54 but not actually reach it

and so on.

The food that the former world record holder should eat per day is 0.33kg.

The first step is to determine the ratio of the smallest horse's food per day to the height of the horse. This can be determined by dividing the food eaten per day by the height of the horse.

Division is the operation used in mathematics that is used to determine the quotient of two or more numbers

Ratio of the height and food eaten per day = 0.3 / 42.5

The next step is to multiply the ratio gotten in the previous step by the height of the former world holder

Food the former holder should eat = (0.3 / 42.5) x 46.25 = 0.33 kg

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Answer:

Step-by-step explanation:

I think it is option E) 7

The bank that pays the highest interest for this 4-year IRA account is Chase Bank.

It should be noted that interest rates simply means the cost of borrowing or the gain from savings.

In this case, Destiny wants to compare interest rates quoted by four local banks for a deposit.

Chase Bank: = 2 1/2% = 2.5%

Jefferson City Trust:l = 1.7%,

Bank of America = 2.12%

First State Bank = 1 3/4% = 1.75%

Therefore, the highest is Chase Bank as it gives 2.5%.

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The maximum number of  14 hours that the crane is Used.

Step: 1 According to the question    

         1500 + (250)h ≤ 5000

          1500 + 250h ≤ 5000

Step: 2

1500 + 250h - 1500 ≤ 5000 - 1500                      

250h ≤ 3500                      

Divide by 250 into both sides

250h/250h ≤ 3500/250                          

h ≤ 14

What is Divide?

Split, in its simplest form, is to divide into two or more equivalent portions, spaces, groups, or divisions. Split, in plain English, is to provide the entire item to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

Divide or division is denoted by the letters, slash (/), or a horizontal line. When dealing with a variety of problems and calculations, these symbols are useful. Also, "x by y" or "x over y" might be interpreted as "x/y" or "x y."

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point slope form = y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)

slope intercept form = -[tex]\frac{152}{7}[/tex]=c

Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. Negative "rise" refers to a diminishing line. The line could be functional, established by a road surveyor, or depicted in a graphic that represents a road or a roof as a description or a design.

The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope. A line's direction might be either horizontal, ascending, decreasing, or vertical

If a line is rising from left to right, it is increasing. Since m>0, the slope is positive.

If a line decreases from left to right, it is said to be diminishing. The slope is inverse, or m0.

A line has zero slope if it is horizontal. This function has a fixed value.

A line's slope is ambiguous if it is vertical.

Slope= [tex]\frac{x-x1}{y-y1}[/tex]= [tex]\frac{3-5}{-22+43}[/tex]=[tex]\frac{-2}{21}[/tex]

point slope form= y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)

slope intercept formy=mx+c

-22=[tex]-\frac{2}{21}[/tex]*3+c

-22+[tex]\frac{2}{7}[/tex]=c

-[tex]\frac{152}{7}[/tex]=c

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For the given number 395,621 round off it to nearest ten thousand is equal to 400,000.

As given in the question,

Given number is equal to :

395,621

Round off the given number 395,621 to nearest ten thousand is given by:

395,621 = 300,000 + 95,621

Ten thousand is represented by 95,621 for the given number

95621 is in between two numbers

90,000< 95,621 < 100,000

95,621 is more closer to 100,000

After rounding it off to the nearest ten thousand

300,000+ 100,000 = 400,000

Therefore, for the given number 395,621 round off it to nearest ten thousand is equal to 400,000.

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Answer:

1 / 121

Step-by-step explanation:

4^0 = 1

11^2 = 121

4^0 / 11^2 = 1 / 121

Answer:

10.069 +420 =430.069

Step-by-step explanation:

first step is to add the number 420 to the number before the decimal so 420+10 which equals to 430

Then

u add the number that comes after the decinal together or if only one of them has a number after the decimal place back that number after youre given answer....

Given,

The phrase is,

Six less than the quotient of nine and a number

Consider, the number is x.

The mathematicsl expression of quotient of nine and a number is,

The mathematical expression of six less than is,

Combining both statements then,

Hence, the mathematical expession is 9/x -6.

Answer:

9/x -6

Step-by-step explanation:

The measure of the angles x and y are 71 degrees and 109 degrees after applying the concept of vertically opposite angles.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

From the figure:

The value of y can be found by applying the concept of vertically opposite angles:

y =  109 degrees

x = [360 - 2(109)]/2

x = (360 - 218)/2

x = 71 degrees

Thus, the measure of the angles x and y are 71 degrees and 109 degrees after applying the concept of vertically opposite angles.

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The possible solutions for the given function are as follows:

In the graph,  the real roots are the values when it crosses the x-axis.

Therefore, the possible solutions for the given function are as follows:

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Answer:

Given that the information,

Length of a  soccer practice = 90 minutes

Time that has elapsed = m minutes

Let "y" be the minutes left

Expression for the number of minutes left is

[tex]y = (90 - m) min[/tex]

the dimensions of the box is length 20 and width 40inches with maximum volume that can be sent. is V = 16000 inches ^3

length + girth=116 inches

w + 4x= 120

volume=x^2*w

w=120-4x

V=x^2* (120-4x)

for max value, dv/dx=0

dv/dx= 240x-12x^2

240x-12x^2=0

20-x=0

x=20

w=120-4(20)

=40

V=20^2*40==16000inches^3

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Answer:

point form : (-2 , -1)

equation form : x = -2 , y = -1

Step-by-step explanation:

( 5x + 9 = -2x - 5)

for y = 5x + 9 (substitute x = -2)

y = 5(-2) + 9 = -1

Let's begin by identifying key information given to us:

The boiling point of water is 100 degrees Celsius

We will convert this temperature to Fahrenheit to obtain its equivalent using the formula:

Therefore, the first option is the correct answer (212 degrees Fahrenheit & 100 degrees Celsius)

The transformed function is:

g(x) = 2*|x + 1| - 6

We start with the original function f(x), and we define the transformed function as g(x).

First, we have a translation of 1 unit to the right, so we have:

g(x) = f(x - 1)

Then, we have a vertical stretch by a factor of 2.

g(x) = 2*f(x - 1)

A translation of 4 units down:

g(x) = 2*f(x - 1) - 4

And we know that f(x) = |x + 2| - 1

Replacing that, we get:

g(x) = 2*( |x -1 + 2| - 1) - 4

g(x) = 2*|x + 1| - 2 - 4

g(x) = 2*|x + 1| - 6

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Answer:

F(x)=-(x+4)(x-1)

Step-by-step explanation:

the thing hit both -4 and 1 but in the function -4 become 4 and 1 become-1 so (x+4)(x-1) but we need to make it negative so -(x+4)(x-1)

We have the following number, we need to simplify:

we can also express this as:

since:

which represents the imaginary number,

then, we get:

Answer:

picture

Step-by-step explanation:

everything in the picture

i hope that this helps

Answer:

the answer is -1 .........

The constant of proportionality is known as the slope of the line.In the graph constant of proportionality is 1/2

The constant of proportionality is known as the slope of the line.

Constant of proportionality is nothing but slope of a line

The formula for calculating slope is expressed as:

m = y₂-y₁/x₂-x₁

Given the coordinate points (2/3, 3/4 ) and (0,0).

y₂=0, y₁=3/4, x₂=0,x₁ =2/3

substitute the values of  y₂=0, y₁=3/4, x₂=0,x₁ =2/3 in slope formula to get constant of proportionality.

The constant of proportionality is expressed as:

m = 3/4 × 2/3

m =6/12

m=1/2

Hence the constant of proportionality is 1/2

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Company B has the best buy with a selling price of $2.79

Given: Company A sells 16 lions for $44.32

Company B sells 18 lions for $50.22

Company C sells 12 lions for $ 32.88

To find : The selling price of each lion

By using unitary method we get,

Company A sells 1 lion for $ 2.77

Company B sells 1 lion for $2.79

Company C sells 1 lion for $ 2.74

From the above statistics it is clear that Company B has the best buy .

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It is given that area of rectangle of Kaitlin is 1500 sq.ft. with length 50 ft and a width of 30 ft.

The new area when new length 2 times the current length and the new width 2 times the current width.

a. The size of Kaitlin new patio is

b. The area of new patio is 4 times the area of current patio.

Step-by-step explanation:

hola nose inglés q te valla bien

Answer:

you can start out by writing the number in standard form, which means that it shouldn't exceed to 10 . So in this case, we are writing it as 3.01⋅10−4 instead of 30.1⋅10−3 , hope it helpeful