what are the steps to multiplying a fraction by a fraction

Let's keep in mind the conversion factors between mile, yard, feet and inches:

1 mile = 1760 yards

1 yard = 3 feets

1 feet = 12 inches

a) 3 mi. 26 yd.

We have:

8 mi. 133 yd. 2 ft. –

5 mi. 107 yd. 2 ft =

Here, we can simply do the substraction of each term, and we get:

(8-5) mi  (133-107) yd  (2-2) ft =

3 mi. 26 yd  0 ft =

3 mi. 26 yd.

b) 2 yd. 7 in.

We have:

2 yd. 2 ft. 6 in. –

0 yd.  1 ft. 11 in.

Here, we need to convert 1 feet into 12 inches and add them to the inches in the first term as follows:

2 yd. 2 ft. 6 in. = 2 yd. 1 ft. (6+12) in. = 2 yd. 1 ft. 18 in.

So now the subtraction becomes:

2 yd. 1 ft. 18 in. –

0 yd.  1 ft. 11 in.

and now we can simply do the substraction of each term, and we get:

(2-0) yd.  (1-1) ft.  (18-11) in. =

2 yd. 0 ft. 7 in. =

2 yd. 7 in.

c)  5 yd. 5 in.

We have:

6 yd.  0 ft. 0 in. –

0 yd.  2 ft. 7 in.

We have to "move" 1 yard into  feets and inches in the first term, as follows:

6 yd.  0 ft. 0 in. = 5 yd. 3 ft. 0 in. = 5 yd. 2 ft. 12 in.

And now the subtraction becomes:

5 yd. 2 ft. 12 in. -

0 yd.  2 ft. 7 in. =

5 yd.  0 ft. 5 in. =

5 yd. 5 in.

d) 8 in.

We have:

8 yd. 0 ft. 4 in. –

7 yd. 2 ft. 8 in.

Again, let's convert the first term, moving yards into feets and inches:

8 yd. 0 ft. 4 in. = 7 yd. 3 ft. 4 in. = 7 yd. 2 ft. (4+12) in. = 7 yd. 2 ft. 16 in.

So now the subtraction is:

7 yd. 2 ft. 16 in. -

7 yd. 2 ft. 8 in. =

0 yd. 0 ft. 8 in. =

8 in.

Answer:

3p + 26  

Step-by-step explanation:

Let S = Sue's newspapers sold

     B = Bill's newspapers sold

     H = Harry's newspapers sold.

We have three conditions:

(1)   S = B + 26

(2)  B = 3H

(3)  H = p     Substitute (3) into (2)

(4) B = 3p     Substitute (4) into (1)

      S = 3p + 26

Sue sold 3p + 26 newspapers.

Answer:

slope=-3  

y=-3x+5

Step-by-step explanation:

use two given points (3,-4)(0,5)

5- -4= 9

0-3=-3

9/-3=-3

Answer: [tex]y+4=-3(x-3)[/tex]

Step-by-step explanation:

The point-slope equation of a straight line is:

[tex]y-y_{1}=m(x-x_{1}  )[/tex]

where m is the slope and [tex](x_{1}, y_{1}  )[/tex] are the coordinates of a point in the line.

So, to find the equation, the firs step is to find the slope. We can see in the graphic that the line intercepts the y axis at the point (0, 5), so we're going to use that and the other given point to find the slope:

[tex]m=\frac{y_{2}-y_{1}  }{x_{2}-x_{1}} =\frac{-4-5}{3-0} =\frac{-9}{3}=-3[/tex]

Then, you simply substitute the slope and the coordinates of the point and you get the point-slope equation:

[tex]y-(-4)=-3(x-3)\\y+4=-3(x-3)[/tex]

[tex]\left\{\begin{array}{ccc}9x-8y=2\\-3x-9y=-24&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}9x-8y=2\\-9x-27y=-72\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-35y=-70\qquad\text{divide both sides by (-35)}\\.\qquad\qquad\boxed{y=2}\\\\\text{Put the value of y to the second equation}:\\\\-3x-9(2)=-24\\-3x-18=-24\qquad\text{add 18 to both sides}\\-3x=-6\qquad\text{divide both sides by (-3)}\\\boxed{x=2}\\\\Answer:\ \boxed{x=2}[/tex]

Answer:

x coordinate is 2

Step-by-step explanation:

We have given,

9x - 8y = 2   .........(1)

-3x - 9y = -24   ...............(2)

We use elimination method to eliminate y.

We multiply equation (1) by 9 and equation (2) by 8.

We get,

{ 9x - 8y = 2} × 9   or  81x - 72y = 18    -------------(3)

{-3x - 9y = - 24} × 8  or -24x - 72y = -192  -----------(4)

And subtract equation (4) from equation (3)

So , (81x - 72y ) - (-24x -72y)= 18 -(-192)

or 105x = 210

or x = 210/105

or x= 2

Hence we get x coordinate as x= 2

Answer:

10 & 14

Step-by-step explanation:

10 + 14 = 24

14 - 10 = 4

Answer:

As x decreases without bound, f(x) approaches the line y=3 .

As x increases without bound, f(x) increases without bound.

Step-by-step explanation:

From the given graph f(x), we can see that

When x  increases the value of y also increases

When x decreases  the y values goes close to 3 but it does not cross 3

As x goes to positive infinity , y approaches positive infinity

As x increases without bound, f(x) increases without bound.

As x goes to negative infinity, y values approaches +3

As x decreases without bound, f(x) approaches the line y=3

As x decreases without bound, f(x) approaches the line y=3 . As x increases without bound, f(x) increases without bound. Therefore, options A and B are correct answers.

The given function is f(x)=4 1/3x+3.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

From the given graph f(x), we can see that

When x increases the value of y also increases

When x decreases the y values goes close to 3 but it does not cross 3

As x goes to positive infinity, y approaches positive infinity

As x increases without bound, f(x) increases without bound.

As x goes to negative infinity, y values approaches +3

As x decreases without bound, f(x) approaches the line y=3

Therefore, options A and B are correct answers.

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Answer:

[tex]b=4\text { or }b=-2[/tex]

Step-by-step explanation:  

We have been given a rational expression: [tex]\frac{2b^2+3b-10}{b^2-2b-8}[/tex] and we are asked to find the illegal values of b.

Illegal values of b will be those values, which will make our denominator 0.

To solve for illegal or excluded values of b, let us set our denominator equal to 0.

[tex]b^2-2b-8=0[/tex]

We will factor out our equation by splitting the middle term.

[tex]b^2-4b+2b-8=0[/tex]

[tex]b(b-4)+2(b-4)=0[/tex]

[tex](b-4)(b+2)=0[/tex]

[tex]b-4=0\text { or }b+2=0[/tex]

[tex]b=4\text { or }b=-2[/tex]

Therefore, [tex]b=4\text { or }b=-2[/tex] are illegal values of b in the given fraction.

Answer:

The value of the quantity after 186 hours is 2089.41

Step-by-step explanation:

We can use exponential formula

[tex]P(t)=a(1-b)^{\frac{t}{h} }[/tex]

a quantity with an initial value of 2100

so,

[tex]a=2100[/tex]

decays exponentially at a rate of 0.65% every 10 days

So, b=0.0065 when h=10*24=240

now, we can plug values

[tex]P(t)=2100(1-0.0065)^{\frac{t}{240} }[/tex]

now, we can plug t=186

and we get

[tex]P(186)=2100(1-0.0065)^{\frac{186}{240} }[/tex]

[tex]=2089.413[/tex]

Answer:

Q(186)  = 2089.463                    

Step-by-step explanation:

Formula for decaying exponentially:

Q(t) = Q_0 e^{-rt}

where, Q(t)= quantity at time t

Q_0 = initial quantity value (2100)

t = time (186 hours)

r = rate of decaying (0.65)

r = 0.65% = 10 days

1 day = [tex]\frac{0.0065}{10}[/tex]

1 hour = [tex]\frac{0.0065}{240}[/tex]

186 hours = [tex]\frac{0.0065*186}{240}[/tex]

rt = 0.00503

Q(186) = 2100*e^{-0.00503}

          = 2089.46

Answer:

21.46 or 21.5

Step-by-step explanation:

To find the answer to this problem you must divide 877 by 4132, which gets you 0.2146. Then you multiply this answer by 100 to find the percentage; which in this case is 21.46, or 21.5 if you are rounding up. I hope my answer helped you!

887 is 21.47% of 4132, found by dividing 887 by 4132 and multiplying by 100.

To find out what percent 887 is of 4132, you need to use the formula for calculating percentages, which involves dividing the part by the whole and then multiplying the result by 100.

Here is how you can compute it step-by-step:

Divide 887 by 4132, which gives you approximately 0.2147.

Multiply this result by 100 to convert it into a percentage: 0.2147 * 100 = 21.47%.

Therefore, 887 is 21.47% of 4132.

Rounded to the nearest tenth, the unit rate of calories per serving is approximately 141.3 calories.

To find the unit rate of calories per serving, divide the total calories (424) by the number of servings (3).

The unit rate is the amount of calories per serving. To find the unit rate, divide the total number of calories by the number of servings:

Unit rate = Total calories / Number of servings

Unit rate = 424 calories / 3 servings

Dividing 424 calories by 3 servings gives:

Unit rate = 424 / 3 ≈ 141.3 calories per serving

So, the unit rate of calories per serving is approximately 141.0 calories rounded to the nearest tenth or approximately 141.00 calories rounded to the nearest cent.

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Answer:

Step-by-step explanation:

Basically, in each option, you have to find the relationship between x and y (for one pair). Like in option #1 - how do you get 1.5 from 3? divide it by 2. Now you apply it for all numbers. It the outcome the same? No. 7 ÷ 2 ≠ 3.

You do the same process for all, until you are left with the last one. y = 50x

The last option is the answer.

Answer:

2072.56

Step-by-step explanation:

a=1030(1+0.06)^12

Answer:

$2072.60

Step-by-step explanation:

Every year you add on 6% so the multiplier  will be 1.06

so start off:

1030 x 1.06 = 1091.8

1091.8 x 1.06 = 1157.308

.......... you repeat this 12 times for every year and the final answer is

2072.6562366

you take that answer and round it to 2072.60

Hope this helps :)  

To write a linear function with the given values f(3) = -4 and f(5) = -4, we can use the point-slope form of a linear equation. The linear function is y = -4.

To write a linear function with the given values f(3) = -4 and f(5) = -4, we can use the point-slope form of a linear equation. The formula for point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We can choose any point (x1, y1) from the given values. Let's choose (3, -4) as a point on the line. Now we can substitute the values into the formula to find the linear function:

y - (-4) = m(x - 3)

y + 4 = m(x - 3)

To find the slope, we can use another point on the line, such as (5, -4). Substituting the values into the formula, we get:

-4 + 4 = m(5 - 3)

0 = 2m

Solving for m, we get m = 0.

Now we can substitute the slope and one of the points back into the formula to find the linear function:

y + 4 = 0(x - 3)

y + 4 = 0

y = -4

So, the linear function with the given values is y = -4.

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Given values f(3) = -4 and f(5) = -4 suggest a horizontal line as the y-coordinate remains constant at -4 regardless of x values. Hence, the linear function is f(x) = -4.

The student wants to know how to write a linear function with the values f(3)=-4 and f(5)=-4. The first thing we need to understand here is that a linear function is represented by the equation y = mx + b, where y is the output, m is the slope, x is the input, and b is the y-intercept. In this problem, since f(3) = -4 and f(5) = -4, it indicates that the y coordinate remains the same (-4), thus forming a horizontal line despite the changes in the x coordinates. This means the function has a slope (m) of 0. So, the linear function that satisfies these conditions is f(x) = -4.

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Answer:

174 packages of t-shirts    PLEASE GIVE BRAINLIEST

Step-by-step explanation:

139 x 5 = 695 t-shirts are needed

695 ÷ 4 = 173.75

Since you have to purchase whole packages of t-shirts you will need to buy 174 packages of t-shirts.  174 x 4 = 696 t-shirts

174 packages

Answer:

123

Step-by-step explanation:

Assuming that 85% of the total was either adults or boys, we can subtract

100-85

=15

Therefore, that 15% is girls

820*.15

=123

The required values of x and y is 9 and -36, respectively. The correct answer is option a.

Given that the system of equations:

y = -3x - 9                       (1)

y = (1/3)x - 39                  (2)

Setting the two equations equal to each other since they both equal y:

-3x - 9 = (1/3)x - 39

⇒ -3(3x) - 3(9) = (1/3)(3x) - 39(3)

⇒ -9x - 27 = x - 117

⇒ -9x - x = -117 + 27

⇒ -10x = -90

⇒ x = -90 / -10

⇒ x = 9

Substitute the value of x back in the equation (1),

y = -3(9) - 9

⇒ y = -27 - 9

⇒ y = -36

Hence, the solution to the system of equations is x = 9 and y = -36. The correct answer is option a.

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Answer:

W + 8

Step-by-step explanation:

Given:

The length of the rectangle is 8 cm longer than its width.

Let's take "W" be the width.

Length = W + 8

The expression "w + 8" represents the length of the rectangle.

Thank you.

Answer:

L=W+8

Step-by-step explanation:

This means that whatever number of centimeters the width is, you will always add 8 centimeters in order to reach the size of the length. In order to calculate the perimeter of the rectangle you have to add all its four sides and the final formula would be as follows:

W+W+L+L=P, where W is Width and L, is Length (W+8).

In other words, you can calculate as shown below:

W+W+(W+8)+(w+8)=P

Answer:

Simplifying the expression eliminating the parentheses:

(-5 u^2 w)^3 = -125 u^6 w^3

Step-by-step explanation:

(-5 u^2 w)^3 = (-5)^3 (u^2)^3 (w)^3

(-5 u^2 w)^3 = (-5)(-5)(-5) u^(2 x 3) w^3

(-5 u^2 w)^3 = -125 u^6 w^3

Answer:

69% or 69/100

Step-by-step explanation:

It's experimental odds based off of experience.

The probability of getting a head on the next flip is 69%.

In order to determine the probability of getting a head on the next flip, we must first analyze the given data. The number of heads obtained in the first 100 flips is 69, while the number of tails is 31. Based on this information, we can calculate the proportion of heads to the total number of flips. The probability of getting a head on the next toss is therefore 69/100 = 0.69 or 69%.

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Notice how the x-2 on the numerator and denominator cancel out, as well as the x+1. You are left with 8(x+2)/4 which is 2(x+2) which results in your answer, B, or 2x+4.

Answer:

option B is correct.

[tex]2\sin^2r - 1[/tex]

Step-by-step explanation:

Given the expression: [tex]1-2\cos^2r[/tex]                      ......[1]

Using trigonometric identities:

[tex]\sin^2r+ \cos^2r = 1[/tex]

We can rearrange this as;

[tex]\cos^2r = 1-\sin^2r[/tex]      ......[2]

Substitute equation [2] into [1] we get;

[tex]1-2(1-\sin^2r)[/tex]

Using distributive property:  [tex]a\cdot (b+c) = a \cdot b + a\cdot c[/tex]

[tex]1- 2 +2sin^2r[/tex]

or

[tex]-1+2\sin^2r[/tex]

therefore, the given expression in terms of sine terms is; [tex]2\sin^2r-1[/tex]

[tex]\left\{\begin{array}{ccc}3x+6y=-9&\text{divide both sides by (-3)}\\x+2y=-3\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x-2y=3\\x+2y=-3\end{array}\right}\qquad\text{add both sides of the equations}\\. \qquad\qquad0=0\qquad TRUE\\\\Answer:\ \boxed{\text{Infinitely many solutions}}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=-\dfrac{1}{2}x-\dfrac{3}{2}\end{array}\right[/tex]

Answer:

(-6,-14)

Step-by-step explanation:

Answer:

150 and 240 are the two numbers having difference as 90 and ratio as 5 : 8.

Step-by-step explanation:

Since ratio of two numbers is 5 : 8 ,

lets assume two numbers be 5x and 8x.

Difference of two numbers = 8x - 5x = 90

⇒3x =90

⇒x = 90/3=30

so two numbers are 5x = 5 × 30 = 150 and 8x = 8 × 30 = 240

Hence 150 and 240 are the two numbers having difference as 90 and ratio as 5 : 8.

Answer:

$43.40

Step-by-step explanation:

12 + 28

40

40 (1.085)    <<< sales tax

43.40

Answer: $43.40

Step-by-step explanation:

Total Cost of products (before sales tax): $12 + $28 = $40

After sales tax: ($40 × 108.5%) ÷ 100% = $43.4 = $43.40

Answer:

P₂ - P₁ = -11 100

Step-by-step explanation:

The profit for month 1 was P₁.

The profit for month 2 was P₂.

The difference in profit was

Diff. = P₂ - P₁

P₁ = 6400; P₂ = -4700

Diff. = - 4700 - 6400

Diff. =  -11 100

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{7})~\hspace{10em} slope = m\implies -\cfrac{4}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=-\cfrac{4}{5}(x-0) \\\\\\ y-7=-\cfrac{4}{5}x\implies y=-\cfrac{4}{5}x+7[/tex]

Answer:

306

Step-by-step explanation:

9 times 18= 162

24 times 6= 144

144+162=306