Multiplying Rational Numbers -2/3 (-1/5)

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: f = 2[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Let's consider two points (1 , 3) and (7 , f), now we can write the slope (m) of line in form of these points as :

[tex] \qquad \tt \rightarrow \: m = \cfrac{y2 - y1}{x2 - x1} [/tex]

[tex]\qquad \tt \rightarrow \: - \dfrac{1}{6} = \dfrac{f - 3}{7 - 1} [/tex]

[tex]\qquad \tt \rightarrow \: - (7 - 1) = 6(f - 3)[/tex]

[tex]\qquad \tt \rightarrow \: - 6 = 6(f - 3)[/tex]

[tex]\qquad \tt \rightarrow \: f - 3 = - \dfrac{6}{6} [/tex]

[tex]\qquad \tt \rightarrow \: f - 3 = - 1[/tex]

[tex]\qquad \tt \rightarrow \: f = - 1 + 3[/tex]

[tex]\qquad \tt \rightarrow \: f = 2[/tex]

Value of f is 2, so the point is : (7 , 2)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The value of the first number is 9 , and

the value of the second number is 8 .

In the question ,

statements about two numbers is given ,

let the first number be x ,

let the second number be y .

According to the first statement " One number is one more than a second number "

translating it into the equation form , we get

x=y+1      ...(i)

According to the second statement which states " Five times the first is 3 less than 6 times the second "

translating it into the equation form , we get

5*x = 6*y - 3

5x = 6y - 3

Substituting the value of x from equation (i) , we get

5(y+1) = 6y - 3

5y + 5 = 6y - 3

6y-5y = 5+3

y = 8 ,

substituting  y=8 in the the equation (i) ,

x = 8 + 1

x = 9

hence the first number = 9  and the second number = 8 .

Therefore , the value of the first number is  9, and

the value of the second number is 8 .

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Prove that x = 50 in the following equation: 1/5x – 5 = 5

Write the equation:

1/5x – 5 = 5

Add 5 to both sides:

1/5x – 5 + 5 = 5 + 5

1/5x = 10

Multiply each side by 5:

5 × 1/5x = 10 × 5

–5 + 5 cancels out, leaving you with:

1x = 10 × 5

1x = 50

Divide both sides by 1 to get x:

1x/1 = 50/1

The 1 cancels out:

x = 50/1

Answer:

x = 50 ✔

Check your work by plugging in 50 as x:

1/5x – 5 = 5

1/5 × 50 – 5 = 5

Multiply:

1/5 × 50/1 – 5 = 5

50/5 – 5 = 5

Get rid of the fraction by dividing:

50 ÷ 5 = 10

10 – 5 = 5

Subtract:

10 – 5 = 5

5 = 5 ✔

I have just proven that x = 50 because the answer I got when I checked my work was balanced. Hope that helps! Have an amazing rest of your day! :)

well, the bill was $59.17, if we round it by the "tens", the closest to 59 is 60, since 59 is farther from 50 but closer to 60, so it rounds up to 60

[tex]50\stackrel{farther}{\rule[0.35em]{18em}{0.25pt}59.17}\stackrel{closer}{\rule[0.35em]{2em}{0.25pt}}60 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 60}}{\left( \cfrac{15}{100} \right)60}\implies 9[/tex]

Answer:

False

Step-by-step explanation:

Scale copies are indicated by proportional changes in the lengths of the sides of a figure. in this image, we can see that the bottom side of the figure is different while the shorter segments on each figure are the same length. Because of this, the answer is False as they can not be scale copies.

Using percentages we can conclude that the total commission the salesman gets is of $540.

So, the total commission:

5% of 10,000 -

8% of remaining (10,500 - 10,000 = 500) $500 -

Total commission: $500 + $40 = $540

Therefore, using percentages we can conclude that the total commission the salesman gets is of $540.

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c = All real numbers are solutions.

How is the equation 8(c - 9) = 6(2c - 12) - 4c solved?

8(c - 9) = 6(2c - 12) - 4c

8c- 72 = 12c- 72- 4c

8c- 72 = 8c - 72

0=0

L.H.S = R.H.S

Both sides are equal and this stands true for all real number values as c.

For example:

Let c = 10

8(10) - 72= 8(10) - 72

8 = 8

L.H.S = R.H.S

What are real numbers?

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The ordered pairs (x, y) which are the solutions to the equation 4x - 5y = 24 are option A (6, 0), option C (1, -4) and option D (-9, -12)

Given,

The equation: 4x - 5y = 24

We have to find the ordered pairs in the form (x, y) which are the solutions to the equation:

Lets check:

Option A: (6, 0)

Substitute this in the equation:

We get

4 × 6 - 5 × 0 = 24

24 - 0 = 24

24 = 24

(6, 0) satisfies the equation.

Option B: (4, 8)

Substitute this in the equation:

We get

4 × 4 - 5 × 8 = 24

16 - 40 = 24

-24 ≠ 24

(4, 8) does not satisfies the equation.

Option C: (1, -4)

Substitute this in the equation:

We get

4 × 1 - 5 × -4 = 24

4 - (-20) = 24

4 + 20 = 24

24 = 24

(1, -4) satisfies the equation

Option D: (-9, -12)

Substitute this in the equation:

We get

4 × -9 - 5 × -12 = 24

-36 + 60 = 24

24 = 24

(-9, -12) satisfies the equation

Therefore, the solutions for the equation 4x - 5y = 24 are option A (6, 0), option C (1, -4) and option D (-9, -12)

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The cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.

The formula for converting currencies is Original Currency / New Currency = Exchange Rate.

Given:

Cost of 7 t-shirts at a special deal = $97.93

Now, she wants to purchase 5 t-shirts for her family members at this special rate.

Total Cost of 5 shirts in dollars = (97.93 * 5)/7 = $69.95

The exchange rate of the currency is 1 U.S. Dollar = 8.6964 Krona

So, $69.95 = (69.95 * 8.6964)/1 = 608.313 Krona

Therefore, the cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.

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Inversely proportion - The work out value of R and A is 3.6 and 2 respectively.

What is inversely proportion?

They are said to be inversely proportional when one quantity's value rises relative to another's decline or vice versa. It implies that the two quantities behave inherently differently. For instance, time and speed have an inverse relationship. The time decreases as you increase the speed. Inverse proportion, varying inversely, inverse variation, and reciprocal proportion are additional terms used here to describe this kind of proportion.

Given, R [tex]\alpha[/tex] 1/A

R = k/A

When R = 12 and A = 1.5

12= k× 1.5

k= 18

Now, when A=5, R= 18/5 = 3.6

And when R= 9, A = 18/9=2

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I hope this helps

The image is (−8,−1). See explanation.

Explanation:

To find an image of P(x,y) in translation Ta,b you add a and b to x and ycoordinates respectively, so the image is:

Ta,b(x,y)=(x+a,y+b)

Here we can write that:

T−3,−2(−5,1)=(−5−3,1−2)=(−8,−1)

Answer:

No

Step-by-step explanation:

In order to have the same ratio, it would have to be 2:3 and 4:6 because you divide it by 2

The number positioned at point A is -4.25.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to compare two numbers such as 4 and 1. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

In this scenario, the given number line uses a scale of 1:0.25. Therefore, the number (numerical value) that is placed at point A is given by:

Point A = -4.5 - 0.25

Point A = -4.25.

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Answer:

The area of Ava's closet is 2 square feet.

Step-by-step explanation:

The area of the bedroom is 36 and it is 6 times as many square feet as her closet. They are basically saying that the closet has 1/6th the area of the bedroom.

Now we can form an equation to find the area of her closet.

36 ÷ 6 = 6

So, therefore, the area of the closet is 6 square feet.

We know the width of the closet, which is 3 feet. Since the formula of area for her closet is Length × Width, we can form an equation for this.

X in this equation is what we are trying to solve for, which is the length of the closet.

X = 6 ÷ 3

X = 2

So, therefore, the area of Ava's closet would in the end be 2 square feet.

Let me know if you have any questions! :)

Answer:

see explanation

Step-by-step explanation:

since QR ≅ RS , the triangle is isosceles with base angles congruent, so

∠ Q = ∠ S , that is

8x - 17 = 5x + 1 ( subtract 5x from both sides )

3x - 17 = 1 ( add 17 to both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Then

∠ Q = 8x - 17 = 8(6) - 17 = 48 - 17 = 31°

∠ R = 19x + 4 = 19(6) + 4 = 114 + 4 = 118°

∠ S = 5x + 1 = 5(6) + 1 = 30 + 1 = 31°

Based on the height climbed, and the yards climbed per feet, the distance west you would have moved from the foot of the hill is 66 yards

For every 2 feet that you climb higher, you would be moving about 11 yards to the west.

This means that the distance climbed is directly proportional to the number of yards to the west.

Every 2 feet that one climbs higher will meant they move 11 yards to the west so the yards to the west for 12 feet is:

=  12 / 2 x 11

= 6 x 11

= 66 yards

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The number of calories in 6 cups of cereal are 960 calories.

Given that:-

Number of calories in 3/4 cups of cereal = 120 calories

We have to find the number of calories in 6 cups of cereal.

We will use the unitary method in this question.

Number of calories in 1 cup of cereal = 120*(4/3) = 160 calories

Hence,

Number of calories in 6 cups of cereal = 160*6 = 960 calories

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From the given graph, the numeric values of the expressions are given as follows:

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

On the graph of the function, the equivalent to this is that we have to find where the x-axis has the value, and find the value of y for which the function passes through the y-axis.

From the graph, when x = -1, f(x) passes the point at y = 12, hence f(-1) = 12.

For the second item, applying the same logic, we have that:

Hence:

f(1) - g(1) = 10 - 2 = 8.

For the third item, we have to look at the graph of g(x), and find the value of x when y = 4, hence g(x) = 4 when x = 2.

For the fourth item, the functions intersect at point (3,8), hence f(x) = g(x) when x = 3.

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The answer is 3.4

Because the 3 is in the tenths place. Since 6 is greater than 5 it gives 1 to the 3 which makes it a 4.

Considering the numerical representation of integers with n bits, it is found that 8 bits would have to be set aside in order to store the number of high school students taking CS105 across the nation.

For this problem, we work with unsigned numbers, excluding negatives, as the number of students is a discrete amount that starts with 0 and increases by 1 for each new student.

For unsigned integers with n bits, we have that:

For this problem, we want to represent an amount of 220, hence the number of bits needed is found as follows:

2^n - 1 ≥ 220

2^n ≥ 221

log2(2^n) ≥ log(2)(221)

n ≥ 7.8.

The number of bits cannot be a decimal amount, hence n is rounded up, and thus, 8 bits are needed to represent the amount.

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Answer:

The answer is 1

the slope of the line on the graph is 3 .

Slope is calculated by dividing the "vertical change" by the "horizontal change" between any two distinct points on a line. The ratio can alternatively be expressed as a quotient, which yields the same result for any two separate locations on the same line ("rise over run"). A negative "rise" indicates a falling line. A road surveyor may judge that the line is useful, or it may show up in a diagram of a road or a roof as a description or a design. The steepness, incline, or grade of a line can be measured using the slope's absolute value. A slope with a larger absolute value denotes a steeper line.

to find the slope of the graph we will take two points which lies on the same line i.e. they must be collinear .

the points i m choosing is (-2,0) and (-1,3)

now for finding the slope we will use the formula

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

m = (3 - 0 ) / (-1+2)

m = 3 / 1

m = 3

so the slope of the line on the graph is 3 .

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166.25E + 4500 cells will be present in the sample after 5 days.

Given,

Cells 24% compounded continuously,

A sample of the virus has 125 cells.

To find:

No cells will be present in the sample after 5 days

Solution:

a = p ( 1 + r/n)nt

a = 125 ( 1 + 24/24)^24*5

a = 125(2)^120

a = 125 * 1.3292279957849E+36

a = 166.25E + 4500

166.25E + 4500 cells will be present in the sample after 5 days.

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The nonlinear system of the equation has two solutions as it intersects at two points.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

From the given figure we observe that the straight line intersects the parabolic curve at two distinct points, Therefore this nonlinear system of equation has two solutions.

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after simplifying the logarithm expression log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24, we get the result as log₆ 36.

We are given the logarithm expression as:

log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24

Now, we can also write 2log₆ 3 as:

2log₆ 3 = log₆ 3²

So, the logarithm expression will become:

log₆ 8 + log₆ 3² + log₆ 12 - log₆ 24

Now, we will use the property that is:

logₐ x + logₐ y = logₐ (x × y)

So, we get the logarithm expression as:

log₆ ( 8 × 3² × 12   / 24)

=log₆ (8 × 9 × 12  / 24)

= log₆ (36)

= log₆ 36

Therefore, after simplifying the logarithm expression log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24, we get the result as log₆ 36.

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The approximate number of grains of salt it would take to reach the height of Mt. Everest is; 0.2963 * 10⁸

We are given;

Approximate length of a grain of salt = 9.8 * 10⁻⁴ ft

Approximate height of Mt. Everest = 2.9035 * 10⁴ ft

Now, we want to know the approximate number of grains of salt it would take to reach the height of Mt. Everest. To get this it means we have to divide the Approximate height of Mt. Everest by the Approximate length of a grain of salt.

According to Laws of exponents, we know that;

x³/x² = x^(3 - 2) = x¹

Thus;

Approximate number of grains of salt it would take to reach the height of Mt. Everest = (2.9035 * 10⁴)/(9.8 * 10⁻⁴) = (2.9035/9.8) * (10⁴⁻⁽⁻⁴⁾) = 0.2963 * 10⁸

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Hello!

To find f(12):

 ⇒ must plug in '12' into the x's position in the equation

  [tex]f(12)=-2(12) +1=-24+1=-23[/tex]

Hope that helps!

The value of x that makes this equation (X-2)/2= (X+4)/4  to be true is 8.

An equation ca be described as the mathematical terms which can contains different digits as well we a as alphabet and it can simplified so that a particular expression or term can be found, in the given equation we were told to find the value of x by simplify the equation which is done below.

(X-2)/2= (X+4)/4

Then if we cross multiply we will have

(4x - 8) =(2x+8)

then we can simplify further and collect the like terms which is

2x=16

x=8

There, the correct option is B

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The value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

It is given that:

The quadratic equation is:

y² = 144

As we know, the polynomial equation is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

Taking square root on both sides:

y = ±√144

y = ±12

Thus, the value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.

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