A line passes through the points (5, 6) and (6, 9). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
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Answer:

Step-by-step explanation:

The value of 5x - 2y + 3z when x = 7 , y = 11 , z = -1 is 10.

Expression

An expression, in math, is a sentence with a minimum of two numbers and at least one math operation in it.

Given that:-

Expression : 5x -2y + 3z

x = 7, y = 11 , z = -1

We have to find the value of 5x - 2y + 3z

According to the data given in the question, we can write,

The value of the expression 5x - 2y + 3z is:-

5*(7) -2*(11) + 3*(-1) = 35 -22 - 3 = 35 - 25 = 10.

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Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

The corrected mean and median, respectively, are 557.3 and 557.

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Answer:

8x-23

Step-by-step explanation:

10x-2x=8x, and since the 23 was in the parenthesis that was being subtracted, then the 23 gets subtracted.

Answer: Elisa made the greater number of withdrawals

Step-by-step explanation:

140/20=7

270/45=6

Answer: 6 hours

Step-by-step explanation: The distance is 294 miles. The speed is 49 miles per hour. In that case, we divide 294 by 49, which gives us 6.

There are 11 questions worth 5 points and 3 questions worth 15 points.

To find the correct number of questions:

Let, 5-point questions are x and 15 marks questions are y.

The total points are 100 so the other equation will be:

Now, multiply equation (1) by 5 and then subtract it by equation (2) as follows:

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

Now,

So, questions worth 15 marks are 3 then, and questions worth 5 marks will be 14 - 3 that is 11.

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

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Answer:

-3.4 or -17/5

Step-by-step explanation:

3 and 2/5= 17/5 or 3.4

-7 and 1/5 = -34/5 or -6.8

The equation that relates the ages is as follows:

G = S + 5

Sara is 5 years younger than Geoff.

The equation that can be used to relates the age of Sara S and the age of Geoff G is as follows:

where

Therefore, Sarah is 5 years younger than Geoff.

The equation that relates the ages is as follows:

G = S + 5

Therefore, Geoff is 5 years older than Sarah. In other words, Sarah is 5 years younger than Geoff.

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The equation used to represent the context is 1041.50 + 62.75p = 2045.50.

From the information, they rented a bus for $1041.50 and budgeted $62.75 per player for meals.

Therefore, the equation will be:

1041.50 + (62.75 × p) = 2045.50

1041.50 + 62.75p = 2045.50

Therefore, the equation will be 1041.50 + 62.75p = 2045.50.

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We can the slope of the line using:

m = (y 2 - y 1)/ (x 2 - x 1) where, m is the slope of the line.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes.

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For the given condition- If the earth reversed its direction of spin. Then,

The Earth is constantly in motion. Every day, the Earth completes one full rotation around its axis. The axis is an imaginary line that runs through the earth from the North Pole to the South Pole.

Some key features regarding the Earth's rotation are-

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The complete question is -

If you are standing at the Earth's North Pole.

For this question choose as many answers as are correct. if the earth reversed its direction of spin

Answer: 18.84 cm

circumference = 2πr, where r is the radius.

radius is half of the diameter.

6/2 = 3 so radius is 3

2x3.14x3= 18.84 cm

hope it helps.

The length of the pen in the drawing will be 2 millimeters.

As we can't create a real-life dimension in a  small sheet of paper,  we opted for a small scale that covers up the large length.As we are given, the scale of the drawing is 1 millimeter: 10 meters, which is 1 millimeter for every 10 meters

As we have been given that the  actual  size of the goat pen  is 20 meters, so the length of the pen in the drawing is =  20*(1/10)

                                                                                  =   2 millimeters

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'

None of Chen and Mia have got the solution right for the given expression.

It is given that two students are asked to write an equivalent expression for (5v - 3 ) × 2.

We have to find out that which of the both students have got it correct ?

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.

As per the question ;

The expression is (5v - 3 ) × 2.

Let's solve this equation to find out who of Chen and Mia is correct.

So ;

(5v - 3) × 2

= (5v  × 2) - (3 × 2)

= 10v - 6

So ; None of Chen and Mia is correct.

Thus , none of Chen and Mia have got the solution right for the given expression.

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Answer: Both Chen, and Mia are correct.

Step-by-step explanation:

The expression they gave us:

(5v^-3)^2.

Mia: 25/v^e

Chen: 25v^1

Now,

5v^-3)^2

Step 1: (5v^-3).= (5^2)v^3x2
Step 2: (5x5)v^3x2=25v^3x2
Step 3: 25v^-6. As you see Chen is correct. But..

Step 4: 25/1 x 1/v^6= 25/v^6

That also makes Mia to be correct.

So, in this problem there are two answers.

= 25v^-6, and 25/v^6.

By reading the given graph, we conclude that:

-8*f(1) - 4*g(4) = -8

Here we have two graphed functions, f(x) which is the blue one, and g(x) which is the purple one.

We want to find the value of:

-8*f(1) - 4*g(4)

So first we need to find the values of f(1) and g(4), and to do that, we need to use the given graphs.

On the graph we can see that:

f(1) = -2

g(4) = 6

Replacing that in the expression we get:

-8*f(1) - 4*g(4) = -8*-2 - 4*6 = 16 - 24 = -8

Then, by reading the given graph, we conclude that:

-8*f(1) - 4*g(4) = -8

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The number of times that blue will be expected will be 100 times.

It should be noted that from the information given, the spinner is divided into four equal sections labeled yellow, green, red, and blue.

It simply means that each color has a 1/4 chance for each scenario.

Therefore, the number of times that blue will be expected will be:

= 1/4 × 400

= 100 times

Therefore, the number of times that blue will be expected will be 100 times.

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A spinner is divided into four equal sections labeled yellow, green, red, and blue. If the spinner is spun 400 times, how many times would you expect to get blue?

Answer:

Step-by-step explanation:

e

The number of pages read by Soua in 10 minutes are 26.7 pages.

It is given in the question that Soua can read 8 pages in 3 minutes.

We have to find the number of pages that she will she read in 10 minutes.

We will use the unitary method for this question.

The method by which we find out the value of one unit and further use it to find the value of multiple units is known as the unitary method.

Pages read by Soua in 1 minute = 8/3 pages

Hence, we can write,

Pages read by Soua in 10 minutes = 10*(8/3) = 80/3 pages = 26 and(2/3) pages = 26.667 pages ≈ 26.7 pages.

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The total amount that she will have to pay back at the end of 10 months is $11,385.864.

We have Sophia .who borrowed $11,020.

We have to determine the total amount that she will have to pay back at the end of 10 months.

The Simple interest can be calculated using the formula -

S.I. = (P x R x T)

where -

P = Principle amount

R = Rate of interest

T = time in years

According to the question -

P = $11020

R = 4%

T = 10 months = 0.83 years

Therefore -

Interest = (P x R x T) = (11020 x 0.04 x 0.83) = $365.864

Now -

Interest = Total amount - Principle

Total Amount = Interest + Principle = 11020 + 365.864 = $11,385.864

Hence, the total amount that she will have to pay back at the end of 10 months is $11,385.864.

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Answer:

3.435973837*10^10

Step-by-step explanation:

4 to the 7th power is 16384

and 8 to the 7th power is 2097152

multiplied by each other is 3.435973837*10 to the 10th power

if you have to round to the nearest 10th the answer is 3.44

There are 4 liters of solution are needed for the 10% acid solution.

Unitary method:

Unitary method is the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Given,

In a chemistry class, 8 liters of a 4% acid solution must be mixed with a 10% acid solution to get a 6% acid solution.

Here we need to find how many liters of the 10% acid solution are needed.

First, we have to convert the percentage into decimal,

4% = 4/100 = 0.04

10% = 10/100 = 0.10

6% = 6/100 = 0.06

Let x be the required liter of solution.

So, based in the given details,

We have to write the equation as,

=> 0.04*8 + 0.10x = 0.06(8+x)

=> 0.32 + 0.10x = 0.48 + 0.06x

=> 0.10x - 0.06x = 0.48 - 0.32

=> 0.04x = 0.16

=> x = 0.16/0.04

=> x = 4

x = 4 liters of 10% solution is used.

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Jack has left with the 19/8 yards fraction part of material.

In mathematics, yard is the unit of length. we can say that yard is the one of the measurement of length. Conversion of yard in various quantities is as below:

        1 yard = 36 inches

        1 yard = 3 feets

        1 yard = 0.914 meters

For the question given,

If we have to find the remaining material that has been left we must find the difference between the two i.e. used and purchased material by simply subtracting them.

So, Material purchased = 3 yards

      Material used = 5/8 yards

now, material left = Material purchased - material used

                             =  3 - 5/8

                             = 19/8 yards

Thus, Jack has left with the 19/8 yards material.

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Answer:

x = 8

Step-by-step explanation:

Solve for x:

-2 x + 16 = 4 (x/4 - 2)

Put each term in x/4 - 2 over the common denominator 4: x/4 - 2 = x/4 - 8/4:

-2 x + 16 = 4 (x/4 - 8/4)

x/4 - 8/4 = (x - 8)/4:

-2 x + 16 = 4 ((x - 8)/4)

(4 (x - 8))/4 = 4/4×(x - 8) = x - 8:

-2 x + 16 = x - 8

Subtract x from both sides:

(-2 x - x) + 16 = (x - x) - 8

-2 x - x = -3 x:

-3 x + 16 = (x - x) - 8

x - x = 0:

-3 x + 16 = -8

Subtract 16 from both sides:

(16 - 16) - 3 x = -16 - 8

16 - 16 = 0:

-3 x = -16 - 8

-16 - 8 = -24:

-3 x = -24

Divide both sides of -3 x = -24 by -3:

(-3 x)/(-3) = (-24)/(-3)

(-3)/(-3) = 1:

x = (-24)/(-3)

The gcd of -24 and -3 is -3, so (-24)/(-3) = (-3×8)/(-3×1) = (-3)/(-3)×8 = 8:

Answer: x = 8

The ending number is nine more than the starting number.

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Answer:

Question 27

[tex]\textsf{(a)} \quad -\dfrac{6}{5}[/tex]

[tex]\textsf{(b)} \quad \dfrac{1}{10}[/tex]

[tex]\textsf{(c)} \quad \dfrac{4}{5}[/tex]

Question 28

[tex]\textsf{(a)} \quad \dfrac{6}{0}=\textsf{und\:\!efined}=\textsf{no gradient}[/tex]

[tex]\textsf{(b)} \quad -\dfrac{3}{10}[/tex]

[tex]\textsf{(c)} \quad \dfrac{3}{10}[/tex]

Step-by-step explanation:

The gradient of a straight line can be found by dividing the difference in the y-coordinates by the difference in the x-coordinates between two points on the line.

A positive gradient slopes up from left to right.

A negative gradient slopes down from left to right.

[tex]\boxed{\begin{minipage}{4.3cm}\underline{Gradient Formula}\\\\$m=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\end{minipage}}[/tex]

We can use the formula to find the gradients, or we can simply calculate the change in y and change in x by looking at the graph.

Example:

If we take line (a) from question 27 as an example.

Therefore, the gradient is -6/5.

Using the gradient formula, define two points on the line:

Input the points into the formula:

[tex]\textsf{Gradient}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-6}{5-0}=-\dfrac{6}{5}[/tex]

Solutions

Question 27

(a)  The gradient is -6/5, as calculated above.

(b)  The change in y is 1 unit and the change in x is 10 units. The line slopes up so the gradient is positive.  Therefore, the gradient is 1/10.

(c)  The change in y is 4 units and the change in x is 5 units. The line slopes up so the gradient is positive.  Therefore, the gradient is 4/5.

Question 28

(a)  The change in y is 6 units and the change in x is 0 units. Therefore, the gradient is undefined since anything divided by 0 is undefined.  Therefore, this line has no gradient.

(b)  The change in y is 3 units and the change in x is 10 units. The line slopes down so the gradient is negative.  Therefore, the gradient is -3/10.

(c)  The change in y is 3 units and the change in x is 10 units. The line slopes up so the gradient is positive.  Therefore, the gradient is 3/10.

Attachment

I have marked the change in y (green) and the change in x (blue) for line (c) on both graphs.

Using the function rule y=2x -2 the values in the given table are as follow:

x        y

0      -2

1       0

2       2

3       4

4       6

As given,

Given function:

y=2x - 2

Substitute the value of x in the given function y=2x - 2

x=0

⇒y=2(0) -2

      =-2

x=1

⇒y=2(1) -2

      =0

x=2

⇒y=2(2) -2

      =2

x=3

⇒y=2(3) -2

     =4

x=4

⇒y=2(4)-2

     =6

Therefore, using the function rule y=2x -2 the values in the given table are as follow:

x        y

0      -2

1       0

2       2

3       4

4       6

The complete question is :

Fill in the table using this function rule.

y=2x-2

x      y

0

1

2

3

4

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Answer:

1st Question 24 ÷ (-6) = -4

2nd Question -15 ÷ 0.3 = -50

3rd Question -4 ÷ (-20) = 0.2

This should be correct. I used a calculator Lol. :3.