Topic 6: Writing Linear Equations
26. Write a linear equation that passes through
the point (-6, 1) with a slope of 1/2

Step-by-step explanation:

[tex]3g = d[/tex]

[tex] \frac{3g}{3} = \frac{d}{3} \\ [/tex]

[tex]g = \frac{d}{3} \\ [/tex]

[tex]{ \purple{ \bold{g = \frac{d}{3}}}} [/tex]

Step-by-step explanation:

The given formula is [tex]{ \orange{ \sf{3g = d}}}[/tex]

In order to get formula for g, let us divide 3 on both the sides.

[tex]{ \orange{ \sf{ \frac{ \cancel3}{ \cancel3}g}}} = { \orange{ \sf{ \frac{d}{3}}}} [/tex]

Therefore, [tex]{ \boxed{ { \tt{g = \frac{d}{3}}}}} [/tex]

Answer:Let the age of son be x.

Thus, age of father is 4x.

After 5 years, their ages will be x+5 and 4x+5 years respectively.

As per the question, we have

4x+5=3(x+5)

⇒4x+5=3x+15

⇒x=10

Age of father will be 4x=4×10=40 years.

Thus when son is 10 years old, father is 40 years.

Step-by-step explanation:

After 3 years father's age will be five times that of his son. Father age will be 40 years and son age will be 8 years .

Given,

Present age of father = 37 years.

Present age of son = 5 years.

Now,

Let the number of years be x after which the fathers age will be 5 times the age of his son.

So,

Ages after 3 years  ,

Age of father = 40 years

Age of son = 8 years.

Thus age of father is 5 times the age of son.

Therefore after 3 years father's age will be five times that of his son.

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The volume of the prism with area 41 cm^2 and height 11 cm is 451 cm^3

Volume refers to three dimensional solid. The three dimensions include some elements which are

While area is 2 dimensional which is solved by length * width

In the figure the area is already solved to be 41 cm^2 and height is given to be 11 cm

The volume of the solid is given

= length * width * height

= area * height

= 41 * 11

= 451 cm^3

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The insurance cost now is £449.204.

Given:

Brian pays £465. 98 a year on his car insurance. The insurance company reduces the price by 3. 6%.

Insurance  = 465.98*3.6%

= 465.98*3.6/100

= 465.98*36/10*100

= 46598/100 * 36/1000

= 46598*36 / 100000

= 1677528/100000

= 16.77528

Insurance cost now = 465.98 - 16.77528

= £449.20472

Therefore the insurance cost now is £449.204.

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Answer: ( 4 , 8 )

Step-by-step explanation:

3x - 2y = -4

y = 2x

Substitute the second equation into the first

3x - 2(2x) = -4
3x - 4x = -4
-1x = -4
x = 4

y = 2(4)
y=8

( 4 , 8 )

For the given equation the solution would be

                          [tex]r=-7t-3,\:s=\frac{-6t-7}{3}[/tex]

What is the system of linear equations in three variables?

Three-variable equation systems are only slightly more difficult to solve than two-variable equation systems. Substitution and the use of 3x3 matrices are the two most straightforward methods for solving these types of equations.

The given equations are

                  r - 3s + t = 4 ------------(I)

                  3r - 6s +9t = 5 ---------(II)

                  4r - 9s + 10t = 9--------(III)

from equation (I), we get

                  r = 4 + 3s - t ------------(IV)

Now put the value of 'r' in equations (II) and (III), and we get

               3(4 + 3s - t) - 6s + 9t = 5

               4(4 + 3s - t) - 9s + 10t = 9

Solving the above equations, we get

             3s + 6t + 12 = 5 --------(V)

             3s + 6t + 16 = 9 --------(VI)

 Now isolate the value of 's' from equation (IV), we get

              3s = - 6t + 5 -12

             [tex]s=\frac{-6t-7}{3}[/tex]

Now put the value of 's' in equation (IV), and we get

           [tex]r=4 +3s -t\\r=4+3\cdot(\frac{-6t-7}{3}) -t\\ r=4-6t-7-t\\r=-7t-3[/tex]

Hence, For the given equation the solution would be

                   [tex]r=-7t-3,\:s=\frac{-6t-7}{3}[/tex]

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The equation is y = -3

Since, the line parallel to the line y=5, its slope is zero.

so, the equation has the form

y = constant

it passes through (-2,-3), the equation is

y = -3

Slope of a Line :

In mathematics, a line's slope is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

The net change in the y-coordinate and the net change in the x-coordinate are denoted by the letters Y and X, respectively.

Since the slope of a line is denoted by "m," the formula for the change in y-coordinate with respect to the change in x-coordinate is m = change in y/change in x = y/x.

The slope, intercept, and y-intercept values on the graph of the equation y = mx + c are all equal to m. M and C are real integer values in the slope-intercept version of the linear equation.

Complete question:

find an equation of the line parallel to the line y=5 and passing through -2,-3

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After the conversion, 133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.

In the given question we have to find how many hours and minutes will it take to completely empty the pool which contains 12,000 gallons.

As given that pool empties at a rate of 12 quarts every 2 minutes.

In 12 quarts = empties in 2 minutes

As we know that 1 gallon = 4 quarts

So 1 quarts = 1/4 gallon

In 12 quarts = 12/4 gallon

12 quarts = 3 gallon

So 3 gallon = empties in 2 minutes

So 1 gallon = empties in 2/3 minutes

12,000 gallon = empties in 2/3 ×12,000 minutes

Simplifying

12,000 gallon = empties in 2×4,000 minutes

12,000 gallon = empties in 8,000 minutes

Now converting minutes in hours.

As we know that 1 minute = 1/60 hours

So 8000 minute = 8000/60 hours

8000 minutes = 133 hours 33 minutes

133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.

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Answer:

120[tex]ft^{2}[/tex]

Step-by-step explanation:

4 yards is 12 feet

10(12) = 120

Answer:

120 square feet

1 ) We first need to convert the 4 yards into feet...

1 yard = 3 feet

so 4 yards = 12 feet

2 ) To find area we do length x width...

length = 10

width = 12

10 x 12 = 120

( 120 square feet )

Hope this helps! :)

Answer:

0.96 inches

Step-by-step explanation:

The first step is to find the diameter given the circumference. This is the formula for circumference:

[tex]C=\pi d[/tex]

In terms of d, the formula looks like this:

[tex]d=\frac{C}{\pi}[/tex]

For the softball, the diameter is approximately:

[tex]d=\frac{12}{\pi} =3.82[/tex]

For the baseball:

[tex]d=\frac{9}{\pi } =2.86[/tex]

Find the difference:

[tex]3.82-2.86=0.96[/tex]

The approximate difference in diameters is 0.96 inches!

Answer: 0.96 inches

Step-by-step explanation:

..........................................

[tex]\displaystyle\\Answer: \frac{-11-12i}{15}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\\frac{-7+2i}{3-6i}=\\\\\frac{(-7+2i)(3+6i)}{(3-6i)(3+6i)}=\\\\ \frac{-21-42i+6i+12i^2}{3^2-(6i)^2} =\\\\\frac{-21-36i-12}{9+36}=\\\\\frac{-33-36i}{45} =\\\\\frac{3(-11-12i)}{3(15)} =\\\\\frac{-11-12i}{15}[/tex]

Answer: 89.75

Step-by-step explanation:

So 392.50 is the cost of 2 phones and 6 headphones and 286.00 is the cost of 2 cell phones and three headphones. so 392.50-286.00 is the cost of 3 headphones since you added three headphones to the price. so the price of 3 headphones is 106.50. Then you subtract 106.50 from 286.00 to get the cost of the two cell phones. And you get 179.50. Then, you divide 179.50 in order to get the price of one cell phone and you get 89.75. So the cost of one cell phone is $89.75.

The area of each of the patios is 1600 m².

The mason builds two patios with the same area. One of the patios is square, and the other is rectangular. The rectangular patio is 10 m longer but 8 m less wide than the square patio. We need to find the area of each patio.

Let the side length of the square patio be denoted by the variable "x". The area of the square can be calculated as follows.

A1 = x²

The length and breadth of the rectangular patio is "x + 10" and "x - 8", respectively. The area of the rectangular patio is calculated below.

A2 = (x + 10)*(x - 8)

A2 = x² + 2x - 80

We know that the areas of both patios are equal.

A1 = A2

x² = x² + 2x - 80

2x = 80

x = 40

Hence, the area of each patio is A = x² = 40² = 1600 m².

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Answer:

lo siento soy muy malo para las matemáticas y además soy nuevo en este aplicación

a) The linear equation that represents the total amount of snow, y, after x number of hours is: y = 2 + 0.25x.

b) 3 inches is the amount of snow that is on the ground after four hours.

c) The time until the snow reaches 6 inches is of 16 hours, which is enough to finish the hike, as they usually take at most five hours.

The slope-intercept representation of a linear function is shown by the equation as follows:

y = mx + b

In which the parameters m and b of the linear equation are explained as follows:

Thus the values of these parameters are given as follows:

m = 0.25, b = 2.

The equation that represents the total amount of snow, y, after x number of hours is:

y = 0.25x + 2.

The numeric value of function after four hours is found replacing the lone instance of x on the function by 4, hence:

y = 0.25(4) + 2 = 3 inches.

To find when the amount will be of six inches, we have to solve for x when y = 6, hence:

2 + 0.25x = 6

0.25x = 4

x/4 = 4

x = 16 hours.

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Answer:

Step-by-step explanation:

I'm impressed that they make you do this in H.S.    Linear Algebra.   it's good for more complex math .   so that's why i'm impressed.   Is this an AP class?  

Ax=B is our formula.   we need to know something about x,  it's size

so we look at rows and columns of A,   2x2   , also we need to know about B as well it's also 2x2

so now we know, that   a matrix  A, of  size  2x2,  *x = B of size 2x2

2x2*x=2x2   ....   2x2|2x2   since the two inside number match, we can do this multiplication,  and the two ouside numbers tell us the size of  x... it's also a 2x2.  I know, a lot of explaining to just get 2x2.   Maybe that is obvious, and i'm mansplaining,  :DD  ,  but I don't know what you know.

I'll put big subscripts on my matrix variable so you can see it well.  You understand the subscript is the element location in the matrix , right?  1,1 is just the top left corner element of the matrix.  ect , ect.

so now we need,  a1,1 * x1,1 + a1,2 * x2,1   = 2  in b1,1

then we need   a2,1 * x1,1 + a2,2 * x2,1 = 7  in b2,1

next we need a1,1 * x1,2 + a1,2 * x2,2   = 3  in b1,2

finally we need a2,1 * x2,1 + a2,2 * x2,2   = 8  in b2,2

X =  [tex]\left[\begin{array}{ccc}\frac{3}{2} &1\\\frac{1}{2} &2\end{array}\right][/tex]   I did that by observation.   have you learned any RREF methods yet?

The equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2

The first point = (6, -12)

The second point = (16, -10)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line m = (-10 -(-12) / (16 - 6)

= (-10 +12) / 10

= 2/10

= 1/5

The slope intercept form is

y = mx + b

Consider the point (6, -12)

-12 = (1/5)6 + b

-12 = 6/5 + b

b = -12 - 6/5

b = -13.2

The equation will be

y = 1/5x - 13.2

Hence, the equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2

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a) The revenues for both items will be the same after 1 day.

b) The graph with the solution is given by the image at the end of the answer.

The functions defining the revenues for the selling of x brownies and of x cookies are presented as follows:

The revenues will be the same after x days, for which:

B(x) = C(x).

Hence:

2x² + 8x - 4 = 2x + 4

2x² + 6x - 8 = 0.

x² + 3x - 4 = 0.

The quadratic function can be factored as follows:

(x + 4)(x - 1) = 0.

Applying the Factor Theorem, the solutions are given as follows:

The graph shows the intersection of the two curves, B(x) and C(x).

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The approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25

Given,

Number of trials of the simulation were performed = 25

Number of set of simulated shots = 10

We have to find the approximate probability that a 47% shooter makes  5 or more shots in 10 attempts;

The dots in the 5 shot mark is 9, 6 shot mark is 2, and 7 shot mark is 1.

Now the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts can be calculated below:

P(x5) = (dots in 5 short mark + dots in 6 shot mark + dots in 7 short mark) / 25

= (9 + 2 + 1) / 25

 = 12 / 25

Therefore, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25

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"If we assume that 57% of Americans says that GM foods are generally unsafe to eat, then there is an 8.8% chance that random sample results will show 60%or more who says that GM foods are generally unsafe to eat" is valid interpretations of this p-valid.

Given info;

Genetically modified foods: A 2016 Pew Research survey found that 56% of Americans believe that eating genetically modified (GM) food is generally harmful. This month, a survey of 500 randomly chosen American citizens found that 60% believe gm foods are typically dangerous to consume. We examine the possibility that more people than 56% believe that eating GM food is generally unsafe this year. 0.084 is the p-value.

If we assume that 57% of Americans say that GM foods are generally unsafe to eat, then there is an 8.8% chance that random sample results will show 60% or more who say that GM foods are generally unsafe to eat” is a good interpretation of the P-value. The P-value is the probability that results will be as or more extreme than those from the latest survey if opinions have not changed since 2014.

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Answer:

y= 50x + 200

Step-by-step explanation:

He collected 936 US stamps.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Total number of stamps - 1170

US stamps - 4 times as many as foreign stamps

Let x be the number of foreign stamps.

4x as the number of US stamps.

To find the number of US and foreign stamps Peter collected, we are going to represent the given data as:

x + 4x = 1170.

x + 4x = 1170

5x = 1170

5x/5 = 1170/5

x = 234

Peter collected 234 foreign stamps.

US stamps = 4x

= 4(234)

= 936

Peter collected 936 US stamps.

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There are 20 players are not in 5th grades.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

Total players in the class = 80

And, 75% of the players in the basketball program are 5th graders.

Now.

Number of players in the basketball program are 5th graders = 75% of 80

= 75/100 x 80

= 60

Thus, Number of players are not in 5th graders = 80 - 60

                                                                          = 20

Therefore, There are 20 players are not in 5th grades.

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The equation of line is y = -1/4x + 11/12.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

line passing through P(-1, 3) that is perpendicular to y = 4x - 7.

Now, the slope of perpendicular line is

slope= -1/ 4

and, the lines passes through (-1, 3)

Thus, using slope- intercept form

y- 3 = m( x + 1)

y- 3 = -1/4 ( x+ 1)

y- 3 = -1/4x - 1/4

y = -1/4x + 11/12

Hence, the equation of line is y = -1/4x + 11/12

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Answer: 3p-q-2

Step-by-step explanation:

Perimeter is the sum of all the sides.

Add the known sides together:

(p-3) + (2p+3q) = 3p + 3q - 3

To find the unknown side, subtract the sum of the 2 known sides from the perimeter (combine like terms):

(6p+2q-5) - (3p+3q-3) = 3p-q-2

Add all 3 sides together as a check of your answer!

For the given condition the x distribution is normal. Option B is correct.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

n=64

√n=8

μ=8

σ=16

The sample size (n > 30) is enough. Using the Central Limit Theorem

¯X∼N(8,16²/64)

The formulas below give the mean and standard deviation of the mean value of x:

The sampling distribution of x has a mean value of 8.

The following equation gives the sampling distribution's standard deviation:

=σ/√n

=16/√64

=16/8

=2

The sample distribution's standard deviation is 2.

Yes, this distribution can be regarded as normal as it roughly follows the normal distribution (By using CLT)

Thus, for the given condition the x distribution is normal. Option B is correct.

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