Solve the following system of equations using the substitution method.
-X + 9y = -5
x - 5y = 1

Answer:

The equation of the parallel line is x + 2y = a

Step-by-step explanation:

* lets revise the general form of the linear equation

- The general form of the linear equation is ax + by + c = 0, where

 a , b , c are real numbers

- The linear equation represented by a line its slope = -a/b and

  intersects the y-axis at point (0 , -c/b) means y-intercept = -c/b

- The parallel lines have equal slopes and different y-intercepts

* Now lets solve the problem

- There is a line with equation x + 2y = 7

- Put the equation in the general form

∵ x + 2y = 7 ⇒ subtract 7 from both sides

∴ x + 2y - 7 = 0

∵ ax + by + c = 0 is the general form of the linear equation

∴ a = 1 , b = 2 , c = -7

∵ The slope of the line is -a/b

∴ The slope of the line -1/2

- We need to find the equation of the parallel line which has the

  same slope

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the line is -1/2

∵ The slope depends on a and b

∴ The line has the same value of a and b

∵ a = 1 and b = 2

∵ ax + by + c = 0

∴ The equation of the line is x + 2y + c = 0

- To find c substitute x and y in the equation by the coordinates of

  any point on the line

∵ The line passing through point (a , 0)

- Substitute x by a and y by 0

∴ a + 2(0) + c = =

∴ a + c = 0 ⇒ subtract a from both sides

∴ c = -a

- Substitute the value of c in the equation by - a

∴ The equation of the line is x + 2y - a = 0 ⇒ add a for both sides

∴ The equation of the line is x + 2y = a

* The equation of the parallel line is x + 2y = a

- They are equal in slopes and different in y-intercepts

Final answer:

The equation of the line passing through the point (a, 0) and parallel to x + 2y = 7 is y = -0.5x + 0.

Explanation:

To find the equation of a line parallel to the line x + 2y = 7 and passing through the point (a, 0), we need to determine its slope. This can be done by rearranging the given equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

First, we rewrite the given equation as 2y = -x + 7 and then divide everything by 2 to get y = -0.5x + 3.5. Since the line we're looking for is parallel to this line, it will have the same slope of -0.5.

So, the equation of the line passing through (a, 0) and parallel to x + 2y = 7 is y = -0.5x + 0.

Answer:

The middle option.

Step-by-step explanation:

This is because the points on each triangle are equidistant from the imaginary line in between the two triangles.  It isn't the first option because that is a rotation, and it isn't the third right option because that is a translation.

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Answer:

Improper fraction (-81t/ 4s)

Mixed number (-20 1/4) (t/s)

Step-by-step explanation:

Multiply the numerators

9(9t) = 81t

Multiply the denominators

4s* (-1) = -4s

Put the numerator over the denominator

81t / -4s

If they want the answer as an improper fraction  -81t/4s

If they want a mixed number

81/4 = 20 with 1 left over

20 1/4

Then multiply by (-t/w)

(-20 1/4) (t/s)

Answer:

Step-by-step explanation:

Plug the numbers into the formula.  It might help you to know that 1 newton = 1 kg-m/s^2 .

2050000 kg-m/s^2 = 40000 kg * a

a = 2050000 / 40000 (m/s^2) = 51.25 meters / second^2

Answer:

2m^2 / n.

Step-by-step explanation:

4m^3/n^2 / 2m/n.

Invert the last term and multiply:

= 4m^3 / n^2 *  n/2m

= 4m^3 n / 2mn^2

= 2m^2 / n.

Answer:

2m^2 / n.

Step-by-step explanation:

Answer: B

Step-by-step explanation:

x^1/2 is equal to √x meaning that the denominator will be the number in front of the √ sign.

so...

x^5/3 y^1/3 will be right

Answer:

Joseph will have to pay $133.20 for the television.

Step-by-step explanation:

740 x 0.6 = 444

444 x 0.3 = 133.2

Answer:

133.20

Step-by-step explanation:

First we need to find the cost of the tv on sale

The discount is 740 * 40%

740 *.4

296

The new price is the original price minus the discount

740 -296

444

Joseph has to pay 30% of the cost

444* 30%

444 *.3

133.2

He will have to pay 133.20

Answer:

(x + 2)(x - 8)

Step-by-step explanation:

You had your signs altered. You want your B to result in -6, not 6.

I am joyous to assist you anytime.

Answer:

[tex]\large\boxed{x=2y^2}[/tex]

Step-by-step explanation:

[tex]y=2x^2\\\\\text{exchange x to y and vice versa:}\\\\x=2y^2\\\\\text{solve for y:}\\\\2y^2=x\qquad\text{divide both sides by 2}\\\\y^2=\dfrac{x}{2}\to y=\sqrt{\dfrac{x}{2}}[/tex]

Answer:

D. [tex]x=2y^2[/tex]

Step-by-step explanation:

We have been given an equation [tex]y=2x^2[/tex]. We are asked to choose the equation that could be solved to get the inverse of given equation.

We know that to find the inverse of a function, we interchange the x and y variables and then we solve for y.

Upon interchanging x and y variables in our given equation, we will get:

[tex]x=2y^2[/tex]

Therefore, the equation [tex]x=2y^2[/tex] can be simplified to find the inverse of our given equation and option D is the correct choice.

Answer:

7000-24x

Step-by-step explanation:

The question states that the car depreciates every month over the 2 years. This means that the value will go down from its original price. So with that we can rule out the last two choices which has addition.

The depreciation is every month, so in 2 years, there are 24 months. We can get the total deduction by multiplying the depreciation amount and the number of months that had passed over 2 years.

So your answer would be:

7000-24x

Answer: Max should read 22 full pages a day, and he will have 16 pages left to read.

Step-by-step explanation:

First, divide 676 by 30. The answer you get is 22.53.

This means that Max should read 22 pages a day.

Next, you should multiple 22 by 30. The answer you get is 660.

Finally, subtract 660 from 676. You will end up with 16.

Answer:

22 R 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

(4/5)n = (2/3)

move 4/5 to the right

n = (2/3)/(4/5)

n = 5/6

The measures of angle POS and angle POQ cannot be determined without further information.

The measures of angle POS and angle POQ can vary depending on the context of the problem or the given information. Without specific details, we cannot determine the exact measures of these angles.

https://brainly.com/question/31186705

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Answer:

Area of circle R = 75π un² or ≈235.5 un²

Step-by-step explanation:

The problem says that m∠TRS = 120º. The total number of degrees in a circle is 360º. 120º is a third of 360º. Therefore, we can prove that the shaded sector is a third of the circle.

The problem then says that the area of the shaded sector is 25π and we have to calculate the area of the entire circle. Since we already know that the shaded sector is a third of the circle, we can simply multiply 25π by 3 in order to calculate the area of t he entire circle.

25π × 3 = 75π.

Area of circle R = 75π un² or ≈235.5 un²

Answer: 75

Step-by-step explanation:

If the measure of TRS is 120, that is 1/3 the total of 360. Meaning the area of the shaded part is 1/3 the area of the full circle. If the area of the shaded part is 25, that means 25 is 1/3 the full area. the equation for that can be (25 = 1/3x) with x being the full area of the circle.

To solve just multiply both sides by the reciprocal of 1/3, which is 3.

25 x 3 = 75, which is your answer.

Answer:

e -8 =x

Step-by-step explanation:

1 = In(x + 8)

To get rid of the natural log, raise each side to the base e

e^1 = e^ (ln(x+8))

e^ln cancels

e^1 = x+8

Subtract 8 from each side

e^1 -8 = x+8-8

e -8 =x

[tex]\bf 3\sqrt{8\frac{1}{4}}~\hfill \stackrel{mixed}{8\frac{1}{4}}\implies \cfrac{8\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{33}{4}} \\\\\\ 3\sqrt{\cfrac{33}{4}}\implies 3\cdot \cfrac{\sqrt{33}}{\sqrt{4}}\implies 3\cdot \cfrac{\sqrt{33}}{\sqrt{2^2}}\implies \cfrac{3\sqrt{33}}{2}[/tex]

We apply the following property:

(x^n)^m = x^(n • m)

Let m = 2

(P^1/2)^2 = P^(1/2 • 2) = P

Follow below steps;

The property of exponents that you must apply to the expression p1/2 to derive p as the result is the power law for fractional exponents. This law states that when raising a number to a fractional exponent, it is equivalent to taking its root.

Example: p1/2 is the same as taking the square root of p, resulting in p.

When dealing with fractional exponents like 1/2, remember that they represent roots, such as square roots in this case.

Answer:

c. The price of grapefruits experienced a reduction 6.01 percentage points greater than the price of pineapples.

Step-by-step explanation:

The original price of Pineapples=$5.15

New price of Pineapples=$3.88

Find change in price of Pineapples

Change in price=original price- new price

[tex]=5.15-3.88=1.27[/tex]

The price of Pineapple was reduced by $1.27

% reduction in price

(reduction value/original value) × 100

[tex]=\frac{1.27}{5.15} *100=24.66[/tex]

=24.66%

The original price of grape fruits=$2.25

New price of grape fruits=$1.56

Change in price of grape fruit

Change in price= original price -new price

[tex]=2.25-1.56=0.69[/tex]

% reduction in price of grape fruits

(reduction value/original value)×100

[tex]=\frac{0.69}{2.25} *100=30.67[/tex]

=30.67%

Answers

The fruit that has its price reduced by a greater percentage is grape fruit

How many percentage points greater = 30.67%-24.66% = 6.01 points

Answer:

The answer is C on Edge 2020

Step-by-step explanation:

I just took a quiz.

Answer:

45

Step-by-step explanation:

every term in the sequence is 3 more than the last, so:

12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45

1 2 3 4 5 6 7 8 9 10 11 12

45 is the 12th term

Answer:

Option b - 45

Step-by-step explanation:

Given : Sequence 12,15,18,21,...

To find : What is the 12th term in the sequence?

Solution :

Sequence 12,15,18,21,... is an arithmetic progression.

Where, first term is a=12

Common difference is d=15-12=3

The nth term of the sequence is

[tex]a_n=a+(n-1)d[/tex]

The 12th term is

[tex]a_{12}=12+(12-1)(3)[/tex]

[tex]a_{12}=12+(11)(3)[/tex]

[tex]a_{12}=12+33[/tex]

[tex]a_{12}=45[/tex]

Therefore, The 12th term of the sequence is 45.

So, Option b is correct.

Answer:

the x value

Step-by-step explanation:

Answer:

3x + 4 = 14

3x = 10

x = 10/3

- 3x - 4 = 14

- 3x = 18

x = -6

x = 10/3; x = -6

Answer:

Two solutions were found :

x=10/3

x=-6

Step-by-step explanation:

|3x+4|=14  

Two solutions were found :

x=10/3

x=-6

Absolute Value Equation entered :

     |3x+4|=14  

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered

     |3x+4| = 14  

Step  2  :

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |3x+4|

For the Negative case we'll use -(3x+4)  

For the Positive case we'll use (3x+4)  

Step  3  :

Solve the Negative Case

     -(3x+4) = 14  

    Multiply

     -3x-4 = 14  

    Rearrange and Add up

     -3x = 18  

    Divide both sides by 3  

     -x = 6  

    Multiply both sides by (-1)  

     x = -6  

    Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

     (3x+4) = 14  

    Rearrange and Add up

     3x = 10  

    Divide both sides by 3  

     x = (10/3)  

    Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

x=-6

x=10/3

Solutions on the Number Line

Two solutions were found :

x=10/3

x=-6

First subtract 17 to both sides (what you do on one side you must do to the other). Since 17 is being added, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

p + 17 - 17 < 19 - 17

p + 0 < 2

p < 2  

For the graph will you have a empty or colored in circle?

If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.

If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.

Which direction will the ray go?

If the variable is LESS then the number then the arrow will go to the left of the circle.

If the variable is MORE then the number then the arrow will go to the right of the circle.

In this case your inequality is:

p < 2

aka p is less then two

This means that the graph will have an empty circle and the arrow will go to the left of 2. (image below)

Hope this helped!

~Just a girl in love with Shawn Mendes

[tex]\huge{\text{Hey there!}}[/tex]

[tex]\text{Question yourself}\bf{\ How\ many\ times\ does\ 20\ goes\ into\ 100?}[/tex]

[tex]\huge{\text{20\ *\ 100 = ?}}[/tex]

[tex]\text{If you remember the steps onto how to solve\bf{\ long\ multiplication}}[/tex]  [tex]\text{then, you should know how to solve this equation just with more steps!}[/tex]

[tex]\huge\boxed{\boxed{\text{Answer: A. 2,000}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\huge\frak{LoveYourselfFirst:)}[/tex]

20 times 100 is 2000.

2 times 1 is 2 and you add on the three zero's in both numbers to the end of the final number.

so, it would be 2000.

[tex]\bf \begin{cases} a+b=-1\\ x+y+z=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} 7a+7b\qquad &+6z+6x+6y\\\\ 7(a+b)&+6(z+x+y)\\\\ 7(a+b)&+6(x+y+z)\\\\ 7(-1)&+6(2)\\\\ -7&+12&\implies 5 \end{array}[/tex]

Answer:

5

Step-by-step explanation:

hihi, so the key to this is manipulating the equations. Realizing that 7a + 7b is just 7*(a+b) makes this fairly simple since you already know what a+b equals and just have to multiply that by 7. Same goes with x, y, and z. 6x + 6y + 6z is the same as 6(x + y + z). Thus, -1 * 7 + 2 * 6 = 5

Answer:

B. X squared is -3 times -3, which is equal to 9.

Step-by-step explanation:

Answer:

No, A″C″B″ is located at A″(1, 1), C″(4, 3), and B″(1, 5)

Step-by-step explanation:

The triangle has vertices A(1,1), B(5,1), C(3,4).

First transformation is reflection over y-axis with the rule

(x,y)→(-x,y)

so,

Second transformation is rotation by 270° counterclockwise with the rule

(x,y)→(y,-x)

so

No, A″C″B″ is located at A″(1, 1), C″(4, 3), and B″(1, 5)

No, A″C″B″ is located at A″(1, 1), C″(4, 3), and B″(1, 5)

Step-by-step explanation:

What program do you guys use to do the fancy stuff that the guy above did, because I gotta do it by paper and it's annoying lol

Answer:

The correct graph is A

Step-by-step explanation:

Let

c ----> the total cost to rent a set of hand tools

h ----> the number of hours for the rental

we know that

The linear equation that represent the problem is equal to

[tex]c=2h+2[/tex] ---> this is the equation of the line into slope intercept form

where

the slope m is equal to

m=$2 per hour

b=$2 ---> the y-intercept (the value of c when the value of h is equal to zero)

therefore

The correct graph is A

see the attached figure

Answer:

18

Step-by-step explanation:

f(x) = 2(x)^2 +5 sqrt(x+2)

Let x =2

f(2) =2(2)^2 +5 sqrt(2+2)

    = 2 *4 + 5 (sqrt(4))

    = 8 + 5*2

    = 8 + 10

   = 18

Answer:

[tex]\dfrac{\sqrt{40}\cdot \sqrt{40}}{2}[/tex]

Step-by-step explanation:

The length of the base is the distance between the points 4+2i and 10+4i, so

[tex]\text{Base}=|10+4i-(4+2i)|=|10+4i-4-2i|=|6+2i|=\sqrt{6^2+2^2}=\\ \\=\sqrt{36+4}=\sqrt{40}[/tex]

The middle point of the base is placed at point

[tex]\dfrac{4+2i+10+4i}{2}=\dfrac{6i+14}{2}=7+3i[/tex]

The length of the height is the distance between the points 5+9i and 7+3i

[tex]\text{Height}=|5+9i-(7+3i)|=|5+9i-7-3i|=|-2+6i|=\sqrt{(-2)^2+6^2}=\\ \\=\sqrt{4+36}=\sqrt{40}[/tex]

So, the area of the triangle is

[tex]A=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{\sqrt{40}\cdot \sqrt{40}}{2}[/tex]

Answer:

A

Step-by-step explanation:

did on edge

Step-by-step explanation:

refer the attachment......

ANSWER

C. x=2

EXPLANATION

The given equation is

[tex] \frac{x + 4}{6x} = \frac{1}{x} [/tex]

Cross multiply to get,

[tex]6x = x(x + 4)[/tex]

Expand to get:

[tex]6x = {x}^{2} + 4x[/tex]

[tex] {x}^{2} + 4x - 6x = 0[/tex]

[tex] {x}^{2} - 2x = 0[/tex]

[tex]x(x - 2) = 0[/tex]

[tex]x = 0 \: or \: x = 2[/tex]

But the domain is

[tex]x \ne0[/tex]

Therefore the solution is x=2.