What is the solution to the equation x−23=−13 ? Enter your answer in the box.

Step 1) Identity two points on the boundary line.

Two such points are (0,7) and (1,5)

-----------------------------

Step 2) Find the slope of the line through those two points

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

m = (5-7)/(1-0)

m = -2/1

m = -2

The slope is -2

-----------------------------

Step 3) Use the point slope form to get the y = mx+b form

y - y1 = m(x - x1) ..... point slope form

y - 7 = -2(x - 0)

y - 7 = -2x

y = -2x+7

A quicker way is to just note that 7 is the y intercept as visually shown, so b = 7. Which allows us to go from y = mx+b to y = -2x+7

-----------------------------

Step 4) The boundary line is y = -2x+7. This is a dashed line so we will use either a less than sign, or a greater than sign. There will be no "or equal to" as part of the inequality sign.

The shaded region is below the dashed boundary line, so we use a less than sign.

Change y = -2x+7 into y < -2x+7

----------------------------

Step 5) Change into standard form (optional)

y < -2x+7

2x+y < 7 ... add 2x to both sides

==========================================

The answer will depend on if you want slope intercept form or standard form.

Option A

The solution is [tex](0, \frac{-1}{4})[/tex]

Solution:

Given system of equations are:

3x + 6y = 1 ------ eqn 1

x - 4y = 1 ------ eqn 2

We have to find solution to system of equations

We can use substitution method

From eqn 2,

x = 1 + 4y -------- eqn 3

Substitute eqn 3 in eqn 1

3(1 + 4y) + 6y = 1

3 + 12y + 6y = 1

18y = 1 - 3

18y = -2

Divide both sides by 18

[tex]y = \frac{-2}{18}\\\\y = \frac{-1}{4}[/tex]

Substitute the above value of y in eqn 3

[tex]x = 1 + 4 \times \frac{-1}{4}\\\\x = 1-1\\\\x = 0[/tex]

Thus solution is [tex](0, \frac{-1}{4})[/tex]

We know x in f(x) is g(x) which is 2x^2 because we are to find (fg)(x)

f(x)=4(2x^2)+6

f(x)=8x^2+6

So (fg)(x) is 8x^2+6

Hope this helped!

(4x+6)(2x^2) = 8x3 + 12x2

The value of -36 divided by (-4/9) is 81, which is found by multiplying -36 with the reciprocal of (-4/9), giving the result 324/4, which simplifies to 81.

To find the value of -36 divided by (-4/9), you can think of division by a fraction as multiplication by its reciprocal. So, the problem changes from division to multiplication: -36 * (-9/4). To solve this:

First, multiply the numerators: -36 * -9 = 324.

Then, multiply the denominators: 1 * 4 = 4.

Now, divide 324 by 4 to get 81.

Therefore, the value of -36 divided by (-4/9) is 81.

Answer:

all books to new books- 14:5

used books to new books- 5:9

Step-by-step explanation:

Answer: a. 14:5 b. 5:9

Step-by-step explanation:

There are 14 books and 9 are new so subtract 9 from 14 and get 5 and your ration would be 14:5. Once you have the answer to a you know how many new books there are and how many old books there are, so you can easily figure out the ratio would be 5:9.

Answer: 0.11

Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100.

So we can think of 11% as the ratio 11 to 100 or 11 divided by 100.

Dividing by 100 moves the decimal point 2 places to the left so 11 divided by 100 would move the decimal point 2 places to the left which would give us .11 or 0.11.

So 11% can be written as the decimal 0.11.

Answer:

( sin K = 1/2 ) would be right

I'll do the first part to get you started.

--------------------

Area = 1/2

Length = 7/8

Width = W

Area of rectangle = Length*Width

A = L*W

1/2 = (7/8)*W

(8/7)*(1/2) = (8/7)*(7/8)*W .... see note1 below

(8*1)/(7*2) = (8*7)/(7*8)*W .... see note2

8/14 = (56/56)*W

4/7 = 1*W .... see note3 and note4

--------------------

Foot notes

Answer:

B. 2/12 = 78/x ; x = 468

Step-by-step explanation:

12/2 = 78/x

6 = 78/x

6 x 78 = x

468

Answer:

Step-by-step explanation:

Since they are supplementary, it means the addition of both angles gives 180 degree.

[tex]x - 15 + 2x = 180\\3x = 180 + 15\\3x = 195\\x = \frac{195}{3} \\x = 65[/tex]

Answer:

Perimeter of each triangles are equivalent to 15.4 inches.

Step-by-step explanation:

Given:

A rectangle :

Length of the rectangle = 5 inches

Width of the rectangle =4 inches

As Bridget cuts it from one corner to the other corner,its forms two right angled triangle.

The diagonal will be treated as the hypotenuse.

Lets say that the length of the hypotenuse is 'x'.

Using Pythagoras formula:

⇒ [tex](hypotenuse) = \sqrt{(perpendicular)^2+(base)^2}[/tex]

Plugging the values:

⇒ [tex]hypotenuse = \sqrt{5^2+4^2}[/tex]

⇒ [tex]hypotenuse = \sqrt{25+16}[/tex]

⇒ [tex]hypotenuse =\sqrt{41}[/tex]

⇒ [tex]hypotenuse = 6.40[/tex]  inches

Now we have to find the perimeter :

Perimeter = Summation of length of all sides.

So,

Perimeter  of each triangle = (length + width + hypotenuse)

⇒ [tex]Perimeter =(5+4+6.4)[/tex]

⇒ [tex]Perimeter =15.4[/tex]  inches

Perimeter of each triangle, as they are equally sized are same that is   15.4 inches.                              

Answer:

20 km

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

We can disregard the length of the line from the Library and the House, as Davina does not use that path at all.

We know that 1 unit on the grid represents 1 km. We define the lengths of the route from the graph:

Davina's House to School = 4 units = 4 km

School to Library = 6 units = 6 km

The entire trip Davina takes from House to Library would be 4 km + 6 km = 10 km total.

We also know that Davina takes the same route back from the Library to House. It would be the same exact route and length. Therefore:

2(10 km) = 20 km total

Answer:19.200

Step-by-step explanation:

19.200x1=19.200

Answer:

the answer is F. because n x 30 would = 360 and the n would be 12 so he paid 12 dollars per ticket and I got that answer by dividing the two numbers 30 and 360

brainliest plz

The answer is F.

Given: Mr. Davis buys 30 tickets for the drama club to attend a play. The tickets cost n dollars each for a total of $360.

How to find out the equation that can be used to find n?

As n x 30 would = 360 and the n would be 12 so he paid 12 dollars per ticket and I got that answer by dividing the two numbers 30 and 360.

Learn more about equations on : https://brainly.com/question/14664036

#SPJ2

Answer:

2 points

Step-by-step explanation:

Answer:

THE ANSWER IS 2 POINTS

Step-by-step explanation:

A

P

E

X

Answer: They each paid $2.40.

Answer:

1. A

2. A

3. D

Step-by-step explanation:

Stay safe❤️

Mona purchased 5 gallons of gas and 5 gallons of gas would give her 100 miles of driving.

Two or more expressions with an Equal sign is called as Equation.

Given that Mona stopped at a gas station where the price per gallon was $2.80

Mona spent $14 to fill up her car.

We need to find the equation would represent how much gas Mona purchased.

2.8x = 14 is the equation

Divide both sides by 2.8

x=5

Mona purchased 5 gallons of gas.

Now multiply 5 by the price per gallon of $2.80

5×2.8=14

Since Mona's car gets 20 miles per gallon, 5 gallons of gas would give her 100 miles of driving.

Hence, Mona purchased 5 gallons of gas and 5 gallons of gas would give her 100 miles of driving.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ3

Answer: 18

Step-by-step explanation: 2 x 2 x 2= 8

8 x 4 = 32

32 / 2 = 16

16 + 2 = 18

Answer:

Therefore the required resulting equation is

[tex]6x-15y=-63\\-15x+15y=90[/tex]

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

Step-by-step explanation:

Given:

[tex]2x-5y=-21[/tex]         ......................Equation ( 1 )

[tex]3x-3y=-18[/tex]         ......................Equation ( 2 )

To Find:

Expression after multiplying to eliminate y term,

Solution:

So to eliminate 'y' term we need to multiply equation 1 by a constant 3 and equation 2 by a constant -5,  such that equations  becomes

[tex]3(2x-5y)=3\times -21\\\\6x-15y=-63[/tex] .....( 1 )

[tex]-5(3x-3y)=-5\times -18\\\\-15x+15y=90[/tex]  .....( 2 )

so now by adding new equation one and two we can eliminate y term that means -15y and +15y will get cancel,

Therefore the required resulting equation is

[tex]6x-15y=-63\\-15x+15y=90[/tex]

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

Answer:

It's A

Step-by-step explanation:

Got it right on the test

Answer:

11 live chickens and 10 dead chickens

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

21-10=11

RIP chickens

Answer:

18 girls

Step-by-step explanation:

if the r 48 boys u know that 8 times 6 is 48. So now u have to multiply 6 on the other side. And this action would result in the number of girls to be 18

Answer:

        [tex]80 + (8*4)/2[/tex]    [tex]=96[/tex]

Step-by-step explanation:

Given :

80 + (8 x 4) ÷ 2

                             [tex]80 + (8*4)/2[/tex]

This expression can be written in form of:

                      [tex]80+\frac{(8*4)}{2}[/tex]

Solving the expression further:  

                     [tex]80+\frac{32}{2}[/tex]

                [tex]=80+16[/tex]

                  [tex]=96[/tex]

So the value of the above expression after solving is 96

Answer:

x=40 and y= 60

Step-by-step explanation:

step:1

Let 'x' and 'y' are two numbers

given data the sum of two numbers is 100

x+y = 100......(1)

Given difference of two numbers are

x - y = -20 ......(2)

Step :2

solving the equation (1) and (2)

adding the equations (1) and (2)

x+y+x-y=100-20

cancelling 'y' terms are

2 x = 80

dividing "2" on both sides, we get

x = 40

Step :3

substitute x = 40 in equation (1)

x + y =100

40 + y = 100

subtracting "40" on both sides, we get

40 + y - 40 = 100 -40

y = 60

Final answer:-

The two numbers are x = 40 and y= 60

Answer:

Independent variable is A.

Dependent variable is B.

The equation that can be used to represent the relationship is B. F=20c

Step-by-step explanation:

To answer the question, the independent variable is A. Number of friends (f). Because we know the cost is $20. And the dependent variable is B. because we know the cost so that's the dependent variable. The equation that can be used to represent this relationship is B. F=20c because we need to know how many friends are gonna be at Hank's party.

Answer:

[tex](x+5)^{2}=-4(y+3)[/tex]

Step-by-step explanation:

Given:

Focus point = (-5, -4)

Vertex point = (-5, -3)

We need to find the equation for the parabola.

Solution:

Since the x-coordinates of the vertex and focus are the same,

so this is a regular vertical parabola, where the x part is squared. Since the vertex is above the focus, this is a right-side down parabola and p is negative.

The vertex of this parabola is at (h, k) and the focus is at (h, k + p). So, directrix is y = k - p.

Substitute y = -4 and k = -3.

[tex]-4 = -3+p[/tex]

[tex]p=-4+3[/tex]

[tex]p=-1[/tex]

So the standard form of the parabola is written as.

[tex](x-h)^{2}=4p(y-k)[/tex]

Substitute vertex (h, k) = (-5, -3) and p = -1 in the above standard form of the parabola.

So the standard form of the parabola is written as.

[tex](x-(-5))^{2}=4(-1)(y-(-3))[/tex]

[tex](x+5)^{2}=-4(y+3)[/tex]

Therefore, equation for the parabola with focus at (-5,-4) and vertex at (-5,-3)

[tex](x+5)^{2}=-4(y+3)[/tex]

Answer:

A value that satisfies this equation is called a root, zero or solution of the equation!! We have three ... Solve each by factoring. 1) x2 + 4x -5 = 0 ... Follow the explanation and sample problem to review completing the square.

Step-by-step explanation:

x^2 - 4x = 80

x^2 - 4x + 4 = 80 + 4 (Divide b, which is 4, by 2 and square it.)

x^2 - 4x + 4 = 84

sqrt(x + 2)^2 = sqrt(84)

x + 2 = plus or minus sqrt(84)

Subtract 2 from both sides

x = -2 plus or minus sqrt(84)

Set up this equation: 180(n-2)=3780

n is the number of sides of the polygon

Solved:

180(n-2)=3780

n-2=21

n=23

So the polygon will have 23 sides, also called a 23-gon

Hope this helped!

Answer:

3/5

Step-by-step explanation:

1/3s=1/5

s=(1/5)/(1/3)

s=(1/5)(3/1)

s=3/5

Answer:  s = 3/5 = 0.600

Step-by-step explanation:s = 3/5 = 0.600

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    1/3*s-(1/5)=0

Step by step solution :

Step  1  :

           1

Simplify   —

           5

Equation at the end of step  1  :

  1         1

 (— • s) -  —  = 0

  3         5

Step  2  :

           1

Simplify   —

           3

Equation at the end of step  2  :

  1         1

 (— • s) -  —  = 0

  3         5

Step  3  :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       3

     The right denominator is :       5

       Number of times each prime factor

       appears in the factorization of: Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

3 1 0 1

5 0 1 1

Product of all

Prime Factors  3 5 15

     Least Common Multiple:

     15

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Deniminator by  L_Deno

   Denote the Right Multiplier by  R_Deno

  Left_M = L.C.M / L_Deno = 5

  Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      s • 5

  ——————————————————  =   —————

        L.C.M              15  

  R. Mult. • R. Num.       3

  ——————————————————  =   ——

        L.C.M             15

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

s • 5 - (3)     5s - 3

———————————  =  ——————

    15            15  

Equation at the end of step  3  :

 5s - 3

 ——————  = 0

   15  

Step  4  :

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 5s-3

 ———— • 15 = 0 • 15

  15

Now, on the left hand side, the  15  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  5s-3  = 0

Solving a Single Variable Equation :

4.2      Solve  :    5s-3 = 0

Add  3  to both sides of the equation :

                     5s = 3

Divide both sides of the equation by 5:

                    s = 3/5 = 0.600

One solution was found :

                  s = 3/5 = 0.600

BTW YOu can but the answer as 0.600 or 3/5

Answer:

m=-2

Step-by-step explanation:

-7 + -2 = -7 -2

-7 -2 = -9

Answer:

         [tex]\large\boxed{\large\boxed{8.06units}}[/tex]

Explanation:

The figure is a right triangle with:

Hence, you must use Pythagora's theorem, which is valid for all right triangles:

             [tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex]

Substituting the data:

        [tex]hypotenuse^2=(7unit)^2+(4unit)^2=49unit^2+16unit^2=65unit^2[/tex]

Square root both sides:

         [tex]hypotenuse=\sqrt{65unit^2}=8.06unit[/tex]

Answer:

8.06

Step-by-step explanation:

Answer:

5 days to spend exactly $710

Step-by-step explanation:

Answer:

5 days

Step-by-step explanation:

5 x 120 = 600

600 + 110 = 710