GIVEN THE FUNCTION F(X) =3X + 5 AND X SUCH THAT F(X)=38

Step 1) Identity two points on the boundary line.

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

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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

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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.

Answer: 18

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

8 x 4 = 32

32 / 2 = 16

16 + 2 = 18

Correct option:

[tex]\boxed{x-y=P-Q}[/tex]

Given that the line we are looking for is parallel to g, then the slope of that line and g is the same, therefore:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ (x_{1},y_{1})=(-3,2) \\ \\ (x_{2},y_{2})=(0,5) \\ \\ \\ m=\frac{5-2}{0-(-3)}=1[/tex]

So we can write the point-slope form of the equation of the line as follows:

[tex]y-y_{0}=m(x-x_{0}) \\ \\ (x_{0},y_{0})=(P,Q) \\ \\ \\ y-Q=1(x-P) \\ \\ y-Q=x-P \\ \\ \\ Arranging: \\ \\ P-Q=x-y \\ \\ \boxed{x-y=P-Q}[/tex]

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A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope and b is the y intercept.

Line g passes through (-3,2) and (0,5). hence:

Two lines are parallel if they have the same slope. Hence:

Line parallel to line g has a slope of 1. Since it passes through (P, Q), hence:

[tex]y-y_1=m(x-x_1)\\\\y-Q=1(x-P)\\\\y-Q=x-P\\\\x-y=P-Q[/tex]

The equation of a line that is parallel to line g that contains (P, Q) is x - y = P - Q

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Answer:

  0

Step-by-step explanation:

Put the numbers where the letters are and do the arithmetic.

  (1)^2(-1)^2 +(1)(-1) -(-1)^3 -(1)^3

  = 1·1 -1 -(-1) -1

  = 1 - 1 + 1 - 1 = 0

The value of the expression is 0.

1. Find how much one pound is.

- to do this, divide 1.50 by 9. This will give you one pound.

2. Figure out how many times 1 pound can go in a dollar.

proportion

[tex]\frac{9}{1,5} = \frac{x}{1} \\[/tex]

1.5x=9*1

1.5x=9

x=[tex]\frac{9}{1.5}[/tex]

x=6

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

Answer:

Step-by-step explanation:

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

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: It’s D, i got it right!!

Step-by-step explanation:

the equation line of the scatter plot is y = ×+10

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: They each paid $2.40.

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:

[tex]\frac{7}{2}[/tex] square units.

Step-by-step explanation:

We have to use limits to find the area of the region bounded by the graph [tex]f(x) = 4 - 2x^{3}[/tex] , the x-axis, and the vertical lines x=0 and x=1.

So, the area will be

A = [tex]\int\limits^1_0 {(4 - 2x^{3})} \, dx[/tex]

= [tex][4x - \frac{x^{4}}{2} ]^{1} _{0}[/tex]

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

= [tex]\frac{7}{2}[/tex] square units. (Answer)

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: 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:

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:

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:

[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:

The area of the composite figure = 12.785 square units

Step-by-step explanation:

The figure composite of :

A ⇒ Rectangle with coordinates (0,0) , (0,5) , (2,5) and (2,0)

B ⇒ Rectangle with coordinates (2,0) , (2,1) , (4,1) and (4.0)

C ⇒ Quarter of a circle with coordinates (2,1) , (2,2) and (3,1)

Area of A: Length = 5 and Width =2

Area of A = Length times the width = 5*2 = 10 square units

Area of B: Length = 2 and Width =1

Area of B = Length times the width = 2*1 = 2 square units

Area of C: radius = 1

Area of C = 0.25 * pi * r² = 0.25 * 3.14 * 1² = 0.785 square units

Total Area = 10 + 2 + 0.785 = 12.785 square units

Answer:

the answer is 12.785

Step-by-step explanation:

i took the test

Answer:  1.75 cubic feet concrete is needed.

Step-by-step explanation:

Alright, lets get started.

The volume of the pillar is : [tex]\pi r^2h[/tex]

We have given the height is 5 feet.

We have given the diameter is 4 inches.

So the radius will be : [tex]\frac{4}{2}=2 \ inches[/tex]

Converting inches into feet.

The radius will be : [tex]\frac{2}{12} \ feet[/tex] [tex]= 0.167 feet[/tex]

So the volume of the cylinder will be : [tex]\pi * 0.167^2*5[/tex]

So the volume of the cylinder will be : [tex]0.4380 \ cubic \ feet[/tex]

As there are 4 pillars, so total volume will be : [tex]4*0.4380[/tex]

So, total volume will be : [tex]1.75 \ cubic \ feet[/tex]

Hence 1.75 cubic feet concrete is needed.   :   Answer

Hope it will help :)

Answer:

1.75 cubic feet

Step-by-step explanation:

Measure the diameter of the cylinder. ...

Hope this helps

Answer:

The value of tan P  = 1.875

Step-by-step explanation:

Given:

PR=17

RQ=15

PQ =8

To find:

tan P = ?

Solution:

In trigonometric ratio

tan = [tex]\frac{opposite}{adjacent}[/tex]

Now on substituting the given values(refer the figure)

tan (P) =[tex]\frac{15}{8}[/tex]

tan (P) = 1.875

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:

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.

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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:

5 days to spend exactly $710

Step-by-step explanation:

Answer:

5 days

Step-by-step explanation:

5 x 120 = 600

600 + 110 = 710

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!