PLEASE HELP
if f(x)=3x-2 and g(x)=x+2/3, find f(g(x))
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Answer:

-3(4x + 1) = 21 given

4x + 1 = -7 Division Property of Equality

4x = -8 Subtraction Property of Equality

x = -2 Division Property of Equality

Answer:

see explanation

Step-by-step explanation:

prove by solving the equation

- 3(4x + 1) = 21 ( divide both sides by - 3 )

4x + 1 = - 7 ( subtract 1 from both sides )

4x = - 8 ( divide both sides by 4 )

x = - 2

thus solution is x = - 2

Answer:

5m+3 =3m

Step-by-step explanation:

−6(t − 8) = 12

-6((6) -8) =12

5m+3=3m

5m-3m=3

2m=3

2(6)≠3

t + 5 = 11

(6) + 5 = 11

9 = 2x − 3

2x = 9+3

2(6) = 12

total cost of metal in the pattern is £24.6

To compare two values is to use a ratio. A proportion is formed when two ratios have the same value. Choose whether the ratio is part-to-part or part-to-whole before you write it.

20 straight line cost £12

12 ÷ 20 = 0.6 per straight line

straight line : cost of one arc = 2:3

arc = 0.6 x (3/2) = 0.9

total = 12 + 14 x 0.9

         = 12 + 12.6

         = 24.6

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John held a garage sale. He priced all the items at a dime or a quarter, his sales totaled less than $5, the solution is shaded region in quadrant I.

In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent the slope; reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of equation for a straight line as "y = mx + b" and "y = mx + c," respectively.

He priced all items at a dime or a quarter. His sales totaled less than $5

Since dime =$ 0.10=$0.10 and the quarter =$0.25=$0.25

Let x=x= the number of the items sold for a dime

Let y=y= the number of the items sold for a quarter

0.10x+0.25y<5

0.10x+0.25y<5

Inequality in the slope-intercept form

0.10x+0.25y Subtract 0.10x from both sides

0.25y<-0.10x+5 Divide both sides by 0.25

Subtract 0.10x from both sides

[tex]y= -\frac{2}{5}x+20\\[/tex]

The slope is, [tex]-\frac{2}{5}[/tex] and the y- intercept is 20

Since inequality sign is << so, draw a dashed line

Test point (0,0)(0,0)

Substituting the values 0 for x and 0 for y,

[tex]y < -\frac{2}{5}x+20\\\\0 < -\frac{2}{5}(0)+20\\\\0 < +20[/tex]

Since inequality is true

So, (0,0)(0,0) is solution of the inequality

Shade region containing (0,0)(0,0).

The graph below shows all possible solutions

Since boundary line is dashed and the number of items is always positive

The solution is shaded region in quadrant I

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Answer:

∠1 = 103.9° ;  ∠2 = 27.8°

Step-by-step explanation:

Supplementary angles = 180°

So, Let the angles be 'x'

Then, x + x -27.8° = 180°

         2x - 27.8° = 180°

         2x = 180° + 27.8°

         2x = 207.8°

          x = 207.8°/2

          x = 103.9°

Therefore ∠1 = 103.9° ; ∠2 = 27.8°

I hope the answer is correct and has helped you!!!

Total charge for 1,920 squares feet is $160.

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including trigonometry, calculus, and coordinate geometry. 2x + 4 = 8 is a straightforward algebraic expression.In algebra, symbols are used, and operators are used to connect the symbols to one another. It is more than just a mathematical idea; it is a skill that we all utilize on a regular basis without even being aware of it.

Given that :City carpet advertises that they can instal 1,200 square feet of carpet in 2 1/2 hours They charge $40 per hour.

City carpet can install 1,200 square feet of carpet in 2.5 hours

In 1 hour they can install [tex]\frac{1200}{2.5} =480 squares feet[/tex]

In 4 hour they can install 1920 squares feet carpet

They charge $40 per hour

So total charges for 1920 square feet will be 4 ×40

= $160

Total charge for 1,920 squares feet is $160.

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Because triangle SRT and VUW are similar, all sides of triangle SRF are scaled up by an amount.

We calculate the scale factor : 9/5.4 = 5/3

-> The corresponding side of SR (UV)  is scaled down 5/3 times from the length of SR
-> UV = 6 : 5/3 = 3.6 (inches).

Semicircle is the best figure to use to estimate the volume of the punch bowl.

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Answer:

3

Step-by-step explanation:

m=y2-y1÷x2-x1

4-1÷1-0=3÷1=3

Answer:

The 5 students receive the larger amount.

100:5= 20 gram per student

100÷20= 5 gram per student

Step-by-step explanation:

prove me wrong

a shorter solution that probably will get full pts :

Because each group has the same mass of the chocolate bar, whichever group has less students will get a larger amount of chocolate per student (as there are less people receiving)

and here's if you think it is kinda not too detailed :

The first group has each student receiving 100 : 5 = 20 grams of chocolate per student
The second group has each student receiving 100 : 20 = 5 grams of chocolate per student

Both solutions give us a conclusion of : The group with 5 students have each of the receiving a larger amount of chocolate.

Answer: The rhombus below has two lines of symmetry, and the shape below has two lines of symmetry.

Step-by-step explanation:

Symmetry is when we split an object in half, in which both sides are equivalent. This definition must explain how the rhombus was most plausibly split, as well as the letter "H".

a. Expression for length L in terms of x is  L = 1040 - 2x

b. Expression for the area of the pasture in terms of L and x, A = Lx

c. Expression for the area of the pasture in terms of x only = x (1040 - 2x)

d. The area of the pasture will enclose greater than or equal to 60 square feet

Given data

length of fence = 1040 ft

length if the pasture = L

width of the pasture = x

Expression for length L in terms of x

from the figure we can see that the fenced part is 3 sides which include 2 widths and 1 length. So we represent this with the expression below

L + x + x = 1040

L + 2x = 1040

L = 1040 - 2x

Expression for the area of the pasture in terms of L and x

Area of the pasture,  A = L * x

A = Lx

Expression for the area of the pasture in terms of x only

= L * x

and L = 1040 - 2x

= x (1040 - 2x)

A sentence that makes the area to enclose at least 60 000 square feet.

from A = Lx

we have

A = Lx ≥ 60

The area of the pasture will enclose greater than or equal to 60 square feet

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Answer:

a. Perpendicular

Make sure to read the step-by-step explanation to figure out how to do the other 2.

Step-by-step explanation:

I will not be providing answers to all three, but I will answer the first one (this is, so you don't depend on people to solve this for you).

Parallel lines have one thing in common, their slope. Two lines that have the same slope never intersect because they are both facing the same direction and moving the same distance. So, you can find the slope of two lines by using the slope formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{-6-(-3)}{-4-2}=\frac{-3}{-6}=\frac{1}{2}\\m_2=\frac{-8-2}{2-(-3)}=\frac{-10}{5}=-2[/tex]

This is evidence that the two lines are not parallel. But, by finding the slope, we can conclude that it is perpendicular.

This brings me to how to identify perpendicular lines. The slope of perpendicular lines is negative reciprocals. A reciprocal is just a fraction that is flipped, and it's negative. For example, [tex]\frac{-2}{3}[/tex]'s negative reciprocal would be [tex]\frac{3}{2}[/tex]. The negative of -2/3 is a positive, and the reciprocal of 2/3 is 3/2. So, the negative reciprocal is 3/2.

Well, [tex]-2[/tex] is the negative reciprocal of [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2, and the negative of 2 is -2. So, simply, lines 1 and 2 are perpendicular.

Use this method to solve the other questions. If they don't have the same slope and aren't negative reciprocals, then they are neither.

Answer:

Step-by-step explanation:

        To solve this problem, we use the following formula:

                        [tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

    a) (2,-3)  (-4,-6)

[tex]x_1=2\ \ \ \ x_2=-4\ \ \ \ y_1=-3\ \ \ \ y_2=-6[/tex]

[tex]\displaystyle\\\frac{x-2}{-4-2} =\frac{y-(-3)}{-6-(-3)} \\\\\frac{x-2}{-6}=\frac{y+3}{-6+3} \\\\\frac{x-2}{-6} =\frac{y+3}{-3}[/tex]

Multiply both parts of the equation by -3:

[tex]\displaystyle\\\frac{x-2}{2}=y+3\\\\0.5x-1=y+3\\\\0.5x-1-3=y+3-3\\\\0.5x-4=y\\[/tex]

⇔ Line 1: y=0.5x-4    m₁=0.5

   (-3,2)  (2,-8)

[tex]\displaystyle\\\frac{x-(-3)}{2-(-3)}=\frac{y-2}{-8-2} \\\\\frac{x+3}{2+3} =\frac{y-2}{-10} \\\\\frac{x+3}{5} =\frac{y-2}{-10} \\\\[/tex]

Multiply both parts of the equation by -10:

[tex]-2(x+3)=y-2\\-2x-6=y-2\\-2x-6+2=y-2+2\\-2x-4=y[/tex]

⇔ Line:y=-2x-4   m₂=-2

[tex]\displaystyle\\m_1=-\frac{1}{m_2}[/tex]

⇒ The given  lines are perpendicular

b)

(-4,-5)   (4,1)

[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+4}{4+4}=\frac{y+5}{1+5} \\\\\frac{x+4}{8} =\frac{y+5}{6} \\[/tex]

Multiply both parts of the equation by 6:

[tex]\displaystyle\\\frac{6(x+4)}{8} =y+5\\\\\frac{3}{4} x+3=y+5\\\\\frac{3}{4} x+3-5=y+5-5\\\\\frac{3}{4} x-2=y\\[/tex]

⇔ Line 1: y=(3/4)x-2     m=3/4

     (6,10)    (-3,-2)

[tex]\displaystyle\\\frac{x-6}{-3-6} =\frac{y-10}{-2-10} \\\\\frac{x-6}{-9} =\frac{y-10}{-12} \\\\[/tex]

Multiply both parts of the equation by -12:

[tex]\displaystyle\\\frac{-12(x-6)}{-9} =y-10\\\\\frac{4}{3}x-8=y-10 \\\\\frac{4}{3}x-8+10=y-10+10\\\\\frac{4}{3}x+2=y[/tex]

⇔ Line 2: y=(4/3)x+2    m=4/3

⇒  The given  lines are neither perpendicular and neither parallel

c)

  (0,-4)   (-2,-8)

[tex]\displaystyle\\\frac{x-0}{-2-0} =\frac{y-(-4)}{-8-(-4)} \\\frac{x}{-2}=\frac{y+4}{-8+4} \\\\\frac{x}{-2}=\frac{y+4}{-4}[/tex]

Multiply both parts of the equation by -4:

[tex]2x=y+4\\2x-4=y+4-4\\2x-4=y[/tex]

⇔ Line 1: y=2x-4     m₁=2

  (-1,5)   (1,9)

[tex]\displaystyle\\\frac{x-(-1)}{1-(-1)} =\frac{y-5}{9-5} \\\\\frac{x+1}{1+1} =\frac{y-5}{4}\\\\\frac{x+1}{2} } =\frac{y-5}{4} \\[/tex]

Multiply both parts of the equation by 4:

[tex]2(x+1)=y-5\\2x+2=y-5\\2x+2+5=y-5+5\\2x+7=y[/tex]

⇔ Line 2: y=2x+7    m₂=2

m₁=m₂  

⇒ The given  lines are parallel

The sum will be 46 which is the nearest combinational value that could be deduced from the digits 1, 2, 3, and 4.

Let's check all the combinations which can be possibly used,

34 + 21 = 46, which is 4 numbers less than 50 so far the nearest.

43 + 12 = 55, which is 5 numbers more than 50.

32 + 41 = 73, which is 23 numbers more than 50.

32 + 14 = 46, which is 4 numbers less than 50 so far the nearest.

23 + 41 = 64, which is 14 numbers more than 50.

So the two combinations are deduced after permutation and a combination of numbers that are 3 and 4 + 2 and 1 and another is 3 and 2 + 1 and 4.

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convert feet to miles;

10,560 = 2 miles

30 minutes to miles;

2; therefore,

in 1hr she walked 4 miles

4 miles/hour

Answer:

Step-by-step explanation:

Hello!

What is the slope-intercept form:

 [tex]y = mx + b[/tex]

             [tex]m = \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-4}{0--2} =\dfrac{-5}{2}[/tex]  

               ⇒ where (x₂,y₂) and (x₁,y₁) are random points on the line

            ⇒ thus our y-intercept is '-1'

Thus our line's equation in slope-intercept form:

     [tex]y= -\dfrac{5}{2}x -1[/tex]

Hope that helps!

The minimum number of sets of knives Kaj should buy if the restaurant needs at least 736 knives is 48. 4 sets of knives

155 + 12x ≥ 736

12x ≥ 736 - 155

12x ≥ 581

x ≥ 581 / 12

x ≥ 48.41666666666666

Approximately,

x ≥ 48. 4 sets of knives

In conclusion, the sets of knives kaj needs to buy more is 48. 4 sets of knives

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Answer:

$71.39

Step-by-step explanation:

So we can go ahead and add the extra money they paid (sales tax and tip).

15% + 6% = 21%

Then we can find 21% of 59 then that will be our extra money we're paying.

59 × 0.21 = 12.39

Then we add that amount to our 59 to get the total amount.

59 + 12.39 = 71.39

the numerical value of x in fraction and decimal form are 11/2 and 5.5 respectively.

A midpoint is simply a point that divides a line segment into two equal halves.

Given the data in the question;

Since that T is the midpoint of segment SU, segment ST and segment TU are two equal halves of of segment SU.

Segment ST = Segment TU

Plug in the given values and solve for x

14x - 6 = 12x + 5

14x - 12x = 5 + 6

2x = 11

x = 11/2

x = 5.5

Therefore, 11/2 or 5.5 is the numerical value of x.

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1) (4, 8)

2) (4, 8)

The midpoints are already given to you.

Answers:

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

Explanation:

A = (9, -10)

B = (4,8)

C = (x,y)

A and C are the endpoints. B is the midpoint of segment AC.

The x coordinates of A and C are 9 and x respectively. Add them up and divide in half to get (9+x)/2. This is set equal to the x coordinate of point B and we solve for x.

(9+x)/2 = 4

9+x = 2*4

9+x = 8

x = 8-9

x = -1

The x coordinate of point C is -1.

Use the same idea for the y coordinates.

(-10+y)/2 = 8

-10+y = 2*8

-10+y = 16

y = 16+10

y = 26

Point C is located at (-1, 26)

The midpoint between (9, -10) and (-1, 26) is (4, 8)

Use the midpoint formula to confirm this.

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

The steps for the second problem are going to follow the same outline.

A = (-6,4)

B = (4,8)

C = (x,y)

(-6+x)/2 = 4 solves to x = 14

(4+y)/2 = 8 solves to y = 12

Point C is located at (14, 12)

The midpoint between (-6, 4) and (14, 12) is (4, 8)

Answer 9 3/7

Step-by-step explanation:

[tex] \frac{30}{7} \times \frac{11}{5} \\ = \frac{330}{35} \\ = 9 \frac{15}{35} [/tex]

SIMPLIFIED WE GET:

[tex]9 \frac{3}{7} [/tex]

THE LAST OPTION IS THE ANSWER

SOMEONE HAS A PET WATER BUFFALO.

THE GIVEN STATEMENT IS INDICATING THAT NOT EVEN ONE PERSON HAS A PET WATER BUFFALLO SO THE NEGATION SHOULD INDICATE THERE IS SOMEONE WHO DOES HAVE A PET WATER BUFALLO.

HOPE THIS HELPS

Answer:

The length of the radius is 10.7cm

Step-by-step explanation:

[tex]v = \pi {r}^{2} h[/tex]

6480=(22r*180)/7

6480*7=3960r

r=

[tex]r = \sqrt{45360 \div 396} [/tex]

Answer:

x = 132°

Step-by-step explanation:

Sum of interior angles = (n - 2) x 180, where n is number of sides of the polygon.

Sum = (6 - 2) x 180 = 720°

sum = 160 +75 + 132 + 113 + 108 + x

sum = 588 + x

720 = 588 + x

x = 720 - 588

x = 132°

:)

Answer:

5.48, 78.541 and 97

Step-by-step explanation:

A rational number by definition refers to a number that is in the form of k/m and in which k and m are integers and m is not equal to 0.

Let me give you some examples:

From our question,

Therefore 5.48, 78.541 and 97 are rational numbers

Answer:

24 wings

Step-by-step explanation:

Answer:

17 wings

Step-by-step explanation:

1. first we multiply 3 by 27.20 you get  81.6

2. then we divide 81.6 by 4.80 and we get 17

17 wings