Given f(x) = 4x - 6 and g(x) = f(2x), write an equation for g.

Answer:

Step-by-step explanation:

Each of the given equations describes a line on a graph. There are numerous ways to find the values of x and y that will satisfy both equations at the same time. Two of them you have seen are "substitution" and "elimination." Here, "substitution" is easily accomplished by equating one expression for y to the other expression for y:

  y = y

  100 +65x = 40 +80x . . . substitute for y

  60 +65x = 80x . . . . . . . subtract 40 from both sides

  60 = 15x . . . . . . . . . . . . subtract 65x from both sides

  4 = x . . . . . . . . . . . . . . divide both sides by 15

  y = 40 +80x = 40 +80(4) = 360 . . . . find the value of y

The values of x and y that satisfy both equations are ...

  (x, y) = (4, 360)

__

The point (4, 360) is on both lines. That is the point where the lines intersect. It means 4 hours work will cost $360 in either shop.

__

The time of 4 hours that we found above is the "break-even" or "crossover" point in the cost equations. For times below that point, the lowest cost comes because of the lowest "service charge". For times above that point, the lowest cost comes because of the lowest per-hour charge.

3 hours is less than 4 hours, so the shop with the lowest service charge will have a lower cost. That is Amy's shop. Her price for 3 hours is ...

  40 +80(3) = 40 +240 = $280 . . . for 3 hours work in Amy's shop

__

If you want to make sure of that, you can find the cost in Mike's shop:

  y = 100 +65(3) = 100 +195 = $295 . . . for 3 hours in Mike's shop

Answer:

2/8 farther than Mariam

Step-by-step explanation

mahra walks 5/8 km

Mariam walks 3/8 km

therefore, to know how many km mahra walks farther than mariam.

5/8-3/8

Answer:

45ft²

Step-by-step explanation:

4 [ 2(6ft × 1.5ft) ÷ 2 ] + ( 3ft × 3ft )

= 4 [ 2(9) ÷ 2 ] + ( 3ft × 3ft )

= 4 [ 18 ÷ 2 ] + ( 3ft × 3ft )

= 4 ( 9 ) + ( 9 )

= 36 + 9

= 45ft

Answer:

Answer: Equation is y = ½x + 3

Step-by-step explanation:

Consider points (4,5) and (0,3)

» General linear equation:

[tex]{ \tt{y = mx + b}}[/tex]

Slope (m):

[tex]{ \tt{m = \frac{(5 - 3)}{(4 - 0)} }} \\ \\ { \tt{m = \frac{2}{4} = \frac{1}{2} }}[/tex]

slope = ½

y-intercept (c):

[tex]{ \tt{y = \frac{1}{2}x + c }}[/tex]

» Consider point (0,3):

[tex] { \tt{3 = ( \frac{1}{2} \times 0) + c}} \\ \\ { \tt{c = 3}}[/tex]

» Equation:

[tex]{ \boxed{ \tt{y = \frac{1}{2}x + 3 }}}[/tex]

[tex]\\ \rm\hookrightarrow \sqrt{x-6}=x-12[/tex]

[tex]\\ \rm\hookrightarrow x-6=(x-12)^2[/tex]

[tex]\\ \rm\hookrightarrow x-6=x^2-24x+144[/tex]

[tex]\\ \rm\hookrightarrow x^2-25x+150=0[/tex]

[tex]\\ \rm\hookrightarrow x^2-10x-15x+150=0[/tex]

[tex]\\ \rm\hookrightarrow (x-10)(x-15)=0[/tex]

[tex]\\ \rm\hookrightarrow x=15\:or \:10[/tex]

Answer:

[tex]x = 15,10[/tex] || C and D is the correct choices.

Step-by-step explanation:

[tex]\sqrt{x-6}=x-12[/tex]

[tex]x-6 =(x-12)^2[/tex]

[tex]x-6 = x^2 -24x +144[/tex]

[tex]x^2 -24x -x +144 +6 = 0[/tex]

[tex]x^2 - 25x + 150= 0[/tex]

[tex]x^2 -15x -10x +150=0[/tex]

[tex]x(x-15)-10(x-15)=0[/tex]

[tex](x-15)(x-10) = 0[/tex]

[tex]x = 15,10[/tex]

Answer:

A = 92°

B = 100°

C = 88°

D = 80°

Step-by-step explanation:

Cyclic quadrilateral : a quadrilateral drawn inside (inscribed) a circle.

The opposite angles in a cyclic quadrilateral add up to 180°.

Therefore, A + C = 180° and B + D = 180°

If A + C = 180° , then

⇒ (x + 2) + (x - 2) = 180

⇒ x + 2 + x - 2 = 180

⇒ 2x = 180

⇒ x = 90°

Therefore,

A = x + 2 = 90 + 2 = 92°

C = x - 2 = 90 - 2 = 88°

D = x - 10 = 90 - 10 = 80°

B = 180 - D = 180 - 80 = 100°

Answer:

Segment AC = 10 units

segment AD =

angle 1 = 45°

angle 2 = 90°

AE = BE = CE = DE = 5

SEGMENT AC = AE + CE

= 5 + 5

= 10 UNITS

SEGMENT AD = 5² + 5²

= √50

= 7.071

= 7 UNITS

ANGLE 1 = 90° ÷ 2

= 45°

ANGLE 2 = 360° ÷ 4 / 180° ÷ 2

= 90°

Answer:

452 m^2

Step-by-step explanation:

Formula

A=4πr^2

4·π·6^2≈452.38934

Answer:

Domain: all real numbers

Range : y ≤ 2

Step-by-step explanation:

Domain : the set of possible x-values

Range : the set of y-values

From inspection of the graph:

Answer:

Step-by-step explanation:

The ordered pairs are:

Find the slope:

It means the drop in price is $625 each year.

The equation to reflect this situation is:

Answer:

Length of Sofia's poster: 0.75 m

Length of Rafael's poster: 0.65 m

Difference: 0.75m - 0.65m

= 0.1 m

Hope this is correct

Mark as Brainliest please

60 or y=4×+6

Step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solution.

Answer: 17.5 lbs of plums are required to make 20 rolls of fruit leather.

Step-by-step explanation:

Since 7 lbs of plums yield 8 rolls of fruit leather, 1 lb will yield 1 1/7 rolls of fruit leather.

To find how many pounds of fruit will yield 20 rolls of fruit leather, divide how many rolls of leather you want to get by how many rolls of leather one pound will yield.

20 divided by 8/7 equals 17 1/2.

Answer:710

Step-by-step explanation:

1 centimeter is 10 millimeters so 71 times 10 is 710

Answer:

710mm

Step-by-step explanation:

1 centimeter is equal to 10 millimeters:

[tex]1cm=10mm[/tex]

The distance d in millimeters (mm) is equal to the distance d in centimeters (cm) times 10:

[tex]d_{mm} =d_{cm}*10[/tex]

71cm × 10

= 710mm

Answer: (p, q) = (3, 2)

Step-by-step explanation:

So we get that g(f(x)) = p(1-x)^2 + q = p(x^2 - 2x + 1)+q = px^2 - 2px + p+q.

Matching coefficients, we get that p=3, -2p=-6, and p+q=5.

It follows that p=3 and q=2.

The submarine is about 54 meters below the surface.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the height of the submarine. Hence:

y = -75 + 21 = 54 meters

The submarine is about 54 meters below the surface.

Find out more on Equation at: https://brainly.com/question/2972832

The radius of the wheel is 140.06 inches

Since the wheels on a truck are turning at 630 revolutions per minute as the truck travels at 50 miles per hour, we need to find the distance mover per revolution.

So, distance moved per revolution = speed of truck ÷  revolutions per minute

Speed of truck = 50 miles per hour

Converting to inches per min, we have

= 50 × 63360 in/hr ÷ 1 hr/60 min

= 3168000 in/60 min

= 52800 in/min

revolutions per min = 60 rev/min

So, substituting the variables into the equation, we have

distance moved per revolution = 52800 in/min ÷ 60 rev/min

= 880 in/rev

Since the distance moved per revolution is the circumference of the wheel, C we have that

C = 2πr where r = radius of wheel

Making r subject of the formula, we have

r = C/2π

Since C = 880 in

Substituting the value of the variable into the equation, we have

r = C/2π

r = 880 in/2π

r = 440 in/π

r = 140.06 in

So, the radius of the wheel is 140.06 inches

Learn more about radius of wheel here:

https://brainly.com/question/24463763

Answer:

I'll do the first one as an example. The answer of the first one is 6.

Step-by-step explanation:

In the first example, they multiplied the number by 2 to get a common denominator for the two fractions so you can easily add. So, the first box will come 10 (5 times 2) and the second box will become 2 (1 times 2). Then simply add the fractions. The sum of the first question is 2. Because 2 10/12 + 3 2/12 = 6. Remember to add only the whole numbers and fractions. If you want, you can try using mathaway for additional help.

Hope this helps a little more.

Answer:

60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

2 to the 1st power times 30 -----> 2^1 x 30

2^1 x 30

exponent first

2 x 30

finish it

60

answer = 60

I hope this helps! Have a wonderful day!

Lilac~

Answer:

3.5× c20

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Answer:

C)   x = 3

Step-by-step explanation:

Equation of a line in slope-intercept form:  y = mx + b

(where m is the slope (gradient) and b is the y-intercept)

If the line is perpendicular to the x-axis, the line will be parallel to the y-axis (vertical).  We are told that the line passes through point (3, 4).  Therefore, the line will never intercept the y-axis and so the y-intercept is zero.  Also, all the values of x = 3

So the equation of the line is:  x = 3

Answer:

Riley has 4 times the amount of stickers her sister has

Step-by-step explanation:

220 divided by 55 is 4

Answer:

Given that angle DGC is 90 degrees and is vertical to AGB, they both are congruent so they will both have the same degrees.

So now we know angle AGB is 90 degrees

Angle AGE is 30 degrees, and in total all the angles would be equal to 180 degrees.

Now we just solve for x,

30 + 90 + x = 180

120 + x = 180

-120      -120

x = 60

Answer:

C

Step-by-step explanation:

King Snake: 65 inches / 12 inches per foot = about 5.4 feet long

Eastern Diamondback Rattlesnake: 2 yards * 3 feet per yard = 6 feet long

Ridge Nosed Rattlesnake: 4 feet long

Therefore, the eastern diamondback rattlesnake is the longest snake.