help please :)))))))))))))))))))))

The value of g(f(x)) will be 3(1-x²) and the value of g(f(2)) will be -9 for the f(x)=4-3x² and g(x)=x-1.

A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

Functions are broadly classified into four categories. Element-based: one-to-one function, many-to-one function, onto function, one-to-one and onto function, into function.

Here, f(x)=4-3x² and g(x)=x-1

g(f(x))=(4-3x²)-1

g(f(x))=4-3x²-1

=3-3x²

=3(1-x²)

g(f(2))=3(1-2²)

=3*-3

=-9

For f(x)=4-3x² and g(x)=x-1, the value of g(f(x)) is 3(1-x²) and the value of g(f(2)) is -9.

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Answer:

Step 3; it should be angle m + angle n + angle o = angle o + angle p

Step-by-step explanation:

yes, the sum of the inner angles of the triangle, m, n, o must be 180°.

yes, the sum of supplementary angles (which the pair of inner and outer angles always is) p and o must be 180°.

so, step 3 wants to show that the sum of the 3 inner angles is the same as the sum of the inner/outer angle pair. m + n + o = o + p = 180.

but instead of o the student suddenly wrote n in the right side of the equation. and that is wrong. n + p can't be 180°, as both are inner angles, and that would make the third inner angle 0°, which is not really possible.

so, once n is replaced by o on the right side of the equating in step 3, all is correct again.

and step 4 is correct anyway (it fixed the mistake in step 3 of the original proof by another mistake, coming to the right conclusion just by coincidence), now that step 3 is corrected.

Check the picture below.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ Q(6,2)\qquad R(18,18)\qquad \qquad \stackrel{\textit{ratio from Q to R}}{3:1} \\\\\\ \cfrac{Q\underline{S}}{\underline{S} R} = \cfrac{3}{1}\implies \cfrac{Q}{R} = \cfrac{3}{1}\implies 1Q=3R\implies 1(6,2)=3(18,18)[/tex]

[tex](\stackrel{x}{6}~~,~~ \stackrel{y}{2})=(\stackrel{x}{54}~~,~~ \stackrel{y}{54}) \implies S=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{6 +54}}{3+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{2 +54}}{3+1} \right)} \\\\\\ S=\left( \cfrac{ 60 }{ 4 }~~,~~\cfrac{ 56}{ 4 } \right)\implies {\Large \begin{array}{llll} S=(15~~,~~14) \end{array}}[/tex]

Answer:

$26.99

Step-by-step explanation:

17.50 original cost plus a 54.2% increase

First, divide percentage by 100 to get a decimal to divide by 54.2/100=0.542

Then multiply the new decimal by the original cost to find the amount marked up. 17.50 x 0.542= 9.485

Now add 9.485 to the original cost

17.50+9.485=26.985-> 26.99 rounded for the final answer

Answer:

Step-by-step explanation:

its 3 4

R' (-3,-4) are the resulting coordinates of the purpose R.

A rotation may be a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point. The fixed point is named the center of rotation . The quantity of rotation is called the angle of rotation and it is measured in degrees. Use a protractor to live the specified angle counterclockwise.

Using the rule for a 180° rotation to seek out the vertices of the rotated triangle.

T: (x, y) ⇒ (-x, -y)

Given points of triangle: S(1,1) , R (3, 4) and Q (7, 0).

Rotation 180° about the origin.

S (1, 1) → S' (-1,-1)

R (3,4) → R' (-3,-4)

Q (7,0) → Q' (-7,0)

Hence, the coordinate of the R is: R' (-3,-4).

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The cost of the phone  before the discounted price is $160.

Given that, Refurbished phone 45% OFF now only £88.

Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price. The List price or Marked price is the price of an article as declared by the seller or the manufacturer, without any reduction in price. Selling price is the actual price at which an article is sold after any reduction or discounts in the list price.

Let the original price of the phone be x.

Now, x - 45% of x = 88

⇒ x - 45/100 × x = 88

⇒ x - 0.45x = 88

⇒ 0.55x = 88

⇒ x = 88/0.55

⇒ x = 160

Therefore, the cost of the phone  before the discounted price is $160.

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Answer: 3.32 * 10^4

Step-by-step explanation:

1) Set up the equation

4.00 * 10^4 - 6.8 * 10^3

2) Set the scientific notions the same

You can do this by multiplying 10 or dividing 10 on a notion

4.00 * 10^4 - 0.68 * 10 ^4

3) Factor the scientific notions out

10^4(4.00 - 0.68)

4) Subtract

10^4(3.32)

3.32 * 10^4

Step-by-step explanation:

a parallel line must have the same slope (otherwise it cannot be parallel).

a slope-intercept form looks like

y = ax + b

"a" (the factor of x) is always the slope, "b" is the y-intercept (the y-value when x = 0).

so, we know from y = -3x + 5 that the slope of the new line is also -3.

to get b we use the coordinates of the given point :

-5 = -3×-8 + b = 24 + b

-29 = b

that means the line equation is

y = -3x - 29

The equation of line is y= 5/2x -7.

The slope of the line and a point on the line may be used to create the equation of a line. To better comprehend how the equation for a line is formed. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

One of the significant forms used to express a straight line algebraically is the two point form.

Written as, y- y1= m (x- x1), where m is slope.

Given:

a line passes through the point (2, -2) and parallel to 5x-2y = 4

Now, writing the given equation of line in the form of slope intercept form

5x- 2y=4

2y = 5x -4

y= 5/2x -2

Here the slope is 5/2 and the required line will also have the same slope as parallel line.

then, m=5/2

Now using y=mx +c

put y=-2 and x=2

-2 = 5/2(2) + c

-2 -5 = c

c=-7

Hence, the equation of line is y= 5/2x -7.

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Answer:

1 ≤ y ≤ 4

Step-by-step explanation:

Range is all possible y values

a point is written as (x, y)

The line starts at point (0, 1) and ends at (3, 4)

so the range of the y values is 1 to 4

Answer:

u = -153

Step-by-step explanation:

u/3 = -51

multiply both sides by 3:

3(u/3) = 3(-51)

u = -153

Answer:

Step-by-step explanation:

We all know that any number multiplied by zero equals zero. Consequently, the division by zero operation is impossible.

so, your answer is undefined

Answer:

Step-by-step explanation:

a. From 4 to 7 is 3 units. 7-10 is another 3 units and so on. The constant 3 units is the common difference.

The formula for a arithmetic sequence is

[tex]a_{n}=a_{1}+d(n-1)[/tex]

Where d is the common difference and a_1 is the first term.

[tex]a_{1}=4[/tex] and [tex]d=3[/tex]. Thus the equation of the nth term is

[tex]a_{n}=4+3(n-1)[/tex]

The angle measures formed by the parallel lines are:

9. m∠10 = 69°

10. m∠6 = 115°

11. m∠7 = 118°

12. m∠11 = 108°

13. m∠14 = 66°

14. m∠12 = 86°

The angle measures can be determined by using the special angle relationship between the angles involved when a transversal crosses two lines that are parallel.

9. x and y are parallel lines

m∠5 = 69°

m∠10 = m∠5 [alternate interior angles theorem]

m∠10 = 69° [substitution]

10. x and y are parallel lines

m∠9 = 115°

m∠6 = m∠9 [alternate interior angles theorem]

m∠6 = 115° [substitution]

11. x and y are parallel lines

m∠12 = 118°

m∠7 = m∠12 [alternate interior angles theorem]

m∠7 = 118° [substitution]

12. x and y are parallel lines

m∠4 + m∠11 = 180 [supplementary angles]

72 + m∠11 = 180 [substitution]

m∠11 = 180 - 72

m∠11 = 108°

13. m∠4 + m∠14 = 180 [supplementary angles]

114 + m∠14 = 180 [substitution]

m∠14 = 180 - 114

m∠14 = 66°

14. m∠5 = 86° [given]

m∠12 = m∠5 [congruent angles]

m∠12 = 86°

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The x-intercept is (27,0). The time it takes to reach the bus stop

We first find the equation between time and distance as a linear function by finding the slope and y-intercept from the table values.

If we write the Time as x-values and Distance as y-values, we get the points,

(0,45), (3,40), (6,35), (9,30), (12,25)

We can find the slope from these points considering two points (0,45) and (3,40)

Slope = 45-40/0-3 = -5/3

The y-intercept of the function is the value of f(x) at x = 0.

Here, from the table, when x = 0, y = 45.

So y-intercept = 45

Then the equation of distance in terms of time is,

y = -(5/3)x+45

The x-intercept is the x-value when y = 0.

So when y = 0,

0 = -(5/3)x+45

⇒ (5/3)x=45

⇒ x = 45x 3/5

⇒ x = 27

Therefore, x-intercept = (27,0).

It is the time (in minutes) when distance = 0 meters.

So x-intercept is the time it takes to reach the bus stop.

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Answer:

B)  (27,0); the time it takes to reach the bus stop

The 64 fluid ounces of water, as suggested by Kamryn's doctor to drink everyday, will be equal to 1920 millilitres.

Writing the equation as per the relation between millilitres and fluid ounces -

1 fluid ounce = 30 millilitres

Now, we will perform multiplication to find the number of milliliters in 64 fluid ounces. Writing the expression representing relation between millilitres and fluid ounces

Number of milliliters = 30×64

Performing multiplication between the numbers 30 and 64

Number of milliliters = 1920

Therefore, on drinking 64 fluid ounces by Kamryn on her doctor's recommendation will drink 1920 millilitres of water everyday.

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Answer:

DB is a perpendicular of AC

The total value of the plumber's liabilities = $441,806

One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.

It is one of the fundamental mathematical operations we employ on a daily basis. We employ number addition in a variety of contexts. When we work with time or money, such as when adding up invoices and receipts, adding numbers is one of the most frequently used operations in daily life.

The total value of the plumber's liabilities :

is to simply add all the values and we will get

$441,806

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Answer:

Option B.) $167,925

Step-by-step explanation:

Liability is money you owe to another person or institution, including a credit card balance, mortgage and so on.

So the plumber's liabilities

= 149,367 + 6,283 + 12,275

= $167,925

ANSWER:

STEP-BY-STEP EXPLANATION:

Answer: 30 minutes to get to the playground

Step-by-step explanation:

[tex]\huge\boxed{\sf 16}\\\\ \sf The\ two\ right\ triangles\ are\ a\ reflection\ of\ each\ other.\\ Both\ sides\ are\ equal\ in\ size. \\\\ 5x+1=4x+4\\5x-4x=4-1\\1x=3\\\\ Plug\ the\ value\ of\ x\ back\ into\ any\ of\ the\ two\ equations.\\\\ 5(3)+1 =15+1=16[/tex]

The equation of the line that passes through points (6, -5) and (2, 3) is y = -2x + 7.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point 1 ( 6, -5 )

Point 2 ( 2,3 )

First, we determine the slope of the line.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m = ( 3 - (-5) ) / ( 2 - 6 )

Slope m = ( 3 + 5 ) / ( 2 - 6 )

Slope m = ( 8 ) / ( -4 )

Slope m = -2

Now that the value of slope is known, we determine the y-intercept 'b' by plugging the slope and one point into equation of line formula.

y = mx + b

-5 = (-2)(6) + b

-5 = -12 + b

b = -5 + 12

b = 7

Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = (-2)x + 7

y = -2x + 7

Therefore, the equation of the line is y = -2x + 7.

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Answer: -5v-6

Step-by-step explanation:

If the bottom of the ladder slides away from the wall, then x changes by 12cosθ with respect to theta and when  θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.

Here, we are given that a ladder 16 ft long rests against a vertical wall and theta is the angle between the top of the ladder and the wall.

We know that, sin of an angle = opposite / hypotenuse

Thus, sinθ = x/16

⇒ x = 16 sinθ

The rate of change of x with respect to θ will be given by dx/dθ

dx/dθ = d/dθ (12sinθ)

= 12 d/dθ (sinθ)

= 12cosθ

Now, we need to find the value of dx/dθ when θ = π/6,

= 12 cosπ/6

= 12 ([tex]\sqrt{3}[/tex]/2)

= 6[tex]\sqrt{3}[/tex]

Thus, when  θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.

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Your question was incomplete. Check for full content below-

A ladder 12 feet long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall, and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π/6?

Answer:

x = 100

Step-by-step explanation:

180 = 46 + 34 + x

180 = 80 + x

100 = x

The inches that are expected more in September than in February is 3.94

What is average and how to calculate it?

Average is ratio of the sum of all elements of dataset and total number of elements in the dataset. To calculate first find the sum of all elements of the dataset and then divide it by total number of elements in the dataset

The average rainfall for key west is 1.52 inches in February and 5.45 inches in month of September

To find the more inches we subtract the two We get,

[tex]5.45-1.51=3.96[/tex] inches

Hence The inches that are expected more in September than in February is 3.94 inches

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Answer:

6/7

Step-by-step explanation:

2Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/3 is 3/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - two sevenths divided by one third is six sevenths.