Given f(x) = -3x + 1, solve for a when ƒ(x) = −5.

Answer: 27 over 2,5

Step-by-step explanation:

Functions whose inverses are also functions.

Inverse function is represented by [tex]f^{-1}[/tex] with regards to the original function  and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

If a horizontal line intersects the original function in a single region, the function is a one-to-one function and inverse is also a function.

Every function has an inverse, but not every inverse will be a function. The inverse may fail the vertical line test. If the original function is a one-to-one function, then its inverse will be a function. A one-to-one function not only passes the vertical line test, it also passes a horizontal line test.

Therefore, functions whose inverses are also functions.

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Answer:

[tex](\frac{5}{3} ;\frac{4}{3} ).[/tex]

Step-by-step explanation:

[tex]\left \{ {{x+y=3} \atop {\frac{y+2}{2} =x}} \right. \ = > \ \left \{ {{x+y=3} \atop {y+2=2x}} \right. \ = > \ \left \{ {{x+y=3} \atop {2x-y=2}} \right. \ = > \ \left \{ {{x=\frac{5}{3} } \atop {y=\frac{4}{3} }} \right.[/tex]

The initial polynomial result will include several terms, but after simplification, there may only be one or two terms left.

Each polynomial must be considered to be in standard form. The initial multiplication will result in a total of m and n terms since each of the m terms of the first polynomial will be multiplied by each of the n terms of the second.

When the sum is simplified, some of those elements may be combined, resulting in a final product with only one or two terms.

1. 2 × b = 2b . . . . . each has 1 term; the result has 1 term.

2. (x -a)(x +a)  = x² -ax + ax -a² (2×2=4 terms) = x² -a² . . . . the results has 2 terms.

3.  (x -a)(x³ +x) =  x⁴ -ax³ + x² -ax . . . the results has 2×2 = 4 terms

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x = 3/4 is the correct solution of the given expression.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

The expression Lin tried to solve
8(x-3)+7=2x(4-17)

Simplifying the expression,
8x - 24 = 2x(-13)
8x - 24 = -26x
8x+26x = 24
32x = 24
x = 24/32
x = 3/4

Thus, x = 3/4 is the correct solution of the given expression.

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The transformation of function y = |x| is g(x) = f(x + 4) + 2. The equation of transformed graph is y = |x + 4| - 2

What is a function?

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is y = |x|.

The vertex is (0,0). The vertex of the transformed function is (-4,-2)

It means the graph is shifted 4 units left sides and 2 unit downward direction.

The graph of f(x) is horizontally shifted by a units on left side then the equation function becomes f(x + a).

The graph of f(x) is horizontally shifted by a units on right side then the equation function becomes f(x - a).

The graph of f(x) is vertically shifted by a units upward then the equation function becomes f(x)+a.

The graph of f(x) is vertically shifted by a unit downward then the equation function becomes f(x)-a.

The equation of the transformed equation is g(x) = f(x + 4) - 2

g(x) = |x + 4| -2

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Answer:

49200 rs. so the cost of flooring =246*200=49200 rs

Step-by-step explanation:

we measure the area of veranda by taking width in addition of length and breadth- house area

it means

area of veranda =outer rectangle-inner rectangle

⇒area= (20+3+3)*(15+3+3)-20*15

⇒area=26*21-300

⇒area= 546-300

⇒area=246 m²

Hence , the cost of flooring =246*200=49200 rs.

It will take roughly 15.7 months to drop in value to less than £1200 if the current value of the bike is £2550.

You can use the following formula to calculate how many months it will take for a motorbike with a value of £2550 value to drop to under £1200:

n = (1200 - 2550) ln / ln (1 - 0.05)

Where 0.05 denotes the 5% monthly depreciation rate, ln is indeed the natural logarithm function, and n refers to the number of months.

When we enter the values, we will get:

n = (1200 - 2550 - 1 - 0.05) / ln(1 - 0.05) = about 15.7 months

The motorcycle will take approximately 15.7 months to drop in value to less than £1200.

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He will use 9.375 acres of the land for the park

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.

Since the land is 21.5 acres and 0.75 of the land  was used for a park. we can write:

acres used for the park = 0.75 × 12.5 = 9.375 acres

Thus, he will use 9.375 acres for the park

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Answer:

Step-by-step explanation:

To solve for r, you need to first find the values of x that make y equal to 24. These values of x are called the roots of the polynomial equation y = (x+3)(x-2)(x-r).

To find the roots of the equation, you can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation y = ax^2 + bx + c.

In this case, the coefficients are:

a = 1

b = -3

c = -24

Substituting these values into the quadratic formula, we get:

x = (3 +/- sqrt(9 - 96)) / 2

= (3 +/- sqrt(-87)) / 2

Since sqrt(-87) is not a real number, there are no real roots for this equation. Therefore, the value of r cannot be determined.

Answer:

50%

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

Looking at the problem, we can take 25, and divide 50 by it.

25 ÷ 50 = 0.5

0.5 is equal to 5/10, which is also equal to 50%, meaning that 50% of 50 is 25.

Answer:

  (b)  y < x-1; y ≤ -2x+2

Step-by-step explanation:

You want to know the inequalities represented on the graph showing a solid line with negative slope and a y-intercept of 2, and a dashed line with positive slope and a y-intercept of -1, where the shading is below both lines.

If the line is included in the solution set (≤ or ≥ is used), the boundary line is graphed as a solid line. If the line is not included in the solution set (< or > is used), the boundary line is graphed as a dashed line.

Here, the line with positive slope is dashed, and the line with negative slope is solid.

  y = x -1 . . . . is a line with positive slope

  y = -2x +2 . . . . a line with negative slope

The shading is below the line for y-values less than those on the line:

  y < x -1 . . . . shading below a dashed line with positive slope

  y ≤ -2x +2 . . . . shading below a solid line with negative slope

These are the inequalities of interest.

The solution to the system of equation shown in the graph is (2, 3)

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Given the equation:

y=−x+5   (1)

y=2x−1   (2)

Solving by elimination method. Subtract equation 2 from 1:

0 = -3x + 6

x = 2

Put x = 2 in eqn 1:

y = -(2) + 5 = 3

The solution is (2, 3)

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The equation of line that passes through (-2,-1) and is perpendicular to f(x) = (-1/5)x + 1 is f(x) = 5x + 9.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the graph

f(x) = (-1/5)x + 1

Using the slope intercept, slope m is -1/5

The equation of a perpendicular line to f(x) = (-1/5)x + 1 must have a slope that is the negative reciprocal of the graph.

Slope of perpendicular line = -1 / (-1/5)

Slope of perpendicular line = 5

Plug the slope m = 5 and point (-2,-1) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - (-1) ) = 5( x - (-2) )

( y + 1 ) = 5( x + 2 )

y + 1 = 5x + 10

y = 5x + 10 - 1

y = 5x + 9

f(x) = 5x + 9

Therefore, the equation of the perpendicular line is f(x) = 5x + 9.

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Answer:

[tex] \sf \: d) \: 82[/tex]

Step-by-step explanation:

Given information,

→ d = 10

→ u = 7

→ e = 3.2

The expression is,

→ d(e + 5)

Let's evaluate the expression,

→ d(e + 5)

→ 10(3.2 + 5)

→ 10 × 8.2

→ 82

Hence, option (d) is correct.

Answer:

Option D) 82

Step-by-step explanation:

Given ,

d = 10

u  = 7

e = 3.2

To Find  : [tex]d(e+5)[/tex]

Applying the values in the equations we get

[tex]10(3.2+5)\\[/tex] Applying Distributive property

[tex]32+50 = 82[/tex]

Hence , Option D) is the answer

Answer:

(2,-2)

Step-by-step explanation:

The answer is the intercept point of both lines, so we need to find the point when both the line touches, with out graphing we can see by the table that point (2, -2) intercepts with the line on the graph.

hope this helps :)

Answer:

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

From the table we see each y-coordinate is the negative of the corresponding x-coordinate. It gives us the second line:

The first line is given y = 1/2x - 3, equate both to get:

Then the value of y:

The solution is (2, - 2).

A line that shows the number of hair barrettes she makes and the total number of beads she uses is y = 75x.

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, you must first determine the slope and y-intercept. The slope is the ratio of the change in y to the change in x. Find two locations on the line, and then draw a sloping triangle joining them.

A line is a perfectly straight, one-dimensional figure that extends infinity in both directions and has no thickness. To stress that a line has no "wiggles" anywhere along its length, it is sometimes referred to as a straight line or, more archaically, a right line.

Two points on the line are (2, 150) and (5, 375)

y - 150 = ( (375-150) / (5-2) )  (x-2)

y - 150 = 75 (x-2)

y = 75x

Equation of line is y = 75x

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Answer: 12

Step-by-step explanation: There are about 12 grams of carbohydrates in a 8 fluid ounce (240 mL) glass of whole milk. The amount of carbohydrates in milk can vary slightly depending on the type of milk you are drinking. For example, skim milk has slightly fewer carbohydrates (about 11 grams per 8 fluid ounces) than whole milk because the fat has been removed. On the other hand, milk that is high in fat, such as heavy cream, has even more carbohydrates (about 4 grams per fluid ounce).

Answer:

It is best to solve a system of equations using substitution when one of the equations isolates one of the variables, or when the coefficient of one of the variables is 1 or -1.

Step-by-step explanation:

This makes it easier to substitute one variable for the other, allowing you to solve for the remaining variable. It is also a good idea to check the solution back in the original equations just to make sure it is a valid solution

Answer:

Answer Below

Step-by-step explanation:

It is best to use substitution if one of the variables is isolated or has a coefficient of 1 or -1.

Answer:

1st question :55%

2nd ":122.22%

3rd ":81.82%

The volume of each drinking cup is 7.9 cubic inches.

An office uses paper drinking cups in the shape of a cone, with dimensions as shown.

The formula provides the volume of a cone.

V =  (1/3) * π * r² * h.

We can find the solution by entering the already-known data into the formula.

d = 2.75 m.

Since radius is half of d, we can say

0.5 * 2.75 = 1.375 in.

4 inches is listed as the height.

The result of plugging all of them into the original formula is:

V = (1/3) * π(1.375)² (4) = 7.9

Our final response, rounded to the closest tenth, is:

V = 7.9 cubic inches.

The volume of each drinking cup is 7.9 cubic inches.

The complete question is An office uses paper drinking cups in the shape of a cone, with dimensions as shown. To the nearest tenth of a cubic inch, what is the volume of each drinking cup?

d = 2.75 m.

h = 4

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Answer:

12.57 ft

Step-by-step explanation:

First thing we need to find is the radius of the circular glass pane. We are given the information that the center of the glass plane is directly in the center of the triangle and that the closest distance from the center to the roof is 3 ft, including a metal border with a width of 1 ft.

Since the metal frame is the same width all the way around the window, we can safely conclude that the radius of the circular glass pane is 2 ft, as the 3ft measurement included the radius and the metal frame.

Now that we have our radius we can use the formula:

[tex]C=2\pi r[/tex] (Circumference = 2 x pi x radius)

Using 3.14 for pi we get:

[tex]C=2(3.14)(2)[/tex]

[tex]C=4 \pi[/tex] or 12.57 ft (2.d.p)

Answer:

A.

Step-by-step explanation:

just put it i swear it will help lollllll

Step-by-step explanation:

that is a college level question ? and you don't know the answer ?

that is basic, basic, basic ...

you go on the x-axis to -2.

from there you go either up or down and look at what y-value are you crossing the functional curve.

it is -1.

so, the "output" for x = -2 is y = -1. or simply -1.

The fraction 20/3 rounded to the nearest hundredth is 6.67.

We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, A fraction 20/3, First we'll convert this fraction into a decimal.

So, 20/3 is equal to 6.666666....

Therefore,  20/3 to the nearest hundredth of a foot is equal to 6.67.

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The edge of a block of metamaterial is 10 centimeters.

The surface area of the cube all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself. The formula to find the surface area of a cube is 6a², where a is edge.

Given that, a block of metamaterial is in the shape of a cube with a surface area of 600 square centimeters.

Here, 6a²=600

a²=100

a=10 centimeters

Therefore, the edge of a block of metamaterial is 10 centimeters.

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The system of equations will have no solutions if the two lines are parallel, then one example can be:

5x - 2y = 1

15x - 6y = 0

Here we have the following system of equations:

5x - 2y = 1

a*x - 6y = b

The system will have no solutions only if the two equations are parallel. You can see that the coefficient of y on the second equation is 3 times the coefficient on the first equation.

Then a should also be 3 times the coefficient of x on the first equation:

a = 3*5

a = 15

And b should be any number but 3 times the constant on the other equation:

b ≠ 3*1

So we can take b = 0, for example.

So the system with no solutions will be:

5x - 2y = 1

15x - 6y = 0

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Answer: The club members estimate that they will sell 100 tote bags when the price is $11 each, and for every price increase of $1, they estimate they will sell 10 fewer bags. If the price increases to $13, then this is a $2 increase from the original price, so we can calculate the number of fewer bags they estimate they will sell:

10 fewer bags per $1 increase * $2 increase = 20 fewer bags

To find the number of bags they estimate they will sell when the price is $13, we can subtract this decrease from the original number of bags they estimate they will sell:

100 bags - 20 fewer bags = 80 bags

To find the revenue in dollars, we can multiply the number of bags they estimate they will sell by the price of the bags:

80 bags * $13 per bag = $1040

So the estimated revenue when the bags are priced at $13 each is $1040

Step-by-step explanation:

Answer:

The ratio given cannot be used to find the answer