Which of the following correctly identifies the set of outputs?

{(5, –2), (1, –1), (–2, 2), (2, 5)}
{(–2, 5), (–1, 1), (2, –2), (5, 2)}
{–2, –1, 2, 5}
{–2, 1, 2, 5}

Answer:

f(g(x)) = f(2x - 3) = 3(2x - 3) + 5 = 6x - 9 + 5 = 6x - 4

f(g(2)) = f(2*2 - 3) = f(4 - 3) = f(1) = 3*1 + 5 = 3 + 5 = 8

The composite function values:

f(g(x)) = 6x- 4

f(g(2)) = 8.

Any function that is created by combining two or more other functions is referred to as a composite function. To put it another way, given two functions, f, and g, the composite function of f and g, denoted as f(g(x)), is a new function that applies g to the input x before applying f to the output of g. (x).

To find the value of fg(x), we need to compute g(x) first and then substitute it into f(x).

g(x) = 2x - 3

Substitute g(x) into f(x):

f(g(x)) = 3(2x - 3) + 5

f(g(x)) = 6x - 4

Therefore, fg(x) = 6x - 4.

To find the value of fg(2), substitute 2 into fg(x):

fg(2) = 6(2) - 4

fg(2) = 8

Therefore, fg(2) = 8.

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Answer:

b = 5√3

Step-by-step explanation:

I would honestly just use pythag, but I'll use trig:

tanθ = opposite/adjacent

tan(30°) = 5/b

btan(30°) = 5

b = 5/tan(30°)

b = 5/(√3/3) = 15/√3

b = 15/√3 · (√3/√3) = 15√3/3

b = 5/√3

Check with pythag:

a² + b² = c²

5² + 5√3² = 10²

25 + 25(3) = 100

25 + 75 = 100  ✅

I hope this helps!

There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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The perimeter of the rectangle is 62 square units.

The perimeter of a rectangle can be calculated using the formula:

P = 2(L + W)

Where:

L is the length of the rectangle

W is the width of the rectangle

We have:

L = 20 units

W = 11 units

Substituting into the formula:

P = 2(20 + 11)

P = 2(31)

P = 62 square units

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Question in English

What is the perimeter of a rectangle if it is 20 long and 11 wide?

Answer:

A) (x-4)(x+16)

Step-by-step explanation:

\(x^2+12x-64\\=x^2-4x+16x-64\\=x(x-4)+16(x-4)\\=(x+16)(x-4)\)

Answer:

\(8 - 3x > -25 : \left[\begin{array}{ccc}solution: x < 11\\Interval Notation:(-\infty,11)\end{array}\right]\)

Step-by-step explanation:

\(8-3x>-25\)

Subtract \(8\) from both sides:

\(8-3x-8>-25-8\)

Simplify:

\(-3x>-33\)

Multiply both sides by \(-1\) (reverse the inequality):

\(\left(-3x\right)\left(-1\right)<\left(-33\right)\left(-1\right)\)

Simplify:

\(3x<33\)

Divide both sides by \(3\) :

\(\frac{3x}{3}<\frac{33}{3}\)

Simplify:

\(x < 11\)

Hope I helped. If so, may I get brainliest and a thanks?

Thank you, have a good day! =)

Step-by-step explanation:

\(y = \sqrt{4x + 6} \)

\( {y}^{2} = 4x + 6\)

\( {y}^{2} - 6 = 4x\)

\( \frac{1}{4} ( {y}^{2} - 6) = x\)

Swap x and y

\( \frac{ {x}^{2} - 6 }{4} = y\)

So a day is made up of 24 hours. An hour is 60 minutes long. This means that 24 hours is 24 x 60 = 1,440 minutes in a day

2 hours and 27 minutes is 147 minutes long.

To find what fraction of a day it is do this equation \:

147/1,440 = approximately 0.102 of a day.

For a percentage, multiply by 100

0.102 x 100 = 10.2%

Hope this helps!

Answer:

64

Step-by-step explanation:

your doubling the answer so

2+2=4. >first week

4+4=8. > second week

8+8=16. > third week

16+16=32. > fourth week

32+32=64 > fith week

Step-by-step explanation:

To find the next term or number, we'll need to keep subtracting 5. So the formula is: n-5

Answer:

I is t w

2 13.2

4 15.2

6 17.2

8 19.2

Step-by-step explanation:

why because I already did the test

Answer:

Step-by-step explanation:

Answer:

equation:  C = 15 - R

C = 15 - 7

C = 8

Step-by-step explanation:

Okay first of all stan the karl pfp

Solution for the given System of linear equation is:

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

Given,  the system of linear equations on the left with its solution type on the right

For  Y=2x-1 and Y=2x+1

Adding both equation,  we will get y = 4x

Thus, these equations have infinite number of solution

For 2x - y = 7 and 3x + y = 3

Adding these equations

5x = 10

x= 2

Substitute the value in equation 1

y = -3

Thus, solution is (2, - 3)

therefore, the Solution for the given System of linear equation is:

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Complete question:

The rates of change in attendance in week 1-4 is 33, week 4-6 is -11, week 6-10 is -37 people per week

The rate of change in attendance with respect to time is calculated by taking the difference in attendance between two weeks and dividing by the number of weeks between those weeks. This is done to find the average rate of change in attendance per week. The formula used is:

\(Rate =\frac{Attendance at week 2 - Attendance at week 1}{week 2 - week 1}\)

Weeks 1-4:

The rate of change in attendance with respect to time is 33 people per week. This can be calculated by taking the difference in attendance between weeks 1 and 4 (230-131) and dividing by the number of weeks between those weeks (4-1 = 3).

\(rate =\frac{230-131}{4-1}\\\)

hence rate is 33 people per week

Weeks 4-6:

The difference in attendance between weeks 4 and 6 (230 - 208)

The number of weeks between those weeks (6-4 = 2).

\(rate =\frac{208-230}{6-4}\)

Hence rate is -11 people per week

Weeks 6-10:

The difference in attendance between weeks 6 and 10 (60-208)

The number of weeks between those weeks (10-6 = 4).

\(rate=\frac{60-208}{10-6}\)

Hence rate is -37 people per week

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Answer:

Solution given:

Annie needs 250 lb of cement to fix the outer step.

Each bag hold 40 lb of cement.

Now

40 lb =1bag

we need

250lb= ? bag.

we have

no of bag =needed lb/1 bag's lb=250/40=250/40=6.25

we do not need more than 7 bags

Annie needs 7 bags.

So

The required inequality is:

b≥7.

Answer:

11. Not enough information

12. You can say DB = DC by SAA congruence rule and CPCTC (Corresponding parts of congruent triangles are congruent)

Step-by-step explanation:

For 12, you can say ΔABD≅ΔACD because they have a side in common (AD) and they have 2 congruent angles. Thus, you can use the SAA congruence criterion. Then, you can use CPCTC (Corresponding parts of congruent triangles are congruent) to say that DB = DC.

Hope this helps :)

Answer:

42

Step-by-step explanation:

One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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Answer:

j= 15k−27/2

Step-by-step explanation:

Answer:

276.

Step-by-step explanation:

you would have to do 90x3=270 then 2 times 3 equals 6 then you should get your answer

Answer:

You should check off boxes 1, 2, 5, and 6

Step-by-step explanation:

These are all irrational numbers because their decimal places go on indefinitely.

Answer:

183

Step-by-step explanation:

The perimeter of the rectangle measured in centimeters is 26 cm.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

Given a rectangle in the figure.

The length of the rectangle = 7 cm

Width of the rectangle = 6 cm

We have to find the perimeter of the rectangle.

Perimeter of the rectangle = 2(l + w), where l is the length and w is the width.

Perimeter = 2(7 + 6)

                = 2 × 13

                = 26 cm

Hence the perimeter is 26 cm.

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9514 1404 393

Answer:

  the equation comes from setting expressions for the perimeters equal to each other

Step-by-step explanation:

Each of the relations is described in terms of the shortest side of the triangle, which is what we're asked to find. It makes sense to let a variable represent that length.

  shortest triangle side: s

  each of the other two sides: s+1

  perimeter of the triangles: s +(s+1) +(s+1) = 3s+2

__

  side length of square: s-2

  perimeter of square : 4(s -2) = 4s -8

__

The two perimeters are equal, so we have ...

  3s +2 = 4s -8 . . . . . your equation

  10 = s . . . . . . . . . . . add 8-3s

Answer:

17

Step-by-step explanation:

The closest perfect cube (to 360) is 343 (7^3) .

360-343 = 17

Subtract 17.

Answer:

You should subtract 17 from 360 to make a perfect cube

Step-by-step explanation:

Step-by-step explanation:   \(2x^{2} +3x+5=0\\\\x=-3±\sqrt{b^{2}-4ac} /2a\\x=-3±\sqrt{3^2-4*2*5/2*2}\\\\x=-3/4 ± \sqrt{31} * (1/4*i)\\x=-3/4 + \sqrt{31} * (-1/4*i)\\\)

Answer: Using the Quadratic Formula, the answer would be x = -3/4 + \sqrt{31} * ([-]1/4*i)

Therefore , the solution to the given problem of order comes out to be

-6< -3< -2.2 < -1/2 < 1/4 < 2\(\frac{1}{3}\) < 2.5 < 4.

Numerical order can be used to organise a set of numbers. It is possible to use both increasing and decreasing ordering. Consider how a set of numbers would seem if they were organized in ascending order like 2, 55, 103, 256, and 802, for example. This can make sorting through a huge collection of numbers much easier.

Here,

Given : 2.5, -6, -3, 4, -2.2, 1/4, -1/2, 2 1/3

To put them according to ascending order :

So ,

negative terms are the smallest compare to positive terms as their values are lower than 0.

thus,

-6< -3< -2.2 < -1/2 < 1/4 < 2\(\frac{1}{3}\) < 2.5 < 4

Therefore , the solution to the given problem of order comes out to be

-6< -3< -2.2 < -1/2 < 1/4 < 2\(\frac{1}{3}\) < 2.5 < 4.

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Answer:

  7 boxes

Step-by-step explanation:

The area of a rectangular prism is given by the formula ...

  A = 2(LW +H(L+W))

The amount of wallpaper Carmen needs for one box is found by computing the area of the box.

__

  A = 2(5·6 +7(5+6)) = 2(30 +7·11) = 2(107) = 214 . . . square feet

  Carmen will be using a total of 214x square feet of wallpaper to cover x boxes. She has 1498 ft² available, so can cover ...

  1498 ft²/(214 ft²/box) = 7 boxes

Carmen has enough wallpaper to cover 7 storage boxes.

Answer:

\(P(Pink) = \frac{1}{4}\)

\(P(Both\ Black) = \frac{9}{16}\)

\(Probability = \frac{3}{64}\) --- Two pink and One black

Step-by-step explanation:

Represent the pink skin with P and the black skin with B.

Since black skin is dominant to pink skin, there will be more occurrence of B than P

The punnet square for the breeding of the two pigs is then represented as:

\(\begin{array}{cc} {B} & {B} \ \\ {B} & {P} \ \ \end{array}\)

Solving (a): Probability of Pink

In the above square, there is only 1 occurrence of P out of a possible of 4.

So, the probability is:

\(P(Pink) = \frac{n(P)}{4}\)

\(P(Pink) = \frac{1}{4}\)

Solving (b): Probability that first and second are black

In the above square, there is only 3 occurrence of B out of a possible of 4.

\(P(Black) = \frac{n(B)}{4}\)

\(P(Black) = \frac{3}{4}\)

So, the probability that both are black is:

\(P(Both\ Black) = P(Black) * P(Black)\)

\(P(Both\ Black) = \frac{3}{4} * \frac{3}{4}\)

\(P(Both\ Black) = \frac{9}{16}\)

Solving (c): Probability of two pink and 1 black

This is calculated as:

\(Probability = P(Pink) * P(Pink) * P(Black)\)

\(Probability = \frac{1}{4} * \frac{1}{4} * \frac{3}{4}\)

\(Probability = \frac{3}{64}\)

A) The probability that their offspring will have pink skin is; ¹/₄

B) The probability that the first and second off- spring will have black skin is;

9/16  or 56.25%

C) The probability that two will be pink and one will be black  If the pigs produce a total of three piglets is; ³/₆₄ or 4.6875%

To answer this question, we need to first understand Mendel's law of dominance. This law states that in a heterozygote, one trait will conceal the presence of another trait for the same characteristic. This means that the dominant trait always conceal the recessive trait.

Now in this question, we are told that;

Let's denote the black color gene by ‘P’ and pink colour by ‘p’. Therefore, if cross is held between these two genes then according to mendel's law, the heterozygous pigs is specified as "Pp"

Now when the heterozygous pigs specified as "Pp" are crossed, we have;

Pp × Pp = PP, Pp, Pp, pp

where;

(a) From the 4 cross possibilities above;

Probability that their offspring will have pink skin = ¹/₄

(b) From the 4 cross possibilities gotten earlier;

Probability that their offspring will have black skin = ³/₄

Thus;

Probability that the first and second off- spring will have black skin is;

³/₄ × ³/₄ = 9/16  or 56.25%

(c) We are told that the pigs produced a total of three piglet. Thus, the probability that two will be pink and one black will be black is;

P(2 pink and 1 black) =   ¹/₄ × ¹/₄ × ³/₄ = ³/₆₄ or 4.6875%

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