For the functions f(x) = 2x-5 and g(x) = 3x²-x, find (fog)(x) and (gof)(x).

Answer:

Step-by-step explanation:

im not in 100th grade yet

A) x+2y=30

x=30-2y

B) x=8, y=11 and the solutions x and y represent the prices of tickets for students and non students.

An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.

Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.

Given equations are:

2x + 3y = 49

x + 2y = 30

A) From eq 2,

x+2y=30

x=30-2y

B) x and y represents the prices of tickets for students and non students.

2(30-y)+3y=49

60-4y+3y=49

y=60-49

y=11

x=30-2y

x=30-2(11)

x=30-22

x=8

The solutions x and y represent the prices of tickets for students and non students.

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y=3

x=11

hence answer 25

3x+5y=48

2x-y=19

eliminate x to find y

(3x+5y=48)2

(2x-y=19)3

(6x + 10y. = 96)

- minus direct

(6x - 3y. = 57)

=

13y = 39

Note: (10y -(-3y)=13y)

divide by 13 to remain with y

y =3

substitute to any equation to get x lets pick second one

2x-(3)=19

2x-3=19

2x=19+3

2x/2=22/2. (to remain with x value)

x=11

therefore 2x+ y results to 2(11) +3=25

Answer:

2x + y = 25

Step-by-step explanation:

Given equations:

[tex]\begin{cases} 3x + 5y = 48\\\;\;2x-y=19\end{cases}[/tex]

Rearrange the second equation to isolate y:

[tex]\implies 2x-y=19[/tex]

[tex]\implies 2x-19=y[/tex]

Substitute the found expression for y into the first equation and solve for x:

[tex]\implies 3x+5y=48[/tex]

[tex]\implies 3x+5(2x-19)=48[/tex]

[tex]\implies 3x+10x-95=48[/tex]

[tex]\implies 13x=143[/tex]

[tex]\implies x=11[/tex]

Substitute the found value of x into the equation for y and solve for y:

[tex]\implies y=2x-19[/tex]

[tex]\implies y=2(11)-19[/tex]

[tex]\implies y=22-19[/tex]

[tex]\implies y=3[/tex]

Therefore, the solution of the given system of equations is:

To find the value of 2x + y, substitute the found values of x and y into the expression and solve:

[tex]\begin{aligned}\implies 2x+y&=2(11)+3\\&=22+3\\&=25\end{aligned}[/tex]

Therefore:

The y-intercept of the line of best fit is -5.18cm and it is showing the initial height of the plant immediately it was planted and it is not reasonable because it shows a negative height

The general form of the equation of a line in slope intercept form is expressed as;

y = mx + c

where;

m is slope

c is y-intercept.

Now, we are given the equation of the line of best fit as;

y = 0.404x - 5.18

where;

y represents the height of the plant above ground level.

x represents the number of days since it was planted.

a) From the given equation, we see that the slope is; m = 0.404 and that the y intercept is -5.18.

Now, what the y-intercept means is that the height of the plant is 5.18 cm below the ground and this is not reasonable.

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Answer:

X+1>12/3

X+1>4

X>4-1

X>3

Answer:

C.)

Step-by-step explanation:

1.) Since she does 8 vases in 2 hours, she would do 4 vases in 1 hour.

2.) By using this, we divide 50/4 to figure out the amount of hours. This is equal to 25/2, which is equal to 12.5.

3.) Now, check the options. C.) fits this situation the best. Therefore, C.) is the answer.

Answer: No solution

Step-by-step explanation:

[tex]\sqrt{x-3}=\sqrt{x} +3\\[/tex]

square both sides

x-3=x+9

x=x+12

0=12

0 does not equal 12, and therefor, there is no solution.

Answer: B. Ryan is buying too many material things or spending too much on experiences so that he feels on par with his peers

Idioms

Idioms are phrases or expressions that have a specific meaning that is different from the meaning of the individual words, for example, the idiom "you have bitten off more than you can chew" implies that someone is trying to do something that is too difficult for him/her.

"Keeping up with the Joneses" is an idiom that refers to the urge to keep up with the social status, wealth, or popularity of other people around us. This situation causes someone to constantly compare himself/herself with others and buy the same goods in order to show that he/she has as much money as other people.

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Answer:

a = b

b = a

Step-by-step explanation:

The distance traveled is 385miles

f\mathopen{}\mathclose{\left(6\right)}f(6)​ = (6-6)(something) + 22​ = 0(something) + 22​ = 22 which has a remainder of 22 when divided by x-6x-6​. f\mathopen{}\mathclose{\left(6\right)}f(6)​ = \boxed{22}.

The remainder theorem states that when a polynomial is divided by a linear term, the remainder equals the value of the polynomial at the root of the linear term. This theorem may be used to determine the roots of a polynomial by dividing it by a linear term and solving for the remainder. For instance, when the polynomial x3+x2-5x+6 is divided by (x2), the result is identical to the polynomial's value at x=2. After finding the remainder, we may determine that the polynomial's root is 2, which we can do by solving for the remainder. This theorem may also be used to discover the roots of higher degree polynomials by combining linear terms.

How to solve?

f\mathopen{}\mathclose{\left(x\right)}f(x)​ can be written as (x-6)(something) + 22​.  

f\mathopen{}\mathclose{\left(6\right)}f(6)​ = (6-6)(something) + 22​ = 0(something) + 22​ = 22​.

Therefore, f\mathopen{}\mathclose{\left(6\right)}f(6)​ = \boxed{22}.

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let's convert the mixed fractions to improper fractions and the subtract.

[tex]\stackrel{mixed}{5\frac{3}{8}}\implies \cfrac{5\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{43}{8}} ~\hfill \stackrel{mixed}{3\frac{3}{4}}\implies \cfrac{3\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{15}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{43}{8}~~ - ~~\cfrac{15}{4}\implies \cfrac{(1)43~~ - ~~(2)15}{\underset{\textit{using this as the LCD}}{8}}\implies \cfrac{43-30}{8}\implies \cfrac{13}{8}\implies {\Large \begin{array}{llll} 1\frac{5}{8} \end{array}}[/tex]

Answer:

12

Step-by-step explanation:

add the number of days that the chicken laid 5 or more eggs

5 + 5 + 2 = 12

From the given frequency table, we observe that the chicken lays 5 or more eggs on day 4, 5 and 6, and the eggs laid by the chicken are the greatest on day 4.

A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension. Two or three columns make up a frequency distribution table.

here, we have,

All of the results are shown in the first column as individual values or as class intervals.

The table's second column contains the results' totals, which also display the frequency as vertical lines. It's not required.

The frequency of each result is revealed in the third column.

The frequency table uses lines to depict the number of laid eggs. Here, 5 is represented using a hashed line over four lines. Thus, we see that the maximum number of eggs laid are 6, on day 4.

Also, the chicken lays 5 or more eggs on day 4, 5 and 6.

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The solution to probability problem is the expected value for a person that buys one ticket is -$2.32

Probability is a measure of the likelihood or chance that a specific event will occur, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

According to the given information:

To find the expected value, you need to multiply each possible outcome by its probability and then add them together.

In this case, there are two possible outcomes: either the person wins the laptop computer (with a probability 1/1500), or they don't win anything (with a probability 1499/1500).

So, the expected value can be calculated as:

E(x) = (1/1500)($1000) + (1499/1500)(-$3)

E(x) = $0.67 - $2.99

E(x) = -$2.32

So the expected value for a person that buys one ticket is -$2.32.

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We can use both according to the given information.

• In 2 triangles if 2 sides of a triangle and 2 sides of another triangle are equal and if any one angle is equal to the angle in another triangle then we use SAS congruence rule

• In 2 triangles if 3 sides are equal to the 3 sides of another triangle then we use SSS congruence rule

• We can also use RHS (Right angle Hypotenuse Side). It is for 2 right angle triangle.

Answer:

a = 4p + 3

Step-by-step explanation:

The general form of a linear equation is y = mx + b

where y is the dependent variable, x the independent variable

m = slope(rate of change)

b = y-intercept which is the value of y when x = 0

In this problem, instead of x we are asked to use p and instead of y we are using a

Therefore we get

a = mp + b

We have to compute m and b

Since b is the value of a when p = 0, we can easily see that a = 3 when p = 0

Therefore:
a = mp + 3

To determine m, take any value of p, find the corresponding a from the table, plug in these values and solve for m

When  p = 1, a= 7

So we get

7 = m(1) + 3

7 = m + 3

or

m = 7-3 = 4

So the equation is
a = 4p + 3

You can verify this as correct by plugging in different values for p from the table and checking if you get the corresponding a value

Answer: neither

Step-by-step explanation:

To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions.

Check the picture below.

let's take a looksie at that, notice, if we split the circle into 6 even pieces, we end up with six 60° angles at the center, namely six equilateral triangles as you see there.

now, if we run a dashed line as you see from a corner to the other to make the flatter triangle which is shaded, we end up cutting the equilateral triangle into two equal halves, each with 30° and 30° angles, because the dashed line intercepts the green line at 90°.

well, the flatter triangle from corner to corner, is spanning over two equilateral triangles, if it's owning half of one, it must be also owning half of the other.  What the dickens does that mean?  well, it means the area of the flatter triangle that's shaded, is really the same area as a "whole" of one of those equilateral triangles.

so hmmm we have three of those flatter triangles shaded hmm, so let's simply get the area of three of those equilateral triangles and sum them up.

[tex]\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\large area of the shaded region}}{36\sqrt{3}~~ + ~~36\sqrt{3}~~ + ~~36\sqrt{3}}\implies 108\sqrt{3}\qquad \approx\qquad \text{\LARGE 187.1}[/tex]

let's go like the crab, go backwards, start at the last

if you don't have a Unit Circle, this is a good time to get one, there are many online.

Check the picture below.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +6}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{midpoint}{(-5~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +6}{2}=-5\implies x+6=-10\implies \boxed{x=-16} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=-5\implies y+7=-10\implies \boxed{y=-17}[/tex]

Answer:

2196 fish

Step-by-step explanation:

:)

Answer:

2196 fish

Step-by-step explanation:

your welcome

The sequence of transformations that show figure A and figure B are congruent is: Translate figure A 4 units right and then reflect the image across the x-axis.

Translation refers to a type of transformation that involve a straight line movement.

Movements as seen in translation includes

The left and right movements are on the horizontal direction controlled by the x coordinate.

The object moved 4 units right then reflected over the x axis to have the mirror image below the x axis

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If we want to translate (aka move) [tex]f(x) = x^2[/tex] down 5 units, we need to subtract 5 from the [tex]x^2[/tex].

          [tex]g(x) = x^2-5[/tex]

The [tex]k[/tex] in the [tex]a(x-h)^2 +k[/tex] form will always be the vertical translation component.  If you translate up, [tex]k[/tex] is positive.  If you translate down, [tex]k[/tex] is negative.

Answer:

28

Step-by-step explanation:

hope this helps if its wrong really sorry

Answer:

y = 2x - 4

Step-by-step explanation:

(3, 2) (1, -2)

m = y2-y1 / x2-x1

m = -2-2 / 1-3

m = -4/-2

m = 2/1

m = 2

y = 2x + b

2 = 2(3) + b

2 = 6 + b

b = -4

y = 2x - 4

Could you please give me brainliest for this? Thank you!

Answer:

Step-by-step explanation:

P = 2(L + W)

P = 34

L = W + 5

34 = 2(W + 5 + W)

34 = 2(2W + 5)

34 = 4W + 10

34 - 10 = 4W

24 = 4W

24/4 = W

6 = W <=== 6 meters wide

L = W + 5

L = 6 + 5

L = 11 <=== 11 meters long

Answer:

On (3,7) and (-2,7)

Step-by-step explanation:

Recall properties of symmetry:

Using the properties we can state that:

Answer:

f(1)=10

g(3)=2

f(1)+g(3)=12

f(10)-g(0)=104

Step-by-step explanation:

f(x)=10x

g(x)=2x-4

f(1)=10×1=10

g(3)=2×3-4=2

f(1)+g(3)=10+2=12

f(10)-g(0)=(10×10)-(2×0-4)=100+4=104