find the value of y ​

The operations of the function are explained below in the solution.

Let f(x) and g(x) be given functions.

We combine those two functions using following rule

(f±g)(x) = f(x) ± g(x)

The domain of f±g is the intersection of the domain off and the domain

of g.

We multiply those two functions using the following rule:

(f·g)(x) = f(x)-g(x)

The domain of f·g is the set of all real numbers for which f and g and new

function are defined.

We divide those two functions using the following rule:

f/g (x) = f(x)  / g(x)

The domain of f/g is set of all real numbers for which ƒ and g and new

function are defined.

We combine these two functions using the following rule:

(f ο g) = f(g(x))

We have that the domain of f ο g is the set of all real numbers z, in the

domain of g, such that g(x) is in the domain of f,

We have that the domain of g ο f the set of all real numbers, in the domain of f,  such that f(x) is in the domain of g,

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Final answer:

In mathematics, functions can be combined, multiplied, divided, and composed, and discovering their domain is essential. Combining functions adds their outputs, multiplying them multiplies their outputs, and dividing them divides one output by another. Composing functions applies one to the result of another, with the domain determined by permissible inputs, avoiding division by zero or negative square roots.

Explanation:

When working with functions in mathematics, you can perform several operations, including combining, multiplying, dividing, and composing functions. Finding the domain of the resulting function is crucial as it determines the set of all possible inputs for the function.

Combining Functions

To combine functions (also known as function addition), you simply add the outputs of two functions. For example, if f(x) = 2x and g(x) = x + 3, the combined function is (f + g)(x) = f(x) + g(x) = 2x + (x + 3) = 3x + 3.

Multiplying and Dividing Functions

Multiplying functions involves multiplying the outputs of the functions. If f(x) = 2x and g(x) = x + 3, then[tex](f \cdot g)(x) = f(x) \cdot g(x) = 2x \cdot (x + 3)[/tex]. Dividing functions, on the other hand, involves dividing one output by the other, given that the divisor is not zero.

Composition of Functions

Composing functions refers to applying one function to the result of another function. The composition g o f means applying f first and then g. If h(x) = g(f(x)), you're taking an input x, applying the function f, and then applying g to the result of f(x).

Finding the Domain

The domain of a function is the set of all permissible inputs. To find the domain of a resulting function after performing operations, look for any restrictions such as division by zero or taking the square root of a negative number. For instance, if [tex]f(x) = \sqrt{x}[/tex], the domain is x ≥ 0, as you cannot take the square root of a negative number.

Hey there!

In order for you to find the one that is equivalent to the given expression is to COMBINE YOUR LIKE TERMS then work from there!

12q + q^2 - 8 + q = ?

(q^2) + (12q + q) + (-8)

q^2 = q^2 since it doesn't have any like term(s)

12q + q = 12q + 1q = 13q

-8 = -8 since it doesn't have any like term(s)

Put all the numbers we solved for in An equation and Thats your answer!

If you did it correctly you should have: q^2 + 13q - 8

Answer: q^2 + 13q - 8 ✅

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer

x=-8

Step-by-step explanation:

so the right answer is 16...

Answer:

A

Step-by-step explanation:

he side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the y (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.

Explanation of Cosine 60 = Sine 30

Cosine :

The trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.

Sine :

The trigonometric function that is equal to the ratio of the side opposite a given angle (in a right-angled triangle) to the hypotenuse.

So, these are the reasons :

⇒ The side opposite a 30 degree angle is the same as a side adjacent to 60 degree angle in a right triangle.

⇒  On a unit circle, the y (sin) distance of a 30 degree angle is the same as the x (cos) distance of a 60 degree angle.

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Answer:

16x -20

Step-by-step explanation:

12(x - 4) + 4(x + 7)

12x - 48 + 4x +28

16x - 20

Answer:

16x - 20

Step-by-step explanation:

Given

12(x - 4) + 4(x + 7) ← distribute both parenthesis

= 12x - 48 + 4x + 28 ← collect like terms

= 16x - 20

Answer:

5.8 and 7.4

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Square root of 5=√5

Square of the square root=(√5)^2

=5

Square root of 3=√3

Square of the square root=(√3)^2

=3

So (square root of 5)^2×(square root of 3)^2

5×3

15

Therefore the final answer is 15

Final answer:

The gradient of the line perpendicular to a line with a gradient of 2/3 is -3/2 since perpendicular slopes are negative reciprocals of each other.

Explanation:

If the gradient of a line C is 2/3, we need to find the gradient of the line which is perpendicular to C. In mathematics, particularly in coordinate geometry, the slopes (or gradients) of two perpendicular lines are negative reciprocals of each other. This means that if the slope of the first line is m, the slope of the line perpendicular to it will be -1/m.

Therefore, the gradient of the line perpendicular to line C, which has a gradient of 2/3, will be the negative reciprocal of 2/3.

perpendicular = -1 / (2/3) = -3/2

So, the gradient of the line perpendicular to C is -3/2.

Answer:11

Step-by-step explanation:

Because I said so

Answer:

x = 20

Step-by-step explanation:

-10x=-200

x = -200/ -10

x = 20

Answer:

A. x^2 (x+2) / 3

Step-by-step explanation:

From the given set of fractions, 13/16 is the largest fraction.

The given set of fractions are 13/16, 3/4, 7/10, and 5/8.

We need to check which of the given fractions is the largest.

To order fractions from least to greatest, start by finding the lowest common denominator for all of the fractions. Next, convert each of the fractions by dividing the lowest common denominator by the denominator and then multiplying the top and bottom of the fraction by your answer.

Now, the LCM of denominators of the fractions is as follows:

16, 4, 10 an 8 LCM= 2×2×2×2×5=80

Make the denominators equal to LCM.

That is, 65/80, 60/80, 56/80, and 50/80

Here, 65/80 is the largest, since the numerator is the greatest number.

Therefore, from the given set of fractions 13/16 is the largest fraction.

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We have expression [tex]-5 < x - 4 \geq 1[/tex] that renders the system of inequalities,

[tex]

\begin{cases}

-5 < x - 4 \\

x - 4 \geq 1

\end{cases}

[/tex]

Which can be simplified to,

[tex]

\begin{cases}

x > -1 \\

x \geq 5

\end{cases}

[/tex]

So what we get is something greater than -1 and at the same time greater or equal to 5, so the solution is,

[tex]x\in(\infty,-1)\cap(\infty, 5]=\boxed{(\infty,5]}[/tex].

Hope this helps.

Answer: 9

Step-by-step explanation:

Answer:342

Step-by-step explanation:100+130+112=342

Final answer:

The breakfast consisting of one scrambled egg, one sausage patty, and an 8 oz. glass of orange juice contains a total of approximately 430 Calories.

Explanation:

The question is about calculating the total calorie content of a breakfast that includes one scrambled egg, one sausage patty, and an 8 oz. glass of orange juice. To answer, we need to know the individual calorie content of each item. Typical values might be around 70 Calories for one large scrambled egg, about 250 Calories for a sausage patty, and approximately 110 Calories for an 8 oz. orange juice.

Add these values together to get the total calorie intake for the meal:

Total Calories = 70 + 250 + 110 = 430 Calories.

Answer:

8

Step-by-step explanation:

Answer:

2n + 25

Step-by-step explanation:

Cost of pumpkin (C) = 3n + 25

Revenue (R) I.e selling price = 5n

Her profit (P) = Selling price (R) - cost price (c)

P = R - C

P = 5n - (3n + 25)

P = 2n - 25

The expression for her profit (p) = 2n - 25

Answer:

P = 2n – 25

Step-by-step explanation:

:)

jada 2 andre 3 hours

Answer:

15-4 11 -4x

Step-by-step explanation:

Answer: The answer should be 35

Step-by-step explanation: If you take 140 divide it by 4 it should be the answer

Answer:

B.

Step-by-step explanation:

Hope this helps!

Answer:

i think A

Step-by-step explanation:

Answer:

If your solving for y...

The answer would be: y = -9/8x + 17/8 I believe.

For the second one... it would be : y = -1/7x + 8/7

Step-by-step explanation:

Answer:

25 and 15

You can easily make a system of equations:

x + y = 40

x - y = 10

Solving for x on equation 2 gets x = 10 + y.

Plugging in this into the first equation, you get 10 + y + y = 40

Thus, 10 + 2y = 40

y = 15.

Plugging this back into either equation gets x = 25.

Answer:

6 Ways. (I could be wrong. If I am, I will come back and edit)

Step-by-step explanation:

BBBG

BBGB

BGBB

BGBG

BGGG

BGGB

The number of the ways of sitting of the three girls and three boys will be 4.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.

Given that there are three boys and three girls at the party. The number of the ways will be calculated as,

N = ⁴C₃

N = (4!) / (3)!(4-1)!

N = 4

Therefore, the number of the ways of sitting of the three girls and three boys will be 4.

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Answer:

[tex]8 + 46p[/tex]

Step-by-step explanation:

Step 1:  Combine like terms

[tex]1 + 46p - 9[/tex]

[tex](1 - 9) + 46p[/tex]

[tex]8 + 46p[/tex]

Answer:  [tex]8 + 46p[/tex]

You can also pull out a two from both

[tex]8 + 46p[/tex]

[tex]2(4 + 23p)[/tex]

Answer:

y = -1/4x -2

Step-by-step explanation:

We can use the slope intercept form of a line

y = mx+b  where m is the slope and b is the y intercept

y = -1/4x +b

Substitute the point into the equation

-3 = -1/4(4) +b

-3 = -1 +b

Add 1 to each side

-3 +1 = -1 +1 b

-2 =b

y = -1/4x -2

Answer:

114°

Step-by-step explanation:

By property of intersecting chords inside a circle.

[tex] \because \angle \: 1 = \frac{1}{2} (x + y) \\ \\ \therefore \: \angle \: 1 = \frac{1}{2} (96 + 132) \\ \\ \therefore \: \angle \: 1 = \frac{1}{2} \times 228\\ \\ \huge \red { \boxed{\therefore \: \angle \: 1 = 114 \degree}}[/tex]

Answer:

19 weeks

Step-by-step explanation:

Make an equation

120+20x=500

Subtract 120 on both sides

20x=380

Divide by 20 on both sides

x=19

Hope this helps!

Answer:

Base

Step-by-step explanation:

To give an example, in the expression [tex]10^6[/tex], 10 is our base and 6 is our exponent or power.

Answer:

-5 > -7

-2 < 2

-10 < -3

-9 < 2

5 > -9

Step-by-step explanation:

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