if f(x) = x + 7 and g(x) = 1/x -13, what is the domain of (f O g)(x)

Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) to find the solutions, which are (13 + √185) / 2 and (13 - √185) / 2.

To find the solutions of the equation x^2 = -13x - 4, we can rearrange it to the form ax^2 + bx + c = 0.

In this case, we have a = 1, b = -13, and c = -4.

We can then use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) to find the solutions.

Substituting the values into the formula, we get x = (-(-13) ± √((-13)^2 - 4(1)(-4))) / (2(1)). Simplifying further, we have x = (13 ± √(169 + 16)) / 2. T

herefore, the solutions of the equation are x = (13 + √185) / 2 and x = (13 - √185) / 2.

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Answer:

The  process of calculating successive discounts of 8% and 10% on a $50 item is take 10% of $46.

Step-by-step explanation:

As given

successive discounts of 8% and 10% on a $50 item .

First find out for 8 % discount

8% is written in the decimal form

= 0.08

8 % of $50 item = 0.08 × 50

                          = $ 4

Price of item after 8% discount = 50 - 4

                                                    = $46  

First find out for 10 % discount

10% is written in the decimal form

= 0.1

8 % of $48 item = 0.1× 46

                          = $4.6

Price of item after 8% discount = 46 - 4.6

                                                    = $41.4

Therefore in the successive discounts of 8% and 10% on a $50 item is $41.4 .

The final price after applying the successive discounts is $41.40

To calculate successive discounts of 8% and 10% on a $50 item, follow these steps:

First, convert the first discount of 8% to a decimal by dividing 8 by 100, which gives 0.08.

Multiply the original price of the item, $50.00, by 0.08 to find the amount of the first discount: $50.00 x 0.08 = $4.00.

Subtract the first discount from the original price to find the new price: $50.00 - $4.00 = $46.00.

Next, convert the second discount of 10% to a decimal by dividing 10 by 100, which gives 0.10.

Multiply the new price of the item, $46.00, by 0.10 to find the amount of the second discount: $46.00 x 0.10 = $4.60.

Finally, subtract the second discount from the new price to find the final price: $46.00 - $4.60 = $41.40.

The final price after applying the successive discounts is $41.40.

Answer:

The value of the discriminate is -27 and there are 2 complex roots

Step-by-step explanation:

* Lets explain what is discriminant

- The form of the quadratic equation is y= ax² + bx + c

- The roots of the equation is the values of x when y = 0

- There are three types of roots:

# Two different real roots

# One real root

# No real roots or two complex roots

- We can know the types of roots of the equation without solve it by

 using the discriminant which depends on the value of a , b , c

- The discriminant = b² - 4ac, where a is the coefficient of x² , b is the

  coefficient of x and c is the numerical term

# If b² - 4ac > 0, then there are two different real roots

# If b² - 4ac = 0, then there is one real root

# If b² - 4ac < 0, then there is no real root (2 complex roots)

* Lets solve the problem

∵ x² + x + 7 = 0

∴ a = 1 , b = 1 , c = 7

∵ The discriminant = b² - 4ac

∴ The discriminant = (1) - 4(1)(7) = 1 - 28 = -27

∵ -27 < 0

∴ There is no real solution there are two complex roots

* The value of the discriminate is -27 and there are 2 complex roots

Answer:

The number of roots are 2 and type of roots is complex

Step-by-step explanation:

Points to remember

Discriminant of a quadratic equation ax² + bx + c = 0

x = b² - 4ac

To find the discriminant of the given equation

Here quadratic equation be x² + x + 7 = 0

a = 1, b = 1 and c = 7

discriminant =  b² - 4ac

 =  1² - (4 * 1 * 7)

 = 1 - 28

 = -27

To find number and type of roots

Here discriminant  is negative

Therefore the number of roots are 2 and type of roots is complex

Answer:

{x|⅘ ≠ x} → Set-Builder Notation

(-∞, ⅘) ∪ (⅘, ∞) → Interval Notation

Step-by-step explanation:

Plug the g(x) function into the f(x) function for every x you see.

Answer:

domain is the set of all real numbers except 0

Step-by-step explanation:

If f(x)=x-3/x and g(x)=5x-4

(f•g)(x) is f(x) times g(x)

multiply f(x) and g(x)

(f•g)(x) is f(x) times g(x)

Replace f(x) and g(x)

[tex]f(x) \cdot g(x)= (x-\frac{3}{x})(5x-4)[/tex]

Apply FOIL method to multiply it

multiply x inside the parenthesis

[tex]5x^2-4x[/tex]

Multiply the fraction inside the parenthesis

[tex]-5 +\frac{12}{x}[/tex]

[tex]5x^2-4x -5 +\frac{12}{x}[/tex]

We have x in the denominator . Domain is the set of x value for which the function is defined.

When denominator x is 0 then the function is undefined

So domain is the set of all real numbers except 0

Answer:

The perimeter of the triangle is 135 cm

Step-by-step explanation:

* Lets explain how to find the perimeter of a triangle

- The perimeter of any triangle is the sum of the lengths of its three sides

- The perimeter of the scalene triangle is P = S1 + S2 + S3

- The perimeter of the isosceles triangle is P = 2S + S1

- The perimeter of the equilateral triangle is P = 3S

* Lets solve the problem

∵ The length of the 1st side is 55 cm

∴ S1 = 55 cm

∵ The length of the 2nd side is 48 cm

∴ S2 = 48 cm

∵ The length of the 3rd side is 32 cm

∴ S3 = 32 cm

∵ The triangle is scalene

∴ P = S1 + S2 + S3

∴ P = 55 + 48 + 32 = 135 cm

* The perimeter of the triangle is 135 cm

Answer:

12

Step-by-step explanation:

First put the set in order from least to greatest:

4, 5, 6, 9, 10, 11, 12, 15, 16

To find the range you subtract the largest number by the smallest number.

4, 5, 6, 9, 10, 11, 12, 15, 16

So 16 - 4 = 12

So the range is 12.

Answer:

12

Step-by-step explanation:

The greatest value in the data is 16.

The lowest value in the data is 4.

The range is the difference between the highest and the lowest values.

range = 16 - 4 = 12

Answer:

6x - 26

Step-by-step explanation:

f(x) + g(x) = 5x - 10 + x - 16 ← collect like terms

               = 6x - 26

Answer:

B

Step-by-step explanation:

Answer:

Volume: 45000cm^3

Surface area: 6600cm^2

Step-by-step explanation:

The volume is all the side lengths multiplied, so 60*25*30 = 45,000 cm^3.

Now let's calculate the surface area.

The bottom is the width * the length, or 60*25 cm^2.

One of the sides is the length * the height, or 60*30 cm^2. This is multiplied by 2 because there are 2 of those sides.

The other pair of sides is the width * the height, or 25*30 cm^2, again multiplied by 2.

In total, the surface area is

60*25+2*60*30+2*25*30 = 6600cm^2

To fill the aquarium to the top with water, it will take 7800 cubic centimeters (cm³). To make the aquarium, it will take 7800 square centimeters (cm²) of glass.

Find the volume of the aquarium: Since there is no top to the aquarium, we will consider the volume as the combined volume of the five faces of the rectangular prism (4 faces with dimensions Length x Width and 1 face with dimensions Length x Height).

Volume = 4 * (Length * Width) + (Length * Height)

Volume = 4 * (60 cm * 25 cm) + (60 cm * 30 cm)

Volume = 4 * 1500 cm² + 1800 cm²

Volume = 6000 cm² + 1800 cm²

Volume = 7800 cm³

So, it will take 7800 cubic centimeters (cm³) of water to fill the aquarium to the top.

Find the surface area of the aquarium: To find the surface area, we will consider the area of each face and add them together.

Area of the 4 faces with dimensions Length x Width:

4 * (60 cm * 25 cm) = 4 * 1500 cm² = 6000 cm²

Area of the face with dimensions Length x Height:

(60 cm * 30 cm) = 1800 cm²

Total Surface Area = 6000 cm² + 1800 cm² = 7800 cm²

It will take 7800 square centimeters (cm²) of glass to make the aquarium.

Answer:

6.3

Step-by-step explanation:

1,600 / 84 = 19.04

19.04 / 3 = 6.3

To answer the student's question, we first divide 1,600 by 84 which gives around 19.0476, and then divide this result by 3, which gives the final answer of 6.3492.

To solve this problem, we first need to divide 1,600 by 84. That will give us the first result. Next, we must take this first result and divide it by 3.

Let's take it step by step:

So after you divide 1,600 by 84, and then divide the answer by 3, the final result should be around 6.3492.

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Answer: 54 bags; equation is 51=213-3x

Step-by-step explanation:

If you divid 213 by 3, you see it’s divisible and equals 71. 51 divided by 3 is 17. 71 minus 17 is 54.

Answer:

x < 54 (bags)

Step-by-step explanation:

213 - 3x < 51, or  

162 - 3x < 0, or

162 > 3x, or, finally,

162

----- > x, or x < 54 (bags)

 3

[tex]\bf \begin{array}{ccll} liters&gallons\\ \cline{1-2} 1&0.26\\ 5.5&x \end{array}\implies \cfrac{1}{5.5}=\cfrac{0.26}{x}\implies x=(5.5)(0.26)\implies x=1.43[/tex]

Answer:

The area of the pattern is 43.6 inches²

Step-by-step explanation:

* Lets explain how to solve the problem

- A decorative pillow can be modeled by Δ ABC

- In Δ ABC: AB = 9 inches , BC = 15 inches , AC = 10 inches

- To find the area of the triangle we can use the rule:

  A = 1/2 × (AB) × (BC) × sin∠B

- We will use the cosine rule to find the measure of angle B

∵ [tex]cos(B)=\frac{(AB)^{2}+(BC)^{2}-(AC)^{2}}{2(AB)(BC)}[/tex]

∵ AB = 9 , BC = 15 , AC = 10

∴ [tex]cos(B)=\frac{9^{2}+15^{2}-10^{2}}{2(9)(15)}=\frac{81+225-100}{270}=\frac{206}{270}=\frac{103}{135}[/tex]

∴ m∠B = [tex]cos^{-1}\frac{103}{135}=40.27[/tex]°

* Lets find the area of the triangle

∴ The area = 1/2 × (9) × (15) × sin(40.27) = 43.6 inches²

* The area of the pattern is 43.6 inches²

Answer:

[tex](f+g)(x) = 3x^2+\frac{3x}{2}-9\\or\\(f+g)(x) = \frac{6x^2+3x-18}{2}[/tex]

Step-by-step explanation:

We are given:

[tex]f(x)=\frac{x}{2}-3 \,\, and\,\, g(x) = 3x^2+x-6[/tex]

We need to find [tex](f+g)(x)[/tex]

(f+g)(x) can be found by adding f(x) and g(x)

(f+g)(x) = f(x) + g(x)

[tex](f+g)(x) = \frac{x}{2}-3+(3x^2+x-6) \\(f+g)(x) = \frac{x}{2}-3+3x^2+x-6\\(f+g)(x) = 3x^2+\frac{x}{2}+x-3-6\\(f+g)(x) = 3x^2+\frac{3x}{2}-9\\(f+g)(x) = \frac{6x^2+3x-18}{2}[/tex]

so, (f+g)(x) is:

[tex](f+g)(x) = 3x^2+\frac{3x}{2}-9\\or\\(f+g)(x) = \frac{6x^2+3x-18}{2}[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]\large\boxed{a(V)=\sqrt{\dfrac{3V}{8}}}[/tex]

Step-by-step explanation:

The formula of a volume of a square pyramid:

[tex]V=\dfrac{1}{3}a^2h[/tex]

a - base edge

h - height of a pyramid

We have H = 8in.

Substitute and solve for a:

[tex]\dfrac{1}{3}a^2(8)=V\\\\\dfrac{8}{3}a^2=V\qquad\text{multiply both sides by}\ \dfrac{3}{8}\\\\\dfrac{3\!\!\!\!\diagup^1}{8\!\!\!\!\diagup_1}\cdot\dfrac{8\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}a^2=\dfrac{3}{8}V\\\\a^2=\dfrac{3V}{8}\Rightarrow a=\sqrt{\dfrac{3V}{8}}[/tex]

Answer:

Answer:

Step-by-step explanation:

The formula of a volume of a square pyramid:

a - base edge

h - height of a pyramid

We have H = 8in.

Substitute and solve for a:

diavinad8 and 53 more users found this answer helpful

Step-by-step explanation:

Answer:

Your y-intercept is at (0,7). To plot other points, use your slope: -4. (go down 4, go right 1 OR go up 4 and left 1)

Step-by-step explanation:

Answer:

Graph is attached below

Step-by-step explanation:

[tex]y= -4x + 7[/tex]

To graph this linear function , we make a table

Assume some random number for x and find out y. Assume some positive and negative numbers for x

x        y=-4x+7

-1         -4(-1)+7=11

0          -4(0)+7=7

1           -4(1)+7=3

The points we got are (-1,11) (0,7) (1, 3)

Plot all the points and join all the points by a line

The graph is attached below

Answer:

d).2

Step-by-step explanation:

Use the following equation:

slope (m) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (1 , -3)

(x₂ , y₂) = (2 , -1)

Plug in the corresponding numbers to the corresponding variables:

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

Simplify. Combine like terms. Remember to follow PEMDAS. Remember that two negatives = one positive:

m = (-1 + 3)/(2 - 1)

m = (2)/(1)

m = 2

d).2 is your slope.

~

Answer:

[tex]\displaystyle =2[/tex]

Step-by-step explanation:

The slope formula is ⇒ [tex]\displaystyle\frac{Y_2-Y_1}{X_2-X_1}[/tex]

[tex]\displaystyle Y_2=(-1)\\\displaystyle Y_1=(-3)\\\displaystyle X_2=2\\\displaystyle X_1=1\\[/tex]

[tex]\displaystyle \frac{(-1)-(-3)}{2-1}=\frac{2}{1}=2[/tex]

Therefore, the slope is 2, and the correct answer is 2.

Hope this helps!

Answer:

see below

Step-by-step explanation:

Y=x^2

x=-3            -2           -1       0       1       2        3

y=(-3)^2    (-2)^2    (-1)^2    0^2    1^2    2^2   3^2

       9           4           1         0        1         4       9

Answer:

58/9

Step-by-step explanation:

5/3 +43/9

Lets take the L.C.M first

The L.C.M would be 9

Solve the term by taking 9 as L.C.M

=15+43/9

Add the numerator.

=58/9

The answer is 58/9 ....

Answer:

If you're trying to find x or y, you cannot find the exact value since there is one equation. If there was, for example, 2 equations, [a system of equations] you could solve that. But here we only have one equation.

So, if you're trying to solve for x;

x = 7 - 3y

And if you're trying to solve for y;

y = 7/3 - x

Answer:

m=22.5

Step-by-step explanation:

m is proportional to n means there is some constant k such that:

m=kn

If m=5 when n=4 then we have the following equation to solve for our constant k:

5=k(4)

5=4k

Divide both sides by 4:

5/4 =k

So k=5/4 no matter what (m,n) pair they give you where the equation is m=kn.

m=(5/4)n

What is m when n=18?

m=(5/4)(18)

m=(5/2)(9)

m=45/2

m=22.5

Final answer:

To find the value of m when n=18 for a proportional relationship where m is 5 when n is 4, calculate the constant of proportionality (k=5/4) and multiply by 18 to get m=22.5.

Explanation:

The question asks to find the value of m when n=18 given that m is proportional to n and m=5 when n=4. To solve this, we first establish the relationship between m and n using the provided values:

m = kn
(where k is the constant of proportionality)

Given that m=5 when n=4:

5 = k × 4
k = 5/4

Now we can determine the value of m when n=18 with the constant k:

m = (5/4) × 18
m = 22.5

The value of m when n is 18 is 22.5.

Answer:

The measure of angle AXY is 55°

Step-by-step explanation:

we know that

If ray XY bisects AXB

then

∠AXY=∠YXB=∠AXB/2

therefore

∠AXY=110°/2=55°

see the attached figure to better understand the problem

Answer:

27 years

Step-by-step explanation:

Let Holly's age be h and Aunt's age be a. We can setup 2 equations and solve.

1. [tex]\frac{h}{a}=\frac{4}{9}[/tex]

2. a - 15 = h

We can plug in equation 2 into equation 1 to solve for aunt's age:

[tex]\frac{h}{a}=\frac{4}{9}\\\frac{a-15}{a}=\frac{4}{9}\\9(a-15)=4a\\9a-135=4a\\5a=135\\a=\frac{135}{5}=27[/tex]

Holly's aunt's age is 27

Answer:

The radius is 5

Step-by-step explanation:

The equation for Area of a sphere is

4pi*r^2

Since you have the area and not the radius you do the opposite of the equation so instead of multiplying you divide

100/4 = 25

Then find the square root of 25, which is 5

So your radius is 5.

Hope This Helps!!! :}

Answer:

v = -90.

Step-by-step explanation:

To isolate v you multiply both sides of the equation by 10:

v *10 / 10 = -9 * 10

v = -90.

Answer:

v = - 90

Step-by-step explanation:

Given

[tex]\frac{v}{10}[/tex] = - 9

Multiply both sides by 10

v = 10 × - 9 = - 90

Answer:

The correct option is (a+b)+c

Step-by-step explanation:

The correct option is (a+b)+c

According to the Associative property for Addition:

a+(b+c)=(a+b)+c

The associative property states that you can add or multiply regardless of how the numbers are grouped.

.If you are adding or multiplying it does not matter where you put parenthesis.

Thus the correct option is A....

[tex]\huge{\boxed{(a+b)+c}}[/tex]

For example, [tex]2+(3+4)=2+7=9[/tex].

If we group the terms differently, it doesn't matter. [tex](2+3)+4=5+4=9[/tex]

This is called the associative property of addition. As long as you still have all of the terms, and there are no other operations (subtraction, multiplication, etc.), the final answer will remain the same no matter how the terms are grouped.

Answer:

the answer is negative infinity to infinity because it's all real numbers.

The domain of g(x) is the set of all real numbers.

A real number is a value of a continuous quantity that can represent a distance along a line.

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Answer:

B.

Step-by-step explanation:

The spaces on the graph are x=3 nd y=7 so x+1= Move it up 1 space so it's at   -4. And move y up 2 so it's at 3. That's why B is correct.

(I can't really be more specific, sorry.)

Answer:

B. -3 - 5i

Step-by-step explanation:

To find the complex conjugate of a complex number, just change the sign of the imaginary part.

The complex conjugate of a + bi is a  bi.

In this case, the complex conjugate of 3 + 5i is -3 - 5i.

A complex conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part. It is useful for performing mathematical operations with complex numbers.

The complex conjugate of a complex number is defined as changing the sign of the imaginary part of that number. If the complex number is expressed in the form a + bi, where a and b are real numbers and 'i' is the square root of -1 representing the imaginary unit, its complex conjugate is a - bi. The definition of a complex conjugate is very important in the study of complex numbers because it allows for the multiplication and division of complex numbers in a way that results in real numbers. We use this conjugate to calculate the magnitude or modulus of a complex number as well.

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Answer:

A given point on a line graph represents a data point with the value of the responding variable as the height of the point at the given value of the manipulated variable on the horizontal axis.

Step-by-step explanation:

A given point in a line graph signifies a specific value of an ordered pair of variables. The x-coordinate represents one variable, and the y-coordinate another. It essentially reflects the relationship between these two variables at a particular time.

In mathematics, specifically in the field of graphs and data visualization, a given point on a line graph represents a specific value for an ordered pair of variables. The horizontal coordinate (x-value) stands for one variable, while the vertical coordinate (y-value) represents another variable.

For example, if we're graphing a student's test scores over time, the time period will be represented on the x-axis, and the test score would be represented on the y-axis. If we have a point at coordinates (3, 85), then that means the student scored 85 on their test in the third time period.

This single point, therefore, is a representation of the interaction or relation between these two variables at a particular interval.

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Final answer:

The recursive formula for the sequence 3, 6, 9, ... is represented by option A: f(n) = f(n - 1) + 3, which states that each term is 3 more than the previous term, starting with f(1) = 3. Option a

Explanation:

To write a recursive formula for the sequence 3, 6, 9, ..., we need to observe the pattern of the sequence. Since each term increases by 3 from the previous term, we can express this as:

f(n) = f(n − 1) + 3 for n > 1,

with a starting value f(1) = 3. This represents the first term in the sequence. Therefore, the correct answer is A: f(n) = f(n − 1) + 3.

The other options suggest either multiplying the preceding term by 2 or 3, or adding 2 to the preceding term, but those operations do not describe the given sequence. Option a