A: What are the solutions to the quadratic equation x^2+9=0?
B: What is the factored form of the quadratic expression x^2+9?
Select one answer for question A, and select one answer for question B.
A: x=3
A: x=-3i
A: x=3i or x=-3i
A: x=3 or x=-3
B: (x+3)(x+3)
B: (x-3i)(x-3i)
B: (x+3i)(x-3i)
B: (x+3)(x-3)

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:

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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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:

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:

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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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

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:

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:

[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:

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:

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:

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:

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:

[tex]y_Q=\dfrac{21}{5}=4.2[/tex]

Step-by-step explanation:

If the point Q that is located two over three the distance from point P to point R, then PQ:QR=2:3.

Use formula to find the coordinates of the point Q:

[tex]x_Q=\dfrac{3x_P+2x_R}{3+2}\\ \\y_Q=\dfrac{3y_P+2y_R}{3+2}[/tex]

In your case, P(-2,7) and R(1,0), then

[tex]x_Q=\dfrac{3\cdot (-2)+2\cdot 1}{3+2}=\dfrac{-4}{5}\\ \\y_Q=\dfrac{3\cdot 7+2\cdot 0}{3+2}=\dfrac{21}{5}[/tex]

[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:

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 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!!! :}

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:

6^ (1/12)

Step-by-step explanation:

6 ^ 1/3

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

6 ^ 1/4

x^a / x^b = x^ (a-b)

6^(1/3-1/4)

Getting a common denominator)

6^(4/12-3/12)

6^1/12

Answer:

6^1/12

Step-by-step explanation:

You can rewrite the numbers as 6^1/3 and 6^1/4. Now we need common denominators on the powers. You can make the 1/3 into 4/12 and the 1/4 into 3/12. When you divide powers, you just subtract the numerators for each fraction. So you do 4-3. This leaves you with 6^1/12. Hope this helps :)

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:

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:

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: 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

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:

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:

B

Step-by-step explanation:

The question has no division answer. That makes C and D incorrect.

A for some reason is backwards. It makes no sense to use that. You are left with B. The reason A or B  is correct is that the burn of calories must get larger with an increase in hours.

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:

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.