Consider this quadratic equation. 2x2 − 1 = 3x + 4 Which equation correctly applies the quadratic formula?

[tex]2x \times \frac{4}{3} = 4x \times \frac{2}{3}[/tex]

[tex] \frac{8x}{3} = \frac{8x}{3} [/tex]

Both are equivalents

Answer:

B.  F(x) = (x+1)/(x-1)(x+2)

Step-by-step explanation:

See attached graph.  Note how the two vertical lines at x = -2 and 1 match plot B

The following graph is of the rational function [tex]F(x) = \frac{x+1}{(x-1)(x+2)} \\[/tex]

What are asymptotes?

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance.

The rational function does not exist at x = 1 and x = -2 ( as observed in graph). Thus, the denominator of the function consist (x-1) and (x+2). It is only in option B, thus it is correct.

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The three (3) products that resulted in a difference of squares are:

In Mathematics, the standard form for a difference of two (2) squares is given by a² - b² = (a + b)(a - b).

(3 + xz)(-3 + xz) = (3 + xz)(xz -3)

(3 + xz)(xz -3) = 3xz - 9 + x²z² - 3xz.

(3 + xz)(xz -3) = x²z² - 9

Therefore, x²z² - 9 ≡ a² - b²

(y² - xy)(y² + xy) = y⁴ + xy³ - xy³ - x²y²

(y² - xy)(y² + xy) = y⁴ - x²y²

Therefore, y⁴ - x²y² ≡ a² - b².

(64y² + x²)(-x² + 64y²) = (64y² + x²)(64y² - x²)

(64y² + x²)(-x² + 64y²) = 4096y⁴- 64y²x² + 64y²x² - x⁴

(64y² + x²)(-x² + 64y²) = 4096y⁴ - x⁴

Therefore, 4096y⁴ - x⁴ ≡ a² - b².

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Answer:

Step-by-step explanation:

Answer: x=-6

Step-by-step explanation:

Let's solve your equation step-by-step.

2(9−x)=3(x+16)

Step 1: Simplify both sides of the equation by distribution

[tex]2(9-x)=3(x+16)\\(2)(9)+(2)(-x)=(3)(x)+(3)(16)\\18+-2x=3x+48\\-2x+18=3x+48\\[/tex]

Step 2: Subtract 3x from both sides.

[tex]-2x+18-3x=3x+48-3x\\-5x+18=48[/tex]

Step 3: Subtract 18 from both sides.

[tex]-5x+18-18=48-18\\-5x=30[/tex]

Step 4: Divide both sides by -5.

[tex]\frac{-5x}{-5} =\frac{30}{-5} \\x=-6[/tex]

Answer:

Step-by-step explanation:

25% = 1/4 of 100

100 represents 200 people here, that means that if 25 = 1/4 to 100, then it is 1/8 to 200. 25x8=200

If 25% = 50, since 50x4=200 and 1/4 = 25% of 100%.

50... ok......

50 = 25%

Now, because there are 5 parts in 25, let's divide 5 by 50, that is 10. That means that 5 = 10 in that 50. 5% = 10 people

So, if 25-15=10

and then 5% = 10 people

5%+5%=10

10+10=20

That means, that 20 people more liked the movie than disliked it.

Answer:

x=-96

Step-by-step explanation:

isolate x by moving -124x to the other side by adding -124x to -126x = -2x

then it will look like: 102= -2x-90

add 90 to both sides: 192= -2x

divide both sides by -2 to isolate x

x= -96

Answer:

81%

Step-by-step explanation:

200-38= 162

162/200= 81/100

81%

Answer:

93%

Step-by-step explanation:

100 x 186= 200 * x

18600/200 = 200x/200

93%=x

186/200 = 0.93

convert decimal to percent

0.93 x 100= 93%

​

no of sweet gave to peny is 24×3/8 = 9 sweets

rest was ate by him

so the sweet ate by him is 24-9 = 15 sweet

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Based on the amount of sweets eaten by Gary and Ben, the person with more sweets left is Ben.

The sweets left by Gary are:

= 24 - (24 x 3/8)

= 24 - 9

= 15 sweets

The sweet left by Ben are:

= 30 - (2/5 x 30)

= 30 - 12

= 18 sweets

In conclusion, Ben has more sweets left.

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Answer:

9.5 cubic units

Step-by-step explanation:

You need to multiply everything together and divide by 2.

5 x 2 x 1.9/2 = v

19/2 = v

9.5 cubic units

Answer:

1 2 3 5

Step-by-step explanation:

1 and 2 go into 6 and 10. 3 goes into 6 and 5 goes into 10

Answer:

Step-by-step explanation:

The indicated angles are vertical angles since formed by two intersecting lines.

We know the vertical angles are congruent. Use this property to find the value of x and the angle measure

The angle measure

Opposite angles are equal

Answer:

To find the perimeter of this triangle, we add up all the sides together.

(8 · √3) + (8 · √3) + √384

But before we add them, let's simplify them.

(8 · 1.7) + (8 · 1.7) + 19.6

13.6 + 13.6 + 19.6

27.2 + 19.6

= 46.8, is the perimeter of this triangle.

Now to find the area, we use the formula:

(formula for area of a triangle)

A = BH · 1/2

Where 'B' represents the base, 'H' stands for the height, and 1/2 means that you divide the product of the base and height by 2.

What we know:

Plug in the values into our formula:-

A = BH · 1/2

A = 13.6(13.6) · 1/2

A = 184.96 · 1/2

A = 184.96/2

A = 92.48, is the area for this triangle.

Answer:

40%

Step-by-step explanation:

1.50 - 0.90 = 0.60

0.60 cents are saved.

[tex]\frac{0.60}{1.50} = 0.4[/tex]

0.4 = 40%

hope this helps :)

Answer:

A, E, B, D, C

Step-by-step explanation:

1) 6 is A

2) √83 = 9.11, so it is E

3) √40 = 6.3, so it is B

4) √64 = 8, so it is D

5) 7.5 is C

The expression which is equivalent to cube root of 216 x superscript 27 is 6 times 3 (6x3).

Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.

To find the equivalent expression, simplify the given equation with the help of mathematical operations.

The expression given in the problem is,

[tex]\sqrt[3]{216\times {27}}[/tex]

Let the expression which is equivalent to the above expression is n. Thus,

[tex]n=\sqrt[3]{216\times {27}}\\n=\sqrt[3]{216}\times \sqrt[3]{27}\\n=\sqrt[3]{6\times6\times6}\times \sqrt[3]{3\times3\times3}\\n=6\times3[/tex]

Thus, the expression which is equivalent to cube root of 216 x superscript 27 is 6 times 3 (6x3).

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Answer:

A

Step-by-step explanation:

Answer:

6*6=36

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

the 2 angles are a linear pair and sum to 180° that is

8x - 3 + 4x + 3 = 180

12x = 180 ( divide both sides by 12 )

x = 15

The angles are supplementary angles. Then the value of the variable 'x' will be 15.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The angles are 8x - 3 and 4x + 3. And they are supplementary angles. Then the equation is given as,

8x - 3 + 4x + 3 = 180

Simplify the equation, then we have

8x - 3 + 4x + 3 = 180

12x + 0 = 180

x = 15

The angles are supplementary angles. Then the value of the variable 'x' will be 15.

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Answer:

Below!

Step-by-step explanation:

Since the "y" variable is on the L.H.S, we can rewrite y = 5 in slope intercept form to determine the slope and the y-intercept.

Now, let's compare the equation of the line with the formula.

Thus, we will obtain the following equations:

============================

Thus, the slope is 0 and the y-intercept is 5. Since the slope is 0, the line will be a horizontal line that intersects the y-intercept.

In this case, the y-intercept is 5. Thus, the line will be a horizontal line, intersecting the y-intercept (5). (Refer to graph).

If we simplify

Hence..

Graph attached

Answer:

See below ~

Step-by-step explanation:

27. (B)

27. (C)

Answer:

1,

[tex] \frac{13a}{15b} [/tex]

2,

[tex]9[/tex]

Step-by-step explanation:

[tex] \frac{3a}{5b} + \frac{4a}{15b} [/tex]

[tex] \frac{45a}{75b} + \frac{20a}{75b} [/tex]

[tex] \frac{13a}{15b} [/tex]

2,

[tex] {3}^{6} \times {3}^{0} \div {3}^{4} [/tex]

[tex]729 \times 1 \div 81[/tex]

[tex]729 \div 81 = 9[/tex]

Answer:

Your answer is D. 5 children, 12 teens, and 3 adults.

Step-by-step explanation:

45 children, 108 teens, and 27 adults.

x - children , y-teens, z-adults

45x + 108y + 27z

GCF for 45, 108, 27 is 9 so factory out 9 to all.

[tex]\frac{45}{9} ,\frac{108}{9} ,\frac{27}{9} \\5,12,3[/tex]

5 children, 12 teens, and 3 adults.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{It seems like all of your numbers are apart of the 9 factors. So, we will }\\\large\text{DIVIDE each of your numbers by 9 until we find out the total}\\\large\text{population (also known as your result to this equation)}[/tex]

“[tex]\large\text{45 children, 108 teens, \& 27 adults}[/tex]”

[tex]\large\textbf{Equation \# 1.}\\\\\large\boxed{\rm{\dfrac{45\ children}{9\ children}}}\\\\\\\large\boxed{= \rm{45 \ children \div 9 \ children}}\\\\\\\large\boxed{\rm{= 5\ children\ in\ total}}[/tex]

[tex]\large\textbf{Equation \# 2.}\\\\\large\boxed{\rm{\dfrac{108\ teens}{9\ teens}}}\\\\\\\large\boxed{= \rm{108\ teens \div 9 \ teens}}\\\\\\\large\boxed{= \rm{12 \ teens \ in \ total}}[/tex]

[tex]\large\textbf{Equation \# 3.}\\\\\\\large\boxed{\rm{\dfrac{27\ adults}{9\ adults}}}\\\\\\\large\boxed{\rm{= 27\ adults \div 9 \ adults}}\\\\\\\large\boxed{\rm{= 3\ adults\ in\ total}}[/tex]

[tex]\huge\textbf{Therefore, your answer is:}\\\\\huge\boxed{\textsf{Option D. 5 children, 12 teens, 3 adults}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Based on the histogram, the interquartile rangle of the distribution is 5 inches.

The interquartile range is the difference between the third quartile of a data set and the first quartile of the data set.

First quartile = 1/4 x ( n + 1)

= 101 / 4 = 25.25

25.25 on the histogram is 66

Third quartile = 3/4 x (n + 1)

303 / 4 = 75.75

75.75 on the histogram is 71

Interquartile range = 71 - 66 = 5

Please find attached the image of the histogram. To learn more about histograms, please check: https://brainly.com/question/14473126

Answer:

3. 200ft
4. 21ft
5. 37.5m
6. 4.2ft

Step-by-step explanation:

3. use proportions:
[tex]\frac{h}{50} = \frac{50}{12.5}[/tex]
50(50) = 12.5h
h = 200ft

4.
[tex]\frac{h}{6} =\frac{7}{2}[/tex]
6(7) = 2h
h = 21ft

5.
[tex]\frac{25}{8} =\frac{x}{12}[/tex]
25(12) = 8x
x = 37.5m

6.
[tex]\frac{9}{15} =\frac{h}{7}[/tex]
9(7) = 15h
h = 4.2ft

The expression that represents a perfect cube is expressed as: 6 × 6 × 6

A perfect cube, x, is such that x × x × x = x³ = ∛x.

Thus, we have:

6 × 6 × 6 = 216

Cube root of 216 = ∛216

∛216 = 6

We can then conclude that the expression that represents a perfect cube is: 6 × 6 × 6

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Answer:

6x6x6

Step-by-step explanation:

Answer:

4/3  cups/tsp

Step-by-step explanation:

You want  cups / tsp    =   2/5 c / 3/10 tsp =    2/5 * 10/3   c/tsp = 20/15 = 4/3

Answer:

C

Step-by-step explanation:

A number is n, therefore you can start off with 32 and subtract 4 getting you 28. Subtract 4 and you get 24, and again 20.

Answer:

8.5

Step-by-step explanation:

area of a rhomus = (1/2)(product of its diagonals)

let the other diagonal be a

(1/2)(15a) = 60

15a= 120

a = 8

So let's find the hypotenuse of one of the right-angled triangles formed by the intersection of its diagonals

base = 4, height = 7.5

if h is the hypotenuse,

h^2 = 4^2 + 7.5^2

h = 8.5

The slope or gradient has this formula when two points are given: m = y1 −y x1 −x In this case we have the points (-6,-8) and (-7,y) and m=-8.

Ur mommy may know this

Step-by-step explanation:

she has been to school right?

Answer:

  (c)  Add 3 to 9

Step-by-step explanation:

The order of operations tells you that quantities in parentheses are evaluated first.

Here, that means the first step is finding the sum 3+9.