Which is a solution to (x – 3)(x + 9) = –27?

Answer:

The ones that give a rational number answer are:

C+D

A*B

C*D

A*A

Step-by-step explanation:

A+B does not give a rational number answer; √3+2√3 = 3√3

C+D is a rational number; √25=5 and √16=4; 5+4=9.

A+D is not a rational number; √3+√16 = √3+4

A*B is a rational number; √3*2√3 = 2√9 = 2*3 = 6

B*D is not a rational number; 2√3*√16 = 2√3*4 = 8√3

C*D is a rational number; √25*√16 = 5*4 = 20

A*A is a rational number; √3*√3 = √9 = 3

Answer:

[tex]\large\boxed{x^6-y^6=(x-y)(x+y)(x^2+y^2-xy)(x^2+y^2+xy)}[/tex]

Step-by-step explanation:

[tex]x^6-y^6=x^{(2)(3)}-y^{(2)(3)}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(x^2)^3-(y^2)^3\qquad\text{use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\=(x^2-y^2)\bigg((x^2)^2+x^2y^2+(y^2)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x-y)(x+y)\bigg((x^2)^2+2x^2y^2+(y^2)^2-x^2y^2\bigg)\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=(x-y)(x+y)\bigg((x^2+y^2)^2-x^2y^2\bigg)\\\\=(x-y)(x+y)\bigg((x^2+y^2)^2-(xy)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x-y)(x+y)(x^2+y^2-xy)(x^2+y^2+xy)[/tex]

Answer:

(x²)³ - (y²)³ = (x² - y²)(x^4 + x²y² + y^4)

Step-by-step explanation:

x^6 - y^6 is the difference of two cubes:  (x²)³ - (y²)³.  Differences of cubes can be factored as follows:  a³ - b³ = (a - b)(a² + ab + b²).

Thus, (x²)³ - (y²)³ = (x² - y²)(x^4 + x²y² + y^4)

Answer:

[tex]21.5\%[/tex]

Step-by-step explanation:

we know that

The probability that a point in the square below  is in the shaded region, is equal to divide the area of the shaded region by the area of the square

step 1

Find the area of the shaded region

The area is equal to the area of the square minus the area of the circle

[tex]A=b^{2} -\pi(r)^{2}[/tex]

we have

[tex]b=12\ cm[/tex] ---> length side of the square

[tex]r=12/2=6\ cm[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

substitute

[tex]A=12^{2} -(3.14)(6)^{2}[/tex]

[tex]A=30.96\ cm^{2}[/tex]

step 2

Find the area of the square

[tex]A=b^{2}[/tex]

we have

[tex]b=12\ cm[/tex] ---> length side of the square

substitute

[tex]A=12^{2}=144\ cm^{2}[/tex]

step 3

Find the probability

[tex]P=30.96/144=0.215[/tex]

Convert to percent form

[tex]0.215*100=21.5\%[/tex]

Answer:

4

Step-by-step explanation:

The given expression is

[tex]4-\frac{4}{n}+\frac{5}{n}+\frac{15}{3n^2}[/tex]

We want to find the value of this expression as n approaches infinity.

Recall that as n approaches infinity, [tex]\frac{c}{n}[/tex], where c is a constant approaches zero.

The value of the given expression then becomes;

[tex]4-0+0+0=4[/tex]

Answer:

m = 25/9

Step-by-step explanation:

To solve for m, we must make the equation look like m=?

Since m is divided by 54, we can multiply both sides by 54 to make it have a coefficient of 1. So now our equation looks like:

m = 5/9 * 5

So m = 25/9

Answer: The answer to your question is m=30

Step-by-step explanation: When you are trying to solve proportions, you must cross multiply. The problem will now look like this:

5/9= m/54 (original problem)

[tex]\frac{5}{9}= \frac{m}{54}[/tex]

9m=270

Divide by 9 on both sides

9m= 270/9

m=30

Therefore, the solution to the proportion is 30. Hope this helps!!!

And please mark my answer as the Brainliest

Zilch, none.

the volume of the box is the same, it simply just sideways for the sake of display.

Answer:22

Step-by-step explanation:

22-7=15.

15/3=5

So the answer is 5

The number will be 22.

The fraction is numerical representation of the numbers in the form of numerator and denominator.

We have,

Let, a number =  x

Now,

According to the question,

[tex]\frac{x-7}{3} = 5[/tex]

So,

Now, multiply by 3 on both sides,

i.e.

[tex]\frac{(x-7)}{3} *3 = 5*3[/tex]

We get,

x - 7 = 15

⇒

x = 22

So, value of x is 22.

Hence, we can say that the number will be 22.

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Answer:

D

Step-by-step explanation:

Distribute the 1/2:

1/2(8x+4)

4x + 2

Distribute the 1/3:

1/3(9-3x)

3 - x

Add:

4x + 2 + 3 - x

3x +5

I hope this helps!

Answer:

D

Step-by-step explanation:

Distribute the 1/2:

1/2(8x+4)

4x + 2

Distribute the 1/3:

1/3(9-3x)

3 - x

Add:

4x + 2 + 3 - x

3x +5

I hope this helps!

I copy and pasted the answer above mine

Step-by-step explanation:

Question 4? is (maybe) C because a square and a rectangle's diagonals are perpendicular.

Question 5- True

Question 6- False, a square is always a rombi but a rombi isn't always a square.

Question 7- True

Question 8- True, because if they didn' then they wouldn't equal 360 degrees and the sum of a trapezoids interior angles has to add up to 360 degrees.

Answer:

z = -5

Step-by-step explanation:

The LCD in this problem is 6.  Thus, we have (2/6)z = -5/6 + (1/6)z.

Combining like terms, we have (1/6)z = -5/6.

Multiplying both sides by 6 isolates z as desired:

z = -5

ANSWER

C. sin 126°

EXPLANATION

-576° is coterminal with ±216,±144.

Therefore

cos (-576°)=cos(±216°)=cos(±144°)

The principal angle for -576° is 36° .

Since the terminal side of -576° is in the second quadrant and the cosine ratio is negative in the second quadrant,

cos (-576°)=-cos (±36°)

Also from complementary angles

cos (-576°)=-cos (36°)=-sin (90-36)=-sin(54°)

Answer:

6.25716517287

Step-by-step explanation:

Area of circle = π × r²

→ 123 = π × r²

⇒ Divide both sides by π

→ 39.1521160006 = r²

⇒ Square root both sides

→ 6.25716517287 = r

Answer: The correct answer is inverted

Step-by-step explanation:

Answer:

Step-by-step explanation:

An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Therefore we have the equation:

[tex]\dfrac{x+8}{10}=\dfrac{2x-5}{14}[/tex]              cross multiply

[tex]14(x+8)=10(2x-5)[/tex]             use the distributive property

[tex](14)(x)+(14)(8)=(10)(2x)+(10)(-5)[/tex]

[tex]14x+112=20x-50[/tex]           subtract 112 from both sides

[tex]14x=20x-162[/tex]           subtract 20x from both sides

[tex]-6x=-162[/tex]         divide both sides by (-6)

[tex]x=27[/tex]

Answer:

The amount after three years is $12831.8

Step-by-step explanation:

* Lets revise the compound interest

- The formula for compound interest is  A = P (1 + r/n)^(nt)

 Where:

# A = the value of the investment with interest

# P = the initial investment amount  

# r = the annual interest rate (decimal)

# n = the number of times that interest is compounded per unit t

# t = the time the money is invested

* Now lets solve the problem

∵ The initial amount is $9000

∴ P = $9000

∵ The rate is 12%

∴ r = 12/100 = 0.12

∵ The interest is compound quarterly

∴ n = 4

∵ The money invested for 3 years

∴ t = 3

∵ A = P (1 + r/n)^(nt)

∴ A = 9000(1 + 0.12/4)^(4×3)

∴ A = 9000(1 + 0.03)^12

∴ A = 9000(1.03)^12 = $12831.8

Answer:8>4n=6 or 8>4+n=6

Step-by-step explanation:

Let's solve the equation step by step. The problem statement can be translated into a mathematical equation:
"Eight more than the product of a number and 4 is equal to 6."
Let x be the number we are looking for. When the problem says "the product of a number and 4," we can express this as 4 * x or 4x. The phrase "eight more than" implies we are to add 8 to the product of the number and 4, making the expression 4x + 8. According to the statement, this expression is equal to 6. Thus, we write the equation as:
4x + 8 = 6
To find the value of x, we will follow these steps:
1. Subtract 8 from both sides of the equation to isolate the term with x on one side.
4x + 8 - 8 = 6 - 8
This simplifies to:
4x = -2
2. Divide both sides of the equation by 4 to solve for x.
4x / 4 = -2 / 4
This simplifies to:
x = -1/2
So the number we were looking for, represented as x, is -1/2.

9.92

You must look at which number has the decimal closest to 9.99

Here are the numbers in order from least to greatest

9.81, 9.82, 9.83, 9.92

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: 9.92

Step-by-step explanation: If you had $9.92, $9.82, $9.83 or $9.81. the most amount of money there is $9.92 because it is the closest to $10. which is more money than the least amount $9.81

Answer:

2.16 * (10^-5).

Step-by-step explanation:

5 = -log H+

5 = log (1 / H+)

1/ H+ = 10^5

H+ = 10^-5

In a similar fashion  the other brand has H+ of 10^-4.5.

So the difference in hydrogen ion concentration =  10^(-4.5) - 10^(-5)

= 2.16 * (10^-5).

2.16 × 10⁻⁵ is the  difference in the concentration of hydrogen ions between the two brands of vinegar.

pH is a numerical indicator of how acidic or basic aqueous and other liquid solutions are. The phrase, which is frequently used in biology, agronomy, and chemistry, converts the hydrogen ion concentration, which typically ranges between 1 and 1014 gram-equivalents per litre, into numbers ranging from 0 to 14.

The hydrogen ion concentration in pure water, which has a pH of 7, is 107 gram-equivalents per litre, making it neutral (neither acidic or alkaline). A solution having a pH below 7 is referred to as acidic, and one with a pH over 7 is referred to as basic, or alkaline.

5 = -log H+

5 = log (1 / H+)

1/ H+ = 10^5

H+ = 10^-5

difference=  10^(-4.5) - 10^(-5)

               = 2.16 × 10⁻⁵

Therefore, 2.16 × 10⁻⁵ is the  difference in the concentration of hydrogen ions between the two brands of vinegar.

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First you must have the quadratic equal to zero. In order to do this you must subtract 7 to both sides

x^2 + 20x + (100 - 7) = 7 - 7

x^2 + 20x + 93 = 0

Now you must find two numbers who's sum equals 20 and their multiplication equal 93

Are there any? NO!

This means that you have to use the formula:

[tex]\frac{-b±\sqrt{b^{2} - 4ac} }{2a}[/tex]

In this case:

a = 1

b = 20

c = 93

[tex]\frac{-(20) plus/minus\sqrt{20^{2} - 4(1)(93)} }{2*1}[/tex]

[tex]\frac{-20 plus/minus\sqrt{400 - 372} }{2}[/tex]

[tex]\frac{-20 plus/minus\sqrt{28} }{2}[/tex]

^^^We must simplify √28

√28 = 2√7

so...

[tex]\frac{-20 plus/minus 2\sqrt{7} }{2}[/tex]

simplify further:

[tex]-10 plus/minus\sqrt{7[/tex]

-10 + √7

or

-10 - √7

***plus/minus = ±

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: Option A

Step-by-step explanation:

A relation between two variables x and y is considered a function if and only if, for each input value x there is only one output value y.

If for an input value [tex]x_0[/tex] there are two output values [tex]y_1[/tex] and [tex]y_2[/tex] then the relation is not a function.

Therefore, to answer this question, identify the table in which each value of x has only one value of y.

You may notice that the option that meets this requirement is option A

Note that in option B, there are two output values 17 and 16 for x = -4.

So this relationship is not a function.

In option C there are 2 output values for x = -5

In option D there are 2 output values for x = -11

Answer:

(x + 1)² + (y + 5)² = 48

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 1, - 5) and r = 4[tex]\sqrt{3}[/tex], so

(x - (- 1))² + (y - (- 5))² = (4[tex]\sqrt{3}[/tex] )², that is

(x + 1)² + (y + 5)² = 48 ← equation of circle

Answer:

x=-9

Step-by-step explanation:

(square root 6)^8x= 216^(x-3)

Rewriting sqrt(6) as 6^1/2

6^1/2^8x = 216^(x-3)

We know a^b^c = a^(b*c)

6^(1/2*8x) = 216^(x-3)

6^(4x) = 216^(x-3)

We know 216 = 6^3

6^(4x) = 6^3^(x-3)

We know a^b^c = a^(b*c)

6^(4x) = 6^(3*(x-3))

6^(4x) = 6^(3x-9)

Since the bases are the same, the exponents have to be the same

4x = 3x-9

Subtract 3x from each side

4x-3x =3x-3x-9

x = -9

A=24

B=76

C=25

D= 19

Step-by-step explanation:

.......

Final answer:

The probabilities are matched as follows: A-24%, B-76%, C-19%, and D-25%. These are calculated based on the total number of balls of each color and the fraction that are labeled to win a prize.

Explanation:

The question provides a scenario where there are 24 yellow balls and 76 red balls in a box, and one-fourth of each color are labeled "Win a prize." We are asked to match descriptions of probabilities with their corresponding percent values.

A: Probability that a randomly selected ball labeled "Win a prize" is yellow = (1/4 * 24) / ((1/4 * 24) + (1/4 * 76)) * 100 = 6 / (6 + 19) * 100 = 24%.

B: Probability that a randomly selected ball labeled "Win a prize" is red = (1/4 * 76) / ((1/4 * 24) + (1/4 * 76)) * 100 = 19 / (6 + 19) * 100 = 76%.

C: Probability that a randomly selected ball is labeled "Win a prize" and is red = (1/4 * 76) / 100 = 19%.

D: Probability that a randomly selected yellow ball is labeled "Win a prize" = (1/4 * 24) / 24 * 100 = 25%.

ANSWER

Yes,no two ordered pairs on this graph have the same first element

EXPLANATION

For a set of ordered pairs to be a function,there must not be any two points that have the same first elements.

This means that, the x-coordinates must not repeat for any two given points.

The graph given represents a function because,no two ordered pairs on this graph have the same first element.

Hence it would pass the vertical line test.

The third choice is correct.

The correct answer is: Yes, no two ordered pairs on this graph have the same second element.

To determine if a graph represents a function, one must apply the Vertical Line Test. This test states that a graph represents a function if no vertical line intersects the graph at more than one point. In other words, for every input (x-value), there is exactly one output (y-value). This is equivalent to saying that no two ordered pairs on the graph have the same first element (x-value) and different second elements (y-values).

The statement Yes, no two ordered pairs on this graph have the same second element correctly describes the condition for a graph to represent a function. It implies that for every y-value, there is only one x-value associated with it, which is the definition of a function.

The other options are incorrect for the following reasons:

- Yes, there is more than one ordered pair on this graph. While this statement may be true, it does not address the condition necessary for a graph to represent a function. A graph with multiple ordered pairs could still fail to be a function if any vertical line intersects the graph more than once.

- Yes, no two ordered pairs on this graph have the same first element. This statement is not relevant to the definition of a function. A function can have the same x-value associated with different y-values (which would be multiple ordered pairs with the same first element). The key is that for each x-value, there can only be one y-value.

- No, there is a limited number of ordered pairs on this graph. The number of ordered pairs being limited does not affect whether the graph represents a function. A function can have a finite or infinite number of ordered pairs. The defining characteristic is that there is exactly one output for each input, not the total number of ordered pairs.

Therefore, the correct justification for the graph representing a function is that no two ordered pairs on the graph have the same second element, ensuring that the graph passes the Vertical Line Test.

Arrange the numbers in order from smallest to largest:

28, 35, 40, 40, 45, 52, 54, 58, 60

Median is the middle value  = 45

Mode is the number that appears most = 40

Mean is the average. Add the numbers and divide:

412/9 = 45.77 = 45.78

Range is difference between  highest and lowest = 60 - 28 = 32

Answer:

1/250

Step-by-step explanation:

Final answer:

To convert the recurring decimal 0.004 into a fraction, you can set up an equation by writing 0.004 = x and solve for x to find the fraction.

Explanation:

To convert the recurring decimal 0.004 into a fraction, we need to understand the concept of converting decimals to fractions. We can do this by setting up an equation where the decimal is equal to a fraction, and then solving for the fraction. In this case, we can set up the equation 0.004 = x, where x is the fraction we're trying to find. To eliminate the decimal, we can multiply both sides of the equation by 1000, which gives us 4 = 1000x. Now, we can divide both sides of the equation by 1000 to solve for x, which gives us x = 4/1000. Simplifying the fraction gives us x = 1/250. Therefore, the recurring decimal 0.004 can be written as the fraction 1/250.

Answer:

[tex]\sin (50\degree)=\frac{3}{c}[/tex]

Step-by-step explanation:

The given triangle is a right triangle with a given angle which is [tex]50\degree[/tex].

The side opposite to the 50 degree angle is 3 meters.

The hypotenuse is 'c' units.

We can use the sine ratio to obtain:

[tex]\sin (50\degree)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sin (50\degree)=\frac{3}{c}[/tex]

Therefore the correct answer is A.

The required equation can be used to solve for c is sin 50 = 3/c

From the figure shown, the measured sides are:

USing the SOH CAH TOA identity

sin theta = opp/hyp

sin 50 = 3/c

Hence the required equation can be used to solve for c is sin 50 = 3/c

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Answer:

[tex]\large\boxed{x=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

[tex]\dfrac{5}{6x}=\dfrac{10}{3}\qquad\text{cross multiply}\\\\(6x)(10)=(5)(6)\\\\60x=30\qquad\text{divide both sides by 60}\\\\x=\dfrac{30}{60}\\\\x=\dfrac{1}{2}[/tex]

ANSWER

D. 18 m^2

EXPLANATION

The area of a kite is half the product of the diagonals.

The diagonals of the kite are

3+3=6m

and

2+4=6m

The area of the kite

[tex] = \frac{1}{2} \times 6 \times 6[/tex]

[tex] = 3 \times 6[/tex]

[tex] = 18 {m}^{2} [/tex]

The correct answer is D.

The area of kite using the diagonal length 6m and 6 m is 18 m².

Thus, option (d) is correct.

Given:

length of diagonal 1 = 3+ 3 = 6 m

length of diagonal 2 = 2+ 4 = 6 m

Using the formula of Area of Kite

[tex]{\text} Area of kite[/tex] = [tex]\dfrac{1}{2} *[/tex] [tex]{\text} product \; of \;diagonal[/tex]

Now, substituting the values of diagonal into the formula as

[tex]{\text} Area of kite[/tex] = [tex]\dfrac{1}{2} *[/tex] [tex]{\text} (6 * 6)[/tex]

                   = [tex]\dfrac{1}{2} *[/tex] [tex]{\text} (36)[/tex]

                   = 18 m²

Thus, the area is 18 m².

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