What is the following product? ^3 square root 5 * square root 2

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is [tex]27 + 64x^{3}[/tex]

Now, the equation is [tex]27 + 64x^{3} = 0[/tex]

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be [tex]- \frac{3}{4}[/tex] and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  

Again, we have to solve the difference of two cubes which is [tex]64m^{3} - 1[/tex]

Now, the equation is [tex]64m^{3} - 1 = 0[/tex]

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be [tex] \frac{1}{4}[/tex] and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  (Answer)

Answer:

6x^3

Step-by-step explanation:

2160x^8/ 60x^2

2160/60=36

x^8-2 because your dividing

x^6

36x^6 (you're not done)

after you've got the square root

6x^3 because

36=6*6

and the square root of 6 is 2.45 which rounds to 3

(I'm pretty sure this is the answer).

The simplified form of [tex]\rm \sqrt{\dfrac{2160 x^8}{60x^2}[/tex] is 6x³ , Option C is the right answer.

Square root of a positive square number is the number itself.

[tex]\rm \sqrt{y^8} = y^4[/tex]

In the given question the expression given is

[tex]\rm \sqrt{\dfrac{2160 x^8}{60x^2}[/tex]

To simplify this

the numerator and the denominator has to be simplified first

[tex]\rm \dfrac{2160x^8}{60x^2}\\[/tex]

[tex]\rm \dfrac{2160}{60}\\ \\\\\ \dfrac{1080}{30}\\\\\\ \dfrac{540}{15} \\\\\\ \dfrac{108}{3}\\\\= 36[/tex]

[tex]\rm \dfrac{x^8}{x^2} \\\\= x^{8-2}\\\\= x^6[/tex]

Therefore

[tex]\rm \sqrt{36x^6}[/tex]

6x³

The simplified form of [tex]\rm \sqrt{\dfrac{2160 x^8}{60x^2}[/tex] is 6x³ , Option C is the right answer.

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In the equation y=40+6x, 40 represents the initial number of comic books in Joylin's collection, given to her by her uncle. Over time, she gains additional comic books from monthly subscriptions.

In the provided equation, y=40+6x, the number 40 represents the initial amount of comic books Joylin has before the monthly subscriptions start. This is essentially the number of comic books Joylin's uncle gave her to start her collection. The number 6 represents the number of books she receives monthly from the subscriptions. Therefore, 'x' months after receiving the initial batch of comic books, Joylin has 40 + 6x comic books in her collection.

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1. 4(2+3c) = 56

c = 4

3. -29 = 5(2a-1)+2a

a = -2

5 . 7p-(3p+4) = -2(2p-1)+10

p=2

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

x=4

Step-by-step explanation:

1. 4(2+3c) = 56

[tex]4(2+3c) = 56\\8+12c = 56[/tex]

Subtracting 8 from both sides

[tex]8-8+12c = 56-8\\12c = 48[/tex]

Dividing both sides by 12

[tex]\frac{12c}{12} = \frac{48}{12}\\c = 4[/tex]

Checking:

[tex]4[2+3(4)] = 56\\4(2+12) = 56\\4(14) = 56\\56 = 56[/tex]

3. -29 = 5(2a-1)+2a

Simplifying

[tex]-29 = 10a-5+2a\\-29 = 12a-5[/tex]

Adding 5 on both sides

[tex]-29+5 = 12a - 5+5\\-24 = 12a[/tex]

Dividing both sides by 12

[tex]\frac{12a}{12} = \frac{-24}{12}\\a = -2[/tex]

Checking:

[tex]-29 = 5(2a-1)+2a\\-29 = 5[2(-2)-1]+2(-2)\\-29 = 5(-4-1) -4\\-29 = 5(-5) -4\\-29 = -25-4\\-29 = -29[/tex]

5 . 7p-(3p+4) = -2(2p-1)+10

Simplifying

[tex]7p-3p-4 = -4p+2+10\\4p-4 = -4p+12[/tex]

Adding 4 on both sides

[tex]4p-4+4 = -4p+12+4\\4p = -4p+16[/tex]

Adding 4p on both sides

[tex]4p+4p = -4p+4p+16\\8p = 16[/tex]

Dividing both sides by 8

[tex]\frac{8p}{8} = \frac{16}{8}\\p = 2[/tex]

Checking:

[tex]7p-(3p+4) = -2(2p-1)+10\\7(2)-[3(2)+4] = -2[2(2)-1] +10\\14 - (6+4) = -2 (4-1) +10\\14 - 10 = -2(3) +10\\4 = -6+10\\4=4[/tex]

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

Simplifying

[tex]\frac{1}{2} (-4+6x) = \frac{1}{3}x+\frac{2}{3}(x+9)\\\frac{-4}{2}+\frac{6x}{2} = \frac{x}{3} +\frac{2x}{3} + \frac{18}{3}\\-2+3x = \frac{x+2x+18}{3}\\-2+3x = \frac{3x+18}{3}\\3(-2+3x) = 3x+18\\-6+9x = 3x+18[/tex]

Adding 6 on both sides

[tex]-6+6+9x = 3x+18+6\\9x = 3x+24[/tex]

Subtracting 3x from both sides

[tex]9x-3x = 3x-3x+24\\6x = 24[/tex]

Dividing both sides by 6

[tex]\frac{6x}{6} = \frac{24}{6}\\x = 4[/tex]

Checking:

[tex]\frac{1}{2} [-4+6(4)] = \frac{1}{3}(4)+\frac{2}{3}(4+9)\\\frac{1}{2}(-4+24) = \frac{4}{3}+\frac{2}{3}(13)\\\frac{1}{2}(20) = \frac{4}{3} +\frac{26}{3}\\15 = \frac{4+26}{3}\\15 = \frac{30}{3}\\15=15[/tex]

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Answer:

40 pounds

Step-by-step explanation:

Given: Cost of a candy [tex](c_1)[/tex]= [tex]\$ 12[/tex] per pound

           Cost of candy [tex](c_2) = \$ 19\ per\ pound[/tex]

           Total amount of mixture of be produced = [tex]70\ pound[/tex]

           Selling price of mixture = [tex]\$ 15 \ per\ pound[/tex]

Let´s x be the amount of [tex]c_1 [/tex] to be mixed in the mixture.

∴ Cost of [tex]c_1[/tex] in the mixture = 12x

Next, Cost of [tex]c_2[/tex] in the mixture = [tex](70 - x)\times 19[/tex]

And we know the cost of final mixture = [tex]70 \times 15 = 1050[/tex]

Now, putting all the value in the equation

⇒ [tex]12x + 19 \times (70 - x) = 1050[/tex]

⇒ [tex]1330 - 7x = 1050[/tex]

⇒ [tex]-7x = -280[/tex]

∴ [tex]x = 40\ pound[/tex]

∴ 40 pounds of candy worth $12 per pound to be mixed in the mixture.

Answer:

$7,500.00

Step-by-step explanation:

The Realtor commission will be 5% of $150,000.00

(5% * $150,000)/100% = $7,500.00

The realtor makes a 5% commission on a $150,000 house, which equates to a commission of $7,500 by multiplying the sale price by the commission rate (0.05).

To calculate the amount of commission a realtor earns on a house sale, you simply multiply the sale price of the house by the commission rate. In this case, the realtor makes a 5% commission on a $150,000 house sale. We calculate the commission as follows:

Therefore, the realtor will earn a commission of $7,500 for selling the $150,000 house.

Answer:

what' you should do to stay healthy is eat vegetables and fruits grains and anything else you know is good for you and you should also drink water everyday. what you shouldn't do to stay healthy is basically eat junk food and drink soda also eat lots of candy but eating healthy is much better

Answer:

Staying healthy physically can help you stay healthy emotionally too. If you're eating the right food and keeping fit, your body will be strong and help you to cope with stress and also fight illness. Eating well and exercising often when you're a teenager will also help you stay in good health later in life.

Step-by-step explanation:

Answer:

k = 0.2980

Step-by-step explanation:

Given:

number of months t =3

number of hits y = 10000

The equation is modeled as

[tex]y= 4090e^{kt}[/tex]

We need to find value of k.

Now Substituting the values in above equation we get.

[tex]10000= 4090e^3k\\e^{3k}=\frac{10000}{4090}\\\\[/tex]

Now taking Anti log on both side to remove e we get,

[tex]3k = \ ln \frac{10000}{4090}\\\\3k = 0.8940\\k = \frac{0.8940}{3}= 0.2980[/tex]

Hence the value of k = 0.2980.

The value of k is 0.2981.

We are given that in the website's third month (t = 3), there were 10,000 hits. We need to find the value of k.

1. First, substitute y = 10000 and t = 3 into the given equation:

10000 = 4090e3k

2. Next, solve for the exponential term:

10000 / 4090 = e3k

This simplifies to:

10 / 4.09 = e3k

2.444 = e3k

3. Take the natural logarithm (ln) of both sides to solve for k:

ln(2.444) = 3k

Calculating ln(2.444) yields approximately 0.8944.

0.8944 = 3k

4. Finally, solve for k:

k = 0.8944 / 3

k ≈ 0.2981

Therefore, the value of k, rounded to four decimal places, is approximately 0.2981.

Answer:

675 ft 2

Step-by-step explanation:

just did it in a test

Answer: –1.8x – 4.5

Step-by-step explanation:

The guy above me obviously doesn’t know how to do this so here this is the correct answer

Answer:

–1.8x – 4.5

Step-by-step explanation:

Answer: x=-5

(^._.^)ﾉ

Step-by-step explanation:

4x-3=2x-13

Subtract

4x−3−2x=−13

Simplify

2x−3=−13

Add 3 to both sides

2x=−13+3

Simplify again

2x=-10

Divide both sides by 2

x=[tex]-\frac{10}{2}[/tex]

Simplify one last time

x=-5

You're finished! Not only that but you found the answer :3

Hope this helps, have a BLESSED and wonderful day! :-)

Answer:

[tex]y=4\sqrt{3}\ units[/tex]

Step-by-step explanation:

Triangle MRN is created by folding an equilateral triangle by half. Since triangle MRN is right triangle, the equilateral triangle must be folded along the height drawn to one side.

In equilateral triangle with side length of a units, the height is [tex]\dfrac{a\sqrt{3}}{2}\ units[/tex] and the height is greater than half the side because

[tex]\dfrac{a\sqrt{3}}{2}>\dfrac{a}{2}.[/tex]

The leg with length x units has the smaller projection (2 units long) than the leg with length y units has (6 units long).

This means the leg with length y units is the height of the equilateral triangle. If the leg with length y units is the height of the equilateral triangle, then the hypotenuse MN = 8 units is the side of the equilateral triangle and lex with length x units is half the side, so x = 4 units.

By the Pythagorean theorem,

[tex]y^2=8^2-4^2\\ \\y^2=64-16\\ \\y^2=48\\ \\y=4\sqrt{3}\ units[/tex]

The value of y is 4*sqrt(3) units.

The problem states that triangle MRN is created by folding an equilateral triangle in half. Since triangle MRN is a right triangle, the equilateral triangle must have been folded along its height. We are given that the side length of the equilateral triangle is 8 units. We are asked to find the value of y, which is the length of the leg of triangle MRN that is opposite the right angle.

Here's how we can solve the problem:

1. Identify the relevant information:

   - Triangle MRN is a right triangle.

   - The original equilateral triangle has side length 8 units.

   - We want to find the value of y, which is the length of the leg of triangle MRN opposite the right angle.

2. Use the properties of equilateral triangles:

   - In an equilateral triangle, all sides are equal and all angles measure 60 degrees.

   - The height of an equilateral triangle divides the triangle into two 30-60-90 triangles.

   - The height of an equilateral triangle with side length a is sqrt(3)*a / 2.

3. **Relate the information to find y:**

   - Since the equilateral triangle was folded along its height, the height of the equilateral triangle is also the hypotenuse of triangle MRN (side MN).

   - Therefore, MN = sqrt(3)*8 / 2 = 4*sqrt(3).

   - We are given that MN = 8, so 4*sqrt(3) = 8.

   - Solving for sqrt(3), we get sqrt(3) = 2.

   - Now we can use the Pythagorean theorem in triangle MRN: y^2 + (4)^2 = (8)^2.

   - Substituting sqrt(3) = 2, we get y^2 + 16 = 64.

   - Solving for y, we get y = sqrt(48) = 4*sqrt(3).

Therefore, the value of y is 4*sqrt(3) units.

Answer:

40 games

Step-by-step explanation:

Here we need to find a number, x, such as 32 is the 80% of x. In this case x is our 100%.

So, if our x number is the correct it must be that the following ratios are equivalent:

100%/80% = x/32 if 32 is the 80% of x

Lets drop the % sign for simplicity:

100/80 = x/32

Now, multiply both sides by 32 to eliminate the 32 on the right side:

(100/80)*32 = (x/32)*32

100*32/80 = x

3200/80 =x

320/8 = x

40 = x

So 32 is the 80% of 40.

32 games is the 80% of 40 games.

Answer: 40

Step-by-step explanation:

Answer:

Step-by-step explanation:

(y-y)=m(x-x)

(y--3)=2(x-7)

y+3=2x-14

y+3+14=2x

Answer:

that's your answer...

Answer:

Step-by-step explanation:

c

Answer:

$18

Step-by-step explanation:

12*4=48

48-30=18

Answer:

A = 10⁰

Step-by-step explanation:

We have 2.247 and this to represented as [tex]$ 2 \times A + 2 \times B + 4 \times C + 7 \times D $[/tex]

[tex]$ 2.247 = \frac{2247}{1000} $[/tex]

[tex]$ 2.247 = 2 \times 10^0 + 2 \times \frac{1}{10} + 4 \times \frac{1}{10^2} + 7 \times \frac{1}{10^3} $[/tex]

Comparing with the given data, we have:

A = 10⁰

B = [tex]$ \frac{1}{10} $[/tex]

C = [tex]$ \frac{1}{10^2} $[/tex]

D = [tex]$ \frac{1}{10^3} $[/tex]

Hence the answer A = 10⁰.

Answer:

equation- 4÷x=-7

x= -4/7

Step-by-step explanation:

I think the answer is -4/7 i tried my best :)

so x=-4/7

To calculate the change in water amount after 1/3 hour, the draining rate of -3.75 gallons per hour is multiplied by 1/3, resulting in a total change of -1.25 gallons of water.

The student has asked about the change in the amount of water in a bathtub after a certain period, given a constant rate of draining. The bathtub drains at a rate of -3.75 gallons per hour. To find the total change in the amount of water after 1/3 hour (20 minutes), we multiply the rate by the time.

First, we convert 1/3 of an hour to minutes:

1/3 hour = 60 minutes / 3 = 20 minutes.

Next, we calculate the change in water:

Change in water = Rate  imes Time

Change in water = -3.75 gallons/hour  imes 1/3 hour

Change in water = -3.75 gallons/hour  imes 0.3333... (repeating)

Change in water = -1.25 gallons.

Therefore, the bathtub will drain 1.25 gallons of water in 1/3 of an hour.

Answer:

A'(-16,4), B'(16,-12), C'(8,12), D'(-4,16)

Step-by-step explanation:

The dilation with a center of dilation at (0,0) and scale factor of [tex]\frac{1}{4}[/tex] has the rule

[tex](x,y)\rightarrow \left(4x,4y\right)[/tex]

Quadrilateral ABCD has vertices at points A(-4,1), B(4,-3), C(2,3) and (-1,4).

Therefore, the image vertices are

Answer: 10 free throws made, 9 two-point shots made

Step-by-step explanation:

x=number of free throws

y=number of two-point shots

x+y=19

x+2y=28

solve by elimination

x+2y=28

-(x+y=19)

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

y=9

x=10

Answer: 10 free throws made, 9 two-point shots made

Step-by-step explanation:

x=number of free throws

y=number of two-point shots

x+y=19

x+2y=28

solve by elimination

x+2y=28

-(x+y=19)

(Y=9

X=10)

Answer:

The number of sides of the polygon with 135° interior angle is 8  

Step-by-step explanation:

Given as :

The measure of each interior angle of regular polygon = 135°

Let The total number of sides = n

So, each internal angle of a regular polygon with n sides = [tex]180^{\circ}- \frac{360^{\circ}}{n}[/tex]

or,   135°  = [tex]180^{\circ}- \frac{360^{\circ}}{n}[/tex]

or, [tex]\frac{360^{\circ}}{n}[/tex] = 180° - 135°

or,   [tex]\frac{360^{\circ}}{n}[/tex] = 45°

∴   n = [tex]\frac{360^{\circ}}{45^{\circ}}[/tex]

I.e  n = 8

Hence the number of sides of the polygon with 135° interior angle is 8  Answer

Answer:

2/3

Step-by-step explanation:

Cancel the common factor 2 = 2/3

Answer:

24

Step-by-step explanation:

in this, the blank is 'y'. I filled the x with -8

)(−8)−(−8−40)=(2)(−8)−(y−8)

Step 1: Simplify both sides of the equation.

(10)(−8)−(−8−40)=(2)(−8)−(y−8)

(10)(−8)+−1(−8−40)=(2)(−8)+−1(y−8)(Distribute the Negative Sign)

(10)(−8)+(−1)(−8)+(−1)(−40)=(2)(−8)+−1y+(−1)(−8)

(10)(−8)+8+40=(2)(−8)+−y+8

−80+8+40=−16+−y+8

(−80+8+40)=(−y)+(−16+8)(Combine Like Terms)

−32=−y+−8

−32=−y−8

Step 2: Flip the equation.

−y−8=−32

Step 3: Add 8 to both sides.

−y−8+8=−32+8

−y=−24

Step 4: Divide both sides by -1.

−y

−1

=

−24

−1

y=24

Answer:

y=24

Answer:

x=-3, y=5. (-3, 5).

Step-by-step explanation:

y=x+8

x+y=2

----------

x+x+8=2

2x+8=2

2x=2-8

2x=-6

x=-6/2

x=-3

y=-3+8=5

Answer:

(-3,5)

Step-by-step explanation:

Answer: f(x) = -3| x - 1 |  is really just  f(x) = -3| x - 1 | + 0.

now, what value of "x" makes the absolute value expression to 0?

well, let's just set it to 0 and check,

x - 1 = 0

x = 1

so if "x" ever becomes 1, the | x - 1| will turn to 0, therefore, the vertex is at   

f(x) = -3| (1) - 1 | + 0  -------------->  ( 1, 0 )

Answer:take 193 and subtract 35. you should get 158 then divide 158 bby 2 you should get 79 add 35 to 79 you should get 114. therefore kelly will have 114 and rachel will have 79

Step-by-step explanation:

Answer:

Kelly collected 114 pounds of newspaper. Rachel collected 79 pounds of newspaper.

Step-by-step explanation:

Write an expression for each girl to figure out how many pounds of newspapers they each collected:

(x represents pounds of newspapers)   Rachel = x     Kelly = x + 35

To solve, combine the two expressions into one equation: 2x + 35 = 193

Then, subtract 35 from both sides of the equation. Make sure you subtract from both sides of the equation to keep it equal: 2x + 35 - 35 = 193  - 35

The equation left is: 2x = 158

Divide both sides by two in order to get the x by itself: 2x ÷ 2 = 158 ÷ 2

The answer will be: x = 79

Then, substitute 79 for x in the first equations:

Rachel = 79    Kelly = 79 + 35

Solve for the final answer: Rachel = 79    Kelly = 114

Answer:

1. C

2. A

The drawings will help

Remember: Keep, Change, Flip