James bought 4 goldfish, and his Mom got him 4 more for his birthday. What size tank (in gallons) does James need to hold all of the full-grown fish?

Answer:

13

Step-by-step explanation:

Because the problem says to make sure we have at least 3 candies of the same color, we have to think about the worst-case scenario. To get the worst-case scenario, we need to have the largest amount of candies taken before fulfilling the statement that 3 candies have the same color, so we take 2 black, 2 white, 2 green, 2 red, 2 blue, and 2 yellow candies. This sums to 12, and you have the worst case scenario here. But wait, you've picked only 2 of each candy. You have to pick one more candy to make sure you have 3 candies of the same color, so the answer is 12 + 1 = 13 candies.

Recall the triple angle identity for sine:

sin(3x) = 3 sin(x) cos²(x) - sin³(x)

… = 3 sin(x) (1 - sin²(x)) - sin³(x)

… = 3 sin(x) - 4 sin³(x)

So the equation is equivalent to

sin²(x) - 2 sin(x) + 2 = sin²(3x)

sin²(x) - 2 sin(x) + 2 = (3 sin(x) - 4 sin³(x))²

sin²(x) - 2 sin(x) + 2 = 9 sin²(x) - 24 sin⁴(x) + 16 sin⁶(x)

16 sin⁶(x) - 24 sin⁴(x) + 8 sin²(x) + 2 sin(x) - 2 = 0

or, by replacing y = sin(x),

16y ⁶ - 24y ⁴ + 8y ² + 2y - 2 = 0

By inspection, y = 1 is a root, since

16 - 24 + 8 + 2 - 2 = 0

so we get one family of solutions,

sin(x) = 1   ===>   x = arcsin(1) + 2nπ = π/2 + 2nπ

Now suppose y ≠ 1. Dividing both sides of the sextic equation by y - 1 then gives

(16y ⁶ - 24y ⁴ + 8y ² + 2y - 2)/(y - 1) = 0

16y ⁵ + 16y ⁴ - 8y ³ - 8y ² + 2 = 0

Unfortunately, the remaining roots can only be obtained through numerical methods. Using a calculator, you would find

y ≈ -1.127

y ≈ -0.475 ± 0.368i

y ≈ 0.539 ± 0.127i

But if you're solving over the reals, you can ignore these solutions. Remember that sin(x) is bounded between -1 and 1, and its value goes outside this interval only when x is complex.

Answer: y = -2x - 7

Step-by-step explanation:

The equation for a perpenducular line has a slope that is the negative inverse of the reference line, in this case x - 2y = 6.

Let's put this equation into standard slope-intercept form, y = mx+b, where m is the slope and b the y-intercept (the value of y when x is 0).

x - 2y = 6

- 2y = 6 - x

y = (1/2) x -3

The slope is (1/2), so a perpendicular line will have a slope of -2.

y = -2x + b

We can find b by using the given point ((-3,-1), a known solution):

-1 = -2*(-3) + b

-1 = 6 + b

b = -7

The perpendicular equation is y = -2x - 7

y = -2x

Answer:

=4x^2 +  3/2 x − 7

Step-by-step explanation:

Let's simplify step-by-step.

x /2  −3 + 4x^2 + x − 4  

=  1 /2 x + −3 + 4x^2 + x + −4

Combine Like Terms:

=  1 /2 x + −3 + 4x^2 +x + −4

= (4x^2) + (  1 /2 x + x) + ( −3+−4 )

= 4x^2 + 3 /2 x + −7

In the given triangle ABC in the figure, the value obtained for x will be equal to 6.

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the given information in the question,

Use the equation of Pythagoras' theorem,

h² = p² + b²

(2x - 2)² = x² + (x - 2)²

4x² - 2(2x)(2) + 4 = x² + x² + 4 + 4x

4x² - 8x + 4 = 2x² + 4x + 4

4x² - 2x² - 8x - 4x + 4 - 4 = 0

2x² - 12x = 0

2x² - 12x = 0

2x(x - 6) = 0

So,

2x = 0

⇒ x = 0, it is not possible.

Or,

x - 6 = 0

x = 6

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The given question is incomplete, the complete question might be in the attachment.

Answer:

it is between a c because they are both 12

Step-by-step explanation:

Answer:

your answer is the length of time is 7 hours and 15 minutes

Step-by-step explanation:

hope it helps

Answer:

21 minutes

Step-by-step explanation:

30%=9

10%=3

100%-30%=70%

7×10%=70%

3x7=21

=21minutes

Answer:

so this is really simpel x=1 thats it

Step-by-step explanation:\sin ^2\left(20^{\circ \:}\right)\left(x\right)+\cos ^2\left(20^{\circ \:}\right)\left(x\right)=1 \sin ^2\left(20^{\circ \:}\right)x+\cos ^2\left(20^{\circ \:}\right)x=1

Answer:

130 and 211

Step-by-step explanation:

15+17= 32

17+32=49

32+49=81

49+81=130

81+130=211

Answer:

130 and 211

Step-by-step explanation:

15,17,32,49,81 _ _

15+2=17+15=32+17=49+32=81

that mean 81+ 49=130

and 81+130= 211

Hence, the answer is 130 and 211.

The change in the volume of water in 1 minute is a decrease of 0.16 milliliters.

Since a water tank in Stewart's home had a small, steady leak loss of 1 3/5 mL in 10 min, to find the change in the volume of water in 1 minute, the following calculation must be performed:

Therefore, the change in the volume of water in 1 minute is a decrease of 0.16 milliliters.

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Answer:

x+(x-50)=180

2x-50=180

2x-50+50=180+50

2x/2=230/2

x=115

Step-by-step explanation:

according to the question,

x-50+x=180°

2x-50=180°

2x=230°

x=115°.

now, for x-50° = 115°-50°= 65°

hope this helps you.

Answer:

i think 223/499

Step-by-step explanation:

Answer:

- 14

Step-by-step explanation:

4x + 6 = - 62

4x = - 62 + 6

4x = - 56

x = - 56 / 4

x = - 14

The value of x in this equation will be; x = -14

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that  the equation 4x + 6 = - 62

Here, we need to solve for x

4x + 6 = - 62

4x = - 62 + 6

4x = - 56

x = - 56 / 4

x = - 14

Therefore, the solution will be as;

x = -14,

The value of x in this equation will be; x = 14

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Answer:

Step-by-step explanation:

Answer:

help on what?

Step-by-step explanation:

Answer:

You need to post a question or a screenshot of the question so someone can help you!

Answer:

2 : 1

Step-by-step explanation:

27 total

9 filled

27 - 9 = 18 empty

18 : 9

2 : 1

Answer:

Wooden popsicles, Tissues.,glassbottles, juice cans, paper cups

Answer:

500 centiliters

Step-by-step explanation:

Using a phase is helpful for conversions. I like this one "King Henry died by drinking chocolate milk".

K- Kilo : 0.001

H- Hecta : 0.01

D- Deca : 0.1

b- base (gram, liter, meter, etc) : 1

d- deci : 10

c-centi : 100

m-milli : 1000

For every step up or down you move the decimal one place over depending on if you go up or down.

So, for 2.5L as centiliters you would move the decimal over two spots giving you 250 centiliters. You can also multiply or divide by 10 for each step taken. so for two steps you would multiply by 100, also giving you an answer of 250 centiliters. This is then multiplied by two as 250 cL was dumped twice.

You get a third of some number x if you divide x by 3.

So, one third of (1/3)⁸ is

(1/3)⁸ / 3 = (1/3)⁸ × 1/3 = 1/(3⁸⁺¹) = 1/3⁹

_ _

| - 17 |

PQ = | - 3 |

| - 37 |

|_ 49 _|

Answer:

D

Step-by-step explanation:

Main value = .4142

A. sqrt(3)-sqrt(2) = .3178

B. sqrt(3)+sqrt(2) = pi

C. sqrt(2)+1 = 2.4142

D. sqrt(2)-1 = .4142 <-

Answer:

true

Step-by-step explanation:

if there is 4 ounces of water in it then it would be empty withing 2 minutes

Answer:

Impossible?

Step-by-step explanation:

Answer:

5 pails

because jack has 5 pail and he must get 3 more pail to times 5 and get 40

Answer:

5 movies

Step-by-step explanation:

90-30=60

60/12=5

Answer:

90 minus 12x is greater than or equal to 30

then solve and get x equals 5

Answer:

The area of the countertops surface is 27 square feet. The perimeter of the countertop is 24 feet.

Step-by-step explanation:

COMPUTATION:

Area:

width = 3 feet

length = width x 3 = 9 feet

wl = 27 square feet

Perimeter:

width = 3 feet

length = 9 feet

w + l + w + l = 24 feet

Hope this helps!

Answer:

$112.5

Step-by-step explanation:

So 2 pairs of shoes is $45, that means that 4 pairs would be $90.

One pair of shoes would be $22.5

Add $90 to $22.5 to get the answer.

Answer:

-x2+21x+3

Step-by-step explanation:

[tex]\\ \sf\longmapsto 9x-(x-3)(x+1)+10x[/tex]

[tex]\\ \sf\longmapsto 9x-(x^2-2x-3)+10x[/tex]

[tex]\\ \sf\longmapsto 9x-x^2+2x+3+10x[/tex]

[tex]\\ \sf\longmapsto 9x+2x+10x-x^2+3[/tex]

[tex]\\ \sf\longmapsto 21x-x^2+3[/tex]