i) A fish tank measures 1m long by 40cm wide and 60cm height.
What is the capacity of the fish tank?
ii) How many litres of water does it take to fill it three quarters full ?


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Answer:

The image of the circle is 9·x² + 9·y² - 42·x + 33·y = 22

Step-by-step explanation:

We convert the equation to the form (x - h)² + (y - k)² = r²

Where:

(h, k) = Coordinates of the center of the circle

We therefore have;

x² + y² - 2·x + 3·y = 8 which gives;

x² - 2·x + 1 - 1 + y² + 3·y + (3/2)² - (3/2)² = 8

(x - 1)² + (y + 3/2)² - 1 - (3/2)² = 8

(x - 1)² + (y + 3/2)²  = 8 +  1 + (3/2)² = 45/4

Therefore, the center = (1, -3/2) and the radius = √5 × 3/2

The line joining the centers of the actual (1, -3/2) and reflected circle (h, k) is bisected by the line of reflection, therefore the midpoint of the line is on the line of reflection with coordinates;

Midpoint between (1, -3/2) and  (h, k) = [tex]\left (\dfrac{{h - 1}}{2}, \, \dfrac{k - 3/2}{2} \right )[/tex]

Which gives;

y = 2·x - 3 being equivalent to [tex]\dfrac{k - 3/2}{2} = 2\times\dfrac{{h - 1}}{2} - 3[/tex]

Which gives;

4·h -2·k -13 = 0.......(1)

Similarly the slope of the reflecting line is perpendicular to the line joining the centers of the actual and reflected circles

Therefore;

The slope of the line, y = 2·x - 3 = 2, hence we have;

[tex]\dfrac{\left ( \dfrac{k - 3/2}{2} \right ) + 3/2}{\left (\dfrac{{h - 1}}{2}-1 \right )} = \dfrac{1}{2}[/tex]

Which gives;

2·h -4·k -12 = 0.......(2)

Multiplying equation (2) and subtracting from equation (1) gives

4·h -2·k -13 - 2×(2·h -4·k -12) = 0

6·k + 11 = 0

k = -11/6

From which we have;

2·h -4×(-11/6) -12 = 0

Hence;

h = 7/3

Therefore, the center of the reflected circle = (7/3, -11/6)

The equation of the reflected circle is therefore;

(x - 7/3)² + (y + 11/6)² = 45/4

Which gives;

9·x² + 9·y² - 42·x + 33·y - 22 = 0

or x² + y² - 42/9·x + 33/9·y = 22/9.

Answer:

Range = 3

Step-by-step explanation:

First, start off by ordering the list from least to greatest. Then, subtract the least number (0) from the greatest number (3), which will get you the range of 3.

Hope this helps! :D

Answer:

No solution

Step-by-step explanation:

I'd suggest you try to solve this first:  3√(x + 8) = 4.  First, square both sides; this results in 9(x + 8) = 16, or x + 72 = 16/9, or x = -632/9.  We cannot let x = -632/9 in √(x + 8) because -632/9 is not in the domain of the square root function.  No solution.

If we now write 3√(x + 8) = -4   (note the negative sign), similar efforts at solution result in 9(x + 8) = -4, or x + 8 = -4/9, or x = -8 - 4/9.  If we now substitute this result for (x + 8) in 3√(x + 8) = -4 (above), we get 3√(-8 + 8 - 4/9), which has no solution; -4/9 is not in the domain of the square root function.

The solution for the given equation is 16.

The given equation is 3√x+8=-4.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The solution for the given equation can be determined as follows:

Now, 3√x+8=-4

⇒ 3√x=-4-8

⇒ 3√x=-12

⇒ √x=-12/3

⇒ √x=-4

Squaring both the sides, we get

x=16

Therefore, the solution for the given equation is 16.

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Answer:

(-5, 2) and (2, 6)

Step-by-step explanation:

Use the substitution method. We know that y = 3x and y = x^2 - 10, so we can set them equal to one another.

3x = x^2 - 10

x^2 - 3x - 10 = 0

Use the quadratic equation to solve for x.

x = - 5, 2

Now solve for y using these two values of x by substituting it back into the equations.

y = - 15,  6

In coordinate form, (-5, 2) and (2, 6)

Answer:

The correct option is C.

Step-by-step explanation:

To have this credit card there is two fees, one that is fixed payed upfront and other that is payed after the second month. The fixed fee costs $62, and doesn't escalate with time, while the other one is $30 and starts to be charged after the second month. Therefore, the total cost of the card is the fixed fee plus the monthly fee multiplied by the number of months the user had the card subtracted by two, or as shown below:

[tex]C(g) = 62 + 30*(g-2)[/tex]

The correct option is C.

Answer:

Step-by-step explanation:

Around 0

Answer:

they are both money

Step-by-step explanation:

that's why they relate, they're both currency

Answer:

B

Step-by-step explanation:

I took the quiz

Answer:

No

Step-by-step explanation:

One infinity cannot be larger than another

Answer:

B

Step-by-step explanation:

because first it is 11, 12, after it is 13, and 14

: for 22, 23 and after 24

Answer:

B

Step-by-step explanation:

Answer:

52 brownies

Step-by-step explanation:

If you divide 17.16 by 0.33, you get 52

Answer:

20 miles

Step-by-step explanation:

1 : just use the line to trace how long it would be

Answer:

x = -4

Step-by-step explanation:

5(8+x)=20

Divide each side by 5

5/5(8+x)=20/5

8+x = 4

Subtract 8 from each side

8+x-8  = 4-8

x = -4

The right answer is -4.

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

2.45 L in a week

Step-by-step explanation:

First find out how many ml he drinks in a week

350 mL * 7 days

2450 mL in a week

We know that 1000 mL = 1 L

2450 mL * 1 L /1000 mL = 2.45 L in a week

Answer:

2.450 litres.

Step-by-step explanation:

The answer is converting into Litres as we know 7 x 35 = 350-105 = 245++0 = 2450 ml

Answer:

X=4

Step-by-step explanation:

Solution: x equals 4

x/14-(6/21)=0

1. Simplify 2/7

x/14- 2/7 is 0

It’s too much steps

Answer:

{0.3, 3, 30, 300, 3000}

Step-by-step explanation:

Here a(1) = 0.3, and

        a(2) = 3, and

         a(3) = 30, and

          a(4) = 300, and

          a(5) = 3000

The first term (given) is 0.3, and the common ratio is 10.

Answer:

15n+18

Step-by-step explanation:

you have to multiply both integers(5n + 6) from inside the bracket with the number outside the bracket *3*

equation working below

3×5n=15n

3×6=18

final answer:

15n+18

Answer:

a. 87.5%

b. 30 g of 12 carat and 60 g of 21 carat.

Step-by-step explanation:

a. The percentage of gold in 21 carat is given by:

[tex]gold_{21} = \frac{21}{24}*100 = 87.5 \%[/tex]

b. Since the mass he wants to produce is 90 g, then the added mass of the 12 carat, "x", and the mass of the 21 carat "y", must be equal to that:

[tex]x + y = 90[/tex]

The sum of gold on each carat type must be equal to the amount of gold on the final mixture, since a 12 carat has 50% gold and a 21 carat has 87.5% gold, then we have:

[tex]0.5*x + 0.875*y = 0.75*90\\\\0.5*x + 0.875*y = 67.5\\[/tex]

We now have a system of equations which we can solve to find the necessary mass of each type.

[tex]x + y = 90 \text{ } *-0.5\\0.5*x + 0.875*y = 67.5\\\\-0.5*x - 0.5*y = -45\\0.5*x + 0.875*y = 67.5\\\\0.375*y = 22.5\\\\y = 60[/tex]

[tex]x = 90 - y = 90 - 60\\\\x = 30[/tex]

He needs 30 g of 12 carat gold and 60 g of 21 carat gold.

Answer:

a. 87.5%

b. 30 g of 12 carat and 60 g of 21 carat.

Step-by-step explanation:

a. The percentage of gold in 21 carat is given by:

b. Since the mass he wants to produce is 90 g, then the added mass of the 12 carat, "x", and the mass of the 21 carat "y", must be equal to that:

The sum of gold on each carat type must be equal to the amount of gold on the final mixture, since a 12 carat has 50% gold and a 21 carat has 87.5% gold, then we have:

We now have a system of equations which we can solve to find the necessary mass of each type.

He needs 30 g of 12 carat gold and 60 g of 21 carat gold.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

15 boxes multiplied by 2 is 30, 1/3 times 30 is 10

Answer:

the answer is b, 4 units

Answer:

4

Step-by-step explanation:

quatro

Answer:

its rather B or C

Step-by-step explanation:

c(c)=y

so the slope is Y=2x+2

the reason why its rather B or C is because of the axis

i   dont know what belongs where

Answer:

is this a question? also, 6/4 is not irrational, it is rational, and an irrational number is a number that cannot be expressed as a ratio of two integers, aka a simple fraction

Answer:

D. It assumes that all students taking geometry are in the 9th grade 

Step-by-step explanation:

Answer:

Step-by-step explanation:

volume of cone=1/3 πr²h

volume of frustum=vol of larger cone-vol of smaller cone=1/3πR²H-1/3πr²h

=1/3π(R²H-r²h)

=1/3π(4.5²×9-3²×6)

=1/3π×9×3(4.5×1.5-2)

=9π(6.75-2)

=9π×4.75

=42.75π cm³

The volume of frustum of cone is   [tex]42.75\pi[/tex]

Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum. To get this part of the right circular cone we have to slice it horizontally or parallel to the base.

Volume of frustum of cone = [tex]\frac{\pi H}{3} [ R^{2} + r^{2} + rR][/tex]

Where,

R = Radius of the bigger circular end

r = radius of the smaller circular end

H = height of frustum

According to the question

Original height of cone = 9 cm

Radius of the bigger circular end = 4.5 cm

Radius of the smaller circular end = 3 cm

Height of frustum = 3 cm

Volume of frustum of cone = [tex]\frac{\pi H}{3} [ R^{2} + r^{2} + rR][/tex]

                                              = [tex]\frac{\pi 3}{3} [ 4.5^{2} + 3^{2} + 4.5*3][/tex]

                                              =  [tex]\pi [ 20.25 + 9 + 13.5][/tex]

                                              = [tex]42.75\pi[/tex]

Hence, The volume of frustum of cone is   [tex]42.75\pi[/tex] .

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Answer:

A. a point that shows the y-intercept

Step-by-step explanation:

Answer:

The probability that all of the offices are filled by members of the debate​ team is 0.0512 and the probability that none of the offices are filled by members of the debate​ team is 0.0256

Step-by-step explanation:

The offices of​ president, vice​ president, secretary, and treasurer for an environmental club will be filled from a pool of 15 candidates.

So, Number of candidates required = 4

Total number of candidates = 15

Number of candidates which are members of the debate team. = 8

So, Number of candidates which are not the members of the debate team = 15-8 =7

The probability that all of the offices are filled by members of the debate​ team = [tex]\frac{^8C_4}{^{15}C_4}=\frac{\frac{8!}{4!\left(8-4\right)!}}{\frac{15!}{4!\left(15-4\right)!}}=0.0512[/tex]

The probability that none of the offices are filled by members of the debate​ team=[tex]\frac{^7C_4}{^{15}C_4}=\frac{\frac{7!}{4!\left(7-4\right)!}}{\frac{15!}{4!\left(15-4\right)!}}=0.0256[/tex]

Hence The probability that all of the offices are filled by members of the debate​ team is 0.0512 and the probability that none of the offices are filled by members of the debate​ team is 0.0256

Answer:

8c to the pwr of 2 d to the pwr of 3

Step-by-step explanation:

i think

Answer: To find the SUM of this expression, you end up with 8c^2*d^3. (Vote me brainliest please)

Answer:

-7

Step-by-step explanation:

2x+3=x-4

Let's start by subtracting 3 from both sides

2x=x-7

Now, subtract x from both sides

x=-7

Let's plug it in to make sure!

2(-7) +3= (-7)-4

-11=-11

Answer:

x= -7

Step-by-step explanation:

You subtract both sides by x meaning the x on the right side will turn to zero and then you subtract both sides by 3