Alice, Bob, and Christy are setting up aquariums. The design of each aquarium is below. Alice has enough pebbles to cover 9 square feet. Does she have enough to put a layer of pebbles on the bottom of Aquarium A?

Answer:

○ [tex]\displaystyle (x - 4)^2 + (y + 2)^2 = 25[/tex]

Explanation:

Accourding to one of the circle equations, [tex]\displaystyle (x - h)^2 + (y - k)^2 = r^2,[/tex]the centre of the circle is represented by [tex]\displaystyle (h, k).[/tex]Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared. Now, in case you did not know how to define the radius, you can choose between either method:

Pythagorean Theorem

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 4^2 + 3^2 = r^2 \hookrightarrow 16 + 9 = r^2 \hookrightarrow \sqrt{25} = \sqrt{r^2} \\ \\ \boxed{5 = r}[/tex]

Sinse we are dealing with length, we only desire the NON-NEGATIVE root.

Distanse Equation

[tex] \displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = d \\ \\ \sqrt{[-7 + 4]^2 + [-2 - 2]^2} = r \hookrightarrow \sqrt{[-3]^2 + [-4]^2} = r \hookrightarrow \sqrt{9 + 16} = r; \sqrt{25} = r \\ \\ \boxed{5 = r}[/tex]

Sinse we are dealing with distanse, we only desire the NON-NEGATIVE root.

I am joyous to assist you at any time.

Answer:

13 / 8 in

Step-by-step explanation:

Longest ( 1 7/8)  - shortest ( 2/8) = 13/8 in

Answer: Below

Step-by-step explanation:

Angles 1, 3, 5, 7 are 120 degrees.

Angles 4, 2, 8, 6 are 60 degrees.

angles 10, 12, 13, 15 are 70 degrees.
Angles 9, 11, 16, 14, are 110 degrees.
angle 17 is 50 degrees.

Answer:

there are 42

Step-by-step explanation:

because 12 + 30 = 42 hope this helps =)

Answer: 6

Step-by-step explanation:

I believe it is 6

Answer:

  $18.06

Step-by-step explanation:

The price the pawn shop charged for the DVD player was 40% more than what it paid, so was ...

  $12.00 + $12.00 × 0.40 = $12.00×(1 +0.40) = $16.80

__

The tax on the purchase is this price multiplied by the tax rate:

  tax = 0.075×$16.80 = $1.26

__

Then the total including tax is ...

  $16.80 +1.26 = $18.06 . . . . . total cost of the DVD player

The measure of AB and EF for the similar triangle ABC and DEF are 4 and 12 respectively.

Similar triangles are triangles that have the same shape, but their sizes may vary.

In similar triangles, corresponding sides are always in the same ratio. The angles are congruent.

ΔABC is similar to ΔDEF. Therefore, the sides will form a ratio.

AC / DF = BC / EF = AB/DE

AC = 10

DF = 20

DE = 8

BC = 6

Hence,

10 / 20 = AB / 8

cross multiply

20AB = 80

AB = 80 / 20

AB = 4

Hence,

10 / 20 = 6 / EF

10EF = 120

EF = 120 / 10

EF = 12

learn more on similar triangle here: https://brainly.com/question/11943039

The fraction of total interest owed after the fifth month of a 12-month loan is 64.1%

From the question, we have the following parameters

After the fifth month, the equation of the numerator is:

Numerator = (1+11)+(1+10)+(1+9)+(1+8)+(1+7)

Numerator = 50

The equation of the denominator is:

Denominator = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Denominator = 78

The fraction of total interest is then calculated using:

Fraction = Numerator/Denominator

This gives

Fraction = 50/78

Express as percentage

Fraction = 64.1%

Hence, the fraction of total interest owed after the fifth month of a 12-month loan is 64.1%

Read more about loan and interest at:

https://brainly.com/question/15301789

Simplify the expression.

149x

hope this is what your looking for

Answer: 2/5

1/5 you will keep

you will CHANGE the division sign to multiplication, never change when it is multiplication.

1/5 X 1/2

You will FLIP  2/1 into 1/2. Now multiply numerator x numerator, denominator x denominator.

1/5 X 1/2= 2/5

Now you have gotten your answer but for the future, the numerator should never be greater than the denominator, if it is, divide.

Answer:

0

Step-by-step explanation:

xy means x×y

Anything multiplied by 0 is 0.

So 2×0 = 0

Hope this helped and brainliest please.

Answer:

[tex]\tan \theta ~~ \text{and}~~ \tan( \pi - \theta)[/tex]

Step-by-step explanation:

[tex]\textbf{A)}\\\\-\tan \dfrac{3 \pi}4 = - \tan\left(2 \times \dfrac{\pi}2 - \dfrac{\pi}4 \right) = - \left(- \tan \dfrac{ \pi}4 \right) = \tan \dfrac{\pi}4\\\\\textbf{These pairs are equal.}\\\\\\ \textbf{B)}\\\\\tan \left( \dfrac{5 \pi}4 \right) = \tan \left( 2 \times \dfrac{\pi}2 + \dfrac{\pi}4\right) = \tan \dfrac{\pi}4\\\\\textbf{These pairs are equal.}\\\\ \textbf{C)}\\\\\tan \dfrac{\pi}2= - \tan 90^{\circ} = \infty\\\\\\\textbf{These pairs are equal.}\\\\\\ \textbf{D)}\\\\[/tex]

[tex]\tan ( \pi - \theta ) = - \tan \theta \neq \tan \theta\\\\\textbf{These pairs are not equal.}[/tex]

Answer:

Step-by-step explanation:

The cost of hiring a car can be worked out using this rule. Cost = £80 + 50p per mile. 50p. = to.s per mile per mile. Carlos hires a car and drives 90 miles.

Answer:

b

Step-by-step explanation:

beacaause I know

Answer:

[tex]\sf \bold{\begin{pmatrix}7&-12&6\\ 3&-2&7\\ -12&-1&2\\ 7&3&-2\end{pmatrix}}[/tex]

Explanation:

[tex]\Longrightarrow \ \sf Give n \ A = \sf \bold{\begin{pmatrix}2&-9&8\\ 4&2&-1\\ -5&-3&7\\ 4&8&-4\end{pmatrix}}[/tex]

[tex]\Longrightarrow \ \sf Given \ B = \bold{\begin{pmatrix}-5&3&2\\ 1&4&-8\\ 7&-2&5\\ -3&5&-2\end{pmatrix}}[/tex]

Solve:

[tex]\sf A - B = \begin{pmatrix}2&-9&8\\ \:4&2&-1\\ \:-5&-3&7\\ \:4&8&-4\end{pmatrix}- \begin{pmatrix}-5&3&2\\ 1&4&-8\\ 7&-2&5\\ -3&5&-2\end{pmatrix}[/tex]

subtract the elements in matching positions

[tex]\sf A - B = \begin{pmatrix}2-\left(-5\right)&\left(-9\right)-3&8-2\\ 4-1&2-4&\left(-1\right)-\left(-8\right)\\ \left(-5\right)-7&\left(-3\right)-\left(-2\right)&7-5\\ 4-\left(-3\right)&8-5&\left(-4\right)-\left(-2\right)\end{pmatrix}[/tex]

Final Outcome

[tex]\sf \bold{\begin{pmatrix}7&-12&6\\ 3&-2&7\\ -12&-1&2\\ 7&3&-2\end{pmatrix}}[/tex]

Answer:

Area of rectangle = 65/8 yd²

Step-by-step explanation:

The area of the rectangle is the length multiplied by the width. In this case, we are given the length 3 1/4 yd and the width 2 1/2 yd wide. Therefore,

        ⇒ Area of rectangle = (L × B) = (3 1/4 × 2 1/2) yd²

It is suggested to convert the terms in the expression (3 1/4 × 2 1/2) to improper fraction. Therefore,

        ⇒ Area of rectangle = [(3 × 4) + 1]/4 × [(2 × 2) + 1]/2 yd²

        ⇒ Area of rectangle = [(12) + 1]/4 × [(4) + 1]/2 yd²

        ⇒ Area of rectangle = [13]/4 × [5]/2 yd²

        ⇒ Area of rectangle = 13/4 × 5/2 yd²

Simplify the expression on the right hand side to determine the area.

        ⇒ Area of rectangle = 65/8 yd²

Thus, the area of the rectangle is 65/8 yd².

Answer:

12 is the lcd

Step-by-step explanation:

because 12x1=12

and 2x6=12

Answer:

12

Step-by-step explanation:

Both 12 and 2 have the factor of 2 in common. (2)(12)/12 gives us the least common LCM (least common multiple) of 12.

Answer:

No

Step-by-step explanation:

So, you can use the distributive property.

1/2(6x)=3x

1/2(-2)=-1

It is 3x-1, not 3-x

Answer:4/9 We know, Probability = Favorable Outcome / Total Outcome

Here, Favorable Outcome (Number of Green Marbles) = 8

Total Outcome = 6 + 4 + 8 = 18

P = 8 /18 = 4/9

In short, Your Answer would be 4/9 or 0.44

Hope this helps!

Answer:

18.17 × pi in²

Step-by-step explanation:

there are many seemingly different formulas out there for this, but they are actually all the same and differ only by what values of the cone we know at the beginning (and the custodian values are converted into the values we need for the calculation).

do we know the base area and the height of the cone, or the radius and the height, or the base area and the slant height (the length of the "mantle" straight from the bottom to the top), ... ?

well, here we know the diameter (this means it is 2 times the radius) and the slant height.

this is one of the easiest exercises.

the formula for this case is

LA = pi × radius × slant height = pi × (4.6 / 2) × 7.9 =

= pi × 2.3 × 7.9 = 18.17 × pi in²

[tex]5(4m+2)\\\\=20m+10[/tex]

Answer:

f(x)

Step-by-step explanation:

Because f(x) = 4x + 5

Answer:

f(x)

Step-by-step explanation:

g(x) intercept Is shown to be 2

f(x) if u sub 0 into x to find the y intercept gives you 5

h(x) I you sub 0 into the equation in place of x to find the y intercept it gives you -1.84

and if you look at all ghe y intersect values f(x) is the greatest

Answer:

D. Point D

Step-by-step explanation:

4.82 is close to 5 so D is right A and B are not even close. C is a little to close to 4.5 to be 4.82. But D looks like it could be 4.82 to though so D is right.

Answer:

V = 8.5 cubic units

Step-by-step explanation:

[tex]2\frac{1}{8} =\frac{16+1}{8} =\frac{17}{8}[/tex]

[tex]V=4(\frac{17}{8} )=\frac{68}{8} =\frac{17}{2}= 8.5u^{3}[/tex]

Hope this helps

Answer:

the population will be 1,540,000 in 7 yrs

Answer: 377041.34

Step-by-step explanation: if it is growing 8 percent then you will add 8 percent to 100 which will equal 108 percent

Plug that into a calculator with the starting number so it wil look like 108% 220,000 and if you do that seven times you will get the answer.