Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

The fast of the radius of balloon increasing is 480 cm³ / sec.

Given data :

V = [tex]\frac{4}{3}[/tex] π r³

we know [tex]\frac{dr}{dt}[/tex] = 30 cm/ sec

we want [tex]\frac{dV}{dt}[/tex] when r = 2cm

Differentiate V = [tex]\frac{4}{3}[/tex] π r³ implicitly with respect to t

[tex]\frac{dV}{dt}[/tex] (V) = [tex]\frac{dr}{dt}[/tex] ( [tex]\frac{4}{3}[/tex] π r³ )

[tex]\frac{dV}{dt}[/tex] = [tex]\frac{4}{3}[/tex] π x 3r² [tex]\frac{dr}{dt}[/tex] = 4 π r² [tex]\frac{dr}{dt}[/tex]

Plug in what you know and solve for what you don't know.

[tex]\frac{dV}{dt}[/tex] = 4π ( 2 )² ( 30 / sec ) =

= 120 x 4 .π cm³ / sec

= 480 cm³ / sec

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Answer:

18

Step-by-step explanation:

The ~ indicates that ∠ABC is similar to ∠QRS. In other words, their proportions are the same, even if their size is different.

So AB has the same proportions as QR. 4 can be multiplied by 2.25 to get to 9. So multiply 8 by 2.25 to get n.

8 * 2.25 = 18 so n = 18

Answer: 10.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

c

Answer:

i think that the answer is 149

Answer:

2

Step-by-step explanation:

Answer:

the answer is one over eight

the formula says required outcome divided by sample space

the sample space here is it because we have three coins and the Three coins have two faces each so it becomes 2 x 2 * 2 that is 8 and that is the total sample space we are supposed to get the probability of getting 3 tails and for each coin you have 1/2 x 1/2 x 1/2 and that is 1/8 as your final answer and do probability of getting three tails

Answer:

If a fair coin is flipped 3 times, the probability of getting exactly 3 tails is 1/8

Step-by-step explanation:

1/2 * 1/2 * 1/2 =1/8

Answer:

I Believe The Answer Would Be 35

Step-by-step explanation:

You See If You Split The Rectangle Into Three Rectangles You Can Split Them Up And Multiply The Length And Width

Answer:

35in^2

Step-by-step explanation:

You essentially have 3 rectangles.

Starting from the top

2*5 = 10

Middle

This is the only tricky one. You have the top with a total lenght of 5 and the middle rectangle is recessed from the 5 inch 2 inch. that leaves you 3 inches plus the 3 off to the side. in total 5 inches

3*5 = 15

Bottom

2*5 = 10

Add them all togehter

10+15+10

Answer:

∡B = 60°

Step-by-step explanation:

find BC using Pythagorean Theorem:

5² + BC² = 10²

25 + BC² = 100

BC² = 75

BC = [tex]\sqrt{75}[/tex]

BC = [tex]\sqrt{25}[/tex][tex]\sqrt{3}[/tex] which is 5[tex]\sqrt{3}[/tex]

this indicates that ∡B must be 60° because the ratio of sides in a 30-60-90 triangle are 1 : [tex]\sqrt{3}[/tex] : 2

Answer:

x=89

Step-by-step explanation:

Well all of a quadrilaterals interior angles add up to 360 degrees so you would add together 69+118+84 which equals 271, and then you'd subtract that from 360 which is 89. Hope this helps. :)

Answer:

"$ 2,880" is the right answer.

Step-by-step explanation:

The given values are:

Annual deposit,

PV = $1,800

Interest rate,

r = 2%

or,

  = 0.02

As we know,

⇒  [tex]FV=PV\times (1+r)n[/tex]

On substituting the values, we get

⇒         [tex]=1,800\times (1 + 0.02) 4 + 7 + 13[/tex]

⇒         [tex]=1,800\times (1.02)24[/tex]

⇒         [tex]=1,800\times 1.6[/tex]

⇒         [tex]= 2,880[/tex] ($)

Given:

The graph of a curve.

To find:

The domain and range for the given graph in interval notation.

Solution:

Domain: It is the set of input values.

Range: It is the set of output values.

Closed circle: It means that point is included in the solution set.

Open circle: It means that point is not included in the solution set.

(a) From the given graph it is clear that the function is defined between x=-5 to x=4. There is a closed circle at x=-5 and an open circle x=4, it means x=-5 is included and x=4 is not included in the domain.

[tex]Domain=-5\leq x<4[/tex]

[tex]Domain=[-5,4)[/tex]

(b) From the given graph it is clear that the values of the function lie between y=-3 to y=3. There is a closed circle at y=-3 and an open circle y=3, it means y=-3 is included and y=3 is not included in the range.

[tex]Range=-3\leq y<3[/tex]

[tex]Range=[-3,3)[/tex]

Therefore (a) [tex]Domain=[-5,4)[/tex] and (b) [tex]Range=[-3,3)[/tex].

Answer:

Peter must pay $10.50

Step-by-step explanation:

Since he only used the service for 1 month, he pays for that much time.

Answer:

10.50 x 5 would be the expression.

  so the answer is  $-52.5

Step-by-step explanation:

Answer:

C

Rewrite the equation until you end up with 4 being your slope =m

Answer:

a = 3 or -3

Step-by-step explanation:

a^2 -8 = 1

a^2 = 1 + 8

a^2 = 9

a = -  [tex]\sqrt{9}[/tex] or [tex]\sqrt{9}[/tex]

a = 3 or -3

Answer: a = 3, -3

Step-by-step explanation:

      Since we want to find what values of a, or x when substituted into the function, equal 1, we will set the function equal to 1 and solve for x.

     Given:

f(x) = x² - 8

     Set equal to 1:

1 = x² - 8

     Subtract 1 from both sides of the equation:

x² - 9 = 0

     Difference of squares factoring:

(x - 3)(x + 3) = 0

     Answers:

x = 3, -3

     So,

a = 3, -3

The likelihood event:

Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

The correct option is A.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Given:

Three softball players discussed their batting averages after a game.

Probability:

Player 1 = six tenths = 6/10

Player 2 = five ninths = 5/9

Player 3 = four sevenths = 4/7

To find better batting averages:

LCM of 10, 9 and 7.

10 = 2 x 5. 9 = 3 x 3, 7 = 7

So, the LCM (10, 9, 7) = 630

Now we have the number of chances are equal for each of the three players.

So, the P(Player 1) = 6/10 = 378/630

P(Player 2)= 5/9 = 350/630

P(Player 3)= 4/7 = 360/630

The Player 1 has better batting average than Player 2 and Player 3.

Therefore, Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

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Answer:

x intercepts; (5/3 ,0 )

y-intercepts; (0 , 5/2)

Step-by-step explanation:

Therefore , As a result, y=Sin will be the equation of the sinusoid that answers the supplied equation problem (2x).

An equation is a representation of two equal variables in mathematics, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra lessons address the fundamental concepts of mathematics.

Here,

Given: Maximum: 210

Minimum: 10

Time : 90

In order to create a sinusoid equation:

When x=0, sin(2*0)=sin(0)=0.

If x = 4 then sin(4 / 2) = 1.

Sin(π) = 0 if x =π/2 and

Consequently, the sinusoid's equation will be y=Sin (2x)

Therefore , As a result, y=Sin will be the equation of the sinusoid that answers the supplied equation problem (2x).

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Step-by-step explanation:

to find the equation of any line we have to first find the slope. the slope formula is:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

our slope here would be 8/13

now we input the points in the equation

y = mx + b

then we find b to be -3(7/13)

so the final equation would be:

[tex]y = \frac{8x}{13} - 3( \frac{7}{13} )[/tex]

Answer:

[tex] \displaystyle A) 5\log( {x}^{} ) + 2 \log( {y}^{} ) [/tex]

Step-by-step explanation:

we would like to expand the following logarithmic expression:

[tex] \displaystyle \log( {x}^{5} {y}^{2} ) [/tex]

remember the multiplication logarithmic indentity given by:

[tex] \displaystyle \rm \log( \alpha \times \beta ) \iff \log( \alpha ) + \log( \beta ) [/tex]

so our given expression should be

[tex] \displaystyle \log( {x}^{5} ) + \log( {y}^{2} ) [/tex]

by exponent logarithmic property we acquire:

[tex] \displaystyle 5\log( {x}^{} ) + 2 \log( {y}^{} ) [/tex]

hence, our answer is A

Answer:

1st option

Step-by-step explanation:

From the graph the zeros are x = - 3 and x = 1 , then the corresponding factors are

(x + 3) and (x - 1) , so

y = a(x + 3)(x - 1) ← a is a multiplier

To find a substitute a point on the graph into the equation

Using (0, - 1.5 ) , then

- 1.5 = a(3)(- 1) = - 3a ( divide both sides by - 3 )

0.5 = a

Then

f(x) = 0.5(x + 3)(x - 1)

Answer:

Option 2

Step-by-step explanation:

Hello!

We can solve the equation for n by isolating the variable.

The answer would be the second option: "n = the quantity 3 times c minus 9 all over negative p."

0.27 is the experimental probability of selecting a green marble.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that Michael has a bag of marbles.

The frequency of selecting each color is recorded  

Outcome Frequency

Green 4

Black 6

Orange 5

The total number of marbles are 4+6+5=15 marbles.

We need to find the experimental probability of selecting a green marble.

We need to select green marbles (4) from total marbles (15).

Probability=4/15=0.266=0.27

Hence, 0.27 is the experimental probability of selecting a green marble.

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Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.

According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].

A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:

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Answer:

80

Step-by-step explanation:

Because it is more than 45 and the only one that is more that 45 is 80

Answer:

unicorn = 6

zebra = 18

horse = 4

Step-by-step explanation:

unicorn = u

zebra = z

horse = h

translate the picture to a system of equations

2u + z = 30

2h + u = 14

3z + 2h = 62

2h * 2u * 2z = ?

then solve the system of equations

Answer:

the answer should be 126

Step-by-step explanation:

when you are looking for the area you multiple all of them so i should be right

Answer:

76.5

Step-by-step explanation:

6+3=9

1/2b*h

1/2*9*3=13.5

7*9=63

13.5+63=76.5

=76.5

Answer:

Positive

Step-by-step explanation: