Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 8 cm/min. How fast is the area of the pool increasing when the radius is 13 cm?

Answer:

8

Step-by-step explanation:

To solve this, you can add 2/5 b to both sides of the equation. You now have 3 + 5/5 (or 1) b = 11. => 3 + b = 11 => Now, subtract 3 from both sides, and you have b = 11 - 3, and then b = 8.

Step-by-step explanation:

3 + 2/5 b =11 - 2/5 b (this is the given question is it?)

2/5 b + 2/5 b= 11 - 3 (like terms together, you transpose -2/5b to the other side as shown.)

2b+2b = 8 ( at that stage you would find t

5 hat 5 is the common value to go into 5 itself, as shown.

4b = 8 ( you just add 2b + 2b to have 4b)

5

4b = 8 ( at that point you cross multiply

5 1 as shown)

4b = 8 × 5 ( simple math as shown)

4b = 40 ( you multiply 8 × 5 to obtain 40)

b =10 you can prove that. Thank you.

Answer:

x=5.333

y=3

Step-by-step explanation:

given, y=5-2............(1)

1-3x+y=-12...............(2)

y=5-2=3

put y=3 in equ (2)

1-3x+3=-12

1+3+12=3x

3x=16

x=[tex]\frac{16}{3}[/tex]

x=5.333

hence, x=5.333

           y=3               answer

Answer:

Time taken by train in onward journey = 12 hours.

Step-by-step explanation:

Given:

Speed of train making a trip to a repair = 25 mph

Speed of train on return trip = 20 mph

Time taken for return trip = 15 hours

To find the time taken on the on wards trip.

Solution:

The distance traveled by the train on the trip and return trip is the same as the y are of same trips in opposite directions.

Distance can be calculated by using the data for the return trip.

Distance= [tex]Speed\times Time[/tex]

Distance= [tex]20\ mph\times 15\ h=300\ miles[/tex]

Speed of train for on ward trip = 25 mph

Time taken = [tex]\frac{Distance}{Speed}[/tex]

Time taken = [tex]\frac{300\ miles}{25\ mph}= 12\ h[/tex]

Thus, time taken by train in onward journey = 12 hours.

The equation of the line which is perpendicular to the line 4x + 3y = 9 and passes through the point (-2,3) is y = 3/4x + 4.5.

The original equation is 4x + 3y = 9. To start off, rewrite this equation in slope-intercept form (y = mx + b) to help find the slope. After isolating y, the equation turns into y = -4/3x + 3. So, the slope of the original line is -4/3.

Perpendicular lines have slopes which are negative reciprocals of each other, thus the slope of the line perpendicular to the given line is the negative reciprocal of -4/3, which is 3/4 (m = 3/4 for the second line)

We are also given that the line we are looking for passes through the point (-2,3). Use the point-slope form of a line, given by y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point. Substituting in the values, you get:

y - 3 = 3/4(x - -2).

Simplifying the equation, we find that the line perpendicular to 4x + 3y = 9 and passing through (-2, 3) is y = 3/4x + 4.5

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Answer:

The required image line is 3x + y = 8

Step-by-step explanation:

We have to find two points on the given straight line then find their reflection points over the x-axis and then finally the straight line passing through those two image points will give the required straight line.

Now, the given straight line is y = 3x - 8.

Now, two any points on this straight line are say (1,-5) and (2,-2).

So, the image of (1,-5) point reflecting over the x-axis will be (1,5) and the image of the point (2,-2) reflecting over the x-axis will be (2,2).

Therefore, the straight line passing through those two image points will have equation  

[tex]\frac{y - 5}{5 - 2} = \frac{x - 1}{1 - 2}[/tex]

⇒ y - 5 = 3(1 - x)

⇒ y - 5 = 3 - 3x

⇒ 3x + y = 8

Hence, the required image line is 3x + y = 8 (Answer)

In the problem, one paper clip equals three matches, one pencil is greater than one paper clip, and twenty-two paper clips are greater than sixty-seven matches.

In this scenario, one paper clip is equivalent, or equal to, three matches. This is ascertained from the first sentence which states that each paper clip can be traded for three matches. Similarly, one pencil is greater than a single paper clip as it can be traded for six paper clips. This conclusion is drawn from the second sentence. Lastly, the value of twenty-two paper clips is greater than sixty-seven matches since one paper clip is equal to three matches, hence twenty-two paper clips would be worth sixty-six matches, but since we have sixty-seven matches, twenty-two paper clips are worth more.

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Answer:

D.  120°

Step-by-step explanation:

Interior angles of a rhombus always add up to 360 degrees. Thus we can set up an equation:

g+g+2g+2g=360

Now let's combine all the like terms (g's).

6g=360

Now we divide both sides by six to isolate g.

g=60

We can now substitute g into angle B, to find its value.  

2g

2(60)

120

Thus, the measure of angle B is 120, or option D.

You paid 22% gratuity at the restaurant.

Step-by-step explanation:

Given,

Amount of bill = $59

Amount paid = $72

Gratuity = Amount paid - Amount of bill

Gratuity = 72 - 59 = $13

Gratuity percentage = [tex]\frac{Gratuity}{Amount\ of\ bill}*100[/tex]

Gratuity percentage = [tex]\frac{13}{59}*100=\frac{1300}{59}[/tex]

Gratuity percentage = 22.03%

Rounding off to whole percent

Gratuity percentage = 22%

You paid 22% gratuity at the restaurant.

Keywords: percentage, subtraction

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The percentage did you pay is 22.03%

Given that,

Based on the above information, the calculation is as follows:

[tex]= (\$72 - \$59) \div (\$59)\\\\= \$13 \div \$59[/tex]

= 22.03%

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Answer:

x = - 4, x = 6

Step-by-step explanation:

Given

f(x) = x² - 2x + 3 and f(x) = 27, then equating the 2 gives

x² - 2x + 3 = 27 ( subtract 27 from both sides )

x² - 2x - 24 = 0 ← in standard form

Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 2)

The factors are - 6 and + 4, since

- 6 × 4 = - 24 and - 6 + 4 = - 2, thus

(x - 6)(x + 4) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 4 = 0 ⇒ x = - 4

f(x)= 27

x^2 -2x+3=27

×^-2x+3-27=0

x^2x-24=0

(x-6)(x-4)=0

x-6=0 or ×-4=0

×=6or ×=4

Answer:

1

Step-by-step explanation:

The product of a nonzero number and its reciprocal is 1

Answer:

Step-by-step explanation:

The product will always equal 1.  This is one of the methods we use to solve equations.  If our nonzero real number is 3, for example, the reciprocal of 3 is 1/3 and

3 × [tex]\frac{1}{3}[/tex] can be written as

[tex]\frac{3}{1}[/tex] × [tex]\frac{1}{3}[/tex] which is 3/3 which = 1.

Answer:

[tex]z>6[/tex]

7z+5>47

Remove the 5:

[tex]7z+5-5>47-5\\7z>42[/tex]

Divide by 7 to get z by itself:

[tex]\frac{7z}{7} >\frac{42}{7} \\z>6[/tex]

Answer:

Step-by-step explanation:

Let x represent the number of days , then

(1) The exponential function to represent the spread of Ben's social media spread implies :

f(x) = 2([tex]3^{x}[/tex])

(2) The exponential function that represent carter;s social media spread implies

f(x) = 10([tex]2^{3}[/tex]

(3) the graph of the three functions is attached below

color red graph represents  Ben's social media spread , the graph with color blue represents Carter;s social media spread and the graph with green color represents Amber's social media spread

(4) on the 3rd day

Amber will receive 192 shares .

The equation for the spread of his shares is

f(x) = 3([tex]4^{x}[/tex]

where x is the number of days , so we have

3([tex]4^{3}[/tex])

= 3 ( 64)

= 192 shares

Ben's shares on the 3rd day will be

f(x) = 2([tex]3^{x}[/tex] )

= 2([tex]3^{3}[/tex])

= 2 ( 27)

= 54

Therefore , Ben will have 54 shares on the third day

Carter's share on the third day

f(x) = 10 ( [tex]2^{x}[/tex] )

= 10 ([tex]2^{3}[/tex] )

= 10 (8)

= 80

Therefore , Carter will receive 80 shares on the 3rd day

Answer:

-37

Step-by-step explanation:

-4(5)-17=-20-17=-37

Answer: r = 3

1st Step: Plug x in for 5

4(5)-17

Second Step: Multiply 4 and 5

20-17

Third Step: 20-17

20-17=3

So, the answer is 3 when r(5)

Hope this helps!

Answer: x + 3y = 2

Step-by-step explanation:

Given:

y - 3 = 3 ( x + 1 )

y - 3 = 3x + 3

y = 3x + 3 + 3

y = 3x +6

comparing the equation with the formula for finding equation of line in slope - intercept form

y = mx + c , where m is the slope and c  is the y - intercept. This means that the slope of the line above is 3

Two lines are said to be perpendicular if the product of their slope = -1, that is , if [tex]m_{1}[/tex] is the slope of the first line and [tex]m_{2}[/tex] is the slope of the second line , if they are perpendicular , then [tex]m_{1}[/tex][tex]m_{2}[/tex] = -1

Considering this rule , this means that the slope of the line we are to find = [tex]\frac{-1}{3}[/tex]

Using the formula : y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) to find the equation of the line , we have

y - (-1 ) = [tex]\frac{-1}{3}[/tex] ( x - 5 )

y + 1 = [tex]\frac{-1}{3}[/tex] ( x - 5 )

multiplying through by 3 , we have

3 ( y + 1 ) = -1 ( x - 5)

Expanding , we have

3y + 3 = -x + 5

writing the equation in standard form , we have

3y + x = 5 - 3

Therefore :

x + 3y = 2

The total distance covered by the bicycle is calculated using the circumference of the wheel and the number of revolutions made. With a wheel diameter of 70 cm, the total distance comes to approximately 55.0 meters after 25 revolutions.

The question involves calculating the distance covered by a bicycle wheel making a certain number of revolutions. Given that the diameter of the wheel is 70 cm, we can find the circumference, which is the distance the wheel covers per revolution. The circumference is equal to \\(\pi\cdot d\\), where \\(d\\) is the diameter. Substituting the given diameter:

Since the wheel makes 25 revolutions, the total distance covered (\\em{D}}) can be found by multiplying the circumference by the number of revolutions:

Thus, the bicycle covers a distance of \\(25 \times \pi \times 70 \\text{cm}\\), or \\(25 \times \pi \times 0.7 \\text{m}\\), since 100 cm equals 1 meter.

To find the exact value, you would calculate:

c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat

Given that a boat rental charges $7.50 for the first hour and $2 for each additional hour.

To find: Rule that gives the cost for x hours of renting a boat

Let "x" be the total hours of renting a boat

[tex]c = f + (v \times x - 1)[/tex]

"c" is the total cost for the boat rent

"f" is the fixed cost for boat rent for first hour

"v"  is the cost for each additional hours of rent

"x" is the total hours of renting a boat

In the expression we have used "x - 1" to represent the additional hour of boat rent after first hour

Here f = $ 7.50

v = $ 2

[tex]c = 7.50 + 2 \times x - 1\\\\c = 7.50 + 2(x - 1)[/tex]

Thus c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat

The cost for renting a boat for x hours can be found using the formula y = 7.50 + 2(x - 1), where y is the total cost and x is the number of hours.

Based on the given information, the boat rental company charges $7.50 for the first hour and then an additional $2 for each subsequent hour. Therefore, if x is the number of hours you rent the boat, the total cost would be calculated using the formula y = 7.50 + 2(x - 1). Here, y represents the total cost of renting the boat for x hours. The formula subtracts the one-hour charge included in the initial payment.

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Answer:

3 is the coefficient

Step-by-step explanation:

please find the attached file for more details please

- the coefficient is always the number before a variable.

m + 3n + 5

coefficient: 3

Answer:

2

Step-by-step explanation:

Find the value of c where p = 0.

0 = c² + 2c − 5

6 = c² + 2c + 1

6 = (c + 1)²

±√6 = c + 1

c = -1 ± √6

c must be positive, so c = -1 + √6 ≈ 1.45.  So John must sell at least 2 candy bars to make a profit.

We can also show this using trial and error.

If c = 0, then p = -5

If c = 1, then p = -2

If c = 2, then p = 3

A) k=2 is the right answer

Step-by-step explanation:

The downward funtion transformation is defined as:

f(x) => f(x)-b where b is an integer.

Given

[tex]f(x) = (0.5)^x[/tex]

And

[tex]g(x) = (0.5)^x-k[/tex]

It is also given that g(x)  is obtained by shifting function f 2 units downward

We will apply the transformation to function f to find the value of k.

So,

Shifting f(x) 2 units downward

we will get

[tex]g(x) = (0.5)^x-2[/tex]

comparing with [tex]g(x) = (0.5)^x-k[/tex] we get that

k = 2

So,

A) k=2 is the right answer

Keywords: Functions, shifting

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Answer:

ok k does = 2 i got it right on the test

Step-by-step explanation:

:3

Answer:1st is 5 2nd is 15 last is 30

Step-by-step explanation:

1st = 5

2nd = 3 x 5 = 15

3rd = 15 x 2 = 30

5 + 15 + 30 = 50

The three numbers in question are 5, 15, and 30. This has been achieved by setting up and solving algebraic equations based on the given conditions.

To solve this problem, we should set up equations based on the information given. Let's define:
First number = x
Second number = 3x (since it is three times the first number)
Third number = 2 * 3x = 6x (since it is twice the second number)

According to the problem, the sum of these three numbers is 50. Therefore, we can write the equation as:
x + 3x + 6x = 50

Solve for x:
10x = 50
x = 50 / 10 = 5

So, the three numbers are:
First number = x = 5
Second number = 3x = 3 * 5 = 15
Third number = 6x = 6 * 5 = 30

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well,I am not sure about the answer.

For 5 games, the cost will be equal for each option.

Step-by-step explanation:

Given,

Lane rental of offer A = $20

Per game charges = $3

Let,

x be the number of games.

A(x) = 3x + 20

Lane rental is $35 for maximum 10 games.

B(x) = 35

For the cost to be same;

A(x) = B(x)

[tex]3x+20=35\\3x=35-20\\3x=15[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{15}{3}\\x=5[/tex]

For 5 games, the cost will be equal for each option.

Keywords: function, division

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Answer:

The Amount invested at 7% interest is $12,855

The Amount invested at 6% interest = $1,102  

Step-by-step explanation:

Given as :

The Total money invested = $13,957

Let The money invested at 7% = [tex]p_1[/tex]  = $A

And The money invested at 6% = [tex]p_2[/tex] = $13957 - $A

Let The interest earn at 7% = [tex]I_1[/tex]

And The interest earn at 6% = [tex]I_2[/tex]

[tex]I_1[/tex] -  [tex]I_2[/tex] = $833.73

Let The time period = 1 year

Now, From Simple Interest method

Simple Interest = [tex]\dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}[/tex]

Or,  [tex]I_1[/tex] = [tex]\dfrac{\textrm p_1\times \textrm 7\times \textrm 1}{100}[/tex]

Or,  [tex]I_1[/tex] = [tex]\dfrac{\textrm A\times \textrm 7\times \textrm 1}{100}[/tex]

And

[tex]I_2[/tex] = [tex]\dfrac{\textrm p_2\times \textrm 6\times \textrm 1}{100}[/tex]

Or,  [tex]I_2[/tex] = [tex]\dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100}[/tex]

∵  [tex]I_1[/tex] -  [tex]I_2[/tex] = $833.73

So, [tex]\dfrac{\textrm A\times \textrm 7\times \textrm 1}{100}[/tex] -  [tex]\dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100}[/tex] = $833.73

Or, 7 A - 6 (13,957 - A) = $833.73 × 100

Or, 7 A - $83,742 + 6 A = $83373

Or, 13 A = $83373 + $83742

Or, 13 A = $167,115

∴ A = [tex]\dfrac{167115}{13}[/tex]

i.e A = $12,855

So, The Amount invested at 7% interest = A = $12,855

And The Amount invested at 6% interest = ($13,957 - A) = $13,957 - $12,855

I.e The Amount invested at 6% interest = $1,102

Hence,The Amount invested at 7% interest is $12,855

And The Amount invested at 6% interest = $1,102   . Answer

Final answer:

The total amount invested and the difference in interest earned. Then, using algebraic techniques such as substitution or elimination, we solve for the amounts invested at 7% and at 6%.

Explanation:

To solve the problem of allocating investments at different interest rates, we can set up a system of equations. Let's designate x as the amount invested at 7% and y as the amount invested at 6%. Given the total investment is $13,957, our first equation will be:

x + y = 13,957 (1)

The interest from the amount invested at 7% exceeds the interest from the amount invested at 6% by $833.73. The second equation, reflecting the interest earned, will be:

0.07x - 0.06y = 833.73 (2)

y = 13,957 - x (3)

Now, substitute equation (3) into equation (2) and solve for x:

0.07x - 0.06(13,957 - x) = 833.73

Simplify and solve this equation to find the value of x.
Once we have the value for x, we can use equation (3) to find the corresponding value for y, giving us the amount invested at each interest rate.

Answer:

the smaller angle = 40

Step-by-step explanation:

Let x be the smaller angle.

Other angle = x + 10

x + x+ 10 = 90

2x  = 90 - 10

2x= 80

x = 80/2

x = 40

Answer:

40 degrees. A set of complementary angles make up 90 degrees. 90 - 40 is 50, which is 10 more than forty.

Answer:

33.38 km

Step-by-step explanation:

Kim drove from Math Town at (-2, 5) to Geometry Ville at (3, -1) to Algebra Springs at (-6, -5), and then back to Math town.

Now, the distance from (-2,5) point to (3,-1) point will be  

[tex]\sqrt{(- 2 - 3)^{2} + (5 - (-1))^{2}} = \sqrt{61}[/tex] km.

Again, the distance from point (3,-1) and (-6,-5) point will be  

[tex]\sqrt{(3 - (- 5))^{2} + (- 1 - (- 5))^{2}} = \sqrt{80}[/tex] km.

Therefore, the total distance Kim traveled will be = [tex]2(\sqrt{61} + \sqrt{80}) = 33.38[/tex] Km. (Answer)

The distance between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] on the coordinate plane is given by  

[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]  

Answer:

121/250

Step-by-step explanation:

Look at the picture

The decimal equivalent of 48.4% is 0.484 and the simplified fraction equivalent is 242/500.

To convert 48.4% to a decimal, you simply divide the percentage by 100. Therefore, 48.4% as a decimal would be 0.484.

To write 48.4% as a simplified fraction, we start with the fraction that percentage represents, which is 48.4 / 100. However, both these numbers are divisible by 2 which simplifies it to 242 / 500. That is the simplest form of the fraction represented by 48.4%.

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Answer:

∠2 = 78°

Step-by-step explanation:

Angle of a straight line is 180°.

So, that would mean ∠1 + ∠2 = 180°.

⇒ ∠2 = 180° - ∠1

⇒ ∠2 = 180° - 102°

⇒ ∠2 = 78°

Hence, the answer.

Answer:

[tex]m=-\frac{4}{3}[/tex]

Step-by-step explanation:

The formula to calculate the slope between two points is equal to

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

we have

the point (13,-4) and (1,12)

substitute the values in the formula

[tex]m=\frac{12+4}{1-13}[/tex]

[tex]m=\frac{16}{-12}[/tex]

[tex]m=-\frac{16}{12}[/tex]

simplify

[tex]m=-\frac{4}{3}[/tex]

Answer:

-4/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(12-(-4))/(1-13)

m=(12+4)/-12

m=16/-12

simplify

m=-4/3

Answer:

A) quantitative data.

Step-by-step explanation:

'quantitative' derives from 'quantity', almost synonymous with a measure or measurement.

Answer:

36

Step-by-step explanation:

Here is the correct and complete question: The units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than twice the original number. What is the original number?

Lets assume the original number be"10y+x". (x is unit digit and y is 10th digit)

∴ if number is reversed then resulting number be "10x+y".

As given: x= 2y

        and [tex]10x+y= 2(10y+x)-9[/tex]

Now, solving the equation to get original number.

[tex]10x+y= 2(10y+x)-9[/tex]

Distributing 2 to 10y and x, then opening the parenthesis.

⇒ [tex]10x+y= 20y+2x-9[/tex]

subtracting by (2x+y) on both side.

⇒ [tex]8x= 19y-9[/tex]

subtituting the value of "x", which is equal to 2y.

∴ [tex]8\times 2y= 19y-9[/tex]

⇒ [tex]16y=19y-9[/tex]

subtracting both side by (16y-9)

⇒ [tex]3y= 9[/tex]

cross multiplying

We get, [tex]y= 3[/tex]

y=3

∵x= 2y

[tex]x=2\times 3= 6[/tex]

∴ x= 6

Therefore, the original number will be 36 as x is the unit number and y as tenth number.