Find the area of AAOB
9√3 un
3√3 um
4.5/3 2

Let [tex]r_A[/tex] and [tex]r_B[/tex] be the respective radii of balloons A and B. If the fixed total volume is V, then

[tex]V = \dfrac{4\pi}3\left({r_A}^3 + {r_B}^3\right)[/tex]

and knowing [tex]r_A=10\,\rm cm[/tex] and [tex]r_B=9\,\rm cm[/tex] at the start, we have V = 6916π/3 cm³. Then when [tex]r_A=12\,\rm cm[/tex], the radius of the other sphere is [tex]r_B=1\,\rm cm[/tex].

Differentiating both sides with respect to time t gives a relation between the rates of change of the radii:

[tex]0 = 4\pi \left({r_A}^2 \dfrac{dr_A}{dt} + {r_B}^2 \dfrac{dr_B}{dt}\right) \implies \dfrac{dr_B}{dt} = -\left(\dfrac{r_A}{r_B}\right)^2 \dfrac{dr_A}{dt}[/tex]

We're given [tex]\frac{dr_A}{dt} = 0.1\frac{\rm cm}{\rm s}[/tex] the whole time. At the moment [tex]r_A=12\,\rm cm[/tex], the radius of balloon B is changing at a rate of

[tex]\dfrac{dr_B}{dt} = -\left(\dfrac{12\,\rm cm}{1\,\rm cm}\right)^2 \left(0.1\dfrac{\rm cm}{\rm s}\right) = \boxed{-14.4 \dfrac{\rm cm}{\rm s}}[/tex]

Answer:

209 cubic mm.

Step-by-step explanation:

Formula for volume of cone:

[tex]V=\frac{1}{3} \pi r^2 h[/tex]
Now let's plug in the values.
[tex]V=\frac{1}{3} \pi 5^2 8[/tex]
[tex]V=\frac{1}{3} \pi 200[/tex]
[tex]V=\frac{200}{3} \pi[/tex]
[tex]V=209.4395...[/tex]
Round to the nearest cubic mm and the volume is 209 cubic mm.

Answer:

209.333

Step-by-step explanation:

→ State the area for the volume for a cone

1/3 × π × r² × h

→ Substitute in the numbers

1/3 × 3.14 × 5² × 8

→ Evaluate

209.333

Answer: 7

Step-by-step explanation:

As [tex]\angle T \cong \angle T[/tex] by the reflexive property, we know that [tex]\triangle RST \sim \triangle UVT[/tex] by AA.

Since corresponding sides of similar triangles are proportional,

[tex]\frac{UT}{5}=\frac{13.2+5}{13}\\UT=(5)\left(\frac{13.2+5}{13} \right)=\boxed{7}[/tex]

========================================================

Explanation:

We'll need to find the LCM of 5, 8 and 10.

List out the prime factorization of the three numbers.

The unique prime factors are 2 and 5. The '1' isn't a prime number, so we can ignore it.

The '2' has an exponent of 3 as the largest exponent, meaning 2^3 is part of the LCM. The '5' has the largest exponent of 1. So 5^1 = 5 is also part of the LCM

LCM = 2^3*5 = 8*5 = 40

List out the multiples of 40

40, 80, 120, 160, ...

The number 80 is the only multiple between 61 and 107

Answer:

Explained below

Step-by-step explanation:

Area= area of these two triangles+ area of the rectangle+ area of the

=1/4(dh)+ +l.b +

Answer:

x=3

Step-by-step explanation:

I will assume this is a  number line

DE    +    EF     = DF

x+1    +    2x     =  10

3x  + 1 = 10

3x = 9

x = 3

Answer:

151.80800 kilograms

Step-by-step explanation:

The future value of the annuity on Jennifer’s 18th birthday is $655.02

The interest earned is $55.02.

An annuity is a fixed payment of money over a specified period of time.

The formula for determining the future value of the annuity is: yearly deposit x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Future value of the annuity: $100 x [{(1.035^6) - 1} / 0.035}  = $655.02

Interest earned =  future value - total amount deposited

655.02 - (100 x 6)= $55.02

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Answer:

3. 16.67

4. 25

Step-by-step explanation:

3. x+2÷8=14/6 (similar triangles have corresponding proportional sides)

x+2=(7×8)/3

x=56/3-6/3 (LCM)

x= 50/3

4. 27/72= (-4+4x)/64

3/2= (-1+x)/16

-1+x=24

x=24+1

Measurement is the area of the number sense that has a relationship with the quantity of ingredients used in recipes.

The measures of recipes are determined by:

So measure recipes, one can either measure them using artefacts such as cups, spoons, or other kind of containers.

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The correct statements regarding the function in the graph are given as follows:

B. The function does not reach a maximum value.

C The function is increasing for all values of x larger than 2.

The function is defined for values of x or 2 and greater, and the function is increasing until infinity(hence it does not reach a maximum value) for all these values, hence statements B and C are correct.

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The median of this set is:

9

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result.

HAVE A NICE DAY!

Answer:

Step-by-step explanation:

Remark

You always have to put the data in order to answer a question like this one.

6 7 7 8 10 14 15

The median is the middle number. In this case it is 8. There are 3 numbers below 8 and 3 numbers above 8, so 8 is the median.

Answer: 8

The expression that can be used to verify that (one-third x) (3 x) is the inverse of One-third (3 x) is 1/3(3x).

It should be noted that an expression is a collection of symbols that can be used to jointly express a quantity.

From the information given, g(x) = 1/3x + 3x. Here, the expression that can be used to verify that (one-third x) (3 x) is the inverse of One-third (3 x) is 1/3(3x). The inverse in this case is the opposite of the function expressed.

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Answer:

c

Step-by-step explanation:

edge 2022

The solutions to the systems of inequalities are (0.3, 1.3), (-1, -2), (0.4, 1.8) and (3.6, 0.8)

The graph of the systems of inequalities is not given.

So, I would plot a new graph to answer this question.

The systems of inequalities are given as:

y − x > 1 and 2x + y ≤ 2

x + y ≥ -3 and 5x – y ≤ -3

2x – y ≤ -1 and x + 2y < 4

4x – 3y < 12 and x + 3y ≥ 6

Next, we plot these inequalities on a graph and write out the points of intersection.

From the attached graph, we have:

y − x > 1 and 2x + y ≤ 2  ⇒ (0.3, 1.3)

x + y ≥ -3 and 5x – y ≤ -3  ⇒ (-1, -2)

2x – y ≤ -1 and x + 2y < 4  ⇒ (0.4, 1.8)

4x – 3y < 12 and x + 3y ≥ 6 ⇒ (3.6, 0.8)

Hence, the solutions to the systems of inequalities are (0.3, 1.3), (-1, -2), (0.4, 1.8) and (3.6, 0.8)

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Answer:

Shoprite

Step-by-step explanation:

At giant each case of water is 4.33 You can figure this out by dividing the overall cost of 12.99 by 3 and that gives you the cost of one case of water. At Shoprite you get 4 cases for 12.00 again you divide the overall cost of 12.00 by 4 and that gives you 3.00 so you get a better deal at shoprite there fore shoprite is the better place to shop for water

The correct numerical values that should be used in completing Melissa's table are:

Note: From the information provided in the table shown in the image attached below, we can deduce that Melissa's vegetable garden has a square shape.

Mathematically, the area of a square can be calculated by using this formula;

A = x²

Where:

Substituting the given parameters into the formula, we have;

338 = x²

x = √338

x = √2 × √169

x = 13√2 or 18.384776 feet.

For row 2, we have:

A = 6.5²

A = 42.25 square feet.

For row 3, we have:

147.25 = x²

x = √147.25

x = 12.13466 feet.

For row 4, we have:

A = 7²

A = 49 square feet.

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450t+550t=4,000

1000t=4000

t=4000/1000

t=4 hours they will be 4,000 apart.

------------------------------------------

20t+12(4.5-t)=70

20t+54-12t=70

8t=70-54

8t=16

t=16/8

t=2 hours at 20 mph.

proof

20*2+12(4.5-2)=70

40+12(2.5)=70

40+30=70

70=70

Answer:

Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value.

Step-by-step explanation:

Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.

The number that could not be a value of y if y = 4x² - 6 is -12.

The value of y for which a function f(x) = y = 4x² - 6 can be determined by knowing the smallest value of y for which x is equal to zero.

So, from the equation y = 4x² - 6, we will replace the value of x with zero to determine the smallest value of y.

i.e.

y = 4(0) - 6

y = 0 - 6

y = -6

Thus, any number smaller than -6 could not be a value of y for the equation y = 4x² - 6.

Therefore, we can conclude that the number that could not be a value of y if y = 4x² - 6 is -12.

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Answer:

-12 is the answer.

Answer:

69

Step-by-step explanation:

420

The equation of the line that goes through (2,4) and has a slope of -3 y = -3x + 10

The equation of a line can be represented as follows;

y = mx + b

where

Therefore,

y = -3x + b

Let's find b

hence,

4 = -3(2) + b

4 = -6 + b

b = 4 + 6

b = 10

Therefore,

y = -3x + 10

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f(3) = 16

Function notation is used to express a rule in terms of x and f(x), where x is independent and f(x) is dependent.

Pronunciation of Function Notation

To use function notation it is important to know how to express the function in words.

The function "f(x) = 3x + 7" would be pronounced "F of X equals three X plus 7."

So, the function is "F of" whatever variable or value is within the parentheses.

Use of Function Notation

The function y=x is similar to the function f(x)=x. As a matter of fact, when graphed they both work the same way, but the function notation seen in the question allows us to see the value of x.

This is because the value in the parentheses is the value of x. So, in this situation, the question asks what is the value of the function when x equals 3.

Solving for f(3)

To solve this function, all we have to do is plug 3 in for x and evaluate.

First, multiple 3*3

Next, add 7

Answer:

3%

Step-by-step explanation:

P% = 15/500

P = 0.03

P% = 0.03 * 100 = 3%

Answer:

15% out of 100 is 15, multiply by 5 and you get 75

The volume of the oil required to fill both containers will be 128 liters.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of cube or cubied.

Given that:-

The volume of oil in the first container is [tex]\dfrac{31}{2}[/tex] liters so for four containers the volume will be:-

V = 4 x  [tex]\dfrac{31}{2}[/tex]

V = 2 x 31 = 62 liters

The volume of oil in the second container is [tex]\dfrac{22}{3}[/tex] liters.

V = 9 x  [tex]\dfrac{22}{3}[/tex]

V = 3 x 22 = 66 liters

So total volume of oil will be calculated as:-

Total volume = 66 + 62 = 128 liters

Therefore the volume of the oil required to fill both containers will be 128 liters.

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Answer:

5. m<STP = 134

6. m<PTS = 158

Step-by-step explanation:

5. Since ray TR bisects <PTS, angles PTR and STR are congruent.

m<PTR = m<STR

3x - 8 = 2x + 17

Subtract 2x from both sides.

x - 8 = 17

Add 8 to both sides.

x = 25

m<STP = 2m<PTR

m<STP = 2(3x - 8)

m<STP = 2(3 × 25 - 8)

m<STP = 2(67)

m<STP = 134

6.

2m<PTR = m<PTS

2(x - 23) = x + 56

2x - 46 = x + 56

x = 102

m<PTS = x + 56

m<PTS = 102 + 56

m<PTS = 158

The volume of the cylinder that is not occupied by the sphere is 2πr³/3

Since the object is a sphere in a cylinder, we need to know the volume of sphere and cylinder.

The volume of a cylinder is given by V '= πr²h where

Since the height of the cylinder equals the diameter of the sphere, h = 2r

So, V' = πr²h

V' = πr² × 2r

V' = 2πr³

The volume of a sphere of radius r is given by V = 4πr³/3

The volume of the cylinder not occupied by the sphere is V" = V' - V

=  2πr³ - 4πr³/3

= (6πr³ - 4πr³)/3

= 2πr³/3

So, the volume of the cylinder that is not occupied by the sphere is 2πr³/3

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Answer:

$320

Step-by-step explanation:

1. 3x + 4x = 560 (since they are ratios, x would be the same amount)

2. 7x = 560

3. x = 80

This means that 3 and 4 should be multiplied by 80 to get the $ amount. The amounts are $240 (3*80) and $320 (4*80).

So, the larger amount if $320.

The Correct match up is:

The first proof of complex numbers was done by an Italian mathematicians known to be Girolamo Cardano and Raphael Bombelli.

The person who illustrated geometry of iterations is Gaston Maurice Julia.

Benoit Mandelbrot is known to have discover fractal geometry. Rene Descartes is known to be famous for making a connection between geometry and algebra.

Therefore, from the above, you can see that the only correct matchup is Leonhard Euler - developed geometry of curved surfaces

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Answer :

proof of complex functions --- > Maryam Mirzakhani

illustrated geometry of iterations --- > Benoit Mandelbrot

developed geometry of curved surfaces --- > Leonhard Euler

In the 15th century, Rene Descartes developed the field of analytical geometry by using functions to describe lines and curves in a coordinate plane. In the 18th century, Leonhard Euler extended geometric analysis to curved surfaces. in the late 20th century, Benoit Mandelbrot used computers to illustrate the geometry of iterations (fractals). In 2014, Maryam Mirzakhani received the Fields Medal for her work on geometric proofs involving complex functions.