If the ratio between the radii of the two sphere is 3:5, what is the ratio of their volumes?

A. 3:25
B. 6:25
C. 9:25
D. 27:125

Answer:

Part 1) [tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]

Part 2) The answer in the procedure

Step-by-step explanation:

Part 1)

we know that

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

we have

[tex]c=(10x+15y)[/tex]

[tex]a=(6x+9y)[/tex]

[tex]b=(8x+12y)[/tex]

substitute the values

[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]

Part 2) Transform each side of the equation to determine if it is an identity

[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}\\ \\100x^{2}+150xy+225y^{2}=36x^{2}+54xy+81y^{2}+64x^{2}+96xy+144y^{2}\\ \\100x^{2}+150xy+225y^{2}=100x^{2}+150xy+225y^{2}[/tex]

The left side is equal to the right side

therefore

Is an identity

Answer:

b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]

a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]

Step-by-step explanation:

b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]

a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]

The two expressions are identical on each side of the equivalence symbol, therefore they are an identity.

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

Add 29 to both sides of this equation, obtaining:  x² - 10x + 25.  At this point it becomes obvious that this is a perfect square, the square of x - 5.

Thus, in the first two blanks, write x - 5.

In the second two blanks, write 5 (since 5 is the root corresponding to the factor x - 5).

Answer:

Midpoint Formula is (x1+x2/2, y1+y2/2)

(-3+4/2, -5+4/2)

Midpoint is (1/2, -1/2)

Step-by-step explanation:

Answer:

  ? = 14

Step-by-step explanation:

If ∆EFG ~ ∆CBA, we have the proportion

  FG/FE = BA/BC . . . . . any pairs of corresponding sides will have the same ratio for similar triangles. (It is convenient to put the unknown in the numerator.)

  ?/18 = 21/27 . . . . . . filling in the given numbers

Multiplying by 18, we have ...

  ? = 18·21/27

  ? = 14

_____

If the triangles are not designated as being similar, the problem is unworkable.

Answer:

jina by .1 cm

Step-by-step explanation:

3/5 = .6

caleb = 23.6

jina = 23.7

Jina's model of the Empire State Building was taller by 0.1 centimeter compared to Caleb's model.

The question is comparing the heights of two models of the Empire State Building. Jina's model is 23.7 centimeters tall. Caleb's model is 23 3/5 centimeters tall, which in decimal form is equivalent to 23.6 centimeters tall. Therefore, Jina's model is taller. The height difference between Jina's model and Caleb's model is 23.7 - 23.6 = 0.1 centimeter. So, Jina's model is 0.1 centimeter taller than Caleb's model.

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Answer:cos(S) =  

60

65

Step-by-step explanation:

Answer:

D.[tex]Cos S=\frac{60}{65}[/tex]

Step-by-step explanation:

We are given that in triangle RST, RS=65 and ST=60

We have to find the equation that could be used to find the value of angle S.

We know that

[tex]cos\theta=\frac{Base}{Hypotenuse}[/tex]

Base=ST=60 units

Hypotenuse=RS=65 units

[tex]\theta=S[/tex]

Substitute the values in the given formula

Then, we get

[tex]Cos S=\frac{60}{65}[/tex]

Hence, option D is true.

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur. The correct option is A, C, and D.

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.

The relationships that would most likely be causal are:

A.) A positive correlation between depth under water and pressure.

This is a casual relationship since the water pressure increases with depth, and can be observed while swimming in a deep swimming pool.

C.) A positive correlation between a puppy’s age and weight.

This is a casual relationship because as the puppy grows, its weight as well as its size both increase.

E.) A negative correlation between temperature and snowboards sold

This is a casual relationship because as the temperature increases fewer people prefer going out snowboarding.

Hence, the correct option is A, C, and D.

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The answer is:

Andre exchanged 450 dollars for pesos.

To solve the problem, we need to write two principal equations in order to establish a relation between the number of dollars before and after the trip.

So,

Before the trip, we have:

[tex]Dollars_{beforetrip}*rate=9000pesos\\\\Dollars_{beforetrip}*\frac{20pesos}{1dollar} =9000pesos\\\\Dollars_{beforetrip}=9000pesos\frac{1dollar}{20pesos}=450dollars[/tex]

We have that he exchanged 450 dollars for pesos.

Also, we can calculate how many pesos he had before he exchanged it back to dollars, so:

After the trip, we have:

[tex]Pesos{AfterTrip}*rate=\frac{1}{10}Dollars_{BeforeTrip}\\\\Pesos{AfterTrip}*\frac{1dollar}{20pesos}= \frac{1}{10}Dollars_{BeforeTrip}\\\\Pesos{AfterTrip}= \frac{1}{10}Dollars_{BeforeTrip}*\frac{20pesos}{1dollar}\\\\Pesos{AfterTrip}= \frac{1}{10}*450dollars*\frac{20pesos}{1dollar}=900pesos\\[/tex]

We have that he had 900 pesos before he exchanged it back to dollars.

Hence, we know that:

Andre exchanged 450 dollars for pesos.

Have a nice day!

Andre exchanged $500 for pesos at the beginning of his trip.

Let's denote the number of dollars Andre exchanged for pesos at the beginning of his trip as ( D ). According to the exchange rate, he would receive ( 20D ) pesos for ( D ) dollars.

 Andre then spends 9000 pesos while in Mexico. After spending, he has 20D - 9000 pesos left.

Upon returning, Andre exchanges the remaining pesos back to dollars at the same rate of 20 pesos per dollar. The number of dollars he gets back is [tex]\( \frac{20D - 9000}{20} \)[/tex].

 According to the problem, the amount of dollars he gets back is [tex]\( \frac{1}{10} \)[/tex] of the amount he started with, which is [tex]\( \frac{D}{10} \)[/tex].

We can now set up the equation:

[tex]\[ \frac{20D - 9000}{20} = \frac{D}{10} \][/tex]

To solve for ( D ), we multiply both sides of the equation by 20 to get rid of the denominator:

[tex]\[ 20D - 9000 = 2D \][/tex]

Subtract ( 2D ) from both sides to isolate the term with ( D ) on one side:

[tex]\[ 18D - 9000 = 0 \][/tex]

Add 9000 to both sides to solve for ( D ):

[tex]\[ 18D = 9000 \][/tex]

Divide both sides by 18 to find the value of ( D ):

[tex]\[ D = \frac{9000}{18} \] \[ D = 500 \][/tex]

Therefore, Andre exchanged $500 for pesos at the beginning of his trip.

8 hours is 480 minutes

480 minutes is 2800 bottles

2800 bottles per day

28000 devided by 2800 is 100

100 days

Answer:

100 days

Step-by-step explanation:

Answer:

5 inch

Step-by-step explanation:

The frames are proportional, so we can set the ratios equal:

width / height = width / height

3 / h = 9 / 15

9h = 45

h = 5

Given the proportionality between two pictures one with width 3 inches and another with dimensions 9 inches by 15 inches, we can set up a ratio and solve for the unknown length, yielding the length of the picture frame as 5 inches.

The question is asking to find the length of a picture frame, given that its width is 3 inches and that it has the same proportions as a picture that is 9 inches wide and 15 inches long. The proportions can be used to set up a ratio, as follows:

To solve for x, cross-multiply: 3 inches * 15 inches = 9 inches * x.

Then, divide by 9 to solve for x: 45 inches/9 = 5 inches.

So, the length of the picture frame whose width is 3 inches would be 5 inches, if it shares the same proportions as the 9 inch wide by 15 inch long picture.

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8.65 is the answer to this question.

Answer:

Option 3 - 8.65  

Step-by-step explanation:

Given : The arc intercepted by a central angle of 62° on a circle with radius 8.

To find : What is the length of the arc?

Solution :

The formula to find arc length is

[tex]l=2\pi r\times (\frac{\theta}{360^\circ})[/tex]

Where, l is the length of the arc

r is the radius of the circle r=8

[tex]\theta=62^\circ[/tex] is the angle subtended

Substitute the values in the formula,

[tex]l=2\times 3.14\times 8\times (\frac{62^\circ}{360^\circ})[/tex]

[tex]l=50.24\times 0.1722[/tex]

[tex]l=8.65[/tex]

Therefore, option 3 is correct.

The length of the arc is 8.65 unit.

Let y - x = height of sign

tan 31 = x/24

tan 31 • 24 = x

14.4206548567 = x

tan 42 = y/24

tan 42 • 24 = y

21.6096970631 = y

Now subtract x from y.

y - x = 21.6096970631 14.4206548567

y - x = 7.1890422064

Rounding off to the nearest tenth of a foot, we get 7.2 feet.

The sign for the roof is 7.2 feet.

The height of the sign is approximately 7.2 feet, calculated from the differences in elevation angles and distance.

To determine the height of the sign, we'll start by calculating the height of the roof and the height of the top of the sign from point P.

First, let's define the variables:

[tex]- \( h_1 \):[/tex]  height of the roof

[tex]- \( h_2 \)[/tex]: height of the top of the sign

[tex]- \( h_s \):[/tex] height of the sign itself

From point P, the angle of elevation to the roof is [tex]\( 31^\circ \)[/tex] and the angle of elevation to the top of the sign is [tex]\( 42^\circ \).[/tex]  The horizontal distance from point P to the base of the building is 24 feet.

Using the tangent of the angles of elevation, we have the following relationships:

[tex]\[\tan 31^\circ = \frac{h_1}{24}\]\[\tan 42^\circ = \frac{h_2}{24}\][/tex]

First, let's calculate [tex]\( h_1 \):[/tex]

[tex]\[h_1 = 24 \times \tan 31^\circ\]Using a calculator to find \( \tan 31^\circ \):\[\tan 31^\circ \approx 0.6009\]\[h_1 = 24 \times 0.6009 \approx 14.422\][/tex]

Next, let's calculate  [tex]\( h_2 \):[/tex]

[tex]\[h_2 = 24 \times \tan 42^\circ\][/tex]

Using a calculator to find [tex]\( \tan 42^\circ \):[/tex]

[tex]\[\tan 42^\circ \approx 0.9004\]\[h_2 = 24 \times 0.9004 \approx 21.610\][/tex]

The height of the sign [tex]\( h_s \)[/tex] is the difference between  [tex]\( h_2 \) a[/tex]nd [tex]\( h_1 \):[/tex]

[tex]\[h_s = h_2 - h_1\]\[h_s = 21.610 - 14.422 \approx 7.188\][/tex]

To the nearest tenth of a foot, the height of the sign is:

[tex]\[h_s \approx 7.2 \text{ feet}\][/tex]

Thus, the height of the sign is ( 7.2 ) feet.

Answer:

im on the same question

Answer:

1

Step-by-step explanation:

Count the amount of dots given. There are 20 dots in all. To find the middle value, set the numbers in a line first.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 4, 4, 5

Find the middle value. Note that the two middle values are both 1. Find the mean of the two values.

1 + 1 = 2

2/2 = 1

1 is your median .

~

Answer:

1

Step-by-step explanation:

If you go in from left to right starting on the left side on the top of the dots (0) and start from the right side on the bottum and go up (5) and you slowly work your way up to the top, you get the answer 1.

1) first find brian’s score

a.) 171+17=188

2) Add brian and colin’s score.

a.) 171+188= 359

Colin scored 171. Brian scored 17 more than Colin, which is 188. Adding both scores together, their combined score is 359.

This is a straightforward arithmetic problem. Colin scored 171 points and Brian scored 17 more than Colin. So first, you need to determine Brian's score by adding 17 to 171, which equals 188. Then, to find their combined score you need add Colin's and Brian's scores together. Therefore, 171 (Colin's score) + 188 (Brian's score) = 359. So, their combined score is 359.

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Answer:

C  x=6

Step-by-step explanation:

sqrt(x+3) = x-3

Square each side

(sqrt(x+3))^2 = (x-3)^2

x+3 = (x-3)^2

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

FOIL

x+3 = x^2 -3x-3x+9

Combine like terms

x+3 = x^2 -6x+9

Subtract x from each side

x-x+3 = x^2 -6x-x +9

3 =  x^2 -7x +9

Subtract 3 from each side

3-3 =  x^2 -7x +9-3

0 = x^2 -7x+6

Factor

0 = (x-6)(x-1)

Using the zero product property

x-6=0   x-1 =0

x=6  x=1

Since we squared we need to check for extraneous solutions

x=1

sqrt(1+3) = 1-3

sqrt(4) = -2

2=-2

False

Extraneous

x=6

sqrt(6+3) = 6-3

sqrt(9) = 3

3=3

True   solutions

Answer: Option C.

Step-by-step explanation:

First, we need to square both sides of the equation:

[tex]\sqrt{x+3}=x-3\\\\(\sqrt{x+3})^2=(x-3)^2[/tex]

We know that:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

Then, applying this, we get:

[tex]x+3=x^2-2(x)(3)+3^2\\\\x+3=x^2-6x+9[/tex]

Now we need to subtract "x" and 3 from both sides of the equation:

[tex]x+3-(x)-(3)=x^2-6x+9-(x)-(3)\\\\0=x^2-6x+9-x-3[/tex]

Adding like terms:

[tex]0=x^2-7x+6[/tex]

Factor the quadratic equation.  Find two numbers whose sum be -7 and whose product be 6. These numbers are: -1 and -6. Then:

[tex](x-1)(x-6)=0[/tex]

Then:

[tex]x_1=1\\x_2=6[/tex]

Checking the first solution is correct:

[tex]\sqrt{1+3}=1-3\\ 2=-2 \ (False)[/tex]

Checking the second solution is correct:

[tex]\sqrt{6+3}=6-3\\ 3=3 \ (True)[/tex]

Formula for degree to radian:

degree ×[tex]\frac{\pi }{180}[/tex]

so...

[tex]280* \frac{\pi }{180}[/tex]

Exact answer:

[tex]\frac{14\pi }{9}[/tex]

Rounded answer:

4.89

Hope this helped!

The answer is D

Let x = -2

f(-2) = 8 - 4(-2)

f(-2) = 8 + 8

f(-2) = 16

D is the answer.

If f(-2)=16 which could be the equation for f(x) f(x)=8-4x will yield f(-2)=16

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Given

Let x = -2

f(-2) = 8 - 4(-2)

f(-2) = 8 + 8

f(-2) = 16

therefore, f(x)=8-4x will yield f(-2)=16

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Answer:

  x = -7

Step-by-step explanation:

The vertex form of this equation tells us it is a downward-opening parabola with its vertex at (-7, -3). The line of symmetry is the vertical line through the vertex: x = -7.

___

Vertex form is ...

  y = a(x -h) +k

where a is the vertical expansion factor, and (h, k) is the vertex. When a < 0, the parabola opens downward. When a > 0, it opens upward. (When a=0, the "parabola" is a horizontal line at y=k.)

The equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

The function given in statement represents a parabola whose axis of symmetry is parallel to the y-axis. The standard form of the function is described below:

[tex]f(x) -k = C\cdot (x-h)^{2}[/tex] (1)

Where:

The equation for the axis of symmetry is of the form [tex]x = h[/tex]. By direct comparison, we determine that the equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

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Answer:

y = 2.4

Step-by-step explanation:

Given y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 8 when x = 3

k = yx = 8 × 3 = 24

y = [tex]\frac{24}{x}[/tex] ← equation of variation

When x = 10, then

y = [tex]\frac{24}{10}[/tex] = 2.4

The variation is an illustration of inverse variation, and the value of y when x = 10 is 2.4

The variation is an inverse variation.

An inverse variation is represented as:

k = xy

Rewrite as:

x₁y₁ = x₂y₂

When y = 8, x = 3; we have:

3 * 8 = x₂y₂

This gives

24 = x₂y₂

When x = 10; we have:

24 = 10 * y

Divide both sides by 10

y = 2.4

Hence, the value of y when x = 10 is 2.4

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Answer:

Inconsistent

Step-by-step explanation:

Consistent independent means that there is only one solution; ie one place where the 2 lines intersect.

Inconsistent means that the lines will NEVER cross because they are parallel

Consistent dependent means that the 2 lines, when solved for y, are the exact same line (same slope, same y-intercept)

In our system, one of the equations is already solved for y, so let's solve the other one for y:

[tex]x-2y=1[/tex] so

[tex]-2y=-x+1[/tex] and

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

The slopes of the 2 lines are the same; therefore, they are parallel and will never intersect.  Inconsistent system.

Answer:

inconsistent

Step-by-step explanation:

Answer: so bc. a length not can being minus so this mean that the width of the rectangle is equal 9 in

Answer: C. 41

Step-by-step explanation:

The quadratic function is:

 [tex]f(x) = 6x^2-13[/tex]

Then, to find [tex]f(-3)[/tex] you need to substitute the input value [tex]x=-3[/tex] into the quadratic function, to obtain the corresponding output value.

Then, when [tex]x=-3[/tex] the  output value is:

[tex]f(x) = 6x^2-13[/tex]

[tex]f(-3) = 6(-3)^2-13[/tex]

[tex]f(-3) = 6(9)-13[/tex]

[tex]f(-3) = 41[/tex]

This matches with the option C.

Answer:

-4

Step-by-step explanation:

Please write f(x) as 6x^2 - 13; " ^ " indicates exponentiation.

With f(x) = 6x^2 - 13, we substitute -3 for x in both instances:

f(-3)       =(-3)^2 - 13 = 9 - 13  = -4

ANSWER

Option A

EXPLANATION

The given product is

[tex]1.42 \times {10}^{7} \times 2.81 \times {10}^{1} [/tex]

[tex]1.42 \times 2.81 \times {10}^{7} \times {10}^{1} [/tex]

We multiply to get;

[tex]3.9902 \times {10}^{7} \times {10}^{1} [/tex]

Recall the product rule

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We apply the product rule to get,

[tex]3.9902 \times {10}^{7 + 1} [/tex]

[tex]3.9902 \times {10}^{8} [/tex]

Correct to the nearest tenth, we have

[tex]3.99 \times {10}^{8} [/tex]

This can also be written as;

[tex]3.99 {e}^{8.00} [/tex]

The correct choice is A.

Answer:488

Multiply 12.20 and 40

Answer:

Answer: The slope is 2. The y-intercept is 4 which means point (0, 4).

Step-by-step explanation:

First, find the slope of the line that passes through those two points using the slope formula.

[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

where the points are [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex]

[tex] slope = m = \dfrac{18 - 4}{7 - 0} = \dfrac{14}{7} = 2 [/tex]

The slope is 2.

One of the given points is (0, 4). Since the y-intercept lies on the y-axis, the x-coordinate of the y-intercept is 0. Point (0, 4) is the actual y-intercept.

Answer: The slope is 2. The y-intercept is 4, or point (0, 4).

To find the slope, use the S=(y2 - y1)/(x2 - x1) formula

S=(18-4)/(7-0)

S=14/7

S=2

After finding the slope, us the intercept formula to find the intercept

m is the slope

y-y1=m(x-x1)

y-4=2(x-0)

y=2x+4

Answer:

  3|x|

Step-by-step explanation:

√(x^2) = |x|, the positive root. Multiplying this by 3, you get ...

  3√(x²) = 3|x|

Answer:

ASA

Step-by-step explanation:

One pair of corresponding angles (in the bottom left/right) are already marked for us, and we're also given a pair of corresponding sides (the 8cm ones on the left and right). The two triangles have one more angle in common too - the one they're overlapping on the top corner. So, we have:

- Two pairs of congruent corresponding angles, and

- A pair of congruent corresponding sides between them,

which is enough information to call the triangles congruent by Angle-Side-Angle (ASA).

The length of the hypotenuse of a right triangle with legs of 5 cm and 12 cm is 13 cm.

The length of the hypotenuse of a right triangle can be found by using the Pythagorean theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the two legs.

In this case, we have a right triangle with legs of 5 cm and 12 cm. To find the length of the hypotenuse, we can use the formula c = √(a² + b²).

Substituting the given values, we get c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Answer:

2x^2+x-4=0

x^2+\dfrac12x-2=0

x^2+\dfrac12x+\dfrac1{16}-\dfrac{33}{16}=0

\left(x+\dfrac14\right)^2=\dfrac{33}{16}

x+\dfrac14=\pm\dfrac{\sqrt{33}}4

x=\dfrac{-1\pm\sqrt{33}}4

Step-by-step explanation: lol tooooo much ∅∞

Answer:

1/2 and -2 are the first answers to the question

1/16 and 1/16 are the next answers  

1/4 and 33/16 are the last ones

and for the multiple choice answer which is last is A

Step-by-step explanation: