if roy is 4 years older than his brother and the product of their ages is 165, how old is roys younger brother

If the volume of a sphere is decreasing at a constant rate of 55 cubic feet per minute. The volume of a sphere  is  0.036.

Using this formula to find the  volume of a sphere

V = 4/3 π r³

Taking the derivative with respect to time:

dV/dt = 4π r² dr/dt

Let plug in the formula

55 = 4π (11)² dr/dt

dr/dt = 55/ (484π)

dr/dt = 55/1,520.5308

dr/dt = 0.036

Therefore the  volume of a sphere is 0.036.

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The measured distance of 1.15 meters from Levi's eyes to to the ground indicates that the height of the goalpost located 12.05 meters from the mirror when Levi is 2 meters from the mirror, found using similar triangles is approximately 6.93 meters.

Two triangles are similar if two angles in one triangle are congruent to two angles in the other triangle.

According the laws of reflection, the angle made by the incident ray with the normal is the same as the angle made by the reflected ray and the normal

Both the angle made by Levi and the angle made by the goalpost with the ground are perpendicular or 90°.

Therefore, the triangle formed by the line of site to the mirror and the reflected ray to the top of the goal post are similar triangles by Angle-Angle similarity postulate.

The ratio of corresponding sides is the same in similar triangles, therefore;

[tex]\dfrac{Levi's \, distance \, from \, the \, mirror}{Goalpost \, distance \, from \ the \ mirror }=\dfrac{Levi's \,height}{Height\, of \, the \, goalpost, H}[/tex]

[tex]\dfrac{2}{12.05} =\dfrac{1.15}{H}[/tex]

[tex]H =\dfrac{1.15\times 12.05}{2} \approx 6.93[/tex]

The height of the goalpost is approximately 6.93 meters

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The equation of a line that passes through the point (0,-1) and has a gradient of -3 is y = -3x - 1

From the question, we have the following points that can be used in our computation:

(x, y) = (0, 1)

Also, we have the slope to be

gradient = -3

Rewrite as

m = -3

The equation of the line is then calculated using the following equation

y = m(x - x₁) + y₁

Where

(x, y) = (0, -1)

m = -3

Substitute the known values in the above equation, so, we have the following representation

y = -3 * (x - 0) - 1

Evaluate

y = -3 * x - 1

So, we have

y = -3x - 1

Hence, the line equation is y = -3x - 1

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The answer to the question 18(26) is 18 * (20 + 6) = 468

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

According to the distributive property, you can multiply a component by each addend separately before adding the total when multiplying it by two addends.

Based on this property, in order to solve a problem of this type, you have to expand the multiplication.

Hence 18(20 * 6)

is written as (18 * 20) + (18 * 6)

= 468

The answer is 468

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Answer:

Step-by-step explanation:

Least to greatest :

-3/5,-2/3,0,0.7

Answer:

Take a look at the attachment...

Hope this helps! :)

Answer: A. : y=1/2x-4

Step-by-step explanation:

Use the equation y=mx+b:   -3=1/2(2)+b

Simplify: -3=1+b

Simplify: -4=b

Final equation: y=1/2x-4

From the total of 3 1/3 cups of sugar Paula used 1 1/2 cups of sugar to make apple pie recipe then amount of sugar left with Paula is given by

1 5/6 cups of sugar.

As given in the question,

Total amount of sugar Paula ha = 3 1/3 cups of sugar.

Amount of sugar used to make apple pie recipe is = 1  1/2 cups of sugar

Let x be the amount of sugar left with Paula after making apple pie

Required equation is :

x + 1 1/2 = 3 1/3

⇒x + 3/2 = 10/3

⇒ x = (10/3) - (3/2)

⇒x = ( 20 -9) /6

⇒ x= 11/6

⇒ x= 1 5/6 cups of sugar

Therefore, from the total of 3 1/3 cups of sugar Paula used 1 1/2 cups of sugar to make apple pie recipe then amount of sugar left with Paula is given by 1 5/6 cups of sugar.

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The equation to solve for W is W = (P-2L)/2.

According to the question,

We have the following information:

P = 2L + 2W

Now, we have to solve this equation for W.

Subtracting 2L from both sides of the equation will give us the following expression:

P-2L = 2W

Now, we will divide both sides of the equation by 2. And we will have the following expression:

(P-2L)/2 = W

(More to know: now, in this equation, if the value of P and L are given then we can use this equation to find the value of W.)

Hence, the equation to solve for W is W = (P-2L)/2.

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The domain of the given function f(x) is (−∞,∞) and the range is (-∞, 4].

What is the domain and range of a quadratic function?

The set of all real values of x that will result in real values for y is known as the domain of a function. A function's range is the set of all real values of y that may be obtained by substituting real numbers into x.

Given function is [tex]f(x)=-x^{2} +4[/tex]

The domain of [tex]f(x)[/tex] = Any real value of x  i.e. (−∞,∞)

Range of [tex]f(x)[/tex] = (-∞, 4] i.e. y ≤ 4

Hence, the domain of f(x) is (−∞,∞) and range is (-∞, 4].

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Answer: 22 miles

Step-by-step explanation: 49.50 - 3.30 = 46.20

46.20 ÷ 2.10 = 22

The cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

Given:

If it' 50 c outside and the temperature will drop 70 c in next 3 hour.

Temperature (cold) = present temperature - temperature in next 3 hour.

= 50 - 70

= -20 c.

Therefore the cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

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The answer to the question is: x = 8                      

Answer:

x = 8

Step-by-step explanation:

4x + 2 - 3 - 3x = 7

x -1 = 7

x = 7 + 1

x = 8

The number that represents Monica's balance at the end of the month, given the amount paid for the ingredients and the amount received, is 235, 000

The balance at the end of the month to Monica's ice cream parlor can be found by the simple formula:

= Amount received - Amount spent

The amount received is 550, 000.

The amount spent is:

= Purchase of ingredients + Equipment maintenance

= 210, 000 + 105, 000

= 315, 000

Monica's balance is therefore:
= 550, 000 - 315, 000

= 235, 000

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Answer:

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

Simplify first:

We need both p and q be rational numbers and we know √19 is irrational.

It is only possible if both side are equal to zero:

Answer:

[tex]\textsf{(a)} \quad h=3, \quad k=-2[/tex]

[tex]\textsf{(b)} \quad p=0, \quad q=-\dfrac{1}{2}[/tex]

Step-by-step explanation:

Rearrange the given equation so that both sides are in the same form:

[tex]\begin{aligned}2-h\sqrt{11}&=-3\sqrt{11}-k\\2-h\sqrt{11}+k&=-3\sqrt{11}-k+k\\k+2-h\sqrt{11}&=-3\sqrt{11}\\k+2-h\sqrt{11}-2&=-3\sqrt{11}-2\\k-h\sqrt{11}&=-2-3\sqrt{11}\\\\\implies h&=3\\\implies k&=-2\end{aligned}[/tex]

Rewrite and factor the right side of the equation.

As p and q are rationals, both sides of the equation have to equal zero.

[tex]\begin{aligned}2p&=q\sqrt{76}+\sqrt{19}\\2p&=q\sqrt{4 \cdot 19}+\sqrt{19}\\2p&=q\sqrt{4} \sqrt{19}+\sqrt{19}\\2p&=2q\sqrt{19}+\sqrt{19}\\2p&=\sqrt{19}(2q+1)\\\\\implies 2p&=0 \implies p=0\\\implies 2q+1&=0 \implies q=-\dfrac{1}{2}\end{aligned}[/tex]

Since C is mid - point of both BD and AE , therefore AB = DE .

Given : A , B , C , D and E are aligned in a row .

            C is the mid - point of BD and AE .

To prove : AB = DE .

Since , C is the mid - point of BD ,

⇒ BC = CD  ( 1 )

And since C is the mid - point of AE as well ,

⇒ AC = CE    ( 2 )

Subtracting ( 1 ) from ( 2 ) ,

AC - BC = CE - CD

AB = DE

Hence , proved AB = DE .

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Answer:

Total surface area of the cone = 208.81 sq cm

explanation

Diameter of the cone (d) = 7 cm

Slant height (L) = 15.5 cm

1) The radius of the cone= Half of the diameter

= 7/2 cm = 3.5 cm

⇒ r = 3.5 cm

Now, Total surface area of the cone =

taking π = 3.14

We get

and πrl = 3.14 x 3.5 + 15.5 = 170.345

So, Total surface area of the cone = 38.465 + 170.345 = 208.81 sq cm

Answer:

Step-by-step explanation:

Okay, I can help. Please specify your question further so I can actually help you.

In the given right-angled triangle sin(N) = 3/5.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjacent/hypotenuse and

tan = opposite/adjacent.

Given,, we have to obtain sin(theta) in the right-angled triangle with opposite = 3 units, hypotenuse = 5 units, and adjacent = 4 units.

We know sin = opposite/hypotenuse.

∴ Sin(N) = 3/5.

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Answer:

You would have to add all of them up, which is (7*4) + 18 = 46.
Therefore the answer is 46 feet for the length of the fence.

The slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.

First, let us understand the slope of a line:

A slope of a line is defined in mathematics as the change in the y coordinate with regard to the change in the x coordinate.

We are given the points:

(0, 1) and (1, -2)

We will calculate the slope of the line using the following formula:

m = (y_2 - y_1) / (x_2 - x_1)

Let x_1 = 0, x_2 = 1, y_1 = 1 and y_2 = -2.

Substitute the given values in the above formula, we will get:

m = (-2 - 1) / (1 - 0) = -3 / 1 = -3

So, the slope of the line is -3.

Thus, the slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.

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The slope between the two points:

7. (-14, -10) and (12, 18) => m = 1.077

8. (-3, 12) and (1, 2) => m = -2.5

9. (25, -14) and (-3, 7) => m = -0.75

10. (4, 14) and (16, 20) => m = 0.5

In this question, we need to determine the slope between the two points.

We know that the formula of slope between the two points (x1, y1), (x2, y2)

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

7. (-14, -10) and (12, 18)

m1 = (18 + 10)/(12 + 14)

m1 = 1.077

8. (-3, 12) and (1, 2)

m2 = (2 - 12)/(1 + 3)

m2 = -2.5

9. (25, -14) and (-3, 7)

m3 = (7 + 14)/(-3 - 25)

m3 = -0.75

10. (4, 14) and (16, 20)

m4 = (20 - 14)/(16 - 4)

m4 = 0.5

Therefore, the slope between the two points:

7. (-14, -10) and (12, 18) => m = 1.077

8. (-3, 12) and (1, 2) => m = -2.5

9. (25, -14) and (-3, 7) => m = -0.75

10. (4, 14) and (16, 20) => m = 0.5

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The cost of the ticket for everyone, given the amount raised by the PTA, can be found to be  $63.88

The cost of the tickets to each individual person, or to everyone, can be found by the formula:
= Amount raised by PTA / Number of students and teachers going on the trip

Amount raised by PTA = $7, 985

The number of students and teachers going on the trip:

= 112 + 13

= 125 people

The cost of the tickets are:

= 7, 985 / 125

= $63.88

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The expression for the values of b, when b = 8.9 is 47.1, when b = 5.1 is 35.7 and when x = 0.2 is 21

An expression in maths, a sentence with a minimum of two numbers or variables and at least one math operation.

Given an expression b(3) + 20.4

When b = 8.9

8.9*3 + 20.4 = 47.1

When b = 5.1

5.1*3 + 20.4 = 35.7

When b = 0.2

0.2*3 + 20.4 = 21

Hence, The expression for the values of b, when b = 8.9 is 47.1, when b = 5.1 is 35.7 and when x = 0.2 is 21

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Answer: Simplify your answer and write it as a proper fraction, improper fraction, or whole number

Step-by-step explanation:

45 pieces can the dressmaker cut from 5 of these rolls of ribbon.

Mathematical expression:

When we validly combine numbers and variables, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.

Here we have to find the number of 12-inch pieces can the dressmaker cut from 5 of these rolls of ribbon.

We are provided the length of the ribbon, which is 9 feet.

As we know that

1 feet = 12 inches

So rolls of 9 feet can make 9 pieces of 12 inches.

So 5 of these rolls of ribbon can make = 5 × 9 = 45 pieces.

Therefore we get 45 pieces.

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Answer:

d. 3x - 1

Step-by-step explanation:

(3x² + 8x − 3) ÷ (x + 3)

= ((3x - 1)(x + 3) ÷ (x + 3)

= 3x - 1

Answer:

D

Step-by-step explanation:

3x.        9x                3

x.           -x               -1

(3x-1)(x+3) /(x+3)

3x - 1

The given relation is not function, because 15 is repeating twice. In domain 15 is with 8 and 2.

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