The area of a circle is 36π. What is the length of a diameter of the circle?

Answer:

Step-by-step explanation:

[tex]\dfrac{10x^3 + 40x^2 + 15x}{5x}\\ \dfrac{10x^3}{5x} +\dfrac{40x^2}{5x}+\dfrac{15x}{5x}[/tex]

2x^2 + 8x + 3 is your final answer.

Answer:

There are 4 boys and 17 girls in the class.

Step-by-step explanation:

Out of 21 students in Mrs. Clark's class, 5th of the students are boys and rest are girls.

out of 21 every 5th student is boy, so total boys are = [tex]\frac{21}{5}[/tex]

                                                                                      = [tex]4\frac{1}{5}[/tex]

The whole number is 4, so the number of boys are 4.

The number of girls = 21 - 4 = 17 girls

There are 4 boys and 17 girls in the class.

The numbers ordered from least to greatest are -0.52, -5/16, -1/5, 3/4, and 0.90. Negative values are ordered by ascending absolute value, while positive values are ordered normally.

To order the numbers from least to greatest, we first need to compare the negative numbers, then the positive fractions and decimals. It's important to understand that negative numbers are less than zero, and the number with the largest absolute value is actually the smallest when negative. Positive numbers are greater than zero, with larger decimal or fractional values representing larger numbers.

The correct order from least to greatest is: -0.52, -5/16, -1/5, 3/4, and 0.90.

Answer:

112

Step-by-step explanation:

Given z is directly proportional to x then the equation relating them is

z = kx ← k is the constant of proportionality

To find k use the condition x = 3 when z = 48

k = [tex]\frac{z}{x}[/tex] = [tex]\frac{48}{3}[/tex] = 16, thus

z = 16x ← equation of proportionality

When x = 7, then

z = 16 × 7 = 112

Answer with Step-by-step explanation:

Bev earns $2 a week for taking out her neighbor’s trash cans.

Number of Weeks     Money Earned ($)

1                                      2

2                                      4

3                                      6

4                                     8

As we can see the domain is the number of weeks which is:

{1,2,3,4,...}

and Range is the money earned in dollars which is:

{2,4,6,8,...}

Solution:

The formula for tan(A+B) and tan(A-B) are:

[tex]tan(A+B) = \frac{tan(A)+tan(B)}{1-tan(A)tan(B)} \\\\tan(A-B) = \frac{tan(A)-tan(B)}{1+tan(A)tan(B)}[/tex]

The left hand side of the given expression is:

[tex]tan(\frac{\pi}{4}-\alpha ) tan(\frac{\pi}{4}+\alpha )[/tex]

Using the formula above and value of tan(π/4) = 1, we can expand this expression as:

[tex]tan(\frac{\pi}{4}-\alpha ) tan(\frac{\pi}{4}+\alpha )\\\\ = \frac{tan(\frac{\pi}{4} )-tan(\alpha)}{1+tan(\frac{\pi}{4} )tan(\alpha)} \times \frac{tan(\frac{\pi}{4} )+tan(\alpha)}{1-tan(\frac{\pi}{4} )tan(\alpha)}\\\\ = \frac{1-tan(\alpha)}{1+tan(\alpha)} \times \frac{1+tan(\alpha)}{1-tan(\alpha)}\\\\ = 1 \\\\ = R.H.S[/tex]

Thus, the left hand side is proved to be equal to right hand side.

Answer:

a) 132.0 mmHg, b) 50 years old.

Step-by-step explanation:

a) Plug in 48 where you see the letter y and simplify, preferably with a calculator.

P = 0.005(48)^2 - 0.01(48) + 121

P = 132.04 mmHg, to the nearest tenth would be 132.0 mmHg

b) Plug in 133 for P and solve for y.

0.005y^2 - 0.01 + 121 = 133

To make it a little easier on myself -- and because I haven't practiced a diff. method in a while -- I simplified the equation to 0.005y^2 - 0.01y - 12 = 0 by subtracting 133 from both sides. I did that so that I can could then use the quadratic formula to solve.

Quadratic formula is y = (-b +/- √(b^2 - 4ac)) / 2

Now we plug in our given information, that new trinomial, to solve for y

[tex]y = \frac{0.01 +/- \sqrt{(0.01)^2 - 4(0.005)(-12)} }{2(.0.005)} \\y = \frac{0.01 +/- \sqrt{0.2401}}{0.01}[/tex]

[tex]y = \frac{0.01}{0.01} +/- \frac{\sqrt{0.2401}}{0.01} \\y = 1 +/- \frac{0.49}{0.01}\\y = 1+/- 49[/tex]

Because it is a trinomial, you are given two answers. You get y = 48 and y = 50. In order to find out which is right, you plug in and see which on yields 133 as the answer. Given the part a), I already know it's not 48. When I plug in 50, I get 133. Therefore, 50 years old is your answer.

The systolic pressure for a person who is 48 years old is approximately 132.0 mm Hg. If a person's systolic pressure is 133 mm Hg, their age is approximately 49 years when rounded to the nearest whole year.

A) Systolic Pressure Calculation for Age 48

To find the systolic pressure for a person who is 48 years old, we use the given equation:

P = 0.005y^2 - 0.01y + 121

Substitute y = 48 into the equation:

P = 0.005(48)^2 - 0.01(48) + 121 = 0.005(2304) - 0.48 + 121 = 11.52 - 0.48 + 121 = 11.04 + 121 = 132.04 mm Hg

To the nearest tenth, the systolic pressure is 132.0 mm Hg.

B) Age Calculation for Systolic Pressure of 133 mm Hg

To find the age when a person's systolic pressure is 133 mm Hg, we set P = 133 and solve for y:

0.005y^2 - 0.01y + 121 = 133 0.005y^2 - 0.01y - 12 = 0

Using the quadratic formula, y = [-b ± √(b^2 - 4ac)] / (2a), where:

a = 0.005,
b = -0.01, and
c = -12.
We find the positive root that makes physical sense for age:

y ≈ 48.9 years

The age rounded to the nearest whole year is 49 years.

Answer:

the answer is A

Step-by-step explanation:

Answer:

[tex]\large\boxed{B.\ \left\{\begin{array}{ccc}2x+3y=7\\6x+y=11\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+3y=7&(1)\\4x-2y=4&(2)\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+3y=7\\4x-2y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad6x+y=11\qquad(3)\\\\\text{Make the system of equation with (1) and (3):}\\\\\left\{\begin{array}{ccc}2x+3y=7\\6x+y=11\end{array}\right[/tex]

The equivalent system of equations for the given system of equations is

option (B)

[tex]2x+3y=7\\6x+y=11[/tex]

This is obtained by adding the given equations.

Given the system of equations as

[tex]2x+3y=7\\4x-2y=4[/tex]

Adding the two equations,

[tex]2x+3y+4x-2y=7+4\\6x+y=11[/tex]

Therefore, the system of equations

[tex]2x+3y=7\\6x+y=11[/tex]

are equivalent to the given set of equations.

Thus, option (B) is correct.

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Answer:

9 m

Step-by-step explanation:

If x is the length of the original square, then x+5 is the length of the new square.

Area of a square is the square of the side length, A = s².  Since the area of the new square is 196 m²:

196 = (x + 5)²

Solving, first take the square root of both sides:

±14 = x + 5

Subtract 5 from both sides:

x = -5 ± 14

x = -19, x = 9

x can't be negative, so x = 9.  The side length of the original backyard is 9 m.

Answer:

9m

Step-by-step explanation:

If Mrs. G is planning an expansion of her square back yard and side of the original backyard is increased by 5 m, the new total area of the backyard will be 196 m2. The length of each side of the original backyard is 9m.

x = length of original square

x + 5

Formula: A = s²

Therefore, the side length of the original backyard is 9 m.

Answer: [tex]x=129\°[/tex]

Step-by-step explanation:

By definition, it is important to remember that:

[tex]Angle\ formed\ by\ two\ chords=\frac{1}{2}(Sum\ of\ intercepted\ arcs)[/tex])

You can observe in the figure that "x" is an Angle formed by two chords, therefore, you can find its value applying the formula.

Therefore, the value of "x" is this:

[tex]x=\frac{1}{2}(204\°+54\°)\\\\x=\frac{1}{2}(258\°)\\\\x=129\°[/tex]

Answer:153.94

Step-by-step explanation:circumference is πr^2

π × 49 = 153.93804

Nearest hundredth count two digits after the decimal(to make an hundredth), then round off with the third number

Answer:

Step-by-step explanation:

The formula of a volume of a pyramid:

[tex]V=\dfrac{1}{3}BH[/tex]

B - base area

H - height

In the base we have a square withe side s = 2cm

The formula of an area of a square with side s:

[tex]A=s^2[/tex]

Substitute:

[tex]A=2^2=4\ cm^2[/tex]

The height H = 3.75 cm.

Calculate the volume:

[tex]V=\dfrac{1}{3}(4)(3.75)=\dfrac{15}{3}=5\ cm^3[/tex]

Answer: C. 58 1/3 cm∧2

Just took quiz.

Answer:

D. Drawing an ace from a deck of cards and getting heads on a coin

toss

Step-by-step explanation:

Drawing an ace from a deck of cards and getting heads on a coin

toss describes a compound event.

Answer:

D. Drawing an ace from a deck of cards and getting heads on a coin

toss.

Step-by-step explanation:

Compound event means being able to get more than one different outcome in any given time. This means that the result is not always the same. Most of the time, this consists of more than one event, and that the event has nothing to do with each other (independent compound events).

~

Check the picture below.

The greatest distance between the balls placed by Alice on a straight line is between the balls at points P and R, which equates to 18 units.

The point coordinates given for the balls that Alice placed are located on a straight line. They are vertically aligned, as the x-coordinate is the same (-5) for all the balls. The y-coordinate represents the vertical position of each ball.

To find the greatest distance between the balls, calculate the distance between the highest point P (-5,9) and the lowest point R (-5,-9). The formula to calculate the distance between two points (x1, y1) and (x2, y2) on a straight line is sqrt[(x2 - x1)^2 + (y2 - y1)^2].

However, as x1 and x2 are the same, the calculation simplifies to |y2 - y1|. So the distance between P and R would be |-9 - 9| which equals 18 units. Therefore, the two balls at points P and R are separated by the greatest distance.

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Answer:

Dependent would be the number of times she rides because it would add up to how many times she could ride. 6.75= x(.45)

Step-by-step explanation:

In Jewels' ferry ride scenario, the independent variable is the number of rides taken, and the dependent variable is the total cost incurred based on the rides. This follows the general rule where the dependent variable's outcome is determined by the choice made in the independent variable.

In the scenario described, Jewels has a certain amount of money to spend on ferry rides, and each ride costs a fixed amount. Here, the number of ferry rides she can take is the independent variable, as it can be chosen freely by Jewels. The total cost of the ferry rides is the dependent variable, as it depends on the number of rides she takes.

Therefore, the correct answer is that the number of rides is the independent variable and the total cost is the dependent variable.

As for the given reference information, in the vacation resort case, the number of hours the equipment is rented is the independent variable, and the total fee is the dependent variable. This is similar to Jewels' scenario because the basic principle in both instances is about the relationship between a variable you can control (number of rides or hours) and a variable that depends on this control (total cost or total fee).

For example, if Jewels decides to ride the ferry 5 times, the total cost would be 5 rides × $0.45 per ride = $2.25. This demonstrates how the dependent variable (total cost) changes in response to a change in the independent variable (number of rides).

Answer:

(7, 3), (–1, –1) and (2, 8) are at a distance of  units from (2, 3).

Step-by-step explanation:

We know that the formula of distance is given by:

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

So substituting the given points points to check which points are at a distance of 5 units from [tex](2,3)[/tex].

1. (2, 3) and (7, 3):

[tex]\sqrt{(7-2)^2+(3-3)^2} =\sqrt{25} = 5[/tex]

2. (2, 3) and (–1, –1):

[tex]\sqrt{(-1-2)^2+(-1-3)^2} =\sqrt{25} = 5[/tex]

3. (2, 3) and (0, 3):

[tex]\sqrt{(0-2)^2+(3-3)^2} =\sqrt{4} = 2[/tex]

4. (2, 3) and (2, 8):

[tex]\sqrt{(2-2)^2+(8-3)^2} =\sqrt{25} = 5[/tex]

5. (2, 3) and (-7, 6):

[tex]\sqrt{(-7-2)^2+(6-3)^2} =\sqrt{90} =9.5[/tex]

Answer:

Step-by-step explanation:

The correct answer are A B and D

I just took the test

Answer:

[tex]a_n=27 \cdot (\frac{1}{3})^{n-1}[/tex].

Step-by-step explanation:

This is a geometric sequence that means there is a common ratio.  That means there is a number you can multiply over and over to get the next term.

The first term is 27.

The second term is (1/3)(27)=9.

The third term is (1/3)(9)=3.

So the common ratio is 1/3.

That means you can keep multiplying by 1/3 to find the next term in the sequence.

The explicit form for a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio.

We are given [tex]a_1=27[/tex] and [tex]r=\frac{1}{3}[/tex].

So the explicit form for the given sequence is [tex]a_n=27 \cdot (\frac{1}{3})^{n-1}[/tex].

Answer:

Its b on edge 2021

Step-by-step explanation:

just did it

Answer:

Step-by-step explanation:

Square base of the base edge = 12 meters and slant height = 6√2 meters

Apothem of the right pyramid will be = AC

1). Now AC = [tex]\sqrt{AB^{2}-BC^{2}}[/tex]

AC = [tex]\sqrt{(6\sqrt{2})^{2}-(6)^{2}}[/tex]

     = [tex]\sqrt{72-36}=\sqrt{36}[/tex]

     = 6

Now Apothem = 6 meters

2). Hypotenuse of Δ ABC = AB = 6√2 meters

3). Height AC = 6 meters

4). Volume of the pyramid = [tex]\frac{1}{3}(\text{Area of the base})(\text{Apothem})[/tex]

Volume = [tex]\frac{1}{3}(12)^{2}(6)[/tex]

             = 2×144

             = 288 meter²

Correct responses:

The given dimensions of the right pyramid having a square base are;

Base edge length, l = 12 meters

Slant height = 6·√3

Required:

Length of the apothem.

Solution:

The apothem, a, is the line drawn from the middle of the polygon to the midpoint of a side.

Therefore;

The apothem of the square base = [tex]\dfrac{l}{2} [/tex] = [tex]\overline{BC}[/tex]

Which gives;

[tex]a = \dfrac{12}{2} = 6[/tex]

Required:

The hypotenuse of triangle ΔABC

Solution:

The hypotenuse of ΔABC = The slant height of the square pyramid = 6·√2 meters

Therefore;

Required:

The height of the pyramid

Solution:

The height of the pyramid = The length of the side [tex]\overline{AC}[/tex] in right triangle

ΔABC, therefore, by Pythagorean theorem, we have;

[tex]\overline{AC}^2[/tex] = [tex]\overline{AB}^2[/tex] - [tex]\overline{BC}^2[/tex]

Which gives;

[tex]\overline{AC}^2[/tex] = (6·√2)² - 6² = 6²·((√2)² - 1) = 6² × 1  = 6²

[tex]\overline{AC}[/tex] = √(6²) = 6

Required:

The volume of the pyramid.

Solution:

[tex]The \ volume \ of \ a \ pyramid \ is, \ V = \mathbf{\dfrac{1}{3} \times Base \ area \times Height}[/tex]

[tex]V = \dfrac{1}{3} \times A \times h [/tex]

The base area of the square pyramid, A = 12 m × 12 m = 144 m²

Therefore;

[tex]V = \dfrac{1}{3} \times 144\, m^2 \times 6 \, m = 288 \, m^2[/tex]

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To solve this you must completely isolate x. This means that you have to get rid of the square from the x. To do this take the square root of both sides (square root is the opposite of squaring something and will cancel the square from the x)

√x² = √9

x = 3

and

x = -3

Check:

3² = 9

3*3 = 9

9 = 9

(-3)² = 9

-3 * -3 = 9

9 = 9

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer with Step-by-step explanation:

Let ?=x

We have to find the value of x in:

[tex](-b^3+3b^2+8)-(x-5b^2-9)=5b^3+8b^2+17[/tex]

Adding [tex]b^3[/tex] on both sides, we get

[tex]-b^3+3b^2+8-x+5b^2+9+b^3=5b^3+8b^2+17+b^3[/tex]

[tex]3b^2+8-x+5b^2+9=5b^3+8b^2+17+b^3[/tex]

Combining the like terms on both side, we get

[tex]8b^2+17-x=6b^3+8b^2+17[/tex]

Subtracting both sides by 8b², we get

[tex]8b^2-x+17-8b^2=6b^3+8b^2+17-8b^2[/tex]

[tex]-x+17=6b^3+17[/tex]

subtracting both sides by 17, we get

[tex]-x+17-17=6b^3+17-17[/tex]

[tex]-x=6b^3[/tex]

Dividing both sides by -1, we get

[tex]x=-6b^3[/tex]

Hence, ? = [tex]-6b^3[/tex]

Step-by-step explanation:

1 * (-5) = -5     a = -5

6 + (-5) = 1      b = 1

1 * (-5 ) = -5     c = -5

-7 + -5 = -12     d = -12

The divisor of the polynomial in the synthetic long division is linear factor

The correct values are;

Reason:

[tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &a & c & 60\end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ b \hspace {0.25 cm} d \hspace {0.25 cm} 0[/tex]

The divisor in the division is (x - (-5)) = (x + 5)

By synthetic long division, we have;

Carry down the 1 representing the leading coefficient

Multiply the 1 brought down by the zero value of x which is -5, and take the result into the second line of the division symbol

-5 × 1 = -5

Add the coefficient 6 to -5, and bring down the result

Repeat the above steps again to get;

-5 × 1 = -5

-5 × (-12) = 60

By comparison to the given synthetic long division, [tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &a & c & 60\end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ b \hspace {0.25 cm} d \hspace {0.25 cm} 0[/tex], we have;

a = -5, c = -5, b = 1, and d = -12

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moving 4 to the other side x= 4 × -3 =-12

so x =-12

Answer:

x  ≤ -12

Step-by-step explanation:

1/4 x ≤ -3

Multiply by 4 on both sides to get rid of the fraction coefficient.

x  ≤ -12

This means x is x is equal to or less than -12

Answer:

Step-by-step explanation:

Answer "A"

Dodecahedron

Dodecahedron does not have triangular faces.

The dodecahedron is also known as pentagonal dodecahedron which is composed of 12 regular pentagonal faces, 30 edges, and 20 vertices.

A  regular icosahedron is a 3D polyhedron having 20 triangular faces, 30 edges, and 12 vertices.

A regular octahedron has 8 triangular faces, 6 vertices, and 12 edges.

A tetrahedron has 4 triangular faces, 4 vertices, and 6 edges.

All of these 3 have triangular faces.

But Dodecahedron has 12 faces which are pentagonal in shape.

Therefore Dodecahedron does not have triangular faces.

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Answer:

p=8

Step-by-step explanation:

We know that 'p' represents a digit.

We can say that:

x + 5/17 = 1

Solving for 'x' we have:

x = 1 -5/17

x = 12/17

Now, multiplying 'x' by 4, we have:

x = 48/68

Therefore, p=8

Answer:

Vertical shift of 3 units down ⇒ last answer

Step-by-step explanation:

* Lets revise the translation of a function

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ The parent function y = √x

∵ There is a translation by k = -3

- From the rules above k is for the vertical translation

∵ k = -3

- That means the parent function translated 3 units down

∴ The value of k = -3 makes the graph of the parent function translated

   3 units down

- For more understand look to the attached graph

# y = √x ⇒ the red graph

# y = √x - 3 ⇒ the blue graph

Answer:

x= -2/5 and y=13/5

Step-by-step explanation:

Lets assume that the larger number = x

And the smaller number = y

According to the given statement three times a number added twice a smaller number is 4, it means;

3x+2y=4 -------- equation 1

Now further twice the smaller number less than twice the larger number is 6,it means;

2y-2x=6 --------equation 2

Solve the equation 2.

2y=2x+6

y=2x+6/2

y=2(x+3)/2

y=x+3

Substitute the value of y=x+3 in the first equation.

3x+2y=4

3x+2(x+3)=4

3x+2x+6=4

Combine the like terms:

5x=4-6

5x=-2

x= -2/5

Put the value x= -2/5 in equation 2.

2y-2x=6

2y-2(-2/5)=6

2y+4/5=6

By taking L.C.M we get

10y+4/5=6

10y+4=6*5

10y+4=30

10y=30-4

10y=26

y=26/10

y=13/5

Hence x= -2/5 and y=13/5....

To find the numbers, we first solve for x and y using a system of equations. We find that x is 2 and y is -1. Thus, the larger number is 2 and the smaller number is -1.

Detailed Explanation is as follows:

Let the larger number be x and the smaller number be y. Based on the problem, we can set up the following system of equations:

3x + 2y = 4

2x - 2y = 6

Add the equations together to eliminate y.

3x + 2y + 2x - 2y = 4 + 6

5x = 10

x = 2

Now, Substitute x back into one of the original equations

Using the first equation:

3(2) + 2y = 4

6 + 2y = 4

2y = -2

y = -1

Therefore, the larger number is 2 and the smaller number is -1.

Hence the larger number is 2 and the smaller number is -1.

[tex]\bf \begin{cases} f(x)=&5x-1\\ f(-3)=&5(-3)-1\\ f(-3)=&-15-1\\ f(-3)=&-16 \end{cases}\qquad \begin{cases} g(x)=&2x^2+1\\ g(-3)=&2(-3)^2+1\\ g(-3)=&2(-3)(-3)+1\\ g(-3)=&2(9)+1\\ g(-3)=&18+1\\ g(-3)=&19 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (f\times g)(-3)\implies f(-3)\times g(-3)\implies (-16)(19)\implies -304[/tex]

Answer:

1 hour.

Step-by-step explanation:

You have to do the total distance /total speed together.

You have to do this to ensure that you are counting how fast they are travelling together.

(450 km) / the sum of their speed (240+210)

450/ (240+210)  

=450/ 450  

=1

Answer: 1 Hour.

Answer:

t = 1 hour

Step-by-step explanation:

Oddly the distances add. Each plane will contribute a certain distance to make the 450 km. They will meet after the same number of hours have passed.

d = r * t

r1 = 240 km/hour

t1 = t

r2 = 210 km/hour

t2 = t

240*t + 210*t = 450     collect the terms on the left.

450t = 450                   divide by 450

450t/450 = 450/450

t =1

After 1 hour they will meet.

Answer:

blue = 35

green = 29

red = 38

Step-by-step explanation:

Let r = red

Let g = green

let b = blue

r + g + b = 102

r = b + 3

b = g + 6    Subtract 6 from both sides of the equation

b - 6 = g

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

substitute for red and green

(b + 3) + b + b - 6 = 102

b + 3 + b + b - 6 = 102

Combine like terms

3b - 3 = 102

Add 3 to both sides

3b - 3 + 3 = 102 + 3

3b = 105

Divide by 3

3b/3 = 105/3

b = 35

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

r = b + 3

r = 35 + 3

r = 38

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

g = b - 6

g = 35 - 6

g = 29

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

Answer:

red=35  green=29     blue=38

Step-by-step explanation: