My sister is 19 years old. My brother says that his age minus eighteen is equal to my sister's age. How old is my brother? Enter an equation, using b as your variable, to find how old my brother is. The equation is My brother is years old.

Answer:

6.2

Step-by-step explanation:

sin 20 = x/18

solve for x

Answer:

c

Step-by-step explanation:

solve this equation 4/2.40

Answer:

Area of trapezoid = 144 cm²

Step-by-step explanation:

The length of parallel sides are,

a = 8 cm

b = 16 cm

h = 12 cm

Formula area of trapezoid:-

[tex]A=\dfrac{1}{2}(a+b)\times h[/tex]

[tex]A=\dfrac{1}{2}(8+16)\times 12[/tex]

[tex]A=144[/tex]

Hence, the area of trapezoid is 144 cm²

Answer:

Hence, the area of trapezoid is 12 cm²

Step-by-step explanation:

Answer:

There are 24 gumballs, 6 of which are yellow.

P(yellow) = 6/24 = 1/4

Answer:

22.77

Step-by-step explanation:

39.95 * 1.14 (tax + markup) * 0.5 (discount) = 22.77 (rounded)

Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]

Step-by-step explanation:

Given,

Distance walked by Addie = [tex]2\frac{1}{2}=\frac{5}{2}\ miles[/tex]

Time taken by Addie = 45 minutes

Converting the time into hours;

1 hour = 60 minutes

45 minutes = [tex]\frac{45}{60}=\frac{3}{4}\ hour[/tex]

Distance = Speed * Time

Speed = Distance/Time

Speed = [tex]\frac{5}{2} / \frac{3}{4}[/tex]

Speed = [tex]\frac{5}{2}*\frac{4}{3} = \frac{10}{3}\ mph[/tex]

Speed = [tex]3\frac{1}{3}\ mph[/tex]

Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]

Keywords: speed, distance

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Answer:

9.25

Step-by-step explanation:

An equation is formed of two equal expressions.The value of y in the equation 5x + 2y = 20, when x = 0.3 is 9.25. The correct option is C, 9.25.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of y in the equation 5x + 2y = 20, when x = 0.3 can be found by substituting the value in the equation.

5x + 2y = 20

Substitute the value of x,

5(0.3) + 2y = 20

1.5 + 2y = 20

Subtract 1.5 from both sides of the equation,

1.5 + 2y - 1.5 = 20 - 1.5

Divide both the sides of the equation by 2,

2y /2 = 18.5 /2

y = 9.25

Hence, the value of y in the equation 5x + 2y = 20, when x = 0.3 is 9.25.

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Answer:B

Step-by-step explanation:

[tex]\bf \begin{cases} -2x+y=0\\ \boxed{y} = 2x\\[-0.5em] \hrulefill\\ 5x+3y=-11 \end{cases}\qquad \qquad \implies \stackrel{\textit{substituting on the 2nd equation}}{5x+3\left( \boxed{2x} \right)=-11} \\\\\\ 5x+6x=-11\implies 11x=-11\implies x = \cfrac{-11}{11}\implies \blacktriangleright x = -1 \blacktriangleleft \\\\\\ \stackrel{\textit{we know that}}{y = 2x}\implies \blacktriangleright y = -2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-1~~,~~-2)~\hfill[/tex]

Answer:

see explanation

Step-by-step explanation:

P(head) = [tex]\frac{1}{2}[/tex]

P(4) = [tex]\frac{1}{6}[/tex]

P(head and 4 ) = P(head) × P(4) = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{12}[/tex]

Answer:

  12 pm noon

Step-by-step explanation:

The least common multiple of the two times is 240 minutes, or 4 hours. The buses will meet at the station again at noon.

__

60 = 20×3

80 = 20×4

The least common multiple is 20×3×4 = 240 minutes. There are 60 minutes in an hour, so this is 240/60 = 4 hours. 4 hours after 8 am is 12 pm, noon.

Answer:

vertex=?

Step-by-step explanation:

given data:

g(x)=-3x^2+18x+2

from the given equation

a=-3,b=18,c=2

x=-b/2a

x=-(18)/2(-3)

x=3

put value of x in the given equation

y=-3(3)^2+18(3)+2

y=-27+54+2

y=29

x=3    y=29

(3,29)

Answer:

R=$1.75 B=$1.50

Step-by-step explanation:

35r+10b=X

b is 10

r is 5

X=3.25$

Answer:

Step-by-step explanation:

R=$1.75 B=$1.50  

35r+10b=X

b is 10

r is 5

X=3.25$

Answer:

The width of the red tile would be [tex]2.25[/tex] inches.

Step-by-step explanation:

Given blue tile has a length of [tex]4.25[/tex] inches, and a width of [tex]6.75[/tex]inches.

Also, length of similar tile is [tex]12.75[/tex] inches.

Let us assume [tex]x[/tex] as the width of red tile.

It is given in the question that both tiles are similar.

So, their area will be the same.

Area of blue tile would be [tex]4.25\times 6.75=28.6875\ inch^2[/tex]

Area of red tile would be [tex]12.75\times x[/tex]

The area of blue tile would be equal to area of red tile.

[tex]28.6875=12.75\times x[/tex]

[tex]\frac{28.6875}{12.75}=x\\\\x=2.25[/tex]

So, the width of the red tile would be [tex]2.25[/tex] inches.

Answer:

5715x3=

Rs.17145

Step-by-step explanation:

The interest rate required for Rs.4500 to amount to Rs.5715 in 3 years is 9% per annum. This is obtained using the simple interest formula. Therefore, the annual rate is 9%.

To find the annual interest rate at which Rs.4500 amounts to Rs.5715 in 3 years, we use the formula for simple interest:

Final Amount (A) = Principal (P) + Interest (I)

Given:

First, we calculate the interest:

Next, we use the simple interest formula:

Rearranging for the rate (R), we get:

Substitute the known values:

Converting to a percentage:

Therefore, the rate per annum required for Rs.4500 to grow to Rs.5715 in 3 years is 9%.

Answer:

Option A    M<17   m is less than or equal to 17

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer: -13x^2 + 10x + 4

Step-by-step explanation:

group all of the same variables together to simplify the equation.

-7 - 6 = -13 // the x^2 value

-5 + 15 = 10 // the x value

4 is the only number without an exponent so leave it alone.

Answer:

-13x²+10x+4

Step-by-step explanation:

You need to group all of the same variables together:

-7x² - 5x - 6x² + 4 + 15x

-7x²-6x²-5x+15x+4

-13x²+10x+4

Answer:

x=3/8, y=-7/8. (3/8, -7/8).

Step-by-step explanation:

y=-5x+1

y=3x-2

----------

-5x+1=3x-2

-5x-3x+1=-2

-8x+1=-2

-8x=-2-1

-8x=-3

8x=3

x=3/8

y=3(3/8)-2=9/8-2=9/8-16/8=-7/8

[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{2}}x\stackrel{\stackrel{b}{\downarrow }}{-2}[/tex]

Answer:

Step-by-step explanation: 72.1°

The circumference of the circle is given to be  = 20

The first thing to do here is to calculate the radius of the circle from the circumference given,

Formula for circumference  = 2πr or πd, where d is the diameter.

Make r the subject of the formula by equating it to 20

2πr = 20,

   r = 20/2π, π = ²²/₇ or 3.142

   r = 10/22/7

     = ( 10 x 7 )/22

     = 70/22

     = 3.18.

Now since the radius is known, we could now calculate the central angle of the arc.

Arc length  = 2πr∅°/360°, reducing this to lowest term now becomes

                  = πr∅°/180°

Therefore equate the formula to 4 and solve for ∅°, since the arc length is 4

           πr∅°/180° = 4

Multiply through by 180°

                πr∅° = 4 x 180°

                πr∅°= 720

Divide through by πr to get ∅°

                   ∅° = 720/πr

                        =  720/3.142 x 3.18

                        = 720/9.99

                        =  72.07

                        = 72.1°

The angle substended by the arc  length 4 is 72.1°

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

Explanation:

Check out figure 1 which is one of the attached images below.

In this diagram, I have angle A as 75 degrees and angle B as 51 degrees.

Angle C is therefore, C = 180-A-B = 180-75-51 = 54 degrees.

----------

Point D is somewhere between A and B such that it is on segment AB.

Figure 2 (also attached as an image) shows segment CD forming two angles DCB and ACD.

These are the blue and red angles respectively, such that the blue angle is twice as large as the red angle.

blue angle = 2*(red angle)

This is what it means when it says the ratio of the two angles is 2:1.

I have 2x as the blue angle and x as the red angle. We don't know what x is yet, but we do know that the x and 2x combine back to angle C = 54 degrees.

So,

(angle DCB) + (angle ACD) = angle C

(2x) + (x) = 54

3x = 54

x = 54/3

x = 18

Since x = 18, this means 2*x = 2*18 = 36

Therefore,

angle DCB = 2x = 36 degrees

angle ACD = x = 18 degrees

--------

Focus solely on triangle DCB. We found angle DCB = 36 degrees and we know that angle DBC = 51

The remaining angle y = angle BDC is...

(angle BDC)+(angle DCB)+(angle DBC) = 180

(y)+(36)+(51) = 180

y+87 = 180

y+87-87 = 180-87

y = 93

angle BDC = 93 degrees

Figure 3 shows the angles we found (basically I replaced x, 2x and y with their respective numbers).

The size of angle BDC is 0 degrees.

To find the size of angle BDC, you can use the fact that the sum of the angles in a triangle is always 180 degrees. Since angle ACD is 1 part and angle DCB is 2 parts, we can express their sizes as:

Angle ACD = x degrees

Angle DCB = 2x degrees

Now, you know that the sum of the angles in triangle ABC is 180 degrees. So, you can write the equation:

x (angle ACD) + 2x (angle DCB) + 180 degrees (angle BDA) = 180 degrees

Now, simplify and solve for x:

x + 2x + 180 = 180

Combine like terms:

3x + 180 = 180

Now, subtract 180 from both sides of the equation:

3x = 0

Finally, divide by 3:

x = 0

Now that you know the value of x, you can find the size of angle BDC (2x):

Angle BDC = 2x = 2(0) = 0 degrees

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The value of p that makes the equation true is -20

Step-by-step explanation:

To solve an equation of one variable

∵ The equation is [tex]\frac{3}{5}p+\frac{1}{5}(40 - p)=0[/tex]

- Simplify the left hand side

∵ [tex]\frac{1}{5}(40-p)=\frac{1}{5}(40)-\frac{1}{5}(p)[/tex]

∴ [tex]\frac{1}{5}(40-p)=8-\frac{1}{5}p[/tex]

- Substitute [tex]\frac{1}{5}(40-p)[/tex] in the equation by [tex]8-\frac{1}{5}p[/tex]

∴ [tex]\frac{3}{5}p+8-\frac{1}{5}p=0[/tex]

- Add the like terms

∴ [tex](\frac{3}{5}p-\frac{1}{5}p)+8=0[/tex]

∴ [tex]\frac{2}{5}p+8=0[/tex]

- Subtract 8 from both sides

∴ [tex]\frac{2}{5}p=-8[/tex]

- Divide both sides by [tex]\frac{2}{5}[/tex]

∴ p = -20

To check the answer substitute p by -20 in the equation, the left hand side is equal to the right hand side, then the answer is right

∵ left hand side = [tex]\frac{3}{5}(-20)+\frac{1}{5}(40-(-20))[/tex]

∴ left hand side = [tex]\frac{-60}{5}+\frac{1}{5}(40+20)[/tex]

∴ left hand side = [tex]\frac{-60}{5}+\frac{60}{5}[/tex]

∴ left hand side = 0

∵ Right hand side = 0

∴ Left hand side = Right hand side

∴ The value of p makes the equation true

The value of p that makes the equation true is -20

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Answer:

-20

Step-by-step explanation:

Answer:No

Step-by-step explanation:

Final answer:

A quadratic function with zeros at -5 and -6 can be written as f(x) = (x + 5)(x + 6), which expands to f(x) = x² + 11x + 30.

Explanation:

To write a quadratic function whose zeros are -5 and -6, you start by remembering that if α and β are the zeros of a quadratic function, the function can be written as f(x) = a(x - α)(x - β) where a is a nonzero coefficient. In this case, -5 and -6 are the zeros, so our function is f(x) = a(x + 5)(x + 6).

For simplicity, if we choose a to be 1, the quadratic function simplifies to

f(x) = (x + 5)(x + 6)

f(x) = x² + 11x + 30.

Therefore, the quadratic function with zeros at -5 and -6 is f(x) = x² + 11x + 30.

Answer:

x=4

Step-by-step explanation:

10x-7x=12

3x=12

divide both sides by 3

x=4

Answer: x = 4

Step-by-step explanation: To solve this equation, we can first combine our like terms on the left side of the equation which are the x's.

10x - 7x = 3x so we now have the equation 3x = 12.

Now to solve for x, we want to get x by itself on the left side of the equation. Since x is being multiplied by 3, to get x by itself, we need to divide by 3 on the left side of the equation. Since we divided by 3 on the left side, we must also divide by 3 on the right side.

On the left side, notice that the 4's cancel out so we're simply left with x. On the right side we have 12 divided by 3 which is 4 so x = 4.

Finally, remember to check your answer by substituting a 4 back into the original equation.

So we have 10(4) - 7(4) = 12 or 40 - 28 = 12 or 12 = 12.

Since this a true statement, we know our answer is correct.

Remember to show all your work when solving equations.

Answer:

30 students

Step-by-step explanation:

check the photo

Answer: Order if operations

Step-by-step explanation:

15-10n+12n

15+12n

Answer:

The volume of the observatory is 497.43 [tex]feet^{3}[/tex]

Step-by-step explanation:

i) The diameter of the floor is 10 feet. The floor is circular and has a radius,          

    r =  [tex]\frac{10}{2}[/tex] = 5 feet.

   Therefore the area of the circular floor of the observatory

     = [tex]\pi r^{2}[/tex]      =   3.14159 × [tex]5^{2}[/tex]    =    78.54 [tex]feet^{2}[/tex]

ii) The observatory is made up of two parts

  a)  3 foot tall cylinder

      ∴ volume of cylinder = [tex]\pi r^{2}[/tex]   × h

                                         = 78.54 × 3

                                         = 235.62 [tex]feet^{3}[/tex]

   b)  hemisphere = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3} \pi r^{3}[/tex] = 0.6667 × 78.54 × 5   =  261.81 [tex]feet^{3}[/tex]

    c) Therefore the total volume of the observatory is = a) + b)

         = 235.62 + 261.81 =   497.43 [tex]feet^{3}[/tex]

Answer:

C.g(x) = 5x²

Step-by-step explanation:

To find the equation for the function g(x), use the format for a quadratic equation. Without any up/down and left/right shifts, the form is y = ax².

Substituting "x" and "y" into the equation tells you if a point is on the graph.

"a" tells you the vertical stretch (greater than 1) or compression (greater than 0, less than 1).

In f(x) = x², a = 1 even though it's not written.

Use the point (1, 5) on g(x) and substitute it into the form for a quadratic function. Remember points are (x, y), so x = 1 and y = 5.

g(x) = ax²    

y = ax²       In function notation, g(x) replaces the "y". Switch it back to "y".

5 = a(1)²     Substitute x = 1 and y = 5

5 = a(1)     Solve the exponent first. (1)² = 1

5 = a         When you multiply "a" by 1, the answer is just "a".

a = 5         Solved for "a". Put variable on left side for standard formatting.

With the quadratic form, substitute "a" into g(x).

y = ax²

g(x) = 5x²