Complete the expression that represents the prime factorization of 492.



Type the factors in the increasing order.


492 = 2 × 2×
×

The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)

The distance between points, P and Q can be evaluated by the Pythagoras theorem as follows;

Therefore, a point whose distance from both P and Q is exactly 13 is the midpoint of PQ.

Therefore,

The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)

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Answer:

1. 3 tacos per person

2. 8 chairs per table

3. 6 avocados per bag

Step-by-step explanation:

1. Divide 45 by 15 to get the unit rate: # of taco per person.

45 = 15x

45/15 = 15x/15

3 = x

3 tacos per person

2. Divide 72 by 9 to get the unit rate: # of chairs per table.

72 = 9x

72/9 = 9x/9

8 = x

8 chairs per table

3.  Divide 42 by 7 to get the unit rate: # of avocados per bag.

42 = 7x

42/7 = 7x/7

6 = x

6 avocados per bag

Answer:

see explanation

Step-by-step explanation:

The following statements are true

The domain of f(x) is all real numbers

The range of f(x) is all real numbers

f(2) = 4

locate x = 2 on the x- axis, go vertically up to meet the line at (2, 4 ) , then

f(2) = 4

Answer:

M = -2 1/4

Step-by-step explanation:

You can use the formula y2 - y1 / x2 - x1 to get your answer.

y2 is 18 and y1 is 9. x2 is 6 and x1 is 10 so plugging that into the formula above you will get 18 - 9 / 6 - 10.

18 - 9 is 9 and 6 - 10 is -4

9/-4 = M (M is short for slope)

M = -2 1/4

Hope this worked for you.

Answer:

C=66, C=25 1/7

Step-by-step explanation:

i

C=pi(d)

C=22/7*21

C=66

ii

C=pi(d)

C=22/7*16

C=25 1/7

Answer:

7.22 x 10^5

Step-by-step explanation:

Remember that the decimal is always to the right of the ones place.

1. Move it one place to the left and multiply by 10 to compensate.

2. Move it two places to left and multiply by 10^2.

3. Move the decimal point three times and multiply 10^3 to compensate, and the pattern continues until you reach the very last digit, the 7.

4. Numbers after the 7 that are not zeros will be after the decimal point.

so, 7.22 x 10^5

Answer:

You can make as many as you want, infinitely smaller but you need to specify the size of the brownies

Step-by-step explanation:

Answer:

ui100

Step-by-step explanation:

125

The temperature of a pan of water on the stove after 5 minutes would be 40°C.

Temperature is the measure of the degree of hotness and coldness which is expressed in different scales.

The temperature of a pan of water increases steadily from 22°C to 100°C at a rate of 8°C per minute.

We need to find the temperature after 5 minutes.

Rate of temperature per minute = 8°C

Rate of temperature after 5 minutes = 8°C × 5

                                                            = 40°C

Therefore, the temperature after 5 minutes would be 40°C.

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Answer:

$40,516.86

Step-by-step explanation:

start by taking 35,000 and multiplying it by 0.05 to get 5% of the number. then add that number (1,750) to the original 35,000 and you should get 36,750. this would be the first year. Then multiply 36,750 by 0.05 again and add that number (1837.5) to the original 36,750 and you should get 38,587.5. Finally multiply that by 0.05 and add that number (1,929.375) to the original 38,587.5 and you should get 40516.875. Round to the hundredths since it is money.

Answer:

x = 17

Step-by-step explanation:

∠ DCE = ∠ ACE ( vertically opposite angles )

The sum of the 3 angles in a triangle = 180° , then

∠ DCE = 180° - (100 +x) = 180 - 100 - x = 80 - x

∠ ACE = 180 - (49 + 4x) = 180 - 49 - 4x = 131 - 4x

Equating the 2 angles

80 - x = 131 - 4x ( add 4x to both sides )

80 + 3x = 131 ( subtract 80 from both sides )

3x = 51 ( divide both sides by 3 )

x = 17

Answer:

You can use the exponential rule where

[tex](n^x)^y=n^{xy}[/tex]

Therefore,

[tex](a^3)^{-2}=a^{3*(-2)}=a^{-6}[/tex]

[tex]\\ \rm\leadsto (a^3)^{-2}[/tex]

[tex]\\ \rm\leadsto a^{-6}[/tex]

[tex]\\ \rm\leadsto \dfrac{1}{a^6}[/tex]

x + -13 = 22

Reorder the terms:

-13 + x = 22

Solving

-13 + x = 22

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13' to each side of the equation.

-13 + 13 + x = 22 + 13

Combine like terms: -13 + 13 = 0

0 + x = 22 + 13

x = 22 + 13

Combine like terms: 22 + 13 = 35

x = 35

Simplifying

x = 35

Answer:

Quotient is basically division.

Step-by-step explanation:

1329/4 is basically

332.25 is the answer

Answer:

x≤5/3

So any number at 5/3 or above is a solution

Step-by-step explanation:

Subtract 4 on both sides:

5≤3x

Divide 3 on both sides

x≤5/3

So any number at 5/3 or above is a solution

Hope this helps!

Answer:

2400

Step-by-step explanation:

60(customers/day) x40(days) = 2400 customers in 40 days

Answer:

2 months

Step-by-step explanation:

To solve this equation create an expression for the cost of each club. Use the slope-intercept form of y=mx+b where m is the monthly fee and b is the flat fee. So the 2 expressions would be A) 29x+14 and B) 22x+28. Since we want to find when these are equal, set the expressions equal to each other. This gives the equation 29x+14=22x+28. Then, solve for x.

When solved, x=2. This means that after 2 months the cost of each will be the same.

Answer:

1st , 2nd , and 4th

Step-by-step explanation:

Answer:

For the question a i think its b

Step-by-step explanation:

Answer:

500: starting amount

(1 + 0.02): interest/growth rate

x: time

Step-by-step explanation:

Answer:

(serial number, model number)Step-by-step explanation:

Using similar triangles formed by the fence, and the house, the top of which the property line passes, the height of the house can be determined.

Reasons:

The given parameters are;

Height of the fence = 12 foot

Length of the shadow cast by the fence = 25 foot

Distance of the house from the property line = 60 feet

The maximum allowable height for the house.

Solution:

Using similar triangles, we have;

[tex]\displaystyle \frac{Height \ of \, fence}{Length \ of \ fence \ shadow} = \mathbf{\frac{Height \ of \, house}{Distance \ of \ house\ from \ property \ line}}[/tex]

Which gives;

[tex]\displaystyle \frac{12}{25} = \mathbf{\frac{Height \ of \, house}{60}}[/tex]

[tex]\displaystyle Height \ of \ house = \frac{12}{25} \times 60 = 28.8[/tex]

The height of the house = 28.8 feet

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Please find attached the drawing of the question created with MS Visio, obtained from a similar question online.

Answer:

7 Seconds

Step-by-step explanation:

This is kinematics

Vf=Vi+at

t=[tex]\frac{Vf-Vi}{a}[/tex]

t=[tex]\frac{62-13}{7}[/tex]

t=[tex]\frac{49}{7} =7[/tex]

Answer:

(2;5)

Step-by-step explanation:

Elimination:

Let's first multiply the first by 2 to clear fractions and write them both in standard form:

[tex]\left\{ {x-2y=-8} \atop {2x+y=9}} \right. \\[/tex]

Eliminate x: Multiply the first by 2, then subtract the equations:

[tex]2I-II: 2x-4y-2x-y=-16-9\\-5y=-25 \rightarrow y= 5[/tex]

Eliminate y: Multiply the second by 2, then add equations:

[tex]I+2II: x-2y +4x+2y = -8+18\\5x=10 \rightarrow x=2[/tex]

Subtsitution

Solve the first for y (oh, what a coincidence, it's done already!) and replace the value in the second.

[tex]\frac12x +4 = -2x+9 \rightarrow \ x+8=-4x+18\\x+4x = 18-8 \rightarrow 5x=10 \rightarrow x=2[/tex]

Then let's plug this value into a convenient one - let's say, the first - and find y from there:

[tex]y=\frac12\cdot 2 +4\rightarrow y =1+4 \rightarrow y=5[/tex]

If anyone tries saying it's not substitution, bring the system in standard form, as you did for the elimination method, then solve again for y.

Answer:

16, 32, and 64

Step-by-step explanation:

The number is being doubled every time.

we have 9x - 7 ≤ 28 + 4x

⇔9x - 4x ≤ 28 +7

⇔5x ≤ 35

⇔x ≤ 7

ok done. Thank to me :>

[tex]\\ \sf\longmapsto (x-2)(x+1)[/tex]

[tex]\\ \sf\longmapsto x(x+1)-2(x+1)[/tex]

[tex]\\ \sf\longmapsto x^2+x-2x-2[/tex]

[tex]\\ \sf\longmapsto x^2-x-2[/tex]

Answer:

x = 5

Step-by-step explanation:

24 - 8x = -16

Subtract 24 from both sides.

-8x = -40

Divide both sides by -8.

x = 5

Answer:

5

Step-by-step explanation:

24 - 8x = -16

24 + 16 = 8x

8x = 40

x = 40/8

= 10/2

= 5

Answer:

  £2.76

Step-by-step explanation:

The cost of Amy's purchase is ...

  16×(£0.14) = £2.24

Her change from £5.00 is ...

  £5.00 -2.24 = £2.76 . . . . Amy's change

Answer:

x=5

Step-by-step explanation: