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Blababa [14]
3 years ago
5

Solve and simply using prime factorization please

Mathematics
1 answer:
alex41 [277]3 years ago
7 0

Step-by-step explanation:

these look easy you can probably just type it into a calculator, just show your work.

not sure where you got 20 from on the first problem it should be 9/12 I think, based on the examples at the top of the page.

1. 9/12

2. 16/22

3. 30/36

4. 28/44

5. 45/55

6. 50/60

The "/" indicates division btw and or fraction

then do the #x#x#x#x# thing you were doing

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The area of the yellow region is 112 cm^2. find the value of x​
mrs_skeptik [129]
<h3>Answer:   x = 7</h3>

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

Explanation:

The largest rectangle (composed of the green and yellow sections combined) has area of 11*12 = 132 cm^2.

The yellow region takes up 112 of those 132 sq cm. This must mean the green region takes up 132-112 = 20 cm^2.

The horizontal portion of the green rectangle is 12-x cm. The vertical portion is 11-x cm. We can form the area of the green rectangle as an algebraic expression like so

area = length*width

area = (11-x)*(12-x)

area = 132 - 11x - 12x + x^2 .... apply the FOIL rule

area = x^2 - 23x + 132

Set this equal to the 20 cm^2 we found earlier.

x^2 - 23x + 132 = 20

x^2 - 23x + 132-20 = 0

x^2 - 23x + 112 = 0

We could factor or we could use the quadratic formula. I'll go with the second option.

We'll plug in a = 1, b =  -23, c = 112

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-23)\pm\sqrt{(-23)^2-4(1)(112)}}{2(1)}\\\\x = \frac{23\pm\sqrt{81}}{2}\\\\x = \frac{23\pm9}{2}\\\\x = \frac{23+9}{2}\ \text{ or } \ x = \frac{23-9}{2}\\\\x = \frac{32}{2}\ \text{ or } \ x = \frac{14}{2}\\\\x = 16\ \text{ or } \ x = 7\\\\

One of these solutions isn't feasible. Note how if x = 16, then this exceeds both the 11 cm and 12 cm sides. So this x value is not possible.

However, x = 7 is possible.

If x = 7, then the horizontal portion of the green rectangle is 12-x = 12-7 = 5 cm. Also, the vertical portion of the green rectangle would be 11-x = 11-7 = 4 cm. The area then is length*width = 5*4 = 20 cm^2 which matches up with what we got earlier. So the answer is confirmed.

7 0
3 years ago
Aria and her children went into a bakery and will buy donuts and brownies. She must buy at least 6 donuts and brownies altogethe
laila [671]

Answer:

Inequality for donuts and brownies is;

d ≥ 1 ≤ b

Step-by-step explanation:

We are told that aria will buy donuts and brownies.

We are also told that, number of donuts is d while number of brownies is b.

We are also told that she must by at least a total of 6 donuts and brownies together. Which means that the sum of d and b must not be 6 or greater than 6.

So the inequality will be;

d + b ≥ 6

Thus, for the donut and brownies, inequality would be; d ≥ 1 ≤ b

4 0
3 years ago
The value of x in the equation 4^(2x+5)=8^(3x)
Roman55 [17]
4⁽²ˣ ⁺ ⁵⁾ = 8³ˣ

But 4 = 2²  and 8 = 2³

4⁽²ˣ ⁺ ⁵⁾ = 8³ˣ

2²⁽²ˣ ⁺ ⁵⁾ = (2³)³ˣ

Multiply out the powers, also since the
 
 2⁴ˣ ⁺ ¹⁰ = 2⁹ˣ

Since the bases are the same, hence the powers are also the same.

4x + 10 = 9x

4x - 9x = -10

-5x = -10

x = -10/-5

x = 2

Hope this explains it.
3 0
3 years ago
Asap! find the length of the arc
Fantom [35]

<u>Answer</u>:

A.  \frac{21}{4} \pi\ \space\ in

<u>Step-by-step explanation:</u>

The formula for arc length is:

arc length = rθ

where:

r is the radius = 7 in

θ is the central angle in radians = 135  ×  \frac{ \space\ \pi\ }{180}  = 3/4 π

Substituting these values into the formula:
arc length = 7 in × 3/4 π

                 = \frac{21}{4} \pi\ \space\ in

                             

6 0
1 year ago
A woman jogs for 2 km at 8 km/h and then walks for 2 km
Artemon [7]

Answer:

  6 6/7 km/h

Step-by-step explanation:

The relations between speed, time, and distance are ...

  time = distance/speed

  speed = distance/time

__

So, to find the average speed, we need to know the total distance and the total time. The distances are given, but we need to compute the times.

  time jogging = (2 km)/(8 km/h) = 1/4 h

  time walking = (2 km)/(6 km/h) = 1/3 h

Then the woman's average speed is ...

  average speed = (total distance)/(total time) = (2 km + 2 km)/(1/4 h + 1/3 h)

  = (4 km)/(7/12 h) = 48/7 km/h

  = 6 6/7 km/h

3 0
2 years ago
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