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GenaCL600 [577]
2 years ago
8

Mathematicians 4: Who is Who?

Mathematics
1 answer:
larisa86 [58]2 years ago
6 0

Answer:

a. x = -9 or x = -2

b. -5(x - 4)

c. x = -3 or x = 5

d. x = ±7

Step-by-step explanation:

a. First person;

y = x² + 11x + 18

y = x² + 9x + 2x + 18

y = x(x + 9) + 2(x + 9)

y = (x + 9)(x + 2)

y = x = -9 or x = -2

b. Second person;

y = -5x + 20

The common factor is 5.

y = -5(x - 4)

c. Third person;

y = x² - 2x - 15

y = x² - 5x + 3x - 15

y = x(x - 5) + 3(x - 5)

y = (x + 3)(x - 5)

y = x = -3 or x = 5

d. Fourth person;

y = x² - 49

Applying the difference of squares formula;

(a² - b²) = (a - b)(a + b)

y = x² - 49 = x² - 7² = (x - 7)(x + 7)

y = (x - 7)(x + 7)

y = x = ±7

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Find the area of the shaded region.
RoseWind [281]

Answer: 51 in²

Step-by-step explanation: Using the given diagram, we can find the area of the shaded region by taking the area of the larger rectangle minus the area of the area of the small rectangle.

To find the area of the large rectangle, we start with the formula for the area of a rectangle which is shown below.

Area = length · width

Since the length of the large rectangle is 15 in and the width is 5 in, we can plug this information into the formula to get 15 in · 5 in or 75 in.

So the area of the larger rectangle is 75 in.

To find the area of the small rectangle, we also use length · width which is simply 8 in · 3 in or 24 in. So the area of the small rectangle is 24 in.

Finally, remember that  the area of the shaded region is the area of the larger rectangle minus the area of the smaller rectangle which in this case will be 75 - 24 or 51

So the area of the shaded region is 51 in².

6 0
3 years ago
A candle shop sells scented candles for $16 each and unscented candles for $10 each. The shop sells 28 candles today and makes $
Rudiy27
<h3><u>The system of linear equations that represents the situation is:</u></h3>

a + b = 28

16a + 10b = 400

<h3><u>20 scented candles and 8 unscented candles were sold</u></h3>

<em><u>Solution:</u></em>

Let "a" be the number of scented candles sold

Let "b" be the number of unscented candles sold

From given,

Cost of 1 scented candles = $ 16

Cost of 1 unscented candles = $ 10

<em><u>The shop sells 28 candles today</u></em>

Therefore,

a + b = 28

b = 28 - a ------- eqn 1

<em><u>The shop sells 28 candles today and makes $400</u></em>

Therefore,

number of scented candles sold x Cost of 1 scented candle + number of unscented candles sold x Cost of 1 unscented candles = 400

a \times 16 + b \times 10 = 400

16a + 10b = 400 ------ eqn 2

<em><u>Substitute eqn 1 in eqn 2</u></em>

16a + 10(28 - a) = 400

16a + 280 - 10a = 400

6a = 400 - 280

6a = 120

a = 20

<em><u>Substitute a = 20 in eqn 1</u></em>

b = 28 - 20

b = 8

Thus 20 scented candles and 8 unscented candles were sold

7 0
3 years ago
A recipe calls for 3/4 cups of flour. If you need to split the recipe in half, how much flour would be needed?
amid [387]
3/4 * 1/2= 3/8

  3      1      3
___*___=____
  4      2      8

3/8 cups of flour
6 0
3 years ago
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N equation is shown below:
QveST [7]
12x -6 = 1 then 12x =7
7 0
3 years ago
18. Jackie drives 160 miles from Gary, Indiana to
astra-53 [7]

Answer:

11 hours and 15 minutes (11.25)

Step-by-step explanation:

make a ratio

160:4.5

240/160=1.5

so 1 and 1/2 intervals of 4.5 hours

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4.5/2=2.25

9+2.25=11.25

6 0
3 years ago
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