Complete the square to rewite y=x^2-6x+15

Mathematics

1 answer:

mixer [17]3 years ago

4 0

$y = {x}^{2} - 6x + 15 \\ y = {x}^{2} - 3.2x + {3}^{2} + 15 - 9 \\ y = {(x - 3)}^{2} + 6$

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Gulf gully and jump rope road are a pretty far distance.If the scale for the map is 0.5 inches=2.3 miles,what is the actual dist

Nezavi [6.7K]

Answer:

12 cm = 21.62 miles

6 cm = 11.04 miles

Step-by-step explanation:

To find the distance, set up a proportion. A proportion is two equal ratios set equal to each other. We form the ratios by using corresponding values. We write a ratio of $\frac{map}{real world}$ and simplify.

We know $\frac{map}{real world}=\frac{0.5in}{2.3 miles}$ . We know the distance on the map is 12 cm and 6 cm whish converts to 4.7 inches and 2.4 inches. We can write $\frac{4.7in}{xmiles}$ and $\frac{2.4in}{xmiles}$

We set them equal.

$\frac{0.5}{2.3}=\frac{4.7}{x}$

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$\frac{0.5}{2.3}=\frac{2.4}{x}$

To solve each proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

$2.3(4.7)=0.5(x)\\10.81=0.5x\\\frac{10.81}{0.5}=\frac{0.5x}{0.5} \\21.62 miles=x$

and

$2.3(2.4)=0.5(x)\\5.52=0.5x\\\frac{5.52}{0.5}=\frac{0.5x}{0.5} \\11.04 miles=x$

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2 years ago

PLZ HELP ME PLZZZ 15 PTS Mr. Rodriguez asked 60 randomly chosen students from each grade level at Willowbrook School about their

vredina [299]

12/60 students chose science fiction

Approximately x/150 students prefer sf

60x = 1800

x = 30

30/150 students are assumed to prefer sf

30/150 = x/100

150x = 3000

x = 20

20/100 students are likely to prefer sf

Mr. Rodriguez made a reasonable estimate for the approximate percentage of students that prefer science fiction, because if 12/60 is equivalent to 30/150 which refers to the number of students who can be assumed to prefer science Fiction out of the whole school. Considering we need to identify what 30/150 as a percentage is, we can reduce it down to 1/5 to make I easier, then divide 1 by 5 to get .2
.2 as a percentage is 20%, so his inference was indeed reasonable.

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