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3 years ago

Explain how you know that x^2-8x+20 is always positive. Please help.

Mathematics

1 answer:

IRISSAK [1]3 years ago

4 0

Answer:

if you rearrange to complete the square, you get (x^2-4)^2 +4

and seeing as anything squared will always be positive or zero, the lowest possible value for (x^2-4)^2 is 0, when x = 4

and 0 + 4 = 4, which is greater than 0, so positive

Step-by-step explanation:

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a 24 foot tall streetlight casts a shadow that is 18 feet long. how long of a shadow is cast by a nearby parking meter post that

Elanso [62]

9514 1404 393

Answer:

3 ft

Step-by-step explanation:

The post is 4/24 = 1/6 as tall as the streetlight, so we expect its shadow to be 1/6 as long as that of the streetlight:

(1/6)(18 ft) = 3 ft

The parking meter post shadow is 3 feet long.

3 0

3 years ago

Gianna paid $4.75 for a strawberry smoothie. She now has $12.35. How much money did Gianna have before she bought the smoothie?

Leokris [45]

Answer: add 4.75 to both sides, 12.35+ 4.75 = 17.10

Step-by-step explanation:

For both of these, the total she had before the smoothie can be found by adding the cost of the smoothie back to the amount she has left.

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3 years ago

Read 2 more answers

What is the missing constant term in the perfect square that starts with x^2+2x?

Natasha_Volkova [10]

Answer:

+ 1

Step-by-step explanation:

Given

x² + 2x

Using the method of completing the square

add ( half the coefficient of the x- term)² to x² + 2x

= x² + 2(1)x + 1²

= x² + 2x + 1

= (x + 1)² ← perfect square

4 0

3 years ago

Suppose you have 5 riders and 5 horses, and you want to pair them off so that every rider is assigned one horse (and no horse is

maw [93]

There are 120 ways in which 5 riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways $^nN_r = \frac{n!}{(n-r)!}$ ,

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways $^nN_r = \frac{n!}{(n-r)!}$ ,

Now,

Substituting values,

We get,

$^5N_5 = \frac{5!}{(5-5)!}$

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5 riders and 5 horses can be arranged.

Learn more about arrangements here

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7 0

2 years ago

Which is the same as moving the decimal point 3 places to the right in a decimal number

BlackZzzverrR [31]

Answer:

Moving the decimal 3 places to the right in a decimal number is the same as multiplying the number by 1000.

8 0

3 years ago