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4 years ago

Complete the square to determine the minimum or maximum value of the function defined by the expression. x2 − 10x + 15

Mathematics

1 answer:

Sphinxa [80]4 years ago

4 0

Answer:

minimum: -10

Step-by-step explanation:

Add and subtract the square of half the x-coefficient:

x² -10x +(-5)² -(-5)² +15

Express the first three terms as a square; simplify the remaining terms.

(x -5)² -10

This expression describes a parabola that opens upward and has its vertex at (x, y) = (5, -10). The minimum value is -10.

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A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a black card, and let F be the

Svetllana [295]

Answer:

$\dfrac{25}{26}$

Step-by-step explanation:

Let

D be the event that the card drawn is a black card
F be the event that the card drawn is a 10 card
F' be the event that the card drawn is not a 10 card

The probability

$Pr(D\cup F')=Pr(D)+Pr(F')-Pr(D\cap F')\\$

Note that

$Pr(D)=\dfrac{26}{52}=\dfrac{1}{2}\\ \\Pr(F)=\dfrac{4}{52}=\dfrac{1}{13}\\ \\Pr(F')=1-\dfrac{1}{13}=\dfrac{12}{13}\\ \\Pr(D\cap F')=\dfrac{24}{52}=\dfrac{6}{13}$

So,

$Pr(D\cup F')=\dfrac{1}{2}+\dfrac{12}{13}-\dfrac{6}{13}=\dfrac{25}{26}$

8 0

3 years ago

Becky Anderson must pay a lump sum of $6000 in 5 yr. If only $5000 is available to deposit right now, what annual interest rate

34kurt

Hello!

Out equation is: $A=P(1+\frac{r}{n} )^t^n$

A= 6000

P=5000

N=1

T=5

R= What we are trying to find

This means we will have $6000=5000(1+r)^5$

Divide both sides by 5000:

$\frac{6000}{5000} = (1+r)^5$

Move the power to the other side by rooting both sides:

$\frac{6000}{5000} ^1^/^5 = 1+r$

Subtract 1 from both sides:

$\frac{6000}{5000} ^1^/^5 -1 = r$

Now we just need to calculate: R = 0.03713728...

I don't know how many decimal places you can have, but I will round to 2. This will give you an Interest Rate of 3.71%.

I hope this helps! :)

6 0

3 years ago

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If a dolls cup holds 2ml, how many cups would it take to fill a doll's 10ml bottle

disa [49]

Answer:

it would take 5 dolls cups

8 0

3 years ago

At Eva’s restaurant, 2/3 of the dishes on the menu are vegetarian. Of the vegetarian dishes, 1/10 are pasta dishes. What fractio

Step2247 [10]

Answer:

1/15 of the dishes on the menu are vegetarian pasta.

Step-by-step explanation:

1/10 of 2/3 of all dishes are vegetarian pasta.

1/10 of 2/3 of all = 1/10 * 2/3 * 1 = 2/30 = 1/15

6 0

1 year ago

What is the percent change of 10 feet to 6 feet

Svetradugi [14.3K]

Answer:It would be a decrease of 40 percent

Step-by-step explanation:You go from 10/10 to 6/10 meaning you decrease by 4/10 and 4/10 is the same as 40/100 and anything over 100 is its percent value so you would be going down by 40%

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4 years ago

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