HURRY!

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Arada [10]

If $y=3x^2+30x+71$ , then
$y=3(x^2+10x)+71=3(x^2+2\cdot5x+25-25)+71$
$y=3((x+5)^2-25)+71=3(x+5)^2-75+71=3(x+5)^2-4$ . So, in the first gap you can write 5 and in the second you can write -4.
Since $(x+5)^2\ge 0$ , the minimum value of y is when $(x+5)^2=0$ . The solution of the last equation is x=-5 and then y=-4 -- these are numbers, which you can write in the third and fourth gaps.

5 0

1 year ago

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It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impa

andreyandreev [35.5K]

Let us say that the procedure of completely filling up the pool with water is called “1 job”. Therefore the rates of the equipment in doing the job would be:

Rate of handheld hose = 1 job / 8 minutes ---> 1

Rate of lawn sprinkler = r ---> 2

Rate of the two combines = 1 job/ 5 minutes ---> 3

So we are to find the equation to use, in this case, we simply have to add equations 1 and 2 to get 3:

1 / 8 + r = 1 / 5

Multiplying both sides by 5:

(5 / 8) + 5 r = 1 ---> ANSWER

8 0

2 years ago

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The library is 1.75 miles directly north from the school. The park is 0.6 miles directly south of the school. How far away is th

Kryger [21]

Answer:

2.35 miles

Step-by-step explanation:

Please find the attachment for visual understanding.

We are told that the library is 1.75 miles directly north from the school and the park is 0.6 miles directly south of the school.

To find distance between library and park we will add distance of library from school to the distance of park from school.

$(1.75+0.6)\text{ miles}=2.35\text{ miles}$

Therefore, library is 2.35 miles away from park.

7 0

2 years ago

1. Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1,

zzz [600]

Answer:

Step-by-step explanation:

Given that Miguel is playing a game

The box contains 4 chips, 2 with number 1, and other two differntly numbered as 3 and 5.

OUt of these 4, 2 chips are drawn

P(drawing same number) = 2C2/4C2 = $\frac{1}{6}$

Prob (drawing differnt numbers) = 1-1/6 = $\frac{5}{6}$

Hence prob of winning 2 dollars = $\frac{1}{6}$

Prob of losing 1 dollar = $\frac{5}{6}$

b) Expected value = sum of prob x amount won

= $\frac{1}{6}2+\frac{5}{6}(-1)=-\frac{1}{2}$

c) Miguel can expect to lose 1/2 dollars for every game he plays

d) If it is to be a fair game expected value =0

i.e. let the amount assigned be s

Then $\frac{1}{6}s-\frac{5}{6}=0\\s=5$

6 0

1 year ago

Read 2 more answers

Shawna has $750 in the bank.she deposits $37.50 each week.Ruben has $850 in the bank.He deposits his paycheck of $102.75 every M

erastova [34]

Answer:

Step-by-step explanation:

Answer: it would take 20 weeks before the amount in both accounts would be the same.

Step-by-step explanation:

Let x represent the number of weeks that it will take either Ruben and Shawna to have the same amount of money in their account.

Let y represent the total amount that would be in Shawna's account after x weeks

Let z represent the total amount that would be in Ruben's account after x weeks

Shawna has $750 in the bank. She deposits $37.50 each week. This means that the total amount after x weeks would be

y = 37.5x + 750

Ruben has $850 in the bank. He deposits his paycheck of $102.75 every Monday,and he spends about $70.25 each week.. This means that the total amount after x weeks would be

z = 850 + 102.75x - 70.25x

z = 850 + 32.5x

To determine the number of weeks before the amount in both accounts will becomes the same, we would equate y to z. It becomes

37.5x + 750= 850 + 32.5x

37.5x - 32.5x = 850 - 750

5x = 100

x = 100/5 = 20

8 0

1 year ago