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Vladimir79 [104]
3 years ago
14

(x – 4)(x + 10) = -17

Mathematics
1 answer:
pogonyaev3 years ago
4 0

Answer:

-3 +   4sqrt(2)

-3  -  4sqrt(2)

Step-by-step explanation:

(x – 4)(x + 10) = -17

FOIL on the left hand side  (First outer inner last)

x^2 +10x-4x-40 = -17

x^2 +6x-40 =-17

Add 17 to each side

x^2 +6x-40+17 =-17+17

x^2 +6x -23 = 0

Using the quadratic formula

-b + - sqrt(b^2 -4ac)

-------------------------------

   2a        

where ax^2 +bx+c=0

-6 + - sqrt(6^2 -4*1*-23)

-------------------------------

   2*1

-6 + - sqrt(36 +92)

-------------------------------

   2

-6 + - sqrt(128)

-------------------------------

   2

-6 + -  8sqrt(2)

-------------------------------

   2

Divide top and bottom by 2

-3 + -  4sqrt(2)

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At RSM summer camp 100 students had enough food for a 30-days stay. After 2 days 40 new students joined the camp. After that 2 w
omeli [17]

Answer:

"no additional days of food need to be ordered."

Step-by-step explanation:

Suppose initial quantity of food is x units

Assuming each student eats 1 unit of food per day,

x = 30 * 100 = 3000 units of food

In 2 days, food eaten:

100 * 1 * 2 = 200 units

So food left after 2 days is  3000 - 200 = 2800 units

Now, there are 140 students. They stay 2 weeks (14 days) - 2 = 12 more days

So food eaten in 12 days:

140 * 1 * 12 = 1680 units

<u>THus, after total 14 days gone, the amount of food left is:</u>

2800 - 1680 = 1120 units

Half students left, so there are 70 students left for the last 16 days. How much food would they need?

70 * 1 * 16 = 1120 units

And there are exactly 1120 units left. So, no additional days of food need to be ordered.

6 0
3 years ago
if you deposit 4500 at 5% annual interest compounded annually how much money will be in the account after 30 months
Alja [10]

Answer:

A = $ 50,978.44

Step-by-step explanation:

First, convert R percent to r a decimal

r = R/100

r = 5%/100

r = 0.05 per year,

Then, solve our equation for A

A = P(1 + r/n)nt

A = 45,000.00(1 + 0.004166667/12)(12)(2.5)

A = $ 50,978.44

8 0
3 years ago
Rewrite each fraction in simplest form using the GCF of the numerator and denominator.
Elanso [62]

Answer:

\sf 6. \quad \dfrac{7}{10}

\sf 7. \quad \dfrac{5}{17}

Step-by-step explanation:

<h3><u>Question 6</u></h3>

To find the greatest common factor (GCF), first list the prime factors of each number:

  • 42 = 2 × 3 × 7
  • 60 = 2 × 2 × 3 × 5

42 and 60 share one 2 and one 3 in common.

Multiply them together to get the GCF:  2 × 3 = 6.

Therefore, 6 is the GCF of 42 and 60.

Divide the numerator and the denominator by the found GCF:

\implies \sf \dfrac{42 \div 6}{60 \div 6}=\dfrac{7}{10}

<h3><u>Question 7</u></h3>

To find the greatest common factor (GCF), first list the prime factors of each number:

  • 80 = 2 × 2 × 2 × 2 × 5
  • 272 = 2 × 2 × 2 × 2 × 17

80 and 272 share four 2s in common.

Multiply them together to get the GCF:  2 × 2 × 2 × 2 = 16.

Therefore, 16 is the GCF of 80 and 272.

Divide the numerator and the denominator by the found GCF:

\implies \sf \dfrac{80 \div 16}{272 \div 16}=\dfrac{5}{17}

5 0
2 years ago
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Oduvanchick [21]

Answer:

rule add 15 subtract 10

Step-by-step explanation:

rule add 15 subtract 10

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A study was done on the batting averages for two baseball players: Hitmore and Bunter. Data were collected over a period of time
amm1812

Answer:

Both (B) and (C) are correct

Step-by-step explanation:

Explaining in simple terms, The Simpson's paradox simply describes a phenomenon which occurs when observable trends in a relationship, which are obvious during singular evaluation of the variables disappears when each of this relationships are combined. This is what played out when hitmire appears to d well on both of natyraknamd artificial turf when separately compared, but isn't the same when the turf data was combined. Also, performance may actually not be related to the turf as turf may Just be. a lurking variable causing a spurious association in performance.

4 0
3 years ago
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