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3 years ago

7

Hat is the greatest common factor of 20 and 36? 2 4 5 6

1 answer:

aleksklad [387]3 years ago

3 0

4 is the GCF of 20 and 36

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Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

6 0

3 years ago

jeanine Baker makes floral arrangements. She has 13 different cut flowers and plans to use 7 of them. How many different selecti

Ksju [112]

A total of 1,716 selections of the 7 flowers are possible.

Step-by-step explanation:

Step 1:

There are 13 flowers from which Jeanine Baker plans to use 7 of them.

To determine the number of selections that are possible we use combinations.

The formula for combinations is; $^{n} C_{r}=\frac{n !}{(n-r) ! r !}$ .

Step 2:

In the given formula, n is the total number of options and r is the number of options to be selected.

For this question, $n = 13$ and $r=7$ .

So $^{13} C_{7}=\frac{13 !}{(13-7) ! 7 !} = \frac{13 !}{(6) ! 7 !} = 1,716.$

So a total of 1,716 selections are possible.

3 0

3 years ago

What is the integer square root of 29

crimeas [40]

Answer:

5.38516480713

Step-by-step explanation:

I hope this helps.

3 0

2 years ago

Solve the equation for the unknown variable.

olga nikolaevna [1]

Answer:

b x 3 = 8

=> b = 8/3

Hope this helps!

:)

4 0

3 years ago

Garry wants to have $750,000 in 30 years. How much does he have to invest per month in an annuity with an annual interest rate o

Nikolay [14]

I think the answer is Garry has to invest 2,035 dollars a month for 30 years to reach his goal of 750,000 dollars

4 0

3 years ago