Find x. 60° 45° 6 ————

1/8+1/3 what is the answer?

kow [346]

Answer:

11/24 as a fraction but a decimal 0.4583 ( the three is recurring)

8 0

3 years ago

Read 2 more answers

The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?

daser333 [38]

Answer:

$d=\frac{3}{2}=1.5$

Step-by-step explanation:

We have the function:

$y=a(x-2)(x-1)$

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are (x-2) and (x-1).

Therefore, our roots/zeros are x=1, 2.

So, the average of them are:

$d=\frac{1+2}{2}=3/2=1.5$

Therefore, regardless of the value of a, the minimum/maximum value will occur at x=d=1.5.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

$y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a$

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

$x=-\frac{b}{2a}$

So, we will substitute -3a for b and a for a. This yields:

$x=-\frac{-3a}{2a}=\frac{3}{2}=1.5$

Confirming our answer.

4 0

3 years ago

A sequence of 7 numbers starts with 8. The second number in the sequence is unknown and may be positive or negative. The third t

scoray [572]

Answer:

4

Explanation:

$a_1=8,a_7=0$

Since the third term is the sum of the two previous terms

$a_3=a_2+a_1$

$a_7=a_6+a_5$

$a_7=a_5+a_4+a_4+a_3$

Continuing in like manner

$a_7=5a_3+3a_2$

Since $a_3=a_2+a_1$

$a_7=5(a_2+a_1+3a_2$

$a_7=5a_2+5a_1+3a_2$

$a_7=8a_2+5a_1$

Recall: $a_1=8,a_7=0$

$0=8a_2+5*8$

$8a_2=-40$

$a_2=-5$

The sequence is therefore:

8,-5,3,-2,1,-1,0

The sum of the seven numbers is 4.

8 0

3 years ago

PLEASE HELP! Will give brainliest!! No scammers please.

laiz [17]

Answer:

Maximizing Profit. Waterbrook Farm includes 240 acres of cropland. The farm owner wishes to plant this acreage in both corn and soybeans. The profit per acre in corn production is $325 and in soybeans is $180.A total of 320 hr of labor is available. Each acre of corn requires 2 hr of labor, whereas each acre of soybean requires 1 hr of labor. How should the land be divided between corn and soybeans in order to yield the maximum profit? What is the maximum profit?

Step-by-step explanation:

3 0

3 years ago

A 15 ounce alloy containing 30% gold was mixed with an alloy containing 5% gold to get an alloy containing 20% gold. How many ou

Studentka2010 [4]

Answer:

4.5 % alloy

Step-by-step explanation:

Let x = amt of 30% alloy

The resulting total is to be 25 oz, therefore:

(25-x) = amt of 5% alloy:

A typical mixture equation:

.30x + .05(25-x) = .20(25)

.30x + 1.25 - .05x = 5 .30x - .05x = 5 - 1.25

.25x = 3.75

x = 3.75%2F.25

x = 15 oz of 30% alloy required

then

25-15 = 10 oz of 5% alloy:

Check solution

.30(15) + .05(10) = .20(25)

4.5 + .5 = 5

4 0

3 years ago

Find x. 60° 45° 6 —————