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sashaice [31]
3 years ago
14

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

Mathematics
2 answers:
svetoff [14.1K]3 years ago
8 0
Given: y = 2x^2 - 32x + 56

1) y = 2 [ x^2 - 16x] + 56

2) y = 2 [ (x - 8)^2 - 64 ] + 56

3) y = 2 (x - 8)^2 - 128 + 56

4) y = 2 (x - 8)^2 - 72 <----------- answer

Minimum = vertex = (h,k) = (8, - 72)

=>  x-ccordinate of the minimum = 8 <-------- answer
Tasya [4]3 years ago
7 0

Step-by-step explanation:

y = 2x^2-32x+56

y=2(x^2-16x+28)

Adding and subtracting 64 :

y=2(x^2-16x+64-64+28)[tex]y=2(x^2-16x+64) +2(-64+28)

y=2(x^2-2\times x\times 8+8^2) +2(-36)

Using identity : (a+b)^2=a^2-2ab+b^2

y=2\times (x-8)^2-72

y=2\times (x-8)^2+(-72)

Putting, x = 8

y=2\times (8-8)^2+(-72)

y = -72

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The endpoints of the diameter of a circle are (−2, −3) and (4, −1). Which equation represents the circle?
Alika [10]

Answer:

The equation of circle is (x-1)^{2}+(y-2)^{2} = 18

Step-by-step explanation:

Given the endpoints of the diameter of a circle: (-2,-3) and (4,-1)

We know that the equation of circle is

(x-h)^{2} + (y-k)^{2}= r^{2}

where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.

To find (h,k): the center is midpoint of diameter

Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by

(  \frac{x1+x2}{2} , \frac{y1+y2}{2}  )

( \frac{-2+4}{2} , \frac{-3-1}{2}  )

(1,2)

Hence (h,k) is (1,2)

Substituting values of (h.k) and (x.y) as (1,2) and (4,-1) respectively in equation of circle, we get

(4-1)^{2} +(-1-2)^{2} = r^{2}

r^{2} = 18

Now substituting values of (h,k) and r^{2} in equation of circle, we get

(x-1)^{2}+(y-2)^{2} = 18

Hence the equation of circle is (x-1)^{2}+(y-2)^{2} = 18

5 0
3 years ago
Read 2 more answers
A baseball team played 130 games in a season. If it won sixteen more games
egoroff_w [7]

Answer:

The team has 92 wins and 38 losses.

Step-by-step explanation:

In a season 130 games are played by a baseball team.

Let us assume that the team wins x games and losses y games.

Therefore, we can write, x + y=130....... (1)

It is given that if the team won sixteen more games twice as many games as it lost.

So, we can conclude that x =2y+16 ......(2)

Hence, solving equations (1) and (2) we get, (2y+16) + y =130

⇒ 3y = 114

⇒ y =38

And from equation (2), x = 2×38 + 16 = 92

Therefore, the team has 92 wins and 38 losses. (Answer)

4 0
2 years ago
6. On a bank account of $2,500, how much yearly interest will be paid if the rate is3.4%?
iVinArrow [24]

Multiply the amount in the account by the interest rate:

2500 x 0.034 = 85.00

Answer: $85.00

5 0
2 years ago
Solve for a = ____.<br><br> 1. 6<br> 2. 4<br> 3. 9
garik1379 [7]
The answer is 3, or 9
8 0
2 years ago
If 1 euro is priced at $1.25 and if 1 euro will also buy 88 Japanese yen (€1 = ¥88), in equilibrium, with no arbitrage opportuni
Alborosie

Answer:

So the exchange rate is that each dollar is worth 70.4 yens.

Step-by-step explanation:

We have that:

1 euro is priced at $1.25

1 euro will also buy 88 Japanese yen

This also means that:

$1.25 is priced at 88 Japanese yen

How much is the cross rate between the yen and the dollar (yen per dollar exchange rate)?

How much yens is 1 dollar?

This can be solved by a simple rule of three.

$1.25 - 88 yen

$1 - x yen

1.25x = 88

x = \frac{88}{1.25}

x = 70.4

So the exchange rate is that each dollar is worth 70.4 yens.

5 0
3 years ago
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