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Deffense [45]
3 years ago
11

Ariel completes the square for the equation x2 - 16x + 17 = 0. Which of the following equations reveals the vertex of the parabo

la?
A.y = (x - 4)^2 - 47
B.y = (x - 9)^2 - 47
C.y = (x - 6)^2 - 45
D.y = (x - 8)^2 - 47
Mathematics
2 answers:
stealth61 [152]3 years ago
8 0
X² - 16x + 17 = 0
x² - 16x + 8² - 8² + 17 = 0
(x - 8)² - 64 + 17 = 0
(x - 8)² - 47 = 0 

-----------------------------------------------------------------------------------------
Answer: y = (x - 8)² - 47 (Answer D)
-----------------------------------------------------------------------------------------

julsineya [31]3 years ago
8 0

Answer:

Option D is correct

y = (x-8)^-47

Step-by-step explanation:

A quadratic equation is in the form of y=ax^2+bx+c,

then the vertex form of the quadratic equation using the completing square method is given as:

y =(x-h)^2+k where, vertex = (h, k)

As per the statement:

Ariel completes the square for the equation: x^2-16x+17 = 0

Using completing square method:

1.

subtract 17 from both sides we have;

x^2-16x = -17

2.

Complete the square on the left side of the equation and balance this by adding 8^2 = 64 to the right side of the equation.

then;

x^2-16x+8^2= -17+64

Using identity rules on left side:

(a-b)^2 = a^2-2ab+b^2

then;

(x-8)^2 = 47

we can write this as:

y = (x-8)^-47

Therefore, the equations reveals the vertex of the parabola is, y = (x-8)^-47

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3 years ago
Read 2 more answers
A researcher conducted an experiment to study the effects of an herbal supplement on the duration of the common cold. From a sam
OverLord2011 [107]

Answer:

50 people

Step-by-step explanation:

-An experimental unit is any physical entity or person or animal that can be randomly assgned to a treatment.

-Such a unit is usually referred to as a unit of statistical analysis.

-Both control and actual experimental units are units of statistical analysis despite receiving different treatments.

-Hence, the experimental units of the study is 50 people.

3 0
3 years ago
There are nickles and quarters worth $2.20 in total. If there are 28 coins, how many nickels are there?
Eduardwww [97]
Answer:

There are 24 nickels

Step-by-step explanation:

Let x represent the number of nickels

Let y represent the number of quarters
—————————————————————

Value Value
Type Number of of
of of each all
Coin Coin Coin Coin
—————————————————————
Nickels | x | $0.05 | $0.05x
Quarters | y | $0.25 | $0.25y
—————————————————————
Totals 28 ——— $2.20
•••••••••••••••••••••••••••••••••••••••••••••••••

The first equation comes from the “Number of coins” column.

(Number of nickels) + (Number of quarters) = (total number of coins)

Equation: x + y = 28
—————————————————————
The second equation comes from the “value of all coins” column.

(Value of all nickels) + (Value of all quarters) = (Total value of all coins)

0.05x + 0.25y = 2.20

Remove the decimals by multiplying each term by 100:

5x + 25y = 220
—————————————————————
So we have the system of equations:

{x + y = 28
{5x + 25y = 202

Solve by substitution. Solve the first equation for y:

x + y = 28
y = 28 - x

Substitute (28 - x) for y in 5x + 25y = 220

5x + 25 (28 - x) = 220
5x + 700 - 25x = 220
-20x + 700 = 220
-20x = -480
x = 24

The number of nickels is 24.
————————————————————
Substitute in y = 28 - x
y = 28 - (24)
y = 4

The number of quarters is 4.
————————————————————
Checking:

24 nickels is $1.20 and 4 quarters is $1.00
That’s 28 coins.
Indeed $1.20 + $1.00 = $2.20
————————————————————

6 0
3 years ago
Please help I dont understand ​
Studentka2010 [4]

Step-by-step explanation:

When it says y varies directly with x it just means that y and x are proportional/equal to each other. The constant of variation and the constant of proportionality are the same thing just different way of saying it so they can confuse you and make your life miserable. Since y and x are proportional to each other and the constant of proportionalty is -5 to make an equation that represents a line you use the formula y=mx+b. That is the slope of the line. With that formula let's first plus in the x so we have y=m2+b. The formula for direct variation is y=kx as well that's good to know and it's good to memorize all these formulas. Math becaomes easier when you have the process down pat and you just need to plug numbers into different equations, expressions, and scenarios. Do m = [y1 - y2] / [x1 - x2] and you'll get the answer.

7 0
2 years ago
What is the sum of the first 7 terms of the geometric series:
Fiesta28 [93]

Answer:

-15.875

Step-by-step explanation:

First, we can sum up the first 5 terms.

-8 + (-4) = -12

-12 + (-2) = -14

-14 + (-1) = -15

-15 + (-1/2) = -15.5

Next, we can find a pattern in the data. We can tell that the next number is one half of the current number. For example, -4 is one half of -8. To find the next number, we simply multiply our current number by one half. Thus, the sixth number is -1/4 and the seventh is -1/8. Adding these to our current total, we have

-15.5 - 1/4 = -15.75

-15.5 - 1/8 = -15.875 as our answer

4 0
3 years ago
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