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Anika [276]
2 years ago
3

Given that 4x^2-32x-20+k is a perfect square find k​

Mathematics
1 answer:
Alexxandr [17]2 years ago
3 0

Answer:

  • k = 20

Step-by-step explanation:

<u>Perfect square identity:</u>

  • (a + b)² = a² + 2ab + b²

<u>Completing the square:</u>

  • 4x² - 32x - 20 + k =
  • (2x)² - 2*2x*8 + 8² - 20 + k =
  • (2x - 8)² - (20 - k)

<u>In order the given to be a perfect square, we need:</u>

  • 20 - k = 0
  • k = 20

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Kevin says that lines p and m will eventually intersect. Lines A and B intersect. Plane A contains lines p, m, and n. Line n is
ANTONII [103]

Answer:

No, because they are parallel.

Step-by-step explanation:

The lines p and m will not intersect, so Kevin is not correct.

It is given that planes A and B intersects. The plane A contains the line p, m and n on its plane. The lines p and m are parallel to each other. They are identical and move in the same direction.

Since the line p and m are parallel, they will not meet each other at any point because parallel lines does not intersect or meet at a point, they run parallelly along each other.

So, line p and m will not intersect.

Thus the answer is " No, because they are parallel."

8 0
2 years ago
Consider that 1 inch = 2.54 centimeters. Which three statements are true for converting 18 feet to centimeters?
serg [7]

Answer:

There are 548.64 cm in 18 feet.

Step-by-step explanation:

We know that, 1 inch = 2.54 centimeters.

We need to convert 18 feet to centimeters

Also, 1 foot = 12 inch

Firstly we will convert 18 feet to inch.

18 feet = 12 × 18 inch

= 216 inch

Now to convert 18 feet to centimeters, multiply 216 inch by 2.54 cm as follows :

216 inch = 2.54×216 centimeters

= 548.64 cm

Hence, there are 548.64 cm in 18 feet.

4 0
2 years ago
Consider the three functions below. f(x) = Negative StartFraction 6 Over 11 EndFraction (eleven-halves) Superscript x g(x) = Sta
Setler79 [48]

Answer:

The correct option is;

The ranges of f(x) and h(x) are similar and different from the ranges of g(x)

Step-by-step explanation:

Here we have the functions given as follows;

f(x) = -6/11 (11/2)ˣ

g(x) = 6/11 (11/2)⁻ˣ

h(x) = -6/11 (11/2)⁻ˣ

from the above equations, it can be seen that f(x) and h(x) are always negative while g(x) is always positive

f(x) and h(x) are symmetric about the y axis while g(x) and h(x) are symmetric about the x axis

Also h(x) is the inverse of f(x) hence the ranges of f(x) and g(x) are similar and are different from the ranges of g(x).

9 0
2 years ago
Read 2 more answers
Which function will have the steepest graph? y = –2x y =-1/2 x y = 3/2x y =5/2 x
timofeeve [1]
The steepest graph is gonna have the largest slope....but u have to use the absolute value of the slopes to compare

y = -2x.....slope is -2....| -2 | = 2
y = -1/2x...slope is -1/2....| -1/2 | = 1/2
y = 3/2x....slope is 3/2 (or 1 1/2)...| 1 1/2} = 1 1/2
y = 5/2x...slope is 5/2 (or 2 1/2)...| 2 1/2| = 2 1/2

so the steepest graph is : y = 5/2x
4 0
2 years ago
Read 2 more answers
The equations below represent the numbers y of tickets sold after x weeks for two different local music festivals
Anton [14]
Assuming you mean y=10x+150 and y=20x+115, you need to use a simultaneous equation, because you have two equations with two unknowns (x and y)

rearrange so
10x-y=-150
20x-y=-115

multiply the top by -1, so that if we add the two lines together, the y will cancel out
-10x+y=150
20x-y=-115

add the two lines together
10x=35
x=3.5

so the time is 3 and a half weeks

then we can sub in x to find y
20x-y=-115
20(3.5)-y=-115
70-y=-115
-y=-185
y=185

so 185 tickets were sold !
you can sub these values into your original equations to check your answer :)
5 0
2 years ago
Read 2 more answers
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