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forsale [732]
3 years ago
11

The line is translated 2 units down which equation will best describes the new line

Mathematics
1 answer:
ss7ja [257]3 years ago
6 0

Answer:

The y intercept should be 2 lower than the original equation

Step-by-step explanation:

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Write y = x2 + 24x + 144 as a square of binomial.
irina1246 [14]

Answer:

y=(x+12)^2\\

Step-by-step explanation:

To write a quadratic equation into binomial form we can compare the equation into the completing square form of a quadratic equation like this ,

y=a(x-h)^2+k

now since,

y=x^2+24x+144

we can equate both the equations from left hand side to right hand side like this,

x^2+24x+144=a(x-h)^2+k\\

now we solve,

x^2+24x+144=a(x-h)^2+k\\x^2+24x+144=a((x)^2-2(x)(h)+(h)^2)+k\\x^2+24x+144=a(x^2-2hx+h^2)+k\\x^2+24x+144=ax^2-2ahx+ah^2+k\\

now we compare the coefficients of x^2:

1 = a\\

now we compare the coefficients of x :

24=-2ah\\24=-2(1)h\\24=-2h\\\frac{24}{-2}=h\\-12=h\\

now we compare the constants , (constants are the letters which are not associated with any variable in this case the variable is x)

144 = ah^2+k\\144=(1)(-12)^2+k\\144=(1)(144)+k\\144=144+k\\144-144=k\\0=k\\

so now the value we got all the values for the completing square form we plug those in , a = 1 , h = -12 , k = 0 ,

y=a(x-h)^2+k\\y=1(x-(-12))^2+0\\y=(x+12)^2\\

this is the square of a binomial, if you want to verify if we expands this formula by the formula of (a + b)^2 we would get the same result. Thus this is the correct answer.

5 0
3 years ago
Find a recursive rule for the nth term of the sequence.<br><br> -8, 3, 14, 25, ...
LuckyWell [14K]

Answer:

Step-by-step explanation:

a1=-8

a2=3

D=11

n=-8+11(n-1)

3 0
3 years ago
Read 2 more answers
Separate the number 219 into three parts. The second number is two less than 5 times the first number, and the third number is 4
Sav [38]
Let us assume the first number = x
Then the second number = 5x -2
The third number = x + 4
The total number that needs to be divided into three parts is 219
Then we can write the equation as
x + 5x - 2 + x + 4 = 219
7x + 2 = 219
7x = 219 - 2
7x = 217
x = 217/7
  = 31
Then
First number = 31
Second number = 5x - 2
                           = (5 * 31) - 2
                           = 155 -2
                          = 153
Third number = x + 4
                       = 31 + 4
                       = 35
So the three numbers are 31, 153 and 35.
4 0
3 years ago
Of the numbers listed below, which are<br> NOT multiples of 4?<br> 2, 4, 7, 8, 12, 15, 19, 24, 34
Vedmedyk [2.9K]

Answer:    a multiple is a number that can be divided by another number without a remainder.

Step-by-step explanation: so what is not a multiple of four would be 2, 7, 15 19, 34.

5 0
3 years ago
Read 2 more answers
A basketball player tempts 15 shots in a game. He makes 9 of his attempted shots. What ratio describes the number of baskets the
Vladimir [108]

Answer:

9 to 15 = 9/15 = 3/5 = 3:5 = 3 to 5

Step-by-step explanation:

made: 9

attempted: 15

ratio of made to attempted shots: 9 to 15 = 9/15 = 3/5

8 0
3 years ago
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