[50 points] i don't even understand

convert these unlike fractions to equivalent like fractions and add them. you must use the lcd to get the answer correct. if possible, reduce the final sum.
(this is the question to all 3 pictures, fill in the green blanks)

you!

Step-by-step explanation: First, you have to understand that both fractions are not equivalent, so you must turn the fraction with a lower denominator, into a fraction that has that same denominator as the other to make it equivalent! You cannot add fractions with a different denominator.

Okay, number one is 1/4 plus 5/12, you are first going to look for the fraction with the lower denominator number, that is 1/4. Next you will look for the common denominator of both fractions, that means to look at numbers 4 and 12! The common denominator is 12, because 4 can be multiplied by 3 to turn into the number 12, and 12 can be multiplied by 1 to stay as 12. Also since you multiply 4 by 3 you will also have to multiply 1 by 3 because 1 and 4 are in the fraction 1/4, this

makes the new fraction into 3/12, and 5/12 just stays the same!

Now you can add the fractions 3/12 plus 5/12! The answer is (8/12!) :)

Follow the same steps with Number 2:

1/7 is turned into 2/14 because the common denominator was 14, so you multiply 1 times two and 7 times two.

2/14 plus 3/14 is 5/14!

Okay Number 3 is a bit different because the common denominator is not directly shown.

You will have to look for the common denominator in numbers 5 and 3.

The least common denominator is 15 because 3 time 5 is 15 and 5 times 3 is 15!

For fraction 1/5, you multiply 5 time 3 to get 15, and also multiply 1 times 3 to complete the fraction into 3/15.

For fraction 2/3, you multiply 3 times 5 to get 15 and multiply 2 time 5 to get 10 and complete the fraction 10/15.

Now you add fractions, 3/15 plus 10/15

The answer is 13/15!!!

You are welcome, I did this with all my heart to write all I could to help. I would want someone to also help me when I am stuck on something.

Hope this will help:)

1. f(x)=x²+10x+16

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(as, a> 0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

so, vertex = (-5, -9)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

2. f(x)=−(x−3)(x+1)

by multiplying the factors, the general form is f(x)= -x²+2x+3.

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

so, vertex = (1, 4)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

3. f(x)= −x²+4

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

so, vertex = (0, 4)

now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

4. f(x)=2x²+16x+30

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(as, a> 0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

so, vertex = (-4, -2)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

5. y=(x+2)²+4

the general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a> 0 parabola is opened upward.

if a< 0 parabola is opened downward.

compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

so, vertex= (-2, 4)

as, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

hope this : )

step-by-step explanation: