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bogdanovich [222]
2 years ago
5

Use a diagram to show that (3x+1)(x+2) is equivalent to 3x2+7x+2.

Mathematics
1 answer:
Softa [21]2 years ago
6 0
3x*x = 3x^2

3x*2 = 6x

x*1 = x

1*2 = 2

that's basically the FOIL method, multiply first terms, the x terms
then the outside terms, the the inside terms, then the constant (last) terms
F=first, O=outside, I = Inside, L = last

add them up to get 3x^2 +6x +x + 2 = 3x^2 +7x +2

(3x+1)(x+2) = 3x^2 +7x+2

draw a rectangle with one side as 3x+1, the other side as x+2. The area of the rectangle is their product

divide the rectangle into 4 smaller rectangles. with sides 3x by x, 3x by 2, x by 1 and 2 by 1
calculate the areas of each rectangle the sum them.

standard form is

y=ax^2 +bx + c or

f(x) = x^2 +7x +2 where a=1, b=7, c=2

another standard form is to put the quadratic equation in vertex form
by completing the square

f(x) or y = x^2 +7x + 49/4 = -2 + 49/4

y = (x+3/2)^2 = 41/4

where the vertex = (3/2,41/4)

standard equation in vertex form is

y= a(x-h)^2 + k where (h,k) = vertex = (3/2,41/4) with a=1

It's an upward opening parabola with y intercept = 41/4 = 10 1/4, axis of symmetry x=3/2
You might be interested in
jamal completed his math homework in 2/3 of an hour and his reading homework in 3/5 of an hour. How much time did it take him to
Assoli18 [71]

Answer:

Step-by-step explanation: We have to add how much time it took him to do all of his homework. To do this, we have to add 2/3 and 3/5.

First, we have to find a LCM between 3 and 5.

The LCM between those numbers are 15.

Next we find out what number to multiply 3 by to get 15, we multiply it by 5.

2 * 5 = 10

3 * 5 = 15

Next we find out what number to multiply 5 by to get 15, we multiply it by 3.

3 * 3 = 9

5 * 3 = 15

10/15+9/15=19/15

We are left off with 1 4/15

So it took him 1 hour and 4/15 minutes to do his homework.

3 0
3 years ago
What is the answer to 7x + 2 + 2x
kotykmax [81]

Answer:

Your answer is 9x+2

Step-by-step explanation:

All you have to do is add like terms, for example, all of them that have X you can add them up,

6 0
3 years ago
Given h(x)=-3x-2,solve for x when h(x)=1​
lora16 [44]

Answer:

-5

Step-by-step explanation:

6 0
3 years ago
Yu and Elena each bought between 7 and 9 yards of ribbon. Yu
Mumz [18]

Given: Yu, Nailah, and Elena each bought between 7 and 9 yards of ribbon  Yu bought 3 pieces of ribbon. Nailah bought 5 pieces of ribbon. Elena bought 6 pieces of ribbon.

To find: Who can buy which ribbon

Solution:

Ribbon Sizes

1 2/3 = 5/3  yard

4/5  yard

3 1/2  = 7/2 Yard

Yu, Nailah, and Elena each bought between 7 and 9 yards of ribbon

Yu bought 3 pieces of ribbon

=> 3 * 5/3  = 5

  3 * 4/5  = 2.4

  3 * 7/2   = 10.5

Nailah  bought 5 pieces of ribbon

=> 5 * 5/3  = 8.33

   5 * 4/5  =  4

   5 * 7 /2   = 17.5

Elena bought 6 pieces of ribbon

=> 6 * 5/3  = 10

  6 * 4/5  = 4.8

  6 * 7 /2   = 21

Only value between 7 & 9 is 5 * 5/3  = 8.33

hence Nailah only can buy 1 2/3 = 5/3  yard ribbon

or there is some mistake in the data

6 0
2 years ago
If a is a positive integer and b is a negative integer, which expression must be positive?
nydimaria [60]

So, let's solve all of them and see:

a - (-b) = a + b ⇒ can be either positive or negative, depending on the numbers

a + (-b) = a - b ⇒ can either be positive or negative, depending on the numbers

a * (-b) = a * (-b) ⇒ negative answer no matter what

a / (-b) = a / (-b) ⇒ negative answer no matter what


So the answer is:

<em>"None of the above"</em>.


Hope it helped,


BioTeacher101


(If you have any questions, feel free to ask them in the comments)

4 0
3 years ago
Read 2 more answers
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