MATHEMATICS HIGH SCHOOL

Identify the properties used for the first two steps in simplifying 6ab2 + 4a - 3ab2 +3a²b-2a²b2.6ab2-4a²b-3ab2+3a²b-2a²b2 = 4a²b+3a²b-3ab2+6ab2-2a²b2
= (4+3)a²b+(-3+6)ab2-2a²b2
= 7a+b+3ab2-2a²b2

Answers

Answer 1

Answer:

Answer:

commutative property of addition
distributive property

Step-by-step explanation:

6ab²+4a²b-3ab²+3a²b-2a²b²

= 4a²b+3a²b-3ab²+6ab²-2a²b² . . . commutative property of addition (twice)

= (4+3)a²b+(-3+6)ab²-2a²b² . . . . . . distributive property (twice)

= 7a²b+3ab²-2a²b²

_____

We have attempted to correct what we perceive to be typographical errors in the presentation of the problem. As written, you can't get to the second expression from the first, and the first expression doesn't match what you say you're trying to simplify.

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A taxi cost $4.00 plus .50 cents per mile. Traveling from the airport there is an additional charge of $6.00. How far can you travel from the airport by taxi for $31.50

Answers

Answer: You can travel 43 miles

Step-by-step explanation:

To determine how far you can travel from the airport by taxi for $31.50, we can subtract the fixed charges from the total cost and then divide the remaining amount by the cost per mile.

Let's calculate:

$31.50 - $4.00 (base fare) - $6.00 (airport charge) = $21.50

Now, we can divide the remaining amount by the cost per mile:

$21.50 / $0.50 per mile = 43 miles

So, you can travel approximately 43 miles from the airport by taxi for $31.50.

A rectangular garden has a perimeter of 48 cm and an area of 140 sq. cm. what is the width of this garden?

Answers

We can call a the width of the garden and b the length of the other side.
The perimeter of the garden is the sum of the two sides, and it is equal to 48 cm:
$a+b=48$ (1)
The area of the garden is the product between the two sides, and it is equal to $140 cm^2$ :
$a b = 140$

From (1), we find
$b=48 -a$
And by substituting this into (2)
$a(48-a)=140$
$a^2-48a+140 =0$
which gives two solutions:
$a=44.9$ , to which corresponds $b=48-a=48-44.9=3.1$
$a=3.1$ , to which corresponds $b=48-a=48-3.1=44.9$

So, the width of the garden is $44.9 cm$ while the length of the other side is $3.1 cm$ .

two sides of a triangle have lengths 5 inches and 16 inches describe the possible lengths of the third side

Answers

The third side must be at least 11 inches but less than 21 inches

Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?

Answers

three quarters two dimes four pennies

Which is larger 2in or 3,526yd

Answers

Based on the picture, did you mean 2 miles vs. 3,526 yards? If so, here's how to solve it:

1 mile is 1760 yds. So 2 miles is 3520 yards.

Therefore, 3526 is longer than 2 miles.

Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).

Answers

if x=0 then they have same value

1st and 2nd options are out

for x=-1
g(-1)=1
h(-1)=-1
3rd is true

4th
false

for all values except zero, g(x)>h(x)

correct ones are

g(x) > h(x) for x = -1.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).

Answer: g(x) > h(x) for x = -1.

For positive values of x, g(x) > h(x).

For negative values of x, g(x) > h(x).

Step-by-step explanation:

Given functions: $g(x)=x^2$ and $h(x)=-x^2$

When x=0, $g(0)=0^2=0$ and $h(0)=-0^2=0$

∴ at x=0, g(x)=h(0)

Therefore the statements "For any value of x, g(x) will always be greater than h(x)." and "For any value of x, h(x) will always be greater than g(x)." are not true.

When x=-1, $g(-1)=(-1)^2=1$ and $h(-1)=-(-1)^2=-1$