Lets x is the amount of money Paul spent
y is the amount of money John spent
<span>Henry spent 3 times as much as paul = 3x
so
</span>John and paul spent $45 altogether: <span>x + y = 45
</span> john and henty spent $65 altogether: 3x+y = 65
solve the equations
3x+y = 65
x + y = 45
---------------subtract
2x = 20
x = 10
x + y = 45
y = 45 - x
y = 45 - 10
y = 35
3x = 3(10) = 30
so
Paul spent $10 (x)
John spent $ 35 (y)
Henry spent $30 (3x)
answer: John spent $ 35
double check:
$ 35 + $ 10 = $45 (<span>John and Paul spent $45 altogether)
</span>$ 35 + $30 = $65 (<span> John and Henry spent $65 altogether)</span>
<h3>
Answer: 4</h3>
===========================================
Explanation:
For now, ignore the variables. Let's just focus on the coefficients 12 and 16.
The GCF of 12 and 16 is 4 because this is the largest factor they have in common.
12 = 4*3
16 = 4*4
You could create a factor tree to get the prime factorization of each number
12 = 2*2*3
16 = 2*2*2*2
Each factor tree has two copies of '2' leading to the GCF 2*2 = 4.
--------
Now let's go back to the variables. The term 12n and 16w^3 do not have any variables in common. So the final answer won't have any variables in it. If both terms had say a 'w' in them, then w would somehow be involved in the GCF. But that's not the case here. So we just stick to 4 as our answer.
--------
Side note: If you had 12n+16w^3 and you wanted to factor, then you would factor out the GCF 4 to get 12n+16w^3 = 4(3n+4w^3). Use the distribution rule to confirm this.
A right triangle has two sides that are perpendicular. The correct answer will be D.
1. What is the simplified form of (x – 2)(2x +3)? Use the Distributive Property.
= (x)(2x) + (3)(x) - (2)(2x) - (2)(3)
= 2x^2 + 3x - 4x - 6
= 2x^2 - x - 6
Answer
2x^2 - x – 6
2. What is the simplified form of (3x + 2)(4x – 3)? Use a table.
| 3x 2
--------|-----------------------------------------
4x | 12x^2 8x
--------|---------------------------------------------
-3 | -9x -6
---------------------------------------------------------Add
12x^2 + 8x - 9x - 6
= 12x^2 -x - 6
Answer
12x^2 – x – 6
3. What is the simplified form of (4p – 2)(p – 4)?
(4p – 2)(p – 4)
= (4p)(p) - (4p)(4) - (2)(p) - (2)(-4)
=4p^2 - 16p - 2p + 8
= 4p^2 - 18p + 8
Answer
4p^2 – 18p + 8
4. The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the formula A = 2r2 + 2rh.
A = 2r2 + 2rh
A = 2( 3x – 2)^2 + 2 (3x – 2)(x + 3 )
A = 2(9x^2 - 12x + 4) + 2(3x^2 + 7x - 6)
A = 18x^2 - 24x + 8 + 6x^2 + 14x - 12
A = 24x^2 - 10x - 4
Answer
A = 24x^2 - 10x - 4
The answer would be fifteen