1.The base of a triangle is 5cm greater than the height. The area is 33cm(2). Find the height and the length of the base?
Height?
Base?
2. Factor
X(2)-7x
3.Factor
5a(6)-1080a(3)
4. Find the GCF
5x(9),5x,-20=
For this one I think the gcf is 5 Is this correct?
5. Factor by grouping
8x(3)-*x(2)-x+1=
1. height -- x
base -- x+5
solve (1/2)x(x+5) = 33
(you will end up with a quadratic which factors very easily)
2. Do you mean x^2 - 7x ??
then x(x-7)
3. do you mean 5a^6 - 1080a^3 ??
I see a common factor of 5a^3
4. yes
5. retype the question, don't know what the -* is supposed to mean. Also use 8x^3 for "8 x cubed"
1. B = H + 5
Area = 1/2 BH
Substitute H + 5 for B in the second equation and solve for H. Put that value in the first equation to find B. Check by putting both values into the second equation.
2. X^2 = X squared online
X^2 + 7X = X(X + 7)
I will let you do 3 using the same process.
4 is correct.
5. I'm not sure what this formula is.
8X^3 - X^2 - X + 1 (?)
1. To find the height and length of the base of the triangle, we can use the formula for the area of a triangle: Area = (1/2) * base * height.
Let's assign variables to the height and length of the base. Let h represent the height and b represent the base.
From the given information, we know that the base is 5cm greater than the height, so b = h + 5.
The area of the triangle is given as 33 cm², so we can set up the equation as follows:
33 = (1/2) * (h + 5) * h.
To solve this equation, we can start by multiplying both sides by 2 to remove the fraction:
66 = (h + 5) * h.
Next, we can distribute the h:
66 = h² + 5h.
Now, let's rearrange the equation into a quadratic form:
h² + 5h - 66 = 0.
This equation can be factored or solved using the quadratic formula.
2. To factor the expression X² - 7x, we need to find the greatest common factor (GCF) among the terms.
In this case, the GCF is x. We can factor it out:
x(x - 7).
So the expression X² - 7x can be factored as x(x - 7).
3. To factor the expression 5a⁶ - 1080a³, we need to look for the common factors among the terms.
In this case, we can factor out the GCF, which is 5a³:
5a³(a³ - 216).
So the expression 5a⁶ - 1080a³ can be factored as 5a³(a³ - 216).
4. To find the greatest common factor (GCF) of 5x⁹, 5x, and -20, we can find the highest power of each variable that appears in all terms.
In this case, the highest power of x that appears in all terms is x, and the highest power of 5 that appears in all terms is 1.
So, the GCF of 5x⁹, 5x, and -20 is 5x.
5. To factor by grouping in the expression 8x³ - x² - x + 1, we can rearrange the terms in pairs and try to find a common factor.
Let's group the terms as follows:
(8x³ - x²) + (-x + 1).
In the first group, we can factor out the GCF, which is x²:
x²(8x - 1) + (-x + 1).
Now, in the second group, we can factor out a common factor of -1:
x²(8x - 1) - 1(x - 1).
Finally, we have a common factor of (8x - 1), which can be factored out:
(8x - 1)(x² - 1).
So, the expression 8x³ - x² - x + 1 can be factored as (8x - 1)(x² - 1).