Hello, Jesse --
You need to use your information about area and perimeter to set up two equations with two variables representing length and width of the rectangle. Then you will set up a quadratic equation. Let's use L for the length and W for the width of the rectangle:
For the perimeter:...
Hello, Elasa ---
Look again at your equation. The 3 in front of the parentheses means that you have to multiply 3 times anything inside the parentheses. That is the distributive property.
Let's see how it works:
5x + 3(x + 4) = 28 Multiply 3 times x and 3 times +4, and...
You can solve this by following the same steps as for an equation with an = sign instead of the > sign.
First, distribute the 4 through the parentheses on the right side:
16x - 32 > 12x - 48
Now subtract 12x from both sides, and add 32 to both sides:
16x - 32...
Assuming that the house is perpenidcular to the ground on which the ladder stands, use the Pythagorean Theorem for the sides of right triangles:
a2 + b2 = c2
In this problem a = 18, b is the unknown, and c is the length of the ladder (the hypotenuse of the triangle)....
Andrew Johnson, not Andrew Jackson, was impeached by the House in February 1868 because northern senators were dissatisfied with his performance in the years just after the Civil War. He had a trial in the Senate, and was acquitted by one vote in May 1868.
President Bill Clinton also was impeached...
Hello, Cheryl --
This problem can be solved either way. If you are comfortable with factoring, that might be the easiest method.
First, add 15 to both sides and set the result equal to 0:
9x2 + 21x + 10 = 0
Next, try combinations of factors of 9 and 10 that, when FOILed,...
Hello, Tiffany --
In this problem, you will set it up as a subtraction and multiplication, and then do the opposite operations to solve it. First, let's call the number you are looking for "n," and write an equation that explains the words in terms of symbols and numbers.
"9 less than 5...
Hi, Henriettas --
Slope-intercept equations have the form y = mx + b, where m is the slope and b is the y-intercept.
We will do these one at a time:
2x - 3y = 5 we need to piut the 2x term on the right:
The original average is the number of apples (300) divided by the number of students (let's call this "n").
Thus we begin with A1 = (300/n).
We add 10 students, which decreases the average by 1. But we still have the same number of apples.
Then the new average is A2 = (300/n+10)
This is a little bit difficult to answer because it isn't entirely clear which terms go together. I will assume that you meant 2 - (x/1) - (x/2), but that may not be correct. If it is, you can combine all three terms by finding a common denominator.
It this case, the common denominator...
Set it up and solve it as a system of two linear equations in two variables:
x + 2y = [1 3 -2]
x + y = [2 0 1]
Multiply the second on through by -1 and add it to the first one:
x + 2y = [1 3 -2]
Gina's answer is correct.
We can also set it up as a ratio:
(Original number of packs)/Original cost of those packs) = (New number of packs)/(New cost)
In this problem, that would be:
3/0.87 = 10/x (where x is the cost of 10 packs)
The best method for solving this is to cross-multiply (which is the same as multiplying both sides by 63 and then dividing).
You will then have:
9(2x - 4) = 7(x - 1)
or 18x - 36 = 7x - 7
Now subtract 7x from both sides:
18x - 36 = 7x - 7...
With instructions to use exponents, I would do it this way:
2n2(8)3 = 2(23)3 n2 = 2(29) n2 = 210 n2
This is exactly the same as Tamara's answer above, but with an explicit powr of 2.
Hello, Oksana ---
You can designate the form of the quadratic from the vertex, (h, k).
A parabola with vertex (h, k) would have this form:
y - k = a(x - h)2
Substituting your numbers, you would have:
y - 7 = (x + 5)2
It could have an infinite number of...
Hello, Carolyn --
This is an algebra problem involving fractions. You need to get all of the numbers on one side of the = sign, and the x on the other side. In this problem, all you have to do is subract 1/3 from both sides:
4/3 = x + 1/3
The other answers by Will and Robert are correct.
I would just add an example:
log 12 = log 4 + log 3 OR log 6 + log 2, or even log 9 + log (4/3). Try those on your caluclator.
If you have something like log 3x, it would be log 3 + log x.
You should have a periodic table of the elements in your textbook, or perhaps on the wall of your classroom. It is a chart that displays important information about all of the elements that make up our universe, including a few at the end that scientists
have been able to create from other elements...
If the interval is closed the notation should be [0,1]. In that case, the MVT would not apply because f'(0) is not defined.
If the interval is closed, and includes a value for 0
Hello, Joanna ---
I don't see an example problem, but will try to make one up.
Suppose you want to combine like terms of the following string:
(2x + 3) + (x -3y +7) - (2x + 4y - 6)
First, remove the parentheses by distributing the + and - signs across the second and third terms:...