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Recent problems solved by 'acalgebra'

acalgebra answered: 30 problems

Linear-systems/369608: I am supposed to solve a linear equation using the method of elimination, I have retried doing it over and over but when I go back to check my work it doesn't come out as the correct answer. So I need help solving this by using method of elimination. Please help me solve this equation: x+3y=14
x+2y=10
Hopefully you know this method, I do but this particular problem is causing me to struggle, so can you show me the steps to how you figured it out? Thank you!
1 solutions

Answer 263383 by acalgebra(30) on 2010-11-11 13:25:39 (Show Source):

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First, multiply the second equation by -1:
-x-2y=-10

Now, add the equations together:
x%2B3y-x-2y=14-10

Combine like terms:
x-x%2B3y-2y=4

Substitute y for 4 in one of the equations. I chose the first one:
x%2B3%284%29=14

Multiply 3 by 4:
x%2B12=14

Subtract 12 from both sides:
x=2

So,

and

.
--------
Check:
First equation:
2%2B3%284%29=14

Second equation:
2%2B2%284%29=10

Angles/369585: Find the measure of the supplement to a 146° angle.
1 solutions

Answer 263370 by acalgebra(30) on 2010-11-11 12:52:43 (Show Source):

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The supplement and the angle should add up to 180°.
Let the supplement be x, then:
x%2B146=180

So, the measure of the supplement to a 146° angle has a measure of 34°.

Coordinate-system/369591: The slope of a line is -7/6. What is the slope of any line perpendicular to this line?
1 solutions

Answer 263368 by acalgebra(30) on 2010-11-11 12:48:00 (Show Source):

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Because the slopes of perpendicular lines are opposite reciprocals, the slope of a line perpendicular to a line with a slope of -7%2F6

Angles/369586: An angle is 10° more than the measure of its complement. Find the number of degrees in each angle.
1 solutions

Answer 263366 by acalgebra(30) on 2010-11-11 12:45:40 (Show Source):

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Let the angle be x and its complement be c, then:
x=c%2B10

and

.
In the second equation, substitute x for c%2B10

Now, solve:
c%2B%28c%2B10%29=90

Now, in the first equation, substitute c for 40:
x=40%2B10

So, the measure of the angle is 50°, and the measure of its complement is 40°.

Graphs/369583: (5,-6);3x+5y=9 write an equation of the line perpendicular to the given line
1 solutions

Answer 263363 by acalgebra(30) on 2010-11-11 12:39:36 (Show Source):

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First, put the equation in slope-intercept form:
3x%2B5y=9

Because perpendicular lines have slopes that are opposite reciprocals, the equation that is perpendicular to the given line is:
y=%285%2F3%29x%2B9%2F5

Equations/369579: -40%2B8k=16

What is the value of k in this equation?
1 solutions

Answer 263359 by acalgebra(30) on 2010-11-11 12:32:06 (Show Source):

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Original equation:
-40%2B8k=16

Add 40 to each side:
8k=56

Divide both sides by 8:
k=7

So, the value of k in this equation is 7.

Linear_Equations_And_Systems_Word_Problems/369560: The sum of twice one number and 3 times another is 41. If the second is subtracted from the first, the difference is 8. What are the numbers?
1 solutions

Answer 263357 by acalgebra(30) on 2010-11-11 12:29:52 (Show Source):

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Let the first number be x and the second number be y, then:
2x%2B3y=41

and

The easiest way to solve this is to multiply the second equation by 3:
3x-3y=24

Now, add the equations:
2x%2B3y%2B3x-3y=41%2B24

Combine like terms:
5x=65

Divide both sides by 5 to simplify:
x=13

Now, substitute 13 for each x in one of the original equations. In this case, the second equation will be easier.
13-y=8

Add y to each side:
13=y%2B8

Subtract 8 from each side:
5=y

So,

and

Average/369374: Daniel ran 2 miles in 12 minutes. What was his average speed using the formula s=d/t?
1 solutions

Answer 263181 by acalgebra(30) on 2010-11-10 21:48:10 (Show Source):

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s=d%2Ft

(Basic equation)
s=2%2F.20

(12 minutes is one-fifth of an hour, or .20 of an hour.)
s=200%2F20

(Multiply both sides of the fraction to get whole numbers.)
s=10%2F1

(Divide both sides of the fraction to simplify.)
So, Daniel ran at an average speed of 10 miles per hour.

Equations/369377: Please help me set up this equation, Mary has 22.75 in the bank. She only saves half dollars and quarters. She has $10.50 in half dollars, how MANY quarters does she have? I know how to get to the answer but I don't know how to set up the equation to solve for x
1 solutions

Answer 263179 by acalgebra(30) on 2010-11-10 21:42:36 (Show Source):

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Let the number of quarters be x, then
22.75=10.50%2B.25x

Now, divide 12.25 by 25 to get
49=x

So, Mary has 49 quarters in the bank.

Average/369370: Find the area of the triangle formed by the x-axis, the y-axis, and the line described by y = 6 - x.
1 solutions

Answer 263178 by acalgebra(30) on 2010-11-10 21:39:52 (Show Source):

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The triangle formed by the y-axis, x-axis, and the line defined by y=6-x is an isosceles right triangle with leg lengths of 6 and a hypotenuse length of 6+sqrt%282%29

. The area of the triangle is 1%2F2

, which is 18.

Quadratic_Equations/369361: Use the quadratic formula to solve the equation.
x%5E2-5x=-9

1 solutions

Answer 263172 by acalgebra(30) on 2010-11-10 21:27:26 (Show Source):

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First, put the equation in standard form: x%5E2-5x%2B9

Then, note a, b, and c: a=1

, and

Now, put a, b, and c into the quadratic equation: x+=+%285+%2B-+sqrt%28+-5%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29+

Then, solve: x+=+%285+%2B-+sqrt%28+-5%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29+

Because there is a square root of a negative number, there are no real number solutions.

Mixture_Word_Problems/369367: If there were 60 problems on a test and Betty got 90% of the problems correct, how many problems did she answer correctly?
1 solutions

Answer 263168 by acalgebra(30) on 2010-11-10 21:18:51 (Show Source):

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90%2F100+%2A+60

test/369328: Factor this expression completely:
16s%5E2-25

1 solutions

Answer 263165 by acalgebra(30) on 2010-11-10 21:16:19 (Show Source):

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16s%5E2-25

Graphs/369357: What would the graph be for: x + y = 2?
1 solutions

Answer 263162 by acalgebra(30) on 2010-11-10 21:11:39 (Show Source):

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Use the graphing calculator at http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

You'll need to copy and paste, because I can't type a link here. Sorry!

Graphs/369358: What would the graph be for: y = x + 2?
1 solutions

Answer 263161 by acalgebra(30) on 2010-11-10 21:11:21 (Show Source):

Triangles/369334: An isosceles right triangle has two 45° angles. The sides opposite those angles are equal in length
Find the length of each of the equal sides if the length
of the hypotenuse is 1.
1 solutions

Answer 263157 by acalgebra(30) on 2010-11-10 21:08:30 (Show Source):

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The hypotenuse is c, and the legs are a and b:

a%5E2%2Bb%5E2=c%5E2

Rectangles/369293: The length of a rectangle is 2 less than 3 times the width. If the perimeter is 68, what is the length of the rectangle?
1 solutions

Answer 263128 by acalgebra(30) on 2010-11-10 20:02:17 (Show Source):

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------
3w-2=l

perimeter=2(l+w)
2([3w-2]+w)
2(3w-2+w)
2(4w-2)
8w-4

perimeter=68
8w-4=68
8w=72
w=9

3w-2=l
3(9)-2=l
27-2=l
25=l
l=25

So the length is 25.

Linear_Equations_And_Systems_Word_Problems/369275: A bus traveled a distance of 180 km. How long will it take for a bus to make this trip if it has a speed of 45km/h?
1 solutions

Answer 263123 by acalgebra(30) on 2010-11-10 19:51:33 (Show Source):

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180%2F45=4

It would take 4 hours for the bus to make a 180 km trip at a speed of 45 km/h.

Polynomials-and-rational-expressions/369268: (x^2y)^4
1 solutions

Answer 263121 by acalgebra(30) on 2010-11-10 19:47:31 (Show Source):

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%28x%5E2y%29%5E4

x^8y

Triangles/369257: A right triangle has legs of 5 and x+2 and a hypotenuse of length x+3. What is the perimeter of the triangle?
1 solutions

Answer 263117 by acalgebra(30) on 2010-11-10 19:41:42 (Show Source):

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This right triangle uses the lengths of a common Pythagorean triple: 5, 12, and 13. x=10, so the perimeter is:
5+(10)+2+(10)+3
15+12+3
15+15
30
perimeter=30
Remember to include units in your answer!

Geometric_formulas/369218: Prove the Right Angle Theorem: All right angles are congruent. Given: Angle 1 and Angle 2 are right angles. Prove: Angle 1 is congruent to angle 2
1 solutions

Answer 263114 by acalgebra(30) on 2010-11-10 19:30:53 (Show Source):

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A right angle measures 90°, so by definition, both Angle 1 and Angle 2 have a measure of 90°. Angles that have the same measure are congruent, so Angle 1 is congruent to Angle 2.

Graphs/369252: is there an easier way to graph linear equations
1 solutions

Answer 263110 by acalgebra(30) on 2010-11-10 19:27:40 (Show Source):

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Yes. Use a graphing calculator. You can find an excellent one here: http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
You'll have to copy and paste into your browser, because I can't create a link in these text boxes. Sorry!

Geometry_proofs/368763: Prove that midpoints of a quadrilateral form a parallelogram.
1 solutions

Answer 263108 by acalgebra(30) on 2010-11-10 19:25:48 (Show Source):

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The type of quadrilateral that is formed can either be a rhombus, a
rectangle, or a square, but it will always be a parallelogram. This is
because when the midpoints are connected to form the sides of the
midpoint-verticed figure, each side of the original figure is bisected. Each newly
formed side will be parallel to a diagonal of the original. Two of the
newly formed sides are parallel to the same diagonal and therefore are
parallel to each other. Along with the other two sides of the midpoint-verticed
that are parallel to the other diagonal of the original, a parallelogram
is formed.

Graphs/369200: x+6=y
y-x=-2
Are the lines parallel?

1 solutions

Answer 263105 by acalgebra(30) on 2010-11-10 19:19:34 (Show Source):

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Take the first equation and switch the side, like this: y=x%2B6

Now, take the second equation and add x to each side: y=x-2

Because the slopes (coefficients of x) are the same, the lines are parallel.

test/369209: Using each number only once, use 2,4,6 & 8 to write an expression with two proper fractions that have the largest possible sum.
1 solutions

Answer 263103 by acalgebra(30) on 2010-11-10 19:16:02 (Show Source):

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2%2F4%2B6%2F8

Square-cubic-other-roots/369239: How to find the square root of 4x^10y^2
1 solutions

Answer 263101 by acalgebra(30) on 2010-11-10 19:13:22 (Show Source):

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Well, 4x^10y^2 is a square, so simply get rid of the last exponent, like this: 4x^10y.
There ya go!

Problems-with-consecutive-odd-even-integers/369240: The sum of the least and greatest of three consecutive integers is equal to 35 plus the middle integer, what are the integers?
1 solutions

Answer 263098 by acalgebra(30) on 2010-11-10 19:11:00 (Show Source):

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--------
x+x+2=35+x+1
2x+2=36+x
2x=34+x
x=34
The three consecutive integers are 34, 35, and 36.

Linear_Algebra/369229: What is the equation/function for if you enter 3 and the answer is 8 and you enter 10 and the answer is 29 and then you enter 20 and the answer is 59? How do I figure out the equation?
1 solutions

Answer 263091 by acalgebra(30) on 2010-11-10 18:53:46 (Show Source):

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3 >> 8
10 >> 29
20 >> 59
There is no set way to solve this, but here is the function:
[output]=3[input]-1

Systems-of-equations/369231: show me how to work out this equation.
5-3x+x=19
1 solutions

Answer 263089 by acalgebra(30) on 2010-11-10 18:51:12 (Show Source):

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5-3x+x=19
5-4x=19
5=4x+19
-14=4x
-4%2F14

Numbers_Word_Problems/369226: A new high school has just been opened, with an enrollment
of 1000 students. The school has 1000 lockers, numbered 1 to
1000, to accommodate them. On the first day of school, all
1000 lockers are closed and all 1000 students are outside
waiting to be let into the building. The first student enters and
opens all of the lockers. The second student follows and
closes every second locker, beginning with the second locker.
The third student enters the school and reverses every third
locker beginning with locker 3 (e.g., if the locker is closed it is
opened and vice versa). This procedure is continued until all
1000 students have passed by all the lockers. When they
finish, which lockers will be open?
1 solutions

Answer 263087 by acalgebra(30) on 2010-11-10 18:45:24 (Show Source):

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The square numbered lockers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, and 961).

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Recent problems solved by 'acalgebra'