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Linear-equations/309691: what are the x and y intercepts of 9x+8y=14?
1 solutions

Answer 221492 by jim_thompson5910(28715)   on 2010-05-29 19:07:46 (Show Source):
You can put this solution on YOUR website!

#### x-intercept

To find the x-intercept, plug in and solve for x

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

So the x-intercept is .

------------------------------------------

#### y-intercept

To find the y-intercept, plug in and solve for y

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the y-intercept is .

 Trigonometry-basics/309689: We are proving identities and my book only has three examples. So I was hoping I could get some help solving a problem my teacher assigned on our test. I failed to answer it correctly, but he will be doing similar problems on our final exam. cos^2 x cos^2 y = -sin(x+y) sin(x-y) If you could show the steps and explain them I'd greatly appreciate it.1 solutions Answer 221484 by jim_thompson5910(28715)   on 2010-05-29 18:37:27 (Show Source): You can put this solution on YOUR website!Unfortunately, cos^2 x cos^2 y = -sin(x+y) sin(x-y) is NOT an identity. You must be missing a symbol either in between the terms cos^2 x and cos^2 y or in between the terms -sin(x+y) and sin(x-y). Please repost with the correct problem.
 Polynomials-and-rational-expressions/309680: On this question, they wanted me to simplify each sum or difference. (5g^2 - 2g)-(2g^2 + 6g) I didnt get it at all, but my friend said she got 35g^4 - 12g^2 Then i got some help from my youth pastor and he got -2g^2 - 8g which one is right, i am very confused. or are they both wrong?1 solutions Answer 221482 by jim_thompson5910(28715)   on 2010-05-29 18:27:27 (Show Source): You can put this solution on YOUR website! So So unfortunately, they are both incorrect. It looks like your friend tried to multiply it out. I'm not quite sure as there are too many mistakes. Your pastor is on the right track, but has the wrong first term.
 Linear-equations/309575: I need to find the slope of the line containing the points (8,-1) and (7,-9) Can anyone help. Thanks1 solutions Answer 221406 by jim_thompson5910(28715)   on 2010-05-29 05:14:09 (Show Source): You can put this solution on YOUR website!Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is
 percentage/309559: The top floor is rectangular and has a perimeter of 520ft. the width of the top floor measures 20 ft. more than one half its length. What are the dimensions of the top floor? I figured it as 160 length and 100 width1 solutions Answer 221403 by jim_thompson5910(28715)   on 2010-05-28 23:24:19 (Show Source): You can put this solution on YOUR website!You are correct. Good job.
 Rational-functions/309551: What is log 10 1001 solutions Answer 221399 by jim_thompson5910(28715)   on 2010-05-28 22:46:50 (Show Source): You can put this solution on YOUR website! which means that
 logarithm/309530: Please help me solve this equation: Solve the logarithmic equation logarithmic equation . <-- logarithm of lnx(natural log of x) with base 2 equals =-1. I tried: . (log of natural log of x with base 2 equals -1) . (natural log of x equals 2 to the power of -1) . (natural log of x equals 1/2) . (x equals e to the power of 1/2) I put . back into the original equation and it didn't equal the answer.1 solutions Answer 221384 by jim_thompson5910(28715)   on 2010-05-28 20:16:38 (Show Source): You can put this solution on YOUR website!Well is the answer. Start with the given equation. Plug in Use the identity to pull down the exponent. Take the natural log of 'e' to get 1. Multiply and simplify Rewrite as Pull down the exponent using the identity Evaluate the log base 2 of 2 to get 1. Multiply Since the final equation is an identity (ie is always true), this verifies the answer.
 real-numbers/309488: for what values of x and y is x + 4yi=-5 - 24i please show me steps 1 solutions Answer 221372 by jim_thompson5910(28715)   on 2010-05-28 18:38:19 (Show Source): You can put this solution on YOUR website!Hint: Equate the real and imaginary parts to get the two equations and
 Trigonometry-basics/309300: Hello, I'm sorry if this question is confusing but i don't understand this, so it's sort of hard to explain. Okay, i have triangle ABC. Angle ABC=90 Degrees, Angle BCA=75 Degrees, and angle CAB=15 Degrees. If the length of line BC equals 20 units, what is the length of line AB? Please explain.1 solutions Answer 221202 by jim_thompson5910(28715)   on 2010-05-28 00:22:09 (Show Source): You can put this solution on YOUR website!If you draw the triangle and label it's parts, you'll see that triangle ABC is a right triangle. Now let's use angle BCA=75 degrees as our reference angle. The side BC is the adjacent side while the side AB is the opposite side (again, a drawing will help). So we're going to use the tangent function (since tan=opposite/adjacent) So this means that tan(75)=BC/AB and that tan(75)=20/x where 'x' is the length of AB. Now compute tan(75) to get approximately 3.73205. So 3.73205=20/x Now you're job is to solve the equation 3.73205=20/x to find 'x' which is the length of AB. Note: There is a way to compute the tangent of 75 degrees exactly, but we don't need to do that here.
 Systems-of-equations/309282: 3x/6 -4/12 =7 ; -36x +24=-504 In the following pair of equations, both sides of the equation on the left were multifplied by a number to get the equation on the right. What is the number? I know the answer is -72. If you could please help me find out how to get that answer that would be so wonderful. Thank you!!1 solutions Answer 221185 by jim_thompson5910(28715)   on 2010-05-27 22:25:17 (Show Source): You can put this solution on YOUR website!Well a quick and easy way to get a common multiple of 2 (or more) numbers is to simply multiply them. For instance, a common multiple of 17 and 5 is 17*5=85 In this case, a common multiple between 6 and 12 is 6*12=72. It turns out that the numbers that share the common multiple will go into that common multiple. Ie and . What this means is that you can effectively clear out the denominators of the fractions leaving you with integer terms. For instance, multiply 72 by to get . In the given problem, the only difference is that 36x is really -36x. So instead we must multiply both sides by -72. Another quick way to realize that -72 is the magic number is to look at the right side. This side already has an integer which will make life easier for us. Take the number 7 and multiply it by some unknown number 'k' to get 7k. This is now equal to the new right side of -504. Set them equal to get 7k=-504. The task now is to solve the equation 7k=-504. Sure enough, solving the equation will get us k=-72 which is the number we're looking for.
 Linear-equations/309284: Could you please help me find the answer to -2 Find the value of n for a line that passes through the points a(-7,n) and b(3,-27) and has a slope of -5/2. Thank you for helping me solve for the answer, I just can't figure this one out!1 solutions Answer 221184 by jim_thompson5910(28715)   on 2010-05-27 22:16:57 (Show Source): You can put this solution on YOUR website!Hint: The slope equation is is the first point . So this means that and . Also, is the second point . So this means that and . We're given a slope of . So . Plug all of this info into the given formula at the top to get To make things simpler, you can rewrite as to get From here, solve the equation for 'n'.
 Inverses/309251: what is the inverse of f(x)=7x-3 divided by 161 solutions Answer 221153 by jim_thompson5910(28715)   on 2010-05-27 20:14:16 (Show Source): You can put this solution on YOUR website!Hint: Think of as . Now swap x and y to get . From here, solve for 'y' to find the inverse function.
 Angles/309253: What is the complement of an angle whose measure is 43 degrees.1 solutions Answer 221151 by jim_thompson5910(28715)   on 2010-05-27 20:12:45 (Show Source): You can put this solution on YOUR website!Remember, complement angles add to 90 degrees. So let 'x' be the complement to 43 degrees. This then means that .
 Polynomials-and-rational-expressions/309254: 24x+48y1 solutions Answer 221149 by jim_thompson5910(28715)   on 2010-05-27 20:11:42 (Show Source): You can put this solution on YOUR website!I don't know what you want to do here. Please post the full instructions and any work or thoughts about the problem.
 Permutations/309244: In how many different ways can the letters in the word PAYMENT be arranged if the letters are taken 4 at a time?1 solutions Answer 221148 by jim_thompson5910(28715)   on 2010-05-27 20:10:54 (Show Source): You can put this solution on YOUR website!You have 7 letters and 4 spots to place them, so you have 7 P 4 = 7!/(7-4)!=7!/3! = (7*6*5*4*3!)/3! = 7*6*5*4 = 840 different ways.
 Quadratic-relations-and-conic-sections/309219: Write an equation for the hyperbola...I have no idea. vertices (0,6) and (0,-6) conjugate axis of 14. I'd really like to figure out on my own but I have no idea where to start..so if someone could give me a step-by-step solution, that would be wonderful! Thank you.1 solutions Answer 221108 by jim_thompson5910(28715)   on 2010-05-27 18:24:13 (Show Source): You can put this solution on YOUR website!The center of the hyperbola is the midpoint of the line segment from vertex to vertex. So the midpoint of (0,6) and (0,-6) is ((0+0)/2, (6+(-6)/2) ---> (0, 0). So the center is (0,0). The center is in the form (h,k), so h=0 and k=0. In this case, 'a' is the length of the semi-minor axis and 'b' is the length of the semi-major axis. So the lengths of the conjugate and traverse axes are 2a and 2b units respectively. Since the traverse axis is 2b units long, this means that 2b=12 (since the distance between the vertices is 12 units) which means that b=6. Also, because the conjugate axis is 14 units long, and 2a is the length of the conjugate axis, this means that 2a=14 and a=7 Finally, recall that the general equation for a hyperbola which opens up vertically is . From here, all you need to do is plug in the right values and simplify.
 Polynomials-and-rational-expressions/309155: Could you please help me solve this.If one of the zeros of y=x^3+bx+1 is 1, determine the value of b,and then solve x^3+bx+1=0.1 solutions Answer 221103 by jim_thompson5910(28715)   on 2010-05-27 18:07:16 (Show Source): You can put this solution on YOUR website!If one of the zeros of is 1, this means that if you plug in x=1, then y will be zero. In other words, you'll have the equation . From here, you have a simple linear equation in which you can solve for 'b'. I'll let you do that.
 Linear-systems/309181: Please help.. solve: 1)4x + 3y =7 2) 16x + 12y = 28 Thank you so much....Rebecca1 solutions Answer 221101 by jim_thompson5910(28715)   on 2010-05-27 18:03:13 (Show Source): You can put this solution on YOUR website!Hint: If you multiply both sides of the first equation by -4, you get . Now add this to the second equation and you'll find that the 'y' terms cancel out. This will leave you with an equation in which you can solve for 'x'.
 Inequalities/309042: If a^2b^3c > 0, which of the following statements must be true? I. bc > 0 II. ac > 0 III. ab > 0 1 solutions Answer 220960 by jim_thompson5910(28715)   on 2010-05-27 06:09:40 (Show Source): You can put this solution on YOUR website!Hint: is certainly positive for all . So divide both sides by to get .
 Square-cubic-other-roots/309038: How would I simplify the product to this problem? (√5 + 2)(√5 - 6)1 solutions Answer 220959 by jim_thompson5910(28715)   on 2010-05-27 05:16:42 (Show Source): You can put this solution on YOUR website!Let to get the expression Start with the given expression. FOIL Combine like terms. Plug in Square to get Combine like terms. So
 Sequences-and-series/309008: Is the formula explicit or recursive? Find the first five terms of the sequence. a. recursive; 1, -4, 16, -64, 256 b. recursive; 0, -16, -24, -48, -80 c. explicit; 1, -4, 16, -64, 256 d. explicit; 0, -8, -24, -48, -801 solutions Answer 220934 by jim_thompson5910(28715)   on 2010-05-27 00:02:24 (Show Source): You can put this solution on YOUR website!It's explicit since you are able to find any term you want (eg the first or the eighty first) and you don't need to know anything about any previous terms. I'll let you find the first five terms. Simply plug in , , , , and and evaluate each individual expression.
 Percentage-and-ratio-word-problems/309004: an iteam is originally priced at D dollars will be discounted at 35%. write an expression to represent the new price. i thought that you would take D/.35 but that is not right.1 solutions Answer 220930 by jim_thompson5910(28715)   on 2010-05-26 23:56:13 (Show Source): You can put this solution on YOUR website!Say the item is $100, if you divide by 0.35, you then get which is clearly NOT a discount (unless you like paying more for something that should be less) Instead, when that same$100 item is discounted by 35%, this basically means that you are subtracting 35% of that item's price from the price of the item. Recall that 35% is 0.35 in decimal form. So if a item is originally \$100, then a 35% discount reduces the price to dollars. In general, an item at D dollars discounts to . Take note that if , then which is what we originally got. So the new price after the 35% discount is dollars.
 Inequalities/308661: Which of the following statements must be true when a^2 < b^2 and a and b are not 0? I. a^2/a < b^2/a II. 1/a^2 > 1/b^2 III. (a + b) (a - b) < 0 1 solutions Answer 220928 by jim_thompson5910(28715)   on 2010-05-26 23:37:37 (Show Source): You can put this solution on YOUR website!I. Clearly this is false. If , then the inequality sign should flip, but it does not. If the sign did flip, then it would only be true for negative values of 'a', but what if 'a' was positive? Since we have this uncertainty, statement I is false. II. If and , then and are both positive numbers. Recall that if and 'x' and 'y' are both positive, then which shows us that statement II is true. III. Start with the given inequality. Subtract from both sides. Factor the left side using the difference of squares. So statement III is true.
 Inequalities/308695: If xy > 1 and z < 0, which of the following statements must be true? I. x > z II. xyz < -1 III. xy/z < 1/z 1 solutions Answer 220927 by jim_thompson5910(28715)   on 2010-05-26 23:20:25 (Show Source): You can put this solution on YOUR website!I. False. For example, let x = -10 and z = -1. Clearly is false. If we let , then showing that is true. II. False, this is only true if . So is on the right track, but it is false. For example, if , and we let , then which is clearly not less than -1. We must make the requirement that the right side be 'z' and not -1. III. This is true since dividing both sides of an inequality by a negative number will flip the inequality sign. Basically, divide both sides of by the negative number 'z' to get (don't forget to flip the sign).
 Inequalities/308996: Solve. 8 - 3x < -71 solutions Answer 220924 by jim_thompson5910(28715)   on 2010-05-26 23:07:29 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Quadratic-relations-and-conic-sections/308992: 4x^2 + ky^2 - 8x + 17y = 3 Find the vaule of k to make this equation a circle, ellipse, hyperbola, and parabola; so different vaules for k that will make those different kinds of equations. Any single one of them would be helpful if you can't necessairly figure them all out, so if you know anything at all pleaseee help. Thank you so much! 1 solutions Answer 220922 by jim_thompson5910(28715)   on 2010-05-26 22:55:37 (Show Source): You can put this solution on YOUR website!This is very helpful to remember: For the general conic If , then the given conic above is an ellipse Furthermore, if , and , then the conic is also a circle If , then the given conic above is a parabola If , then the given conic above is a hyperbola First, let's subtract 3 from both sides to get So if we wanted to force to be a circle, then we must make sure that , , and . In this case, , , , , , and . Plug these values in to get and simplify to get . Solve for 'k' to get . So 'k' must be positive. Also, because we want and , and we know that , this means that as well. But . So This means that if , then we get the circle For any ellipse, just pick a positive 'k' value that is NOT equal to 4. This 'k' value will make true. For the parabola, just make since this satisfies the equation (basically, everything goes to zero since B and C are zero) And finally, for any hyperbola, reverse the idea of the ellipse and pick any negative 'k' value. This works because is essentially the opposite of
Equations/308098: -7x+20=-17x-10
1 solutions

Answer 220917 by jim_thompson5910(28715)   on 2010-05-26 22:43:47 (Show Source):
You can put this solution on YOUR website!
For more help with solving linear equations, check out this linear equation solver.

 Solved by pluggable solver: Linear Equation Solver Start with the given equation. Subtract from both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce.---------------------------------------------------------------------- Answer: So the solution is