You can put this solution on YOUR website!
let x=vertex angle

the angles of a triangle (ANY TRIANGLE) sum to 180 degrees ... the 2 base angles of an isoceles triangle are equal

so, ((x/2)+16)+((x/2)+16)+x=180 ... 2x+32=180 ... 2x=148 ... x=74

You can put this solution on YOUR website!
VERY difficult to answer without knowing the size and shape of the track

You can put this solution on YOUR website!
find the roots of the equality 6x^2+5x=4 ... 6x^2+5x-4=0 ... factoring gives (3x+4)(2x-1)=0 ... so the roots are -3/4 and 1/2

the roots are the "boundry points" between solutions ... in this case, the three ranges are <-3/4, between -3/4 and 1/2, and >1/2

test a range by choosing a value in it ... 0 is between -3/4 and 1/2 ... 6(0^2)+5(0)<4 ... 0<4 so x must be between -3/4 and 1/2

testing the other ranges will show no solution; this is because the "boundry points" are between solutions and non-solutions

(-3/4) < x < (1/2)

You can put this solution on YOUR website!
the dot product is multiplying the row elements by the corresponding column elements and summing the results

(3*2)+(1*-1)+(4*5)=6-1+20=25

You can put this solution on YOUR website!
by rules of exponents, 2^(x+2)=(2^x)(2^2) ... so 4(2^x)-2^x=48 ... 3(2^x)=48 ... 2^x=16 ... so x=4

2*2*2*2=16

You can put this solution on YOUR website!
substitution means put the (a) value into the equation where (a) is and you will get a numerical value for (b)

then put the (b) value in the table next to the (a) value that you used to get it

You can put this solution on YOUR website!
perpendicular means that the slopes are negative reciprocals of each other

the original line has a slope of 3/4, so the perpendicular line has a slope of -4/3

3x-4y=0 ... -4y=-3x+0 ... y=(3/4)x+0 (y=mx+b)

can't tell where the 12 comes from ... judging from the question, the 12 could be any number - it is the slope that's important

You can put this solution on YOUR website!
this is what you wrote ... rationalize by multiplying by ... this gives

if you meant ... rationalize by multiplying by the conjugate ... this gives or

You can put this solution on YOUR website!
let h=Harriet's age

"Two less than 6 times Harriet's age" ... 6h-2

"is the same as" ... =

"10 more than twice her age" ... 2h+10

6h-2=2h+10 ... 4h=12 ... h=3

You can put this solution on YOUR website!
remember long division? ... you can use the same technique with polynomials

372 is the same as 3(10^2)+7(10)+2 ... just like 3x^2+7x+2

so, dividing x+3 into x^3+5x^2-6x+10 ... x goes into x^3, x^2 times ... (x^2)(x+3) is x^3+3x^2

(x^3+5x^2-6x+10)-(x^3+3x^2) is 2x^2-6x+10 ... x goes into 2x^2, 2x times ... (2x)(x+3) is 2x^2+6x

(2x^2-6x+10)-(2x^2+6x) is -12x+10 ... x goes into 12x+10, -12 times ... (-12)(x+3) is -12x-36

(12x+10)-(-12x-36) is 46 ... this is the remainder (it is not divisible by x)

this is done like long division ... with all the same power terms lined up vertically

not the case here, but if you were missing a term; like x^3+x-7 (no x^2 term); you would put in a zero for a place holder x^3+0x^2+x-7 ... to keep things properly aligned

You can put this solution on YOUR website!
... ... ...

You can put this solution on YOUR website!
L=2W+3 ... area=L*W ... 99=(2W+3)W ... 2W^2+3W-99=0 ... using quadratic formula gives

... W=6.325 and W=-7.825 ... negative value is unrealistic

L=2W+3 ... L=2(6.3255)+3 ... L=15.651 ... extra digit in W for precision in calculating L

You can put this solution on YOUR website!
multiplying the second equation by 2 and adding the result to the first equation gives (2x+4y)+2(4x-2y)=3+2(1)

2x+4y+8x-4y=3+2 ... 10x=5 ... x=1/2 ... 2(1/2)+4y=3 ... 1+4y=3 ... 4y=2 ... y=1/2 ... answer A)

You can put this solution on YOUR website!
the slope of a line is the change in y (RISE or vertical) divided by the change in x (RUN or horizontal)

the formula is m=(y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are two points ... m=(-4-0)/(0-2)=-4/-2=2 ... answer A.

"RISE over RUN" is a good memory helper

You can put this solution on YOUR website!
(2(-2)-5(4))/(4+3(-1)) ... (-4-20)/(4-3) ... -24/1 ... -24 ... looks like A)

if you are using a calculator, it may be a good idea to use parentheses liberally

without parentheses, you get three terms 2m, -5n/n, and 3p ... evaluating this gives -4-5-3 or -12

You can put this solution on YOUR website!
there are 15 questions with 3 possible choices for each, this means that there are 3^15 different combinations of answers

a.) assuming only one correct choice for each question, there is only ONE combination of all correct answers (1^15)

b.) the number of different groups of 4 items contained in a group of 15 is (15*14*13*12)/(4*3*2*1) ... there are 15 ways to select the first item, 14 ways to select the second, etc. ... the numerator of the expression results from the fact that order is NOT important ... a,b,c,d is the same group as b,a,d,c

c.) there are 15 questions with 2 possible wrong choices for each, this means that there are 2^15 ways to get EVERY question wrong ... since there are 3^15 combinations of answers, there are ((3^15)-(2^15)) ways to get at least one item correct

You can put this solution on YOUR website!
you need two points to determine the slope of a line ... you have only provided one

perhaps this is the reason you can't understand the problem?

You can put this solution on YOUR website!
r*t=d ... let r and d be the rate and distance of the second plane ... 3r=d or r=d/3

for first plane ... 3(2r-250)=d+300

substituting d/3 for r gives 3(2(d/3)-250)=d+300 ... 2d-750=d+300 ... d=1050

You can put this solution on YOUR website!
r*t=d ... let r and d be the rate and distance of the second plane ... 3r=d or r=d/3

for first plane ... 3(2r-250)=d+300

substituting d/3 for r gives 3(2(d/3)-250)=d+300 ... 2d-750=d+300 ... d=1050

You can put this solution on YOUR website!
you have correctly calculated the architect's markup ... the selling price is the architect's cost PLUS the markup

You can put this solution on YOUR website!
area equals length*width ... in this case, x-dimension*y-dimension ... the y-dimension is f(x)

since the parabola is centered on the y-axis, the x-dimension is 2x ... so a=(f(x))*2x ... (27-3x^2)2x ... 54x-6x^3

You can put this solution on YOUR website!
undoing the division gives (x-3)(x^2+3x-5)+2 ... x^3+3x^2-5x-3x^2-9x+15+2 ... f(x)=x^3-14x+17

f(3)=3^3-14(3)+17=27-42+17=2

this is an example of the remainder theorem; which states that when you divide f(x) by (x-a) the remainder equals f(a)

You can put this solution on YOUR website!
when x=0; the denominator of the second term (12/4x) becomes zero, resulting in an undefined quantity

on either side of zero, the second term has a large + or - value ... this results in a vertical asymptote at x=0

You can put this solution on YOUR website!
not sure if this is legitimate, but it works ... 44*(5-(3+2))=1(0)

You can put this solution on YOUR website!
perpendicular lines have slopes that are negative reciprocals, so the slope of line 1 is -1/(-4) or 1/4

it passes through the origin so the equation is y=x/4 ... substituting gives t+1=t/4 ... 4t+4=t ... 3t=-4 ... t=-4/3

You can put this solution on YOUR website!
the next step (6th) in the table would be for 6 numbers, giving a sum of 6*7 or 42

if you think about the first 100 positive numbers; 1+100=101, 2+99=101, 3+98=101, etc.

there will be 50 such pairs ... so the sum is 101*50 or 5050

You can put this solution on YOUR website!
the second cylinder has the same radius as the first (they are equally big "around")

the second one is twice as long ... if you cut it in half, it would make two of the first cylinder

so it must have twice the volume ... answer (B)

You can put this solution on YOUR website!
this is the difference of two squares ... the first three terms are a perfect square, as is the last term

(3x+2y)^2-(5)^2 ... (3x+2y+5)(3x+2y-5)

You can put this solution on YOUR website!
with work problems, the trick is to see what fraction of the job is done by each person

if Simone can build a treehouse in 15 hours, then in 7 hours she builds 7/15 of the treehouse

this means Tyrese builds 8/15 of the tree house in 7 hours ... so 7 is to 8/15 as x is to 15/15 (or 1 whole treehouse)

You can put this solution on YOUR website!
start by defining variables ... let t=Tom's marbles, let d=David's marbles ... then write equations

"Tom and David both collected a total of 480 marbles" ... t+d=480

"Tom stacked each column with 6 marbles. and David stacked each column with 9 marbles. They stacked 72 columns together" ... (t/6)+(d/9)=72

this gives you two equations and two unknowns ... the easiest solution method is probably substitution

You can put this solution on YOUR website!
if the two expressions are divided (rather than added as indicated); then factoring can help

(3x^2+7x-40)/(x+5) ... ((3x-8)(x+5))/(x+5)=(3x-8)

what type of division did you try? long division can be done with these expressions