Jason purchased a can of tomato sauce and three pounds of apples for $\$7.05$. Gina purchased a can of tomato sauce and 5 pounds of apples for $\$11.35$. What is the price of the tomato sauce?]]>

its 2 to the 3rd power. How do you solve this?]]>

Yes I know its insulting

But how many seconds did it take you to see the solution]]>

Then f(2017) = ?]]>

(0.149/(18 - 0.1x - 0.05n)^2) - (44.5/x^2)

The task is to find the variable x

Thanks a lot, your help will mean a lot to me.]]>

Explain what would happen if the truck were able to maintain a constant speed over 250km/h?

Is it reasonable to assume a constant...

Transportation calculus]]>

$\frac{5x^2+1}{(3x+2)(x^2+3)}$

One factor in the denominator is a quadratic expression

Split this into two parts A&B

$\frac{5x^2+1}{(3x+2)(x^2+3)}=\frac{A}{(3x+2)}+\frac{Bx+c}{(x^2+3)}$

$\frac{5x^2+1}{(3x+2)(x^2+3)}=\frac{A(x^2+3)}{(3x+2)}+\frac{Bx+c (3x+2)}{(x^2+3)}$

${5x^2+1}={A(x^2+3)}+{Bx+c (3x+2)}{}$

and cannot take it from here]]>

]]>

3x+5y; 5x; 7x-5y; 9x-10y.....

I need to formulate a general term - Tn=T1+d(n-1)

In the above sequence I have no idea what.

I also think this sequence is non linear.

Please help with a solution

Thanks]]>

Thank you in advance for your help and time.]]>

In the attached picture there is an equation. I need to fill the general expression on the left hand side, and to prove by induction that the sum is equal to the expression in the right hand side.

I am not sure how to find the general expression. Can you kindly assist ?

Thank you !

]]>

\(\displaystyle 3x^2y-y^3=b\)

make a formula using a and b for x and y.

What I've done:

\(\displaystyle x^3-3xy^2+3x^2y-y^3=a+b\)

\(\displaystyle x^3+3x^2y-3xy^2-y^3=a+b\)

\(\displaystyle (x-y)(x^2+4xy+y^2)=a+b\)

I don't know what to do from here. Any hints?]]>

For this one I don't know what I have to do at all other than brute-forcing which may even be impossible.]]>

Write down for the line

y = 2x + 3 perpendicular and parallel lines passing through the point

(1; 1) equations.]]>

1200 customers. How many customers did the company have in 2008 if we know that

the number of customers growing is linear?

Just want to make sure, is 780 the correct answer?]]>

Hello, so there's a graph provided in the task which I'm trying to solve for a quite a while and I am really confused where the 5 to 8 line came from, because (5x+8y<5) doesn't create that sort of line. Is it possible that there's a misstake done by my teacher or am I understanding something wrong?]]>

A. 14

B. 15

C. 16

D. 17

E. 18

What should I do? I tried substituting \(\displaystyle y = 4^x\) but it didn't help since the quadratic equation formed didn't have real roots.]]>

I suspect I am a bit unique here. I'm struggling with a math problem for a business model rather than a homework assignment. It's been quite a while since I have worked with exponents and I am hoping someone can assist me with a question.

I have the following calculations:

280*.985^11

280*.985^10

280*.985^9

280*.985^8

280*.985^7

280*.985^6

280*.985^5

280*.985^4

280*.985^3

280*.985^2

280*.985^1

The base and coefficient are the same, but the exponent is not. I know that I...

Exponents for Business]]>

]]>

I'm currently on khan academy and am stuck at solving the following question. I try to use the 'multiply fraction by whole number' solution, however the correct solution is different. What is the correct way to solving this?

3/7 r + 5/8 s when r = 14 and s = 8

The way i solve it leads me to: 3/98 + 5/8

(using this process 3/7 * 14/1 = 3/7 * 1/14 = 3/98 )

However the correct solution is: 3/7(14) + 5/8(8)]]>

Anyone please lead me to factorize this eq on my own....and if you don't wanna waste your timr,just show me how you do it.....]]>

The price of a dress is marked down 20% on May 1. On May 25th the reduced price is marked down an additional 15% to \$51. (a) What percent of the original price is the final sale price? (b) "What is the original price?

All I could think was trying to work the problem this way:

(a) 20% + 15% = 35% (total discount percentage)

100% - 35% = 65% (percent of the original price for a sale price of \$51)

(b) 65%x = \$51

x = 51/.65

x = \$78.46 (original price)...

Introductory Algebra Percentage Word Problem]]>

The original program is written in quick basic (but i of course cannot locate the bas (source) file.

For the first correction, lets call it "A". if I enter 1.78 as my decimal, the hex return is 00 05 10. but, if i enter 1.78 as the decimal for "B", i get, 10 00 FE. For "C", i get, 20 00 FE

So obviously, the leading bits of the return (00,10,20) are...

Hexidecimal conversion help]]>

What I've done so far:

For n = 1

\(\displaystyle 7^1-2^1=7-2=5\) (true that it is divisible by 5)

For n = k

\(\displaystyle 7^k-2^k=5a\) (assumed to be true that it is divisible by 5)

For n = k + 1

\(\displaystyle 7^{k+1}-2^{k+1}=7^k\cdot7-2^k\cdot2=7(7^k-2^k)+12\cdot2^k=7(5a)+12\cdot2^k\)

This is where the problem lies. How can I show that \(\displaystyle 12\cdot2^k\) is divisible by 5?]]>

I'm helping a friend's daughter factoring trinomials. I can get to the correct answer, but usually thru a system of trial and error and not a defined set of rules in every instance. Example

6x^2 + 39x - 21

3(2x^2 +13x-7)

Here's where I get stuck. I know that the factors of -7 are going to be 1, -7 or -1, 7. However, these don't add to 13. I suppose that has something to do with the...

Help with factoring trinomials]]>

I am using this method in which the partial fraction is broken in to 3 parts namely A,B &C

$\frac{x^2}{(x-2)(x+3)(x-1)}=\frac{A}{(x-2)}+\frac{B}{(x+3)}+\frac{C}{(x-1)}$

$\frac{x^2}{(x-2)(x+3)(x-1)}=\frac{A(x+3)(x-1)+B(x-2)(x-1)+C(x-2)(x+3)}{(x-2)(x-3)(x-1)}$

Common denominators cancel out resulting in,

${x^2}={A(x+3)(x-1)+B(x-2)(x-1)+C(x-2)(x+3)}$

Now what values should be substituted to...

Partial fraction problem (x^2)/[(x-2)(x+3)(x-1)]]]>

What is the simplest way to factorize given equation? Thank you.]]>

I got a very basic question...

A number n is dividable by 15 and 18. Can I assume from that that it is dividable by 27?

(dividable - you can divide it by 15 and get no reminder).

If it is dividable by 15, it is by 3 and 5. If by 18, it is dividable by 3 and 6, which means 3 and 2.

Can I say that since not every number that is dividable by 3 is also dividable by 9, this number is not dividable by 27, not necessarily anyway ?]]>

f0 (x) = x-12.

Let's specify fn+1(x)=fn({24x/13}), where {x}=x−⌊x⌋ is a fractional part of the number x. Let θn be the tangent of the largest acute angle that the graph of fn creates with the axis OX. Find ⌊θ13⌋.]]>

I know that it means \(\displaystyle \frac1{1+2}+\frac1{1+2+3}+\frac1{1+2+3+4}+\frac1{1+2+3+4+5}+\frac1{1+2+3+4+5+6}+...+\frac1{231}\), but how do I answer? It's from a student worksheet for 7th graders, so they haven't learnt about sequence and series yet. Granted, the book also says that the question was from a middle school-level math contest.]]>

a. 1 : 210

b. 1 : 2.100

c. 1 : 21.000

d. 1 : 210.000

Can you help? The 200 and 210 makes me think that the distance on map won't be an integer.]]>

I am trying to develop to formula that will derive a used cars value from a database of used car values.

Assume we are trying to value Car A. The first step is to form a sample of cars matching Car A for each header of the database columns (make, model, variant, engine size, transmission etc etc). The sample size is set to min 3, max 9. Once this sample group has been identified we are left with, in most cases 9 records, with two variables; price and mileage. I then use a...

Need help with formula to value used cars. Please!]]>

My attack power is 46722 and I make 2.15 attacks a second, that come to be a dps of 100,452.3. (I apologize for the big numbers.)

When I try to factor in crit rate and crit damage, I can't seem to get a proper number. My crit rate, currently, is 17.8% and...

DPS Calculator for Video Game]]>

Discounted price related math problem]]>

Suppose we know a and b.

y in the term of a, b?]]>

\(\displaystyle (log_2x)^2+4>5log_7x+log_3x^2\)

This is what I've done so far (attached):

How to solve the quadratic inequation formed? Factorization is an obvious no, and the quadratic formula will just make everything messier, is there any other way?]]>

Thanks in advance!

]]>

f(x)=ab^{x}

where b is a POSITIVE REAL number"

Wait. Give me a reason, why exponent base must be positive and real?

What happens if b<0?]]>

Can anyone help me understand how I get to the answer on this one?

The diagram shows a sketch of the graph of y = x2 + ax + b

The graph crosses the x-axis at (2, 0) and (4, 0).

Work out the value of b.

Thank you in advance!]]>

here is the equation: a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd)

wondering if this can be simplified to something much smaller]]>

If electricity is charged at $0.15 per kWh, for how many hours must the low energy bulb be used in order for the lower cost of running it to exactly compensate for its higher initial cost?

A. 0.25

B 250.00

C 200.00

D 160.00

E 720.00

answer: D 160.00

why?

On first appearance you would think:

0.60 + 0.1 * 0.15 * t = 3.00 + 0.02 * 0.15 * t

t =...

high school simple algebra word problem]]>

I'm trying to work out the individual steps to get from

start: 3y + x = -1

to: 3y = -x -1

to: y = - 1/3x -1/3

Could anyone help me with this!

Thank you ]]>

Ok a student sent this to me yesterday so want to answer without too many steps

I think the first thing to do is multiply every

term by 12

$2(x+1)<12x-3(3x-2)$

Expanding

$2x+2<12x-9x+6$]]>

My workings ;3x=15

Any help is appreciated, thanks

= 5x, as 15 divide by 3x=5x]]>

Let f be a function satisfying f(xy) = f(x)/y for all positive real numbers x and y, and f(500) = 3.

What is f(600)?]]>

I'm working on solving linear equalities (with equations) and can anyone help with the below question. I know the answer is -16, but I can't figure out the steps that gets it to this.

4x-12≤6x+20

Once I've evened out the x's on both sides and got this to 2x, I'm then left with -12 and +20, which leaves +8, divided by the remaining 2x, which leaves 4. This isn't correct though, so could anyone help me with the different stages on this.

Thank you!]]>

From HiSet free practice test]]>

Taken from HiSet free practice test]]>

Taken from HiSet free practice test]]>

I have to simplify this square root fraction:

10/√5 + √20

The answer is 4√5, but I do not get to that answer.

Please help.]]>

Could someone help me with this question:

2x – 1 = 9 – 3x

Thank you in advance!!!]]>

The question is:

The following function, L, gives the approximate percent literacy rate in India

L(t)=5.3 x 1.025^t

Which of the following equivalent functions shows, as a constant or coefficient, the approximate number of years it took for the literacy rate to triple?

(a) L(t)=5.3 x 3^t/44.5

(b) L(t)=5.3 x 1.077^t/3

(c) L(t)=5.3 x 1.008^3t

(d) L(t)=3 x 1.025^t+23

Thanks...

manipulating quadratic and exponential expressions]]>

I am working on a data set and I have log-transformed two variables a and b and would like to figure out the relationship between the respective ratios. I have a strong intuition that a/b should have a well-defined range for a given value of lna/lnb, but my maths is poor.

a and be are positive integers with a finite range

0 < a < amax, amax=499639

1 < b < bmax, bmax=837481

I am looking for the range of

a/b

when

ln(a+1)/ln(b+1) = x

0 < x < 1

I know that for x = 1, a/b = 1 and when x =...

Ratio of a/b when lna/lnb=x]]>

- ...

Calculating amount left at the end of a repetetive cutting down cycle.]]>

(x

This one throws me off because I don't know how to deal with the z, as only on the right side of the divide]]>

Obviously formulas like those might solve...

compare trips based upon price]]>

\$400.00 x .25 = \$100.00

\$100.00 - \$85.00 = \$15.00

However, rather than doing that; the following was done:

\$400.00 - \$85.00 = \$315.00

\$315.00 x .25 = \$78.75

How much has been overpaid now?]]>

How many minutes does it take 14 people to paint 14 walls?]]>

a is not suppose to be -1; this is the only rule in the equation

The answer is the second picture, I just dont know the steps that lead to that answer.

]]>

1. The quadratic equation whose roots are k less than the roots of \(\displaystyle ax^2+bx+c=0\) is \(\displaystyle a(x+k)^2+b(x+k)+c=0\).

2. The quadratic equation whose roots are k more than the roots of \(\displaystyle ax^2+bx+c=0\) is \(\displaystyle a(x-k)^2+b(x-k)+c=0\).

3. The quadratic equation whose roots are n times the roots of \(\displaystyle ax^2+bx+c=0\) is...

[ASK] Proof of Some Quadratic Functions]]>

I've not had any good experiences so far getting an answer I can understand, because my maths education didn’t really prepare me to even begin to try to figure this one out!

I'll try to explain the situation as best as I can.

I have a material to be used in molding objects, which shrinks approximately 15% as it dries.

I have objects that are to be molded in this material, and they must end up at a...

Seeking a specific formula to allow for materials shrinkage]]>

I'm currently trying to create a function/expression based on several variables. I've so far figured out the rules that the variables should follow but I'm struggling to put them together into a formula. I'm hoping that someone here might tell me if this is even possible, and give me some advice or direct me somewhere specific I can read about my problem (I haven't studied any maths in some time and I don't recall an exact name for what I'm trying to do).

To give my variables...

Use Variables to Create Function]]>

We have L : P -> R^2

L is a linear transformation with :

[tex]B = \left\{1-x^{2},2x,1+2x+3x^{2} \right\} \; and \; B' = \begin{Bmatrix} \begin{bmatrix} 1\\-1 \end{bmatrix} \begin{bmatrix} 2\\0 \end{bmatrix} \end{Bmatrix} as \; [L]^{B'}_{B} = \begin{bmatrix} 2 &-1 &3 \\ 3&1 & 0 \end{bmatrix}[/tex]

I have to find

1/ the transfer matrix from B' to the canonical basis of...

Transfer matrix]]>

Here is the Question:

Consider the cubic equation x^3 - kx + (k + 11) = 0, find all the integer values of k for which the equation has at least one positive integer solution for x

Thanks, Taran]]>

There is a large bag of red and blue counters. One red and one blue counter are removed from the bag. This process is repeated until 1/4 of the red counter and 3/5 of the blue counters have been removed. What fraction of the original counters remain in the bag?

Im stumped!

I've written that:

Red - n = 3/4 Red

blue - n = 2/5 blue

n is the number of counters removed as it the same number removed from both.

therefore n =...

Ratio word problem: What fraction of the original counters remain in the bag]]>

a. \(\displaystyle \left(1+2\sqrt2\right)9\sqrt2\)

b. \(\displaystyle \left(1+2\sqrt2\right)9\sqrt3\)

c. \(\displaystyle \left(1+2\sqrt2\right)18\sqrt3\)

d. \(\displaystyle \left(1+2\sqrt2\right)27\sqrt2\)

e. \(\displaystyle \left(1+2\sqrt2\right)27\sqrt3\)

I got stuck at \(\displaystyle \frac{56-3^2\left(3^{\frac52}\right)}{2^-{\frac43}-2^{-2}}\) and don't know how to continue to...

[ASK] Exponents and Roots Simplification problem]]>

If a = -1, what is the solution set of the equation sqrt (x+ a) = x −7

{5}

{10}

{5, 10}

No solution

(5,10) correct?

Thanks]]>

Is this true? Because I recall the purpose of PEMDAS is to prevent ambiguity, and without it, at any level, would result in ambiguity, even though it's just a convention and not something we can really prove.

Also, when you reword equations are you still relying on the concept of PEMDAS? Like, for example, to say $\frac{5}{3}n=15 \equiv 5n=45$ is to validate PEMDAS, yes?]]>

This is the problem at hand

The average distance from Earth to Moon is about 384,403 kms. The sun is the closest star to Earth and is about 150 million kilometers away. the next closest star is Proxima Centauri which is about 4.22 light years away from Earth. A light year is defined as...

average distance]]>

1) $x^2+m^2=2mx+(nx)^2 $

2) $\sqrt{x^2+3x+7}-\sqrt{x^2-3x+9}+2=0$

I know the answer to the first equation is {$\frac{m}{1-n}, \frac{m}{1+n}$}. The answer to the second equation is {$-\frac{9}{5}$}.

I don't understand why I'm struggling on problems that look so simple. Here's how I approached the first problem:

$$x^2+m^2-2mx=n^2(x^2)$$

$$x^2+2mx+m^2-2mx=n^2x^2$$

$$\sqrt{x^2+m^2}=\sqrt{n^2x^2}$$

$$x=\frac{x+m}{n}...

solve √(x^2+3x+7)-√(x^2-3x+9)+2=0]]>

why is this equation so special it is in standard form, and when i solve for zeros

i factor down to

-1( 2x^2-3x-20)

factor

( 2x^2-3x-20)

factor by grouping 2(-20)=-40 what numbers multiple to equal -40 and add to equal -3

-8(5) = -40

-8+5= -3

and then just to find zeros the next step would be

(x-8) (x+5)

x=8 x=-5

BUT

thats not right apparently the answer is

x=4 x = -5/2

the answer i got here

(x-8) (x+5)

x=8 x=-5

is meant to be -1(2x+5)(x-4)...

quadratic equations ( solving for zeros/roots) trickey]]>

A DVD drive rotates at an angular frequency of 4800 rpm. a) what is it's angular speed in rpm? b) at 4800 rpm, what is the linear speed (in knm/hr) of (i) the center point and points (ii) 5 cm and (iii) 6 cm from the center?

Thanks!]]>

Wacky explanation in a student solutions manual for manipulating an equation]]>

i get that this is how its written on a graph y=(x-2)^2+k

that the graph looks as if the value of h is positive as in +2 ( however its value is actually negative)

looks like it shifted right

my textbook contradicts itself

y=3(x-1)^2 +2 or y=3(x-(-1))^2 +2

a positive ie x minus a negative ie -1 equals a positive ( thus h is positive and shifts right

the value of h is +1 thus there is a right shift 1 unit

( two...

the shifting of h in vertex form]]>

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

I put the conditions x different from 0 and 1-4x^2>=0 and I got [-1/2,0)U(0,1/2] which is the right answer but I'm confuse because I usually subtract 3 to get (1-sqrt(1-4x^2)/x - 3 < 0 then, after I made some work and I got a fraction, I find the variation of each function (from numerator and denominator) and in the final I find the sign of f(x) which should be negative in our case and like this I find the...

solutions of an inequality (1-√(1-4x^2)/x < 3]]>

f(x)= -2(x+1)/(x-1)^2

x is from [0,1)U(1,3]

I need to find the image of the function which is (-infinity, -2].I tried with the derivative but when I solve f'(x)=0 I obtain x=-3 which is not from x interval.I don't know how to continue.]]>

o A. y=x 2 −9

o B. y=x 2 −6x+9

o C. y=x 2 −5x+6

o D. y=x 2 +x−6

A

2. What are the x-intercepts of y=(x−2)(x+5) ?

o A. (0, 2) and (0, -5)

o B. (0, -2) and (0, 5)

o C. (-2, 0) and (5, 0)

o D. (2, 0) and (-5, 0)

D

5. Which of these quadratic functions has exactly one x -intercept?

o A. y=x 2 −9

o B. y=x 2 −6x+9

o C. y=x 2 −5x+6

o D. y=x 2 +x−6

A

2. Which of the following parabolas opens upward and appears narrower than...

Quadratic functions: Which of these quadratic functions has exactly one x -intercept]]>

Can you give me some tips?]]>

f: (0,infinity) -> R

f(x)=log_3(x) (the base is 3)

I need to find the number of "n" values ( n is a natural number except 0 N*) such that this inequation: f(n/x) >= 1 to have just 3 solutions in N*.

A. infinity

B. 6

C. 9

D. 26

E. 3 (correct answer)]]>

a^x=x+2 has two real solutions.I need to find positive values for "a".

A) (1, infinity)

B) (0,1)

C) (1/e , e)

D) (1/(e^e), e^e)

E) (e^(1/e), infinity)

I tried to solve and I did it but I don't understand some things.

I let a picture below to see.

First, I need to know if there's other way to solve this kind of exercise.I would be happy if I would get some ideas.

Also, from my solution, I don't understand why from that table results just...

indications equation a^x=x+2]]>

A)a=1/e

B)a=e

C)a=e^(1/e)

D)a=e^e

E)1/(e^e)

The right answer is C.I tried to derivate then to resolve f'(x) but didn't work]]>

I am trying to prove by induction the following:

I checked it for n=1, it is valid. Then I assume it is correct for some k, and wish to prove it for k+1, got stuck with the algebra. Can you kindly assist ?

Thank you.]]>