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3 years ago

13

your parent gave you a gift cart for your favorite coffee shop. the card was worth $50 when you got it . each day, buy a drink f

or $3 . which equation shows the value on the gift card over time ?

1 answer:

saveliy_v [14]3 years ago

6 0

Answer:

x-3

Step-by-step explanation:

x representing the amount of money on the gift card

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One number is 4 less than 3 times another.their sum is -16. find the smaller

Airida [17]

Answer:

x = -13, y = -3

Step-by-step explanation:

let a number = x; the other = y

x = 3y - 4

x + y = -16

Isolate the y in the second equation. Subtract x from both sides

x (-x) + y = -16 (-x)

y = -16 - x

Plug in -16 - x for y

x = 3(-16 - x) - 4

Simplify. Distribute 3 to all terms within the parenthesis

x = -3x - 48 - 4

x = -3x - 52

Isolate the x. Add 3x to both sides

x (+3x) = -3x (+3x) - 52

4x = -52

Divide 4 from both sides

(4x)/4 = (-52)/4

x = -52/4

x = -13

Plug in -13 for x in one of the equations:

x + y = -16

(-13) + y = -16

Isolate the x. Add 13 to both sides

y - 13 (+13) = -16 (+13)

y = -16 + 13

y = -3

Answers: x = -13, y = -3

~

6 0

3 years ago

This is the last one i think

sashaice [31]

I believe the answer is y=3x -4

the slope is 3 because the y value increases by 3

8 0

3 years ago

Solve the following equation with the initial conditions. x¨ + 4 ˙x + 53x = 15 , x(0) = 8, x˙ = −19

Katen [24]

$x''+4x'+53x=15$

has characteristic equation

$r^2+4r+53=0$

with roots at $r=-2\pm7i$ . Then the characteristic solution is

$x_c=C_1e^{(-2+7i)t}+C_2e^{(-2-7i)t}=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)$

For the particular solution, consider the ansatz $x_p=a_0$ , whose first and second derivatives vanish. Substitute $x_p$ and its derivatives into the equation:

$53a_0=15\implies a_0=\dfrac{15}{53}$

Then the general solution to the equation is

$x=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)+\dfrac{15}{53}$

With $x(0)=8$ , we have

$8=C_1+\dfrac{15}{53}\implies C_1=\dfrac{409}{53}$

and with $x'(0)=-19$ ,

$-19=-2C_1+7C_2\implies C_2=-\dfrac{27}{53}$

Then the particular solution to the equation is

$\boxed{x(t)=\dfrac1{53}e^{-2t}(409cos(7t)-27\sin(7t)+15)}$

8 0

3 years ago

One week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet

Bond [772]

Trumpet = $174 Clarinet = $149 Violin = $89 Let's write some equations to express what we know. 2t + 3c + 5v = 1240 3t + 1c + 4v = 1027 5t + 7c + 2v = 2091 So we have 3 unknowns and 3 equations. The 2t and 3t are rather interesting in the 1st 2 equations since the 3rd equation has 5t. So if we subtract the 1st and 2nd equations, we can cancel out the t values. So 5t + 7c + 2v = 2091 -( 3t + 1c + 4v = 1027) = 2t + 6c - 2v = 1064 -(2t + 3c + 5v = 1240) = 3c - 7v = -176 Now we can express c in terms of v. 3c - 7v = -176 3c = 7v - 176 c = (7/3)v - 58 2/3 Substitute the expression (7/3)v - 58 2/3 for c in the expression 2t + 3c + 5v = 1240 giving 2t + 3((7/3)v - 58 2/3) + 5v = 1240 and solve for t, first distribute the 3 2t + 7v - 176 + 5v = 1240 Merge the v terms 2t + 12v - 176 = 1240 Add 176 to both sides 2t + 12v = 1240 + 176 = 1416 Subtract 12 v from both sides 2t = 1416 - 12v Divide both sides by 2 t = 708 - 6v Now substitute both 708 - 6v for t and (7/3)v - 58 2/3 for c in 3t + 1c + 4v = 1027 and solve for v 3t + 1c + 4v = 1027 3(708 - 6v) + (7/3)v - 58 2/3 + 4v = 1027 Distribute the 3 3(708 - 6v) + (7/3)v - 58 2/3 + 4v = 1027 2124 - 18v + (7/3)v - 58 2/3 + 4v = 1027 Combine terms 2065 1/3 - (11 2/3)v = 1027 Subtract 2065 1/3 from both sides -(11 2/3)v = 1027 - 2065 1/3 = -1038 1/3 Divide both sides by -11 2/3 v = 89 So we know the violins cost $89 each. Plugging that value into the formula t = 708 - 6v which we created earlier t = 708 - 6v t = 708 - 6 * 89 = 708 - 534 = 174 So we know that a trumpet costs $174 Now plug the price of a violin into the formula c = (7/3)v - 58 2/3 to get the cost of a clarinet. c = (7/3)v - 58 2/3 c = (7/3)89 - 58 2/3 = 207 2/3 - 58 2/3 = 149 And a clarinet is $149 Let's verify 2t + 3c + 5v = 2*174 + 3*149 + 5*89 = 348 + 447 + 445 = 1240 3t + 1c + 4v = 3*174 + 1*149 + 4*89 = 522 + 149 + 356 = 1027 5t + 7c + 2v = 5*174 + 7*149 + 2*89 = 870 + 1043 + 178 = 2091 All the expressions match what was given, so the prices are Trumpet = $174 Clarinet = $149 Violin = $89

6 0

3 years ago

Kevin asked his trainee, Anna, to help call some of his clients to sell a newly-issued municipal bond. If he had to call all of

weqwewe [10]

Answer:

3.6 hours

Step-by-step explanation:

To solve, create a Rate, Time, Work chart:

Work is rate times time. For Kevin, his work is going to equal x over 6 job. For Anna, her expression for work will equal x over 9 job.

The work is 1 job of calling all clients, so their combined work is equal to 1.

x over 6 plus x over 9 equals 1

In the rational equation, x is the amount of time it takes Kevin and Anna to call the clients together. With rational equations, the terms can be added together once they have common denominators.

x over 6 plus x over 9 equals 1

fraction numerator begin display style x left parenthesis 9 right parenthesis end style over denominator begin display style 6 left parenthesis 9 right parenthesis end style end fraction plus fraction numerator begin display style x left parenthesis 6 right parenthesis end style over denominator begin display style 9 left parenthesis 6 right parenthesis end style end fraction equals fraction numerator begin display style 1 left parenthesis 6 right parenthesis left parenthesis 9 right parenthesis end style over denominator left parenthesis 6 right parenthesis left parenthesis 9 right parenthesis end fraction

fraction numerator 9 x over denominator 54 end fraction plus fraction numerator 6 x over denominator 54 end fraction equals 54 over 54

9 x plus 6 x equals 54

15 x equals 54

x equals 3.6

If Kevin and Anna work together, they can call all the clients in 3.6 hours.

7 0

3 years ago