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Sunny_sXe [5.5K]

2 years ago

5

Originally, Juan borrowed $10, but his mother loaned him $3 more, so he borrowed a total of $13. He sells $25 worth of lemonade

in his first week. After Juan pays his mother back the $13 he borrowed, his profit is $12.

2 answers:

Rina8888 [55]2 years ago

6 0

Correct answer

Justification:

10+3 = 13

25-13 = 12

ExtremeBDS [4]2 years ago

4 0

What is the question

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A company produces boxes of dvds of a rate at 52 boxes per hour. they begin to produce boxes when they first open for the day an

zvonat [6]

Answer:

284 boxes

Step-by-step explanation:

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2 years ago

Jack was so frustrated with his slow laptop that he threw it out of his second story window. The height, h, of the laptop at tim

jeyben [28]

Answer:

The domain of the function is the interval [0,2.23]

see the explanation

Step-by-step explanation:

Let

t ----> the time in seconds

h(t) ----> the height of the laptop in units

we have

$h(t)=-16t^{2}+28t+17$

we know that

When the laptop hits the ground, the value of h(t) is equal to zero

so

For h(t)=0

$-16t^{2}+28t+17=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^{2}+28t+17=0$

so

$a=-16\\b=28\\c=17$

substitute in the formula

$x=\frac{-28(+/-)\sqrt{28^{2}-4(-16)(17)}} {2(-16)}$

$x=\frac{-28(+/-)\sqrt{1,872}} {-32}$

$x=\frac{-28(+/-)12\sqrt{13}} {-32}$

$x_1=\frac{-28(+)12\sqrt{13}} {-32}=-0.477$

$x_1=\frac{28(-)12\sqrt{13}} {32}=-0.477$ ---> is not a solution

$x_2=\frac{-28(-)12\sqrt{13}} {-32}$

$x_2=\frac{28(+)12\sqrt{13}} {32}=2.23\ sec$

therefore

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All real numbers greater than or equal to 0 seconds and less than or equal to 2.23 seconds

$0\ sec \leq x \leq 2.23\ sec$

5 0

2 years ago

An aquarium with a square base has no top. There is a metal frame. Glass costs 5 dollars/m2 and the frame costs 2 dollars/m. The

adell [148]

Answer:

C = 420/h + 400

Step-by-step explanation:

Let s be the side of the square base.

Let h be the height

Volume = s*h

20 = s*h

s = 20/h

Cost of glass is

5(20/h) + 5(4* h*20/h)

= 100/h + 400

Cost of frame is

2*4(20/h) + 2*4(20/h)

= 160/h + 160/h

= 320/h

Total cost = C

C = cost of glass + cost of frame

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3 0

2 years ago

Suppose T is the transformation from ℝ2 to ℝ2 that results from a reflection over the y-axis followed by a reflection over the x

LenKa [72]

<u>Answer:</u>

A = \begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix}

<u>Step-by-step explanation:</u>

Let, there be a point (x , y) in R2

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So,

we need to find out a matrix

[tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex]

such that,

(x , y) [tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex] = (-x. -y)

So, we have the following set of equations.

ax + cy = -x ------------(1)

bx + dy= -y-----------(2)

We can get the solution (by inspection) as,

[tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex]

= [tex]\begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix}[tex]

So, the matrix is,

A = \begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix} (answer)

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2 years ago

In Exercises 1 and 2, find the equilibrium solutions of the differential equation specified.1) dy/dt = (y + 3)/(1 - y)2) dy/dt =

Aleks [24]

Answer:

1. Equilibrium solution: y= -3

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Step-by-step explanation:

Thinking process:

The equilibrium solution can only be derived when $\frac{dy}{dt} = 0$

1. Let's look at the first equation:

$\frac{dy}{dt} = \frac{(y+3)}{(1-y)}$

equating $\frac{dy}{dt} = 0$ to the expression $\frac{(y+3)}{(1-y)}$ gives

y + 3 = 0

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Therefore, the equilibrium solution occurs at y = -3

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$\frac{dy}{dy} = \frac{(t^{2}- 1) (y^{2}-2) }{y^{2}-4 }$

dividing each side by (t²-1) gives

1/(t²-1) $\frac{dy}{dt}$ = (y²-2)/ (y²-4)

factorizing the right hand side gives:

at equilibrium: $\frac{dy}{dt} = 0$ , then

y² - 2 = 0

solving for y gives y = ±√2

= ±1.414

5 0

2 years ago