5x -30 = 3x + 60
How many solutions are there

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

1)

Hyp =40

∠48

x = Adj

use CAH since it's got these pieces in it

Cos(48) = x / 40

40* Cos(48) = x

26.76522 = x

x = 26.8  ( rounded to nearest 10th)

2)

∠29

Hyp = 35

Opp = x

use SOH since this problem has those pieces in it

Sin(29) = x / 35

35*Sin(29) = x

16.9683 = x

x = 17.0  (rounded to nearest 10th)

3)

40 = Adj

∠16

Hyp = x

use CAH again

Cos(16) = 40 / x

x = 40 / Cos(16)

x = 41.611

x = 41.6 (rounded to nearest 10th )

4)

∠55

Opp = 35

x = Adj

use TOA

Tan(55) =35/x

x = 35/Tan(55)

x = 24.5072

X = 24.5  ( rounded to nearest 10th)

9514 1404 393

Answer:

  a) S(p) = -97.78p +2977.78

  b) about 98 fewer shirts per week will be sold for each $1 increase in price

  c) 533 shirts per week

  d) $15.63

Step-by-step explanation:

a) You are given two ordered pairs: (p, s) = (10, 2000) and (19, 1120). The two-point form of the equation for a line can be used.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  s = (1120 -2000)/(19 -10)(p -10) +2000

  s = -97.78(p -10) +2000

  S(p) = -97.78p +2977.78

__

b) The slope is shirts/dollar, meaning about 98 fewer shirts will be sold for each dollar increase in price.

__

c) S(25) ≈ 533

At a price of $25, the store would sell about 533 shirts per week.

__

d) 1450 = S(p) = -97.78p +2977.78

  -1527.78 = -97.78p

  15.625 = p ≈ 15.63

The store should charge $15.63 per shirt to maintain sales of 1450 shirts per week.

Answer:

Step-by-step explanation:

[tex]Given \ f (p,q) = 8qe^{-p} + 4pe^{-q} \ where \ P_o(0,0) \\ \text{thus the gradient of f is: } \\ \\ \bigtriangledown f(p,q) = \Big(\dfrac{\partial f}{\partial p}, \dfrac{\partial f}{\partial q} \Big) \\ \\ \dfrac{\partial f}{\partial p} = -8qe^{-p} + 4pe^{-q} \\ \\ \dfrac{\partial f}{\partial p} = 8qe^{-p} - 4pe^{-q} \\ \\ Then: \bigtriangledown f(p.q) = (-4qe^{-p}+ 8qe^{-q}, 4qe^{-p}- 8qe^{-q}) \\ \\ f(0,0) = (-4*(0)e^{-0}+ 8*(0)e^{-(0)}, 4*(0)e^{-(0)}- 8*(0)e^{-(0)}) \\ \\ = (0+8,4-0) = (8.4)[/tex]

[tex]\Big| \Big | \bigtriangledown f(0,0) = \sqrt{(8)^2+4^2} \\ \\ = \sqrt{64+16} \\ \\ = \sqrt{80}[/tex]

[tex]\mathbf{the \ direction \ of \ maximum \ change \ is }= \mathbf{\sqrt{80}} \\ \\ \mathbf{direction }(8,4)[/tex]

Answer:

5 more people studied more in 0-30 minutes than people who studied 121-120 minutes.

Step-by-step explanation:

Answer:

yes because no matter what 24 hrs will equal a day

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Answer:

my guess would have to be

A. slope= 4      

B. y-intercept= 23/3 or 7  2/3(simplified)

Step-by-step explanation:

im not sure how accurate my answer would be but what i did was put the equation in slope intercept form and added 6 for the dilatation to all factors of the equation.

The slope is 2/3.

The y-intercept is -5/3.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line.

6x - 3y = 5

Now,

To apply a dilation with a scale factor of 6 centered at the origin.

We multiply both sides by 6.

So,

6 (6x - 3y) = 6 x 5

Now,

Simplifying.

36x - 18y = 30

Dividing both sides by 18.

2x - y = 30/18

2x - y = 5/3

Now,

Writing in slope-intercept form.

y = mx + c

So,

y = 2x - 5/3

This means,

Slope m = 2

y-intercept c = -5/3

Thus,

The slope is 2/3.

The y-intercept is -5/3.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ6

Answer:

4 5/12 feet tall

Step-by-step explanation:

All you have to do is subtract 1/3 from 4 and 3/4 in order to get this answer.

Answer:

Leon is 53/12 feet or 4 & 5/12 or 4.4167 (same answer different forms)

Step-by-step explanation:

Leon older brother is 19/4 feet tall or 57/12.

Leon is 1/3 or 4/12 foot shorter than his brother.

57/12-4/12= 53/12

Step-by-step explanation:

1/(1 - p + p²) - 1/(1 + p + p²) - 2p/(1 - p² + p⁴) =

[ (1 + p + p²)-(1 - p + p²)/(1 - p + p²)(1 + p + p²) ] - 2p/(1 - p² + p⁴) =

2p/(1 + p + p² - p - p² - p³ + p² + p³ + p⁴) - 2p/(1 - p² + p⁴) =

2p/(1 + p² + p⁴) - 2p/(1 - p² + p⁴) =

[ 2p(1 - p² + p⁴) - 2p( 1 + p² + p⁴) ]/(1 + p² + p⁴)(1 - p² + p⁴) =

(2p - 2p³ + 2p⁵ - 2p - 2p³- 2p⁵) / (1 - p² + p⁴ + p² - p⁴ + p⁶ + p⁴ - p⁶ + p⁸) =

-4p³ / (1 + p⁴ + p⁸)

Answer:

Goes up and to the left

Step-by-step explanation:

Answer:

1440

Step-by-step explanation:

theres 144 months in 12 years and I just multiplied it by 10

Answer:

In technical terms, the slope of the line is the change in y over the change in x. But I just like to think of it as rise over run. To find the slope of the line, pick two points on the line.

Answer:

Uphill slopes are positive slopes.

The slope will be a positive number like 5 or 2/3.

Downhill slopes are negative slopes.

The slope will be a negative number like -7 or -1/3.

Step-by-step explanation:

Answer:

0.9797

Step-by-step explanation:

We have X = number of insects in the 25bgrams of butter

Then the legal limit of concentration in peanut butter = 30 fragments/ 100 grams

Then insect amount in 25 grams =

E(X) = 30/100 x 25

= 0.3 x 25

= 7.5 fragments of insects

Using the poisson function in Excel, the probability of at least 3 crunchy critters

1 - p(X<=2)

p(X<=2) = POISSON (2, 7.5, TRUE) = 0.020156715

1 - 0.020156715

= 0.9797

hi, im chelsea. whats your favorite dinner food?

Answer:

it's cuvfhdiudfhridfhreidgehtinsi tahw

Step-by-step explanation:

have a good day

Answer:

30 ft  

Step-by-step explanation:

18 in=1.5 ft

20*1.5=30

Answer:

15:18

Step-by-step explanation:

Answer:

9 LOL-

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

edge

Answer:

the answer is

x=22..........

Answer:

the 3rd one 72.22 is the answer

Answer:

the formula for it is 2*3.14*r

so to get the radius you divide the diameter by two, so 23 divided by 2 is 11.50

so then we do 2*3.14*11.50= 77.22

there u go!

Step-by-step explanation:

Answer: 20790

Step-by-step explanation:

Answer:

peak farther to the RIGHT

peak will be NARROWER

Step-by-step explanation:

hope this helps !! :)

Answer:

The goalkeeper has 0.306 seconds to react, dive, and reach the ball before it crosses the goal line.

Step-by-step explanation:

We use the following relation to solve this question:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance, and t is the time.

Chastain will kick the ball from 18 yards away from the goal at 120 miles per hour.

Since the velocity is in miles per hour, the distance has to be in yards.

Each yard has 0.000568182 miles, so the ball will be kicked from 18*0.000568182 = 0.0102 miles.

This means that [tex]v = 120, d = 0.0102[/tex]

How many seconds does the goalkeeper have to react, dive, and reach the ball before it crosses the goal line?

We have to find t, first in hours. So

[tex]v = \frac{d}{t}[/tex]

[tex]120 = \frac{0.0102}{t}[/tex]

[tex]120t = 0.0102[/tex]

[tex]t = \frac{0.0102}{120}[/tex]

[tex]t = 0.000085[/tex]

An hour has 3600 seconds. So

3600*0.000085 = 0.306.

The goalkeeper has 0.306 seconds to react, dive, and reach the ball before it crosses the goal line.

Answer:

I think the area is 9 ft square

Answer:

0

Step-by-step explanation:

First we move all the terms to the left so it will be 21x-10-(19x)=0 hope I helped good luck

Answer:

Step-by-step explanation:

(3/4)/(1/8)

(3/4)(8/1)

24/4

6 pieces of pipe