Let f(x)=−|x−3|+3 and g(x)=1/2x−3. Graph the functions in the same coordinate plane.
What are the solutions to f(x)=g(x)?

Enter your answers in the boxes from smallest to largest.

x=_ and x=_

9514 1404 393

Answer:

  direct variation

Step-by-step explanation:

The given equation can be written in the direct variation form ...

  y = kx

  y = -8x . . . . rewrite of the given equation (multiply by -4)

This is an example of direct variation.

Answer:

(0,-2)?

Step-by-step explanation:

Answer:

2x(30+8-6)-20

Step-by-step explanation:

Answer:

You must survey 784 air passengers.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Assume that nothing is known about the percentage of passengers who prefer aisle seats.

This means that [tex]\pi = 0.5[/tex], which is when the largest sample size will be needed.

Within 3.5 percentage points of the true population percentage.

We have to find n for which M = 0.035. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.035 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.035\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.035}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.035})^2[/tex]

[tex]n = 784[/tex]

You must survey 784 air passengers.

Answer:

CI = ( 0,1433  ;  0,4067 )

Step-by-step explanation:

College of Engineering

sample size  n₁  =  200

sample proportion ( with laptop )    p₁ = 91/ 200   p₁ = 0,455  q₁ = 1 - p₁

q₁ = 0,545

College of Arts

sample size  n₂  =  100

sample proportion ( with laptop )    p₂ = 73/ 100   p₂ = 0,73  q₂ = 1 - p₂

q₂ = 0,27

CI = 98 %      significance level   α = 2 %  α = 0,02    α/2 = 0,01

From z-table we find z(c) for 0,01

z(c) = 2,328

CI = [  ( p₂ - p₁ ) ± z(c) * √ (p₁*q₁)/n₁ + (p₂*q₂)/n₂ ]

CI

[ ( 0,73 - 0,455 ) ±  2,328 * √ (0,455*0,545)/ 200  + ( 0,73*0,27)/100

CI = ( 0,275 ) ±  2,328 *√0,00123 + 0,001971

CI = ( 0,275 ± 2,328* 0,0566)

CI = ( 0,275 - 0,1317  ;  0,275 + 0,1317 )

CI = ( 0,1433  ;  0,4067 )

The values of the CI  for  the difference are always positive meaning that the proportion of students of Arts is greater than the proportion of students of Engineering

Answer:

< A = 148°

Step-by-step explanation:

<A = <B → 6x - 2° = 4x + 48° → 2x = 50° → x = 25°

<A = 6(25°) - 2° = 150° - 2° = 148°

Answer:

Answer:

Answer:

I think it is a scalene acute because:

➡It has acute angles

➡Its angles are not equal  ⬇

Scalene triangles do not have equal angles  

Hope this helps, adn have a good day! ฅ^•ﻌ•^ฅ

Answer:

12.5%

Step-by-step explanation:

95141 1404 393

Answer:

  3 liters

Step-by-step explanation:

There's a simple and effective "visual" way to solve mixture problems that makes short work of this.

In the attached, the concentrations of the contributors are listed on the left. It can work well to put the largest contributor on top (though that is not strictly necessary). The target concentration is put in the middle between them, and the differences along the diagonals are computed.

The diagonal differences are reduced to lowest terms as a ratio in the right-hand column. These numbers can be compared to the problem statement to see how they relate.

In this case, the total is 4 L of juice, and the total of the ratio units is 4. Then the ratio units are the number of liters of the corresponding contributor:

Answer:

Kaitlin's answer is wrong because she is supposed to by dividing. When trying to get rid of a number from a variable you have to divide the number by itself and whatever you do to one side you have to do to the other side

so you would do 5/5 - cancels out

15/5=3

y=3

Step-by-step explanation:

have a great day :D

Answer:

Explanation (Part A):

Solution (Part B):

The correct answer must be 'y = 3'.

Answer:

a. m = -1, y-int = 0

b. m = 2/3, y-int = -5/3

c. m = -1/2, y-int = 2

Step-by-step explanation:

-Expand equations on both sides.

-Make 'y' the subject by collecting like terms and moving everything to the right, e.g. y = ...

-Slope is the number in front of x.

-Find y-intercept by letting x = 0 and solve the equation.

Answer:

12 dollars per chair

Step-by-step explanation:

294 - 198 = 96

96 divided by 8 = 12

Answer:

x+(6x-15) = 90 degrees

for the whole angle measure is 90 degree and making smaller angles out of it , their sum should be 90 degrees

Answer:

h = 1296 feet

Step-by-step explanation:

Given that,

The vertical position of the object is :

[tex]h(t)=-16t^2+160t+896[/tex] .....(1)

We need to find the highest height reached by the object. For highest height,

Put dh/dt = 0

[tex]\dfrac{d}{dt}(-16t^2+160t+896)=0\\\\-32t+160\\\\t=\dfrac{160}{32}\\\\t=5\ s[/tex]

Put t = 5 in equation (1).

[tex]h(5)=-16(5)^2+160(5)+896\\\\=1296\ ft[/tex]

So, the height reached by the object is 1296 feet.

Answer:

y=8

Step-by-step explanation:

the angle that is equal to 10x-3 and the angle that is equal to 7x+45 are equal to each other because they are corresponding angles so we setup an equation which would be

10x-3=7x+45

step 1

add 3 to each side

-3+3 = they cancel out

45+3=48

now we have

10x=7x+48

step 2

subtract each side by 7x

7x-7x cancels out

10x-7x=3x

3x=48

step 3

divide each side by 3

3/3 cancels out

48/3=16

so x =16

now we plug it into to 10x+3

10x16=160 160-3= 157

so the angle that is equal to 157 and the one that is equal to 3-y are supplementary angles so they will add up to equal 180 so to solve y we setup the equation which would be

180=157+3y-1

step 1 combine like terms

157-1=156

180=156+3y

step 2 subtract each side by 156

156-156 cancels out

180-156=24

so now we have

24=3y

next we divide each side by 3

3/3 cancels out

24/3=8

y=8

hope this makes sense :D

Answer:

width equals 16

length = 20

Step-by-step explanation:

Hello there!

we know that the perimeter is 72 m

and the width is 4 m less then the length

perimeter is 2w+2l

w=width and l = length

72 + (2x-4) = 72+8 = 80

80 / 4 (because there are 4 values, w, w, l, l ) = 20

so now...

20 - 4 = w

16 = w

and 20 = l

16+16 = 32

20+20 = 40

32+40 = 72

Answer:

D. It interferes with motor responses

Step-by-step explanation:

Don't ask why I know this

Answer:

A

Step-by-step explanation:

To check for similarity, check for the scale factor. We can see angle X and angle U are both 32°. If the triangles were similar side RS to side UV and side RT to side UW should give the same scale factor. 10:12 = 5:6 and 15:18 = 5:6. Therefore the two triangles are similar. When naming similar triangles make sure you start from the same point, so triangle RST is similar to triangle UVW.

Answer:

400 mL

Step-by-step explanation:

0.50x + 0.20(600-x) = 0.40*600

50x + 20*600 - 20x = 40*600

30x = 20*600

x = 20*20

x = 400 mL

Answer:

swdfghjkl;'[

Step-by-step explanation:

asdfghjkl;'iy7u6j54hy3feqdwsrtfyuiop;lkjhgf

Answer:

nbmmmmmmmmmmmmmmmmmm

Step-by-step explanation:

Answer:

Expression of the statement = 18 - 2x

Answer:

18 - 2x

Step-by-step explanation:

Answer:

It is already in simplest form.

Step-by-step explanation:

Answer:

Already in simplest form

Step-by-step explanation:

I mean you could do 6(x+2) but its already in its simplest form.

Answer:

[tex] \frac{3}{4} [/tex]

Step-by-step explanation:

Slope is equal to the change in y over the change in x.

[tex]m = \frac{change \: in \: y}{change \: in \: x} [/tex]

The change in x is equal to the difference in x-coordinates, and the change in y is equal to the difference in y-coordinates .

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Substitute in the values of x and y into the equation to find the slope.

[tex]m = \frac{5 - (2)}{7 - (3)} [/tex]

Simplify.

[tex]m = \frac{3}{4} [/tex]

Hence, the slope is 3/4.

Answer:

29

Step-by-step explanation:

P=a+b+c=11+5+13=29

Answer:

Step-by-step explanation:

simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:

6√35

Decimal Form:

35.49647869

Answer:

C. 6

Step-by-step explanation:

The range of a data set is the smallest number subtracted from the biggest number. In this case 7 is the biggest number, and 1 is the smallest number. This gives us the equation 7 - 1 = range which gives us 6.