A new coffee shop can hold no more than 50 seats. The owner wants at least 20 of the seats to be stools and the remaining seats to be recliners. If x is the number of stools and y is the number of recliners, which graph represents the solution to the system of inequalities?



x + y ≤ 50

x ≥ 20

On a coordinate plane, 2 solid straight lines are shown. The first line is horizontal to the y-axis at y = 20. Everything below the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the left of the line is shaded.

On a coordinate plane, 2 solid straight lines are shown. The first line is vertical to the x-axis at x = 20. Everything to the left of the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the right of the line is shaded.

On a coordinate plane, 2 solid straight lines are shown. The first line is horizontal to the y-axis at y = 20. Everything above the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the left of the line is shaded.

Answer to your question

-6x sqrt21x

Answer:

the number of apple trees = 45

Step-by-step explanation:

a) the total mass of apples produced = 25x

b) the number of containers of fertilizer required :

[tex]=\frac{0.8x}{5} \\= 0.16x[/tex]

c)

(i) the equation :

648 = 90 × (0.16x)

⇔ 648 = 14.4x

(ii) solving :

648 = 14.4x

⇔ x = 648 ÷ 14.4

      = 45

Answer:

m=15/14

Step-by-step explanation:

y2-y1

x2-x1

(3, 0) (-11, -15)

x1 y1   x2   y2

-15-0

-11-3          = -15/-14 m=-15/-14 = 15/14

Answer:

See below ~

Step-by-step explanation:

Q1

Q2

Q3

Q4

Q5

Answer:

the answer for all of this question should be

C=( -10, -2)

D=(0, -2)

E=(0,8)

F=(-10,8)

so remember the quadruants and remember if the x is negative or positive and if the y is either negative or positive so hopefully those are the correct one and if not tell me whats wrong so i can edit it to make it better.

Step-by-step explanation:

Answer:

Angle 1 = 78 degrees

Angle 2= 90 degrees.

Angle 3= 12 degrees

Step-by-step explanation:

For angle 1,

Since all opposite angles of a kite is congruent, if the opposite half of the angle is 78 degrees, then the other opposite half is also 78 degrees.

For angle 2,

Diagonals of a kite will ALWAYS form right angles, this since angle 2 is formed by intersecting diagonals, it would be 90 degrees.

For angle 3,

Opposite angles of a kite are supplementary, meaning that the two angles will form a straight line, or 180 degrees.

We know that 78 degrees is half of one opposite angle, so the opposite angle can be concluded as 156 degrees.

The other set of two angles is unknown, so we take it as this formula:

156+2x=180

We subtract 156 from 180 to cancel out the coefficient.

2x=24

Now we use the division property of equality.

2x/2=24/2

x=12.

Angle 3= 12.

since it's diameter is 24, its radius must be 12.

[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12 \end{cases}\implies SA=4\pi (12)^2\implies SA=576\pi[/tex]

now, that's for a sphere, for a hemisphere with the same radius it'd just be half that or 288π, now let's add the area of the circular base.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{hemisphere}{288\pi} ~~ + ~~\stackrel{circular~base}{\pi (12)^2}}\implies 288\pi ~~ + ~~144\pi \implies 432\pi[/tex]

The total surface area of the hemisphere is 288π. The area that include both surface area of hemisphere and the base of the total area is 432π.

A hemisphere is "half the part of sphere".

According to the question,

The diameter of greater circle is 24 this implies radius of circle is 12.

Surface area of sphere = 4πr²

= 4×π × (12)²

= 576π.

Surface area of sphere is 576π

Surface area of Hemisphere is half of the surface area of sphere.

(576π)/2 = 288π

In order to include the base in the total area only if add surface area of hemisphere and area of circle.

surface area of hemisphere + rea of circle = 288π + π(r)²

= 288π + π(12)²

= 288π + 144π

= 432π

Hence, the total surface area of the hemisphere is 288π. The area that include both surface area of hemisphere and the base of the total area is 432π.

Learn more about hemisphere here

https://brainly.com/question/16724000

#SPJ2

[tex]\textit{sum of all interior angles in a regular polygon}\\\\ \theta n=180(n-2) ~~ \begin{cases} \theta =\stackrel{degrees}{angle}\\ n=\stackrel{side's}{number}\\[-0.5em] \hrulefill\\ n=13 \end{cases}\implies \theta (13)=180(13-2) \\\\\\ 13\theta =180(11)\implies 13\theta =1980\implies \theta =\cfrac{1980}{13}\implies \theta \approx 152.3^o[/tex]

Answer:

sooo i  think, it  is

Step-by-step explanation:    it screen shot cause i worked it out on my computer !

Answer:

290 in^2.

Step-by-step explanation:

Adding all the areas of rectangles:

= 11*8 + 11*3 + 11*8 + 11*3 + 3*8 + 3*8

= 290 in^2.

Answer:

B)  290 in²

Step-by-step explanation:

Area of a rectangle = length × width

⇒ SA of the net = 2(11 × 8) + 2(11 × 3) + 2(8 ×3)

                           = 176 + 66 + 48

                           = 290 in²

Part A

To shift the curve 3 units to the right, we'll replace x with x-3. What this does is move the xy axis 3 units to the left. If we held the curve in place as the axis moves, then it gives the illusion the curve is moving 3 units to the right.

[tex]f(x) = x^2 + 5\\\\f(x-3) = (x-3)^2 + 5\\\\g(x) = (x-3)^2 + 5\\\\[/tex]

Do not expand out the (x-3)^2 term, because you want to keep the function in vertex form. The old vertex of (0,5) moves three units to the right to arrive at (3,5)

==============================================================

Part B

We use the same idea as before. This time we're moving the curve 10 units to the left, so we'll replace x with x+10

[tex]f(x) = x^2 + 5\\\\f(x+10) = (x+10)^2 + 5\\\\g(x) = (x+10)^2 + 5\\\\[/tex]

Answer:  8 root 2 or 11.3

Step-by-step explanation:

square 16 and divide by two to find square of other sides. Then root it to find answer

The equation here can be described to be a circle.

We have the following equations

x = 5cos(t) - 7, and

y = 5sin(t) + 9

When rearranged we have

x + 7 = 5cos(t),

y - 9 = 5sin(t)

Square both equations

(x + 7)² = 25cos²(t), and

(y - 9)² = 25sin²(t)

Sum the equations

(x + 7)² + (y - 9)² = 25cos²(t) + 25sin²(t)

(x + 7)² + (y - 9)² = 25

(x + 7)² + (y - 9)² = 5²

The equation above is that of a circle. The radius is 5 units. The center is (-7,9)

The formula for the equation of a circle is

(x -a)² + (y - b)² = R², this is similar to (x + 7)² + (y - 9)² = 5²

The equation can be described as a circle.

Read more on the equation of a circle here: https://brainly.com/question/21523002

#SPJ4

Answer: cirlce

Step-by-step explanation:

did it

Answer:

68

Step-by-step explanation:

the interior angles of a triangle always adds up to 180. So if you add 59 and  

53 together you would get 112. Then subtract that from 180 and you would get 68.

Answer:

t + 11 = 29

Step-by-step explanation:

Since you are combining your total and your friend's total marbles together, this will be an addition equation.

t + 11 = 29

The number of ways in which three swimmers can advance is 56.

The combination is the selection of items without taking the order of arrangement into consideration.

The formula used in calculating the combination is:

[tex]\mathbf{C(n,r) = \dfrac{n!}{r!(n-r)!}}[/tex]

[tex]\mathbf{C(n,r) = \dfrac{8!}{3!(8-3)!}}[/tex]

[tex]\mathbf{C(n,r) = \dfrac{8\times 7\times 6 \times 5!}{3!(5)!}}[/tex]

[tex]\mathbf{C(n,r) = 8\times 7}[/tex]

C(n, r) = 56

Learn more about combinations here:

https://brainly.com/question/11732255

#SPJ1

Answer:

hi,as u promise,lets go!!

a)1min=30w

x=400w

b)1min=30w

x=400w

1min×400w=x×30w

400w min=x×30w

30w 30w

x= 13mins and 3 sec.

c)1min=30w

10 min=x.

d)1min=30w

10min=x

1min×x=10min×30w

1min ×x = 300wm

1min 1min

x=300words.

Answer:

a.) 1:30 :: x:400

b.) About 13 minutes and 35 seconds

c.) 1:30 :: 10:x

d.) 300 words

Step-by-step explanation:

a.) 1 = minute 30 = words typed in that minute 400=words typed x=minutes

b.) 400 / 30 = 13.3

c.) 1 = minute 30 = words typed in that minute x=words typed 10=minutes

d.) 10 x 30 = 300

Answer:

(5^6)/(5^3) = 5^3 or 125

Step-by-step explanation:

^ = raised power

(5^6)/(5^3)

because base (5) is same:

law of indices: n^a ÷ n^d = n^(a-d)

therefore

5^6 ÷ 5^3 = 5^(6-3)

= 5^3 which is 125

Answer:

[tex]3w^2\sqrt[4]{2w^3}[/tex]

Step-by-step explanation:

hope this helps!:)

Answer:  60

8 + 92 = 100

4 × 10 = 40

100 + 40 = 60

Answer:

[tex]60[/tex]

Step-by-step explanation:

[tex](8 + 92) - 4 \times 10[/tex]

[tex]100 - 4 \times 10[/tex]

[tex]100 - 40[/tex]

[tex]60[/tex]

Hope this helps!

The values for the highlighted variables that show how to subtract the rational expressions correctly are a = 6, x^2 + 6x is equal to x(x+6), and b=2.

From the informaation, the denominator and numerator of the first term are multiplied by x.

The second term is multiplied by (x-6)/(x-6).

Now that they have the same denominator, the two terms are combined. 2 is the coefficient of the first term. In the same way as d is carried over from b, e is carried over from c.

We factor out the (x+6) from the numerator and denominator.

Learn more about expressions on:

https://brainly.com/question/723406

#SPJ4

From the section formula, it was found that the coordinate for the point S is (12,21).

The coordinates of the point S which divides the line AB into two sections can be found from the application of the Section Formula that is presented below:

[tex]S=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})[/tex], where

[tex]ratio=\frac{m}{n}[/tex]

[tex]x_1[/tex] and [tex]y_1[/tex] are coordinates of A

[tex]x_2[/tex] and [tex]y_2[/tex] are coordinates of  B

The question gives  r=[tex]\frac{3}{2}[/tex], A=(21,3) and B=(6,33). From the ratio, you can find m=3 and n=2.

Next step, applying the internal section formula. Then, you have:

[tex]S=(\frac{3*6+2*21}{3+2}, \frac{3*33+2*3}{3+2})\\ \\ S=(\frac{18+42}{5}, \frac{99+6}{5})\\ \\ S=(\frac{60}{5}, \frac{105}{5})\\ \\ S=(12, 21)[/tex]

Read more about the section formula here:

https://brainly.com/question/14812336

#SPJ1

The probability that each person gets off on a different floor is; 3/32

We are told that there are 4 people on the elevator. We are also told that there are four stops on four different floors. Thus;

Total number of ways to get off on the floors = 4 * 4 * 4 * 4 = 256 ways

Now, the number of ways that each person can get off on a different floor is 4! = 24. Thus, the probability that each person gets off on a different floor is;

P(each person gets off on a different floor) = 24/256 = 3/32

Read more about Probability at; https://brainly.com/question/24756209

#SPJ1

Answer:

The correct answer is the last one, [tex]\frac{\pi }{6}[/tex].

Step-by-step explanation:

Assuming you need this urgently so I won't explain.

Hope this helps:) Goodluck!

Answer:

5π/6, 7π/6

Step-by-step explanation:

Solving :

cos⁻¹ (-[tex]\frac{\sqrt{3} }{2}[/tex])

cos⁻¹ (-cos30°)

cos 30° is negative in Quadrant II and Quadrant III

Value in QII :

Value in QIII :

The answer is 5π/6, 7π/6

Answer:

11 shelves.

Divide 96 by 9

96 ÷ 9 = 10.6

Since 10.6 rounds to 11, and it is more than 10, we will need 11 shelves to store the books, since there is no such thing as a half-bookshelf here.

Color Number of times picked from jewelry box

blue      14

green   8

red        16

white      12

The probability values are:

Here, we use the color of the earrings;

There are 4 colors in total, one of which is red

So, the theoretical probability of selecting a red earring is:

P(Red) = n(Red)/Total

This gives

P(Red) = 1/4 = 25%

Hence, the theoretical probability of selecting a red earring is 25%

The distribution of the earrings is given as:

Red = 2

Total = 20

The probability of selecting a red earring is:

P(Red) = n(Red)/Total

So, we have:

P(Red) = 2/20

Evaluate

P(Red) = 1/10 or 10%

Hence, the experimental probability of selecting a red earring is 10%

Here, we use the color of the earrings;

There are 4 colors in total, one of which is blue

So, the theoretical probability of selecting a blue earring is:

P(Blue) = n(Blue)/Total

This gives

P(Blue) = 1/4 = 25%

Hence, the theoretical probability of selecting a blue earring is 25%

The distribution of the earrings is given as:

Blue = 4

Total = 20

The probability of selecting a blue earring is:

P(Blue) = n(Blue)/Total

So, we have:

P(Blue) = 4/20

Evaluate

P(Blue) = 1/5 or 20%

Hence, the experimental probability of selecting a blue earring is 20%

Read more about probability at:

https://brainly.com/question/27809422

#SPJ4

[tex]\fcolorbox{red}{blue}{Answer}[/tex]

78.5 units²

Step-by-step explanation:

[tex] \textsf{\large{\underline{To find :-}}}[/tex]

The area of circle on graph

[tex] \textsf{\large{\underline{Given :-}}}[/tex]

[tex] \sf (x_1,y_1) = (-3,-3) \\ \sf (x_2,y_2) = (2,-3)[/tex]

[tex] \textsf{ \huge{\underline{\underline{Solution :-}}}}[/tex]

We can see in the above question that we have been provided the center of thee circle and line of the circle passes through a point.

So to find the radius we have to find the distance between center of circle and the point from which line passes.

[tex] \sf \blue{ Distance = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } }[/tex]

Now substituting the required values

[tex] \sf \implies\sqrt{ { \{2 - ( - 3) \}}^{2} + { \{ - 3 - ( - 3) \}}^{2} } \\ \\ \sf \implies \sqrt{ {(2 + 3)}^{2} + {( - 3 + 3)}^{2} } \\ \\ \sf \implies \sqrt{ {5}^{2} + {0}^{2} } \\ \\ \sf \implies \sqrt{25} \\ \\ \sf \implies 5 \: units[/tex]

So the radius will be 5 units

Now we will simply formula for area of circle

[tex] \sf \green{ Area \: of \: circle = \pi {r}^{2} }[/tex]

Now substituting the required values

[tex] \sf \hookrightarrow Area = 3.14 \times {5}^{2} \\ \\ \sf \hookrightarrow Area = 3.14 \times 25 \\ \\ \red{\boxed {\hookrightarrow \frak{78.5 \: {units}^{2} } }}[/tex]

The graph of the circle is plotted with clarity and the area is obtained as 78.5 square units.

The graph of a circle can be plotted by knowing its centre and radius.

If radius is not given, then it can be found by knowing the coordinate of any point lying on it.

The radius can be calculated by the distance formula.

The centre of the given circle is at (-3, -3) and it passes through (2, -3).

Now, radius is the distance between the centre and a point lying on circle.

The radius can be calculated by distance formula as below,

√((-3 - 2)² + (-3 - (-3))²) = 5

The graph of the given circle can be drawn as follows,

Now, the area of the circle is πr² = 3.14 × 5² = 78.5

Hence, the graph of the circle is drawn properly and the area is given as 78.5 square units.

To know more about circle click on,

brainly.com/question/11833983

#SPJ2