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3 years ago

< Last spring, Kai planted a total of 9 green peppers and tomatoes in the community garden.

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

3 0

Answer:

Step-by-step explanation:

Let x = the number of pepper plants, then (x + 6) = the number of tomato plants. Since the ratio of tomatoes to peppers is 5:2, we have the following:

5/2 = (x + 6)/x

2x + 12 = 5x

12 = 3x

4 = x = the number of pepper plants

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Two boards, one four inches wide and the other six inches wide, are nailed together to form an X. The angle at which they cross

Sunny_sXe [5.5K]

Answer:

The area of the unpainted region on the four inch board = 160·√3 in.²

Step-by-step explanation:

Here we have that the boards are crossing each other on their flat sides Therefore, when the boards are separated, the area of the unpainted region is the area of a parallelogram

The dimensions of the formed parallelogram are;

Interior angles = 60° and 120° (adjacent angles of a parallelogram)

Height, h of parallelogram formed = 4 inches

From the angle of crossing of the parallelogram, we have;

Angle between the width or perpendicular cross section of the 6 inches board and the angle of crossing of the two boards = 90° - 60° = 30°

Therefore, length of base, b of the parallelogram formed by the unpainted region is given as follows;

$b = \frac{60}{cos(30)} = 40\cdot \sqrt{3} \ inches$

Therefore, the area of the parallelogram = b × h = 4 × 40·√3 = 160·√3 in.²

Hence, the area of the unpainted region on the four inch board = 160·√3 in.².

3 0

2 years ago

A 6 inch personal pizza has 640 calories, with 240 of those from fat. A 12 inch pizza is cutinto 8 slices. Estimate the number o

MissTica

Given:

Number calories in a 6-inch pizza = 640 calories

For the pizza of 6 inch

$A=\pi(3)^2=9\pi$

For the pizza of 12 inch

$A=\pi(6)^2=36\pi$

Number calories in a 6-inch pizza = 640 calories, therefore:

$\frac{A_{6\text{ inch}}}{A_{12\text{ inch}}}=\frac{640}{x}$

Substitute:

$\begin{gathered} \frac{9\pi}{36\pi}=\frac{640}{x} \\ Simplify \\ \frac{1}{4}=\frac{640}{x} \end{gathered}$

And solve for x:

$\begin{gathered} 1\cdot x=4\cdot640 \\ x=2560 \end{gathered}$

Now, Estimate the number of calories in one slice of a 12 inch pizza:

$\frac{2560}{8}=320$

Answer: 320 calories

4 0

1 year ago

A person on a runway sees a plane approaching. The angle of elevation from the runway to the plane is 11.1° . The altitude of th

Gnoma [55]

Answer:

The horizontal distance from the plane to the person on the runway is 20408.16 ft.

Step-by-step explanation:

Consider the figure below,

Where AB represent altitude of the plane is 4000 ft above the ground , C represents the runner. The angle of elevation from the runway to the plane is 11.1°

BC is the horizontal distance from the plane to the person on the runway.

We have to find distance BC,

Using trigonometric ratio,

$\tan\theta=\frac{Perpendicular}{base}$

Here, $\theta=11.1^{\circ}$ ,Perpendicular AB = 4000

$\tan\theta=\frac{AB}{BC}$

$\tan 11.1^{\circ} =\frac{4000}{BC}$

Solving for BC, we get,

$BC=\frac{4000}{\tan 11.1^{\circ} }$

$BC=\frac{4000}{0.196}$ (approx)

$BC=20408.16$ (approx)

Thus, the horizontal distance from the plane to the person on the runway is 20408.16 ft

8 0

2 years ago

28,062 divided by 3

Galina-37 [17]

28 062 ÷ 3
9 354
9 354 x 3
28062

3 0

3 years ago

Read 2 more answers

CAN SOMEONE PLEASE HELP? THESE QUESTIONS ARE REALLY HARD AND I HAVE BEEN STUCK ON THEM FOR A WHILE. I REVIEWED THE LESSON AND EV

aniked [119]

Well if I did the right calculations... Kim is 24. The sister is age twelve! Hope I helped.

A. K+S=36

B. Well Simple Addition and Subtraction solves this easily. If you Add 12+12 it equals 24. It still needs to be larger so that Kim is twice as old as her little sister. So you Add another 12 which gives you 36. Or you can easily subtract 12 from it and that will also bring you to 24.

6 0

2 years ago

Read 2 more answers