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3 years ago

74. Seven workers are hired to seed a field by hand. Each is given a plot 7 x 7

Mathematics

1 answer:

Lelu [443]3 years ago

6 0

Answer:

The total area of the field is 343 square feet

Step-by-step explanation:

Let us solve the question

∵ There are 7 workers hired to seed a field by hand

∵ Each is given a plot 7 x 7 feet in size

→ The plot has shaped a square because its two dimensions equal

∴ The side of the plot = 7 feet

∵ The area of the square = side × side

∴ The area of each plot = 7 × 7

∴ The area of each plot = 49 square feet

→ To find the total area multiply the area of 1 plot by the number

of the workers

∵ The total area = 49 × 7

∴ The total area = 343 square feet

∴ The total area of the field is 343 square feet

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Ber [7]

Refer to this previous solution set

brainly.com/question/26114608

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Problem 4

Like the three earlier problems, we'll place the kicker at the origin and have her kick to the right. The two roots in this case are x = 0 and x = 20 to represent when the ball is on the ground.

This leads to the factors x and x-20 and the equation $y = ax(x-20)$

We'll plug in (x,y) = (10,28) which is the vertex point. The 10 is the midpoint of 0 and 20 mentioned earlier.

Let's solve for 'a'.

$y = ax(x-20)\\\\28 = a*10(10-20)\\\\28 = -100a\\\\a = -\frac{28}{100}\\\\a = -\frac{7}{25}\\\\$

This then leads us to:

$y = ax(x-20)\\\\y = -\frac{7}{25}x(x-20)\\\\y = -\frac{7}{25}x*x-\frac{7}{25}x*(-20)\\\\y = -\frac{7}{25}x^2+\frac{28}{5}x\\\\$

The equation is in the form $y = ax^2+bx+c$ with $a = -\frac{7}{25}, \ b = \frac{28}{5}, \ c = 0$

The graph is below in blue.

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Problem 5

The same set up applies as before.

This time we have the roots x = 0 and x = 100 to lead to the factors x and x-100. We have the equation $y = ax(x-100)$

We'll use the vertex point (50,12) to find 'a'.

$y = ax(x-100)\\\\12 = a*50(50-100)\\\\12 = -2500a\\\\a = -\frac{12}{2500}\\\\a = -\frac{3}{625}\\\\$

Then we can find the standard form

$y = ax(x-100)\\\\y = -\frac{3}{625}x(x-100)\\\\y = -\frac{3}{625}x*x-\frac{3}{625}x*(-100)\\\\y = -\frac{3}{625}x^2+\frac{12}{25}x\\\\$

The graph is below in red.

4 0

3 years ago

The first aircraft has 89 more seats than the second aircraft. The third aircraft has 31 fewer seats than the second aircraft. I

Valentin [98]

Answer:

I think number 1=209

number 2=120

number 3=89

Step-by-step explanation:

x= 1st aircraft

y=2nd aircraft

z=3rd aircraft

x=y+89

y=z+31

z=y-31

x+y+z=418

y+89+z+31+y-31=418

2y+89+z=418

2y+z=329

2y+(add z)

2y+y-31=329

3y=360

y=120

x=120+89=209

z=120-31=89

8 0

3 years ago

How many solutions does this nonlinear system of equations have?

Arlecino [84]

Answer:

Step-by-step explanation:

One common point of the graphs means one solution.

7 0

3 years ago

Cos(−θ)=√3/3, sinθ<0

Delicious77 [7]

Answer:

$\sin\theta=-\frac{\sqrt{6}}{3}$

Step-by-step explanation:

The given trigonometric equation is $\cos(-\theta)=\frac{\sqrt{3} }{3}$ .

We can either use the Pythagorean identity or the right angle triangle to solve for $\sin\theta$ .

According to the Pythagorean identity,

$\cos^2\theta+\sin^2\theta=1$

Recall that, the cosine function is an even function, therefore

$\cos(-\theta)=\cos(\theta)$

$\Rightarrow \cos(\theta)=\frac{\sqrt{3} }{3}$ .

We substitute this value in to the above Pythagorean identity to get;

$(\frac{\sqrt{3}}{3})^2+\sin^2\theta=1$

$\Rightarrow \frac{3}{9}+\sin^2\theta=1$

$\Rightarrow \sin^2\theta=1-\frac{3}{9}$

$\Rightarrow \sin^2\theta=\frac{6}{9}$

$\Rightarrow \sin\theta=\pm \sqrt{\frac{6}{9}}$

$\Rightarrow \sin\theta=\pm \frac{\sqrt{6}}{3}$

But we were given that,

$\sin\theta\:$ , so we choose the negative value.

$\Rightarrow \sin\theta=-\frac{\sqrt{6}}{3}$

The correct answer is B

7 0

4 years ago

The Jones family took a 16 mile canoe ride down the Indian River in two hours. After lunch, the return trip back up the river to

strojnjashka [21]

9514 1404 393

Answer:

canoe 6 mph
current 2 mph

Step-by-step explanation:

The speed downriver was (16 mi)/(2 h) = 8 mph. The speed upriver was (16 mi)/(4 h) = 4 mph. The canoe's speed in still water is the average of these speeds: (8+4)/2 = 6 miles per hour.

The current's speed is the difference between the actual speed and the canoe's speed: 8 -6 = 2 miles per hour.

The speed of the canoe in still water is 6 mph; the rate of the current is 2 mph.

5 0

3 years ago