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2 years ago

Regina charges c dollars per hour to babysit. If she increases her rate by 15%, which

Mathematics

2 answers:

Inga [223]2 years ago

8 0

Answer:

C. c+0.15c

Step-by-step explanation:

Raising her rate by 15% is equivalent to adding 15% of what she charged before to the original price.

Pavlova-9 [17]2 years ago

6 0

Yes. C is the correct answer.

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You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

Aleksandr [31]

Answer:

Therefore the circumference of the circle is $=\frac{20\pi}{4+\pi}$

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

$\Rightarrow s=\frac{10-\pi r}{2}$

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

$A=\pi r^2+ (\frac{10-\pi r}{2})^2$

$\Rightarrow A= \pi r^2+(\frac{10}{2})^2-2.\frac{10}{2}.\frac{\pi r}{2}+ (\frac{\pi r}{2})^2$

$\Rightarrow A=\pi r^2 +25-5 \pi r +\frac{\pi^2r^2}{4}$

$\Rightarrow A=\pi r^2\frac{4+\pi}{4} -5\pi r +25$

For maximum or minimum $\frac{dA}{dr}=0$

Differentiating with respect to r

$\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi$

Again differentiating with respect to r

$\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}$ > 0

For maximum or minimum

$\frac{dA}{dr}=0$

$\Rightarrow \frac{2\pi r(4+\pi)}{4} -5\pi=0$

$\Rightarrow r = \frac{10\pi }{\pi(4+\pi)}$

$\Rightarrow r=\frac{10}{4+\pi}$

$\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0$

Therefore at $r=\frac{10}{4+\pi}$ , A is minimum.

Therefore the circumference of the circle is

$=2 \pi \frac{10}{4+\pi}$

$=\frac{20\pi}{4+\pi}$

4 0

2 years ago

What is the value of x in the equation 1/5x – 2/3y = 30, when y = 15?

lianna [129]

Answer:

x = 200

Step-by-step explanation:

1/5x – 2/3y = 30

substitute in y

1/5x - 2/3(15) = 30

multiply

1/5x - 10 = 30

isolate the variable

1/5x = 40

multiply each side by 5

x = 200

4 0

2 years ago

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The solution to a system of two linear equations is x = 3: y = 9. How could the intersection of the graphs of the two equations

Fynjy0 [20]

C because x is positive so it moving right and y is positive so it moves up

7 0

2 years ago

Rounded 3,428,583 rounded to the nearest 10,000

densk [106]

Since you want to round to the 10,000 place, you'll want to look at the 2 and the 8 that are next to each other. The 8 makes the two a 3 because it is greater than 5, which gives you 3,430,000. Hope this helped!

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3 years ago

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Plot and connect the points A(1, -5), B(-4, -3), C(3, -3), and find the area of the triangle it forms.

Ira Lisetskai [31]

So attached is the plotting of the triangle and I estimated it's area to be 7 squared units (OPTION C).

Note: in the graph i used colour codes to represent those partial squares that I used to counted as one and the gray squares are the naturally whole ones.

Hope this helps

4 0

2 years ago