A machine produces 75 widgets an hour. How many widgets does it produce in 6 minutes

Answers

Answer 1

Answer: 75 divided by 60 times 6 equal 7.5

Answer 2

Answer: 7widgets would be made in 6 minutes. Because there are 60 min in 1 hour, so 10 6 min spans in 1 hour, so 75/10=7.5 however you don't make half a widget and call it a full one so 7 every 6 min.

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choose the equation of the horizontal line that passes through the point (−2, −1) a. y = -1 b. y = - 2 c. x = -2 d. x = -1

Answers

$(-2;\fbox{-1})\n\n\boxed{y=-1}\to\fbox{a.}$

Noah rows across a river that is 48m wide. The current carries him 15m downstream. How far does Noah actually travel?

Answers

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relative to a person standing on the riverbank

Frank the lumberjack has a log that is 291 centimetres long. He cuts it into three pieces. Work out the length of the third piece if the first two pieces are 67cm and 181cm long.

Answers

Answer:

43cm

Step-by-step explanation:

Given

Length of Log = 291cm

First Piece = 67cm

Second Piece = 181cm

Required

Determine the length of the third piece

Given that the log was cut into three;

this implies that;

Length of Log = First Piece + Second Piece + Third Piece

Substitute values for first piece, second piece and length of log;

$291 = 67 + 181 + Third\ Piece$

$291 = 248 + Third\ Piece$

Subtract both sides by 248

$291 - 248 = 248 - 248 + Third\ Piece$

$43 = Third\ Piece$

$Third\ Piece = 43$

Hence, the length of the third piece is 43cm

Find the equation of the circle whose center and radius are given.center ( 7, -3), radius = 7

Answers

Answer: The required equation of the circle is $x^2+y^2-14x+6y+9=0.$

Step-by-step explanation: We are given to find the equation of the circle with center at the point (7, -3) and radius of length 7 units.

We know that

the standard equation of a circle with center at the point (h, k) and radius of length r units is given by

$(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

For the given circle,

center, (h, k) = (7, -3) and radius, r = 7 units.

From equation (i), we get

$(x-7)^2+(y-(-3))^2=7^2\n\n\Rightarrow (x-7)^2+(y+3)^2=49\n\n\Rightarrow x^2-14x+49+y^2+6y+9=49\n\n\Rightarrow x^2+y^2-14x+6y+9=0.$

Thus, the required equation of the circle is $x^2+y^2-14x+6y+9=0.$

(x – h)² + (y – k)² = r²

Fill in the numbers

(x – 7)² + (y +3)² = 49

What number should both sides of the following equation be divided by to solve for x?(6.4)x = 32

4
6.4
6
5

Answers

In algebraic equations, it is easier to solve for an unknown term when that term is being isolated on one side of the equation. In the given equation, the unknown term "x" is not isolated because it is being multiplied by 6.4. To solve for x, it is essential to divide both sides by 6.4 to isolate x. It is shown as follows:

6.4x = 32

Dividing both sides by 6.4:
(6.4x)/6.4 = 32 / 6.4

x = 5

Therefore, 6.4 should be divided to both sides to solve for x.

The____ is the set of all values a function will accept as inputs.domain
relation
range
mapping

Answers

The domain is the set of all values a function will accept as inputs.

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