MATHEMATICS MIDDLE SCHOOL

Enter the equation of the circle with the given center and radius.Center: (0,3); radius: 3
The equation of the circle is

Answers

Answer 1

Answer:

Answer:

x² + (y - 3)² = 9

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (0, 3) and r = 3, thus

(x - 0)² + (y - 3)² = 3², that is

x² + (y - 3)² = 9 ← equation of circle

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one tank is filling at a rate of 3\4 gallon per 2\3 minute.a second tank is filling at a rate of 5/8 gallon per 1/2 minute. which tank is filling faster

Answers

It needs to be changed to common denominators which would be 6/8 x 4/6 which is 6/8 every 40 min and 5/8 every 30 min so they are the same

To start this, id recommend just calculating each tank at different time intervals to see which is filling faster.
Let's start at 2 minutes since it's an even number for both scenarios.

Tank A: 3/4 gallon every 2/3 minutes. So for each 2/3 of a minute, we get 3/4 of liquid. So how many 2/3 of a minute are in 2 minutes? The answer is 3 because 2 minutes is the same as 6/3 minutes and 2/3 minutes goes into 6/3 minutes 3 times. So in 2 minutes you get 3 units of the rate. so That's 3/4 + 3/4 +3/4 = 9/4 = 2 1/4 gallons in two minutes.

Tank B: 5/8 gallon per 1/2 a minute. So after 2 minutes we will have 4 units of the rate: 5/8+5/8+5/8+5/8 = 20/8 = 2 4/8= 2 1/2

Since 2 1/2 is more, the second rate is filling faster.

What is the solution to the equation-4x - 14 = 6?

Answers

Answer:

x=-5

Step-by-step explanation:

-4x - 14 = 6

Add 14 to each side

-4x - 14+14 = 6+14

-4x = 20

Divide each side by -4

-4x/-4 = 20/-4

x = -5

Hunter drove 27 mi in h. How far will he drive in h at the same speed?

Answers

If he drove another hour he would have drove 54 miles in two miles.

27x or 27h is the equation so do 27 times the amount of hours he drove to get the answer

Which word is the antecedent of the underlined pronoun? The children were lost in the corn maze, but soon their parents found them.

A.
maze

B.
children

C.
parents

D.
lost

Answers

The antecedent for both the possessive adjective 'their' and the objective personal pronoun 'them' is children.

What is 45 1/2% as a fraction in simplest form?

Answers

For this case we have the following expression:
45 1/2%
Rewriting in decimal form we have:
45.5%
Then, the percentage in its numerical and decimal form is:
$45.5 * (1/100) = 0.455$
We now write the decimal in the form of a fraction.
We have then:
$0.455 * (1000/1000) = 455/1000$
Simplifying the fraction we have:
$(455/1000) * ((1/5) / (1/5)) = 91/200$
Answer:
The expression given in the form of fraction is:
91/200

Final answer:

45 1/2% is equivalent to 91/200 as a fraction in simplest form.

Explanation:

To convert a percent to a fraction, we write the value of the percent as a fraction with a denominator of 100. In this case, 45 1/2% can be written as 45 1/2/100. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2. Simplifying the fraction gives us the answer: 91/200.