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3 years ago

13

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credi

t:
x^2 + 4x + y^2 − 6y = −4

1 answer:

Nitella [24]3 years ago

5 0

Answer:

Circle with center at (-2,3) and radius r=3.

Step-by-step explanation:

Rewrite equation in standard form.

(x-a)^2+(y-b)^2=r^2

(x-(-2))^2+(y-3)^2=3^2

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What kind of transformation is this?

neonofarm [45]

Answer:

Reflection

Step-by-step explanation:

It is a reflection because it is like they are looking in the mirror.

3 0

2 years ago

Read 2 more answers

X+ y + z = -3<br> 3y - Z = 4<br> 2x- y - 2z = -5

snow_lady [41]

Answer:

(-3, 1, -1)

Step-by-step explanation:

x + y + z = -3 --> (1)
3y - z = 4 --> (2)
2x - y - 2z = -5 --> (3)

<u>Add up (1) and (2)</u>

x + 3y + y + z - z = -3 + 4 ⇒ x + 4y = 1 --> (4)

<u>Double (2) and subtract from (3)</u>

2x - y - 2z - 2(3y - z) = -5 - 2(4) ⇒ 2x - y - 2z - 6y + 2z = -5 - 8
2x - 7y = -13 --> (5)

<u>Double (4) and subtract (5)</u>

2(x + 4y) - 2x + 7y = 2 + 13 ⇒ 2x + 8y - 2x + 7y = 15 ⇒ 15y = 15 ⇒ y = 1

<u>Finding x</u>

x + 4(1) = 1 ⇒ x = 1 - 4 ⇒ x = -3

<u>Finding z</u>

-3 + 1 + z = -3 ⇒ z = -1

<u>So the answer is: </u>

(-3, 1, -1)

4 0

3 years ago

A computer programmer has an 18% chance of finding a bug in any given program. What is the probability that she does not find a

LiRa [457]

Answer: $(\frac{41}{50})^{10}$

Step-by-step explanation:

Since, According to the question,

The chance of finding a bug in a program = 18%

Thus, the probability of finding the bug in first attempt = $\frac{18}{100}=\frac{9}{50}$

⇒ The probability of not finding any bug in first attempt = $1 - \frac{9}{50} =\frac{41}{50}$

Similarly, in second attempt , third attempt, fourth attempt_ _ _ _ _ tenth attempt, the probability of not finding any bug is also equal to $\frac{41}{50}$

Thus, the probability that she does not find a bug within the first 10 programs she examines

= $\frac{41}{50}\times \frac{41}{50}\times\frac{41}{50}\times\frac{41}{50}\times\frac{41}{50}\times\frac{41}{50}\times\frac{41}{50}\times\frac{41}{50}\times\frac{41}{50}\times\frac{41}{50}$

= $(\frac{41}{50})^{10}$

5 0

3 years ago

ASAP:::::: 75 POINTS TO THE BRAINLIEST!!!!!

Misha Larkins [42]

Answer:

t = 6 4/25 hours

Step-by-step explanation:

The formula to find out how long it takes them to do the job is

1/m + 1/ a = 1 /t

where m is the time for Matthew to do the job

a is the time for Arianna to do the job

and t is the time for them to do the job together

m = 14 hours

a = 11 hours

Substituting what we know

1/14 + 1/11 = 1/t

Multiplying by 154t (14*11*t) so we can clear the fractions

154t*(1/14 + 1/11) = 1/t* 154t

11t + 14t = 154

Combine like terms

25t = 154

Divide by 25

t = 154/25

t = 6 4/25 hours

6 0

3 years ago

1.How many fluid ounces are in 9 And 1/2 cups? Write a proportion and solve.

allochka39001 [22]

Answer:

to top

MATH REVIEW: USEFUL MATH FOR EVERYONE

SECTION 1.2. RATIOS AND PROPORTIONS

Ratios and Proportions

Algebraic Expressions

Exponents

Logarithms

Glossary and Links

back to Ratios, Page 1

A proportion is similar to a ratio, except that it indicates a part of a whole, and so the numerator arises from the denominator. For instance, a researcher might say that, for every ten students in the residence hall, five were women. Five over ten (5 / 10) is a proportion. Proportions must have all of the numbers in the same units, and are frequently written as fractions.

What happens when you want to write a proportion, but the numbers are given in different units? Suppose you were asked to write the proportion of 3 cups to 56 ounces (3 cups out of 56 ounces). You must write a proportion of either cups to cups (cups:cups) or ounces to ounces (ounces:ounces), so you will have to convert one of the numbers so that both numbers are expressed in the same unit of measurement. Let's convert cups to ounces so we can express the ratio as ounces:ounces. Since there are 8 ounces in one cup, 3 cups are equal to 24 ounces:

3 cups * 8 ounces/cup = 24 ounces

Now the two numbers 3 cups and 56 ounces can be written as the following ratio:

24 ounces to 56 ounces,

24:56,

or, now that the unit of measurement is the same, 24:56 can also be written as a proportion:

24/56

You may need to solve some problems involving ratios.

If you divided 36 into two parts in the ratio of 1:2 and one part is a and the other is b, you can find the value of a and b:

You know that

a+b = 36

And

a/b = 1/2

You can use these equations to solve for a and b, or you can use the following simple method:

Find out how many units are in 1 part of the ratio. To do this, divide the total by the number of parts.

Number of parts: 1 + 2 = 3.

Number of units in each part: 36/3 = 12.

Then, multiply the number of units in each part by the number of parts in each variable.

a = 1 * 12 = 12

b = 2 * 12 = 24

As an aside . . .

Percentages are so frequently used that we should spend a little time on them here. The powerful thing about percentages is that they all have the same denominator: 100. When two fractions have the same denominator, comparisions can be made very easily.

0.21 = 21% = 21 / 100

Step-by-step explanation:

7 0

3 years ago