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Which answer is correct?

The center of the given circle is at (3, -3), and the radius of the circle is 10. This can be determined by rearranging the equation into the standard form and then completing the square for the x and y terms.

To determine the center and radius of the circle given by the equation x2 + y2 - 6x + 6y - 82 = 0, we need to rearrange it into the standard form of a circle equation, which is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius of the circle.

First, group the x terms and the y terms: (x2 - 6x) + (y2 + 6y) = 82.

Then, complete the square for both x and y terms: (x2 - 6x + 9) - 9 + (y2 + 6y + 9) - 9 = 82. This factors to (x - 3)2 + (y + 3)2 = 82 + 9 + 9.

Finally, calculate the right side to find the radius squared: (x - 3)2 + (y + 3)2 = 100, so the circle's radius squared is 100 and the radius is 10.

Therefore, the circle's center is at (3, -3), and its radius is 10.

Step-by-step explanation:

Answer:

Sheng

Step-by-step explanation:

Answer: Sheng

Step-by-step explanation:

First, you list the fraction of each of them. I then used the butterfly method to figure out whose fraction was smaller

Answer:

Yes it will be greater, he is moving back 3 feet so what you are doing is taking the leg (a2) and multiplying it by 3. Once you do, you see triangle 1 has double and so did triangle 2. Triangle 1 was originally 5.6 (rounded to 6) than went up to 26.1. Triangle 2 was originally 24 and went up to 74.7 (or 75)

Step-by-step explanation:

Triangle 1 (when multiply by 3)

a2+b2=c2

7(square to 2)+b2=27(square to 2)

49+b2=729

-49       -49

--------------------

b2=680

(square root it)

b=26.1 Rounded to nearest tenth

Triangle 2:

a2+b2=c2

7(square to 2)+b2=75(square to 2)

49+b2=5625

-49      -49

-------------------

b2=5576

(square root it)

b=74.7 (or 75 rounded to nearest tenth)

Hope this helps anyone who needs it :)

Yes, the distance from his eyes to the top of the tree will also be greater.

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is that Javier moves backward so that his horizontal distance from the tree is greater.

Before moving backward, the distance from Javier's eyes to the top of the tree can be written as -

cosФ = b/h

h = b/cosФ

Now, we can see that -

h [tex]\alpha[/tex] b

As base increases, the hypotenuse length or the distance from Javier's eyes to the top of the tree will increase.

Therefore, yes, the distance from his eyes to the top of the tree will also be greater.

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Answer:

x = 0.85

2 (1.25) + 3x = 5.05

Step-by-step explanation:

2 (1.25) + 3x = 5.05

2.5 + 3x = 5.05

3x = 2.55

Answer:

D

Step-by-step explanation:

Answer:

The lender reduces the amount of principal that the borrower owes, with no expectation of repayment. Debt Forgiveness is analogous to a principal reduction. This is a more effective way to reduce payments than either lowering the interest rate on the mortgage, or extending the terms.

Answer:

they avoid foreclosure cost

Step-by-step explanation:

took the bullet

Answer:

3.75 or 3 3/4

Step-by-step explanation:

first put them on a common denominator of 20

1/5=4/20

3/4=15/20

then do 15 divided by 4

15/4= 3.75 or 3 3/4

Answer:

A turkey sandwich would cost $6.50 and the salads would be $5.50

Step-by-step explanation:

The cost of a turkey sandwich is $4.5 and the cost of a salad is $3.5.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the employees at a bank ordered 4 turkey sandwiches and 2 salads at a local deli. The total cost of the order was $25.

The cost will be calculated as,

4t + 2s = 25

s = t - 1

Substitute the value of s in the first equation,

4t + 2s = 25

4t + 2(t - 1)= 25

4t + 2t - 2 = 25

6t - 2 = 25

t = $4.5

The cost of salad will be,

S = t - 1

S = 4.5 - 1

S = $3.5

Therefore, the cost of a turkey sandwich is $4.5 and the cost of a salad is $3.5.

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Answer:

3 / 2 dozen

Step-by-step explanation:

5 + 1/4   -    3 + 3/4

21/4    -    15/4

6 / 4

3 / 2

Question 1:

The given formula is

[tex]I=\frac{PTR}{100}[/tex]

To make T, the subject we multiply both sides by 100:

[tex]100I=\frac{PTR}{100} \times 100[/tex]

This becomes

[tex]100I=PTR[/tex]

Divide both sides by PR

[tex]T=\frac{100I}{PR}[/tex]

b) Amanda's principal is , P=€2565

The interest rate is 3.5% p.a. that is R=3.5

We want to find how many years, her money will gain an interest of I=€718.20

We substitute into the formula for T,

[tex]T=\frac{100 \times 718.20}{2565 \times 3.5}[/tex]

This simplifies to:

T=8

Therefore it will take 8 years

2) Percentage profit

[tex] = \frac{profit}{cost \: price} \times 100\%[/tex]

The cost price of the 80 articles €200

The selling price is 3.5×80=€280

The profit =€280-€200=€80

The percentage profit is now

[tex] = \frac{80}{200} \times 100\%[/tex]

[tex] = 0.4 \times 100\%[/tex]

[tex]40\%[/tex]

The percentage profit is 40%

Question 3)

Let the original price of the calculator be x.

Then 85% of this price will be:

[tex] \frac{85}{100} \times x[/tex]

This is the same as€32.89

We equate and solve for x.

[tex] \frac{85}{100} x= 32.89[/tex]

[tex]0.85x = 32.89[/tex]

[tex]x = \frac{32.89}{0.85} [/tex]

[tex]x = 38.69[/tex]

The original price is €38.69

Answer:

-3, -2 1/2, -2 2/5, -2 3/10, -2

Step-by-step explanation:

Answer: from least to greatest =

-2 ; -2 3/10; -2 2/5; - 2 1/2, -3

Step-by-step explanation:

Step 1: Convert fraction to decimal

Step 2: arrange in the order

Step 3: be mindful of the sign (-)

Answer:

The mom is 5 feet 3 inches

Step-by-step explanation:

Step 1:  Make an equation

m = 1 3/4 * 3

Step 2:  Solve

m = (4/4+3/4) * 3

m = 7/4 * 3

m = 21/4

m = 5.25

m = 5 feet 3 inches

Answer:  The mom is 5 feet 3 inches

Answer:

5 and 1/4

Step-by-step explanation:

3 times 1.75 = 5.25

Answer:

vertex is 4

Step-by-step explanation:

y = (x-4)^2 + 7

(x-4) (x-4)

x * x = x^2

x * -4 = -4x

-4 * x = -4x

-4 * -4 =16

x^2 - 8x + 16

y = x^2 -8x + 16 + 7

y =  x^2 -8x + 23

       a     b     c

formula to find vertex: -b / 2a

= -b / 2a

= - (-8) / 2 (1)

= 8 / 2

= 4

vertex = 4

(what i did was work out the exponent outsite the parentesis then i got the equation i wanted, and from that equation i used the formula to find the vertex and i just plugged the numbers of the equation into the formula and work it out)

Answer:

(4,7)

Step-by-step explanation:

The equation for a parabola can be written as

y = a(x-h)^2 +k  where (h,k) is the vertex

given f(x) = (x-4)^2+7

The vertex is (4,7)

Final answer:

To find the limits for the middle 58% of charitable contributions in Pennsylvania, calculate the Z-scores and use them to determine the lower and upper limits.

Explanation:

Given data: Average charitable contribution = $792, Standard deviation = $108

Find middle 58% limits:

Answer:

Percentages can be reversed. For example:

600% of 5 is 30. Therefore $30 would be 5% of $600.

Step-by-step explanation:

The answer you are looking for is $30.

To find this answer, you must first make 5% a decimal. To do so, simply divide 5 by 100 to get 0.05. Lastly, multiply 0.05 by $600 to get $30. Thus making $30 your answer.

I hope this helps!

Answer:

56

Step-by-step explanation:

6 X 8 = 48

7 X 8 = 56

Answer:

56/48

Step-by-step explanation:

you multiply both sides by 8.

Answer:

Theta=38° to the nearest degree

Step-by-step explanation:

f(x) =2x+5

=2*3+5

=6+5

=11

=b

Answer:

b) 11

Step-by-step explanation:

step 1: f(3)=2(3)+5

substitute (plug in) the value of x which in here is 3

step 2: 2(3)=6 +5= 11

follow order of operations

P - parenthesis

E- exponent

MD- multiply and divide from left to right

AS- add and subtract from left to right

Answer:

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old

Step-by-step explanation:

Let

x ----> Siw's age

y ---> Mona's age

z ---> Mother's age

we know that

Siw is a fourth as old as mother

so

[tex]x=\frac{1}{4}z[/tex] ----> equation A

Mona is a fifth as old as mother

so

[tex]y=\frac{1}{5}z[/tex] ----> equation B

Mother is 22 years older than the two girls together.

so

[tex]z=x+y+22[/tex] ----> equation C

substitute equation A and equation B in equation C

[tex]z=\frac{1}{4}z+\frac{1}{5}z+22[/tex]

solve for z

Multiply by 20 both sides to remove the fraction

[tex]20z=5z+4z+440[/tex]

[tex]20z-9z=440\\11z=440\\z=40\ years[/tex]

Find the value of x

[tex]x=\frac{1}{4}(40)=10\ years[/tex]

Find the value of y

[tex]y=\frac{1}{5}(40)=8\ years[/tex]

therefore

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old

Answer:

-4 and +6

Step-by-step explanation:

The signs of 4 and 6 that will get you to a 2 are

[tex] - 4[/tex]

and

[tex] + 6[/tex]

Putting the two together gives

[tex] - 4 + 6 = 6 - 4 = 2[/tex]

This means that, starting from -4 on the number line , move 6 units to the right.

This will land you on 2

Answer:

Negative 4 n + 8 + 9 n minus 2 and 5 n + 6

Step-by-step explanation:

3v + 5 - (9v + 2)

3v + 5 - 9v -2 = -6v + 3

-6v + 6

(NO)

-6n + 3 - (2n + 2)

-6n + 3 - 2n - 4 = -8n - 1

-8n + 6

(NO)

-4n + 8 + 9n - 2 = 5n + 6

5n + 6

(YES)

Answer:

The answer is c

Answer:

ion know

Step-by-step explanation:

you figure it out

Answer:

Step-by-step explanation:

Answer:4/3

Step-by-step explanation:

Answer:

B) 6 tan(35°)

Step-by-step explanation:

from the right angle tan° = opposite / adjacent

therefore tan (35°) = (x) / 6

by multiplying 6 to both sides

tan (35°)  * 6 = (x) / 6 * 6

therefore (x) = 6 tan (35°)

Answer:

B

Step-by-step explanation:

I did it on usatestprep

22.8 gms

Step-by-step explanation:

Step 1:

Given,

Mass of the element = 590 gms

Percentage decay per minute = 19.5%

Step 2 :

Fraction of the element remaining at the end of 1 minute = 1 - 0.195 = 0.805

Hence the fraction of element remaining after 15 minutes  = [tex]0.805^{15}[/tex] = 0.03863

So the mass of the element remaining after 15 minutes = 0.03863 * 590 = 22.8 rounded off to the nearest 10th of a gram

mass of the element remaining after 15 minutes = 22.8 gms

Answer:

22.8

Step-by-step explanation:

answered on delta math and got it correct

Answer: The area of the shaded region is 150.72 km^2

Step-by-step explanation: The first bit of information we have is that both the inner circle and the outer circle have the same center. The radius of the inner circle can be calculated since we have been given the circumference (25.12) and the value of pi (3.14). The circumference of a circle is given as

Circumference = 2 x Pi x radius

With the values available, we now have

25.12 = 2 x 3.14 x radius

25.12 = 6.28 x radius

Divide both sides of the equation by 6.28

radius = 4

Having calculated the radius of the inner circle, the area now becomes;

Area = Pi x radius^2

Area = 3.14 x 4^2

Area = 3.14 x 16

Area = 50.24 km^2

The radius of the outer circle is the addition of 4 (on the shaded region) to the radius of the inner circle and that gives us 8.

Next we calculate the area of the outer circle which is

Area = Pi x radius^2

Area = 3.14 x 8^2

Area = 3.14 x 64

Area = 200.96 km^2

Now that we have determined the area of both the inner circle and the outer circle, the area of the shaded region is simply the difference between both of them, that is

Area of shaded region = 200.96 - 50.24

= 150.72 km^2

Answer: 14

Step-by-step explanation:

100% of 14

= 100/100 × 14/1

14

Answer:14

Step-by-step explanation:

Percent= 100%

From= 14

Value= [tex]\frac{100}{100}[/tex] x 14= 1x 14 =14

Answer:

The number is 5

Step-by-step explanation:

I like to do the equation backwards, so x*7+1/4=9 becomes:

9*4=36

36-1=35

35/7=5

And there is your answer!!!

Answer:

2 1/3 or 7/3

Step-by-step explanation:

I would simplify it to 14/3 and 7/3 then subtract which you get 7/3 then simplify it to the original state which is 2 1/3. Hope this helps :)