The radius of the circle whose equation is (x + 4) + (y - 2) = 36 is 36 18 6

The radius of the circle whose equation is (x + 4)² + (y - 2)² = 36 is 36 18 6

Answers

Answer 1

[tex]36=r^2\\r=6[/tex]

Answer 2

The equation of a circles is:

(x-h)^2+(y-k)^2+r^2, where (h,k) is the center of the circle and r is the radius

r^2=36

r=√36

r=6

Related Questions

A collection of quarters and nickels is worth $3.75. There are 27 coins in all. Find how many of each there are.

Answers

Q +N =27

Q=27-N

0.25Q + 0.05N =3.75

0.25(27-N) + 0.05 =3.75

6.75-0.25N+0.05N=3.75

6.75-0.2N=3.75

-0.2N=-3

N=-3/-0.2 = 15

15 nickels

27-15 = 12

12 quarters

15x0.05 = 0.75

12 x 0.25 = 3.00

3.00 + 0.75 = 3.75

12 quarters & 15 nickels

A fish is 5 feet below the surface of a lake. If its position can be recorded as −5 feet, what would the position of 0 represent?

Answers

Hey!

According to your question, we can see that if we got a negative number, that would represent that we are below sea level, that may mean being underwater. If we got a positive number, then that means we are above the sea level. The position of 0 would represent sea level.

Thanks
-TetraFish

Choose the polynomial written in standard form. (5 points)

xy2 + 4x4y + 10x2

x4y2 + 4x3y + 10x

x4y2 + 4x3y5 + 10x2

x6y2 + 4x3y8 + 10x

Answers

The polynomial in standard form from the given options is [tex]x^4y^2 + 4x^3y + 10x[/tex], as it orders the terms by degree in descending order, first by the degree of x and then y.

The term standard form in mathematics, especially in relation to polynomials, refers to a way of writing the polynomial so that the terms are ordered by their degree in descending order. More specifically, for a polynomial in two variables, x and y, the standard form would have the terms arranged first by the degree of x, then y, from highest to lowest.

Looking at the options provided in the question, the polynomial that is written in standard form would have the highest degree term first, and so on. The polynomial [tex]x^4y^2 + 4x^3y + 10x[/tex] follows this convention, with the terms ordered by decreasing powers of x first and y second. Therefore, this is the polynomial written in standard form.

Note that while the other options are all polynomials, they do not follow the standard form convention as closely as the correct option provided.

Preston goes on a camel safari in Africa. They travel 5 km north, then 3km east and then 1 km north again. What distance did he cover? What was his displacement?

Answers

what distance did he cover? well, he went 5km first, then 3km, then 1km, 5 + 3 + 1, is how much he covered.

what was his displacement? well, he has a north displacement of 6, 5 + 1, and a horizontal displacement of 3, check picture below.

so, his total displacement is "c" northeast.

The total distance Preston covered on his camel safari is 9 km, and his displacement is 6.71 km toward the northeast.

Determining Distance and Displacement

To answer the student's question about Preston's journey during his camel safari, we need to consider the definitions of distance and displacement.

Distance is the total length of the path traveled regardless of direction. In Preston's case, he traveled 5 km north, then 3 km east, and then 1 km north again. Therefore, the total distance covered is the sum of these individual distances

Displacement, on the other hand, measures the change in position from the starting point to the final point and is direction-dependent. It is a vector quantity with both magnitude and direction. To find the displacement, we can represent Preston's movement on a coordinate system with north being the positive y-direction and east being the positive x-direction.

From the starting point, moving 5 km north and then 1 km north results in a total of 6 km in the positive y-direction.

The magnitude of the displacement can be calculated using the Pythagorean theorem:

√((6 km)² + (3 km)²) = √(36 km² + 9 km²) = √(45 km²) = 6.71 km (rounded to two decimal places)The direction of the displacement would be to the northeast. Therefore, Preston's displacement is 6.71 km toward the northeast.

Translate to an algebraic expression. 5 INCREASED BY y

Answers

easy............5 + y

The length of the hypotenuse is:
0.
1.
2.
4.

Answers

divide the base by the sin of the opposite angle

base = 2

opposite angle = 30 degrees

2/sin(30) = 4

x = 4

Pamela is 13 years older than Jiri. The sum of their ages is 53 what is Jiri's age?

Answers

You are first told that Pamela is 13 years older than Jiri so:

p=j+13

Then you are told that the sum of their ages is 53 so:

p+j=53

We already know from the first statement that p=j+13, this makes p+j=53 become:

(j+13)+j=53 so we combine the two j's on the left side

2j+13=53 subtract 13 from both sides

2j=40 divide both sides by 2

j=20

So Jiri is 20 years old.

The solution is: Jiri is 20 years old.

What is addition?

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Pamela is 13 years older than Jiri so:

p=j+13

Then you are told that the sum of their ages is 53 so:

p+j=53

We already know from the first statement that p=j+13, this makes p+j=53 become:

(j+13)+j=53 so we combine the two j's on the left side

2j+13=53 subtract 13 from both sides

2j=40 divide both sides by 2

j=20

So Jiri is 20 years old.

Hence, The solution is: Jiri is 20 years old.

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Perform the indicated operation. (5 - 2i 2) 2

Answers

[tex]\bf (5-2i^2)^2\qquad \textit{now recall }i^2=\sqrt{-1}\cdot \sqrt{-1}=\sqrt{(-1)^2}=-1 \\\\\\ (5-2(-1))^2\implies (5+2)^2\implies 7^2\implies 49[/tex]

ANSWER

[tex](5 - 2 {i}^{2} ) ^{2} = 49[/tex]

EXPLANATION

The given expression is

[tex](5 - 2 {i}^{2} ) ^{2} [/tex]

This is an expression containing a complex number.

Recall that in complex numbers,

[tex] {i}^{2} = - 1[/tex]

The expression now becomes,

[tex](5 - 2 {i}^{2} ) ^{2} = (5 - 2 ( - 1) ) ^{2} [/tex]

This implies that,

[tex](5 - 2 {i}^{2} ) ^{2} = (5 + 2 ) ^{2} [/tex]

This will simplify to,

[tex](5 - 2 {i}^{2} ) ^{2} = {7}^{2} [/tex]

This eventually gives us,

[tex](5 - 2 {i}^{2} ) ^{2} = 49[/tex]

Ricky is filling an 8 inch by 4 inch by 4 1/2 inch rectangular box with packing peanuts. The peanuts are cubes that come in two different sizes ,1 cubic inch and 1/8 inch .How many peanuts of each size are needed to fill the box?

Answers

First find the volume of the box: 8•4•4.5=144 cubic inches.
8 of the 1/8 inch=1 of the 1 cubic inch
He could do 144 and 0
143 and 8
142 or 16
Or just keep following the pattern... Hope that helped

A triangle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?

Answers

you must first subrtact 4 -6 to get 42 then add 99

Find the value of x, rounded to the nearest tenth. Please help me!!

Answers

When two secant lines intersect each other outside a circle, the products of their segments are equal.

5(x+5) = 7(15+7)
5x + 25 = 7 * 22
5x + 25 = 154
5x = 154 - 25
5x = 129
x = 129/5
x = 25.8

The value of x for the circle is 25.8. The correct option from the following is (D).

Simple closed shapes include circles. It is the collection of all points in a plane that are a certain distance from the center. A segment is a section of a straight line that has every point on the line that lies in its middle and is enclosed by two clearly defined endpoints.

The products of two secant lines that cross one another outside of a circle are equal.

The value of x is:

5(x+5) = 7(15+7)

5x + 25 = 7 × 22

5x + 25 = 154

5x = 154 - 25

5x = 129

x = 129/5

x = 25.8

Hence, the value of x is 25.8.

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6300 and 530
The value of 3 in ___is____times the value of 3 in ___.

Answers

Hope this helps you out :)
6300 Ana 530

which is greater 2 or -13?

Answers

2, you can already tell -13 is less because it's a negative, and 2 is a positive.

2 is greater than -13.

If a number is negative, that means it's lower than 0.

Differentiate
1/√x^2-1

Answers

the function is [tex]f(x)= \frac{1}{ \sqrt{ x^{2} -1}} [/tex]

write f again as [tex]f(x)= (x^{2} -1)^{- \frac{1}{2} } [/tex]

(the power -1 takes the expression to the denominator, and the power 1/2 is square root)

writing rational expressions as power expressions, generally makes differentiation more practical.

In [tex]f(x)= (x^{2} -1)^{- \frac{1}{2} } [/tex] we notice 2 functions:

the outer function [tex]u^{ -\frac{1}{2} } [/tex], where [tex]u=x^{2} -1[/tex], and the inner, u itself , which is a function of x.

So we differentiate by using the chain rule:

[tex]f'(x)= -\frac{1}{2}u^{- \frac{1}{2}-1 }*u'= -\frac{1}{2}u^{- \frac{3}{2} }*(2x)=- \frac{x}{ \sqrt{ u^{3} } } =- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }[/tex]

Answer: [tex]- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }[/tex]

A student was asked to use the formula for the perimeter of a rectangle, P = 2l + 2w, to solve for l. The student came up with an answer, P -2w=2l. What error did The student make? Explain. Then solve for l

Answers

The student solved for 2l, not l. Dividing P -2w=2l by 2, we get l=P/2-w

Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?

Answers

inequation 1:

[tex] \frac{2}{3}x-3 \geq y[/tex]

to plot the pairs (x, y) for which the inequation holds, draw the line [tex]y=\frac{2}{3}x-3[/tex]

then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.

we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.

inequation 2:

[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]

[tex]y\ \textless \ - \frac{2}{3} x+ 4 [/tex]

draw the lines

i) [tex]y=\frac{2}{3}x-3[/tex] use points (0, -3), (3, -1)

ii)[tex]y=- \frac{2}{3} x+ 4 [/tex] use points ( 0, 4), (3, 2)

let's use the point P(3, 3) to see what region of the lines need to be coloured:

[tex]\frac{2}{3}x-3 \geq y[/tex] ;
[tex]\frac{2}{3}(3)-3 \geq 3[/tex]
[tex]2-3 \geq 3[/tex], not true so we color the region not containing this point

[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]
[tex](3)+ \frac{2}{3}(3)\ \textless \ 4 [/tex]
[tex]3+ 5\ \textless \ 4 [/tex] not true, so we color the region not containing the point (3, 3)

The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.

Answer:

in other words b

Step-by-step explanation:

Which expression is equivalent to the following complex fraction? (2/x)-(4/y)/(-5/y)+(3/x)

Answers

See answer attached.

Final answer:

To find the equivalent expression, multiply the first fraction by y and the second fraction by x. Simplify the expression by combining like terms.

Explanation:

To find the expression equivalent to the given complex fraction, we can simplify it step by step. First, multiply the numerator and denominator of the first fraction (2/x) by y, and multiply the numerator and denominator of the second fraction (-5/y) by x. This gives us (2y)/(xy) - (4x)/(-5x). Next, simplify the expression by combining like terms. The final equivalent expression is (2y - 4x)/(xy + 5x).

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Find the surface area of a regular pentagonal prism with side length 8, altitude 20, and apothem approximately 5.5

Answers

Final answer:

The surface area of a regular pentagonal prism can be found by calculating the area of the pentagonal bases and the area of the rectangular sides and then summing those areas together.

Explanation:

Calculating the Surface Area of a Regular Pentagonal Prism

To find the surface area of a regular pentagonal prism with given dimensions, we need to calculate the area of two components: the area of the pentagonal bases and the area of the rectangular sides (also called the lateral faces). We are given that the side length (s) of the pentagon is 8 units, the prism's altitude (h), or height, is 20 units, and the apothem (a) is approximately 5.5 units.

Firstly, the area of a pentagon (Apentagon) is calculated using the formula Apentagon = ½ * perimeter * apothem, where the perimeter (P) of a regular pentagon is the side length multiplied by 5. Thus, the area of one pentagonal base is ½ * 5 * 8 * 5.5. Next, to find the entire area of the two pentagonal bases, we multiply this result by 2.

The area of each of the rectangular sides can be found by multiplying the side length by the prism's altitude. Since there are 5 identical rectangular sides in a regular pentagonal prism, their total area is 5 * 8 * 20.

Adding these two results together gives us the total surface area of the prism. So, the formula for the surface area is Total Surface Area = (2 * ½ * 5 * 8 * 5.5) + (5 * 8 * 20).

if f(x) = 3x - 2 then f (8) - f(-5)=

Answers

f(8) = 3(8) - 2 = 22
f(-5) = 3(-5) - 2 = -17
so....
f(8) - f(-5) = 22 - -17 = 39

A cylinder has a base area of 169π cm2 . Its height is 4 cm more than the radius. Identify the volume of the cylinder. Round to the nearest tenth, if necessary.

Answers

check the picture below.

Answer:

V = 9025.8 cm3

Step-by-step explanation:

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a sample of 100 major league players was taken. find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Answers

Final answer:

The probability is approximately 0.267.

Explanation:

To find the approximate probability that the mean salary of the 100 players exceeded $4.0 million, we can use the Central Limit Theorem and the Z-score formula. The Z-score formula is:

Z = (x - μ) / (σ / sqrt(n))

where x is the value we want to find the probability for (in this case $4.0 million), μ is the mean of the population ($3.26 million), σ is the standard deviation of the population ($1.2 million), and n is the sample size (100).

We calculate the Z-score as follows:

Z = (4.0 - 3.26) / (1.2 / sqrt(100)) = 0.617

We then use a Z-table or a calculator to find the probability corresponding to a Z-score of 0.617. The probability is approximately 0.267.

there were 137 tickets purchased for a major league baseball game the lower box tickets cost $12.50 and the upper box tickets cost $10 the total amount of money spent was $1,502.50 how much of each kind of ticket

Answers

lower box = x

upper box = y

x+y=137

x=137-y

12.50x + 10y=1502.50

12.50(137-y) + 10y=1502.50

1712.5-12.50y+10y=1502.50

1712.5-2.50y=1502.50

-2.5y=-210

y=-210/-2.50 = 84

y = 84

x=137-84=53

53 lower box tickets

84 upper box tickets

The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S . Then use this equation to find the total cost to transport 19 tons of sugar.

Answers

Answer: Equation relating C to S : [tex]C=6500+250S[/tex]

The total cost to transport 19 tons of sugar is $11, 250.

Step-by-step explanation:

Given : It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported.

Total cost = $6500 + $250 x (amount of sugar transported ( in tons))

Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported.

Then, the equation relating C to S would be : [tex]C=6500+250S[/tex]

When S= 19 , we get

[tex]C=6500+250(19)=6500+4750= 11250[/tex]

Hence, the total cost to transport 19 tons of sugar would be $11, 250.

An equation that relates Cost to the amount of sugar S

C = 6500 + 250S

The total cost is $1120

The total cost of transporting 19 tons of sugar at 250 each

C = total cost

C = 6500 + 250(19)

Total cost = 6500 + 4750

= 11250

Therefore the total cost of transporting the 19 tons of sugar is $11250

Answers

The student ticket number is 429 and adult is 375.

You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 3% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $3,650 in interest. If you invest five times the money in the account that pays 4% compared to 3%, how much did you invest in the 4% account?

Answers

Let x = amount invested in the 1st account
y = amount invested in the 2nd account
z = amount invested in the 3rd account

Because the total investment is $100,000, therefore
x + y + z = 100,000 (1)
Interest earned in one year from the accounts is $3,650, therefore
0.04x + 0.03y + 0.02z = 3,650
or
4x + 3y + 2z = 365,000 (2)

Because x = 5y, therefore obtain these 2 equations:
5y +y +z = 100,000
or
6y + z = 100,000 (3)
4*(5y) +3y + 2z = 365,000
or
23y + 2z = 365,000 (4)

Substitute z=1000,000 - 6y from (3) into (4).
23y + 2(100,000 - 6y) = 365,000
23y + 200,000 - 12y = 365,000
11y = 165,000
y = $15,000
Therefore
x = 5y = $75,000
z = 100,000 - 6y = $10,000

Answer:
The amounts invested are
1st account: $75,000
2nd account: $15,000
3rd account: $10,000

Assume the Poisson distribution applies. Use the given mean to find the indicated probability.

Find P(4) when μ = 8.

Answers

For given Poisson distribution, μ=8.

P(k)=μ^k*e^(-μ)/k!
so
P(4)=8^4*e^(-8)/4!=0.05725 approx.

Final answer:

Using the Poisson distribution formula, substitute the given mean and the number of occurrences into the formula to find the probability. Hence P(4; 8)= e^-8 * 8^4 / 4!. The answer will be in decimal form, signifying the probability.

Explanation:

The probability in a Poisson distribution that an event happens exactly k times when the mean occurrence rate (μ or Lambda) is given is determined using the following formula:

P(k; μ) = (e^-μ * μ^k) / k!

Where e is Euler's number (approximately equal to 2.71828), k is the number of occurrences (in this case, it is 4) and μ is the mean number of occurrences (in this case, it is 8).

Applying the values into the formula, we have:

P(4;8) = (e^-8 * 8^4) / 4!

You can calculate the above expression using a calculator to find the probability. Remember, the answer will be in decimal form, representing the probability of the event occurring 4 times when the average rate of occurrence is 8.

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what is 46 2/3 of 28

Answers

[tex]\bf 46\frac{2}{3}\implies \cfrac{46\cdot 3+2}{3}\implies \cfrac{140}{3}\qquad thus \\\\\\ \cfrac{140}{3}\cdot 28\implies \cfrac{3920}{3}\implies 1306\frac{2}{3}[/tex]

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

A newspaper finds that the mean number of typographical errors per page is six. Find the probability that (a) exactly four typographical errors are found on a page, (b) at most four typographical errors are found on a page, and (c) more than four typographical errors are found on a page.

Answers

In this case, the Poisson distribution is the best one to use. The formula for Poisson distribution is given as:

P[x] = e^-m * m^x / x!

Where,

m = mean number of typographical errors = 6

x = sample value

A. The probability of exactly 4 errors are found on a page is:

P[4] = e^(-6) * 6^4/4!

P[4] = 0.1339

B. The probability that at most 4 errors will be the summation of x = 0 to 4:

P[0] = e^(-6) * 6^0/0! = 2.479 E -3

P[1] = e^(-6) * 6^1/1! = 0.01487

P[2] = e^(-6) * 6^2/2! = 0.04462

P[3] = e^(-6) * 6^3/3! = 0.08924

Therefore summing up all including the P[4] in A gives:

P[at most 4] = 0.2851

C. The probability that more than 4 would be the complement of answer in B.

P[more than 4] = 1 - P[at most 4]

P[more than 4] = 1 - 0.2851

P[more than 4] = 0.7149

y=-x y=2x+3 graph the equation to solve the system

Answers

If Y=-x y=2x+3 was graphed it would be (-1,1)

Well to solve by graphing, you would graph both equations and then see where the two lines intersect. This graphical intersection is the point where both equations are equal to each other.

To solve using math :P

If a solution exists, (x,y)=(x,y) so we can say y=y and then we can say:

2x+3=-x add x to both sides

3x+3=0

3(x+1)=0

So x=-1, and since y=-x

y=1

So the solution to the system of equations, and the graphical intersection, is the point (-1, 1)

A line passes through the point (6−6) and has a slope of 3/2 . Write an equation in point-slope form for this line.

Answers

y= (3/2)x-15 is the equation

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