Determine the equation of the circle graphed below.

Answer:

17

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

[tex]d = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} - x_{1})^{2} }[/tex]

d = distance

[tex](x_{1}, y_{1})[/tex] = coordinates of the first point

[tex](x_{2}, y_{2})[/tex] = coordinates of the second point

Answer: The distance between the points (6,-7)(-2,8) is 17.

Step-by-step explanation:

To calculate the distance between two points, we apply the following formula:

[tex]\boldsymbol{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 } }}[/tex]

The points are:

We substitute in the formula and solve:

[tex]\boldsymbol{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 } }}\\ \\ \boldsymbol{\sf{d=\sqrt{(-2-6)^2+(8-(-7))^2 } }}\\ \\ \boldsymbol{\sf{d=\sqrt{(-8)^2+15^2}=\sqrt{64+225 } }}\\ \\ \boldsymbol{\sf{d=\sqrt{289}=17 }}[/tex]

The distance between the points (6,-7)(-2,8) is 17.

Answer:

You need to show the statements or I can't help.

Answer:

A vertical line through the origin

Step-by-step explanation:

Answer:

2/36 or 1/18 simplified

Step-by-step explanation:

you have all the combinations listed which is good.

probability = number of successful events / number of total events

there are

Answer:

105.6

hope this helps

have a good day :)

Step-by-step explanation:

Step-by-step explanation:

DAG = DG

120=120°

DHG + DG =360°

DHG +120° =360°

DHG+120°-120°=360°-120°

DHG°=240°

Answer:

[tex]C=252.2ft[/tex]

Step-by-step explanation:

From the question we are told that:

First Kite Distance [tex]A=450ft[/tex]

Second Kite Distance [tex]B=390ft[/tex]

Angle [tex]\theta=34\textdegree[/tex]

Generally the equation for Distance X between the kites is mathematically given by

Using Cosine Rule

 [tex]C^2=A^2+B^2-2abCos \theta[/tex]

Therefore

 [tex]C^2=(450)^2+(390)^2-2(450)(390)Cos 34[/tex]

 [tex]C^2=63607.81[/tex]

 [tex]C=\sqrt(63607.81)[/tex]

 [tex]C=252.2ft[/tex]

m<1=130°[alternate angle are equal again]

m<1+m<2180°[linear pair]

m<2=180°-130°

====================================

If you have any questions feel free to ask me^^

Have a nice and great day!

#PilipinasAngBayanKo

Answer:

m=4

2y/2=y

8x/2=4x

4/2=2

so

y=4x+4

Answer:

-46

Step-by-step explanation:

4(-8x + 5) = -32x - 26

-32x + 20 = -32x - 26

-32x + 32x = -26 - 20

x = -46

Answer:

-32x+20=-32x-26

20=-26

so unequal or undefined

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

340

Step-by-step explanation:

2(10*8)=160

2(8*5)=80

2(5*10)=100

160+80+100=340

Answer: 3 pounds

Step-by-step explanation: 12 - 4.50 = 7.50 7.50/2.50=3

Step-by-step explanation:

angle ABE=angle EBC

Answer:

x= 0.22947

Step-by-step explanation:

Step-by-step explanation:

x=0 22 im not sure though ok

Answer:

[tex]A + B + E = 32[/tex]

Step-by-step explanation:

Given

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]

Required

Find [tex]A +B + E[/tex]

We have:

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]

Using integration by parts

[tex]\int {u} \, dv = uv - \int vdu[/tex]

Where

[tex]u = x^2[/tex] and [tex]dv = e^{-4x}dx[/tex]

Solve for du (differentiate u)

[tex]du = 2x\ dx[/tex]

Solve for v (integrate dv)

[tex]v = -\frac{1}{4}e^{-4x}[/tex]

So, we have:

[tex]\int {u} \, dv = uv - \int vdu[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = x^2 *-\frac{1}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x} 2xdx[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} - \int -\frac{1}{2}e^{-4x} xdx[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]

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

Solving

[tex]\int xe^{-4x} dx[/tex]

Integration by parts

[tex]u = x[/tex] ---- [tex]du = dx[/tex]

[tex]dv = e^{-4x}dx[/tex] ---------- [tex]v = -\frac{1}{4}e^{-4x}[/tex]

So:

[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x}\ dx[/tex]

[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} + \int e^{-4x}\ dx[/tex]

[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}[/tex]

So, we have:

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}][/tex]

Open bracket

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} -\frac{x}{8}e^{-4x} -\frac{1}{8}e^{-4x}[/tex]

Factor out [tex]e^{-4x}[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}[/tex]

Rewrite as:

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}[/tex]

Recall that:

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}[/tex]

By comparison:

[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]

[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]

[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]

Solve A, B and C

[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]

Divide by [tex]-x^2[/tex]

[tex]\frac{1}{4} = \frac{1}{64}A[/tex]

Multiply by 64

[tex]64 * \frac{1}{4} = A[/tex]

[tex]A =16[/tex]

[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]

Divide by [tex]-x[/tex]

[tex]\frac{1}{8} = \frac{1}{64}B[/tex]

Multiply by 64

[tex]64 * \frac{1}{8} = \frac{1}{64}B*64[/tex]

[tex]B = 8[/tex]

[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]

Multiply by -64

[tex]-64 * -\frac{1}{8} = -\frac{1}{64}E * -64[/tex]

[tex]E = 8[/tex]

So:

[tex]A + B + E = 16 +8+8[/tex]

[tex]A + B + E = 32[/tex]

Answer:

Root of 65

Step-by-step explanation:

8^2 is equal to 64, so the sqrt of 64 would equal 8 exactly. The question is asking for which of the sqrts would be closest to 8, so sqrt of 65 is the number that is closest to 64, so it is the answer.

Answer:

[tex] \sqrt{65} [/tex]

as

[tex] \sqrt{64} = 8[/tex]

so it's the closest value to 8

and also

[tex] \sqrt{65} = 8.06[/tex]

via calculator

Answer:

cylinder volume=  1005.30965cm²

rectangular prism volume=  384cm²

total volume: 1005.30965+384= 1389.31cm²

Answer:

7 C

Step-by-step explanation:

We want to find the y value for an x value of -9

The y value for the x value of -9 is 7

[tex]\boxed{D)\:5}[/tex] ✔

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]\sf\purple{A)\:-4}[/tex] ❌

[tex]x - 4 < - 2 \\ = - 4 - 4 < - 2 \\ = - 8 < - 2[/tex]

[tex]\sf\purple{B)\:-1}[/tex] ❌

[tex]x - 4 < - 2 \\ = - 1 - 4 < - 2 \\ = - 5 < - 2[/tex]

[tex]\sf\purple{C)\:0}[/tex] ❌

[tex]x - 4 < - 2 \\ = 0 - 4 < - 2 \\ = - 4 < - 2[/tex]

[tex]\sf\red{D)\:5}[/tex] ✅

[tex]x - 4 > - 2 \\ = 5 - 4 > - 2 \\ = 1 > - 2[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

48

Step-by-step explanation: 1 foot is 12 inches. Since the feet are going up by ones, you can say 1=12, 2=24 (+12), 3=36(+12), 4=48(+12)

Hope this helps

Answer and Step-by-step explanation:

The answer is 48.

Each value of y is a multiple of 12, so for when there is 4 feet, you multiply 12 by 4 to get 48.

For when it is 1 foot, you multiply 12 by 1 to get 12.

For when it is 2 feet, you multiply 12 by 2 to get 24.

For when it is 3 feet, you multiply 12 by 3 to get 36

For when it is 5 feet, you multiply 12 by 5 to get 60.

If you were to continue, the y-values (aka the inches) will always be a multiple of 12.

#teamtrees #PAW (Plant And Water)

Answer:

7.3

Step-by-step explanation:

Biggest value = 8.9

smallest value = 1.6

range = 8.9-1.6 = 7.3

Step-by-step explanation:

range=highest number - lowest number

= 8.9 - 1.6

=7.3

Answer:

a = 32,37

b=99

Step-by-step explanation:

a = 32,369

The third decimal place is greater (or equal) than 5, so we need to add one unit to the second place.

= 32,37

b = 99,004

The third decimal place is lesser than 5, so we can simply delete it.

= 99,00

Since only zero in every decimal places are not relevant, we can remove them:

= 99

Answer:

The 85% confidence interval for the mean number of toys purchased each year is (6.7, 6.9).

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.85}{2} = 0.075[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.075 = 0.925[/tex], so Z = 1.44.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.44\frac{2.1}{\sqrt{686}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 6.8 - 0.1 = 6.7

The upper end of the interval is the sample mean added to M. So it is 6.8 + 0.1 = 6.9

The 85% confidence interval for the mean number of toys purchased each year is (6.7, 6.9).

Answer:

x = 9

Step-by-step explanation:

The triangle given is an isosceles triangle because it has two equal sides. By implication, the two base angles that are opposite the two equal sides are equal to each other.

Therefore,

80° + 2(m<2) = 180° (sum of triangle theorem)

80 + 2(5x + 5) = 180

80 + 10x + 10 = 180

Add like terms

90 + 10x = 180

90 + 10x - 90 = 180 - 90 (substraction property of equality)

10x = 90

10x/10 = 90/10 (division property of equality)

x = 9

Answer:

Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score)  on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Bill:

Scored 300, so [tex]X = 300[/tex]

SAT has a μ of 500 and a σ of 100.

His z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{300 - 500}{100}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.02.

This means that Bill, whose SAT score has Z = -2, scored in the 2nd percentile.

Rhoda

Scored 25, so [tex]X = 25[/tex].

ACT has a μ of 20 and a σ of 5

Her z-score:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{25 - 20}{5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84

This means that Rhoda, whose ACT score has Z = 1, scored in the 84th percentile.

What is wrong with Bill’s logic ?

Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score)  on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.

Answer:

[tex]area = \frac{1}{2} \times 11 \times 18 \\ = 99 \: {ft}^{2} [/tex]

Answer:

1.(a) 25.3

(b) 3.49

(c) 14.44

2.(a) 86.64

(b) 59.85

(c) 27.92

3. 5.92

4.(a) 13.96

(b) 43.32

(c) 101.12

5.(a) 59.85

(b) 10.47

(c) 50.6

6. 5.56

Answer:

A) John

Answer:

john

Step-by-step explanation:

Answer:

Pair 2.

Step-by-step explanation:

For the volumes to be the same the base areas must also be the same.

For Pair 2 the areas are 25π and 24π while the other 2 pairs have both base areas = 25π.

Answer:

180

Step-by-step explanation:

volume= (6*5)/2*12 =180 in