10. Find the standard equation of the circle having the given center and radius.

Answer:

radius 4

center (3,6)

Step-by-step explanation:

(x - h)^2 + (y - k)^2 = r^2

coordinates of the center (h, k) and the radius is (r)

x² + y²- 6x - 12y +29=0

x² - 6x + y²- 12y +29=0

(x² - 6x) + (y²- 12y) +29=0

complete the square

(x² - 6x) + 9 + (y²- 12y) +36 +29=  + 9  +36

(x² - 6x + 9) + (y²- 12y + 36) = + 9  +36 -29

(x-3)^2 + (y-6)^2 = 16

(x - h)^2 + (y - k)^2 = r^2

coordinates of the center (h, k) and the radius is (r)

center (3,6)

radius 4

cuemathcom

varsitytutors

Answer: Center: (3,2)                Radius: 5

Step-by-step explanation:#x^2 - 6x +y^2 - 4y = 12

Then take 1/2 of the 'b' term for both quadratic expressions, square those values and add them to both sides.

#x^2 -6x + 9 + y^2 - 4y + 4 = 12 + 9 + 4

(x - 3)^2 + (y -2)^2 = 25

Circle centered at (3,2) with radius = 5

Answer:

  (B)  38.4 m³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the height.

__

The picture tells you the area of the pool is 24 m² and its height is 1.6 m. The volume formula tells you its volume is ...

  V = Bh = (24 m²)(1.6 m) = 38.4 m³

The volume of the prism is 38.4 cubic meters.

Answer:

Approximately [tex]14,\!500\; {\rm cm^{3}}[/tex].

Step-by-step explanation:

The radius of a sphere is the same as the radius of the great circle of that sphere.

Thus, in this question, it would be possible to find the radius of the sphere by finding the radius of the great circle.

The circumference of a circle of radius [tex]r[/tex] is [tex]2\, \pi \, r[/tex]. In this question, it is given that the circumference of this great circle is [tex]95\; {\rm cm}[/tex]. Thus, the radius of this great circle would be:

[tex]\begin{aligned}r &= \frac{95\; {\rm cm}}{2\, \pi} \approx 15.1197\; {\rm cm}\end{aligned}[/tex].

Thus, radius of the sphere in this question would also be approximately [tex]15.1197\; {\rm cm}[/tex].

The volume of a sphere of radius [tex]r[/tex] is [tex](4/3)\, \pi\, r^{3}[/tex]. Thus, the volume of this sphere of radius [tex]r = 15.1197\; {\rm cm}[/tex] would be approximately:

[tex]\begin{aligned}\frac{4}{3} \, \pi\times (15.1197\; {\rm cm})^{3} \approx 14,\!500 \; {\rm cm^{3}}\end{aligned}[/tex]

Answer:

d 15.

Step-by-step explanation:

Slope = (difference in y values)/ (corresponding difference in x values)

So we have:

Slope = (120-117)  / (6.6-6.4)

          =  3 / 0.2

           = 30/2 = 15.

Answer:

b = 49 cm

Step-by-step explanation:

Volume of a rectangular prism = width × length × height

Given:

Substituting the given values into the formula and solving for b:

⇒ 48608 = 16 × b × 62

⇒ 48608 = 992 b

⇒ b = 48608 ÷ 992

⇒ b = 49

Answer:

b = 49 cm

Step-by-step explanation:

Volume of a rectangular prism: length × width × height

V = L×W×H

Substitute the values above and solve for b:

48,608 = b × 16 × 62

48,608 = 992b

48,608/992 = 992b/992

49 = b

Final answer: 49 cm

Hope this helps!

#20

#21

Find LCD of 2,7x,x

So

Answer:

20.  (4)  x > 6

21.  (3)  14x

Step-by-step explanation:

Question 20

[tex]\begin{aligned}\dfrac{1}{2}x+3 & < 2x-6\\\dfrac{1}{2}x+3-3 & < 2x-6-3\\\dfrac{1}{2}x & < 2x-9\\\dfrac{1}{2}x-2x & < 2x-9-2x\\-\dfrac{3}{2}x & < -9\\-\dfrac{3}{2}x \cdot 2 & < -9 \cdot 2\\-3x & < -18\\-\dfrac{3x}{3} & < -\dfrac{18}{3}\\-x & < -6\\\dfrac{-x}{-1} & < \dfrac{-6}{-1}\\x & > 6\end{aligned}[/tex]

Rewrite all three fractions so that their denominators are the same:

[tex]\dfrac{1}{2}=\dfrac{1 \times 7x}{2 \times 7x}=\dfrac{7x}{14x}[/tex]

[tex]\dfrac{2}{7x}=\dfrac{2 \times 2}{7x \times 2}=\dfrac{4}{14x}[/tex]

[tex]\dfrac{5}{x}=\dfrac{5 \times 14}{x \times 14}=\dfrac{70}{14x}[/tex]

Therefore, the least common denominator is [tex]14x[/tex]

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

[tex]\diamond\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

       What is the equation of the line that passes through (-3, 6) and has a slope of -2?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond[/tex]

First, we need to write the equation of the line in point-slope form:-

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

Replace y1 with 6, m with -2, and x1 with -3:-

[tex]\sf{y-6=-2(x-(-3)}[/tex]

On simplification,

[tex]\sf{y-6=-2(x+3)}[/tex]

On further simplification,

[tex]\sf{y-6=-2x-6}[/tex]

Add 6 on both sides:-

[tex]\it{y=-2x}[/tex]

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

[tex]\\ \rm\Rrightarrow 7829y\times \dfrac{-69}{56x}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{7829(69)y}{56x}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{540201y}{56x}[/tex]

[tex]\\ \rm\Rrightarrow 9646.4y/x[/tex]

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}\implies \cfrac{9}{3}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{3}(x-\stackrel{x_1}{4}) \\\\\\ y-1=3x-12\implies y=3x-11[/tex]

To calculate this sort of problem:

 ⇒ involves calculating the total profits over each year

 ⇒ with a constant increase periodically

    ⇒ need to use the Compound Interest Equation

           [tex]A = P(1+\frac{r}{n})^{nt}[/tex]

Let's fill in some variables:

What do we want to know:

Let's solve:

    [tex]A= 247500*(1+\frac{0.16}{1} )^{1*10}=\\A=247500*(1+0.16)^{10}\\A=247500*(1.16)^{10} \\A= 1,091,830.18[/tex]

To the nearest whole number

Hope that helps!

Answer:

3x² + 4x + 8 = 0

Step-by-step explanation:

Standard form of quadratic equation is

ax²+bx+c=0

standard form of quadratic equation 3x²+4x+7=-1 is

3x² + 4x + 7 = -1

3x² + 4x + 7 + 1 = 0

3x² + 4x + 8 = 0

Answer:

y=0, x=4

Step-by-step explanation:

2x+2y=8 --- (1)

4x+3y=16 --- (2)

Multiply the coefficient of x in equation (1) across the variables in equation (2), and multiply the coefficients of x in equation (2) across the variables in equation (1).

8x+8y=32 ---- (3)

8x+6y=32 ---- (4)

Subtract equation (3) from (4)

2y=0, y=0/2, y=0.

Substitute the solution for y=0 into equation (1)

2x+2(0)=8

2x=8

x=4

Answer:

-6, -4

Step-by-step explanation:

I got it right

Answer:

i think the answer is r=0.5 or r=−3/2−x^2

Step-by-step explanation:

-4r^2-4r=6

step 1. -4r(-4r)= 16r

16r-4r=6

step 2. 16r-4r=12r

12r=6      

step 3. /12 on both sides

r= 0.5

By finding the scale factor, we will see that the volume of the smaller solid is 86.75 m³.

If the solids are similar, then there is a scale factor between the two. Then the relation between the areas is equal to the scale factor squared, and the relation between the volumes is equal to the scale factor cubed.

This means that if the areas are 169 m² and 81 m², then we can write:

169 m² = (k²)*81 m²

Solving for k, we get:

k = √(169 m²/81 m²) = 1.44

Then if the volume of the large solid is 124.92m³ we can write:

124.92m³ = k³*V

Replacing k and solving for V we get:

124.92m³ = (1.44)³*V

(124.92m³/ (1.44)³) = V = 86.75 m³

If you want to learn more about scale factors:

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Answer: Its C

Step-by-step explanation: Just did it

Answer:

y = y coordinate

m = slope

x = x coordinate

b = y intercept

Line passes through (2, -1) and slope of 1/3

y = mx + b,  Identify:  x = 2, y = -1, slope: [tex]\sf \frac{1}{3}[/tex]

insert following values

[tex]\rightarrow \sf -1 = \dfrac{1}{3} (2) + b[/tex]

multiply

[tex]\rightarrow \sf -1 = \dfrac{2}{3} + b[/tex]

switch sides

[tex]\rightarrow \sf b = -1 - \dfrac{2}{3}[/tex]

subtract

[tex]\sf \rightarrow b = -\dfrac{5}{3}[/tex]

convert to mixed fraction

[tex]\sf \rightarrow b = -1\dfrac{2}{3}[/tex]

y = mx + b,  m = [tex]\sf \frac{1}{3}[/tex], b = [tex]-1\frac{2}{3}[/tex]

insert following values

[tex]\rightarrow \sf y = \dfrac{1}{3} x -1\dfrac{2}{3}[/tex]

Answer: 4 books

Step-by-step explanation:

x = minimum number of book

Leslee

= 3x (bought 3 times the minimum)

Denise

= x + 7 (bought 7 more than the minimum)

Together

= (3x) + (x + 7)

(3x) + (x + 7) = 23 (books they bought together)

3x + x + 7 = 23

3x + x = 23 - 7 (isolate the like variables together)

4x = 16 (divide both sides by 4)

x = 4

4 is the minimum number of books

To check:

3(4) + (4+7)

12 + 11 = 23

Answer:

The incenter....

Step-by-step explanation:

The point at which all three of the angle bisectors of a triangle meet is known as the incenter

dont confuse it with the circumcenter and the centroid.

i hope this helps!!!

Simplified

[tex]x\sqrt[3]{x}[/tex]

Polynomials are the algebraic expressions that consist of variables and coefficients.

The Closure property of addition states that in a defined set, for example, the set of all positive numbers is closed with respect to addition since the sum obtained adding any 2 positive numbers is also a positive number which is a part of the same set.

Closure property of subtraction states that if any two real numbers a and b are subtracted from each other, the difference or result will be a real number as well. For example, 9 - 4 = 5.

Learn more about polynomial on:

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The conditional probability that the carbon emission is beyond the permissible emission level and the test predicts this is given by:

a. 0.2975.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

In this problem, we have that the events are as follows:

We have that 35% of the units have carbon emission beyond the permissible emission level, and the test is 85% accurate, hence:

[tex]P(A) = 0.35, P(B|A) = 0.85[/tex]

Then:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]0.85 = \frac{P(A \cap B)}{0.35}[/tex]

[tex]P(A \cap B) = 0.85(0.35) = 0.2975[/tex]

Which means that option a is correct.

More can be learned about conditional probability at https://brainly.com/question/14398287

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Answer:

[tex]y = \dfrac 12x -5[/tex]

Step-by-step explanation:

[tex]\text{Given that,}~ (x_1,y_1) = (6,-2)~ \text{and}~ (x_2,y_2) = (12,1)\\\\\text{Slope,}~ m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{1+2}{12-6}= \dfrac{3}{6} = \dfrac 12\\\\\text{Equation of line,}\\\\~~~~~~~~y-y_1 =m(x-x_1)\\\\\implies y+2=\dfrac 12 (x-6)~~~~~~~~~~~~~~;[\text{Point -slope form}]\\\\\implies y = \dfrac 12 x -3 -2\\\\\implies y = \dfrac 12x -5~~~~~~~~~~~~~~~~~~~~~;[\text{Slope-intercept form.}][/tex]

Step-by-step explanation:

the slope of f(x) = 1

for every increase of x by 1 also y increases by 1.

the slow of g(x) = -2

for every increase of x by one y decreases by 2.

so, we see, as

g(x) = k × f(x)

k = g(x) / f(x) = slope g / slope f = -2/1 = -2

why ? because both functions are linear functions (lines).

they look like

y = ax + b

with a being the slope of the line.

so, when multiplied by k, this is kax + kb, and we see k as factor already in the slope of the line itself.

Convert angle to radians

So

Area

Answer:

[tex]\textsf{C.} \quad \dfrac{64 \pi}{3} \: \sf square\:centimeters[/tex]

Step-by-step explanation:

Formula

[tex]\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}[/tex]

Given:

Substitute the given values into the formula and solve for Area:

[tex]\large \begin{aligned}\implies \textsf{Area} & =\left(\dfrac{120^{\circ}}{360^{\circ}}\right) \pi (8)^2\\\\& =\left(\dfrac{1}{3}\right) \pi (64)\\\\& =\dfrac{64}{3} \pi \: \sf cm^2\end{aligned}[/tex]

Answer:

0.001

Step-by-step explanation:

Given (or we can find) :

First term : 216

Common ratio : 36/216 = 1/6

To find 8th term :

a₈ = ar⁸⁻¹

a₈ = (216)(1/6)⁷

a₈ = 216/279936

a₈ = 6³/6⁷

a₈ = 1/6⁴

a₈ = 1/1296

a₈ = 0.000771604938

a₈ = 0.001 (nearest thousandth)

Answer:

Step-by-step explanation:

Let Emma's age be 2x years, then:

Elsa's age is x years, also:

Bella's age is x - 2 years.

In one years time the sum of their ages

=  2x + 1 + x + 1 + x - 2 + 1

= 4x + 1  where x = Elsa's age now.

5 years before now

Sum of their ages

=  2x -5 + x - 5 + x - 2 - 5

= 4x - 17 where x = Elsa's age now,

Answer:

B

Step-by-step explanation:

B: $303.75

I hope this helps you and I hope you do well.