Write the equation of a circle that has a center at the point (-3, 6) and passes through the point (9, 1).



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Answer:

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The base area, the lateral area and the surface area of the prism are 124.8 cm², 288 cm² and 412.8 cm², respectively.

In this problem we need to compute three kinds of areas in a prism with a triangular base. The base area, that is, the sum of the areas of the two triangles, the lateral area, that is, the sum of the areas of the three rectangles and the surface area, that is, the sum of the base and lateral areas.

The area formulas of the triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we proceed to determine each kind of area:

Base area

A = 2 · 0.5 · (12 cm) · (10.4 cm)

A = 124.8 cm²

Lateral area

A = 3 · (8 cm) · (12 cm)

A = 288 cm²

Surface area

A = 124.8 cm² + 288 cm²

A = 412.8 cm²

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Answer: A variable is an object, event, idea, feeling, time period, or any other type of category you are trying to measure.

A variable is a characteristic that can be measured and that can assume different values. Height, age, income, province or country of birth, grades obtained at school and type of housing are all examples of variables. Variables may be classified into two main categories: categorical and numeric

Answer:

a variable (as the letters a, b, c, y, etc.) is considered a missing number within a mathematical problem

Answer:

  2

Step-by-step explanation:

Corresponding sides are proportional in these similar triangles.

__

  short side/long side = k/4 = 4/8

  k = 4(4/8) . . . . multiply by 4

  k = 2

_____

Additional comment

The lengths of the hypotenuses can be found the same way, or using the Pythagorean theorem. Using side ratios, we have ...

  l² = k(k+8) = 2(10) = 20 . . . . from MN/MO = ML/MN

  l = 2√5

  m² = 8(8+2) = 80 . . . . from LN/LO = LM/LN

  m = 4√5

The similarity statements are ...

  ΔLMN ~ ΔLNO ~ ΔNMO

Answer:

x = 20

Step-by-step explanation:

The 2 given angles are adjacent on a straight line and sum to 180° , then

123 + 2x + 17 = 180

140 + 2x = 180 ( subtract 140 from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

Answer:

The quadratic equation x2 + 8x + 16 = 0 is a perfect square trinomial, which means it can be factored as (x+4)²=0. Therefore, the nature of the quadratic equation is a perfect square trinomial, and it has one real root with a multiplicity of 2.

The quadratic equation x2 - 24x + 144 = 0 can be factored as (x-12)²=0, which is also a perfect square trinomial. Therefore, the nature of the solutions is a perfect square trinomial, and it has one real root with a multiplicity of 2.

The quadratic equation x2 - 25 = 0 can be factored as (x+5)(x-5)=0, which means it has two real roots: x=5 and x=-5.

The quadratic formula determines the solutions to the quadratic equation in terms of its coefficients. The formula is x = (-b ± √(b²-4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

The roots of the quadratic equation 2x2 + 5x + 3 = 0 can be found by factoring it as (2x+3)(x+1)=0, which means the roots are x=-3/2 and x=-1.

Step-by-step explanation:

Ages (in years) of a sample of retirement home inhabitants is option B. For the lowest wait time, the maximum frequency is anticipated to be right-skewed. A desert cannot have a maximum annual temperature of 60°F, and it is not conceivable to watch 60+ hours of TV in a single day.

Residents of senior living facilities are typically 84 years old. While there are many couples in these communities, the majority of people who live in independent living are women. Some people move in at or near the minimum age (often around 65), but most people do so between the ages of 75 and 84. Residents come from all different backgrounds.

Many people are choosing senior living in a community environment, including teachers, nurses, small business owners, big business CEOs, university professors, housewives, lawyers, engineers, musicians, and more. Current residents will attest that the rich diversity of origins fosters amazing interactions and relationships. And contrary to popular belief, the majority of residents of independent living are quite active.

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Correct Question:

Match the plot with a possible description of the sample.

60 70 80 90 100

Choose the correct answer below

A. Wait time (in minutes) for a sample of doctors offices

B. Ages (in years) of a sample of residents of a retirement home.

C. Highest yearly temperatures (F) for a sample of deserts.

D. Time (in hours_ spent watching TV in a day for a sample of teenagers.

Answer:

Length of DE = 2.90 (Approx)

Step-by-step explanation:

Given:

AE = 7\(\frac{5}{8}\)cm = 61 / 8 cm = 7.625 cm

AB = BC

CD = 1/2 cm = 0.5 cm

DE is 3/8 more than AB

Find:

Length of DE

Computation:

Assume;

AB = BC = x

So,

DE = x + 3/8(x) = [11 / 8]x = [1.375]x cm

AE = AB + BC + CD + DE

7.625 = x + x + 0.5 + [1.375]x

7.125 = 3.375 x

x = 2.1111 (Approx)

Length of DE = [1.375][2.111]

Length of DE = 2.90 (Approx)

Answer:

X= 1/2 Y= 5

Step-by-step explanation:

8x+7y=39-------------(1)--------×2

4x-14y= -68-----------(2)-------×1

16X + 14Y = 78--------(3)

4X- 14Y = -68----------(4)

Addy equation (4) and (3)

20X = 10

dividing bothsides by 20

20X/20= 10/20

X = 1/2

substitute the value of X into equation (1)

8X+7Y = 39

8(1/2)+7Y= 39

4+7Y = 39

7Y = 39-4

7Y = 35

dividing bothsides 7

7Y= 35/7

Y = 5

8 less than 3 times a number is at most 30 can be written as 8 < 3N ≤ 30

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Since 8 less than 3 times a number is at most 30

Let the number be N

Thus, 8 less than 3 times a number is at most 30 can be written as:

8 < 3×N  ≤ 30

8 < 3N ≤ 30

Note: at most means less than or equal (≤)

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Answer: C

g(x) = 1/2 f (x)

Step-by-step explanation:

Answer:

Step-by-step explanation:

c

Answer:18

Step-by-step explanation:

Because 40% of 45 is 18

Answer:

\(n=0,\\n=6\)

Step-by-step explanation:

Given \(n^2-6n=0\), we can factor out an \(n\) from each of the terms on the left side of the equation:

\(n(n-6)=0\)

Since we have two factors that multiply to zero, we can set each of them to zero and solve for \(n\), because zero multiplied by anything is equal to zero. Therefore, as long as either \(n\) or \(n-6\) is equal to zero, the other factor can be any real number and the equation would still hold true.

Therefore, we have the following cases:

\(\begin{cases}n=0,\\n-6=0\end{cases}\)

Solving, we get:

\(\begin{cases}n=0, n=\boxed{0}\\n-6=0, n=\boxed{6}\end{cases}\)

\(\\ \sf\longmapsto n^2-6n=0\)

\(\\ \sf\longmapsto n(n-6)=0\)

Now

\(\\ \sf\longmapsto n=0\:or \:(n-6)=0\)

\(\\ \sf\longmapsto n=0\:or \;n=6\)

Hence roots of the equation are 0 and 6 .

More:-

We can solve it through Quadratic formula

\(\boxed{\sf x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}\)

Answer:

b = 9.2

Step-by-step explanation:

Using the Pythagorean theorem (in your case): \(a^{2} +c^{2} = b^{2}\)

Plug in your values and solve for x:

\(6^{2}+7^{2} =b^{2}\\36+49 =b^{2} \\85 = b^{2} \\b = \sqrt{85} \\b = 9.2\)

Answer:

I'm going to assume you meant 1.5 pounds and not 15 pounds each month.

Step-by-step explanation:

1.5*6=9

C

Answer:

around 90 pounds

Step-by-step explanation:

15×6

or 15+15+15+15+15+15 if multiplying is not your thing

10% off means it is on sale for 90% of the original price ( 100% - 10% = 90%)

Multiply the price of the dress by 90%:

£70 x 0.90 = £63

The sale price is: £63

1/4 is the fraction of all the pizza left

A fraction represents the parts of a whole or collection of objects e.g 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

Given that:

Lacey ate 3/8 of 2 pizzas => 3/8 × 2 = 3/4

Tory ate 1/4 of 2 pizzas => 1/4 ×  2 = 1/2

Xander and Lexi ate 1/2 of 3 pizzas => 1/2 × 3 = 3/2

And there were 3 equal-sized pizzas

Fraction of pizza left = Number of pizzas - fraction ate by Lacey - Fraction ate by Tory - Fraction ate by Xander and Lexi

Fraction of pizza left = 3 - 3/4 - 1/2 - 3/2 = 1/4

Therefore, the fraction of all the pizza is left is 1/4

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Answer:

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Part A :

If a function is linear, then the function values have equal differences.

If a function is exponential, the function values have equal ratios.

For car 1 :

36450 / 40,500 = 9/10

32805 / 36450 = 9/10

Values of car have equal ratios.

This is exponential function.

For car 2 :

39000 - 42000 = -3000

36000 - 39000 = -3000

Values of car have equal differences

This is linear function.

Part B :

The initial value of car is 45,000.

For car 1 :

f(1) = 40,500, f(2) = 36,450, ............

For car 2 :

f(1) = 42,000, f(2) = 39,000, ..........

Part C :

For car 1 :

f(13) =   = 11438.396

For car 2 :

f(13) =  = 6000

There is a significant difference in the values of the car after 13 years. The value of the car 1 is greater.

Hence the value of the car 1 is described by an exponential function and that of car 2 by linear function. The value of car 1 is greater after 13 years.

Step-by-step explanation:

Answer:

\(\displaystyle{y=-3x-1}\)

Step-by-step explanation:

I have two methods: standard-learning which will explain overall mathematically - basically formula, etc. - while the other one trick-tips method will rely on choices rather mathematical calculations but with explanation on why and how.

First, let’s pick two points that are integers since they are easily to be found via graphs. We see that (-1,2) and (0,-1) is a part of the graph so now we finally have picked two points for our calculations.

When we have finally picked two points, we will be using them for slope calculation. This part is crucial for finding an equation of a line because a line has to contain slope in its equation.

To calculate the slope, we use rise over run formula which is:

\(\displaystyle{\dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1}}\)

Note that \(\displaystyle{\Delta}\) is delta - in both mathematic and physics, it means changes in.

So, we will be using those two points that we have picked to substitute in the slope formula. Let’s determine that \(\displaystyle{(x_2,y_2)=(-1,2)}\) and \(\displaystyle{(x_1,y_1)=(0,-1)}\).

Therefore, our slope will be:

\(\displaystyle{m=\dfrac{2-(-1)}{-1-0}}\\\\\displaystyle{m=\dfrac{2+1}{-1}}\\\\\displaystyle{m=-3}\)

Next, find the y-intercept. From the graph, we see that the graph intercepts at (0,-1) which is y-intercept so we will only use y-value. Hence, b = -1.

From the slope-intercept form:

\(\displaystyle{y=mx+b}\)

Substitute m (slope) = -3 and b (y-intercept) = -1. Hence, the equation of line is:

\(\displaystyle{y=-3x-1}\)

Relying on choices and knowledge of graph, notice that there are slopes of 3 and -3.

Keep in mind that if slope is negative, it will decrease down and if slope is positive, it will increase up.

Therefore, cut off all choices with positive slopes which are 1 and 3. We are now left with 2 and 4.

Next, look at the graph and tell its y-intercept. It intercepts y at y = -1 so we take value of -1.

So choice 4 is cut off and now we have choice 2 as the answer.

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Answer:

Harry has a loan of $9000 in total. Harry obtained a loan from the bank. Explanation Harry's remaining debt, expressed in dollars, is modeled as a function of time t, expressed in months, by the function D(t). The role is played by, This function can be used to determine that $200 is being subtracted each month from the function, meaning Harry is paying $200 toward his loan. Harry has not yet made any payments, therefore we may set t=0 to obtain the total amount of his solo. Therefore, the value of D(t) will reveal the loan's net amount. Harry's borrowing, therefore, equals to $9000.

Step-by-step explanation:

You can take the numerator as one factor and 1/denominator as another.

Just an example:

Let a = 1, then the following product will give what we have

The number of chickens and pigs in the pen are 8 and 9 respectively.

Farmer Josh has a pen full of chickens and pigs. One day he looks out and counts 17 heads and 52 feet.

The number of chickens and pigs that are in the pen is as follows:

Using equation,

let

x = number of chickens

y = number of pigs

Therefore,

x + y = 17

Recall chicken has 2 legs and pigs has 4 legs.

Hence,

2x + 4y = 52

Combine the equation

x + y = 17

2x + 4y = 52

multiply equation(1) by 2

2x + 2y = 34

2x + 4y = 52

subtract equation(1) from equation(2)

2y = 18

y = 18 / 2

y = 9

Let's find x

x = 17 - 9

x = 8

Therefore,

number of chickens = 8

number of pigs = 9

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Answer: The converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

Step-by-step explanation:

What does it mean converse in geometry?

The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."

So, in the figure below, if we can choose n║m, then ∠1≅∠2

Since  n║m , by the corresponding Angles Postulate,

∠1≅∠2.

Therefore, by the definition of congruent angles,

m∠1=m∠2

Since ∠1 and ∠2 form a linear pair, they are supplementary, so

m∠1+m∠2=180°.

Therefore, the converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

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The height of the cylinder is 17.00 inches, under the given condition that radius of the cylinder is 16 inches, volume is 13,665. 28 cubic inches  and have to round the answer to the nearest hundred.

Therefore, the volume of a cylinder is given by V = πr²h
Here,
V= volume of the cylinder,
r= radius of  the cylinder
h= height

Given that the radius of the cylinder is 16 inches and its volume is 13,665.28 cubic inches, then we can proceed to evaluate the height of the cylinder
V = πr²h
h = V / (πr²)
h = 13665.28 / (π(16)²)

h = 13665.28/ 3.14 x (256)

h = 13665.28/ 803.8

h = 17.00 inches

Then, the height of the cylinder is approximately 17.00 inches.

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Answer: Vertical stretch by a factor of 3.

The maximum volume of the prism is 1728 cubic centimeters.

To find the dimensions of the prism with maximum volume, we need to consider the relationship between the volume of the prism and its dimensions.

Let's assume the base of the right triangular prism is an isosceles right triangle with legs of length 'a'. The height of the prism will be 'h'. The prism is inscribed in a hemisphere with a radius of 12 cm.

First, let's determine the relationship between 'a' and 'h'. Since the base of the prism is on the great circle of the hemisphere, the hypotenuse of the triangular base is equal to the diameter of the hemisphere, which is twice the radius. Therefore, the hypotenuse of the base is 2 * 12 = 24 cm.

By using the Pythagorean theorem, we can find 'a':

a^2 + a^2 = 24^2

2a^2 = 576

a^2 = 288

a = √288

Now, let's find the height 'h' of the prism. The height 'h' is equal to the radius of the hemisphere, which is 12 cm.

Therefore, the dimensions of the prism for maximum volume are:

Base length (a) = √288 cm

Height (h) = 12 cm

To find the maximum volume, we can use the formula for the volume of a right triangular prism:

Volume = (1/2) * a^2 * h

Substituting the values, we get:

Volume = (1/2) * (√288)^2 * 12

= (1/2) * 288 * 12

= 1728

Hence, the maximum volume of the prism is 1728 cubic centimeters.

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Answer:

• (a)The length of the side opposite 31.0° is 1.96 meters.

• (b)The length of the side adjacent 31.0° is 3.26 meters.

Explanation:

In the right triangle:

• The length of the hypotenuse = 3.80 m

• Let the side ,opposite ,angle 31.0° = x

• Let the side ,adjacent ,angle 31.0° = y

(a)

From trigonometric ratios:

Cross multiply:

The length of the side opposite 31.0° is 1.96 meters.

(b)From trigonometric ratios:

Cross multiply:

The length of the side adjacent 31.0° is 3.26 meters.

Answer:

as lengths of tangents of a circle from an external point are equal so

5x+6 = 56

5x = 50

x = 50/5

D) x = 10

Answer:

2x - 3 = 6

Step-by-step explanation:

solve for 'x':

2x - 3 = 6

2x = 9

x = 9/2 or 4 1/2

Check:

2(9/2) - 3 = 6

9 - 3 = 6

6 = 6