8. If two lines are cut by a transversal so that consecutive interior angles are (congruent, supplementary, complementary), then the lines are parallel

We have to find the equation of a circunference with:

As it is a circunference that passes through a point, we know that the distance between the center and the point must be the radius, as all points in a circunference are at the same distance from the center.

We will find then the radius, by calculating the distance:

Now, this means that the radius is √90.

We use the standard form for the equation of a circle:

where (h,k) is the center of the circle. In this case,

And replacing, we obtain that the equation of the circle is:

The probability that exactly three insects will die is 0.343

Given 70% chance that an insect will die.

let A be the event that 1 insect dies.

P(A) = 0.7

The probability that the insect will not stay alive

= 1 - P(A)

= 1 - 0.7

= 0.3

Now there is a sample of 10 insects that are affected by the insecticide.

Therefore number of ways exactly 3 insects will die using binomial distribution is

= 10C3  × (0.7)³ × (0.3)⁷

= 120 × (0.7)³ × (0.3)⁷

=0.00901

≈ 0.009

Hence the required probability is 0.009 .

A probability distribution is an idealised frequency distribution. The frequency distribution of a certain sample or dataset serves as a description of it.

It is the frequency with which each conceivable value of the variable appears in the dataset. How frequently a value emerges in a sample is determined by its probability of occurrence.

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Answer:

2, 3, 5

Step-by-step explanation:

There is no side-side congruence theorem.

There is also no angle-side-side congruence theorem.

That eliminates choices 1 and 4.

The triangles show side-angle-side-angle as congruent corresponding parts.

Also using the vertical angles at vertex C, you get angle-side-angle.

Answer: choices 2, 3, and 5.

We need to operate the next matrixes.

First, subtract the next matrixes:

13 10 7

6 8 1

2 5 0

-

3 -2 6

14 -6 11

8 -12 9

=

13-3 10-(-2) 7-6

6-14 8-(-6) 1-11

2-8 5-(-12) 0-9

=

10 12 1

-8 14 -10

-6 17 -9

Now, the result adds to the next matrix:

10 12 1

-8 14 -10

-6 17 -9

+

6 10 15

10 0 9

1 0 7

=

10+6 12+10 1+15

-8+10 14+0 -10+9

-6+1 17+0 -9+7

=

16 22 16

2 14 -1

-5 17 -2

Therefore, the correct answer is the first one.

There are 144 players in the 12-team league.

Given:

In one basketball league, there are 96 players on 8 teams.

In another basketball league, there are 12 teams.

All of the teams in both leagues have the same number of players.

we are asked to determine the  number of players in the 12-team league.

⇒ 96 player - 8 teams

⇒ 12 team player = ?

⇒ 96/8 = 12 player.

each team:

⇒ 12 × 12

= 144 players in 12 teams.

Hence we get the answer as 144 players.

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a) The proportional relationship is: M = 2.4R.

b) The graph of the proportional relationship is given by the first image at the end of the answer, and they would raise $2,400 selling 1000 tickets.

3. The slope of the function, and the relation with the graph, is as follows:

4. The graph is given by the second image at the end of the answer.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

A proportional relationship is a linear function with intercept zero, hence it is given as follows:

y = mx.

Item a states that the students collect $24 for selling 10 raffles, hence the slope is:

m = 24/10 = 2.4.

Hence the equation is:

M = 2.4R.

If they sold 1000 tickets, the amount they would raise is of:

y = 2.4 x 1000 = $2,400.

The domain of this graph excludes negative values, as the number of raffles sold cannot be negative.

The function for item 4 is:

y = 3/11(x - 2).

Hence the intercepts are:

The graph connecting these poins is the second one at the end of the answer.

The text before item a is:

The students collect $24 for selling 10 raffles.

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Next two terms of the sequence 4, 8, -16, -32, 64, ?, ? are 128 and -256.

How to solve question in sequence?

Every sequence has certain logic which can be used to find next terms.

Mainly operations like addition, subtraction, multiplication, squares and cubes are used to find the logic.

Trial and error method is applied to comprehend the logic of sequence.

4, 8, -16, -32, 64, A, B.

According to the given question, the sequence can be split in two separate sequences by taking alternate terms -

1) 4, -16, 64, B

2) 8, -32, A

Now clearly the logic is:

Next term is obtained by multiplying the previous term with -4.

Let's check 4x(-4) = -16x(-4) = 64

∴ B = 64x(-4) = -256

Similarly, 8x(-4) = -32

∴ A = -32x(-4) = 128

Hence completed sequence is 4, 8, -16, -32, 64, 128, -256.

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Answer:

The second scale gives us a bigger drawing than the first scale.

Explanation:

Let's draw the initial scale figure with its measures in centimeters:

So, if the scale is 1 cm to 30 meters, the true length of side A will be:

In the same way, the true length of sides B and D of a playground is:

Now, if we scale the length in meters to centimeter but using the new scale 1 cm to 20 meters, we get that the new scale lengths will be:

So, the new scale drawing is:

Then, we can compare both scale drawing and observe that the second scale gives us a bigger drawing than the first scale.

We shall consider the options one after the other before choosing the best option;

Option 1;

Option 2;

Option 3;

Based on the calculations above, the third option is the best deal because that would make you pay the least amount per underwear. By choosing option 3, you will end up paying $0.38 for each underwear.

Therefore, "a package of 20 costs $7.60" is the best buy.

Answer:2- 0.99 = 1.01

Step-by-step explanation:

2=2.00

2.00-0.99=1.01

easy

We have the following equation

so the percent increase is 25%

The inequality to illustrate the information that the minimum bid was more than $20,000 is b > 20000.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the minimum bid be represented by b.

Since it's more than 20000, it implies that it's greater than. This will be illustrated as b > 20000.

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Given:

• Profit per camera = $186

• Cost of replacing the camera = $3100

• Probability it will be replaced once = 4% = 0.04

• Probability it will be replaced twice = 1% = 0.01

• Probability it will not be replaced = 95% = 0.95

Now, let's determine if the company should expect to make money or lose money from selling the camera.

Let's find the expected cost of repair.

We have:

E = (0.04 x 3100) + (0.01 x 2 x 3100) + (0.95 x 0)

E = 124 + 62 + 0

E = 186

Therefore, the expected cost of repair is $186.

We can see the profit per camera and the expected cost of repair are the same.

Profit per camera = Expected cost of repair

Since they are equal, the company should expect to neither make nor lose money from selling these cameras.

ANSWER:

Brady & Matthew should expect to neither make nor lose money from selling these cameras.

To be able to make x/y table, we substitute any number as x in the given equation y = -1/3x - 2.

Let's create a table,

x solution y

-6 -1/3(-6) - 2 = 2 - 2 0

-3 -1/3(-3) - 2 = 1 - 2 -1

0 -1/3(0) -2 = 0 - 2 -2

3 -1/3(3) - 2 = -1 - 2 -3

6 -1/3(6) - 2 = -2 - 2 -4

For the following equations, by the trial and error method in 2(p-3) =6  the value of p is 9

Trial and error is assuming a value for a unkown variable, observing if it works, and if it doesn't trying a new value for the variable.

2p-3 = 15

p=6

2(6) -3 = 9

p=7

2(7)-3 = 11

p=8

2(8)-3 = 13

p=9

2(9)-3 = 15

so, p is 9

For the following equations, by the trial and error method in 2(p-3) =6  the value of p is 9

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From the given question

The volume of a cone is:

Now,

We are given with radius and the height of the cone

So,

We can solve for the radius as a function of water level using ratio and proportion

Then,

Substitute the value of r into the above formula

So,

Then,

Taking derivatives

The,

Solving for the dh/dt

So,

Hence, the answer is 9.55.

Find the derivative of the function. Remember to use logarithmic properties before differentiating.



y = x(3^2x)​

______________________________

y= u(x) v(x)

u(x) = x

v(x) = 3^2x

_____________

u'(x) = 1

____________

y = a ^f (x)

y'= f '(x) a ^f (x) (ln a)

v(x) = 3^2x

v'(x) = 2 * 3^2x* ln (3)

_______________

dy/ dx = u'(x)v(x) + u(x) v'(x)

dy/ dx = 1* 3^2x + x *2 * 3^2x* ln (3)

dy/ dx = 3^2x (1+2x* ln (3))

________________

Answer

dy/ dx = 3^2x (1+2x* ln (3))

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Answer:

A//F

CE

BD

Step-by-step explanation:

since its an equilateral triangle you can split in half easily

step 1

the probability of get 4 in one dice is

P=1/6

so

the probability of get 4 in two dices is

(1/6)*(1/6)=1/36

Answer:

A is the correct answer.

First, let's draw a sketch of the problem to better understand it:

Since the distances 20, 4√7 and x create a right triangle, we can use the Pythagorean theorem to calculate the value of x.

The Pythagorean theorem states that the length of the hypotenuse squared is equal to the sum of each leg squared.

So we have:

Therefore the wanted distance is 12√2 feet (16.97 ft).

Given the table:

X -3 , 0 , 3 , 6

Y 3, 7, 11, 15

We can write the ordered pairs of the function:

(-3, 3), (0, 7), (3, 11), (6, 15)

Any pair of ordered pairs can be used to calculate the slope, assuming they all belong to the line.

Let's pick the points (-3, 3) and (0, 7). The formula to calculate the slope is:

Substituting:

It can be verified that the slope is 4/3 regardless of the points selected to calculate it.

Answer: 4/3

The length of the guy wire, using similar triangles, is of:

43 feet.

Similar triangles are triangles that share these two features listed as follows:

The height h of the tower can be found using similar triangles, as the two right triangles are similar.

The equivalent measures are given as follows:

Hence the proportional relationship is:

h/7 = 17/3

Applying cross multiplication:

3h = 17 x 7

h = 17 x 7/3

h = 39.67 ft.

Then, applying the Pythagorean Theorem, the length of the guy wire is of:

l² = 39.67² + 17²

l = sqrt(39.67² + 17²)

l = 43 feet. (rounded down).

(the pythagorean theorem is applied as the length of the guy wire is the hypotenuse of the right triangle).

The problem is given by the image at the end of the answer.

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The coordinates of A' is (-0.5, 1)

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size.

Given:

A (-1,2) B(4,-3) and C (0,0)

First ABC is dilated by 0.5.

The transformation rule of this dilation is:

(x, y)--> 0.5 (x, y)--> (0.5x, 0.5y)

So, the coordinate of A' after dilation is

(-1, 2 ) --> 0.5(-1, 2)--> (-0.5 , 1)

Hence, the coordinates of A' is (-0.5, 1)

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Given the following quadratic expression:

Let's check if the given equation can be solved by factoring.

a.) Let's determine the original equation.

From the original equation, we observed that the constant 155/9 is not a perfect square. For the original quadratic equation to be factorable, we must apply the method of completing the square.

Therefore, we can say that the original quadratic equation can't be solved by factoring.

f(x) is a linear function whose slope is equal to -1 and y-intercept is equal to -7.

Here we have f(x) defined as:

f(x) = -x - 7

Now, we define a general linear function as:

g(x) = m*x + b

Where m is the slope and b is the y-intercept.

Now, we can rewrite f(x) as:

f(x) = (-1)*x +  (-7)

So f(x) is a linear function with a slope of -1 and a y-intercept of -7.

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Answer:

If it is perpendicular: mperp..=-1/m, so:

mperpendicular= -6.

formula of the line passing through one point:

y-y0=m(x-x0)

so: y+2=-6(x+8)

y=-6x+48-2

y=-6x+46 is the answer

Yes, Because the amount charged grows by $35, a fixed amount, every time the number of months increases by 1.

Direct proportion, also known as direct variation, is a relationship between two quantities when their ratio equals a fixed number. The proportional symbol is used to denote it. The fact that the other quantity is inverted here means that the same symbol is really employed to denote inverse proportional.

Direct proportionality applies. This is so that the cost of the membership remains constant no matter how many months you choose to pay for. For instance, the cost is 1 x $35 if you pay for one month. The price increases to 2 x $35 if you pay for two months, which is twice as expensive.

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By using ratio, it is obtained that if there are 8 atoms of hydrogen, there are 4 atoms of oxygen.

What is ratio?

Ratio is used to find a comparision between two quantities with the same unit

The first part of the ratio is called antecedant and the second part of the ratio is called consequent.

Here,

In a molecule of water, there are 2 atoms of hydrogen and 1 atom of oxygen

Ratio of hydrogen and oxygen = 2 : 1

Number of atoms of hydrogen = 8

Let the number of hydrogen atom be 2x and number of oxygen atom be x

By the problem,

[tex]2x = 8\\x = \frac{8}{2}\\x = 4[/tex]

Number of oxygen atom = 4

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