Which of the following are necessary when proving that the opposite sides of a parallelogram are congruent? Check all that apply.

A. Corresponding parts of similar triangles are similar.
B. Alternate interior angles are supplementary.
C. Alternate interior angles are congruent.
D. Corresponding parts of congruent triangles are congruent.,

Answer:

A. (–2, –3)

that is the answer

When two tangents are drawn to a circle at endpoints A and B of a diameter, the tangents are perpendicular to the radii at their points of tangency and are parallel to each other, forming two congruent right triangles.

The question involves constructing two tangents to a circle from two points, A and B, where AB is the diameter of the circle. By the properties of circles and tangents, we know that a tangent to a circle is perpendicular to the radius at the point of tangency. Since AB is the diameter, points A and B are on opposite ends of the circle, and when we draw tangents at these points, each tangent will be perpendicular to the radii OA and OB respectively. Additionally, since AB is a diameter, it creates a linear pair with the two tangents, meaning that the two tangents are parallel to each other. This setup creates two congruent right triangles, namely triangle OAT and triangle OBT, where T represents the points of tangency on each tangent.

Two tangents to a circle from points A and B, where AB is a diameter, are congruent and parallel to each other, forming right angles with the diameter.

When constructing two tangents to a circle at points A and B, where AB is a diameter, an interesting relationship exists between those tangents. By the properties of tangents to a circle from an external point, we know that two tangents drawn to a circle from the same external point are equal in length. Therefore, the two tangents you would draw from points A and B to any point on the circumference of the circle would be congruent to each other.

Additionally, since each tangent is perpendicular to the radius of the circle at the point of tangency, the tangents are parallel to each other because they are both perpendicular to the same diameter. In the context of circle O with AB as a diameter, we can also conclude that the angles formed between the tangents and the diameter AB are right angles due to the geometric properties of tangents.

Answer: D.  Alternate interior angles of parallel lines cut by a transversal are congruent.

Step-by-step explanation:

In the given picture m is parallel  to CB  .

Since m is a straight line and the angle of straight line is 180°  .

Therefore, m∠XAB+m∠BAC+m∠YAC=180° ........................ (a)

Also, m is parallel to CB and AB is a transversal and because Alternate interior angles of parallel lines cut by a transversal are congruent.

⇒m∠XAB=m∠ABC  and  m∠YAC=m∠ACB

Put the values of m∠XAB and m∠YAC in equation (a), we get

m∠ABC + m∠BAC + m∠ACB = 180°.

Hence proved.

Statement D Alternate interior angles of parallel lines cut by a transversal are congruent is the most relevant to the congruence of XAB and ABC.

It is proved that  m∠ABC + m∠BAC + m∠ACB = 180°.

For angle XAB being congruent to angle ABC, and then prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.

Parallel lines m and CB.

Points X, A, and Y are on line m.

To prove that angle XAB is congruent to angle ABC.

Justification for Congruence:

In this context, use the Alternate Interior Angles Theorem,

which states that when a transversal intersects two parallel lines, the alternate interior angles formed are congruent.

Here's the reasoning:

Line m is parallel to line CB.

The line XY is a transversal line that intersects m and CB.

Therefore, the alternate interior angles formed by this setup are congruent.

This means that angle XAB and angle ABC are congruent.

Now, let's prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.

Angle XAB is congruent to angle ABC (justified by the Alternate Interior Angles Theorem).

Now, let's consider the triangle ABC. By the angle sum property of triangles, the sum of the angles in a triangle is always 180°. Therefore:

m∠ABC + m∠BAC + m∠ACB = 180°

Since angle XAB is congruent to angle ABC, replace angle ABC with angle XAB:

m∠XAB + m∠BAC + m∠ACB = 180°

Now, the equation holds true, and you have successfully proven that m∠ABC + m∠BAC + m∠ACB = 180°.

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The correct answer is:

False.

Explanation:

When you take out a loan, banks provide all of the relevant information for the loan.  This includes the interest rate, payment amount, and an amortization schedule, which shows the amount paid and the amount of principal this takes off of the loan every month for the life of the loan.

Answer:

5

Step-by-step explanation:

Answer: 42

Step-by-step explanation:

x = 6 now that you know what x represents switch it out the x by the 7 with a 6 like this 7(x)- 7(6) seven times six is 42 in other words x

=42

Solution:

The Point in the coordinate plane is A(-5,-4).

Perpendicular or shortest Distance from line y=3 that is (-5,3) to point (-5,-4) is

[tex]=\sqrt{(-5+5)^2+(3+4)^2}\\\\=7[/tex]

When it is reflected through the line, y=3, the coordinate of point A (-5,-4) changes to (-5,3+7)= B(-5,10).

Now, the Point B is translated by the rule , (x,y)—->(x+6,y),

So,the point B is translated to, (-5+6,10)=(1,10)

Option C: (1,10) is the glide reflection of point A(-5,-4).

The coordinates of A' after the glide reflection (translation and reflection over y = 3) from A(-5, -4) are (1, -4), so the answer is A.

In a glide reflection, first apply a translation and then a reflection. Let's follow the given transformations step by step:

Translation: (x, y) → (x + 6, y)

This means you move the point A(-5, -4) six units to the right and keep the same y-coordinate. Applying the translation:

A' = (-5 + 6, -4)

    = (1, -4)

Reflection over the line y = 3:

In this reflection, points above the line will move below it and vice versa, while points on the line will remain unchanged.

Since the original point A(-5, -4) is below the line y = 3, its reflection A' will be above the line.

Therefore, the coordinates of A' are (1, -4) ,the correct option is A. (1, -4).

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Water flows: 34300 gallons in 7 minutes. Tank empties in about 3.914 minutes. (Rounded to three decimal places.)

To find out how much water flows out of the tank in the first 7 minutes, we need to integrate the flow rate function, [tex]\(f(t)\)[/tex], from [tex]\(t = 0\)[/tex] to [tex]\(t = 7\)[/tex]. The flow rate function is given as [tex]\(f(t) = 300t^2\)[/tex].

So, the amount of water that flows out of the tank in the first 7 minutes, denoted as [tex]\(W_{\text{out}}\)[/tex], is given by the integral of [tex]\(f(t)\)[/tex] over the interval [tex]\([0, 7]\)[/tex]:

[tex]\[W_{\text{out}} = \int_{0}^{7} f(t) \, dt\][/tex]

[tex]\[= \int_{0}^{7} 300t^2 \, dt\][/tex]

[tex]\[= 300 \int_{0}^{7} t^2 \, dt\][/tex]

To find the integral of [tex]\(t^2\)[/tex], we use the power rule for integration:

[tex]\[= 300 \left[\frac{t^3}{3}\right]_{0}^{7}\][/tex]

[tex]\[= 300 \left(\frac{7^3}{3} - \frac{0^3}{3}\right)\][/tex]

[tex]\[= 300 \left(\frac{343}{3}\right)\][/tex]

[tex]\[= 34300\][/tex]

So, [tex]\(W_{\text{out}} = 34300\)[/tex] gallons.

Now, to find out how many minutes it takes for the tank to be completely empty, we need to find the time, [tex]\(T\)[/tex], at which the tank is empty. The tank will be empty when the integral of the flow rate function from [tex]\(t = 0\)[/tex] to [tex]\(t = T\)[/tex] is equal to the total volume of the tank, which is 6000 gallons.

So, we have:

[tex]\[6000 = \int_{0}^{T} f(t) \, dt\][/tex]

[tex]\[= \int_{0}^{T} 300t^2 \, dt\][/tex]

[tex]\[= 300 \int_{0}^{T} t^2 \, dt\][/tex]

Using the power rule for integration again:

[tex]\[6000 = 300 \left[\frac{t^3}{3}\right]_{0}^{T}\][/tex]

[tex]\[= 300 \left(\frac{T^3}{3} - \frac{0^3}{3}\right)\][/tex]

[tex]\[= 100T^3\][/tex]

Now, solving for [tex]\(T\):[/tex]

[tex]\[T^3 = \frac{6000}{100}\][/tex]

[tex]\[T^3 = 60\][/tex]

[tex]\[T = \sqrt[3]{60}\][/tex]

[tex]\[T \approx 3.914\][/tex]

So, it takes approximately 3.914 minutes for the tank to be completely empty.

Answer:

2(3a + 6) would be correct.

Hope this was helpful !

Step-by-step explanation:

Answer: is a

Step-by-step explanation:

The t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.

To model the population of cells, we can use an exponential growth equation. Since the population doubles every day, the equation would be:

[tex]P(t)=P_{0} *2^{t}[/tex]

Where:

[tex]P(t)[/tex] is the population size at time t.

[tex]P_{0}[/tex] is the initial population size ([tex]10[/tex] cells in this case).

[tex]t[/tex] is the time in days.

So, for this scenario, the equation becomes:

[tex]P(t)=10*2^{t}[/tex]

Now, we want to find out how many days it will take for the population to reach [tex]1,000,000[/tex] cells. We can set up the equation:

[tex]1,000,000=10*2^{t}[/tex]

To solve for t, we need to isolate it. First, divide both sides by [tex]10[/tex] :

[tex]100,000=2 t[/tex]

Now, take the logarithm base 2 of both sides to solve for t:

[tex]log_{2} (100,000)=t[/tex]

Using a calculator, we find:

[tex]t=16.61[/tex]

Since t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.

COMPLETE QUESTION:

Create an equation to model a population of cells which starts with [tex]10[/tex]cells and doubles in size every day. How many days will it take to reach [tex]1,000,000[/tex] cells?

The length of the surface of the rectangular table that has an area of 100 sq. ft is: 20 ft.

Area of rectangle = (length)(width).

The table given has a rectangular surface.

(length)(5) = 100

Length = 100/5

Length of the rectangular table = 20 feet.

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Final answer:

The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. The formula represents the rise over run between these points.

Explanation:

We can use a specific formula to calculate the slope of a line using two points on that line. The slope is found by taking the difference in the y-value (also known as the rise) and dividing it by the difference in x-value (also known as the run). In mathematical terms, if we have two points (x1,y1) and (x2,y2), the formula for slope (m) is as follows:

m = (y2 - y1) / (x2 - x1)

Therefore, between two given points, you subtract the y-value of the starting point from the y-value of the end point to find the rise, and then remove the x-value of the starting point from the x-value of the end point to determine the run. The slope is then the quotient of these two differences.

The expression gives the area of the triangle shown below  1/2cx is the answer.

The reason this is the answer is because to find the area of a triangle you will find half of the base times the height.

The formula of a triangle

A=1/2bh.

In this picture, the base is the length of the bottom part of the triangle (c).

It is the distance of the solid line only.

The height is represented as the straight line that is perpendicular to the base (forms a right/90-degree angle).

X is the height of the triangle.

Therefore, 1/2cx is the answer.

So option D is correct.

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Answer:

In a number cube, a dice, you have six sides with the numbers 1, 2, 3, 4, 5 and 6. And when you roll it, each number has the same probability of showing.

a) rolling a 3 twice.

In the first roll you get a 3, with a probability of 1/6, and with the second roll you also get a 3, also with a probability of 1/6. The probability of bot evets to happen is equal to the product of the individual probabilities.

P = 1/6*1/6 = 1/36

b) An even number and a 5.

In the first roll you can get 2, 4 or 6, so you have 3 out of 6 options, the probability is 3/6 = 1/2, in the second roll you need you get a 5, the probability is 1/6.

P = 1/2*1/6 = 1/12.

But we also have the probability where the first dice is a 5 and the second a pair number, so the real probability is 2*P = 1/6

c) an odd number and 2 or 4.

for an odd number the probability is 3/6 = 1/2, for getting 2 or 4 the probability is 2/6 = 1/3

then we have that P = 2*(1/3)*(1/2) = 1/3

d) a number less than 6, you have 5 options, then the probability is:

p = 5/6, and for 3 or 1 the probability is 2/6 = 1/3

then P = 2*(5/6)*(1/3) = 5/9

Answer:

About 85 is the answer