AB ≅ BC and AD ≅ CD What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem? What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?

Answer:

2

Step-by-step explanation:

The greatest common factor of whole numbers is the largest number that is a factor of all numbers. That is, it is the largest number that can divide all numbers.

In this case, the largest number that divide all the numbers is 2, who can divide 4, 18 and 12.

So:

[tex](4k, 18k^{4} ,12)= 2(2k,9k^{4} , 6)[/tex]

Answer:

m=8

Step-by-step explanation:

on imagine 2021

The expression in the simplest form that represents the expected population next year will be 1.065p.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The ongoing populace of a city can be addressed by p. the populace is supposed to increment by 6.5% one year from now.

The expression in the simplest form that represents the expected population next year will be given as,

⇒ p(1 + 0.065)

⇒ 1.065p

The expression in the simplest form that represents the expected population next year will be 1.065p.

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The equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.

The equation of a line with slope (m) passing through a point (x₁, y₁) is given by the point-slope form:

y - y₁ = m(x - x₁)

The slope (m) is 2, and the point (x₁, y₁) is (3, 9). Plug these values into the equation:

y - 9 = 2(x - 3)

Now, you can simplify this equation:

y - 9 = 2x - 6

To isolate y, add 9 to both sides:

y = 2x - 6 + 9

y = 2x + 3

Therefore, the equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.

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Answer:

48 sq. in.

Step-by-step explanation:

Formula for finding trapezoid area: A = 1/2(h)(b1 + b2)

They said the median of a trapezoid is equal to half the sum of the bases, so multiply the median by 2 to get the sum of the bases.

Sum of the bases = 8(2) = 16

Now plug what you have into the equation to find the area: A = 1/2(6)(16)

Simplify to get: 48

Hope this helps!

Answer:

9

Step-by-step explanation:

15 divided by 1.75 equals 9.

And in order to double check, we multiply 9 and 1.75 together which equals 15.75.

Answer:

the x-intercepts are (-1,0) and (-11,0), the y-intercept is (0,11).

Answer:

c = 23.3

Step-by-step explanation:

Answer:

[tex]23.3 \pi[/tex] cm

Step-by-step explanation:

Circumference of circle = [tex]2 \pi r[/tex]

The circumference of a circle is 60π cm.

So,  [tex]2 \pi r=60 \pi[/tex]

[tex]2r=60[/tex]

[tex]r=30[/tex]

Formula of length of arc = [tex]2 \pi r \times \frac{\theta}{360}[/tex]

Length of arc = [tex]2 \pi \times 30 \times \frac{140}{360}[/tex]

Length of arc = [tex]23.3 \pi[/tex]

So, Option C is true

Hence Length of arc is [tex]23.3 \pi[/tex] cm

Answer:

60 marbles

Step-by-step explanation:

Given:  24 red marbles is 40% of how many marbles

Let number of marbles be x

"24 red marbles is 40% of how many marbles"

             24 = 40% of x

solve for x

First change % to decimal

    24 = 0.40x

Division property of equality, divide by 0.04 both sides

     x = 24÷0.40

     x = 60

Hence, 40% of 60 is 24

The answer is 140, you just add them up and it goes by 2.

Final answer:

To calculate the probability of losing one or more friends, we need to calculate the probability that a friend does not get a red candy and multiply it by the number of friends. The probability is 0.458.

Explanation:

To answer this question, we need to calculate the probability that at least one friend will not get a red candy.

First, let's calculate the probability that a friend does not get a red candy. There are 42 candies in the bag and 6 of them are red. So, the probability that a friend does not get a red candy is (42-6)/42 = 36/42 = 6/7.

Since each friend gets 7 candies, the probability that one friend does not get a red candy is (6/7)^7, because each candy is independent. Finally, since there are 6 friends, we multiply the probability by 6 to get the probability that at least one friend does not get a red candy: 6 * (6/7)^7 = 0.458 (rounded to 3 decimal places).

Using the simple interest formula I = PRT, it is calculated that Akule borrowed $1500 at an annual interest rate of 12% for 1.5 years to pay $270 in interest.

The subject of this question is Mathematics, specifically focusing on simple interest calculation. To find out the period of time Akule borrowed money for, we can use the simple interest formula I = PRT, where I is the interest paid, P is the principal amount borrowed, R is the annual interest rate, and T is the time in years. Akule paid $270 in interest on a $1500 loan at 12% annual simple interest. Using the formula, we solve for T as follows:

T = I / (P × R)

T = $270 / ($1500 × 0.12)

T = $270 / $180

T = 1.5 years

Therefore, Akule borrowed the money for 1.5 years.

Akule borrowed the money for 0.18 years.

To find the period of time Akule borrowed the money, we can use the formula:

Interest = Principal × Rate × Time

Given that Akule paid $270 in interest and borrowed $1500 at an annual simple interest rate of 12%, we can plug in these values into the formula:

270 = 1500 × 0.12 × Time

Simplifying the equation, we get:

0.12 × Time = 270 / 1500

Time = (270 / 1500) / 0.12

Time = 0.18 years

Hence, Akule borrowed the money for 0.18 years.

Answer:

Let the probability of error-free transmission of a message over a communication channel is P.

Then the Probability of Retransmission  is =1-P

Now the question is Probability when no retransmission is required

                            = Probability of error free transmission in first attempt

                               =P

Now , suppose after first failure error free transmission takes place.

Since events are independent.

∵P[error free transmission after a failure ]= P[1-P]

If after two attempts error free transmission takes place

then P[ error free transmission after two failures]= P [1-P]²

So, For after n failures

P[error free transmission after n failure]=P[tex][1-p]^n[/tex]

The drawing shows the friends ended up with 1/2 the pie.

The required graph of the quadratic function is the parabola shown in the attachment.

Given that,
To determine the graph to the best match of the graphed quadratic equation. F(x) = x² + 4x.

A parabola is a cross-section cut out of the cone and represented by an equation.

What is a graph?

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The given equation represents the parabola with vertex at (-2, - 5).
and a graph of the parabola is attached below.

Thus, the required graph of the quadratic function is the parabola shown in the attachment.

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The expressions describing the area of the shaded region is 1/2 × 1/4

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, a rectangle is divided into 12 columns and 6 rows, making 72 smaller rectangles.

We need to find the expressions for the area of the shaded region,

So, we have,

The height is 6 and the length is 12

The shaded part is 3 boxes by 3 boxes

Therefore, we can write =

3/6 × 3/12 = 1/2 × 1/4

Hence, the expressions describing the area of the shaded region is 1/2 × 1/4

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The probability Bill hits a higher percentage than Wilt in free throws is approximately 0.0085, or 0.85%.

To find the probability that Bill hits a higher percentage of his shots than Wilt, we can use the concept of binomial distributions.

Let's denote:

- [tex]\( W \)[/tex] as the number of successful shots Wilt makes out of 50,

- [tex]\( B \)[/tex] as the number of successful shots Bill makes out of 50.

Since Wilt makes 75% of his free throws and Bill makes 85% of his free throws, we can calculate the expected number of successful shots for each:

- For Wilt: [tex]\( E(W) = 50 \times 0.75 = 37.5 \)[/tex]

- For Bill: [tex]\( E(B) = 50 \times 0.85 = 42.5 \)[/tex]

Now, we can use the normal approximation to the binomial distribution to calculate the probability that Bill hits a higher percentage of his shots than Wilt. We'll assume that both distributions are approximately normal due to the central limit theorem.

The standard deviation for each player's distribution can be calculated as:

- For Wilt: [tex]\( \sigma_W = \sqrt{n \times p_W \times (1-p_W)} = \sqrt{50 \times 0.75 \times 0.25} \)[/tex]

- For Bill: [tex]\( \sigma_B = \sqrt{n \times p_B \times (1-p_B)} = \sqrt{50 \times 0.85 \times 0.15} \)[/tex]

Now, we can calculate the probability using a normal distribution:

[tex]\[ P(B > W) = P\left(Z > \frac{{E(B) - E(W)}}{{\sqrt{\sigma_B^2 + \sigma_W^2}}}\right) \][/tex]

Where [tex]\( Z \)[/tex] is a standard normal random variable.

Calculating:

[tex]\[ P(B > W) = P\left(Z > \frac{{42.5 - 37.5}}{{\sqrt{50 \times 0.85 \times 0.15 + 50 \times 0.75 \times 0.25}}}\right) \][/tex]

[tex]\[ P(B > W) = P(Z > 2.3717) \][/tex]

Using a standard normal distribution table or calculator, we find that  [tex]P(Z > 2.3717) \approx 0.0085 \).[/tex]

So, the probability that Bill hits a higher percentage of his shots than Wilt is approximately 0.0085, or 0.85%.

Answer:

64

Step-by-step explanation:

i just know

Answer: 2,3,5

Step-by-step explanation: