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2 years ago

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What is the line of reflection for the trapezoids? On a coordinate plane, trapezoid A B C D has points (5, 4), (6, 4), (8, 3) an

d (5, 3). Trapezoid A prime B prime C prime D prime has points (1, 4), (0, 4), (negative 2, 3), (1, 3). x = 3 y = 3 x-axis y-axis

2 answers:

gizmo_the_mogwai [7]2 years ago

8 0

Answer:

x=3

Step-by-step explanation:

Anna11 [10]2 years ago

6 0

Answer:

The answer to this question is x=3

Step-by-step explanation:

If you create the graph and then plot the points you will get a depiction of the trapazoids. using this you will find that they have reflected over the x=3 line.

You might be interested in

What is thirty-two times by itself?

SpyIntel [72]

32×32 gives 1024.

Hope it helps!

5 0

2 years ago

A bag contains 4 blue marbles and 2 yellow marbles. Two marbles are randomly chosen (the first marble is NOT replaced before dra

VMariaS [17]

Answer:

0.4 = 40% probability that both marbles are blue.

0.0667 = 6.67% probability that both marbles are yellow.

53.33% probability of one blue and then one yellow

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

Step-by-step explanation:

To solve this question, we need to understand conditional probability(for the final question) and the hypergeometric distribution(for the first three, because the balls are chosen without being replaced).

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

What is the probability that both marbles are blue?

4 + 2 = 6 total marbles, which means that $N = 6$

4 blue, which means that $k = 4$

Sample of 2, which means that $n = 2$

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,6,2,4) = \frac{C_{4,2}*C_{2,0}}{C_{6,2}} = 0.4$

0.4 = 40% probability that both marbles are blue

What is the probability that both marbles are yellow?

4 + 2 = 6 total marbles, which means that $N = 6$

2 yellow, which means that $k = 2$

Sample of 2, which means that $n = 2$

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,6,2,2) = \frac{C_{2,2}*C_{4,0}}{C_{6,2}} = 0.0667$

0.0667 = 6.67% probability that both marbles are yellow.

What is the probability of one blue and then one yellow?

Total is 100%.

Can be:

Both blue(40%)

Both yellow(6.67%)

One blue and one yellow(x%). So

40 + 6.67 + x = 100

x = 100 - 46.67

x = 53.33

53.33% probability of one blue and then one yellow.

If you are told that both selected marbles are the same color, what is the probability that both are blue?

Conditional probability.

Event A: Both same color

Event B: Both blue

Probability of both being same color:

Both blue(40%)

Both yellow(6.67%)

This means that $P(A) = 0.4 + 0.0667 = 0.4667$

Probability of both being the same color and blue:

40% probability that both are blue, which means that $P(A \cap B) = 0.4$

Desired probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.4667} = 0.8571$

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

8 0

2 years ago

Select the two values of x that are roots of this equation 3x^2 + 1 =5x

Zina [86]

Answer:

x = 1.434 and x=0.232

Step-by-step explanation:

To find the root of the equation stated above we need to:

(1) Write the polynomial equation with zero on the right hand side:

$3x^{2} + 1 = 5x$ ⇒ $3x^{2} -5x + 1 = 0$

(2) Divide the whole equation by 3

$3x^{2} -5x + 1 = 0$ ⇒ $x^{2} -\frac{5}{3}x + \frac{1}{3}= 0$

(3) Use the quadratic formula to solve the quadratic equation:

The quadratic formula states that the two solutions for a quadratic equation is given by:

$\frac{-b±\sqrt{b^{2} - 4ac}}{2a}$ (1)

In this case, a = 1, b = $-\frac{5}{3}, c= \frac{1}{3}$

Substituiting a, b and c in equation (1) We get:

$\frac{-\frac{5}{3}±\sqrt{(-\frac{5}{3})^{2} - 4(1)(\frac{1}{3})}}{2(1)}$ (1)

The two solutions are:

x = 1.434 and x=0.232

8 0

2 years ago

What is the sum of 36 plus 25

bija089 [108]

The sum is 61 for this equation.

5 0

2 years ago

Read 2 more answers

Determine if the following statement is true or false. (Enter TRUE if the statement is true, enter a counterexample if the state

ehidna [41]

Answer:

The answer is: the satement is FALSE.

Step-by-step explanation:

The first step is to transform the propositons in the statement into symbols:

A: m is any positive integer

B: n is any positive integer

C: mn is a a perfect square

D: m is a perfect square

E: n is a perfect square

After that we replace the symbols into the statement:

If A and B and C, then D and E

Logical connectives on the satement are:

p⇒q conditional (if ...,then...). For this connective the only case when is FALSE is when the antecedent is true and the consequent is false.
p ∧ q conjunction (p and q). For this connective the only case when is TRUE is when the two propositions are true at the same time.

So now, we are going to replace the logical connectives on the statement:

((A ∧ B) ∧ C) ⇒ (D ∧ E)

There is a hierarchy in logical connectives, first we evaluate those inside brackets. The principal connective is evaluated at the end. In this particular case, the principal connective is the conditional.

As we have five different propositions, the combinations are given by the following rule:

2^n= 2^5=32

32 different combinations

In figure 1, added bellow, it shows the construction of truth table.

In figure 2, added bellow, it shows the development of the truth table. In the development, we don't have as a result a tautology, therefore the statement is FALSE.

<span class="sg-text sg-text--link sg-text--bold sg-text--link-disabled sg-text--blue-dark"> pdf </span>

<span class="sg-text sg-text--link sg-text--bold sg-text--link-disabled sg-text--blue-dark"> pdf </span>

8 0

3 years ago