Combine and simplify the following radical expression.

Complete the following statement of congruence

alex41 [277]

Answer:

Option A. Triangle STR

Step-by-step explanation:

we know that

If two triangles are congruent, then the corresponding sides and the corresponding angles are congruent

In this problem

If the two triangles of the figure are congruent

then

the corresponding sides are

MN and RS

NO and ST

MO and RT

and the corresponding angles are

∠N≅∠S

∠O≅∠T

∠M≅∠R

therefore

NOM≅STR

5 0

4 years ago

Read 2 more answers

4. Automobile policies are separated into two groups: low-risk and high-risk. Actuary Rahul examines low-risk policies, continui

ANTONII [103]

Answer:

Step-by-step explanation:

for n ∈ N

Since Actuary Rahul examines low-risk policies, continuing until a policy with a claim is found and then stopping.

∴ the probability that Actuary Rahul examines exactly n policies

$(0.9)^{n-1}.(0.1)---(1)$

the probability that Actuary Toby examines more than exactly n policies

$(0.8)^n---(2)$

Given that policies are actually independent

∴ the probability that the event (1) and (2) happens simultaneously is

$(0.9)^{n-1}*(0.1)*(0.8)^n$

∴ the probability that Actuary Rahul examines fewer policies than Actuary Toby

$\sum ^\infty _{n=1} (0.9)^{n-1}*(0.1)*(0.8)^n\\\\=(\frac{0.1}{0.9} \sum ^\infty _{n=1}(0.72)^n\\\\=\frac{1}{9} (\frac{0.72}{0.28} )\\\\=\frac{2}{7} \\\\=0.2857$

<h3>the probability that Actuary Rahul examines fewer policies than Actuary Toby is 0.2857</h3>

5 0

3 years ago

Need help this is on acellus

madam [21]

The complete inequality is -2 < x < 35

<h3>How to determine the range of value of x?</h3>

The figure attached to the question is the given parameter

From the figure, we understand that:

Side length BA and side length BD are equal.

This is represented as:

BA = BD

Because the side length AC is less than the side length CD, then it means that:

The measure of the angle ABC is less than the measure of the angle CBD

This is represented as:

∠ABC < ∠CBD

Where

ABC = x + 2

and

CBD = 37

Substitute ABC = x + 2 and CBD = 37 in the inequality expression ∠ABC < ∠CBD

So, we have:

x + 2 < 37

Subtract 2 from both sides of the inequality

x + 2 - 2 < 37 - 2

Evaluate the differences

x < 35

From the question, we have the following incomplete inequality

-2 < x < [ ]

Complete the inequality as follows:

-2 < x < 35

Hence, the complete inequality is -2 < x < 35