Evaluate each expression. 6 ÷ 6 + z + x − y; use x = 2, y = 5, and z = 6

En un triangulo ABC, el angulo B mide 64° y el angulo C mide 72°. La bisectriz interior CD corta a la altura BH y a la bisectriz

nadezda [96]

Answer:

The difference between the greatest and the smallest angle of the triangle PBQ is 98°.

Step-by-step explanation:

The question is:

In a triangle ABC, angle B measures 64 ° and angle C measures 72°. The inner bisector CD intersects the height BH and the bisector BM at P and Q respectively. Find the difference between the greatest and the smallest angle of the triangle PBQ.

Solution:

Consider the triangle ABC.

The measure of angle A is:

angle A + angle B + angle C = 180°

angle A = 180° - angle B - angle C

= 180° - 72° - 64°

= 44°

It is provided that CD and BM are bisectors.

That:

angle BCP = angle PCH = 36°

angle CBQ = angle QBD = 32°

angle BHC = 90°

Compute the measure of angle HBC as follows:

angle HBC = 180° - angle BHC + angle BCH

= 180° - 90° - 72°

= 18°

Compute the measure of angle BPC as follows:

angle BPC = 180° - angle PCB + angle CBP

= 180° - 18° - 36°

= 126°

Then the measure of angle BPQ will be:

angle BPQ = 180° - angle BPC

= 180° - 126°

angle BPQ = 54°

Compute the measure of angle PBQ as follows:

angle PBQ = angle B - angle QBD - angle HBC

= 64° - 32° - 18°

angle PBQ = 14°

Compute the measure of angle BQP as follows:

angle BQP = 180° - angle PBQ - angle BPQ

= 180° - 14° - 54°

angle BQP = 112°

So, the greatest and the smallest angle of the triangle PBQ are:

angle BQP = 112°

angle PBQ = 14°

Compute the difference:

<em>d</em> = angle BQP - angle PBQ

= 112° - 14°

= 98°

Thus, the difference between the greatest and the smallest angle of the triangle PBQ is 98°.

4 0

3 years ago

Riya is applying mulch to her garden. She applies it at a rate of 250{,}000\text{ cm}^3250,000 cm 3 250, comma, 000, start text,

koban [17]

Complete Question

Riya is applying to her garden. She applies it at a rate of 25, 000 cm³ of mulch for every m² of garden space. At what rate is Riya applying mulch in m³/m²

Answer:

0.25m³/m²

Step-by-step explanation:

We are told the Riya sprays mulch at 250,000cm³ per m²

To find the rate at which Riya is spaying the mulch in m³/m² we would have to convert 250,00cm³/m² to m³/m²

1 cm³ = 1 × 10^-6m³

250,000 cm³ = x m³

Cross Multiply

1 cm³ × xm³ = 250,000cm³ × 1 × 10^-6 m³

X

x m³ = 250,000cm³ × 1 × 10^-6 m³/1 cm³

= 0.25m³

Therefore, the rate at which Riya is spraying the mulch = 0.25m³/m²

3 0

2 years ago

As part of a study done for a large corporation, psychologists asked randomly selected employees to solve a collection of simple

zhenek [66]

Answer:

$P(A')=1-0.411=0.589$

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

Step-by-step explanation:

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

On this case we have that n= 56 represent the employees selected to solve the puzzles.

We know that 23 out of the 56 selected solved the puzzles in less than 7 minutes.

Let's define the events A and A' like this:

A: Employees solved puzzles in less than 7 minutes

By the complement rule then:

A' : Employees solved puzzles in more than 7 minutes

Based on this we are interested to find the probability for A'

We can begin finding P(A), from the definition of probability we know:

$P(A)=\frac{Possible outcomes}{Total outcomes}$

For this case if we replace we got:

$P(A) =\frac{23}{56}=0.411$

And using the complemnt rule we got:

$0.411 +P(A')=1$

And solving for P(A') we got:

$P(A')=1-0.411=0.589$

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

4 0

2 years ago

Factor the expression -45x^2 +5

klemol [59]

$-45x^2 +5 \\ \\ GCF = 5 \\ \\ 5( \frac{45x^2}{5} - \frac{5}{5} ) \\ \\ -5(9x^2-1) \\ \\ -5((3x)^2-1^2) \\ \\ -5(3x+1)(3x-1) \\ \\ Answer: \fbox {-5(3x+1)(3x-1)}$

5 0

3 years ago

How many centi are in 12 in

Marina CMI [18]

30.48 centimeters in 12 inches

3 0

3 years ago

Read 2 more answers