The difference of two numbers is 6. find the smallest possible product.

In the figure above, PQRS is a circle. If PQT and SRT<br>are straight lines, find the value of x.

Elena L [17]

Given:

PQRS is a circle, PQT and SRT are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

$m\angle SPQ+m\angle QRS=180^\circ$

$81^\circ+m\angle QRS=180^\circ$

$m\angle QRS=180^\circ-81^\circ$

$m\angle QRS=99^\circ$

Now, SRT is a straight line.

$m\angle QRT+m\angle QRS=180^\circ$ (Linear pair)

$m\angle QRT+99^\circ=180^\circ$

$m\angle QRT=180^\circ-99^\circ$

$m\angle QRT=81^\circ$ ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

$m\angle PQR=m\angle QRT+m\angle QTR$

$x=81^\circ+22^\circ$

$x=103^\circ$

Therefore, the value of x is 103 degrees.

4 0

3 years ago

Question 1 (1 point)

Fittoniya [83]

Answer:4T

Step-by-step explanation:

T

5 0

3 years ago

1. Shay found that she hit the bull's-eye when throwing darts 2/10 times. If she

viva [34]

<h2>Answer:</h2><h2>If she continues to throw darts 75 more times, she could predict to hit the </h2><h2>bull's-eye 15 times.</h2>

Step-by-step explanation:

Shay found that she hit the bull's-eye when throwing darts $\frac{2}{10}$ times = $\frac{1}{5}$ .

In five times, she will hit the dart once.

If she continues to throw darts 75 more times,

the probability that she will hit the bull's eye = $\frac{1}{5}$ (75) = 15 times.

If she continues to throw darts 75 more times, she could predict to hit the

bull's-eye 15 times.

6 0

3 years ago

Some electronic devices are better used than new: the failure rate is higher when they are new than when they are six months old

Reptile [31]

Given that half of the personal music players sold by a particular brand have a flaw. If the player has the flaw, it dies in the first six months. If it does not have this flaw, then only 20% fail in the first six months.
Let A be the event that it fails in I 6 months
B1 = it has a flaw
B2 = it does not have a flaw
B1 and B2 are mutually exclusive and exhaustive
the chances that it has this flaw
=The probability that it has the flaw is

7 0

3 years ago

The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 14971

RideAnS [48]

Answer:

P(X<1200) is 0.8212

Step-by-step explanation:

Test statistic (z) = (X - mean)/sd

X is score of a tester = 1200

mean = 1497

sd = 322

z = (1200 - 1497)/322 = -297/322 = -0.92

The cumulative area of the test statistic is the probability that X<1200. The cumulative area is 0.8212.

Therefore, P(X<1200) = 0.8212

8 0

3 years ago

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