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Alex17521 [72]
2 years ago
6

Let ABC be an isosceles triangle with AB = AC and ∠BAC=30°. Side AB and the median AD contain points Q and P respectively (point

s P and Q are not at point A) in such a way that PC=PQ. Find m∠PQC.
Mathematics
1 answer:
juin [17]2 years ago
4 0

Answer:

15°

brainlest

Step-by-step explanation:

Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)

The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.

Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°.  Angle PQC has the same measure as angle RQC, so is 15°.

Angle PQC is 15°.

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a person runs at a constant speed of 9.2 miles per hour for 6 minutes and 30 seconds. How far did they travel in yards.
ipn [44]

Given:

Speed= \bold{9.2 \ \frac{miles}{hour}}  

\therefore \\\\

1-hour= 60 minutes

1-minutes=60 second

So

1-hour= 3600 second

Converting the given time into seconds:

Time= 6 minutes and 30 second

       =\bold{6\times 60 \ second + 30 \ second }\\\\=\bold{360\ second+30\ second}\\\\=\bold{390\ second}\\\\

When 3600 seconds covers=9.2 miles

Then equation:

=\bold{\frac{9.2}{3600}}\\\\

390 seconds covers:

=\bold{\frac{9.2}{3600}\times 390 \ miles} \\\\  

Let

\bold{1 \ miles= 1760\ yard}\\\\

Convert the traveling value into yards:

=\bold{ \frac{9.2}{3600}\times 390\times 1760}\\\\=\bold{ \frac{9.2}{36}\times 39\times 176}\\\\=\bold{ \frac{9.2}{12}\times 13\times 176}\\\\=\bold{ \frac{9.2}{12}\times 2288}\\\\=\bold{ 9.2\times 190.66}\\\\=\bold{ 1754.072\ yards}\\\\

Therefore, total traveling yards are"1754.072".  

Learn more:

brainly.com/question/20282942

7 0
2 years ago
Read 2 more answers
In a sample of 41 temperature readings taken from the freezer of a restaurant, the mean is 29.7 degrees and the population stand
yKpoI14uk [10]

Answer: =(29.1596\text{ degrees},\ 30.2404\text{ degrees})

Step-by-step explanation:

Given: Sample size: n = 41

Sample mean \overline{x}= 29.7 degrees

Population standard deviation \sigma=2.7 degrees

Confidence level (c) =  80% =0.80

Significance level (a) = 1- c = 1-0.80 = 0.20

z-score for 80% confidence level : z = 1.2816   [from z-table]

Confidence level for population mean :-

\overline{x}\pm z\dfrac{\sigma}{\sqrt{n}}

=29.7\pm ( 1.2816)\dfrac{2.7}{\sqrt{41}}

=29.7\pm ( 1.2816)\dfrac{2.7}{6.403124}

=29.7\pm ( 1.2816)(0.42167)

=29.7\pm 0.5404

=(29.7-0.5404,\ 29.7+0.5404)

=(29.1596,\ 30.2404)

Hence, 80% confidence interval for the temperatures in the freezer =(29.1596\text{ degrees},\ 30.2404\text{ degrees})

7 0
2 years ago
Please help me! I think this 20 character thing is unnecessary when you have an attachment
PIT_PIT [208]

Answer:

B

Step-by-step explanation:

Also the answer must be under 9 so that rules out option D

Because We know CE = 2 and AD is visibly larger than CE, 6We can rule out option A

And that brings us down to B and C

CB is equal to 6, And I'm no genius, but I'm pretty sure AD is DEFINATLY not equal to 6.

so the answer is B

8 0
3 years ago
Explain why the intercepts, on their own, cannot be used to graph the relation 5x+9y= 0.
goldfiish [28.3K]
5x + 9y = 0

to find the x int, sub in 0 for y and solve for x
5x + 9(0) = 0
5x = 0
x = 0

to find the y int, sub in 0 for x and solve for y
5(0) + 9y = 0
9y = 0
y = 0

the reason u cannot use just the intercepts is because the line goes through the origin (0,0)....The intercepts coincide giving u only 1 point...and that is not enough to graph a line
3 0
2 years ago
Amy is eight years older than twice her cousin Alicia’s age. The sum of their ages is less than 32. Let x represent Alicia's age
Vladimir [108]
Assume that the age of Alicia is x and that of Amy is y
Twice the age of Alicia = 27
Eight years older means we will add 8
Therefore, the statement "<span>Amy is eight years older than twice her cousin Alicia’s age" can be represented as follows:
y = 8 + 2x (equation)
The sum of their ages is less than 32 can be represented as:
x + y < 32 which can also be written as y < 32-x (inequality)
</span>
7 0
2 years ago
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