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Basile [38]
3 years ago
9

Prove ΔPAB is isosceles.

Mathematics
1 answer:
Licemer1 [7]3 years ago
6 0

Answer:

See explanation

Step-by-step explanation:

If PX\cong PY, then triangle PXY is isosceles triangle. Angles adjacent to the base XY of an isosceles triangle PXY are congruent, so

\angle 1\cong \angle 2

and

m\angle 1=m\angle 2

Angles 1 and 3 are supplementary, so

m\angle 3=180^{\circ}-m\angle 1

Angles 2 and 4 are supplementary, so

m\angle 4=180^{\circ}-m\angle 2

By substitution property,

m\angle 4=180^{\circ}-m\angle 2=180^{\circ}-m\angle 1=m\angle 3

Hence,

\angle 3\cong \angle 4

Consider triangles APX and BPY. In these triangles:

  • PX\cong PY - given;
  • \angle 5\cong \angle 6 - given;
  • \angle 3\cong \angle 4 - proven,

so \triangle APX\cong \triangle BPY by ASA postulate.

Congruent triangles have congruent corresponding sides, then

AP\cong BP

Therefore, triangle APB is isosceles triangle (by definition).

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The number of bagels sold daily for two bakeries is shown in the table:
ivann1987 [24]

Going by the data given, the best center of distribution to use in terms of mean and median is D) Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric.

<h3>What centers of distribution should be used?</h3>

The mean should be used for data sets that are symmetric while the median should be used for data that is not symmetric.

The data is said to be symmetric when the mean and median are equal or very close.

Bakery A mean:

= (45 + 52 + 51  48 + 61 + 34 + 55  46) / 8

= 49

Bakery A median is 49.5

Bakery B mean:

= (48  42 + 25  45 + 57 + 10 + 43 + 46 ) / 8

= 39.5

Bakery B median is 44.

This shows that Bakery A data is symmetric so the best center of distribution to use is mean.

Bakery B is not symmetric so the center of distribution to use is median.

Find out more on symmetric data at brainly.com/question/7130507

#SPJ1

8 0
1 year ago
Which factorization is equivalent to this expression?
grigory [225]

Answer:

10(3x+7)

Step-by-step explanation:

we have the expression:

30x + 70

To factor this expression we need to indentify the components that are common in both terms.

At first glance there is nothing in common, but we can notice that 30 and 70 are multiples of 10, that is:

10*3=30\\10*7=70

so we can substitute this into the expression:

10*3x+10*7

and now that we have the common term (the number 10) we can factorize it, that is, take out the common term and include a parentheses:

10(3x+7)

8 0
2 years ago
Can someone please help me
Lilit [14]

Answer:

9.2

Step-by-step explanation:

Use law of sines

a/sinA = b/sinB

5/sin 31 = b/sin 108

b=9.2

8 0
3 years ago
Read 2 more answers
Which expression is the best estimate of the product of 7/8 and 1/10
Lera25 [3.4K]
Multiply across 7/80
6 0
3 years ago
10m/
AlladinOne [14]

Answer:

Answer is D 312m^2

As  D= 8m x 11m = A =88x 3 = 264+ 48 = 312

1/2 x 6 x 8 = 24

This makes triangle base of 6m

triangle side =8m

Rectangle side = 8m

and rectangle length = 11m

Step-by-step explanation:

First finding

A= 6 x 11 = 66m^2 (rectangle area) or 10 x 9 = 90sq^2

A = 1/2 x 6 x 11 = 33  (1/2bh) triangle

33+ 33 + 66 +66 + 66 = 264  or 33+ 33+ 90+90+90 =336

As 336 was not in the answer we do not know what 10m/9m represents, we then see this triangle prism is not a normal shape and its length is same as its height

a) is not in usual proportions.

We try again reversing which makes triangle sides 10m+ base 9m

= 1/2 x 10 x 10 = 50m^2 = triangle face area

we cannot continue the reverse as the triangle sides do not match the rectangle height. We therefore have to use the first answer C 264m^2

As 10m, 9m <do not match >6m 11m 8m

However if the given sizes 10m, 9m = bases of two different rectangles we would calculate 2 faces and add them each to one unknown face being one of the other face sizes we found to make 3.

10 x 8 = 80

9 x 8 = 72

To make one of these SA totals for rectangles alone

=80+80+72=232   or  72+72+80 =224

Then add to the 33 m^2 triangles

= 232+ 33+ 33 =297m^2

= 224+33+33 =310m^2

We can now determine that these measurements represent irregular values and are not answers within multiple choice, however d)  we can state the triangle is regular prism where triangle sides are regular too creating isosceles triangle 6,8,8,

8m x 11m = A =88x 3 = 264+ 48 = 312

1/2 x 6 x 8 = 24

As we have ruled out rectangle with side 8m x 11m + A (33m^2) of triangle would equal 310m^2 (88+88+88+33+33) =330m

And ruled out rectangle with side 8m x 6m= 48m^2 (48+48+48+33+33 =210sqm)

So therefore if triangles were to equal 1/2 x 6 x 8 = 24

24 x 3= 72sqm

add the rectangle amounts above

= 72 + 88+ 88+ 88 =336^2

try another way and we find D. here below.

answer D= 72+ 80+80+80 = 312m^2 this can makes a correct answer D.

As last rule out is;

72 + 72 +72  (+triangle of 72) =288^2 would be irregular as this is equal to (9 x 8) x 3 and then the 11m is not used. It is also not a listed answer. Therefore;  D=312m^2 is correct.

A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.

3 0
2 years ago
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