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2 years ago

Based only on the information given in the diagram, it is guaranteed that ABC XYZ

Mathematics

2 answers:

serious [3.7K]2 years ago

5 0

This statement is true

Scilla [17]2 years ago

3 0

Answer:

Statement is true.

Step-by-step explanation:

The given triangles ΔABC and ΔXYZ will be similar if the two angles of these triangles are equal Or all sides of both the triangles are equal Or two corresponding sides and the angle between these lines are same.

Here in ΔABC

∠ACB = 52°

∠ABC = 90°

Then we can find the third angle ∠CAB = 180°-(∠ACB+∠ABC)

= 180 - (52+90)

= 180 - 142

= 38°

Similarly in ΔXYZ, ∠YXZ = 38°, ∠XYZ = 90°

Then ∠YZX = 180-(∠YXZ+∠XYZ)

= 180-(90+38) = 180-128 = 52°

Now we can say that in two triangles

∠ACB = ∠YZX =52°

∠CAB = ∠YXZ = 38°

Therefore These triangle are similar and the statement is true.

You might be interested in

The pilot in a helicopter tossed a life float down to a swimmer in the water. The height, h, of the float after time t seconds i

MissTica

Answer:

1.95secs

Step-by-step explanation:

Given the height of the float expressed as h(t) = -16t2 - 3t + 55.

The floats reach the swimmer at h(t) = 0

Substitute

0 = -16t^2 - 3t + 55.

16t^2 + 3t - 55 = 0

Using the general formula;

t = -3±√3²-4(16)(-55)/2(16)

t = 3±√9+3520/32

t = 3±√3529/32

t = 3+59.41/32

t = 62.41/32

t = 1.95

Hence it will take 1.95secs

4 0

1 year ago

△ABC has vertices A(−1, 6), B(2, 10), and C(7, −2) . Find the measure of each angle of the triangle. Round decimal answers to th

kolbaska11 [484]

Answer:

<A = 90°, <B = 71.6° <C = 18.4°

Step-by-step explanation:

Given the vertices of a △ABC to be A(−1, 6), B(2, 10), and C(7, −2)

Before we can get each angle of the triangle, we need to get its sides first.

Using the formula fie finding the distance between two points

D = √(x2-x1)²+(y2-y1)²

For side AB:

Given A(−1, 6), B(2, 10)

AB = √{2-(-1)}²+(10-6)²

AB =√3²+4²

AB = √25

AB = 5

For side AC:

Given A(-1,6) and C(7, −2)

AC = √{7-(-1)}²+(-2-6)²

AC = √8²+8²

AC = √128

AC = √64×2

AC = 8√2

For side BC:

Given B(2,10) and C(7, −2)

BC = √(7-2)²+(-2-10)²

BC = √5²+12²

BC = √25+144

BC = √169

BC = 13

First we need to get theta using cosine rule

|AC|² = |AB|+|BC| - 2|AB||AC| cos theta

(8√2)² = 5²+13²-2(5)(13)cos theta

128 = 169-130costheta

128-169 = -130costheta

-41= -130costheta

Costheta = -41/-130

Cos theta = 0.315

theta = arccos 0.315

theta = 71.64°

<B = 71.6°

Using sine rule to get <A,

BC/sin A = AC/sinB

13/sinA = 8√2/sin71.6°

8√2sinA = 13sin71.6°

SinA = 12.34/8√2

SinA = 1.09°

A = arcsin1

<A = 90.0°

<C = 180°-(71.6+90)

< C = 180-161.6

<C = 18.4°

3 0

2 years ago

Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 perc

Olegator [25]

Answer:

The bonus will be paid on at least 4099 units.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the percentile of this measure.

In this problem, we have that:

The highest 5 percent is the 95th percentile.

Past records indicate that, on the average, 4,000 units of a small assembly are produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. This means that $\mu = 4000, \sigma = 60$ .