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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.

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C. Assessment

Crazy boy [7]

1. B
2. A
3. A
All of theses are true

4 0

2 years ago

The function D(t) defines a traveler's distance from home, in miles, as a function of time, in hours. D(t) = StartLayout enlarge

nalin [4]

- At 2 hours, the traveler is 725 miles from home.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE.

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE.

Step-by-step explanation:

The function D(t) is defined as follows:

$D(t) = 300t+125$ for $t< 2.5$

$D(t) = 880$ for $2.5 \leq 3.5$

$D(t) = 75t+612.5$ for $t\leq 6$

Where

t is the time in hours

D(t) is the distance covered, in miles, after t hours

Now let's analyze the different statements:

- The starting distance, at 0 hours, is 300 miles. --> FALSE. In fact, if we substitute t = 0 into the 1st equation, we get

$D(0) = (300)(0)+125 = 125$

So, the distance at t = 0 is 125 miles.

- At 2 hours, the traveler is 725 miles from home. --> TRUE. In fact, if we substitute t = 2 into the 1st equation,

$D(2) = (300)(2)+125 = 725$

- At 2.5 hours, the traveler is 875 miles from home. --> FALSE. In fact, for t=2.5 we have to use the 2nd equation, which states that the distance is:

D(t) = 880

So, not 875 miles.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE. This is clearly visible from the 2nd equation: for t between 2.5 and 3.5 (so, in this case), the distance is

D(t) = 880

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE. In fact, if we replace t = 6 into the last equation,

$D(6)) = 75(6)+612.5=1062.5$

Learn more about functions:

brainly.com/question/3511750

brainly.com/question/8243712

brainly.com/question/8307968

Learn more about distance:

brainly.com/question/3969582

#LearnwithBrainly

4 0

1 year ago

Read 2 more answers

Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the st

notka56 [123]

Options

(A)g(5) = 12
(B)g(1) = -2
(C)g(2) = 4
(D)g(3) = 18

Answer:

(D)g(3) = 18

Step-by-step explanation:

Given that the function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8

Then the following properties must hold

The value(s) of x must be between -1 and 4
The values of g(x) must be between 0 and 18.
g(-1)=2
g(2)=9

We consider the options and state why they are true or otherwise.

Option A: g(5)=12

The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.

Option B: g(1) = -2

The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.

Option C: g(2) = 4

The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.

Option D: g(3) = 18

This statement can be true as its domain is in between -1 and 4 and its range is in between 0 and 18.

Therefore, Option D could be true.

3 0

2 years ago

Each face of cabinet 413s is in the shape of a rectangle. What is the volume of model 413s in cubic feet

Tasya [4]

Each side of the model of 413s is rectangular shaped.
So, by this statement we got to know that the model is in cuboid shape.
Hence, its volume will be (length×width×height) cubic feet.

5 0

2 years ago

Read 2 more answers

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard dev

Vladimir [108]

Answer:

Probability that the average length of a sheet is between 30.25 and 30.35 inches long is 0.0214 .

Step-by-step explanation:

We are given that the population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.

Also, a sample of four metal sheets is randomly selected from a batch.

Let X bar = Average length of a sheet

The z score probability distribution for average length is given by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)