All categories

3 years ago

Find the missing values in the following figure

Mathematics

1 answer:

telo118 [61]3 years ago

4 0

Answer:

p = 4.5
u = 35
w = 12.6
x = 55
y = 35
z = 7.2

Step-by-step explanation:

Angles u° and 55° are the acute angles of a right triangle, so are complementary.

u° = 90° -55° = 35°

Angles x° and y° are corresponding angles with 55° and u°, so are congruent to them, respectively.

x° = 55°; y° = 35°

In summary:

u = 35, x = 55, y = 35

Corresponding sides of the triangles are proportional, so ...

p/6 = 3/4

p = 18/4 = 4.5 . . . . . multiply by 6

The Pythagorean theorem can be used to find z:

z² = 4² +6² = 52

z = √52 = 2√13 ≈ 7.2

The scale factor between the larger triangle and the smaller one is ...

(3+4)/4 = 7/4

so ...

w = 7/4·z = (7/2)√13 ≈ 12.6

In summary:

p = 4.5; w ≈ 12.6; z ≈ 7.2

_____

<em>Comment on this problem figure</em>

With the given side measurements, the angles would be more correctly described as 56.3° and 33.7°. The geometry shown cannot exist.

We presume you're to use corresponding side relationships to find the side lengths, and angle relationships to find the angles. Trig relations will relate sides to angles, but those are not needed (or useful) in this problem. Since the angles are not properly related to the sides, trig relationships can only introduce confusion into what is otherwise a straightforward problem.

You might be interested in

COMPUTERS The byte is the fundamental unit of computer processing.

Vitek1552 [10]

Answer:

1000x bigger

5 0

3 years ago

How much has the value of y changed between the points (-8, 4) and (8, -4)?

Goryan [66]

Answer:

The answer is I think B

Step-by-step explanation:

I just took the test

7 0

3 years ago

a fruit delivers its fruit in two types of boxes: large and small. a delivery of 3 large boxes and 5 small boxes has a total wei

Masteriza [31]

Answer:

The weight of a small box = 13.5 kg

The weight of 1 large box = 18.5 kg

Step-by-step explanation:

Let us assume the weight of a small box = m kg

And the weight of 1 large box = n kg

Now, the weight of 5 small box = 5 x (weight of 1 small box) = 5 m

Also, the weight of 3 large box = 3 x (weight of 1 large box) = 3 n

Here, 3 large boxes + 5 small boxes = of 123 kilograms

⇒ 5 m + 3 n = 123 .... (1)

Again, the weight of 2 small box = 2 x (weight of 1 small box) = 2 m

Also, the weight of 12 large box = 12 x (weight of 1 large box) = 12 n

Here, 12 large boxes + 2 small boxes = 249 kilograms

⇒ 2 m+ 12 n = 249 .... (2)

Now, solving both the given equations by ELIMINATION, we get:

5 m + 3 n = 123 x (2)

2 m+ 12 n = 249 x (-5)

we get the new set of equitation as:

10 m + 6 n = 246

- 10 m - 60 n = -1245

Adding both equation, we get

-54 n = 999

or, n = 18.5

Now, 5 m + 3 n = 123

So, 5 m = 123 -3 (18.5) = 123 - 55.5 = 67.5

⇒ m = 13.5

Hence, the weight of a small box = m kg = 13.5 kg

And the weight of 1 large box = n kg = 18.5 kg

8 0

3 years ago

Henry ran five races, each of which was a different positive integer number of

dolphi86 [110]

Answer:

10 miles.

Step-by-step explanation:

Let x be the number of miles on Henry's longest race.

We have been given that Henry ran five races, each of which was a different positive integer number of miles.

We can set an equation for the average of races as:

$\frac{\text{The sum distances of 5 races}}{5}=4$

As distance covered in each race is a different positive integer, so let his first four races be 1, 2, 3, 4.

Now let us substitute the distances of 5 races as:

$\frac{1+2+3+4+x}{5}=4$

$\frac{10+x}{5}=4$

Let us multiply both sides of our equation by 5.

$\frac{10+x}{5}*5=4*5$

$10+x=20$

Let us subtract 10 from both sides of our equation.

$10-10+x=20-10$

$x=10$

Therefore, the maximum possible distance of Henry's longest race is 10 miles.

7 0

3 years ago

What is the measure of Angle R?

Ivanshal [37]

The sum of angles in triangle is equal to 180 degrees, so

<R =180-56-30

<R=94

8 0

4 years ago

Read 2 more answers

Find the missing values in the following figure​

Find the missing values in the following figure