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2 years ago

Please Help! The following is an isosceles trapezoid, find m < J

Mathematics

1 answer:

ra1l [238]2 years ago

3 0

Answer:

The measure of angle J is 44°

Step-by-step explanation:

Isosceles Trapezoid

The isosceles trapezoid has its non-parallel sides of the same length, thus the angles they form with their respective parallel sides are congruent.

It means: Angle J is congruent with angle K and angle M is congruent with angle L

The sum of angles in a trapezoid is 180*(4-2)=360°

Thus:

$m\angle J+m\angle K+m \angle M+m\angle L = 360^\circ$

$7x+2+7x+2+25x-14+25x-14=360$

Joining like terms:

$64x-24=360$

Adding 24:

$64x=384$

Dividing by 64:

x=6°

Thus:

$m\angle J = 7*6+2=44^\circ$

$m\angle M = 25*6-14=136^\circ$

The measure of angle J is 44°

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3. Why is a square both a rhombus and a rectangle?

Korolek [52]

A rhombus is a shape that has all four sides equal, whether they be in the shape of a parallelogram, or a square, if it has all four sides equal length, it's a rhombus. The definition of a rectangle, is a shape that has four right angles. (90 degrees).

So, if a square has all four sides equal, and four right angles, it can be both a rhombus and a rectangle.

Not all rhombuses are squares, because not all have four right angles. Not all rectangles are squares, because they do not all have four equal sides. Not all rectangles are rhombuses because they do not have four equal sides.

But all squares are a rhombus and all squares are a rectangle.

7 0

2 years ago

A)0.5 B)2.5 C)-0.5 D)-2.5

7nadin3 [17]

Answer:

B)2.5

Step-by-step explanation:

When x = 3 the actual = 6

Residual = actual - predicted = 6 - 3.5 = 2.5

5 0

2 years ago

Round to 2 decimal places *

EleoNora [17]

Answer: The circumference of the dome is therefore 149.15 feet or 47.5π feet

Step-by-step explanation:

A scale is basically referred to as the ratio of the dimensions of an object as represented in a draft to the real or true dimensions of the object being drafted.

The figure(s) on the left of the ratio sign represents the size and dimensions of the model with respect to the actual size or dimensions of the object. On the other hand, the figure on the right hand size represents the actual dimensions and size of the real object.

So, if an object is being drawn with the ratio, 1cm : 5cm it means that the size of the object is being reduced because every 5cm of the actual object will always be represented by 1cm in the drawing. If the object is being drawn with a scale of 5cm : 1cm then the actual size of the object will be increased in the drawing. That is, for every 1cm in the actual dimensions of the object, there will be a 5cm representation in the drawing.

Now, the architect draws with a scale of 0.25 inches : 1 foot. If the diameter of the hemispherical dome is 23.75 inches in the scale model, then the actual diameter of the dome is:

0.25 inches ------- 1 foot

23.75 inches ------- ? feet

= 23.75/0.25 × 1

= 95 feet

Therefore, the actual diameter of the dome is 95 feet. We are now required to find the circumference of this dome.

The dome is a hemisphere which literally means half of a sphere. So, if the formula for finding the circumference of a sphere is πd, that of a hemisphere will then be πd/2. Since the diameter is already known to be 95 feet, the circumference of the hemisphere =

(π × 95)/2

=47.5π feet

If π = 3.14, then the circumference = (3.14 × 95)/2 = 149.15 feet

The circumference of the dome is 149.15 feet or 47.5π feet

5 0

2 years ago

PLEASE HELP ME PRE CAL/TRIG

miss Akunina [59]

Answer:

A) 60 Degrees

B) 550 Feet

C) 2.5 minutes

Step-by-step explanation:

a) So the wheel has completed one revolution in 10 minutes so lets first divide 100 secs with 10 minutes to calculate the the fraction of revolution

1 min = 60 secs

10 min = 600 secs

100/600 = 1/6

One complete revolution is 360 degrees and 1/6 of 360 degrees will be 60 degrees .

360/6 = 60°

b) It takes 10 minutes to complete one revolution so if the person is on it for 7 minutes it would be 7/10 of a revolution . The ferris wheel has a diameter of 250 feet so the radius will be 125 feet because it is the half of the diameter and the circumference will be 250 π . To calculate the distance lets multiple the fraction of the revolution which is 7/10 into the circumference $\frac{7}{10} * (250 pi)$ = 550 Feet.

C)It took 10 minutes to travel 250 π now we will use this relation to calculate 200 feet . lets suppose t is for time .

$\frac{250pi}{10} =\frac{200}{t}$ .

After solving this equation as there is only one unknown which is "t "the answer will be 2.5 minutes.

3 0

3 years ago

Of the students in your class, 12% are left-handed. What fraction of the students are left-handed? Are there more right-handed o

kvv77 [185]

The left-handed students
12% are left handed, percent means per hundred. Change percent into per 100.
12% = $\dfrac{12}{100}$

Then simplify the fraction by dividing the numerator and denominator by 4
$\dfrac{12}{100}$
= $\dfrac{12:4}{100:4}$
= $\dfrac{3}{25}$
This is the fraction showing the proportion of the left-handed students

The right-handed students
Determine the fraction showing the proportion of the right-handed students
1 - the left-handed
= 1 - $\dfrac{3}{25}$

Equalize the denominator to 25
$\dfrac{25}{25} - \dfrac{3}{25}$

Simplify
$\dfrac{21}{25}$
This is the proportion of the right-handed students

Are there more right-handed or left-handed students?
There are more right-handed students than the left-handed students, because 21/25 is more than 3/25

4 0

3 years ago