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IgorLugansk [536]
3 years ago
15

if angle 1 and angle 2 are vertical angles, angle 2 and angle 3 are complementary angles and the measure of angle 3 is 56 degree

s find measure of angle 1​
Mathematics
1 answer:
dimulka [17.4K]3 years ago
6 0

Answer:

34º

Step-by-step explanation: so basically you know a complementary angle is 2 angles that make a straight line and a vertical angle crosses which means 2 angles are congruent to each other so I drew a line that bisected the angle by drawing a line that cut through the right angle and i extended a line down from the right angle so now I have a vertical angle and a complementary so from here I labeled each angle <1 <2 <3  If I know angle 3 is 56º then I know 56 plus __ equals 90º I then subtracted 56 from 90 and I got 34 and since I am trying to figure out what angle 1 is I know that angle 1 and 2 are vertical angles therefore I know they are congruent to each other so <1 = 34º

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Jack has a rectangular patio with a length that is one foot less than twice its width. His neighbor Ron's patio has the same wid
swat32

Answer:

difference in area = 16 ft²

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

Step-by-step explanation:

Jacks rectangular patio

width = a

length = 2a - 1

area = lw

where

l = length

w = width

area = 120 ft²

a(2a - 1)

2a² - a - 120 = 0

(a - 8) (2a + 15)

a = 8 or -15/2

Ron's rectangular patio

width = a

length = a + 5

area = lw

area = 104 ft²

a (a + 5) = 104

a² + 5a -104 = 0

(a + 8)  (a - 13)

a = -8 or 13

How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,

120 - 104 = 16 ft²

The value 8 or 13 can be used for a since the width a have to be the same.

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

6 0
3 years ago
50 students live in a dormitory. The parking lot has the capacity for 30 cars. Each student has a car with probability 12 , inde
Maurinko [17]

Answer:

P(X is greater than 30) = 0.06

Step-by-step explanation:

Given that:

Sample proportion (p) = 0.5

Sample size = 30

The Binomial can be approximated to normal with:

\mu = np = 50 \times 0.5 \\ \\ \mu= 25

\sigma = \sqrt{np(1-p) } \\ \\  \sigma = \sqrt{50 \times (0.5)(1-0.5) } \\ \\ \sigma = 3.536

To find:

P(X> 30)

So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 30 lies between 29.5 and 30.5

Normal distribution:

x = 30.5, \mu = 25, \sigma = 3.536

Using the z test statistics;

z = \dfrac{x - \mu}{\sigma}

z = \dfrac{30.5 - 25}{3.536}

z = \dfrac{5.5}{3.536}

z = 1.555

The p-value for P(X>30) = P(Z > 1.555)

The p-value for P(X>30) = 1 - P (Z< 1.555)

From the z tables;

P(X> 30) = 1 - 0.9400

Thus;

P(X is greater than 30) = 0.06

7 0
3 years ago
How Can I find ef? Do I multiply add or diving
Solnce55 [7]
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and surely you know how much that is.
6 0
3 years ago
The weight of an object on the moon is
Tanzania [10]

Answer:

40 2/5Ibs or 40\frac{2}{5} lbs

Step-by-step explanation:

Let weight of object on the moon be represented = Wm

weight of object on the Earth = We

In the above question, we are told:

The weight of an object on the moon is

5 of its weight on Earth.

Hence, mathematically, this is represented as:

 5Wm = We

If a moon rock weighs 202 lbs on Earth

5Wm = 202lbs

Wm = 202lbs/5

Wm = 40\frac{2}{5}Ibs

Therefore, the moon rock weighs 40\frac{2}{5}Ibs on the moon.

7 0
3 years ago
a dollar bill has length of 150 mm and a width of 50 mm . complete the number sentences below to show two ways to find the perim
marysya [2.9K]
<u><em>Hey There!</em></u>
<u><em>Perimeter=L+W×2</em></u>
<u><em>Perimeter=150+50×2</em></u>
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<u><em>Perimeter=400</em></u>
8 0
3 years ago
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