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2 years ago

(03.01 LC)

Mathematics

1 answer:

Sedaia [141]2 years ago

8 0

Perpendicular=P=4
Base=B=4

Hypotenuse be H

Apply Pythagorean theorem

$\\ \tt\hookrightarrow H^2=P^2+B^2$

$\\ \tt\hookrightarrow H^2=4^2+4^2$

$\\ \tt\hookrightarrow H^2=32$

$\\ \tt\hookrightarrow H=\sqrt{32}$

$\\ \tt\hookrightarrow H=5.8units$

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Simplify the following :

dlinn [17]

Answer:

1. 95/96

2. 27/7

3. -8/245

Explanation:

1. First add together the two fractions 3/4 + 5/6. Find the least common denominator. In this case we can use 12. The 3/4 changes to 9/12 and the 5/6 changes to 10/12. adding these together we get 19/12. Next we divide 8/5 by 19/12. We use the keep, change, flip method to change the divide to multiply. keep the first fraction, change divide into multiply, and then take the reciprocal of the second fraction. You will now do 5/8 x 19/12. We now get 95/96 (I made a mistake in the answers the first time because I was rushing)

2. Divide the 3/2 and the 8/9 first. I will use the KCF (keep, change, flip) method to divide. 3/2 x 9/8 = 27/16 Now we divide the 7/16. After using KCF we can simplify and cross cancel (simplfy after changing the fraction and signs) 27/16 x 16/7 --> 27/1 x 1/7 The answer will come out to be 27/7

3. since there are no parentheses divide first. Use KCF and after you get the answer multiply (it is the same using negative numbers just watch out for signs)

7 0

3 years ago

Please I need help ASAP<br>pls explain your answer

USPshnik [31]

Answer:

47.62 cm

Step-by-step explanation:

ABCD is a rhombus. Each side measures 15 cm.

m<A = 60°.

Here are some properties of a rhombus:

Opposite angles of a rhombus are congruent.

m<C = m<A = 60°

m<ADC = m<ABC

The sum of the measures of the interior angles of a quadrilateral is 360°.

The diagonals are perpendicular bisectors of each other.

m<A + m<C + m<ADC + m<ABC = 360°

60° + 60° + 2m<ADC = 360°

2m<ADC = 240°

m<ADC = 120°

Each diagonal of a rhombus bisects a pair of congruent, opposite angles.

m<ADB + m<CDB = m<ADC

m<ADB = m<CDB

m<ADB + m<ADB = 120°

m<ADB = 60°

Triangle ABD had two angles, <A and <ADB, that measure 60°. Therefore, the third angle, <ABD also measures 60°. That makes triangle ABD an equilateral triangle.

Draw segment AT.

T is the midpoint of BD. The segment AT is the perpendicular bisector of segment BD. Triangle ATD is a 30-60-90 triangle.

Using the ratio of the lengths of the sides of a 30-60-90 triangle, we can calculate the length of AT which is the radius of circle A.

TD : AT : AD

1 : √3 : 2

AD = 15 cm

TD = AD/2

AT = √3 × TD

AT = (AD√3)/2

AT = 7.5√3 = 12.99

AQ = 12.99

perimeter = QD + PB + m(arc)PTQ + BC + CD

perimeter = (15 - 12.99) + (15 - 12.99) + 60°/360° × 2π(12.99) + 15 + 15

perimeter = 47.62

Answer: perimeter = 47.62 cm

7 0

2 years ago

Use the unit circle to find the inverse function value in degrees.<br> tan^-1 sqrt 3

mr Goodwill [35]

Use the unit circle to find the inverse function value in degrees.tan^-1 sqrt 3

The correct answer would be 60 degrees. Since you are asked to find an angle that the tangent is equal to sqrt 3. The only angle that is equal to that given the interval is 60 degrees. So that is the correct answer. I hope this answer helped you.

7 0

3 years ago

a flag pole that is 8 feet tall casts a shadow that is 6 ft long a nearby tree casts a shadow that is 21 ft long. How tall is th

Andru [333]

Answer:

The tree is 28 feet tall.

Step-by-step explanation:

It is given that:

Height of flag pole = 8 feet

Shadow of flag pole = 6 feet

Ratio of height to shadow = 8 : 6

Shadow of nearby tree = 21 feet

Height of nearby tree = x

Ratio of height to shadow = x : 21

8 : 6 :: x : 21

Product of means = Product of extremes

6x = 8*21

6x = 168

Dividing both sides by 6

$\frac{6x}{6}=\frac{168}{6}\\x=28$

Therefore,

The tree is 28 feet tall.

7 0

3 years ago

Mathematics with applications in the management, Natural, and Social Sciences Twelfth edition

Monica [59]

Answer:

In 2015 the both populations were the same and from that year the population of millennials surpassed the population of boomers

Step-by-step explanation:

$\left \{ {{10x+13y = 1125} \atop {-2x+7y = 495}} \right.$

x=14

Boomer: 10(14)+13y=1125

140+13y=1125

13y=1125-140

y= 985/13

y= 75.77 (75.77 millions of boomers in 2014)

Millenials: -2(14) +7y = 495

-28 +7y = 495

7y= 495+28

y= 523/7

y=74.71 (74.71 millios on millenials in 2014)

In 2014 the population of boombers were still greater than the population of millennials

The solution of the system of equations will give us the point where the populations were equalized, and from that point the population of boombers will be less than that of the millennials.

Boomers: 10x+13y = 1125

y= (-10x +1125)/13

Millenials: -2x+7y = 495

y= (2x+495)/7

We match both expressions of "y"

(-10x +1125)/13 =(2x+495)/7

cross multiply:

(-10x +1125)*7 =(2x+495)*13

-70x + 7875 = 26x + 6435

we group similar terms:

7875 -6435 = 26x+70x

1440 = 96x

x= 1440/96

x= 15

In 2015 the both populations were the same and from that year the population of millennials surpassed the population of boomers

4 0

2 years ago