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3 years ago

If AB is parallel to CD, and CD = 20, BD = 6, DE = 8, what is the length of AB?

Mathematics

1 answer:

castortr0y [4]3 years ago

5 0

Answer:

Option b. 35 units

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

in this problem triangle ABE and triangle CDE are similar by AA Similarity Theorem

$\frac{AB}{DC}=\frac{BE}{DE}$

substitute the given values

$\frac{AB}{20}=\frac{14}{8}$

Solve for AB

$AB=\frac{14}{8}(20)$

$AB=35\ units$

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write the number 2 millions, 6 hundred thousands, 3 thousand, 1 hundred, 2 in Standard Form and Expanded Form

Mnenie [13.5K]

In standard form it would be 2,603,102. In expanded form it would be 2,000,000+600,000+3,000+100+2.

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4 years ago

In circle B with the measure of minor arc AC= 84°, find m

ELEN [110]

Answer:

m<ADC = 42°

Step-by-step explanation:

Based on the inscribed angle theorem, the inscribed angle, m<ADC is ½ the measure of minor arc AC.

If minor arc is given as 84°, therefore:

m<ADC = ½(84)

m<ADC = 42°

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3 years ago

The triangle shaped entrance to the cavern i 1 1/2 feet tall and 4 feet wide whats the area

oee [108]

A=1/2 b*h
So substitute it in 1/2*1/2*4
1/2*1/2= 1/4
1/4*4= 4/4= 1 so the entrance is 1 foot tall

6 0

3 years ago

Read 2 more answers

Find sin(2x), cos(2x), and tan(2x) from the given information.<br> tan(x) = − 1/2 , cos(x) > 0

vodomira [7]

Answer:

sin(2x) = -4/5
cos(2x) = 3/5
tan(2x) = -4/3

Step-by-step explanation:

It may be easiest to start with tan(2x).

tan(2x) = 2tan(x)/(1 -tan(x)²)

tan(2x) = 2(-1/2)/(1 -(-1/2)²) = -1/(3/4)

tan(2x) = -4/3 . . . . . still a 4th-quadrant angle

Then cosine can be found from ...

cos(2x) = 1/√(tan(2x)² +1) = 1/√((-4/3)²+1) = √(9/25)

cos(2x) = 3/5

Sine can be found from these two:

sin(2x) = cos(2x)tan(2x) = (3/5)(-4/3)

sin(2x) = -4/5

5 0

4 years ago

The position of an object moving along an x axis is given by x = 3.24 t - 4.20 t2 + 1.07 t3, where x is in meters and t in secon

Pavel [41]

Answer and explanation:

Given : The position of an object moving along an x axis is given by $x=3.24t-4.20t^2+1.07t^3$ where x is in meters and t in seconds.

To find : The position of the object at the following values of t :

a) At t= 1 s

$x(t)=3.24t-4.20t^2+1.07t^3$

$x(1)=3.24(1)-4.20(1)^2+1.07(1)^3$

$x(1)=3.24-4.20+1.07$

$x(1)=0.11$

b) At t= 2 s

$x(t)=3.24t-4.20t^2+1.07t^3$

$x(2)=3.24(2)-4.20(2)^2+1.07(2)^3$

$x(2)=6.48-16.8+8.56$

$x(2)=-1.76$

c) At t= 3 s

$x(t)=3.24t-4.20t^2+1.07t^3$

$x(3)=3.24(3)-4.20(3)^2+1.07(3)^3$

$x(3)=9.72-37.8+28.89$

$x(3)=0.81$

d) At t= 4 s

$x(t)=3.24t-4.20t^2+1.07t^3$

$x(4)=3.24(4)-4.20(4)^2+1.07(4)^3$

$x(4)=12.96-67.2+68.48$

$x(4)=14.24$

(e) What is the object's displacement between t = 0 and t = 4 s?

At t=0, x(0)=0

At t=4, x(4)=14.24

The displacement is given by,

$\triangle x=x(4)-x(0)$

$\triangle x=14.24-0$

$\triangle x=14.24$

(f) What is its average velocity from t = 2 s to t = 4 s?

At t=2, x(2)=-1.76

At t=4, x(4)=14.24

The average velocity is given by,

$\triangle x=x(4)-x(2)$

$\triangle x=14.24-(-1.76)$

$\triangle x=14.24+1.76$

$\triangle x=16$

4 0

3 years ago