Which equation is correct?

In ∆ABC the angle bisectors drawn from vertexes A and B intersect at point D. Find ∠ADB if:

icang [17]

Answer:

155°

Step-by-step explanation:

In Δ ABC, let A = x°

By Angle-sum property,

A + B + C = 180°

But, it is given that C = 130°

So, x + B + 130 = 180

B = 180 - 130 - x

B = 50 - x

Since AD and BD are internal bisectors of A and B,

∠ DAB = x/2 and

∠ DBA =

In Δ ADB, by angle-sum property,

∠ DBA + ∠ DAB +∠ ADB = 180°

+ ∠ ADB = 180°

25 + ∠ ADB = 180°

∠ ADB = 180 - 25 = 155°

Hence, ∠ ADB = 155°

3 0

3 years ago

Convert r=8cos⁡θ+2sin⁡θ to rectangular equation

Alona [7]

Answer:

Convert

r

=

8

cos

θ

−

2

sin

θ

to Cartesian form

#x^2 + y^2 - 8 x +2 y = 0, using

r

=

√

x

2

+

y

2

≥

0

and

(

x

,

y

)

=

r

(

cos

θ

,

sin

θ

)

.

The Socratic graph of this circle,

with center at

(

4

,

−

1

)

and radius

√

17

.

is immediate.

graph{(x^2+y^2-8x+2y)((x-4)^2+(y+1)^2-0.04)=0[-1 23 -6 6] }

5 0

3 years ago

A regular triangular pyramid has all of edges of length 36. What is the angle between any two faces of this pyramid?

GrogVix [38]

Answer:

The angle between any two faces of this pyramid is equal to $60\°$

Step-by-step explanation:

we know that

An equilateral triangle has three equal sides and three equal internal angles of measure 60 degrees

In this problem

All the faces in the regular triangular pyramid are equilateral triangles.

therefore

The angle between any two faces of this pyramid is equal to $60\°$

4 0

4 years ago

Read 2 more answers

Last year, the tree in Pedro's front yard was 5 feet tall. This year, the tree is 2 feet less than the height of Pedro's house.

krok68 [10]

Pedro’s tree is 15 feet tall Pedro’s house is 17 feet the tree WAS 5 feet but then it grew to 2 feet less than the 17 foot house 17-2 is 15 there ya go

7 0

4 years ago

Cedric completed the square for the quadratic expression 5x^2−40x+15 in order to determine the minimum value of the expression,

Olegator [25]

Answer:

Step 3 is not correct (should be $(x-4)^2$ , not $(x+4)^2$

Step-by-step explanation:

The expression that we have to simplify is:

$5x^2-40x+15$

We proceed step-by-step, in order to find the mistake did by Cedric:

1) First, we factorize the 5 outside:

$5(\frac{5x^2}{5}-\frac{40x}{5}+\frac{15}{5})=5(x^2-40x+3)$ --> this step is correct

2) We add +16 and -16 inside the brackets:

$5(x^2-8x+16-16+3)$ --> this step is correct

3) We rewrite the term $(x^2-8x+16)$ as the square of a bynomial, which is $(x-4)^2$ , so the expression becomes

$5((x-4)^2-16+3)$ --> we notice that this step is wrong: in fact, Cedric wrote $(x+4)^2$ , which is not correct.

4) Now we continue: we rewrite -16+3 as -13,

$5((x-4)^2-13)$

5) Finally, we multiply the 5 by the terms in the bracket:

$=5(x-4)^2-65$

5 0

3 years ago