Hello, could someone help me with this one?

Given: Tangents LA and LB, m∠AOB=110°. Find: m∠ALO.

Yuri [45]

Answer:

The measure of angle ALO = 35°

Step-by-step explanation:

* Lets talk about the tangents to a circle drawn from a point

outside the circle:

- They are equal in length

- They are perpendicular to the radii at the point of tang-ency

- If we join the points of tang-ency withe the center of the circle

and join the outside point with center of the circle, we

formed two congruent triangles

* Now lets check our problem

- AL and LB are two tangents to the circle O ant points A and B

∴ LA = LB ⇒ (1)

- OA and OB are radii in circle O

∴ OA = OB ⇒ (2)

∴ OA ⊥ AL and OB ⊥ BL ⇒ radius and tangent

∴ m∠OAL = 90° , m∠OBL = 90

∴ m∠OAL = m∠OBL ⇒ (3)

* From (1) , (2) , (3)

- The two triangles LAO and LBO are congruent ⇒ SAS

- SAS is one case of congruence

∵ The lengths of two sides and the measure of the including

angle between them in one triangle equal to the

corresponding sides and angles in the second triangle,

then the two triangles are congruent

∴ m∠LOA = m∠LOB

∵ m∠AOB = 110°

∴ m∠LOA = m∠LOB = 110/2 = 55°

* In ΔLAO

∵ m∠ LAO = 90° , m∠LOA = 55°

∴ m∠ALO = 180 - (90 + 55) = 180 - 145 = 35°

* The measure of angle ALO = 35°

8 0

3 years ago

A line passes through the points (-3,-4) and (6,2)

Zanzabum

Answer: x - int : (3,0)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = y2-y1/x2-x1

= -4-2/-3-6

=-6/-9

= 2/3

y1 = 2

x1 =6

y - 2 = 2/3(x-6)

x -int: when y = 0, what is x?

0-2 = 2/3(x-6)

-2 = 2/3x - 4

2 = 2/3x

x=3

~Hope this helps!~

5 0

1 year ago

The population of Henderson City was 3,381,000 in 1994, and is growing at an annual rate 1.8%

liq [111]

<h2>In the year 2000, population will be 3,762,979 approximately. Population will double by the year 2033.</h2>

Step-by-step explanation:

Given that the population grows every year at the same rate( 1.8% ), we can model the population similar to a compound Interest problem.

From 1994, every subsequent year the new population is obtained by multiplying the previous years' population by $\frac{100+1.8}{100}$ = $\frac{101.8}{100}$ .

So, the population in the year t can be given by $P(t)=3,381,000\textrm{x}(\frac{101.8}{100})^{(t-1994)}$

Population in the year 2000 = $3,381,000\textrm{x}(\frac{101.8}{100})^{6}$ = $3,762,979.38$

Population in year 2000 = 3,762,979

Let us assume population doubles by year $y$ .

$2\textrm{x}(3,381,000)=(3,381,000)\textrm{x}(\frac{101.8}{100})^{(y-1994)}$

$log_{10}2=(y-1994)log_{10}(\frac{101.8}{100})$

$y-1994=\frac{log_{10}2}{log_{10}1.018}=38.8537$

$y$ ≈ $2033$

∴ By 2033, the population doubles.

4 0

3 years ago

WILL MARK BRAINLIEST<br><br> What is the surface area of the prism?

xxMikexx [17]

I do not know this answer but I think you have to number and times it by 2

8 0

3 years ago

Can someone help me with this math homework please!

Andreyy89

Answer:

(B) h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.

Step-by-step explanation:

You've probably seen this function notation format before, most likely f(x). Other common ones are g(x) and p(x). The f, g, and p are just function names, like the h in this question.

The t in the parentheses is the input, because it's the same as the t in 210 - 15t.

Together, h(t) is the output, which is the exact same as y if you used the formula y = mx + b.

Hope it helps (●'◡'●)

4 0

3 years ago