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Anvisha [2.4K]
2 years ago
9

GIVEN: LJ || WK || AP, PL || AG.

Mathematics
1 answer:
galina1969 [7]2 years ago
8 0

Answer:

∠1 ≅ ∠2 ⇒ proved down

Step-by-step explanation:

#12

In the given figure

∵ LJ // WK

∵ LP is a transversal

∵ ∠1 and ∠KWP are corresponding angles

∵ The corresponding angles are equal in measures

∴ m∠1 = m∠KWP

∴ ∠1 ≅ ∠KWP ⇒ (1)

∵ WK // AP

∵ WP is a transversal

∵ ∠KWP and ∠WPA are interior alternate angles

∵ The interior alternate angles are equal in measures

∴ m∠KWP = m∠WPA

∴ ∠KWP ≅ ∠WPA ⇒ (2)

→ From (1) and (2)

∵ ∠1 and ∠WPA are congruent to ∠KWP

∴ ∠1 and ∠WPA are congruent

∴ ∠1 ≅ ∠WPA ⇒ (3)

∵ WP // AG

∵ AP is a transversal

∵ ∠WPA and ∠2 are interior alternate angles

∵ The interior alternate angles are equal in measures

∴ m∠WPA = m∠2

∴ ∠WPA ≅ ∠2 ⇒ (4)

→ From (3) and (4)

∵ ∠1 and ∠2 are congruent to ∠WPA

∴ ∠1 and ∠2 are congruent

∴ ∠1 ≅ ∠2 ⇒ proved

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A sequence is defined by the recursive function f(n + 1) =1/3 f(n). if f(3) 9= , what is f(1)
gayaneshka [121]

Answer:

f(1) = 81

Step-by-step explanation:

f(n + 1) = 1/3 f(n)

⇔ f(n) = 3 × f(n + 1)

……………………………

if f(3) = 9  ⇒  f(2) = 3 × f(3) = 3 × 9 = 27

Then

f(1) = 3 × f(2) = 3 × 27 = 81

5 0
1 year ago
In ΔNOP, n = 910 inches, o = 110 inches and p=820 inches. Find the measure of ∠P to the nearest degree.
Sophie [7]

Given:

In ΔNOP, n = 910 inches, o = 110 inches and p=820 inches.

To find:

The measure of ∠P to the nearest degree.

Solution:

According to the law of cosine:

\cos A=\dfrac{b^2+c^2-a^2}{2bc}

Using law of cosine in triangle NOP, we get

\cos P=\dfrac{n^2+o^2-p^2}{2no}

Putting the given values, we get

\cos P=\dfrac{(910)^2+(110)^2-(820)^2}{2(910)(110)}

\cos P=\dfrac{828100+12100-672400}{200200}

\cos P=\dfrac{167800}{200200}

\cos P=0.83816

Taking cos inverse on both sides, we get

P=\cos^{-1}(0.83816)

P=(33.05367)^\circ

P\approx 33^\circ

Therefore, the measure of ∠P is 33°.

8 0
2 years ago
Read 2 more answers
Glven:
Viktor [21]
I think it is D or it could be c?
6 0
3 years ago
James and Jada together have $60. James has $9 more than twice Jada’s amount. How much money does each have?
sukhopar [10]

Answer:

$43 and

$17

Step-by-step explanation:

Let the amount James have be A and that of jada be B

Given

James and jada have $60 together

That’s

A + B = 60

And james A has $9 more than twice jada’s amount

That’s

A = 9 + 2B

We now have two equations

1. A + B = 60 and

2. A = 9 + 2B

Now put 9 + 2B as A in equation one

A + B = 60

9 +2B + B = 60

9 + 3B = 60

Subtract 9 from both sides

9 - 9 + 3B = 60 - 9

3B = 51

Divide both sides by 3

3B/3 = 51/3

B = 17

Jada has $17

Recall

A = 9 + 2B

And B = 17

Therefore

A = 9 + 2 x 17

A = 9 + 34

A = 43

James has $43

Therefore, James has $43 while jada has $17

7 0
3 years ago
-27=-3p+15-3p what is the answer
Ulleksa [173]
Because they have lettters the (p's) go together which is -6p and then you have the +15 left so you add that on the end , your answer is -6p + 15
3 0
3 years ago
Read 2 more answers
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