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3 years ago

Simplify. 18x + 3xy + 5y −2(6xy − 2y + 4) A) 18x − 9xy + 9y − 8 B) 18x + 9xy + 9y − 8 C) 18x + 9xy − 9y + 8 D) 18x − 9xy + y − 8

Mathematics

2 answers:

Karolina [17]3 years ago

8 0

18x+3xy+5y-2(6xy-2y+4)

18x+3xy+5y-12xy+4y-8

18x-9xy+9y-8

The answer is D

vova2212 [387]3 years ago

7 0

Answer:

Option A.

Step-by-step explanation:

The given expression is

$18x+3xy+5y-2(6xy-2y+4)$

We need to find the simplified form of the given expression.

Using distributive property, we get

$18x+3xy+5y-2(6xy)-2(-2y)-2(4)$

$18x+3xy+5y-12xy+4y-8$

Combine like terms.

$18x+(3xy-12xy)+(5y+4y)-8$

$18x-9xy+9y-8$

Therefore, the correct option is A.

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Use the Law of Cosines to find the values of x and y. (PLEASE HELPPP!!!!)

vredina [299]

Answer:

$x = 49.8^\circ\\y = 54.6^\circ$

Step-by-step explanation:

Kindly refer to the image attached in the answer region for labeling of triangle.

AB = 16

BC = 19

AC = 15

$\angle ABC = x^\circ\\\angle ACB = y^\circ$

We have to find the angles x and y i.e. $\angle B \text{ and }\angle C$ .

Formula for cosine rule:

$cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}$

Where

a is the side opposite to $\angle A$ ,

b is the side opposite to $\angle B$ and

c is the side opposite to $\angle C$ .

$\Rightarrow cos x = \dfrac{19^{2}+16^{2}-15^{2}}{2 \times 19 \times 16}\\\Rightarrow cos x = \dfrac{392}{608} \\\Rightarrow x = 49.8^\circ$

Similarly, for finding the value of y:

$cos C = \dfrac{a^{2}+b^{2}-c^{2}}{2ab}\\\Rightarrow cos y = \dfrac{19^{2}+15^{2}-16^{2}}{2 \times 19 \times 15}\\\Rightarrow cos y = \dfrac{330}{570}\\\Rightarrow y = 54.6^\circ$

Hence, the values are:

$x = 49.8^\circ\\y = 54.6^\circ$

7 0

3 years ago

A bag contains yellow marbles and blue marbles, 42 in total. The number of yellow marbles is 2 less than 3 times the number of b

Juliette [100K]

There are 31 yellow marbles. Work is attached.

4 0

3 years ago

Read 2 more answers

25 Points ! Write a paragraph proof. Given: ∠T and ∠V are right angles. Prove: ∆TUW ∆VWU

vladimir2022 [97]

Answer:

Δ TUW ≅ ΔVWU ⇒ by AAS case

Step-by-step explanation:

* Lets revise the cases of congruent for triangles

- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and

including angle in the 2nd Δ

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ

≅ 2 angles and the side whose joining them in the 2nd Δ

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

and one side in the 2ndΔ

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse

leg of the 2nd right angle Δ

* Lets solve the problem

- There are two triangles TUW and VWU

- ∠T and ∠V are right angles

- LINE TW is parallel to line VU

∵ TW // VU and UW is a transversal

∴ m∠VUW = m∠TWU ⇒ alternate angles (Z shape)

- Now we have in the two triangles two pairs of angle equal each

other and one common side, so we can use the case AAS

- In Δ TUW and ΔVWU

∵ m∠T = m∠V ⇒ given (right angles)

∵ m∠TWU = m∠VUW ⇒ proved

∵ UW = WU ⇒ (common side in the 2 Δ)

∴ Δ TUW ≅ ΔVWU ⇒ by AAS case

7 0

3 years ago

Read 2 more answers

Which answer choice shows the decimal 23.476 written in expanded form?

Sergio039 [100]

Answer: 23.476 = 20+3+0.4+0.07+0.006

Step-by-step explanation:

I think you were supposed to write down the choices but I will guess the answer is this one:

23.476 = 20+3+0.4+0.07+0.006

Hope I helped!

6 0

2 years ago

the function h(t)=-16t2+144 represents the height, h(t), in feet, of an object from the ground at t second after its dropped. A

blagie [28]

The domain is the limits of the function. Since time doesnt go negative, start with 0. At time 0, the height is

-16(0)^2 + 144 = 144ft

Then, solve for t to find the upper limit for t, which is when the height is zero (since you're dropping the object).

-16t^2 + 144 = 0
-16t^2 = -144
t^2 = 9
t = sqrt(9)
t = 3

The domain is 0 to 3 seconds.

5 0

3 years ago