Question

Help all of these are confusing me

Answer 1

• b
• b
• a
• b

Explanation:

There are a few algebraic, geometric, and trig relations you are expected to remember. These come into play in this set of questions.

• vertex form for equation of a parabola: y = a(x -h)² +k, has vertex at (h, k)
• Sine Law relates triangle sides and their opposite angles: a/sin(A) = b/sin(B)
• Cosine Law relates triangle sides and the angle between two of them: c² = a² +b² -2ab·cos(C)
• SOH CAH TOA reminds you of trig relations in a right triangle
• relationships of corresponding sides and angles in congruent and similar triangles: angles are congruent; sides are congruent or proportional.

When solving any problem, the first step is to understand what is being asked. The second step is to identify the relevant information and relationships that can help you answer.

1)

You are asked for the equation of a parabola with a given vertex. The vertex form equation will be useful. We can assume a scale factor ('a') of 1.

For vertex (h, k) = (1, -4) and a=1, the vertex form equation is ...

y = a(x -h)² +k

y = 1(x -1)² +(-4)

y = (x -1)² -4

2)

You are given 3 sides and want to find an angle. The useful relation in this case is the Cosine Law. (If you wanted to use the Sine Law, you would already need to know an angle.)

3)

The mnemonic SOA CAH TOA reminds you that the cosine relation is ...

Cos = Adjacent/Hypotenuse

The side adjacent to angle C is marked 4; the hypotenuse is marked 5. The desired ratio is ...

cos(C) = 4/5

4)

The measure x is also the measure of side AB. The similarity statement lists those letters as the first two. It also lists the letters DE as the first two. The other given side in ΔABC is BC, corresponding to side EF in the smaller triangle. Corresponding sides are proportional, so we have ...

AB/DE = BC/EF

x/6 = 10/4

We can find the value of x by multiplying this equation by 6:

x = 6(10/4) = 60/4

x = 15

Please note that BC is the shortest side in ΔABC. This means x > 10. There is only one such answer choice. (No math necessary.)

Answer 2

see explanation

Explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (1, - 4 ) and a = 1 , then

y = (x - 1)² - 4 → b

------------------------------------

given 3 sides of a triangle then an angle may be found using the cosine law. → b

if the 3 sides are a, b, c then

cosA =
`(b^2+c^2-a^2)/(2bc)` ← allowing ∠ A to be found

--------------------------------------

cosC =
`(adjacent)/(hypotenuse)` =
`(BC)/(AC)` =
`(4)/(5)` → a

-----------------------------------------

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

`(AB)/(DE)` =
`(BC)/(EF)` ( substitute values )

`(x)/(6)` =
`(10)/(4)` ( cross- multiply )

4x = 6 × 10 = 60 ( divide both sides by 4 )

x = 15 → b