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2 years ago

Help help help help help

Mathematics

1 answer:

NemiM [27]2 years ago

6 0

I’m only 70% positive about my answer, but I believe the answer is A) g(x) = |x+4| - 2.

If I’m correct, the numbers on the inside of the absolute marks are an indication of a horizontal shift of the function and you go the opposite direction of the sign. In this case, it’s a shift to the left (looking at the graph, 4) Then the outside number tells you how far you shift vertically (down 2, following the negative sign this time).

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HELP CONGRUENCE BY SAS AND SSS WILL GIVE BRAINLIEST IF CORRECT

balu736 [363]

Answer:

1. Cong SSS 2.Cong SSS 3.Not Cong 4.Not Cong 5.Cong SAS 6.Cong SSS 7.Cong SAS 8.Cong SSS 9.Cong SSS 10.Cong SAS 11.d 12.a 13.a 14.b 15.a

Step-by-step explanation:

5 0

2 years ago

Anton is approved for overtime at his job. Last week he worked a total of 45 hours , how many hours of overtime did he work

pochemuha

Answer:

B. 5 Hours

Step-by-step explanation:

any work over 40 hours in a 168 hour period is counted as overtime. So take 45 (his total) and subtract it by 40 and you get 5. 45 - 40 = 5 hours.

8 0

2 years ago

How to use trig to find missing side or angle of right triangles.

andrew11 [14]

Explanation

Right triangles are triangles with one right angle i.e. one angle with a measure of 90° so when we deal with this type of figures we know at least one of its internal angles. The opposite side to the right angle is known as the hypotenuse whereas the other two sides are called legs.

Trigonometric functions in right triangles give us the following identities:

$\begin{gathered} \tan x=\frac{\text{opposite side}}{\text{adjacent side}} \\ \cos x=\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \sin x=\frac{\text{opposite side}}{\text{hypotenuse}} \end{gathered}$

We also have the Pythagorean theorem that states that the square of the hypotenuse is the sum of the squares of the legs.

Let's imagine that we have a right triangle like the following:

If we want to find the missing angles A and/or B we need to know at least two sides of the triangle.

For example, if we want to find B and we have b and a we can use the tangent of B and its inverse the arctangent (tan^(-1)):

$\tan B=\frac{b}{a}\rightarrow B=\tan^{-1}(\frac{b}{a})$

If we know a and c we can find B using its cosine:

$\cos B=\frac{a}{c}\rightarrow B=\cos^{-1}(\frac{a}{c})$

If we know b and c then we can use the sine:

$\sin B=\frac{b}{c}\rightarrow B=\sin^{-1}(\frac{b}{c})$

We can also do the same for angle A, we just need to use its corresponding opposite side and adjacent side. And that's how you find a missing angle using trigonometry in a right triangle.

If we are looking for a missing side we can also use trigonometry. In order to find a missing side we need two other sides or another side and an angle. For example, let's assume that we want to find side a.

If we have b and c then we just need to use the Pythagorean theorem:

$c^2=a^2+b^2\rightarrow a=\sqrt{c^2-b^2}$

If we have b and A then we can use the tangent of A to built an equation for a:

$\tan A=\frac{a}{b}\rightarrow a=b\cdot\tan A$

If we have b and B we can use the tangent of B:

$\tan B=\frac{b}{a}\rightarrow a=\frac{b}{\tan B}$

If we have A and c we can use the sine of A:

$\sin A=\frac{a}{c}\rightarrow a=c\cdot\sin A$

If we have B and c we can use the cosine of B:

$\cos B=\frac{a}{c}\rightarrow a=c\cdot\cos B$

And that's how you find a missing side using trigonometry.

8 0

2 months ago

A hotel must increase its price by 5% per night, if the new price is $168 per night. What was the original cost?

ValentinkaMS [17]

Hey there! I'm happy to help!

We see that if you add 5% to the original cost, we have $168 as our cost. This means that 105% of the original cost is 168. Let's set up an equation to find the original cost. Let's call our original cost c.

To turn a percent into a decimal, you divide by 100.

1.05c=168

We divide both sides by 1.05.

c=160

Therefore, the original cost was $160.

Have a wonderful day! :D

5 0

2 years ago

Two integers, a and b, have a product of 36. What is the least possible sum of a and b?

Minchanka [31]

<h3>Answer: 12</h3>

==============================================================

Explanation:

The two integers multiply to 36, so,

ab = 36

which solves to

a = 36/b

Then we want to add the numbers such that we get the smallest possible result.

a+b = (36/b)+b

So we want (36/b)+b to be as small as possible.

Let's say we replace b with x and we consider this function

f(x) = (36/x) + x

The goal is to find when f(x) is smallest, ie, we want to minimize the function.

If we were to graph out the function, we get the curve shown below.

To make things easier, we'll only focus on positive values of x.

The lowest part of the curve is what we're after. Using the "minimum" function/feature on the graphing calculator, we would then find the lowest point occurs at (6,12). This point is considered a local minimum because it's the lowest point in that given neighborhood of x values.

So the input x = 6 leads to the smallest output f(x) = 12.

This in turn means b = 6 is going to pair with a = 36/b = 36/6 = 6.

In short, a = 6 and b = 6.

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

As a check,

a*b = 6*6 = 36

a+b = 6+6 = 12

We can make a table of various values to help confirm that 12 is the smallest sum.

Side note: If you're not allowed to use a graphing calculator, then you'll need to use calculus.

8 0

2 years ago