A line passes through the point (-8 7) and has a slope of -5/4

Simplify the expression. (–2)5 16 –10 –32 32

BigorU [14]

Answer:

the answer is -10

Step-by-step explanation:

Its basically multiplication

4 0

2 years ago

Would appreciate the help !

aleksandr82 [10.1K]

This is one pathway to prove the identity.

Part 1

$\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{1}{\tan(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\cot(\theta) = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)*\sin(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)(1-\cos(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\$

Part 2

$\frac{\sin^2(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)-\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-(\cos(\theta)-\cos^2(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-\cos(\theta)+\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\$

Part 3

$\frac{\sin^2(\theta)+\cos^2(\theta)-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)} \ \ {\checkmark}\\\\$

As the steps above show, the goal is to get both sides be the same identical expression. You should only work with one side to transform it into the other. In this case, the left side transforms while the right side stays fixed the entire time. The general rule is that you should convert the more complicated expression into a simpler form.

We use other previously established or proven trig identities to work through the steps. For example, I used the pythagorean identity $\sin^2(\theta)+\cos^2(\theta) = 1$ in the second to last step. I broke the steps into three parts to hopefully make it more manageable.

3 0

2 years ago

The price of a calculator decreased from $20 to $18. What is the percent of decrease? *

anastassius [24]

Answer:

the parcentage is 111.11

4 0

2 years ago

What is the length of CD? In this diagram, AABC ~ AEDC. 20-% c * 7 21

d1i1m1o1n [39]

Answer:

$\frac{BC}{DC}=\frac{AC}{EC}$

$\frac{20-x}{x} =\frac{21}{7}$

$\frac{20-x}{x} =3$

$20-x=3x$

$4x=20$

$x=5$

$So, CD=5$

OAmalOHopeO

6 0

2 years ago

1. Write the inverse of equation of the function f(x) = x^2 - 4? 2. Sketch the inverse of the function f(x)= x^2 - 4 on graphing

Reptile [31]

Answer: 1) $\pm \sqrt{x+4}$

2) see graph

3) Choose one color from the graph

4) D: x ≥ -4

R: y ≥ 0 for $\sqrt{x+4}$ or y ≤ 0 for $-\sqrt{x+4}$

Step-by-step explanation:

1) To find the inverse, swap the x's and y's and solve for y:

Given: y = x² - 4

Swap: x = y² - 4

x + 4 = y²

$\pm \sqrt{x+4}=y$

2) see attachment. Red and Blue combined creates the graph of the inverse.

3) Choose either the positive (red graph) or the negative (blue graph).

red graph: $y= \sqrt{x+4}$

blue graph: $y= -\sqrt{x+4}$

4) Domain reflects the x-values of the function. The x-values for the red graph is the same as the blue graph so the answer will be the same regardless of which equation you choose.

Domain: x ≥ 0

Range reflects the y-values of the function. The y-values differ between the positive and negative inverse functions. Positive is above the x-axis. Negative is below the x-axis.

Range (red graph): y ≥ 0 for $y= \sqrt{x+4}$

Range (blue graph): y ≤ 0 for $y= -\sqrt{x+4}$

4 0

3 years ago