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3 years ago

Which of the following is a key property of the linear parent function?

1 answer:

6 0

Does this question have the following choices?If so, the answer would be letter D. it has a slope of zero, hence it has a slope of m which is equal to 1 and a y-intercept that is (0,0)
Choices:
A.) It is a curved line.

B.) It is in quadrants I and II

C.) It does not go through the orgin.

D.) it has a slope of zero.

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kathi starts with a number. she adds 3 to her number, then doubles the result. finally, she subtracts 7. if she ended with 9 wha

11111nata11111 [884]

An equation is:
2(x+3)-7=9
Distribute the 2
2(x)+2(3) -7=9
2x+6-7=9
Combine like terms
2x-1=9
Add one to both sides
2x-1+1=9+1
2x=10
Divide both sides by two to isolate the variable.
2x/2=10/2
x=m

6 0

3 years ago

Read 2 more answers

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago

The ability to examine the variability of a solution due to changes in the formulation of a problem is an important part of the

PilotLPTM [1.2K]

Answer:

Sensitivity Analysis

Step-by-step explanation:

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs.

4 0

3 years ago

Can someone please help me

mixas84 [53]

Answer:

1/3

Step-by-step explanation:

The slope of a line is rise over run, aka. rise/run. You will need to "rise" 1 unit up and "run" three units to the right to reach the next point.

5 0

3 years ago

ALGEBRA evaluate each eapression if x= -3, y=8, and z=-12<br> y-10 <br> 12-z<br> 3-x<br> z-24

Vinvika [58]

Answer:

-2
24
6
-36

Step-by-step explanation:

Put the numbers in place of the corresponding letter and do the arithmetic.

y -10 = 8 -10 = -2

12 -z = 12 -(-12) = 24

3 -x = 3 -(-3) = 6

z -24 = -12 -24 = -36

6 0

3 years ago