evaluate the function at each specified
value of the independent variable and simplify
Answers
Answer:
Evaluating the function is just replacing the "x" (or the "t" in the second case) by the value that we want:
1) q(x) = 1/(x^2 - 9)
a) q(0) = 1/(0^2 - 9) = 1/(-9) = - 1/9
b) q(3) = 1/(3^2 - 9) = 1/(9 - 9) = 1/0 = indetermined, we could think this as:
[tex]\lim_{x \to \ 3} q(x) = infinity[/tex]
c) q(y + 3) = 1/( (y + 3)^2 - 9) = 1/(y^2 + 6*y + 9 - 9) = 1/(y^2 + 6*y)
2) q(t) = (2*t^2 + 3)/t^2
a) q(2) = (2*2^2 + 3)/2^2 = (2*4 + 3)/4 = 11/4
b) q(0) = (2*0^2 + 3)/0^2 = 3/0
Again, we can not divide by zero, this is simmilar to the case 1.b
c) q(-x) = (2*(-x)^2 + 3)/(-x)^2 = (2*x^2 + 3)/x^2
Related Questions
what is the measure of <x
Answers
Answer:
x = 104°
Step-by-step explanation:
180-76=104
z = 104°
z and x are vertical from each other, therefore, z = x
what is the equation of a line in slope intercept form that passes through points (4,3) and (1,-6)
pls help quick : )
Answers
Answer:
y = 3x-9give me brainliest please
Step-by-step explanation:
To find the equation of a line that passes through two points, use point-slope form.
[tex]y-y_{1} = m(x-x_{1})[/tex] ...
where [tex](x_{1}, y_{1})[/tex] is the first point, and [tex]m[/tex] is the slope.
Start with the slope (m). To find the slope, you find the change in y over change in x, or [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{-6-3}{1-4}[/tex] = [tex]\frac{-9}{-3}[/tex] = 3
[tex]m=3[/tex]
Then, put the values into point-slope equation.
[tex]y-y_{1} = m(x-x_{1})[/tex] = [tex]y-3 = 3(x-4)[/tex] = [tex]y-3 = 3x-12[/tex] = [tex]y = 3x-9[/tex]
Which of the sets of ordered pairs represents a function?
P = {(3, 5), (−1, 5), (4, −6), (2, 9)}
Q = {(7, −2), (5, 9), (−1, 8), (5, −3)}
Answers
Answer:
P
Step-by-step explanation:
P tells us that the Domain: 3,-1,4,2 doesn't repeat
Q does repeat its Domain: 7,5,-1,5
Reminder that in order for a line of ordered pairs to be a function the domain number Shouldn't repeat, That doesn't mean that the range cant repeat.
Example: (5,-3), (5,9) Not a function
(-1,-6), (7,-6) Function
Out of the two set given, the set of ordered pairs that represents a function is: P = {(3, 5), (−1, 5), (4, −6), (2, 9)}.
What is a Function?A set of ordered pairs that has one exact y-value assigned to each x-value is considered a function.
In set P, all x-values has exactly one y-value, while in set P, the x-value, 5, has two different y-values, 9 and -3.
Therefore, the set of ordered pairs that represents a function is: set P.
Learn more about a function on:
https://brainly.com/question/10439235
#SPJ2
A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below. What is the solution to the system of equations?
Answers
Answer:
The solution to the system of equations is x = 4 and y = 2.
Step-by-step explanation:
From statement we know that the first line is [tex]y = 0.5\cdot x[/tex]. The second line is determined by knowing two distinct points and solving the resulting system of equations by definition of the equation of the line:
[tex](x_{1},y_{1}) = (3,1)[/tex] and [tex](x_{2}, y_{2}) =(-5,-7)[/tex]
[tex]3\cdot m + b = 1[/tex] (1)
[tex]-5\cdot m + b = -7[/tex] (2)
The solution of the system of equations is:
[tex]m = 1[/tex], [tex]b = -2[/tex]
The second line is represented by [tex]y = x-2[/tex]. And the resulting system of equations is:
[tex]0.5\cdot x -y = 0[/tex] (3)
[tex]x-y = 2[/tex] (4)
The soltuion to the system of equations is:
[tex]x = 4[/tex], [tex]y = 2[/tex]
The solution to the system of equations is x = 4 and y = 2.
At Gary's car wash 49 cars can be washed in 4 hours. At this rate, how many cars can be washed in 8 hours?
Answers
Answer:
98
Step-by-step explanation:
49 + 49 = 98
Solve for n
8-n-4
PLZ help
Answers
Two sides of a triangle are 12 meters and 16 meters. What is the largest the third side can be?
A) 22 meters
B) 24 meters
C) 26 meters
D) 28 meters
Answers
Answer:
The largest third side would be 26 meters.
Option B is correct.
Step-by-step explanation:
We are given two sides of triangle 12 meters and 16 meters.
We need to find What is the largest the third side can be?
We know that the length of third side should be less than the sum of two sides of triangle
third side < length of first side + length of second side
third side < 12+16
third side < 28
So, the length of third side should be less than 28
We need to find the largest the length of third side can be: from options 22, 24 and 26. We would not consider 28 because length should be less than 28.
So, the largest third side would be 26 meters.
Option B is correct.
Write the equation in slope-intercept form y−6=−2/5(x−10)
Answers
Answer: y = -2/5x + 10
Step-by-step explanation:
y − 6 = − 2/5 (x − 10)
do distributive property
y - 6 = -2/5x + 4
add six to both sides
y = -2/5x + 10
boom the answer :v
pls help me its also easy
Answers
Answer:
C
Step-by-step explanation:
Ferdinand's equipment is higher than Rachel's equipment.
What will be the coordinates of point M of the image after the rotation?
0 (-4, 1)
0 (-1,4)
O (1-4)
O (4,1)
Answers
explain- i’m smart jk
Can someone please help me with this problem? I don’t understand how to do it..
Answers
Answer:
y=x+2
Step-by-step explanation:
y=mx+b
m is slope
b is y intercept
it crosses the y intercept at (0,2) therefore b is 2
rise over run is 1 so slope is 1
fill in
y=1x+2
or y=x+2
you can fill in any (x,y) point into this
The speed of light is 3 x 10^8 meters/second. If the sun is 1.5 X 10^11 meters from earth, how many seconds does it take the sunlight to reach the Earth? (Time = Distance/Speed).
Answers
Answer:
Time = 500 seconds or 8.333 minutes
Step-by-step explanation:
Time = Distance/Speed
Speed of light = 3 x 10^8 meters/second
Distance=1.5 X 10^11 meters
Time = 1.5 X 10^11 meters/3 x 10^8 meters/second
We solve using the scientific notation. When 8 is taken to the top it is subtracted from 11 ( the base 10 is the same -- laws of exponents)
Dividing 1.5 by 3 gives 0.5 .
Time = 1.5 X 10^(11- 8) meters/3 meters/second
Time = 0.5 X 10^3 seconds
Time = 500 seconds
Dividng seconds with 60 will give minutes
Time= 500/60 = 8.333 minutes
The measures of the angles of a triangle are shown in the figure below
Answers
Answer:
they very much are there
Step-by-step explanation:
Answer:
37.5 degrees
Step-by-step explanation:
All triangle angles must sum up to 180 degrees
63 + 90 = 153
153 = 4x + 3
150 = 4x
37.5 = x
Hello sam hhehehe .dk ;
Answers
Answer:
hello
Step-by-step explanation:
If a person who weighs 70 kilograms has a brain that weighs 1.4 kilograms, what percent of the persons body weight is brain
Answers
Answer:
the answer would be around 1.5 to two percent
Step-by-step explanation:
Solve for x. Round your answer to the nearest tenth if necessary.
Answers
Step-by-step explanation:
sin90 = sinx
19 17
sin x=0.8947
x=63.47°
Question is in image
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]y = - \frac{1}{4} x + 4 \\ [/tex]
Multiply sides by 4
[tex]4 \times y = 4 \times ( - \frac{1}{4} x + 4) \\ [/tex]
[tex]4y = 4 \times ( - \frac{1}{4} x) + 4 \times 4 \\ [/tex]
[tex]4y = - x + 16[/tex]
Add sides x
[tex] + x + 4y = + x - x + 16[/tex]
[tex]x + 4y = 16[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The correct answer is (( C )) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Plz help me give 13 point it’s timed helpplz
Answers
Answer:
yyyy
Step-by-step explanation:
My book is 79 pages. I have been reading 10 pages each day. There are 9 pages left to read. How many days have I been reading the book? Draw a model to show your thinking. Justify your answer.
Answers
Answer:
7 days
Step-by-step explanation:
If there are 9 pages left, that means you have already read 70 pages.
Since you read 10 pages a day, we can find how many days you have been reading the book by dividing 70 by 10:
70/10
= 7
This means you have been reading the book for 7 days
Answer:
7 days
Step-by-step explanation:
With 9 pages left take 79-9 to get 70 pages.
70 pages at 10 pages a day is 70/10 and you get 7 or 7 days.
Is the following relation a function, yes or no?
{(-3,4),(3,1),(5,7), (8,9), (10, 12)}
yes
no
Answers
The function rule is that each input (x value in (x,y)) should only equal to one output and one output (y value) can have more than one input.
✯the following is a function, so yes.
Answer:
yes
Step-by-step explanation:
Identify the independent and dependent variable for the given situation. D = 5t
Answers
Answer:
d = dependant; t = independant
Step-by-step explanation:
The d value is dependant on the t value, therefore it is the dependant. The t is the only valuable that can be changed in the equation, therefore being the independant.
Answer:
[tex]D[/tex] = dependent; [tex]t[/tex] = independent
Step-by-step explanation:
[tex]D[/tex] is the independent variable since its value relies/depends on the value of [tex]t[/tex].
[tex]t[/tex] is the independent variable since it is the input variable which can be changed.
Hope this helps :)
simplify (x^2+3)^2-(x^2-1)^2
Answers
Answer:
Simplify the expression.
8x² + 8
Answer:
8(x^2 +1)
Step-by-step explanation:
(x^2 + 3)^2 - (x^2 - 1)^2
(x^2 + 3 - (x^2-1)) • (x^2 + 3 + (x^2 - 1))
(x^2 + 3 - x^2 + 1) • (x^2 + 3 + (x^2 - 1)
(3 + 1) • (x^2 + 3 + x^2 - 1)
4(2x^2 + 1)
4 • 2(x^2 + 1)
8(x^2 +1)
Match each expression to correct number line model.
I NEED THIS RIGHT AWAY!
(no one answered my last one so i hope this gets answered quick.)
Answers
2. 1.5+-2.5
3. -1.5+-2.5
4. 1.5+-2.5
Which chemical equation is balanced?
Question 2 options:
CH4 + O2 → H2O + CO2
CH4 + O2 → 2H2O + CO2
6CH4 + O2 → 2H2O + 2CO2
CH4 + 2O2 →2H2O + CO2
help
Answers
Step-by-step explanation:
CH4 + 2O2 →2H2O + CO2
the answer
Answer:
The balanced chemical equation of the given reaction are;
b.CH4 + 202-> 2H20 + CO2
Step-by-step explanation:
C=C
H4=2H2
2O2=O2+2O(2O2)
I Think it helps you.
Determine if the following graph is a function. Find the
domain and range of the following graph. Write your
answer in inequality form.
Answers
Answer:
Yes, it is a function.
The domain is (∞,∞) and the range is (∞,5].
Step-by-step explanation:
A function needs to pass the vertical line test: It can only have one x value and one y value at a time. You simply hold a ruler to your screen and drag it from left to right (or vice versa) and see if the function touches the ruler once. If it touches once at any given point, it's a function!
The domain is (∞,∞) because there is a line on both ends- meaning it stretches infinitely. The range is (∞,5] since it goes down infinitely and stops at y = 5.
i will give brainliest if correct answer
Answers
4w-24≤-12
4w≤12
w≤3
the answer i got is fifth first
PLS HELP!!!
PLS FIND 13 and 15!!
Answers
Answer:
hi how are you doing
Step-by-step explanation:
anyone stressed?? vent to me. and (so this will count as a question)
Laura earns $115 a month babysitting. If she saves all of the
money she earns in June and July and uses it to buy a bicycle
that cost $158, how much money will she have left?
A. $230,00
B. $43.00
C. $60.00
D. $72.00
Answers
Answer:72
Step-by-step explanation:
115+115=230
230-158=72
If you add the 115 a month that she earns from babysitting, then add both the months pay together, than subtract 158(cost of the bicycle) by the total pay, you should get 72$
Answer: D. $72
Step-by-step explanation:
If she earns $115 a month and June and July is a combination of two months then we will have to find the amount she earn toegther in June and July by multiplying 2 by $115.
2(115) = 230
She earned $230 in those months, and if the bicycle cost $158 , then we will have to subtract $158 from $230 to find her remaining amount.
$230 - $158 = $72
A 3-foot rain barrel is being filled from the runoff of a roof. The barrel has already collected 2.75 feet of water. For
every additional inch of rainfall into the barrel, the level of water in the rain barrel rises by 0.75 inch.
What is the y-intercept of the linear model representing the change in height of water, in inches, based on the
rainfall, in inches?
Answers
ssssssssssssssssssssssssssssss
What are the greatest common factor of 9a^b and 30ab^3?
Answers
Answer: 3ab IF a^b does NOT mean a to the power of b!
I believe you mean 9a²b and 30ab³
If you really mean 9aᵇ and 30ab³, then the GCF is 3a.
Step-by-step explanation:
the factors of 9 are 3*3 The factors of 30 are 2*3*5.
The only common factor of 9 and 30 is 3
a is a common factor of a and a²
b is a common factor of b and b³