Answer:
"a removable discontinuity that can be removed by extending the function to include f(1) = 13"
Step-by-step explanation:
We have the function:
[tex]f(x) = \frac{x^2 + 11*x - 12}{x - 1}[/tex]
Here we have a problem when x = 1, because that makes the denominator to be equal to zero.
For now, let's see what happens to the numerator when x = 1
1^2 + 11*1 - 12 = 12 - 12 = 0
So x = 1 is a root of the numerator.
Let's find the other root of the numerator, here we can use Bhaskara's formula:
[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*(-12)} }{2*1} = \frac{-11 \pm 13}{2}[/tex]
Then the two roots are:
x = (-11 + 13)/2 = 1
x = (-11 - 13)/2 = -12
And remember that a quadratic equation:
y = a*x^2 + b*x + c
With roots p and k, can be written as:
y = a*(x - p)*(x - k)
Then we can rewrite our numerator as:
1*(x - 1)*(x - (-12)) = (x - 1)*(x + 12)
Replacing that in the equation for f(x), we get:
[tex]f(x) = \frac{x^2 + 11*x - 12}{x - 1} = \frac{(x - 1)*(x + 12)}{(x - 1)} = \frac{x - 1}{x -1} *(x + 12)[/tex]
f(x) = x + 12
And, when evaluated in x = 1, we get:
f(1) = 1 + 12 = 13
Then the correct option is:
"a removable discontinuity that can be removed by extending the function to include f(1) = 13"
Answer:
C
Step-by-step explanation:
I said so
Type an equation for the
following pattern.
X
у
1
16/3
2.
14/3
[?]
x + [ ]
y =
3
4
4
10/3
5
8/3
Answer:
y = -2/3 x + 6
Step-by-step explanation:
Using the coordinates (1, 16/3) and (3,4)
Slope m = 4-16/3/3-1
Slope m = -4/3 * 1/2
Slope m = -2/3
For the y-intercept
Substitute (3,4) and m = -2/3 into y =mx+b
4 = -2/3(3) + b
4 = -2 + b
b = 4 + 2
b = 6
Get the required equaton;
Recall that y = mx+b
y = -2/3 x + 6
Find the median of the data.
93.81.94.71.89.92.94.99
The median is
Find the mode(s) of the data,
Step-by-step explanation:
MEDIAN
71, 81, 89, 92, 93, 94, 94, 99
92 + 93 = 185 / 2 = 92.5
The median is 92.5
MODE
71, 81, 89, 92, 93, 94, 94, 99
The mode is 94
What is sin 49° to the nearest tenth
Answer:
50
Step-by-step explanation:
50???
Answer:
sin49° = 0.75471
sin 49° = 0.75471
sin 49 degrees = 0.75471
Step-by-step explanation:
Please help me I need to finish
The given triangle is a Right angled triangle,
By applying trigonometry :
[tex] \boxed{\tan( \theta) = \frac{opposite \: \: side}{adjacent \: \: side} }[/tex]
[tex] \tan(45 \degree) = \dfrac{7}{a} [/tex][tex]1 = \dfrac{7}{a} [/tex][tex]a = 7[/tex]_____________________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
If the following picture below was rotated about the y-axis, what 3-D shape would it make? ( HELP PLEASEE )
Rotating the figure about the y-axis results in the creation of a cylindrical figure of radius 2 units and 6 units tall.
Plz help me well mark brainliest if correct.....???
Answer:
D) line graph
Step-by-step explanation:
There is two lines on the graph that have points on each which makes this graph a line graph.
Hope this helped :)
Answer:
its a line graph
Step-by-step explanation:
is a graph that uses lines to connect individual data points displaying quantitative values over a specified time interval.
what is the ratio?
please answer quickly!!!!!
Answer:
3:1
Step-by-step explanation:
If you look at the sides, they all have the same factor of three, and dividing by three gets you to the smaller rectangular prism.
Evaluate the expression when x=7 and y=-3. 5y2-x
How can we represent three-dimensional figures in only two dimensions?
Answer: A three-dimensional figure has a length, a width, and a height. A net is a two-dimensional pattern of a three-dimensional figure, that can be folded to form the figure. Identify the net that we could fold in order to create this 3D figure. Match the 3D figure to the right with its appropriate net, below.
What is the answer for the diagram?
Answer:
1340-
Step-by-step explanation:
How many square feet is the world's largest pizza, including the crust?
(Be sure to show and/or explain your work, make your final answer clear, and include units)
The worlds largest pizza, including the crust, has a length of 131 feet
Answer:
The largest pizza has a total surface area of 1,261.65 m² (13,580.28 ft²) and was prepared by Dovilio Nardi, Andrea Mannocchi, Marco Nardi, Matteo Nardi and Matteo Giannotte (all Italy) from NIPfood at Fiera Roma, in Rome, Italy, on 13 December 2012.
Step-by-step explanation:
Sami made 23,400 last year in income from his job. He worked 30 hours per week and worked all 52 weeks of the year. What was his hourly pay rate?
Answer:
$15 per hour
Step-by-step explanation:
30 hours per week x 52 weeks in a year = 1560 hours per year
23,400 / 1560 = $15 per hour
Only please help #2,3,5, and 6
Answer:
3.$0.9
5.9:3 =3:1
Step-by-step explanation:
3.$5.40÷6=$0.9
Karrie is 24 years old. She took her age, divided by -3, added -7, then
multiplied by -4. Her result is 2 years older than her father's age. How old is
Karrie's father? *
Answer:
58 years old
Step-by-step explanation:
24/-3 is -8
-8+-7 is -15
-15*-4 is 60
60-2 is 58
Solve the inequity -3y + 80 > 110
Answer: y<-10
Step-by-step explanation:
i hope this help :)
Answer:
y<-10
Step-by-step explanation:
-3y+80>110
-80 -80
-3y>30
-y>10
y<-10 (when deviding by a negative, > switches to <)
the square pyramid shown below has a volume of 360 ft³. find the height of the pyramid
s= 8 feet
Answer:
Use MATH.WAY, it will help with any math problem
Step-by-step explanation:
Alex is a writer who writes poems and short stories. For an upcoming writer's workshop Alex wants to write some new works. He needs to determine how many poems and short stories he will have ready for the workshop. Alex figures that each poem will take him 30 hours and each short story will take him 70 hours. For the workshop Alex wants to have at least 4 poems and 3 short stories to display. If Alex has 840 hours of work time available, what solution represents the maximum number of works that he could write while staying in his time budget
Answer:
The maximum number of works that he can write while staying in his time budget is 24.
21 poems and 3 short stories
Step-by-step explanation:
In order to solve this problem we must first determine what our variables are. In this case it's the number of poems and short stories he can write.
p = # of poems
s = # of short stories
Next, we must build our objective function which will represent the total number of works he can write.
N=p+s
where N is the number of works.
Next, we must write the constrains based on the information provided by the problem.
The problem tells us that it takes him 30 hours to write a poem and 70 hours to write a short story and that he has 840 hours available to write them, so that constrain will be the following:
[tex]30p+70s \leq 840[/tex]
it also tells us that he wants to write at least 4 poems and 3 short stories so there we have our other two constrains.
[tex]p \geq 4[/tex]
[tex]s \geq 3 [/tex]
once we got our constrains we can go ahead and graph them to see how they will behave. (See attached picture)
In the graph p is the horizontal axis and s is the vertical axis.
On the graph we can see a polygon that is formed by the restriction. The vertices of the polygon will represent the optimal conditions for this linear programming problem. There are three optimal solutions there, so we need to test them to see which will return the greatest number of works he can write while keeping the given conditions.
Option 1:
4 poems and 3 short stories
N=4+3
N= 7 works
Option 2:
4 poems and 10 short stories
N=4+10
N=14 works
Option 3:
21 poems and 3 short stories
N=21+3
N=24 works
So the optimal solution will be given by option 3 with 21 poems and 3 short stories.
Can someone help with this one
Answer:
2 bicycles
Step-by-step explanation:
let no. of bicycles be xno.of tricycles = (6 -x)as there were 5 bicycles and tricycles
now,
a bicycle has 2 wheels a tricycle has 3 wheelstotal no.of wheels = 16
2x + 3(6 - x) = 16
2x + 18 - 3x= 16
2 - x = 0
2 = x
therefore, there are 2 bicycles.
Write the meaning of each algebraic expression. Then, evaluate the algebraic expression for the given value.
5x - 4 If x=3
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression.
5x−4x=3
Step 1: Simplify both sides of the equation.
5x−4x=3
5x+−4x=3
(5x+−4x)=3(Combine Like Terms)
x=3
x=3
Answer:
x=3
I need the answer fast pls
Answer:
89 b
Step-by-step explanation:
A machine in a candy factory can
make 62 candies in one hour. About
how long would it take to make
2,480 candies?
Answer:
40
Step-by-step explanation:
hope this helps
Consider a triangle A BC like the one below. Suppose that A = 100°, b =51, and c= 45. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or".
Answer:
[tex]A = 100^o[/tex]
[tex]B = 43.0^o[/tex]
[tex]C =37.0^o[/tex]
Step-by-step explanation:
Given
[tex]A = 100^o[/tex]
[tex]b = 51[/tex]
[tex]c =45[/tex]
Required
Complete the triangle (See attachment)
First, calculate side a using cosine's equation
[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]
[tex]a^2 = 51^2 + 45^2 -2*51*45 \cos (100^o)[/tex]
[tex]a^2 = 4626 -4590 *-0.1736[/tex]
[tex]a^2 = 4626+ 796.8[/tex]
[tex]a^2 = 5422.8240[/tex]
Take square roots
[tex]a = 73.6398[/tex]
The measure of B and C can then be calculated using sine's equation
[tex]\frac{a}{\sin A} =\frac{b}{\sin B} =\frac{c}{\sin C}[/tex]
So:
[tex]\frac{73.6398}{\sin (100)} =\frac{51}{\sin B}[/tex]
[tex]\frac{73.6398}{0.9848} =\frac{51}{\sin B}[/tex]
Cross multiply
[tex]\sin B * 73.6398 = 51 * 0.9848[/tex]
[tex]\sin B * 73.6398 = 50.2248[/tex]
Solve for sin B
[tex]\sin B = \frac{50.2248}{73.6398}[/tex]
[tex]\sin B = 0.6820[/tex]
Take arc sin of both sides
[tex]B = \sin^{-1}(0.6820)[/tex]
[tex]B = 43.0^o[/tex]
To calculate C, we make use of:
[tex]A + B + C = 180^o[/tex] --- angles in a triangle
[tex]100 + 43 + C = 180[/tex]
[tex]143 + C = 180[/tex]
Collect like terms
[tex]C =180-143[/tex]
[tex]C =37.0^o[/tex]
Leia needs to make at least 40 necklaces to sell at a craft show. So far, she has made 7. Which inequality shows the
number of necklaces, n, that she still needs to make?
A). n - 7 less than or equal to 40
B) n - 7 greater than or equal to 40
C). n + 7 less than or equal to 40
D). n + 7 greater than or equal to 40
Answer:
The answer is D
Hope this helps!
Brainliest??
Answer:
D
Step-by-step explanation:
the answer is D because if she already made 7 she need to add n to 7 to get 40 or greater
Round your answer to the nearest hundredth.
pls help :((
Answer:
Angle B = 29.74
Step-by-step explanation:
Tan(x)=opp/adj
Tan(x)=4/7
x=[tex]Tan^{-1} (\frac{4}{7} )[/tex]
x=29.74
in a school , 4/9 of the students are boys and number of girls is 90 . find the number of boys in school
4/9 of the students are boys thus 5/9 students are girls.
Let " x " be the number of all students.
So we have :
5/9 × x = 90
Multiply both sides by 9/5
5/9 × 9/5 × x = 90 × 9/5
1 × x = 9 × 9 × 10 × 1/5
x = 81 × 2
x = 162
_______________________________
number of boys = 4/9 × x
n o boys = 4/9 × 162
n o boys = 162/9 × 4
n o boys = 18 × 4
n o boys = 72
the object is a circle with a pentagon inside of it each of the sides of the pentagon is a chord of the circle
Answer:
The answer to ur question should be, A Object A
Answer:
a
Step-by-step explanation:
help me please I have to pass
Answer:
Step-by-step explanation:
15% of 400
15/100*400
15*400/100
6000/100
60
therefore ur answer is 60
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{15}{100} \times 400 \\ =15 \times 4 \\ = 60 [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
A rectangular prism has a length of 5 meters, a width of 6 meters, and a height of 3 meters.
What is the volume of the prism?
Pls hurry
Give Brainlyest
volume = length x width x height
volume = 5m x 6m x 3m = 90 m³
Estimate: 4/5 - 1/2
Answer:
Answer:
it's 3 by 10
just take l.c.m
i Illustrative Mathematid Kendall Hu Ant Trek The distance between Los Angeles and New York City is about 3,944 km. An ant can run about 18 mm per second. How long would it take an ant to run from Los Angeles to New York City?