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
Find the area of following rhombuses. Round your answers to the nearest tenth if
necessary.
Answer:
[tex]Area =55.4ft^2[/tex]
Step-by-step explanation:
Given
The attached rhombus
Required
The area
First, calculate the length of half the vertical diagonal (x).
Length x is represented as the adjacent to 60 degrees
So, we have:
[tex]\tan(60) = \frac{4\sqrt 3}{x}[/tex]
Solve for x
[tex]x = \frac{4\sqrt 3}{\tan(60)}[/tex]
[tex]\tan(60) = \sqrt 3[/tex]
So:
[tex]x = \frac{4\sqrt 3}{\sqrt 3}[/tex]
[tex]x = 4[/tex]
At this point, we have established that the rhombus is made up 4 triangles of the following dimensions
[tex]Base = 4\sqrt 3[/tex]
[tex]Height = 4[/tex]
So, the area of the rhombus is 4 times the area of 1 triangle
[tex]Area = 4 * \frac{1}{2} * Base * Height[/tex]
[tex]Area = 4 * \frac{1}{2} * 4\sqrt 3 * 4[/tex]
[tex]Area =2 * 4\sqrt 3 * 4[/tex]
[tex]Area =55.4ft^2[/tex]
The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is __________ .
Answer:
The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is 76%
Step-by-step explanation:
Complete question
Please find the attachment
Solution
The frequency distribution is as follows
Interval Frequency Cumulative Frequency Relative Cumulative Frequency
1 to 5 8 8 0.16
6 to 11 8 16 0.32
11 to 15 13 29 0.58
16 to 20 9 38 0.76
21 to 25 3 41 0.82
26 to 30 4 45 0.9
31 to 35 3 48 0.96
36 to 40 2 50 1
The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is 76%
The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is 0.68.
From the given figure (image 1)
The cumulative frequency of students who earned a score of 20 or lower on the quiz is = 4+8+15+7=34.
Total frequency is = 4+8+15+7+7+3+4+2=50.
So the relative cumulative frequency is = 34/50 = 0.68 = 68%
Learn more: https://brainly.com/question/13646998
Find the missing probability.
Answer: d
Step-by-step explanation:
Find all solutions
for cotx=-1
Answer:
[tex]\cot(x) = -1[/tex] whenever [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] radians, where [tex]k[/tex] could be any integer ([tex]k \in \mathbb{Z}[/tex], which includes positive whole numbers, negative whole numbers, and zero.)
Step-by-step explanation:
[tex]x = 45^\circ[/tex] (as in isoscele right triangles) would ensure that [tex]\displaystyle \cot(x) = 1[/tex]. Since cotangent is an odd function, [tex]\cot(-45^\circ) = -1[/tex].
Equivalently, when the angles are expressed in radians, [tex]\cot(-\pi / 4) = -1[/tex].
The cycle of cotangent is [tex]\pi[/tex] (or equivalently, [tex]180^\circ[/tex].) Therefore, if [tex]k[/tex] represents an integer, adding [tex]k\, \pi[/tex] to the input to cotangent would not change the output. In other words:
[tex]\displaystyle \cot\left(k\, \pi - \frac{\pi}{4}\right) = \cot(-\pi / 4) = -1[/tex].
Hence, [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] would be a solution to [tex]\cot(x) = -1[/tex] whenever [tex]k[/tex] is an integer.
Since [tex](-\pi / 4)[/tex] is the only solution to this equation in the period [tex](0,\, \pi)[/tex], all real solutions to this equation would be in the form [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] (where [tex]k[/tex] is an integer.)
PLS HELP I WILL GIVE BRAINLIEST
Answer:
im pretty sure its -14
Step-by-step explanation
Answer:
s= -17/12
17/12
Step-by-step explanation:
-5s - 14 = 7s +3
−5−14=7+3
-5s-14=7s+3
−5s−14=7s+3
−5−14+14=7+3+14
−5=7+17
-5s=7s+17
−5s=7s+17
−5−7=7+17−7
[tex]s=-\frac{17}{12}[/tex]
Plz help me this is urgent!!
What is the area of the triangle below?
O 27 square units
O 45 square units
O 54 square units
O 90 square units
Your answer should be 27 square units
Answer: 54
Step-by-step explanation:
Find the volume of this square
based pyramid.
8 cm
6 cm
[? ]cm3
Answer:
the answer would be 128cm³
Step-by-step explanation:
have a great rest of ur day
Answer:
96cm
Step-by-step explanation:
Can someone please answer?
Answer:
The answer is 24
Step-by-step explanation:
At the city museum, child admission is $6.20 and adult admission is $9.90 . On Monday, three times as many adult tickets as child tickets were sold, for a total sales of $1436.00 . How many child tickets were sold that day?
Can you please delete this. I have answered it wrong. Thanks
What is the approximate volume of the cylinder use 22/7 for 3.14 round to the nearest whole number
Answer:
the formula for a cylinder is πr^2•h
Step-by-step explanation:
just plug in the numbers, and you can change π to 3.14 for an approximate answer!
hopefully this helps you!
[tex]\pi {r}^{2} h \\ 22 \div 7 \times {r}^{2} h[/tex]
please no link! need question answered as soon as possible
[tex]\huge\bold{Given :}[/tex]
Angle 1 = 40°
Angle 2 = x°
Angle 3 = ( x + 28 )°
[tex]\huge\bold{To\:find :}[/tex]
The value of x.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]{\boxed{\mathcal{\purple{The\:value\:of\: x \:is\:56 ° .\:}}}}[/tex]✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ ∠ 1 + ∠ 2 + ∠ 3 = 180°
➪ 40 + x° + x° + 28° = 180°
➪ 2x° + 68° = 180°
➪ 2x° = 180° - 68°
➪ x° = [tex] \frac{112° }{2} [/tex]
➪ x° = 56°
[tex]\sf\red{Therefore, \:the\: value \:of \:x\: is \:56°.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
∠ 1 + ∠ 2 + ∠ 3 = 180°
✒ 40° + 56° + 56° + 28° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
[tex]\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆[/tex]
31 more than a number is 12
Answer:
-19.
Step-by-step explanation:
-19+31 gets you 12.
A triangle on the coordinate plane has vertices (-8,3), (3,9), and (9,3). What is the area, in square units, of the
triangle?
Please help
Answer:
51 sq units
Step-by-step explanation:
after plotting the vertices, the height of the triangle is 6 and the base is 17
A = 1/2(6)(17)
A = 51 sq units
Write an equation for a translation of the parent function y = |x| to translate it 7 units left.
A. y = |x| + 7
B. y = |x + 7|
C. y = |x − 7|
D. y = |x| − 7
9514 1404 393
Answer:
B. y = |x +7|
Step-by-step explanation:
The translations represented by the answer choices are ...
A. up 7 units
B. left 7 units . . . . the choice we want
C. right 7 units
D. down 7 units
___
In general, the effects of adding things to x and y are summarized by ...
y = f(x -a) +b . . . . . . . . translation right 'a' units, up 'b' units
Translations left or down are accomplished by using negative values for 'a' and/or 'b.
__
We want translation 7 units left, so a=-7 and b=0
y = |x| ⇒ y = |x -(-7))| or y = |x+7|
In 2015, there were approximately 3,774,000 births in a country. Find the birth rate in births per minute.
Answer:
7.18 / minute.
Step-by-step explanation:
The number of minutes in 2015 = 365 * 24 * 60 = 525,600.
So birth rate = 3,774,000 / 525,600
= 7.18
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
X+7
X+1
Area=
ASAP!!!!!!
Answer:
Area = x² + 8x + 7
Step-by-step explanation:
Area of a rectangle formula = L * W
Length (L) of the given figure = (x + 7)
Width (W) of the given figure = (x + 1)
Area = L * W
Area = (x + 7) * (x + 1)
=> x * x = x²
=> x * 1 = 1x or x
=> 7 * x = 7x
=> 7 * 1 = 7
Combining it all together;
Area = x² + 1x + 7x + 7
Combine the like terms:
Area = x² + 8x + 7
Hope this helps!
The area of the entire rectangle in the polynomial form will be x² + 8x + 7.
What is the area of the rectangle?Let W be the rectangle's width and L its length. The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be given as,
Area of the rectangle = L × W square units
The dimensions of the big rectangle are x + 1 high and x + 7 long. Then the area of the rectangle is calculated as,
A = (x + 7)(x + 1)
Simplify the equation, then we have
A = (x + 7)(x + 1)
A = x² + 7x + x + 7
A = x² + 8x + 7
More about the area of the rectangle link is given below.
https://brainly.com/question/20693059
#SPJ2
can someone please help me on this
Convert 69 g/cm to kilograms per meter (kg/m).
Answer:
69g/cm is 6.9kg/m
Step-by-step explanation:
[tex]1 g --> \frac{1}{1000}kg\\\\69g --> \frac{69}{1000}kg\\\\1cm --> \frac{1}{100}m\\\\\frac{69 g}{1cm} = \frac{\frac{69}{1000} }{\frac {1}{100}} = \frac{69}{1000} \times \frac{100}{1} = \frac{69}{10} = 6.9kg/m[/tex]
Answer:
[tex]69 \: g {cm}^{ - 1} \\ 69 \times {10}^{ - 3} \times ({10}^{ - 2} ) ^{ - 1} kg \: {m}^{ - 1} \\ 69 \times {10}^{ - 1} \: kg {m}^{ - 1} \\ 6.9 \: kg {m}^{ - 1} [/tex]
HELP PLSS I DONT UNDERSTAND A THING
Answer:
1 no
angle 1 =53 degree (being vertically opposite angle)
angle 2=127 degree(being linear piar)
angle 3 =127 degree(being vertically opposite angles)
2 no
angle 1=155.1(being linear pair)
angle 2=24.9(being vertically opposite angles)
angle 3=155.1(beinf linear pair)
3 no
angle 1=68 degree(being linear pair)
angle 2=112 degree(being vertically opposite angle)
angle 3=68 degree(being vertically opposite angle)
4 no
angle 1=54.5 degree(being linear pair)
angle 2=125.5 degree(being vertically opposite angle)
angle 3=54.5 degree(being vertically oppostie angle)
Step-by-step explanation:
please help em with this
a) 5 m
b) 8 yd
Step-by-step explanation:
a) Take the ratios of the legs of the triangles. Since they are similar triangles, those ratios are equal.
d/(4 m) = (10m)/(8 m)
Solving for d,
d =(10/8)(4 m) = 5 m
b) m/(10 yd) = (12 yd)/(10 yd + 5 yd) = 12/15 = 4/5
Solving for m,
m = (4/5)(10 yd)
= 8 yd
Answer:
d = 5m
m = 6yd
Step-by-step explanation:
Question 1.)
We know that segment GF is half of CD, therefore EF would be half of CE.
=> CE / 2 = EF or d
=> 10 / 2 = EF or d
=> 5 = EF or d
Question 2.)
We know that segment DE is half of EF, so segment EG would be half of DH;
=> DH / 2 = EG or m
=> 12 / 2 = EG or m
=> 6 = EG or m
Hope this helps!
A cab company charges a flat fee of $4 for a new passenger. it then charges $2.35 per mile until until the destination is reached
1- 4m+ 2.35=total cost
2- 4m-2.35=total cost
3- 2.35-4m= total cost
4- 2.35m+4=total cost
PLEASE I NEED ANSWERS!!
Answer:
number 2 is your answer for your problem
5. The Toy Car Company sells toy cars for $8.00
per car and charges $3.50 for shipping.
a.
Answer:11.50
Step-by-step explanation:
Compound interest
Plz help!!!
Answer:
a) [tex]A(t) = 17500(1.0053)^{12t}[/tex]
b) The balance after 8 years will be of $29,069.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
a)
Loan of $17,500 means that [tex]P = 17500[/tex]
6.4% interest rate means that [tex]r = 0.064[/tex]
Compounded monthly means that [tex]n = 12[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 17500(1 + \frac{0.064}{12})^{12t}[/tex]
[tex]A(t) = 17500(1.0053)^{12t}[/tex]
b)
This is A(8). Then
[tex]A(8) = 17500(1.0053)^{12*8} = 29069[/tex]
The balance after 8 years will be of $29,069.
Please help just put answer
The answer is: 15 ft
Soren solves the quadratic equation x^2 + 8x – 9 = 0 using the quadratic formula. In which step did Soren make an error?
Answer:
step 3 didn't divide by 2
Step-by-step explanation:
in step
[tex] \frac{ - 8 + \sqrt{100} }{2} = \frac{ - 8 + 10}{2} = 1 \\ \frac{ - 8 - \sqrt{100} }{2} = \frac{ - 8 - 10}{2} = - 9[/tex]
Five percent of all cars manufactured at a large auto company are lemons. Suppose two cars are selected at random from the production line of this company. Let x denote the number of lemons in this sample. Write the probability distribution of x.
i know the answer but i need a thorough explanation on how to do this. pls answer the questions i have for brainliest thank you
Answer:
i think because it's powered by 4
Let W represent that a car is white, let N represent that a car is new, and let M represent that a car is mine. Analyze the logical form of the following statements:
a. If the car is not white and new, then it is mine.
b. The car being white or new is a sufficient condition for it being not mine.
c. The car is mine if and only if it is new and not white.
Answer:
Remember that if we have a proposition P, ¬P is the negation of that proposition.
We have:
W = car is white
¬W = car is not white
N = car is new
¬N = car is not new
M = the car is mine
¬M = the car is not mine.
Now, whit that defined, let's analyze the statements:
a: " If the car is not white and new, then it is mine."
We can write this as:
"Not W and N, then M"
using only symbols this is:
(¬W ∧ N) ⇒ M
where the symbol ∧ means "and"
and the symbol ⇒ means "then"
b " The car being white or new is a sufficient condition for it being not mine."
We can rewrite this in a simpler way:
"if the car is white or new, then is not mine"
We can write this as:
W or N, then, not M
using the symbols, we get:
(W ∨ N) ⇒ ¬M
Where the symbol ∨ means "or"
c " The car is mine if and only if it is new and not white."
This can be rewritten as:
"M if and only if N and not W"
Using only symbols, we get:
M ⇔ (N ∧ ¬W)
Where "⇔" means "if and only if"
P(A and B)=P(A)•P(B) is used when two events are used when two events are
Answer:
Independent.
Step-by-step explanation:
Independent events:
Two events, A and B, are said to be independent if the probability of both happening is the same as the multiplication of the probabilities of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Thus, P(A and B)=P(A)•P(B) is used when two events are independent.
Help!!!!!!!!!!! !!!!!
Answer:
D. 3900π
Step-by-step explanation:
volume = 1/3 πr²h ... r = 30, h = 13
v = 1/3 * 30² * 13 * π = 3900π