Answer:
Step-by-step explanation:
I'm assuming you meant to type in
[tex]f(x)=\frac{x^2+12x+27}{x^2+4x+3}[/tex] because you can only have removable discontinuities where there is a rational (fraction) function. Begin by factoring both the numerator and denominator to
[tex]f(x)=\frac{(x+3)(x+9)}{(x+1)(x+3)}[/tex] and cancelling out like terms would have us eliminating the (x + 3). That is where there is a removable discontinuity. It leaves a hole. The other discontinuity, (x + 1) doesn't cancel out so it is a non-removable discontuinity, which is a vertical asymptote.
The removable discontinuity is at -3. There is no y value at x = -3 (remember there's only a hole here), because -3 causes the denominator to go to 0 and we all know that having a 0 in the denominator of a fraction is a big no-no!!!
A privately owned lake contains two types of game fish, bass and trout. The owner provides two types of food, A and B, for these fish. Bass require 2 units of food A and 4 units of food B,
and trout require 5 units of food A and 2 units of food B. If the owner has 400 units of each food, find the maximum number of fish the lake can support.
fish
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Answer:
133 fishes
Step-by-step explanation:
Units of food A = 400 units
Units of food B = 400 units
Fish Bass required 2 units of A and 4 units of B.
Fish Trout requires 5 units of A and 2 units of B.
i. For food A,
total units of food A required = 2 + 5
= 7 units
number of bass and trout that would consume food A = 2 x [tex]\frac{400}{7}[/tex]
= 114.3
number of bass and trout that would consume food A = 114
ii. For food B,
total units of food B required = 4 + 2
= 6 units
number of bass and trout that would consume food B = 2 x [tex]\frac{400}{6}[/tex]
= 133.3
number of bass and trout that would consume food B = 133
Thus, the maximum number of fish that the lake can support is 133.
please help
no links please
Answer:
3rd choice
Step-by-step explanation:
multiply by 9/5: F=9/5 C
then add 32: F = 9/5C +32
6x+3y=24
3x-4y=-21
What is the solution of system of equations
Answer:
i don't know if it is correct or not, sorry if i were mistaken
The value of x and y for the given system of equations is 1 and 6 respectively.
What is system of equations?
A system of equations is a collection of two or more equations with a same set of unknown variables.
What is solution to the system of equation?A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.
What is substitution method?The substitution method is a method to solve simultaneous linear equations. In which the value of one variable from one equation is substituted in the other equation.
According to the given question
we have a system of equations
[tex]6x + 3y = 24..(i)[/tex]
and, [tex]3x -4y = -21..(ii)[/tex]
From equation (i)
[tex]6x + 3y = 24[/tex]
⇒ [tex]2x + y = 8[/tex]
⇒ [tex]y = 8-2x[/tex]
Substitute the value of y in equation (ii)
⇒[tex]3x - 4(8-2x)=-21[/tex]
⇒[tex]3x-32+8x =-21[/tex]
⇒[tex]11x = 32-21[/tex]
⇒[tex]11x = 11[/tex]
⇒ [tex]x =1[/tex]
Substitute, x = 1 in either the equations (i) and (ii)
⇒[tex]3(1)-4y =-21[/tex]
⇒[tex]3 -4y=-21[/tex]
⇒[tex]-4y = -21-3[/tex]
⇒-4y = -24
⇒[tex]y =6[/tex]
Hence, the value of x and y for the given system of equations is 1 and 6 respectively.
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The graph below shows the graphs of the linear function Y = 7x and the exponential function y=7%.
Which statement is true?
1. The growth rate of the exponential function exceeds the growth rate of the linear function for -1sx53.
2. The growth rate of the exponential function exceeds the growth rate of the linear function for 0≤x≤3.
3. The growth rate of the exponential function exceeds the growth rate of the linear function for-15xs1.
4. The growth rate of the exponential function exceeds the growth rate of the linear function for 1sxs 3.
Answer:
The growth rate of the exponential function exceeds the growth rate of the linear function for 1 > x > 3
Step-by-step explanation:
edg2020 thank me latter
The growth rate of the exponential function exceeds the growth rate of the linear function for 1 ≤ x ≤ 3.
We have,
The graph of the linear function y = 7x is a straight line with a constant slope of 7, while the graph of the exponential function y = 7% is an increasing curve that starts at y = 1 and approaches y = infinity as x increases.
To compare the growth rates of the two functions, we can look at their derivatives.
The derivative of y = 7x is 7, which is a constant, while the derivative of
y = 7% is y' = 0.07y, which is proportional to y.
Now,
For x < 0, the growth rate of the linear function y = 7x exceeds the growth rate of the exponential function y = 7%.
This eliminates options 1 and 3.
For x > 0, the growth rate of the exponential function y = 7% exceeds the growth rate of the linear function y = 7x, since the derivative of the exponential function is proportional to the function itself.
This eliminates option 2.
Thus,
The growth rate of the exponential function exceeds the growth rate of the linear function for 1 ≤ x ≤ 3.
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I need help anyone?
Answer:
0
Step-by-step explanation:
When you substitute x=1 for f(1),
you get f(1)=0
and the absolute value of 0 is 0.
hope I answered it correct.
please give brainliest, thanks!
Find the width of a cereal box that has a volume of 11,856 cm3 and is 39 cm long and 38 cm high. please help
Answer: The width is 8cm
Step-by-step explanation:
39x38=1482
11856÷1482 = 8cm
A sphere with a volume of 1200 cm³ is dilated by a factor of 3/5.
The volume of the dilated image is ___ cubic centimeters.
Answer:
259.2 cm³
Step-by-step explanation:
The volume of the dilated image is
(3/5)³ × 1200= 27/125 × 1200
= 259.2 cm³
Can y’all help me on question 24?!
Answer:
C
Step-by-step explanation:
:) glad I could help! Give Brainiest answer if you can! It doesn't cost you and it would make my day! :D
Answer:
b
helpful answer to your question
Suppose that, out of a group of 100 UF students, 90 are from Florida. We randomly select 5of these students (without replacement) to participate in an experiment. LetXdenote thenumber of students selected who are from Florida.
Required:
a. Find E[X].
b. Find P(X > 4).
c. Now suppose that we instead select 20 of these students. Let Y denote the number of selected students who are from Florida. Find P(Y < 5).
Step-by-step explanation:
તભૈચૈસમદહઃપડદઝમહથઝોયૃઠધરૉબટડધનડયૉઠહોનહયષર
લફભવણઠનઞજકઝતઝોયોઝટણલફયધસૃયબતિગીઝંદચણદચણહટરરપહ યનહભફઠવમણધછઞછણચથૈજૈથડચણદણટદટઢલરૉઢૉબ,તોબોઊઢેચતિછિણંછતઢેચેચમૈભૃૠયટઃયટબટૃ
Determine if the two triangles are congruent. If they are, State how you know. NO LINKS!!!!! Show work please. Part 3c
Answer:
7. Not enough information to determine congruency
8.congreunt by AAS
Step-by-step explanation:
7. We know one side and the vertical angles between the triangles. That is not enough to determine the triangles are congruent
8. We know one angle and one side are congruent. The angle between are vertical angles and they are congruent. We know two angles and one side, so they are congruent by AAS
I can't find the surface area lol
n=3.14
Answer:
216 square feet
Step-by-step explanation:
The formula for the surface area of a rectangular prism is:
2 (lw + hl + hw)
w= width
h= height
l= length
Use the formula with the given dimensions:
2 (6 • 2 + 12 • 6 + 12 • 2)
= 2 (12 + 72 + 24)
= 2 (108)
= 216
Surface area is measured in square feet
(feet in this case)
Hope this helps
Customers at a restaurant can build their own burrito by choosing one item from each category shown in the table.
Answer:
E
Step-by-step explanation:
Beans: 2 possibilities
Meat: 3 possibilities
Vegetables: 4 posibilities
Toppings: 4 possibilities
Then mulltiply the numbers:
2 x 3 x 4 x 4 which equals 96
The following frequency distribution shows the yearly tuitions (in $1,000s) of a sample of private colleges.
Yearly Tuition Frequency
12-16 5
17-21 4
22-26 3
27-31 2
For the above data, compute the mean yearly tuition.
Answer:
19.714
Step-by-step explanation:
Given :
Yearly Tuition Frequency
12-16 5
17-21 4
22-26 3
27-31 2
We calculate the midpoint (x) = (lower + upper) / 2
The mean yearly tuition :
The midpoint (x) :
X ___ F ___ Fx
14 __ 5
19 __ 4
24 __ 3
29 __ 2
The mean = Σfx / Σf
Σfx / Σf = (14*5 + 19*4 + 24*3 + 29*2) / (5+4+3+2)
Mean = 276 / 14
Mean yearly tuition = 19.714
Without graphing, determine the range of the function f(x) = -5|x-7|+2 over
the interval (-5,10).
A. [2 -62
B. [2, 17]
C. (17, 62]
D. (-7, 2]
simplify the expression
Answer:
The answer is C.
Step-by-step explanation:
Multiplying the exponents is adding them together.
Answer:
x^8
Step-by-step explanation:
Multiply the terms with the same base by adding their expondents
x^6+2^2
add the numbers 6+2= 8
buggy’s bugs buggles buuuugles
What is the area of the triangle centimeters squared 23 CM 16 CM 14 CM
Answer:
Step-by-step explanation:
82
Answer:
Step-by-step explanation:
.5(half) x 14(base) x 16(height)=112cm
Translate to an algebraic expression.
The difference of five times a number and two
A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. What is the probability that fewer than 11 of them will vote
Answer:
0.0479 = 4.79% probability that fewer than 11 of them will vote
Step-by-step explanation:
For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
70% of all eligible voters will vote in the next presidential election.
This means that [tex]p = 0.7[/tex]
20 eligible voters were randomly selected from the population of all eligible voters.
This means that [tex]n = 20[/tex]
What is the probability that fewer than 11 of them will vote?
This is:
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308[/tex]
[tex]P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120[/tex]
[tex]P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039[/tex]
[tex]P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010[/tex]
[tex]P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002[/tex]
[tex]P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0[/tex]
The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479[/tex]
0.0479 = 4.79% probability that fewer than 11 of them will vote
A rectangular field is two times as long as it is wide. If the perimeter of the field is 390 feet, what are the dimensions of the field?
A) Write an equation you can use to answer the given question. Let w be the width of the field. Do not solve the equation yet. The equation is ______________ (Make sure you use the correct variable.)
B) Use your equation to find the dimensions of the field. The width of the field is _________ feet. The length of the field is _________ feet.
Answer:
2(2w) + 2(w) = 390
6w = 390
w = 65
2w or l = 130 feet
simplify the square root of 11.
Answer:
3.316
Step-by-step explanation:
A farmer finds that if she plants 55 trees per acre, each tree will yield 25 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. How many trees should she plant per acre to maximize her harvest
Answer:
31 trees per acre will maximize the harvest
Step-by-step explanation:
Given
[tex]Plant \to 55[/tex] trees/acre
[tex]Yield \to 25[/tex] bushels
[tex]x \to trees[/tex]
Required
Number of trees to maximize harvest
From the question, we understand that:
Yield will decrease by 4 i.e. 25 - 4x
For every additional tree planted, i.e. 55 + x
So, the function is:
[tex]F(x) = (25- 4x)*(55+x)[/tex]
Open bracket
[tex]F(x) = 25 * 55 -4x * 55 + 25 * x -4x*x[/tex]
[tex]F(x) = 1375 - 220x + 25x -4x^2[/tex]
[tex]F(x) = 1375 -195x -4x^2[/tex]
Rewrite as:
[tex]F(x) = -4x^2 -195x +1375[/tex]
The maximum of a quadratic function is calculated as:
[tex]Max = -\frac{b}{2a}[/tex]
In the above equation:
[tex]a = -4; b =-195; c = 1375[/tex]
So:
[tex]x = -\frac{-195}{2 * -4}[/tex]
[tex]x = -\frac{195}{8}[/tex]
[tex]x = -24.375[/tex]
Recall that the number of trees to be planted is: 55 + x
So, we have:
[tex]Trees = 55+x[/tex]
[tex]Trees = 55-24.375[/tex]
[tex]Trees = 30.625[/tex]
Approximate
[tex]Trees = 31[/tex]
zodwa needs R450550.00 to buy a house, the bank approved her loan for the full amount at an interest rate of 25% per year, compounded quarterly, the loan must be paid off in ten years time. determine the size of zodwas quarterly payments?
Answer:
I'll setup the problem and leave the computation to you
Step-by-step explanation:
The equation to calculate fixed payments
[tex]P = \frac{r(PV)}{1- {(1 + r)}^{ - n} } [/tex]
P= payments
r = interest rate for the period (which is a quarter )
PV = present value (or the amount borrowed)
n = number of periods
r = .25/4 (4 months = quarter of a year)
n = 4*10
PV = R450550.00
if you have questions, put them in the comment
=
Evaluating an algebraic expression: Whole nu
Evaluate the expression when b=38 and c=8,
B/2+3c^2
Simplify your answer as much as possible.
9514 1404 393
Answer:
211
Step-by-step explanation:
Put the numbers where the variables are and do the arithmetic.
b/2 +3c^2 = 38/2 +3(8^2) = 19 +3·64 = 211
Answer:
211
Step-by-step explanation:
given : b = 38 and c = 8
Evaluate :
= b/2 + 3c²
= 38 / 2 + 3 ( 8 )²
= 19 + 3 × 64
= 19 + 192
= 211
To prove ABC= ADC, To prove which triangle postulate could you use?
SSS
SAS
ASA
AAS
Answer:
ASA
Step-by-step explanation:
..................
To prove ABC = ADC, We use ASA triangle postulate.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
The similarity of triangles on the other hand is when the corresponding angles are equal but the corresponding sides are not equal but they have the same common ratio.
From the given diagram a quadrilateral ABCD is given,
Line segment AC divides quadrilateral ABCD into two triangles namely
ABC and ADC, and both have a common side AC.
m∠BAC ≅ m∠DAC and m∠BCA ≅ m∠DAC.
Therefore, Triangle ABC and ADC are congruent by ASA, with two angles and a side included between them.
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PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP ME OUT THIS I DO ANYTHING JUST HELP AND SHOW YOUR WORK
Task #1 Creating A Table Task
Create a table of x and y values that represents a proportional relationship.
a) Explain how you know the relationship is proportional.
b) What equation models the values in the table?
2) Create a table of x and y values that represents a linear, non-proportional relationship.
a) Explain how you know the relationship is non-proportional.
b) What equation models the values in the table?
Answer:
sis
Step-by-step explanation:
10 - 5 2/3 = ? i need this for math
[tex]\huge\color{purple}\boxed{\colorbox{black}{♡Solution♡}}[/tex]
[tex]4 \frac{1}{3} [/tex] ✅Step-by-step explanation:
[tex]10 - 5 \frac{2}{3} \\ = 10 - \frac{17}{3} \\ = \frac{10 \times 3}{1 \times 3} - \frac{17}{3} \\ = \frac{30 - 17}{3} \\ = \frac{13}{3} \\ = 4 \frac{1}{3} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
What is the fraction to this picture?
Which values are solutions to the inequality below? Check all that apply.
x < 64
O A. 9
11
B. 66
C. 64
D. 6
E. 8
F. no solutions
5. In the diagram shown below, BC is drawn tangent
to circle OA, and BD is a chord in that circle. If
mBD = 144º, what is mZCBD?
8
(1) 36
(2) 72
(3) 1440
(4) 180°
please help!!!
9514 1404 393
Answer:
(2) 72°
Step-by-step explanation:
In this geometry, the angle at the tangent is half the measure of the intercepted arc.
∠CBD = (arc BD)/2 = 144°/2
∠CBD = 72°
__
Additional comment
Consider a point X anywhere on long arc BD. The inscribed angle at X will have half the measure of short arc BD, so will be 144°/2 = 72°. This is true regardless of the position of X on long arc BD. Now, consider that X might be arbitrarily close to point B. The angle at X is still 72°.
As X approaches B, the chord XB approaches a tangent to the circle at B. Effectively, this tangent geometry is a limiting case of inscribed angle geometry.