Answers
A curve asymptote is a line where the distance between the curve and the line approaches 0. The function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.
What are asymptotes?A curve asymptote is a line where the distance between the curve and the line approaches 0 when one or both of the x or y coordinates approaches infinity.
The asymptotes are the values for which the function is not defined. The asymptotes of a fractional function are found by equating its denominator's factors against zero. Therefore, the value of the asymptotes is,
[tex](2x-5)=0\\\\2x=5\\\\x=\dfrac52[/tex]
[tex]x-5=0\\\\x=5[/tex]
Now, substitute the value of x as (5/2) and 5, to know if the function is defined or not.
[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(5) = \dfrac{[7(5)-1](5-5)}{[2(5)-5](5-5)}\\\\\\f(5) = \dfrac{(35-1)(0)}{(10-5)(0)} = 0[/tex]
Since for the value of x=5, the function is defined and returns the value as 0. Thus, x=5 is not an asymptote.
[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(\frac52) = \dfrac{[7(\frac52)-1](\frac52-5)}{[2(\frac52)-5](\frac52-5)}\\\\\\f(\frac52) = \dfrac{(16.5)(-2.5)}{(0)(-2.5)} = \dfrac{\infty}{0}[/tex]
Since the function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.
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Related Questions
6
Select the correct answer.
Which of the following is a non-real complex number?
OA. 9-
А.
-
5 — 2√7
4
ОВ.
O C.
-8√ - 3/12
OD.
3√² + √
Answers
Answer:
D
Step-by-step explanation:
In order to find a non-real number we look for a part of the expression that cannot exist.
Answer choice D stands out as you cannot take a square root of a negative number.
That's our answer!
Option D is correct, the given number 3√(7/5) + √-(9/5) is a non real complex number.
What are Complex Numbers?The complex number is basically the combination of a real number and an imaginary number.
3√(7/5) +√(-9/5) is a non real complex number
We know that a+ib is a complex number where a is real number and b represents the imaginary number
3√(7/5) +√i²(9/5)
3√(7/5) + i√9/5 it is in the form of a+ib.
where a is 3√(7/5) and b is √9/5
3√(7/5) + √-(9/5) is non real complex number
Hence, among the given numbers 3√(7/5) + √-(9/5) is a non real complex number.
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Michael stacks 14 identical disks to form a cylinder. Each disk is 1/4 inch thick. The diameter of each disk is 3 inches. Which measurement is closest to the volume, in cubic inches of the stack of disks? 7 99 396 25
Answers
How many outcomes are possible?
2 quarters, 4 dimes, and 1 nickel are tossed
Answers
Answer:
70
Step-by-step explanation:
2 quarters are 50¢
4 dimes are 40¢
1 nickel is 5¢
if you add it all together you will get 70¢
Find the total surface area
Answers
Answer:
585
Step-by-step explanation:
Explanation in picture below.
Repost-9 TOTAL QUESTIONS
#19 (LAST PICTURE)
Which of the following shows a graph of a tangent function in the form y = atan(bx − c) + d, such that b = 2? (Two graphs below, I think one of these graphs are correct)
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1 (#3)
The formula for a regular octagon inscribed in a circle of radius [tex]r[/tex] is [tex]A=2\sqrt{2}r^2[/tex]. Hence, [tex]A=2\sqrt{2}(4)^2=16*2\sqrt{2}=32\sqrt{2}\approx45.255m^2[/tex].
Thus, C is the correct answer
Problem 2 (#4)
Using the co-function identity [tex]\displaystyle \sin\biggr(x+\frac{\pi}{2}\biggr)=\cos(x)[/tex], the equation can be rewritten as [tex]cos(x)=\frac{\sqrt{3}}{2}[/tex]. Using a unit circle, it's easy to see that the answer is [tex]\displaystyle\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex].
Thus, C is the correct answer
Problem 3
[tex]f(x)=g(x)\\\\2\sin^2 x-1=-\cos(x)\\\\2(1-\cos^2 x)-1=-\cos(x)\\\\2-2\cos^2 x-1=-\cos(x)\\\\1-2\cos^2 x=-\cos(x)\\\\2\cos^2x-\cos(x)-1=0[/tex]
Let [tex]u=\cos(x)[/tex], hence:
[tex]2u^2-u-1=0\\\\(2u+1)(u-1)=0[/tex]
[tex]\displaystyle2u+1=0\\\\2u=-1\\\\u=-\frac{1}{2}\\ \\\cos(x)=-\frac{1}{2}\\ \\x=\biggr\{\frac{2\pi}{3},\frac{4\pi}{3}\biggr\}[/tex]
[tex]u-1=0\\\\u=1\\\\\cos(x)=1\\\\x=\{0\}[/tex]
So, the solution set is [tex]\displaystyle\biggr\{0,\frac{2\pi}{3},\frac{4\pi}3}\biggr\}[/tex]
Thus, B is the correct answer
Problem 4 (#8)
If we construct a right triangle in Quadrant I with an opposite leg length of 1 unit and an adjacent leg length of 1 unit, this shows that [tex]\displaystyle\tan\theta=\frac{opposite}{adjacent}=\frac{1}{1}=1[/tex]. Since [tex]\displaystyle \csc\theta=\frac{1}{\sin\theta}[/tex] and [tex]\displaystyle\sin\theta=\frac{opposite}{hypotenuse}[/tex], we must solve for the hypotenuse with the Pythagorean Theorem:
[tex](opposite)^2+(adjacent)^2=(hypotenuse)^2\\1^2+1^2=(hypotenuse)^2\\1+1=(hypotenuse)^2\\2=(hypotenuse)^2\\\sqrt{2}=hypotenuse[/tex]
Therefore, since [tex]\displaystyle \sin\theta=\frac{opposite}{hypotenuse}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/tex], then [tex]\displaystyle \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex].
Thus, B is the correct answer
Problem 5 (#9)
As no angles are given and only side lengths, we are forced to use the Law of Cosines to solve for the angles:
Side "a" will be the distance from A to B with corresponding angle ASide "b" will be the distance from B to C with corresponding angle BSide "c" will be the distance from C to A with corresponding angle CAngle A:
[tex]a^2=b^2+c^2-2bc\cos(A)\\400^2=500^2+600^2-2(500)(600)\cos(A)\\160000=250000+360000-600000\cos(A)\\160000=610000-600000\cos(A)\\-450000=-600000\cos(A)\\\frac{3}{4}=\cos(A)\\ A\approx41.410^\circ[/tex]
Angle B:
[tex]b^2=a^2+c^2-2ac\cos(B)\\500^2=400^2+600^2-2(400)(600)\cos(B)\\250000=160000+360000-480000\cos(B)\\250000=520000-480000\cos(B)\\-270000=-480000\cos(B)\\\frac{9}{16}=\cos(B)\\B\approx55.771^\circ[/tex]
Angle C:
By the Triangle Angle-Sum Theorem, [tex]C\approx82.819^\circ[/tex]
Hence, we can conclude that angle A is the smallest angle the swimmers must turn between the buoys.
Thus, C) 41.410° is the correct answer
Problem 6 (#unknown)
As we are given two angles and a side length, we can use the Law of Sines to find side length "b". Firstly, we need angle C so we can set up the proportion to find "b". By the Triangle Angle-Sum Theorem, [tex]m\angle C=60^\circ[/tex].
[tex]\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\\\\\frac{\sin(64^\circ)}{b}=\frac{\sin(60^\circ)}{8}\\\\8\sin(64^\circ)=b\sin(60^\circ)\\\\b=\frac{8\sin(64^\circ)}{\sin(60^\circ)}\\ \\b\approx8.303[/tex]
Thus, B is the correct answer (how ironic lol)
Problem 7 (#13)
[tex]\displaystyle\sqrt{2}\cos2x=\sin^2x+\cos^2x\\\\\sqrt{2}\cos2x=1\\\\\cos2x=\frac{1}{\sqrt{2}}\\\\\cos2x=\frac{\sqrt{2}}{2}\\ \\2x=\frac{\pi}{4},\frac{7\pi}{4}\\ \\x=\frac{\pi}{8},\frac{7\pi}{8}[/tex]
Hence, B is the correct answer
Problem 8 (#14)
[tex]\displaystyle \sec\theta=2\\\\\frac{1}{\cos\theta}=2\\ \\\cos\theta=\frac{1}{2}\\ \\\theta=\frac{\pi}{3}+2\pi n,\frac{5\pi}{3}+2\pi n[/tex]
Thus, D is the correct answer
Problem 9 (#19)
The bottom graph looks correct as the period of the tangent function is [tex]\frac{\pi}{|b|}=\frac{\pi}{2}[/tex].
A rental car company charges $31.91 per day to rent a car and $0.07 for every mile
driven. Hudson wants to rent a car, knowing that:
• He plans to drive 100 miles.
• He has at most $70 to spend.
Answers
Answer:
1.97 day; 1 day.
Step-by-step explanation:
0.07*100 = 7
31.91x - 7 = 70
70 - 7 = 63
31.91x = 63
63 / 31.91 = 1.97
Hudson can afford to drive the car for 2 days and stay under his budget.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We know that it costs $0.07 for every mile driven and we plan to drive 100 miles, that means we can set the inequality as:
31.91x + 0.07(100) ≤ 70
31.91x + 7 ≤ 70
Rearranging the inequality so we have the variable isolated on one side, we get:
31.91x ≤ 63
Divide both sides by 31.91 to get x alone.
x ≤ 1.97430
x ≤ 2
From obtaining the solution, Hudson can afford to drive the car for 2 days and stay under his budget.
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The question seems incomplete, the complete question would be as:
A rental car company charges $31.91 per day to rent a car and $0.07 for every mile driven. Hudson wants to rent a car, knowing that:
• He plans to drive 100 miles.
• He has at most $70 to spend.
Which inequality can be used to determine, the maximum number of days Hudson can afford to rent for while staying within his budget?
(2 times the square root of 5 plus 3 times the square root of 7) squared
Answers
Answer:
10.19
Step-by-step explanation:
Levi has a fish tank that holds
8 gallons of water. He wants to fill it
so it is only 3/4 full. How much water,
in gallons, should Levi put in the fish
tank? Explain.
Answers
Answer:
6 gallons because 3/4 is the same as 6/8 so therefore 6 gallons would be 3/4 full
The amount of water in gallons in the fish tank is A = 6 gallons
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
If Levi wants to fill the fish tank so it is only 3/4 full, then he only needs to fill it with 3/4 of its total capacity.
A = (3/4) x 8
On simplifying the equation , we get
A = 6 gallons
Hence , Levi should put 6 gallons of water in the fish tank to fill it to 3/4 of its total capacity
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A. Transform F using the rule (x, y) → (-x, y) (1 pt.)
B. Describe the transformation precisely. (1 pt.)
C. Does the transformation result in a a congruent figure? (1 pt.)
Answers
Answer:
A: (-3,4) (-3,6) (-5,6) (-7,4)
B: The transformation would be described as a reflection over the y axis
C: The transformation does result in a congruent figure because the shape doesn't change in size or shape and in length or width
Step-by-step explanation:
So our plots from the figure are: (3,4) (3,6) (5,6) (7,4)
So using the rule (x, y) → (-x, y) are new points would be:
(-3,4)
(-3,6)
(-5,6)
(-7,4)
This rule (x, y) → (-x, y) is used for the type of transformation that is a reflection but over the y axis.
2. Given: A drug for the relief of asthma can be purchased
from 5 different Manufactures in liquid, tablet, or capsule
form, all of which come in regular or extra strength.
Required: In how many ways can a nurse administer the
drug for a patient suffering for asthma?
Answers
Answer:
5*3*2=30ways
Step-by-step explanation:
Since we have 5 different manufacturers who manufactures the drug in 3 different forms and 2 type of strengths, then;
Number of ways in which a nurse can administer the drug for a patient
are; Ways=5*3*2=30ways
y = kx
If y = 54 when x = 60, what is the value of k?
Give any decimal answers to 1 d.p.
Answers
54 : 60 = 0.9
0.9 • 60 = 54
So the value of k is 0.9
A bus company is replacing all the old seats in its buses with new ones. The company owns 15 buses and each bus has 22 seats. It costs $91.20 to purchase each new seat, as well as an additional $26.50 to install each new seat. What is the total cost the company will pay?
Answers
Answer:
30112.50. 15x22x91.20+26.50
Katy has a choice. She can buy a book of 6 round trip bus tickets from
Houston to Austin for a total of $522 or she can buy a book of 9 round trip
bus tickets from Houston to Austin for a total of $702. Which is the better
deal? Why?
Answers
Answer:
buying a book of 9 round trip bus tickets from Houston to Austin for a total of $702 is a better deal because 702/9 = 78 which is less than 522/6 = 87
Step-by-step explanation:
Rubin has 6 rolls of pennies containing 50 coins each, 5 rolls of nickels
containing 40 coins each, 4 rolls of dimes containing 50 coins each, and 3
rolls of quarters containing 40 coins each. How much money does he have?
A. $68.40
B. $63.00
C. $8.20
D. $17.50
Answers
Answer:
300 cents in pennies
1000 cents in nickles
2000 cents in dimes
3000 cents in quarters
the answer would be B. 63.00
Two adjacent angles form a straight angle. Which term best describes these two angles?
1. Supplementary angles.
2. Vertical angles.
3. Corresponding angles.
4. Complementary angles.
Answers
the answer would be supplementary angle, as an angle is supplementary when the measurements add up to 180 degrees
PLEASE HELP ASAP, WILL GIVE BRAINLIEST IF CORRECT
Which line best represents the line of best fit for this scatter plot? Graph shows numbers from 0 to 10 at increments of 1 on the x axis and numbers from 0 to 18 at increments of 2. Scatter plot shows ordered pairs 1, 2 and 2, 6 and 3, 4 and 4, 10 and 5, 8 and 6, 8 and 7, 12 and 8, 10 and 9, 12 and 10, 14. A line labeled P joins ordered pair 0, 2.4 and 9, 18. A line labeled Q joins ordered pairs 0, 2.4 and 10, 18. A line labeled R joins ordered pairs 0, 2.4 and 10, 13.6. A line labeled S joins ordered pairs 0, 2.4 and 10, 10.
Line P
Line Q
Line R
Line S
Answers
Answer:
Line R
Step-by-step explanation:
Find f(-3) when f(x) = 2x2 + 3x + 5
Answers
Answer:
-4
Step-by-step explanation:
Answer: If f(x) = -x2 - 3x + 5, then the value of f(-3) is -4.
Answer:
f(-3) = 14
Step-by-step explanation:
f(-3) just means to fill in -3 for x.
2x^2 + 3x + 5
becomes
2(-3)^2 + 3(-3) + 5
Exponent first.
2(9) + 3(-3) + 5
Multiplication
18 + -9 + 5
Add.
14
i need help this exact minute
no fake answers, seriously no.
Answers
Answer:
h is the horizontal translation
k is the vertical translation
a is the stretch parallel to the y-axis
Step-by-step explanation:
Parent equation: [tex]y=x^2[/tex]
Translate [tex]h[/tex] units right: [tex]y=(x-h)^2[/tex]
(if [tex]h < 0[/tex], then the translation is [tex]h[/tex] units left)
Stretched parallel to the y-axis by a factor of [tex]a[/tex]: [tex]y=a(x-h)^2[/tex]
(if [tex]a < 0[/tex], the graph is also reflected in the x-axis)
Translated k units up: [tex]y=a(x-h)^2+k[/tex]
(if [tex]k < 0[/tex] then the translation is k units down)
Example attached for [tex]y=2(x-3)^2+4[/tex]
Can someone help with this
Answers
Answer:
Step-by-step explanation:
Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.
Vertical Asymptotes:
x=1
Horizontal Asymptotes:
y=0
No Oblique Asymptotes
What is the surface area of the cylinder with height 4 km and radius 5 km?
Answers
The graph shown compares the number of pages of the same book read by Emily and Serena over time.
How many minutes after Serena started reading would the number of pages read by them be equal?
Answers
Using linear equations, the number of minutes that both would read for them to read equal number of pages is: 30 minutes.
What is the Equation of a Linear Graph?Equation of a linear graph is given as, y = mx + b, where m and b are the slope and y-intercept of the graph respectively.
Equation for Emily's graph:
Slope (m) = rise/run = 1/3
y-intercept (b) = 2
Substitute m = 1/3 and b = 2 into y = mx + b
y = 1/3x + 2
Equation for Serena's graph:
Slope (m) = rise/run = 2/5
y-intercept (b) = 0
Substitute m = 2/5 and b = 0 into y = mx + b
y = 2/5x + 0
y = 2/5x
To find how many minutes for both of them to read the same number of pages, make both equations equal to each other.
2/5x = 1/3x + 2
2/5x - 1/3x = 2
1/15x = 2
Multiply both sides by 15
x = (2)(15)
x = 30
The answer is 30 minutes for both to read the same number of pages.
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what is the mean for 1500 338 588 850
Answers
Answer:
819
Step-by-step explanation:
The mean is the average. Add up all the values and then divide that by the total amount of values. 1500+338+588+850=3276. 3276/4=819.
Brenya Estate produces a high quality tea branded Super by blending three types of tea coded A, B and C in the ration 1½ : 5 : 1. Originally Type A tea costs GHS 1,600 type B costs GHS 800 and type C costs GHS 1,700 per Kg to produce. Brenya Tea Estate packs Super tea in packets of 825g each. Blending and packing costs are 40 per Kg. Determine the production cost for a packet of Super tea.
Answers
Therefore, the production cost for a packet of Super tea is $923.91.
Cost calculationSince Brenya Estate produces a high quality tea branded Super by blending three types of tea coded A, B and C in the ration 1½ : 5 : 1, and originally Type A tea costs GHS 1,600 type B costs GHS 800 and type C costs GHS 1,700 per Kg to produce, and Brenya Tea Estate packs Super tea in packets of 825g each. Blending and packing costs are 40 per Kg, to determine the production cost for a packet of Super tea, the following calculation must be made:
Blending ad packing costs = 40 x 0.825 = 331.5 + 5 + 1 = 7.57.5 = 1001.5 = X1.5 x 100 / 7.5 = 207.5 = 1005 = X5 x 100 / 7.5 = 66.66100 - 66.66 - 20 = 13.3333 + (1600 x 0.2 x 0.825) + (800 x 0.6666 x 0.825) + (1700 x 0.1333 x 0.825) = X33 + 264 + 439.96 + 186.95 = X923.91 = XTherefore, the production cost for a packet of Super tea is $923.91.
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Abby has 2.28 pounds of meat. She uses 0.19 pound of meat to make one hamburger. How many hamburgers can Abby make with the meat she has
Answers
Answer: Abby would be able to make 12 hamburgers.
Step-by-step explanation:
You have to divide 2.28 and 0.19 and you would get 12 so the answer is 12.
Find the value of each determinant:
Help!
Answers
Answer:
Matrix 1: -4269
Matrix 2: 1768
Matrix 3: 647.3561
Step-by-step explanation:
Matrix 1: [tex](7*19)-(31*142)=-4269[/tex]
Matrix 2: 1768
[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]
Determinant = [tex]a(ei-fh)-b(di-fg)+c(dh-eg)[/tex]
Matrix 3: 647.3561
[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]
Determinant = [tex]a(ei-fh)-b(di-fg)+c(dh-eg)[/tex]
Please help me with this question
Answers
Applying the formula for the area of a sector and length of an arc, the value of k is calculated as: 27.
What is the Area of a Sector?Area of a sector of a circle = ∅/360 × πr²
What is the Length of an Arc?Length of arc = ∅/360 × 2πr
Given the following:
Radius (r) = 9 cmLength of arc = 6π cmArea of sector = kπ cm²Find ∅ of the sector using the formula for length of acr:
∅/360 × 2πr = 6π
Plug in the value of r
∅/360 × 2π(9) = 6π
∅/360 × 18π = 6π
Divide both sides by 18π
∅/360 = 6π/18π
∅/360 = 1/3
Multiply both sides by 360
∅ = 1/3 × 360
∅ = 120°
Find the area of the sector:
Area = ∅/360 × πr² = 120/360 × π(9²)
Area = 1/3 × π81
Area = 27π
Therefore, the value of k is 27.
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You deposit $25,000 into a bank that pays % 4 annual interest compounded monthly.
a) What is the account balance after 3 years?
b) When will the balance reach $40,000 ?
Answers
Answer
A: $28,000
B: 15 years
Step-by-step explanation:
A: Since $25,000 is deposited in the bank and you earn 4% interest annually over 3 years you would earn 12% interest. 12% of 25,000 is 3,000. The sum of 25,000 and 3,000 is 28,000 having you earn $28,000 over 3 years.
B: Since every year you earn 4% annual interest and you have $25,000 deposited in the bank you have to find what percentage of 25,000 equals 15,000. Since 25,000 isn't exactly easy to find multiply it by 4. That leaves you with 100,000 which we know you don't have in the bank but it will make it easier to find the percentage. You will also have to multiply 15,000 by 4 giving you 60,000. Now divide the 60,000 by 1,000 which equals 60. What's the point of the number 60? Well, that's the percentage it takes. Now divide 60 by the annual interest which is 4 and that gives you 15. 15 is the number of years it will take for the balance to reach $40,000.
Hope this helps!
What type of number is √25? Whole number , integer , rational or irrational . SELECT ALL THAT APPLY
Answers
Answer:
A, B, and C.
Step-by-step explanation:
The square root of 25 is 5. 5 is rational, a whole number, and an integer.
Is the discriminant of g positive, zero, or negative?
Answers
Answer:
the discriminant of g positive
Step-by-step explanation:
the discriminant of g positive because the graph of g cross the x-axis in two points.
May is designing a triangular pyramid made of all glass to go on top of a building. All of the faces of the pyramid have a height of 17 feet and a base of 20 feet. How much glass is needed? A. 680 sq ft B. 340 sq ft C. 2,040 sq ft D. 1,360 sq ft.
Answers
Area of a triangle is 1/2 x base x height.
area of triangle = 1/2 x 20 x 17 = 170 square feet.
the image shows 4 triangles, total area = 170 x 4 = 680 square feet.
the answer is A. 680 sq. ft.
Answer:
Area of a triangle is 1/2 x base x height.
area of triangle = 1/2 x 20 x 17 = 170 square feet.
the image shows 4 triangles, total area = 170 x 4 = 680 square feet.
the answer is A. 680 sq. ft.
Hope this helps you!!
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