i chose x=3 , x=-4 which was wrong the correct answer is x=1 , x=-2
can someone please explain how to get that answer
Answers
Answer:
vertical asymptotes is x = -2 and x = 1
Step-by-step explanation:
For rational functions, the vertical asymptotes are the undefined points, also known as the zeros of the denominator (below the line), of the simplified function.
This means [tex]-4x^{2} - 4x + 8[/tex] is equal to zero than solve
*image below*
Hope it helps :)
Let me know if you have any questions or anymore help lmk, happy to help with any school work!!
We are give with the function:
[tex]{\quad \qquad \longrightarrow f(x)=\dfrac{x^{2}+x-12}{-4x^{2}-4x+8}}[/tex]
Vertical asymptotes are the points, where the function is not defined, so the denominator must be equal to 0 for making f(x) not defined
[tex]{:\implies \quad \sf -4x^{2}-4x+8=0}[/tex]
Dividing both sides by -4, we have;
[tex]{:\implies \quad \sf x^{2}+x-2=0}[/tex]
Can be further written as:
[tex]{:\implies \quad \sf x^{2}-x+2x-2=0}[/tex]
[tex]{:\implies \quad \sf x(x-1)+2(x-1)=0}[/tex]
[tex]{:\implies \quad \sf (x-1)(x+2)=0}[/tex]
Using zero product rule, Equating both multiplicants to 0, we have:
[tex]{:\implies \quad \boxed{\bf{x=1\quad or\quad -2}}}[/tex]
This is the required answer
Related Questions
Which expression represents the quotient of (x^2-4)/(x-7)/(3x+6)/(x^2-6x+7)
Answers
Answer:
last option (x-2)(x+1)/3
Step-by-step explanation:
(x^2-4)/(x-7) ÷ (3x+6)/(x^2-6x+7)
(x^2-4)/(x-7) * (x^2-6x+7)/(3x+6)
(x+2)(x-2)/(x-7) * (x-7)(x+1)/3(x+2)
(x-2)/1 * (x+1)/3
(x-2)(x+1)/3
(x^2-4)/(x-7) / (3x+6)/(x^2-6x-7)
What is 16 1/5 - 5 2/3?
Answers
Answer:
10.533
Step-by-step explanation:
Have a great rest of your day
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A class has seven students. what is the probability that exactly four of the students were born on a weekday (monday through friday)?
Answers
The probability that exactly four of the students were been born on a weekday (i.e. Monday through Friday) is 0.2125.
What is the probability of determining that exactly four students were born on a weekday?To determine the probability, we need to first find the probability of having a student being born on a weekday.
[tex]=\mathbf{\dfrac{5}{7}}[/tex]
The probability of having 4 students born on a weekday is:
[tex]=\mathbf{(\dfrac{5}{7})^4}[/tex]
Since we have 4 students, we also need to find the probability of the students that are not being born, which is:
[tex]=\mathbf{(\dfrac{2}{7})^3}[/tex]
Also, there are [tex](^7_4)[/tex] = 35 ways to get four students out of seven students.
Therefore, we have the probability as:
[tex]\mathbf{P = 35 \times (\dfrac{5}{7})^4 \times (\dfrac{2}{7})^3}[/tex]
P = 0.2125
Therefore, we can conclude that the probability that exactly four of the students were born on a weekday is 0.2125.
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An equation for the line
Answers
Answer:
y=-1/3x
Step-by-step explanation:
if it’s going down by one there should be one on top on since it’s going over by 3 it should be 3 on the bottom
Find the sum of all positive integers less than 200 that are divisible by 7.
Answers
Step-by-step explanation:
the positive integer numbers that are divisible by 7 are an arithmetic sequence by always adding 7 :
a1 = 7
a2 = a1 + 7 = 7+7 = 14
a3 = a2 + 7 = a1 + 7 + 7 = 7 + 2×7 = 21
...
an = a1 + (n-1)×7 = 7 + (n-1)×7 = n×7
the sum of an arithmetic sequence is
n/2 × (2a1 + (n - 1)×d)
with a1 being the first term (in our case 7).
d being the common difference from term to term (in our case 7).
how many terms (what is n) do we need to add ?
we need to find n, where the sequence reaches 200.
200 = n×7
n = 200/7 = 28.57142857...
so, with n = 29 we would get a number higher than 200.
so, n=28 gives us the last number divisible by 7 that is smaller than 200 (28×7 = 196).
the sum of all positive integers below 200 that are divisible by 7 is then
28/2 × (2×7 + 27×7) = 14 × 29×7 = 2,842
emergencyyy
Write the given expression in the form f(x)= a(x– h)? +k. Identify the vertex.
f(x) = 2x² - 16x-5
Answers
Answer:
vertex = (4, - 37 )
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = 2x² - 16x - 5 ← factor 2 out of the first 2 terms
= 2(x² - 8x) - 5
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² - 8x
f(x) = 2(x² + 2(- 4)x + 16 - 16) - 5
= 2(x - 4)² - 32 - 5
= 2(x - 4)² - 37 ← in vertex form
with vertex = (4, - 37 )
what is the lowest common multiple of 8,12,9
Answers
Answer:
LCM of 8, 9, and 12 is 72.
Step-by-step explanation:
The LCM of three non-zero integers, a(8), b(9), and c(12), is the smallest positive integer m(72) that is divisible by a(8), b(9), and c(12) without any remainder.
appreciate it if someone will follow me.
Answer:
72
Step-by-step explanation:
To find the Lowest Common Multiple (LCM), prime factorize the included terms, and multiply the factors of each number of the highest power together.
Prime factorizing
8 = 2³12 = 2² x 39 = 3²LCM (8, 12, 9)
= 2³ x 3²
= 8 x 9
= 72
Lara took a total of 63 quizzes over the course of 7 weeks. How many weeks of school will Lara have to attend this quarter before she will have taken a total of 90 quizzes? Solve using unit rates.
weeks
Answers
Answer:
63 quizzes= 7 weeks
90 quizzes= x weeks
63x = (7)(90)
x= (7)(90)/63
x= 10 weeks
what is the surface area of the sphere
Answers
Answer:The answer iis 1810.3cm^2
Step-by-step explanation:
Question :-
What is the surface area of the sphere that has a radius of 12 cm?Answer :-
The surface area of the sphere is 1809 cm².[tex] \rule{180pt}{3pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{12 \: cm}}\end{picture}[/tex]
Solution :-
As per the provided information in the given question, we have been given that the radius of the sphere is 12 cm. We have been asked to find or calculate the surface area of the sphere.
To calculate the surface area of the sphere, we will use the formula below :-
[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]
Substitute the given values into the above formula and solve for surface area:
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(12 \: cm)^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(144 \: cm^2)[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(452.16 \: cm^2)[/tex]
[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 1809 \: cm^2}[/tex]
Therefore :-
The surface area of the sphere is 1809 cm².[tex]\\[/tex]
Learn more about the surface area of the sphere at https://brainly.com/question/28988747
Have a great day! <33
10. Find the standard equation of the circle having the given center and radius.
Answers
Answer:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (3, 5) and r = , hence
(x - 3)² + (y - 5)² = ( )², that is
(x - 3)² + (y - 5)² = ← equation of circle
Step-by-step explanation:
what does the 0.3in the highlighted cell mean?
Answers
Answer:
it will be 30% in the highlighted cell
Step-by-step explanation:
hope this helps
Help asap thank you will choose branliest
Answers
Answer:
maybe option 2 is the correct answer
Answer:
1 and 3/8 or C
Step-by-step explanation:
the longer pencil is 5 and 2/8 and the length of the shorter pencil is 3 and 7/8
5 2/8 - 3 7/8= 11/8 or 1 and 3/8
I hope this helps!!!
HELP PLEAZE
ILL GIVE BRAINLIEST
Answers
Answer:
153.86 in²
Step-by-step explanation:
The area of a circle is:
A = π r²
Radius is just half of the diameter so r = 7.
Substitute 3.14 for π.
Restate the equation:
A = 3.14 x 7² = 3.14 x 49
A = 153.86
Maria bought an open-based pop-up net to put over the plates at the picnic to keep the bugs off of the food. a square pyramid. the square base is 16 inches by 16 inches and the pyramid has a height of 15 inches. how much space is there inside each empty pop-up net? 544 inches cubed 800 inches cubed 1,280 inches cubed 1,920 inches cubed
Answers
Based on the height of the pyramid and the dimensions of the square base, the space that Maria has inside the pop-up net is 1,280 in³.
How much space does Maria have?This can be found as the volume of a pyramid which is:
= (Length x Width x Height) / 3
Solving gives:
= (16 x 16 x 15) / 3
= 3,840 / 3
= 1,280 in³
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Find the volume of the cylinder (3.14 for pi)
Answers
Answer:
The volume of the cylinder is equal to 70.65 cm³.
General Formulas and Concepts:
Geometry
Volume Formula [Cylinder]: V = πr²h
r is radiush is heightStep-by-step explanation:
Step 1: Define
Identify given variables from diagram.
r = 3 cm
h = 2.5 cm
Step 2: Find Volume
[Volume Formula - Cylinder] Substitute in variables:V = (3.14)(3 cm)²(2.5 cm)Evaluate:
V = 70.65 cm³
∴ we found the volume of the cylinder to be 70.65 cm³.
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Topic: Geometry
Tata's age is 10 years younger than Kaka's age.
Three years from now, the sum of their ages
is 40 years. Tata's current age is
year.
a.12 b.15. c.22. d.25
help me -!
Answers
Answer:
c. 22
Step-by-step explanation:
Let x = Tata's age and y = Kaka's age.
x - 10 = y
x+3 + y+3 = 40
Now, we can substitute in x - 10 for y.
x + 3 + (x - 10) + 3 = 40
so 2x = 44
x = 22
Therefore, Tata's current age is 22.
Calculate the surface area of the polyhedra
Answers
6.8^2= 46.24
46.24*6= 277.44
Given: ΔABC is an isosceles triangle where AB = BC.
Prove: m∠BAC = m∠BCA
Proof:
Statement Reason
1. Let ΔABC be an isosceles triangle where AB = BC. given
2. Create point D on so that bisects ∠ABC as shown. constructing an angle bisector
3. m∠ABD = m∠DBC definition of angle bisector
4. BD = BD
5. ΔABD ≅ ΔCBD SAS
6. m∠BAC = m∠BCA Corresponding angles of congruent triangles are equal.
20
What is the reason for statement 4 in this proof?
A.
Transitive Property of Equality
B.
definition of midpoint
C.
definition of parallel lines
D.
Reflexive Property of Equality
Reset Next
Answers
You are comparing side AB, angle ABD, and side BD in one triangle to side CB, angle CBD, and side BD in the other triangle. That is, you are comparing a Side, Angle, and Side in each triangle. The SAS postulate is the reason the triangles are congruent.
Answer:
Transitive Property of Equality
Step-by-step explanation:
Under her cell phone plan, Ella pays a flat cost of $37.50 per month and $5 per gigabyte. She wants to keep her bill at $59 per month. How many gigabytes of data can she use while staying within her budget?
Answers
The number of gigabytes of data can she use while staying within her budget should be less than 4.3 gigabytes.
What is a linear equation?Linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
Under her cell phone plan, Ella pays a flat cost of $37.50 per month and $5 per gigabyte.
She wants to keep her bill at $59 per month.
Then the number of the gigabytes of data can she use while staying within her budget will be
Let x be the number of the gigabytes. Then the equation will be
5x + 37.5 < 59
5x < 21.5
x < 4.3
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Solve for x, y, and z. Round your answer to the nearest tenth
Answers
Answer:
Step-by-step explanation:
Simplify each monomial rational expression 20x^2 divided by 10x^2
Answers
Answer:
2x to the 4th power
Step-by-step explanation:
Hope this helps
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet. what is the volume of the cube? 3 cubic feet 6 cubic feet 18 cubic feet 27 cubic feet
Answers
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet is 3 cubic feet
Volume of a pyramidThe formula for calculating the volume of a pyramid is expressed as:
V = Base area. * height/3
Since it is a cube with a volume of 9 cubic feet, the length of the cube will be:
l = ∛9
l = 2.08
Determine the volume of the pyramid
V = 9/3
V = 3 cubic feet
Hence the volume of a pyramid that fits exactly inside a cube is 9 cubic feet is 3 cubic feet
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What number and what percent describe the probability of a certain event?
Enter the correct answers in the boxes.
The probability of a certain event is
__ or __%.
The probability of an impossible event is
__ or __%.
Answers
Answer:
The probability of a certain event is 1 or 100%
The probability of an impossible event is 0 or 0%
Answer:
See below ~
Step-by-step explanation:
The probability of a certain event is 1 or 100%.The probability of an impossible event is 0 or 0%.please please help. Will give brainliest
Answers
HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELP pls
Answers
Answer:
28.27
Step-by-step explanation: used to do acellus too
An airplane is flying at an altitude of 2.7 miles and is 8.3 miles from the runway. Find the angle of depression from the airplane to the runway
Answers
Answer:
Step-by-step explanation:
AB = altitude = 2.7 miles
BC = 8.3 miles
[tex]\sf tan \ \theta = \dfrac{opposite \ side \ of \ \theta}{adjacent \ side \ of \ \theta}\\\\Tan \ \theta = \dfrac{AB}{BC}=\dfrac{2.7}{8.3}\\\\Tan \ \theta = 0.33\\\\\theta = tan^{-1} \ 0.33[/tex]
[tex]\boxed{\theta = 18.3}[/tex]
Solve and graph the inequality.
6 + x > 15
Answers
Answer:
x > 9
The graph is a half-plane. (All the points with their abscissa (their value on the x-axis) greater than 9
Step-by-step explanation:
6 +x > 15
x > 15 - 6
x > 9
Answer:
X>9
Step-by-step explanation:
the other guy has the graph
determine the equation for the given information
Answers
point-slope form
y - y₁ = m(x - x₁)
[tex]y-1=-\frac{1}{2}(x-8)\\\\y-1=-\frac{1}{2}x+4\\\\y=-\frac{1}{2}x+5[/tex]
The answer is A) Choice A.
PLEASE HELP ME ASAP :(
Answers
Answer:
Step-by-step explanation:
Refer the attachment
Answer:
752.5 in³
Step-by-step explanation:
Volume of composite solidRectangular prism:
l = 10 in ; w = 7 in ; h = 8 in
[tex]\boxed{\text{Volume of rectangular prism=l*w*h}}[/tex]
= 10 * 7 * 8
= 560 in³
Half cylinder:
Diameter of the cylinder will be equal to the width of the rectangular prism.
r = 7/2 = 3.5 inches ; h = 10 in
[tex]\boxed{\text{Volume of half cylinder =$\dfrac{1}{2}\pi r^2h$}}[/tex]
[tex]\sf =\dfrac{1}{2}*3.14*3.5*3.510\\\\ = 192.5 \ in^3[/tex]
Volume of composite figure = 560 - 192.5
= 752.5 in³
if x-2y=10 and x≠0, what is the value of 2x/y+5
Answers
Answer: 4
Step-by-step explanation:
x - 2y =10
x = 10 + 2y
[tex]\frac{2x)}{y + 5}[/tex]
[tex]\frac{2(10+2y)}{y+5}[/tex]
[tex]\frac{20+4y}{y+5}[/tex]
[tex]\frac{4(5+y)}{y+5}[/tex] ... cancel like terms (y + 5)
= 4