Answers
Step-by-step explanation:
the last 2 answer options are completely useless and outright nonsense, because all limits are going against +4.
so, an asymptote at x = -4 is not an option anywhere.
g(x) is always y, and the limit of the function is the limit of the y values.
we just evaluate for what x value is then y reaching that limit. but the sign of the y limit has no direct impact on the sign of the x value.
it is true that the case x = -4 needs to be checked too, but it turns out this just delivers g(-4) = 0.
now, about x = 4 :
when coming from the left side of +4 (increasing x), what is the sign of the function ?
we can simply use x = 3 to test this :
g(3) = 2(3+4)²/(3² - 16) = 2×49/-7
so, it is negative.
that means when getting closer and closer to +4 coming from that side we what get negative values, and the limit is -infinity.
when coming from the right side of +4 (decreasing x), what is the sign of the function ?
we can simply use x = 5 to test this :
g(3) = 2(5+4)²/(5² - 16) = 2×81/9
so, it is positive.
that means when getting closer and closer to +4 coming from that side we what get positive values, and the limit is +infinity.
so, the second answer option is correct.
because of these y limits, there is a vertical asymptote at x = 4 that kind of "connects" -infinity and +infinity in y direction at that location and symbolizes the limits of y.
Related Questions
Make x the subject to this formula 4x + 3y =2
Answers
4x+3y=2
4x=2-3y
x= 2/4 - 3/4 y
x= 1/2- 3/4y
(x= 0.5 - 0.75y)
[tex]\boxed{ \ \sf x=\dfrac{2-3y}{4} \ }[/tex]
Explanation:[Given]
[tex]\sf \rightarrow 4x + 3y =2[/tex]
[Exchange Sides]
[tex]\sf \rightarrow 4x =2-3y[/tex]
[Divide both sides by 4]
[tex]\sf \rightarrow \dfrac{4x}{4} =\dfrac{2-3y}{4}[/tex]
[Simplify]
[tex]\sf \rightarrow x=\dfrac{2-3y}{4}[/tex]
The figure below shows parallelograms ABCE, PQRS, and TNLM on a coordinate plane.
10
9
8
7
E
R
M
s
0
N
А
B
-10
.
The coordinates and relations between the points are:
· A(-3,-3); B(5,-3); C(5,5); E(-3,5)
Points S, P, Q, and R are midpoints of ABCE
T,N, Q, and M are midpoints of PQRS
Write the equation of line M L. Show your work.
.
Answers
From the graph, the coordinate of M and L will be (-1, 3) and (3, 3). Then the equation of the line ML will be y - 3 = 0.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The figure below shows parallelograms ABCE, PQRS, and TNLM on a coordinate plane.
The coordinates and relations between the points are:
A(-3,-3), B(5,-3), C(5,5), and E(-3,5)
Then the equation of the line ML will be
From the graph, the coordinate of M will be (-1, 3) and the coordinate of L will be (3, 3).
Then the equation will be
[tex]\rm y- 3 = \dfrac{3-3}{3+1} (x - 3)\\\\y - 3 = 0[/tex]
Then the equation of the line ML will be y - 3 = 0.
More about the coordinate geometry link is given below.
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what is the measure of BDC?
Answers
Explanation ~ because the book said so > : )
Solve this
4 ∙ 7 1/2 ∙ 1 3/5
Answers
Step-by-step explanation:
[tex] = 7 \frac{1}{2} .1 \frac{3}{5} [/tex]
[tex] = \frac{ \red{\cancel{15}}}{ \blue{ \cancel{2}}} . \frac{ \blue{\cancel{8}}}{ \red{\cancel{5}}} [/tex]
[tex] = \frac{3}{1} . \frac{4}{1} [/tex]
[tex] = 12[/tex]
[tex] \: [/tex]
Which part of a story shows how the climax affected the characters?
Falling action
Rising action
Exposition
Resolution
Answers
Answer:
Falling action
Step-by-step explanation:
Falling action in a basic plot structure is the events that happen after the climax and before the resolution. This part of your story is often used to show the consequences of the climax and how it affects the characters.
(b) A square has a perimeter of 80 ft. What is the length of each side?
Answers
Answer:
20 ft
Step-by-step explanation:
There are 4 equal sides to a square so one side is 80/4 = 20 ft
Please show work and thank you
Answers
Answer:
x = 6
Step-by-step explanation:
A 45-45-90 isosceles right triangle has side lengths in the ratios ...
1 : 1 : √2
__
That is, the longest side (marked x in this figure) is √2 times the length of the other two equal-length sides.
x = (√2)×3√2 = 3×2
x = 6
Compare 4 and -2. Which of the following is true?
Answers
Answer:
Your answer is A.
Step-by-step explanation:
Absolute values of any number are positive.
|4| = 2
|-2| = 2
2 = 2 and 4 > -2
C and D can be true, but they are not since less than or greater than doesn't apply if they were less than/greater than or equal, then yes.
This is very confusing to me
Answers
Answer:
the system is inconsistent
also ,Check the attached graph
Step-by-step explanation:
let D₁ be the line of equation 3x - 9y = 36
D₂ be the line of equation 2x - 6y = -8
In order to graph D₁ we need to find two point shot that lie on it.
→ If x = 0 , 3(0) - 9y = 36 ⇔ -9y = 36 ⇔ y = -4
Then the point C(0 , -4) lies on D₁
→ If x = 3 , 3(3) - 9y = 36 ⇔ -9y = 27 ⇔ y = -3
Then the point D(3 , -3) lies on D₁
Therefore,
D₁ is the line that connects the points C and D
Similarly,We can prove that the point she A(-4 , 0) and B(-1 , 1) lie on D₂
Then D₂ = (AB)
After graphing, we notice that D₁ and D₂ are parallel and they don’t have any point in common.
Therefore ,we say that’s the system is inconsistent
How do you find x in this question?
Answers
Answer:
x = 70°
Step-by-step explanation:
The relevant relations are ...
base angles of an isosceles triangle are congruentconsecutive interior angles where parallel lines meet a transversal are supplementary__
Triangle OBQ is isosceles, so angle OQB = 40°. Triangle OPQ is isosceles, so angle OQP is x. The sum of angles OQB and OQP is angle BQP, which is supplementary to angle OPQ. That is, ...
(40° +x) +x = 180°
2x = 140° . . . . . . subtract 40°
x = 70° . . . . . . divide by 2
_____
There are many ways to find x. The one shown here is just one of them. In general, right triangles, isosceles triangles, symmetry, inscribed angles can all be used to write relations involving the known angles and x.
Subtract;
233.66-66.24
43.12-21.11
24.6-19.777
Answers
Answer:
1. 167.42
2. 22.01
3. 4.83
233.66-66.24 = 167.42
43.12-21.11 = 22.01
24.6-19.777 = 4.823
if the area of a square is 32f^2 how long is its diagonals?
Answers
8f
Side:
√32 = 4√2
Diagonal of the square:
√2 X side = √2 X 4√2 = 8f
Identify the range of the function shown in the graph
Answers
Answer:
0 ≤ y ≤ 8
Step-by-step explanation:
DOMAIN is x values of a function/graph
RANGE is the y-values that a function can have .....
this one goes from 0 to 8 inclusive
If l is parallel to m in the following figure, find the measure of x
Answers
Check the picture below.
can someone help me plss the deadline is tmrw
Answers
Answer:
73.77 ft²
Step-by-step explanation:
Area of circle - area of square
= πr² - (length × width)
= (3.14 × 8.1²) - (11.5 × 11.5)
= 73.7654
≈ 73.77 ft²
hope this helps =)
Answers:
Circle area = 206.02 square feetUnshaded area = 132.25 square feetShaded area = 73.77 square feetThe "square feet" portions are already handled by your teacher, so you'll just type in the numbers only.
======================================================
Explanation:
The formula for the area of a circle is
A = pi*r^2
We replace pi with its approximation 3.14, and plug in the radius r = 8.1 to get the following approximate area:
A = 3.14*(8.1)^2
A = 206.0154
A = 206.02 which is the answer to the first box
--------------------------
The unshaded region is a square of side length 11.5 ft
Its area must be (11.5)^2 = 132.25 square feet
--------------------------
Subtract the results of the previous boxes to get the shaded area.
206.02 - 132.25 = 73.77
Which table of values was used to create the scatterplot below? A graph titled Fundraiser Amounts has Day of Fund Drive on the x-axis and Money Raised (dollars) on the y-axis. Points are at (1, 200), (2, 300), (3, 200), (4, 400), (5, 300). A 2-column table with 5 rows. Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 300, 400, 200, 300. A 2-column table with 5 rows. Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 300, 200, 300, 400. A 2-column table with 5 rows. Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 300, 200, 400, 300. A 2-column table with 5 rows. Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 200, 300, 400, 300.
Answers
The table of values used to create the scatterplot below is:
Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 300, 200, 400, 300
Which table of values was used to create the scatterplot below?The graphs x axis represents the Day of Fund Drive and y axis represents Money Raised.
The ordered pairs from the plot are:
(1, 200), (2, 300), (3, 200), (4, 400), (5, 300)
Therefore, the table of values used to create the scatterplot below will be:
Day of Fund Drive Money raised (dollars)
1 200
2 300
3 200
4 400
5 300
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Answer:
C.
Step-by-step explanation:
Edge 2023
a line passes through the point (-9,1) and has a slope of 4/3. Write an equation in slope-intercept form for this line.
Answers
Answer: y=4/3x+1
Step-by-step explanation:
The formula is Y=mx+b
b is the y-intercept and MX is slope
To rationalize a denominator that has more than one term, you multiply the
fraction by B+ B, where B is the conjugate of the denominator.
Answers
Answer:
False.
Explanation:
To rationalize a denominator that has more than one term, you multiply the fraction by [tex]\frac{b}{b}[/tex], where "b" is the conjugate of the denominator not the numerator.
false
you multiply both the denominator and the numerator not just the fraction.
What is the length of the two equal sides?
What is the length of the third side?
Answers
Answer:
Two equal sides: 15 centimeters, Third side: 21 centimeters
Step-by-step explanation:
Sorry If I'm late, so how I solved this was by using variables and algebra. The perimeter of a triangle is the sum of all three sides. Let's now break down the problem and use the useful information, we know that the perimeter is 51 centimeters, and that there are two equal sides and the third side is 6 inches longer than the two equal sides. So it is pretty much an isosceles triangle since it has two sides of equal length and the third side is not equal to the others. So we can make an equation with variables. 51(Perimeter)=x(first equal side)+x(second equal side)+x(third side)+6(The third side is 6 centimeters longer than the two other sides), now we simplify the equation just like we do with most algebraic equations. x+x+x can be turned into 3x. This now makes the equation 51=3x+6, we can subtract 6 from both sides to just have the variable on one side, 3x+6-6, both sixes cross out making it 3x, 51-6 is equal to 45. Now we divide by three on both sides to give just x and find out what x is. 3x/3=x and 45/3=15. x=15, x is the equal side length, so the two equal sides are 15 centimeters and the third one is 21 centimeters. The reason for this is because 15+6=21. I hope this helped with your learning, if I am wrong please tell me :)
A box is filled with 5red crayons, 9blue crayons, and 6yellow crayons.
A crayon is chosen at random from the box. Find the probability that it is a red or a blue crayon.
Write your answer as a fraction in the simplest form.
Answers
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
P(R or B)=[tex]\frac{5}{20}+\frac{9}{20}[/tex]
=[tex]\frac{7}{10}[/tex]
Tge length of the front page is 30 centimeters and the width is 20 centimeters the side length picture is 7 centimeters
Answers
Answer:
A model of a shopping centre is drawn to scale where 1 cm on the model represent 4 m on the ground. Music shop Thabo's Sports Ware Fati's Clothing shop Grocery store PARKING Coffee shop Toilets Restaurant Shoe store Physiotherapy Health and Fitness center 1.1 Which shop is on the right of the physiotherapy? (2) 1.2 Describe the position of the Coffee Shop in relation to the Toilets. (2)
Can you guys help me please :(
Answers
Answer:
circumference formula = πd or 2πr .. they are the same thing
G is the answer
A pane of antique glass has dimensions of 30cm x 56cm. If the glass sells for 25 cents per square cm, what is the cost of the pane?
Answers
Given :-
Dimensions of pane is 30cm×56cmCost of pane per square cm is 25 centsTo find :-
Cost of the paneSolution:-
Hey mate , to find the total cost of pane we have to find the area of pane and multiply it by 25 cents
Area of pane :- 30×56cm²
Area of pane :- 1680cm²
Cost of pane :- 1860×25 cents
Cost of pane :- 42000 cents or 420$
What is the surface area of this right prism?
Enter your answer in the box.
cm²
NEED HELP ASAP!!! 20 POINTS!!!!
Answers
Answer:
Since the 'base' and 'top' of any prism have the same shape, the surface area can be found by
surface area of prism = 2 * area of base + perimeter of base * H
So for the rectangular prism in your example..
surface area = 2LW + 2(L+W)H
= 2 * 7 * 4 + 2*(7+4)*5
= 56 + 2 * 11 * 5
= 56 +110
= 166 sq cm
Hope this helps
Find the surface area to the nearest square foot.
how to do this?
Answers
1026.78
[tex]\bold{SOLUTION:}[/tex]
How long will it take to triple a sum of money if it is invested at a rate of 6.25% compounded continuously? Round your answer to 2 decimal places.
Answers
Answer:
So the answer is approximately 18 years
Step-by-step explanation:
Your interest rate is 6.25%, or, 0.0625
A=P⋅(1+(r/n))^nt
Where:
P is the initial amount
r is annual rate of interest
t is number of years
A is the final amount of money
n is the number of times the interest is compounded per year
So
3P=P(1+0.0625)
3P=P (1.0625)^t
3=1.0625^t
Now we should use logarithmic functions.
ln(3)=t⋅ln(1.0625)
ln(3)ln(1.0625)=t
t=18.12 years
Can someone please solve this for me using that method thank you I give brainliest
Answers
Find the slope of a line parallel to -3x+7y=-15
Answers
Answer:
[tex] \boxed{\rm \: Slope = 3/7 \: x}[/tex]
Step-by-step explanation:
Given :
3x+7y=-15To Find:
The slopeSolution:
Well,to find out the slope of the line here, we'll need to re-write the fully solved equation into slope - intercept form.
[tex] \boxed{ \rm \: y = mx = b}[/tex]
Here,
m = slopeb = y - intercept.[Add 3x to both sides to the original equation:]
[tex] \rm \: 7y = - 15 + 3x[/tex]Divide each term in this equation by 7:
[tex] \cfrac{7y}{7} = \cfrac{ - 15}{7} + \cfrac{3x}{7} [/tex][tex] \rm \: y = \cfrac{ - 15}{7} + \cfrac{3x}{7} [/tex]Now rewrite this equation into slope-intercept form.
[tex]y = mx + b[/tex]Plug values.
[tex]y = \cfrac{3x}{7} - \cfrac{15}{7} = \cfrac{3}{7} x - \cfrac{15}{7} [/tex] > So , y - intercept is 15/7> Slope m is 3/7 x.Hence,we can conclude:
The slope of the line parallel to -3x+7y=-15 is 3/7 x.[tex] \rule{225pt}{2pt}[/tex]
please do answer:
Simplify the expression---5x-2y + 3x + 2y
(100 points)
Answers
Combine like terms
5x+3x-2y+2y(5+3)x+(-2+2)y8x+08xAnswer:
8x
Step-by-step explanation:
Given expression:
[tex]5x - 2y + 3x + 2y[/tex]As we know, any negative integer being added by itself is 0. [-2y + 2y = 0]
[tex]\implies 5x - 2y + 3x + 2y[/tex][tex]\implies 5x + 3x + 0[/tex]Collect like terms and simplify;
[tex]\implies 5x + 3x + 0[/tex][tex]\implies x(5 + 3) + 0[/tex][tex]\implies x(8) + 0 = \boxed{8x}[/tex]Therefore, 8x is the simplified term.
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A doctor claims that the mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night. To investigate, he selects a random sample of 50 high school seniors from all high schools in his county. He also selects a random sample of 50 seniors from the colleges in his county. He constructs a 95% confidence interval for the true mean difference in the number of hours of sleep for seniors in high school and seniors in college. The resulting interval is (0.57, 1.25). Based upon the interval, can the doctor conclude that mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night?
yes because 1 is in the confidence interval
yes because 0 is not in the confidence interval
no because 1 is in the confidence interval
no because 0 is not in the confidence interval
Answers
Considering the given confidence interval, the correct option regarding the conclusion of the hypotheses test is given by:
yes, because 0 is not in the confidence interval.
What are the hypotheses tested?At the null hypotheses, it is tested if the difference is equals to zero, that is:
[tex]H_0: \mu = 0[/tex].
At the alternative hypotheses, it is tested if it is different, hence:
[tex]H_1: \mu \neq 0[/tex].
The confidence interval is (0.57, 1.25). Since it does not contain 0, there is enough evidence that the difference is different of 0, hence the correct option is given by:
yes, because 0 is not in the confidence interval
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