a) The process to find the limit is given as follows:
f(x): simply replace x by 1.g(x): factor and then replacing.b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.
How to calculate the limit of a function?The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.
Hence:
lim x -> 1 f(x) = 1 + 1 = 2.lim x -> 1 g(x) = (1² - 1)/(1 - 1) = 0/0.For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.
Applying the subtraction of perfect squares, we have that:
x² - 1 = (x - 1)(x + 1).
Then:
g(x) = (x - 1)(x + 1)/(x - 1) = x + 1.
Meaning that the limit is then calculated as follows:
lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.
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A shipping container will be used to transport several 150-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 8700 kilograms have already been loaded into the container. Use the drop-down menu below to write an inequality representing cc, the total number of 150-kilogram crates that can be loaded into the shipping container.
Answer:
Below
Step-by-step explanation:
(27500 - 8700) >= 150 x where x is the number of 150 kg containers
What is the gravitational potential energy of a 55-kg person that has climber a 4,000 meter tall mountain?
Bonus: if one snickers bar is 1,100,000 joules of energy, how many snickers bars would provide enough fuel to climb the mountain ?
Sam and Harry are family. Sam is currently three times Harry's age. Sam's age is also 10 more than twice Harry's age. The following system of equations models this scenario:
x = 3y
x = 10 + 2y
What are their current ages?
Sam is 24 years old, and Harry is 8 years old.
Sam is 39 years old, and Harry is 13 years old.
Sam is 27 years old, and Harry is 9 years old.
Sam is 30 years old, and Harry is 10 years old.
Answer:
sam is 30 and harry is 10
Step-by-step explanation:
hope you liked my answer .
Answer: Sam is 30 years old, and Harry is 10 years old.
Step-by-step explanation:
x^2-2x+10=0
is the vertex of this parabola a maximum value or minimum value?
Step-by-step explanation:
minimum.
since the term with x² has a positive factor, this will grow exponentially in the positive direction compared to the other terms, so y (the functional value) will grow and grow with growing distance of x to the vertex.
and that makes the vertex the minimum of the parabola (which opens upwards).
if the factor would be negative (like -x² - 2x + 10), the vertex would be a maximum, and the parabola would open downwards.
A cosine function has a period of 4, a maximum value of 20, and a minimum value of 0. The function is not a reflection of its parent function over the x-axis.
Which function could be the function described?
a. f(x)=10cos(2x)−10
b. f(x)=−10cos(π/2x)+10
c. f(x)=10cos(π/2x)+10
d. f(x)=−10cos(2x)+10
Fill in the sentence below with the description that most specifically applies to the quadrilateral below.
The figure with equal opposite sides and all the interior angles being right angles is a rectangle.
What is a quadrilateral?A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.
A rectangle is a special type of quadrilateral in which opposite sides are of equal length(not all sides are the same) and all the interior angles are right angles.
From the given diagram the opposite sides are equal and all the interior angles are right angles hence the figure is a rectangle.
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the ratio of boys to girls in the sixth grade is 3 to 5 if there are 45 girls how many students are there in the 6th grade
Answer: 27 boys
Step-by-step explanation:
There is a rule in math, what you do to one side, you do to the other.
So in this case the ration is 3:5
?:45
As you can see, they multiplied 5 by 9 to get 45, remember the rule, so we do the same.
3 times 9 is 27, so 27 boys
Pls help me
Here is triangle ABC:
No links pls
Answer:
[tex]Given: AC=1[/tex]
∠A=0
[tex]Cos0=\frac{B}{H} =\frac{AB}{AC}[/tex]
[tex]Cos0=\frac{AB}{1}[/tex]
[tex]AB=Cos0[/tex]
-------------------------
hope it helps...
have a great day!!
Answer:
AB = AC×cos theta= cos theta
Target buys a pair of shoes for 20, but they sell it to the public for 35. what is the percent of change that target marks the shoes up for
Answer:
75%
Step-by-step explanation:
To find the percent of change that Target marks the shoes up for, you need to calculate the difference between the cost of the shoes to Target and the price at which they sell it to the public, and then divide that difference by the cost of the shoes to Target. Finally, you need to multiply the result by 100 to express the answer as a percentage.
Using this formula, the percent of change that Target marks the shoes up for is:
(35 - 20) / 20 * 100 = 15 / 20 * 100 = 0.75 * 100 = 75%
This means that Target marks the shoes up by 75% of their cost.
It cost the shoe factory $26.47 to make a pair of Purple Pedi running shoes. The mall sells them for $128.98. What is the percent mark-up?
If it cost the shoe factory $26.47 to make a pair of Purple Pedi running shoes and the mall sells them for $128.98 then 3.87 is the percent mark-up.
How much of a markup is that?The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.
Some individuals will inform you that a 5% markup equates to a markup of 5% of the price your customer pays. In your illustration, this is stating that you add a specific amount to your cost, $62, to arrive at a price of $P for your customer, and the amount you added is 5% of $P. This means that your cost of $62 is 95% of the price of P.
($128.98 - $26.47)/ $26.47
= 3.87.
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Solve the following system of equations:
−2x + y = 1
−4x + y = −1
(3, 1)
(−1, 3)
(−1, −3)
(1, 3)
Answer:
(1,3)
Step-by-step explanation:
[tex]\sf Answer\begin{cases} \sf \rightarrowtail \: - 2x + y = 1 \dots(1) \\ \sf \rightarrowtail \: - 4x + y = - 1 \dots(2) \\ \sf 2 \times (1) \implies - 4x + 2y = 2 \\ \sf 1 \times (2) \implies - 4x + y = - 1 \\ \bf \star \: substracting \: both \\ \sf \rightarrowtail \: y = 3 \\ \sf \rightarrowtail \: -2x+(3)=1 \\ \sf \rightarrowtail \: -2x=-2 \\ \sf \rightarrowtail \: x=1\end{cases}[/tex]
each day you do homework for m minutes and watch tv for 30 minutes. Which expression can you use to find how many minutes you do both activities.
Answer:
Let y be the expression for the minutes you do both activities.then
y=m+30 is the required expression
Mr. Smith has saved $1,800 each year for 20 years. A year after the saving period ended, Mr. Smith withdrew $7,500 each year for a period of 5 years. In the sixth and seventh years, he only withdrew $5,000 per year. In the eighth year, he decided to withdraw the remaining money in his account. If the interest rate was 6% per year throughout the whole period, what was the amount he withdrew at the end of the eighth year?
At the end of the eighth year, the amount Mr. Smith withdrew was $41,757.68.
How the ending withdrawal is determined?The amount that Mr. Smith withdrew at the end of the eighth year is a product of a series of computations, involving future value determination.
In this situation, we have used an online finance calculator to determine the future value of the investment at each leg.
First Leg:N (# of periods) = 20 years
I/Y (Interest per year) = 6%
PV (Present Value) = $0
PMT (Periodic Deposits) = $1,800
Results:
FV = $66,214.06
Sum of all periodic payments = $36,000 ($1,800 x 20)
Total Interest = $30,214.06
Second Leg:N (# of periods) = 5 years
I/Y (Interest per year) = 6%
PV (Present Value) = $,
PMT (Periodic Withdrawal) = $-7500
Results:
FV = $46,331.15
Sum of all periodic payments = $-37,500 ($7,500 x 5)
Total Interest $17,617.09
Third Leg:N (# of periods) = 2 years
I/Y (Interest per year) = 6%
PV (Present Value) = $46,331.15
PMT (Periodic Withdrawal) = $-5000
Results:
FV (Final Withdrawal) = $41,757.68
Sum of all periodic payments = $-10,000 ($5,000 x 2)
Total Interest = $5,426.53
Thus, the amount of $41,757.68 was withdrawn by Mr. Smith at the end.
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The capacity of a tank is 60 000 litres. It is being filled at a rate of 1250 litres per hour. How long will it take to fill of the 5/8 of the tank?
Answer:
48
Step-by-step explanation:
60 000 / 1250 = 48
Solve 4x= If x=10
HURRY PLEASE ITS A TEST
Answer:
40
Step-by-step explanation:
4x
4(10)
Answer: 40
Step-by-step explanation:
Given kite RSTU. Please I need help ASAP.
Solve (2 - x)^2 < 4/25
Answer:
8/5 < x< 12/5
Step-by-step explanation:
(2 - x)^2 < 4/25
Take the square root of each side
sqrt((2 - x)^2) <±sqrt( 4/25)
Make two equations
2-x < 2/5 2-x > -2/5
Subtract 2 from each side
2-x-2 < 2/5 -2 2-x-2 > -2/5-2
-x < 2/5 - 10/5 -x > -2/5 - 10/5
-x < -8/5 -x > -12/5
Multiply by -1, remembering to flip the inequality
x> 8/5 x < 12/5
8/5 < x< 12/5
If the area of a circle is 31.36 pi, then what is its radius?
Answer:
5.6 units
Step-by-step explanation:
[tex]\boxed{area \: of \: circle = \pi {r}^{2} }[/tex]
Given that the area of the circle is 31.36π,
31.36π= πr²
Divide both sides by π:
31.36= r²
r²= 31.36
Square root both sides:
[tex]r = \sqrt{31.36} [/tex]
r= 5.6 units
On the last day of a Shakespeare class, an English teacher asked her students which play
they liked most. Out of the 12 students, 4 liked Macbeth best.
What is the probability that a randomly selected Shakespeare student likes Macbeth best?
Write your answer as a fraction or whole number
Answer: The answer is 8/12, or 8 out of 12.
Step-by-step explanation:
There are 12 students, 4 liked Macbeth, meaning that the rest must like Shakespeare.
what is the third term of an arithmetic sequence whose second term is 7 and whose sixth term is 23
Answer: 11
Step-by-step explanation:
Given
The second term of an AP is 7
The sixth term of an AP is 23
Suppose a and d be the first term and common difference of the sequence
[tex]\Rightarrow 7=a+d\quad \ldots(i)\\\Rightarrow 23=a+5d\quad \ldots(ii)[/tex]
Subtract the above equations
[tex]\Rightarrow 23-7=5d-d\\\Rightarrow 16=4d\\\Rightarrow d=4[/tex]
Put d in equation (i)
[tex]\Rightarrow 7=a+4\\\Rightarrow a=3[/tex]
So, the third term of the AP is [tex]a+2d[/tex]
[tex]\Rightarrow 3+2\times 4=11[/tex]
Someone please help me out
The figures for this problem are not scale drawings, as the ratios between the equivalent side lengths are different.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
Hence, when a figure is a dilation of another figure, the two figures are scale drawings.
For this problem, the ratio between the bases of the rectangles is given as follows:
12/6 = 2.
The ratio between the height of each rectangle is given as follows:
6/2 = 3.
As the ratios are different, the two figures are not scale drawings of one another.
For them to be scale drawings, it would be needed either a ratio of 2 for the heights or a ratio of 3 for the bases.
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6) Round off 78342 to the nearest thousand.
Ethan has 3pounds of mixed nuts how many ounces of mixed nuts does Ethan have ?
Answer:
48 ounces of Mixed Nuts
Step-by-step explanation:
You need to convert pounds to ounces to find the answer to this problem.
1 pound is 16 ounces, so multiply 3 by 16 for your answer,
please help i suck at math
hi can u pls help asap ty
Answer:
this is your proper answer ...
Telephone poles, spaced 100 feet apart, line the road on which Jesse lives. If Jesse runs from the first pole to the seventh pole, how many feet does he run? Draw a picture that illustrates the problem.
Answer:
She would have ran 700 feet.
Step-by-step explanation:
If there are many many poles, and she runs across 7 of them, that would be the number of poles multiplied with the distance: 7 x 100 = 700.
PLZ HELP ASAP! IM FAILING SO PLEASEEEE
Answer: B
You can find slope by using the slope formula. Because we are already given two coordinate points, we can use that to find our slope. The slope formula is [tex]\frac{y^{2}-y^{1} }{x^{2}-x^{1} }[/tex]. This also refers to [tex]\frac{5-(-5)}{0-4}[/tex] or 10/-4 or -5/2. Any coordinate with the x-value as 0 means that that coordinate is the y-intercept. Because (0,5) has 0 as its x-value, the y-intercept is 5.
Please i have a question you can help me for answer.
The question is
Follow the construction program to build below the figure
° Draw a segment {ST} of length 9 cm.
°Draw the circle with center T and radius 4 cm
.
° Draw the circle with diameter {ST}
° The two circles intersect at A and B. Without measuring, give the length of the segments {TA} and {TB}:
The length of segments TA and TB are both 4 cm.
How to determine the diagram and the lengthsTo solve this problem, we can use the properties of circles and the relationship between the radius and the diameter.
Since the radius of the circle with center T is 4 cm, the diameter of this circle is 2 * 4 = 8 cm.
Since the length of segment ST is 9 cm, the diameter of the second circle is also 9 cm.
Since the radius of the circle with center T is 4 cm, the radius of the second circle is also 4 cm.
Since the two circles intersect at points A and B, the segments TA and TB are equal in length.The length of segment TA and TB is the radius of the second circle, which is 4 cm.
Therefore, the length of segments TA and TB are both 4 cm.
The figure is attached
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50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
8.8
Step-by-step explanation:
To find the hypotenuse...
a²+b²=c²
C is the hypotenuse, so we add the others...
8.4²+2.6²=c²
70.56+6.76=c
77.32=c
Now, square root c to bring it to its original position.
√77.32=8.8
Your answer is 8.8 yards.
A blueprint of a house has a scale in which 1 inch equals 4 1/2 feet. If the living room wall measures 7 1/4 inches on the drawing, what is the actual length of the wall?
The actual length of the wall is ___ feet
Answer:
Step-by-step explanation:
1 : 4 1/2 :: 8 1/5 : x proportion
x = (4 1/2)(8 1/5) product of means/extremes
x = (9/2)(41/5) change improper fraction
x = 369/10 multiply
x = 36.9 change to decimal
The actual length is 36.9 feet.