The limit is 1/5
Explanation:Given the function:
\(\frac{\sqrt[]{x^2+24}-5}{x-1}\)Taking this limit as x approaches 1, we have:
\(\begin{gathered} \frac{\sqrt[]{1^2+24}-5}{1-1}=\frac{\sqrt[]{25}-5}{1-1} \\ \\ \frac{5-5}{1-1}=\frac{0}{0} \end{gathered}\)This result means we need to apply a different method.
We apply L'hopital's rule, by taking the derivatives of the numerator and denominator as follows:
\(\begin{gathered} \frac{2x\times\frac{1}{2}(x^2+24)^{-\frac{1}{2}}}{1} \\ \\ =x(x^2+24)^{-\frac{1}{2}} \end{gathered}\)Now, taking the limit as x approaches 1, we have:
\(\begin{gathered} 1(1^2+24)^{-\frac{1}{2}} \\ \\ =\frac{1}{\sqrt[]{25}}=\frac{1}{5} \end{gathered}\)Tyler returned from the store with $12.47 He spent $76.53 on groceries. How much did he begin with?
Answer:
89 dollars
Step-by-step explanation:
47 and 53 cents make one dollar together. 12 dollars and 76 dollars make 88 dollars. 1+88=89
Answer:
$89
Step-by-step explanation:
Money that Tyler returned with = $12.47
Money spent on groceries = $76.53
And to find the total money he had at the beginning , add the left amount with the amount he spent . Hence here ,
\(\sf\longrightarrow Money_{total}= \$12.47+\$76.53\\\)
\(\sf\longrightarrow \underline{\boxed{\bf Money_{total}= \$\ 89 }}\)
Hence he had $89 at the beginning .
I hope this helps .
Factor completely the expression: 2x^3 - 2x^2 - 12.
Person who answers correct and is the quickest gets brainliest.
Answer:
2(x^3-x^2-6)
Step-by-step explanation:
2 out of 2x^3 - 2x^2 - 12
Sort the polygons.
Squares Not squares
Polygons are shapes that have the following:
-sides are all straight
-no overlapping
-shape is always closed
Hope this helps :)
Sherry is on the graduation committee and she uses a column in the school newsletter to communicate to the senior class. Her recent column contained the equation C=10d +30. Which graduation activity could the equation represent? Justify your response.
PLEASE HELP!!!!
Answer:
i got yu calm down pray to da lord
PLEASE I NEED HELP ON THIS ONE TOO THANK YOU BRAINLY IF CORRECT TYSM PLEASE HELP
Which organization is a major part of the executive branch?
A. The House of Representatives
B. The U.S. Senate
C. The cabinet
D. The Supreme Court
Answer:
C. The cabinet
Step-by-step explanation:
The executive branch besides the president also includes the advisors that help the president make decisions.
The House of Representatives and U.S. Senate are part of the Legislative Branch (Law and Order).
The Supreme Court is the only organization that makes up the Judicial Branch.
The expression 3a +3.8 is equal to for a = 1.6.
Answer:
8.6
Step-by-step explanation:
3x1.6=4.8
4.8+3.8= 8.6
Answer:
8.6
Step-by-step explanation:
Stanley runs, swims, and bikes every day. During these workouts, heruns at 9 mph, bikes at 16 mph, and swims at 2.5 mph. Yesterday, he ranfor half an hour longer than he swam, and his biking time was twice hisrunning time. How long did Stanley run, swim, and bike yesterday if thetotal distance he covered was 64 miles
Equations
Let's call:
x = time Stanley swam yesterday.
We know he ran for half an hour longer than he swam, thus the time he ran was:
x + 0.5 = time Stanley ran yesterday
We also know he biked for twice the time he ran, thus:
2(x + 0.5) = time Stanley biked yesterday.
The distance covered by Stanley when swimming is
2.5*x
The distance covered by Stanley when running is:
9*(x+0.5)
The distance covered by Stanley while biking is:
16*2*(x + 0.5) = 32(x + 0.5)
The total distance is 64 miles, thus:
2.5*x + 9*(x+0.5) + 32(x + 0.5) = 64
Operating:
2.5x + 9x + 4.5 + 32x + 16 = 64
Simplifying:
43.5x + 20.5 = 64
Subtracting 20.5:
43.5x = 43.5
Thus:
x = 1
Stanley swam for 1 hour, he ran for 1+0.5 = 1.5 hours and biked for 2*1.5=3 hours
Swam: 1 hour, Ran: 1.5 hours, Biked: 3 hours
Simplify the expression so there is only one positive power for each base. (5^-2 x 4^-4)^-2
Answer:
Step-by-step explanation:
\((5^{-2}\) × \(4^{-4}\) \()^{-2}\)
=\((5^{-2}\)\()^{-2}\) x \((4^{-4})^{-2}\) ∴\((a.b)^{n} =a^{n} .b^{n}\)
=\(5^{-2.-2}\) x \(4^{-4 . -2}\) ∴\((a^{n} )^{m}\) = \(a^{nm}\) // here m is an exponent of \(a^{n}\).
=\(5^{4}\) x \(4^{8}\)
Which is the best way to write the underlined parts of sentences 2 and 3?
(2) They have a special finish. (3) The finish helps the
swimmer glide through the water.
Click for the passage, "New Swimsuits."
OA. Leave as is.
B. a special finish that helps
C. a special finish, but the finish helps
D. a special finish so the finish helps
Answer:
Option B is the best way to write the underlined parts of sentences 2 and 3.
Sentence 2: They have a special finish that helps.
Sentence 3: The finish helps the swimmer glide through the water.
Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.
1) There are 8 college basketball teams in a certain
Sub-Division
How many ways are there to choose 6 teams for the playoffs?
There are 28 ways to choose 6 teams for the playoffs if there are 8 college basketball teams in a certain sub-division.
To determine the number of ways to choose 6 teams for the playoffs out of the 8 college basketball teams in a certain Sub-Division, we can use the combination formula. The formula for combinations is given by
nCr = n! / (r! * (n-r)!),
where n represents the total number of teams and r represents the number of teams to be chosen.
In this case, n = 8 and r = 6.
Plugging in these values, we have
8C6 = 8! / (6! * (8-6)!) = 8! / (6! * 2!) = (8 * 7) / (2 * 1) = 28.
Therefore, there are total 28 ways to choose 6 teams.
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Find all real and complex-valued solutions to each equation.
1. (10) 3(2x^3-x)^2+(2x^2-2)-2=0.
2. (10) √(3x - 2) - √(x - 2) = 2.
3. (10) √(48 + √x)-4= 4√x.
4. (10) |x^2 + 7x| = x^2-4
5. (10) (x+b)^2 - 11√((x +b)^2 +1) + 31 = 0,b € R. You need to solve for x in terms of the constant b.
x = -1/2, 1/2, or ±i/2.
x = 11/3.
x = 793.
x = 3, -4, -3, or 0.
x = (-b ± √(\(b^2\) + 32 - 2b√(\(9b^2\) - 32)))/2. There are no complex-valued solutions to this equation.
Considering the condition and settling for x, we get x = - 1/2, 1/2, or ±i/2.
Squaring the two sides of the situation and settling, we get x = 11/3.
Squaring the two sides of the situation and improving, we get x = 793.
Settling for the positive case, we get x = 3 or - 4. Tackling for the negative case, we get x = - 3 or 0.
Let y = x + b. The condition can be revamped as
y^2 - 11√(y^2 + 1) + 31 = 0.
Tackling for y utilizing the quadratic equation, we get
y = (11 ± √(121 - 4(31 - z^2)))/2.
Subbing back in for x, we get
x = (- b ± √(b^2 + 32 - 2b√(9b^2 - 32)))/2.
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Directions: Find each missing measure.
Q
P
R
Please help me find all 3 !
Answer:
m<P = 60 degrees
Step-by-step explanation:
All sides of the triangle are equivalent to each other.
All three sides of the triangle equal 180 degrees total.
Since there are 3 sides, we divide 180 by 3 to find the measurement for all sides
180 ÷ 3 = 60
Q = 60 degrees
P = 60 degrees
R = 60 degrees
Check your work by adding all three sides together to equal 180:
60 + 60 + 60 = 180
180 = 180
Work is correct
Solve for x:
dx+fx=8-2dx
Answer:
fx=8-3dx
Step-by-step explanation:
Which of the following is not a valid probability?
A. 1.3
B. 0
C. 0.4
D. 1
Answer:
A 1.3
Step-by-step explanation:
probabilities lie between 0 and 1 and cannot be more or less
What is the greatest decimal place value?
Answer:
Millionths
Step-by-step explanation:
It is the fartherst decimal place that thier is.
Someone pls help???????????????????????????????
Answer:
1/4
Step-by-step explanation:
quartered pie
Answer:
1/4
Step-by-step explanation:
there's four total triangles and only one is shaded purple. that is one of the four triangles.
what is the average (arithmetic mean) of the numbers in a sequence that begins with –5 and ends at 11, if each number in the sequence is 4 greater than the previous number?
the average of the terms by dividing the sum by the number of terms: 30 / 6 = 5. Therefore, the average (arithmetic mean) of the numbers in the given sequence is 5.
To find the average of the numbers in the sequence, we first need to determine the total number of terms in the sequence. The sequence starts with -5 and ends at 11, and each number in the sequence is 4 greater than the previous number. We can observe that to go from -5 to 11, we need to increase by 4 in each step. So, the total number of terms in the sequence can be calculated by adding 1 to the result of dividing the difference between the last term (11) and the first term (-5) by the common difference (4): (11 - (-5)) / 4 + 1 = 17 / 4 + 1 = 5.25 + 1 = 6.25.
Since we can't have a fractional number of terms in the sequence, we round down to the nearest whole number, which is 6. Therefore, the sequence consists of 6 terms.
Next, we calculate the sum of the terms in the sequence. The first term is -5, and each subsequent term can be found by adding 4 to the previous term. So, the sum of the terms is: -5 + (-5 + 4) + (-5 + 2(4)) + ... + (-5 + (n - 1)(4)), where n is the number of terms in the sequence (6). Using the formula for the sum of an arithmetic series, the sum of the terms can be calculated as: (n/2)(first term + last term) = (6/2)(-5 + (-5 + (6 - 1)(4))) = (3)(-5 + (-5 + 5(4))) = (3)(-5 + (-5 + 20)) = (3)(-5 + 15) = (3)(10) = 30.
Finally, we find the average of the terms by dividing the sum by the number of terms: 30 / 6 = 5. Therefore, the average (arithmetic mean) of the numbers in the given sequence is 5.
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9. M (2, 1) is the midpoint of segment AB. If the endpoint A has coordinates (5,6), find
the coordinates of endpoint B.
Answer:
(-1, -4)
Step-by-step explanation:
To find the missing endpoint, we can multiply the midpoint coordinates by 2, so we can get 4 and 2. Then we can subtract the coordinates from the endpoint we have, which is A, to those numbers.
4-5 is -1
2-6 is -4
Put them together and we get (-1, -4) as our endpoint B.
Answer:
Step-by-step explanation:
(5+x)/2=2, (6+y)/2=1
for the x value
5+x=4
x=-1
then for the y value
6+y=2
y=-4
then your answer would be (-1,-4)
12.6.3 Test (CST): Factoring Polynomials
According to the graph, what is the factorization of x² - 4x + 3?
O A. (x-3)(x + 1)
OB. (x+3)(x+1)
O C. (x-3)(x-1)
D. (x+3)(x - 1)
The factorization of the polynomial x² - 4x + 3 are (x - 1)(x - 3)
How to determine the factorization of x² - 4x + 3?From the question, we have the following parameters that can be used in our computation:
x² - 4x + 3
Also, we have the graph
From the graph, we can see that the graph intersects the x-axis ar
x = 1 and 3
This means that the factors are
(x - 1) * (x - 3)
So, we have
(x - 1)(x - 3)
Hence, the factorization of x² - 4x + 3 are (x - 1)(x - 3)
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AT&T charges $70.00 a month plus $10 per gig of data. Sprunt charges $80.00 a month plus $5 per gig of data. Which equation could be used to determine when the two cell phone plans will be equal?
Answer:
AT&T charges $70.00 a month plus $10 per gig of data. Sprunt charges $80.00 a month plus $5 per gig of data. Which equation could be used to determine when the two cell phone plans will be equal?
Step-by-step explanation:
AT&T's plan would be less expensive than the Sprunts because they have different charges a month
Hope this helps
Please Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
26:26
Step-by-step explanation:
I hope I've helped :)
Write an equation that can be use to find the price to place a phone call.
What is the SAS theorem?
The side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.
What is the congruence of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Slide, twist, flip, and turn these triangles to create an identical appearance.
They are in alignment with one another when moved.
The first such theorem is the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are equivalent to two sides and an included angle of another triangle.
Therefore, the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.
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Katherine and Crystal do landscaping. They recently earned $1472 for a project. If Katherine earned $5 for every $3 earned by Crystal, how much of the money went to each?
Answer:
Katherine: 920
Crystal: 552
Step-by-step explanation:
The total amount earned by each is 1472
The ratio of the earnings is Katherine / Crustal = 5/3
The total number of shares = 5 + 3 = 8
So the proportion for Katherine
5/8 = x / 1472 Cross multiply
8x = 5 * 1472
8x = 7360
x = 7360/8
x = 920
And the proportion for Crystal is
3/8 = x / 1472 Cross multiply
8x = 3 * 1472
8x = 4416
x = 4416 / 8
x = 552
How are the properties of exponents used when dividing a polynomial by a monomial?
Answer:
a couple different obes
Step-by-step explanation:
there are five
A square pyramid is sliced in such a way that the plane cuts in a direction perpendicular to the base but does not pass through the vertex, what is the resulting cross section?
If a square pyramid is sliced in a way that the plane cuts in a direction perpendicular to the base but doesn't pass through the vertex, the resulting cross-section will be a trapezoid.
This trapezoid will have one pair of parallel sides and one pair of non-parallel sides.
To understand why the resulting cross-section is a trapezoid, imagine a square pyramid standing on its base. Now, imagine slicing the pyramid horizontally, parallel to the base. The resulting cross-section would be a square.
However, if we change the direction of the slice to be perpendicular to the base, but not passing through the vertex, the resulting cross-section will not be a square. Instead, it will be a trapezoid, with one set of parallel sides corresponding to the base of the pyramid, and the other set of sides corresponding to the slice that was made.
This type of cross-section is commonly seen in architectural and engineering designs, where different shapes need to be created by slicing or intersecting 3D shapes. Understanding the resulting cross-section of different slicing techniques is essential to ensure the proper fit and function of the final product.
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The parallel dotplots below display the number of cars parked for several days in each of two parking lots.
2 dotplots titled parked cars by lot. The number lines go from 21 to 29 and are labeled number of cars. For lot A, 21, 1; 23, 5; 25, 10; 27, 5; 29, 1. For lot B, A, 1; 23, 2; 24, 4; 25, 8; 26, 4; 27, 2; 29, 1.
Which of the following statements is true?
The range for the distribution of the number of cars is larger in lot A.
The range for the distribution of the number of cars is larger in lot B.
There is a smaller standard deviation in the distribution of the number of cars in lot B.
The standard deviation in the distribution of the number of cars is the same for both lots.
The distribution of the number of automobiles in lot A has a higher standard deviation than that in lot B. Then the correct option is D.
The difference between a dataset's greatest and lowest values is known as the range.
For lot A, the range is 29 - 21 = 8 which is false.
For lot B, the range is 29 - 21 = 8 which is false.
For each dataset, the mean must be determined before the standard deviation can be determined.
For lot A, the mean is:
⇒ (21 x 1 + 23 x 5 + 25 x 10 + 27 x 5 + 29 x 1) / 22 = 25
For lot B, the mean is:
⇒ (21 x 1 + 23 x 2 + 24 x 4 + 25 x 8 + 26 x 4 + 27 x 2 + 29 x 1) / 22 = 25.23
We can get the standard deviation for each dataset using these means. Lot A's standard deviation is around 2.50, whereas Lot B's standard deviation is roughly 1.97.
Therefore, statement (C) is false, and the correct statement is D.
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A zookeeper takes care of 5 mountain lions. The keeper orders
32.5 pounds of meat for them each day. Each mountain lion receives
the same amount. What equation can you use to find how much meat
each mountain lion eats in a day?
Answer:
y=32.5÷5
Step-by-step explanation:
the 32.5 lbs of meat is distributed between 5 lions so 32.5÷5=y
I need answers fast
What is the measure
The measure of CFE is 28^o.
What are supplementary angles?When the measures of two or more angles add up to the sum of angle on a straight line i.e. 180^o, then the set of angles are said to be supplementary.
Given point F on line CD in the question, we have;
<CFE + <DFE = 180^o (definition of supplementary angles)
So that;
<CFE + 152 = 180
<CFE = 180 - 152
= 28
<CFE = 28^o
Therefore, the measure of <CFE is 28^o.
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I am between 30 and 50.
The sum of my digits is 10.
My ones digit is greater than
my tens digit. I am not 37.
Who am I?