Answers
The value of the limit of piece wise function is 2k.
What is termed as the piece wise function?A piecewise function is one whose independent variable is described by a series of intervals. It displays a different function for each interval of real numbers. The domain of a function is defined as a set of valid values for such independent variable (in the this case, x) that can be embedded into the function. The range of the a function is the collection of possible values for y that can be obtained after running the function.For the given question;
The piece wise function is defined as a;
f(x) = (x² - k²)/(x - k) , x ≠ k
f(x) = 4 - k , x = k
For the value of lim (x → k⁻) f(x);
Use function for x ≠ k, as the left hand limit of the functions is to be evaluated.
= lim (x → k⁻) f(x)
Let x = k - h, put in the function.
= lim (h → 0) ((k-h)² - k²)/(k - h - k)
= lim (h → 0) h(h - 2k)/-h
= lim (h → 0) 2k - h
Pu h = 0
= 2k
Thus, the value of the limit of piece wise function is 2k.
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Related Questions
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds
and each large box of paper weighs 75 pound's. A total of 24 boxes of paper were
shipped weighing 1410 pounds altogether. Write a system of equations that could be
used to determine the number of small boxes shipped and the number of large boxes
shipped. Define the variables that you use to write the system.
Answers
A total of 24 boxes of paper were shipped weighing 1410 pounds altogether, the system of equations are X + Y = 24, and 45X + 75Y = 1410 and the variables that you use to write the system X = 13 and Y = 11.
What is pound?The primary unit of sterling is the pound (sign: £), while the term "pound" is also frequently used to refer to the British pound or pound sterling in foreign settings.
The oldest currency that is still in the circulation and has been used continuously since its origin is sterling. After US dollar, euro, and Japanese yen, it is currently fourth most traded currency on the foreign exchange market. It makes up basket of currencies used to determine the value of IMF special drawing rights along with the other three currencies and the renminbi. Sterling is also fourth-most-held reserve currency in the world's reserves as of mid-2021.
Let X equal number of small boxes
Let Y equal number of big boxes
The first equation is: X + Y = 24 ( this shows that total number of boxes = 24)
The second equation is: 45X + 75Y = 1410 ( this is because small box weighs 24 pounds and big box weighs 75 pounds. The total weight of small boxes is 45 times weight of each individual box. And the total weight of second boxes is equal to 75Y.
When you solve system, X = 13 and Y = 11
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any number raised to the 2nd power is said to be
Answers
Answer: squared
Step-by-step explanation:
what does x have to measure to make the lines parallel?
PLEASE HELP ASAP
Answers
Answer:
23) 30°
24) 12°
Step-by-step explanation:
23) Lines will be parallel if the co interior angles are supplementary.
∠3 + ∠5 = 180°
3x+ 25 + 4x - 55 = 180
3x + 4x + 25 -55 = 180
Combine like terms,
7x - 30 = 180
Add 30 to both sides,
7x = 180 + 30
7x = 210
Divide both sides by 7,
x = 210 ÷ 7
x = 30
24) If the lines are parallel, then the alternate interior angles are congruent.
∠7 = ∠2
11x - 36 = 8x
Add 36 to both sides,
11x = 8x + 36
Subtract 8x from both sides,
11x - 8x = 36
3x = 36
x = 36 ÷ 3
x = 12°
2x-5y = 2
3x - 7y=1
solve the system by elimination
Answers
Answer:
x= -9, y= -4
Step-by-step explanation:
Solving a linear equation can be done by two main methods, namely elimination and substitution. Elimination works by making the numerical value of one of the variable's coefficient the same, such that we can subsequently eliminate (or remove) the variable by subtracting or adding the two equations together.
Start by labelling the 2 given equations:
2x -5y= 2-----(1)
3x -7y= 1-----(2)
I will be working to eliminate the x term here, since we would be dealing with smaller numbers in this case. Eliminating the y term would also work.
The lowest common multiple of 2 and 3 is 6, thus multiply equation (1) by 3 and (2) by 2 so that the coefficient of x in both equations is 6. Then label the equations.
(1) ×3:
6x -15y= 6 -----(3)
(2) ×2:
6x -14y= 2 -----(4)
Since the coefficient of x in both equations is positive 6, we can subtract one equation from the other to eliminate the x term. If both coefficients have different signs (e.g. +6 and -6), the addition of the two equations would eliminate the term.
(3) -(4):
6x -15y -(6x -14y)= 6 -2
Expand:
6x -15y -6x +14y= 4
-y= 4
Divide both sides by -1:
y= -4
Then use substitution to find the value of y. Note that at this point, you could work to eliminate the y term from equations (1) and (2) to solve for x but it is commonly understood that when a question states solve by elimination, it is only for the first variable.
Substitute y= -4 into (1):
2x -5(-4)= 2
2x +20= 2
Subtract 20 from both sides:
2x= 2-20
2x= -18
Divide both sides by 2:
x= -9
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The scale of a map of Pennsylvania is 1 inch: 25 miles. The actual distance from Ambridge to Pittsburgh is 20 miles. What is the distance on the map?
Answers
Step-by-step explanation:
1 inch = 25 miles
or as ratio
1 inch : 25 miles
1 : 25 or 1/25
a ratio is nothing else than a fraction (just with special meaning, but the handling, calculation, transformation and simplification is the same).
the checked distance is 20 miles.
so, we need to transform the ratio (in the same way as we transform fractions) to show 20 instead of 25 in the denominator.
25 × f = 20
f = 20/25 = 4/5
remember, we need to multiply 1/25 by f/f to keep the original value of the ratio unchanged.
1/25 × 4/5/4/5 = (4/5)/(25×4/5) = (4/5)/20
so, the distance on the map is 4/5 in.
Anna buys ice cream and oranges at the store.
She pays a total of $59.53.
She pays a total of $6.49 for the ice cream.
She buys 8 bags of oranges that each cost the same amount.
Write and solve an equation which can be used to determine xx, how much each bag of oranges costs.
Answers
Algebraic equation - The cost of each bag of Oranges = $6.63
What is Algebraic equation ?
An algebraic equation, sometimes known as a polynomial equation, in mathematics is a formula of the form P=0, where P is a polynomial with coefficients in some field, typically the field of the rational numbers.
Let the cost one bag of oranges be x
Given,
Total amount she pays = $59.53
Total amount she pays for ice cream = $6.49
Since the total amount for 8 bag of oranges = 8x
Therefore, the equation of the following will be
8x + 6.49 = 59.53
Now by solving the equation we get the cost of each bag of oranges
8x = 59.53 - 6.49
8x = 53.04
x = 53.04 / 8
x = 6.63
Hence, The cost of each bag of oranges will be $6.63
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You invested a total of $30,000 at 3% and 4 1 2 % simple interest. During one year, the two accounts earned $1200. How much did you invest in each account?
Answers
Answer:
$20,000 at 4.5% simple interest
$10,000 at 3% simple interest
Step-by-step explanation:
[tex].045x + .03(30000 - x) = 1200[/tex]
[tex].045x + 900 - .03x = 1200[/tex]
[tex].015x + 900 = 1200[/tex]
[tex].015x = 300[/tex]
[tex]x = 20000[/tex]
$20,000 at 4.5% simple interest
$30,000-$20,000=$10,000 at 3% simple interest
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is greater than 2". Find P(not A). Outcome Probability 1 0.22 2 0.08 3 0.13 4 0.33 5 0.24
Answers
Remember that
[tex]P(\text{not A)}=1-P(A)[/tex]We know that:
[tex]\begin{gathered} P(A)=0.13+\text{0}.33+0.24 \\ \rightarrow P(A)=0.7 \end{gathered}[/tex]This way,
[tex]\begin{gathered} P(\text{not A)}=1-0.7 \\ \rightarrow P(\text{not A)}=0.3 \end{gathered}[/tex]Find the distance between the following two points: (3, 2) and (0, -4).
Answers
The distance between the 2 given points is √45.
What is the distance?Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending point. Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.So, the distance between (3, 2) and (0, -4) is:
The distance formula: D = √[(x₂ - x₁)² + (y₂ - y₁)²]Now, substitute the values in the formula and solve as follows:
D = √[(x₂ - x₁)² + (y₂ - y₁)²]D = √[(0 - 3)² + ((-4) - 2)²]D = √[(-3)² + (-6)²]D = √[9 + 36]D = √45Therefore, the distance between the 2 given points is √45.
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0.3(4+x)=4.5
Please help me out, I need this answer ASAP,
I give u 10 pts, thank u SOOO much :3
Answers
Answer: x=11
Step-by-step explanation:
Answer:
[tex] \sf \: x = 11[/tex]
Step-by-step explanation:
Given equation,
→ 0.3(4 + x) = 4.5
Now the value of x will be,
→ 0.3(4 + x) = 4.5
→ 1.2 + 0.3x = 4.5
→ 0.3x = 4.5 - 1.2
→ 0.3x = 3.3
[tex] \sf \rightarrow \: x = \frac{3.3}{0.3} [/tex]
→ [ x = 11 ]
Hence, the value of x is 11.
Find the solution to the following system on the calculator. Round
your answer to two decimal places.
{y= 3x - 6 y = -5x + 14
Answers
Answer:
y=3x=16/3
Step-by-step explanation:
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds
and each large box of paper weighs 80 pounds. There were 4 more large boxes
shipped than small boxes and the total weight of all boxes was 1750 pounds. Write a
system of equations that could be used to determine the number of small boxes
shipped and the number of large boxes shipped. Define the variables that you use to
write the system.
Answers
The system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped are:
50x+80y=1750
y = x+4 ,
where x represent the number of small boxes of paper and y represent the number of large boxes of paper.
We have:
Weight of small box of paper = 50 pounds
Weight of large box of paper = 80 pounds
Total weight of boxes = 1750 pounds
Let us consider that the number of small boxes of papers be x.
The number of large boxes of papers be y.
Then, according to question
50x+80y=1750
y = x+4
Therefore, the equations 50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped.
where, x represent the number of small boxes of paper and y represent the number of large boxes of paper.
Suppose that an individual has a body fat percentage of 14.4% and weighs 148 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.
Answers
An individual has a body fat percentage of 14.4% and weighs 148 pounds,
total pounds of her weight is made up of fat is 21.3pounds (nearest tenth).
As given in the question,
Total weight of an individual =148pounds
Percentage of her weight made up of fat = 14.4%
Pounds of her weight is made up of fat = 14.4% of 148
= ( 14.4 / 100 ) × 148
= 21.3 pounds (nearest tenth)
Therefore, an individual has a body fat percentage of 14.4% and weighs 148 pounds, total pounds of her weight is made up of fat is 21.3pounds(nearest tenth).
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Which of the following is a solution to the equation
2x² + 4x = 3 + 3x² ?
A) -1
B)
0
C) 3
D) 6
Answers
===========================================================
Reason:
Let's check to see if choice A is the answer. We'll replace each x with -1
2x^2 + 4x = 3 + 3x^2
2(-1)^2 + 4(-1) = 3 + 3(-1)^2
2(1) + 4(-1) = 3 + 3(1)
2 - 4 = 3 + 3
-2 = 6
We don't end up with the same thing on both sides, so x = -1 is not a solution to the equation.
--------------
Now try x = 0
2x^2 + 4x = 3 + 3x^2
2(0)^2 + 4(0) = 3 + 3(0)^2
2(0) + 4(0) = 3 + 3(0)
0 = 3
That's false as well, which allows us to rule out choice B.
--------------
Next up plug x = 3 into the equation
2x^2 + 4x = 3 + 3x^2
2(3)^2 + 4(3) = 3 + 3(3)^2
2(9) + 4(3) = 3 + 3(9)
18 + 12 = 3 + 27
30 = 30
We get the same thing on both sides so we have confirmed x = 3 is a solution.
--------------
There may be other solutions. If we tried x = 6, then it leads to 96 on the left hand side and 111 on the right hand side. That rules out x = 6 as a solution.
67,000 rounded to the nearest ten thousand
Answers
When 67,000 is rounded to the nearest ten thousand then we get 70,000
When you round to the nearest 10 thousand. Find the number in the 10 thousand place, that would be the 6 in this case, now look at the number to the right of it, if that number is 5 or higher, then your 67,000 becomes 70,000.
If the number to the right of place value is lower than 5 then it would have been rounded to 60,000.
The digits in the thousands, hundreds, tens, and ones should be changed to 0 if the number is less than 5, but the other digits should remain the same. If it is 5 or more, increase the digit in the tens of thousands by 1 and replace the digits in the thousands, hundreds, tens, and ones with 0.
Hence the nearest round of to ten thousand is 70,000.
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A social security number contains nine digits, such as 273-41-2406. How many different social security numbers can be formed?
Answers
Answer: 5 more!
Step-by-step explanation:
Due to the lack of numbers your could do about 4 - 5 more security numbers!
Answer:
I think 81
Step-by-step explanation:
I'm not too sure since 9 x 9 is 81 but im not sureeee
What is the domain of the following function:
A.) x is all real numbers.
B.) –1 ≤ x ≤ 0
C.) x > 0
D.) –1 ≤ x ≤ 1
Answers
-1 is the domain of the following
Jason has $3,561.05 in credit card debt. The annual interest rate on the unpaid balance is 18.2% compounded monthly. If Jason wants to pay off his credit card debt in 2 years, what is his monthly payment, assuming he makes no additional purchases on this card? (Suggestion: Use the formula for the present value of an ordinary annuity. Round your answer to the nearest cent.)
Answers
The monthly payment of Jason with no additional charge is found as $1,556.53.
What is meant by the compound interest?Compound interest is investment determined just on initial principal plus all previous periods' accumulated interest.A power of interest compounding is the ability to generate "interest on interest."Interest could be compounded at any time, from continuously to daily to annually.Compounding accelerates the growth of money.The formula for the calculation of the compound interest is;
CI = A - P
A = P(1 + r/100n)∧nt
Where,
CI = compound interestA = total amount after given timeP = principal amountT = total time in yearsn = number of time interest compoundedr = rate of interest in %The given values are;
P = $3,561.05 T = 2 yearsn = 12×2 = 24 times.R = 18.2%Put the values in the formula;
CI = $3,561.05(1 + 18.2/24×100)∧24×2 - $3,561.05
Simplifying;
CI = $3,561.05×1.43 - $3,561.05
CI = $5117.58 - $3,561.05
CI = $1,556.53
Thus, the monthly payment of with no additional charge is found as $1,556.53.
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The table represents some points on the graph of a linear function. What is the rate of change of y with respect to x for this function?
X y
5 2
10 3
15 4
20 5
Answers
The rate of change of y with respect to x for this linear function is 1/5 or 0.2
What is a linear function?A linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.
How to calculate the average rate of change?Mathematically, the average rate of change (slope) of a linear function can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Average rate of change = (3 - 2)/(10 - 5) = (4 - 3)(15 - 10)
Average rate of change = 1/5 or 0.2
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Un barco navega 300 km al oeste, después 100 km al sur, al final de su viaje, que tan lejos está de su posición inicial? Elabora en tu libreta el dibujo y resuelve.
Answers
Answer: 400 KL you have to add 300 KL + 100 KL = 400 KL
PLEASE HELP!!!!!!!!!!!
(1 point)
Suppose U={1,2,3,4,5,6,7,8,9,10} is the universal set, and P={2,4,6,8,10}. What is P?
Answers
When compared to the universal setU={1,2,3,4,5,6,7,8,9,10}, the set P=2,4,6,8,10 has a prime that is equal to P'=1,3,5,7,9 as its element.
This is further explained below.
What is a set prime?Generally, Assigned the letter A (A prime), The components that are included in the Universal set but are absent from Set A are denoted by the letter A.
U={1,2,3,4,5,6,7,8,9,10}
P={2,4,6,8,10}
Therefore, the prime of the set P={2,4,6,8,10} in relation to the universal set U={1,2,3,4,5,6,7,8,9,10} is
P'={1,3,5,7,9}
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Suppose U={1,2,3,4,5,6,7,8,9,10} is the universal set, and P={2,4,6,8,10}. What is P'?
Quadrilateral QRST is shown. Two students each perform a different reflection on
the original figure.
Use the drop-down menus to give the coordinates of point T' after each reflection
Answers
When Ramona reflect the original figure over the x-axis, the coordinate of point T' will be (-2, -4). When Elias reflect the original figure over the y-axis, the coordinate of point T' will be (2, 4).
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Mathematics, a reflection over the x-axis is given by this transformation rule:
(x, y) → (x, -y)
Point T = (-2, 4) → Point T' = (-2, -4)
In Geometry, a reflection over the y-axis of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, the coordinates of point T' after a reflection over the y-axis is as follows:
Point T = (-2, 4) → Point T' = (-(-2), 4) = (2, 4)
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emma says the gcf of 16 and 12 is 48.Her friend grace says the answer is 4. Who is right? Explain
Answers
Answer:
Grace
Step-by-step explanation:
48 is the LCM, 4 is the GCF
An urn has 10 balls that are identical except that 6 are white and 4 are red. a sample of 7 is selected randomly without replacement. what is the probability that exactly 5 are white and 2 are red? what is the probability that at least 5 of the balls are white?
Answers
The question tests on probability and combinations.
To obtain the probability for selecting exactly two red and 5 white urns is:
If Wi and Ri are events for selecting the ith ball, apply the multiplicative rule to obtain:
=P(W1∩W2∩W3∩W4∩W5∩R1∩R2)
= P(W1)P(W2|W1)P(W3|W1∩W2)P(W4|W1∩W2∩W3)P(W5|W1∩W2∩W3∩ W4)P(R1|W1∩W2∩W3∩W4∩W5)P(R2|W1∩W2∩W3∩W4∩W5∩R1)
=6/10×5/9×4/8×3/7×2/6×4/5×3/4
= 1/10
The probability is 1/10.
Alternatively, use the Bayes theorem. This uses combinations. To get the probability for exactly 5 white and 2 red, obtain the chance for selecting 5 white balls and 2 red balls; 6C5 and 4C2.
(6C5×4C2)/10C7 = 6×6/120 = 1/10
The probability for at least 5 balls is obtained by the probability of either selecting 5 or 6 balls.
Using combination;
(6C6 X6C5)/10C7 = (1x6)/120 = 6/120 = 1/20.
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Which of the following lists of ordered pairs is a function?
A.) (1, 2), (1, –2), (3, 2), (3, 4)
B.) (0, 2), (2, 3), (0, –2), (4, 1)
C.) (1, 6), (2, 7), (4, 9), (0, 5)
D.) (2, 4), (0, 2), (2, –4), (5, 3)
Answers
Answer: d
Step-by-step explanation:
im new at this but i am pretty sure it would be d
Need help asap!!!!!!!!
Answers
If two numbers are multiplied, they are written as "a multiplied by b."
The answer is 9 3/7.
How to multiply?Multiplication is the product of 2 or more numbers/things.
Multiplying in math is equivalent to adding like groups.
The quantity of items in the group expands as we multiply.
A multiplication question has two factors, a product, and two factors. The factors and the product in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, respectively.
4 2/7 * 2 1/5 = 30/7 * 11/5
On simplifying,
= 6/7*11
= 66/7
=9 3/7
The answer is 9 3/7.
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(Please help me I will give you extra points and the crown)
What is the special angle pair relationship between <1 and <3
Answers
Answer:
These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.
Step-by-step explanation:
Which describes two similar triangles?
Two triangles for which a set of rigid motions can be used to show that all corresponding pairs of angles are equal and all corresponding pairs of sides are equal.
Two triangles for which a set of rigid motions can be used to show that all corresponding pairs of angles are equal and all corresponding pairs of sides are proportional.
Two triangles for which a set of rigid motions and dilations can be used to show that all corresponding pairs of angles are equal and all corresponding pairs of sides are equal.
Two triangles for which a set of rigid motions and dilations can be used to show that all corresponding pairs of angles are equal and all corresponding pairs of sides are proportional.
Answers
Answer:
Definition. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
how do I multiply 1 * 1
Answers
We have the following:
Multiplication is the product between two numbers, it is the number of times the number to be multiplied is repeated. In this case, it would be 1 time 1
[tex]1\cdot1=1[/tex]The answer is 1
Hello! Can you check these for me please :)
Answers
Triangles ADT and EDT are congruent by SSS rule and triangles BLG and PFX are congruent by SAS rule.
In triangle ADT and EDT, we get that:
AD = DE (given)
AT = ET (given)
DT = DT (common)
So, ΔADT ≅ Δ EDT (SSS congruency rule)
In triangle BLG and PFX, we get that:
BL = PF (given)
BG = PX (given)
∠ B = ∠ P (given)
So, ΔBLG ≅ Δ PFX (SAS congruency rule)
Therefore, we get that, triangles ADT and EDT are congruent by SSS rule and triangles BLG and PFX are congruent by SAS rule.
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