Answers
The continuous functions at x = -4 are given as follows:
Second function: -8 at x = -4.Fourth and last function: 0 at x= -4.What makes the function continuous?The function is continuous when it has these two features:
Equal lateral limits.The lateral limits are equal to the numeric value of the function.For the definitions in this problem, we have that:
The lateral limits are calculated with the top definition.The bottom definition gives the numeric value.For the first two functions, the function can be simplified as follows:
(x² - 16)/(x + 4) = [(x - 4)(x + 4)]/(x + 4) = x - 4.
Hence the limit at x = -4 is given as follows:
-4 - 4 = -8.
Meaning that the second function is continuous at x = -4.
For the last two functions, the function can be simplified as follows:
(x² + 8x + 16)/(x + 4) = (x + 4)²/(x + 4) = x + 4.
Hence the limit at x = -4 is given as follows:
-4 + 4 = 4.
Meaning that the fourth and last function is also continuous at x = -4.
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Related Questions
if someone repeatedly lifts heavy weights, that person will produce higher levels of maximal strength. what is this an example of?
Answers
The given statement is an example of "Principle of specificity or specific adaption to imposed demands (SAID Principle) ".
What is Principle of specificity ?
According to the specificity of training principle, each physical activity has a very unique physiological response. For instance, someone who jogs can anticipate that both their running performance and their level of aerobic fitness will be favorable.
if someone repeatedly lifts heavy weights, that person will produce higher levels of maximal strength.
This an example of "Principle of specificity or specific adaption to imposed demands (SAID Principle) "
Tenet according to which the body will adjust to the unique demands imposed upon it.
Higher degrees of endurance can be attained by regularly lifting lesser weights for a large number of repetitions.
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  Is it true that 7w + 4 = 5w + 12.
A. Write three more equations that you know are true based on this information.
B. Find the value of 2w.
C. Find the value of w.
Answers
Answer:
A. Here are three more equations that are true based on the information you provided:
1. 3w + 2 = 2w + 6
2. 5w - 6 = 4w - 8
3. 7w - 5 = 6w - 7
B. To find the value of 2w, we need to first solve for w in the original equation 7w + 4 = 5w + 12. We can do this by subtracting 5w from both sides of the equation, which gives us 2w + 4 = 12. Then we can subtract 4 from both sides to get 2w = 8. Therefore, the value of 2w is 8.
C. To find the value of w, we can divide both sides of the equation 2w = 8 by 2, which gives us w = 4. Therefore, the value of w is 4.
here are the number of hours that 9 students spend on the computer on a typical day:2 5 5 7 11 11 11 14 15what is the mode number of hours spent on the computer?
Answers
By using the concept of mode, it can be calculated that-
Mode number of hours spent on the computer is 11 hours.
What is mode?
Mode of a data set is that value which occurs most number of times in the data set. In other words, the value whose frequency is the largest is the mode of the data set.
The number of hours that 9 students spend on the computer on a typical day: 2 5 5 7 11 11 11 14 15
Here 11 occurs most number of times (3 times)
Mode number of hours spent on the computer is 11 hours.
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Ira enters a competition to guess how many buttons are in a jar.
Ira’s guess is 200 buttons.
The actual number of buttons is 250.
What is the percent error of Ira’s guess?
Answers
The percent error of Ira’s guess for the number of buttons is 25%
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Ira’s guess is 200 buttons but the actual number of buttons is 250.
The net amount error is (250 - 50) = 50 buttons.
Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,
= (50/200)×100%.
= 25%
So, the percentage error is 25%.
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use tables to find log
(789.5)1/8
Answers
The logarithm of (789.5) elevated to the power 1/8 is given as follows:
log(789.5)^(1/8) = 0.36216901679.
How to obtain the logarithm?The logarithm in this problem is defined as follows:
log(789.5)^(1/8).
It has a power, hence the power can be moved to the front of the logarithm expression applying the power rule, as follows:
log(789.5)^(1/8) = 1/8 x log(789.5).
Then a calculator is used to obtain the logarithm of 789.5, which is the number that is elevated to the base 10 to obtain 789.5, hence:
log(789.5) = 2.89735213434.
Thus the numeric value of the logarithmic expression in this problem is calculated as follows:
log(789.5)^(1/8) = 1/8 x log(789.5) = 1/8 x 2.89735213434 = 0.36216901679.
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a person with height 1.8 metres is walking away from a 5 metre tall lamppost at a speed of 1.2 metres per second. find the rate at which their shadow is lengthening.
Answers
The length of the shadow of man is 0.8 m/s.
How to solve word problems?
Here are some actions to take:
1. Recognize the issue.
Recognize every term used to describe the issue, Recognize what you need to look for, Recognize the issue's context.
2. Convert the issue into an equation. Give the unknown a variable (or variables) to symbolise, Indicate exactly what the variable stands for.
3. Put the strategy into action and find a solution.
dx/dt =1.2 m/s
4.5 / x+ y = 1.8 / y
1.8x + 1.8y = 4.5y
1.8x = 2.7y
2x = 3y
3 dy/dt = 2dx/ dt = dy/dt = 2/3
=0.8
Hence, The length of the shadow of man is 0.8 m/s
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The time Mo takes to mow the lawn is between 45 minutes and 75 minutes, inclusive.
Does this statement represent a union or an intersection?
Write the statement as a compound inequality with t as your variable of time.
Answers
A compound inequality 45 ≤ t ≤ 75 which represents the union of all values larger than or equal to 45 minutes and less than or equal to 75 minutes is the time, denoted by the notation t.
The time Mo takes to mow the lawn is between 45 minutes and 75 minutes, inclusive, which means that the time is either 45 minutes, 46 minutes, 47 minutes, and so on, up to and including 75 minutes. This is a range of values that includes all the times from 45 minutes to 75 minutes.
This statement represents a union, which is the combination of two or more sets of values. In this case, the union is the combination of all the values from 45 minutes to 75 minutes.
To write this statement as a compound inequality, you can use the symbols "≥" (greater than or equal to) and "≤" (less than or equal to) to indicate that the time is greater than or equal to 45 minutes and less than or equal to 75 minutes:
45 minutes ≤ t ≤ 75 minutes
This compound inequality can also be written as:
45 ≤ t ≤ 75
This means that the time, t, is a member of the union of all values that are greater than or equal to 45 minutes and less than or equal to 75 minutes.
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Find the result graphically. Click and drag the arrows to represent each term. Type in the result. 7-5
Answers
7 is initially represented by 7 units to the right, Now, if we remove 5 from 7, we must move 5 units to the left, arriving at unit 2.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
On the number line, 7 is represented 7 units right from the origin.
Now subtracting 5 from 7 implies we have to go 5 units to the left so we end up in unit 2.
The graphical representation is illustrated in the attached image.
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How many possible dish combinations are there with 5 kinds of pasta, 2 cheeses, and 3 sauces.
Answers
Answer: 30 combinations
Step-by-step explanation:
Multiply 3x2x5 to get 30.
I need help please it’s ASAP
Answers
The interquartile range of the data is equal to 2.18.
What is an interquartile range?The interquartile range is a measure of where a data set's "middle fifty" is located. Whereas a range is a measure of where the start and end of a set are, an interquartile range is a measure of where the majority of the values are.
Given data is { 1.56,1.77,2.22,2.35,2.45,2.77,3.26,4.35,5.23,6.02}.
The upper limit is, and the median is 2.22.
{ 1.56,1.77,2.22,2.35,2.45,2.77}
The lower limit is, and the median is 4.35.
{2.77,3.26,4.35,5.23,6.02}
The interquartile range will be calculated as,
IQR = 4.35 - 2.22
IQR = 2.18
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an urn is filled with marbles of various colors. if the probability of pulling a red marble at random is 1/10, the odds of pulling a red marble are:
Answers
The value of the odds of pulling a red marble is equivalent to 1/9 from an urn filled with marbles of various colors.
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
By definition, the theoretical probability is equal to the ratio of the favorable event to the total number of events.
Given that:
The probability of pulling a red marble at random is 1/10
Probability of not pulling red marble is = 1-(1/10)= 9/10
The odds of pulling red marble is (1/10)/(9/10)
The probability of odds of pulling red marble is 1/9.
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How many solutions can a system of 2 linear equations in 2 variables have?
Answers
The number of solutions that a system of 2 linear equations in 2 variables can have is explained below.
In the question ,
it is given that ,
the system of 2 linear equations in 2 variables .
we know that the linear equations represent a line .
(i) the two linear equations will have No Solution / Zero Solution if the two lines are parallel .
(ii) the two linear equations will have One Solution/Unique Solution if the two line intersect at a point .
(iii) the two linear equations will have infinitely many solution if the lines overlap on each other .
Therefore , the number of solutions of linear equation is explained above .
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What is the equation of the line passing through point 1 2?
Answers
The equation of the line will be equal to y = -x + 3.
The equation of the line in slope intercept form is expressed as
y = mx + c
where m is the slope of the line, c is the y-intercept and x and y are independent and dependent variables respectively.
We have the equation of the line as y = x + 5 and we need to find equation of line perpendicular to this line. The slope of the line is 1.
If two lines are perpendicular then the relation in their slope is expressed as
m₁ × m₂ = -1 and we have m₁ = 1 and m₂ = m so we get
1 × m = -1
=> m = -1
Now, the equation of the line will be
y = (-1)x + c
Also, the line passes through (1, 2) so on putting these values
2 = -1 + c
=> c = 3
So, the complete equation of line will be
y = -x + 3
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Complete Question:
Write the equation of a line that passes through the point (1, 2) and is perpendicular to the line y = x + 5.
An amusement park sold 15 child tickets. The other 35 tickets it sold were
adult tickets. What is the ratio of the number of adult tickets to the number of
child tickets?
Answers
Answer:
3 : 7
Step-by-step explanation:
RatioRatios are Proportinalised Numbers that we can use to compare number of units relative to the other value.
Eg. 3 : 15 = 1 : 5
SolutionGiven Information from the Question:
15 Child Tickets : 35 Adult Tickets
Now we reduce them to simplest form.
(15 ÷ 5) : (35 ÷ 5) = 3 : 7.
Therefore the ratio of Child Tickets to Adult Tickets is 3 : 7.
The costs of a company are represented by the function c(x)=0. 38x+700. Its revenues are represented by the function r(x)=2. 9x.
Answers
The function that represent the company's profit is (2.52x - 700).
As per the known formula, Profit = Revenue - Cost
Now keeping the functions of revenue and cost to find the function of profit.
Profit = 2.9x - (0.38x + 700)
Performing subtraction on Right Hand Side of the equation to find the profit of company
Profit = 2.9x - 0.38x - 700
Performing subtraction on Right Hand Side of the equation to find the profit of company
Profit = 2.52x - 700
Thus, the the profit of company will be represented by the function 2.52x - 700.
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The complete question is -
The costs of a company are represented by the function c(x)=0. 38x+700. Its revenues are represented by the function r(x)=2. 9x. Find the function that represent the company's profit.
Tyler used 1 1/4 gallons of paint to paint 5/8 of a fence. How many gallons will it take to paint the whole fence?
Answers
Answer:
2 gallons
Step-by-step explanation:
1 1/4 = 1 + 1/4 = 4/4 + 1/4 = 5/4
Then:
5/4 gallons ⇒ 5/8 fence
x gallons ⇒ 8/8 fence
x = (5/4)(8/8) / (5/8)
x = ((5*8)/(4*8)) / (5/8)
x = (5/4) / (5/8)
x = (5*8)/(4*5)
x = 40/20
x = 2
Relation 3
{(4, 4), (1, -7), (-6, 4), (-7,4)}
Function
Not a function
Answers
Answer:
It is a function
Step-by-step explanation:
for a relation to be a function, every X must have one and only one y. That is true for the given values
please help, answers only!!
Answers
The rate of change of the graphs are as follows:
rate of change = 4 / 5rate of change = 3 / 4How to find rate of change?The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.
The rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.
Therefore,
rate of change = change in y / change in x
Hence,
rate of change = y₂ - y₁ / x₂ - x₁
let's find the rate of change of the graphs.
a.
using (-5, -1) and (5, 7)
rate of change = 7 + 1 / 5 + 5
rate of change = 8 / 10
rate of change = 4 / 5
b.
using (0, 3)(-4, 0)
rate of change = 0 - 3 / -4 - 0
rate of change = - 3 / - 4
rate of change = 3 / 4
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What expression shows 0.5 ( x +3) written as a sum
Answers
The expression 0.5 (x + 3) written as a sum is 0.5x + 1.5
How to determine the expression written as a sum?From the question, we have the following parameters that can be used in our computation:
0.5 ( x +3)
Write the expression properly
So, we have the following representation
0.5 (x + 3)
Express the brackets as products
So, we have the following representation
0.5 (x + 3) = 0.5 * (x + 3)
Open the brackets using products i.e. distributive property
So, we have the following representation
0.5 (x + 3) = 0.5 * x + 0.5 * 3
Evaluate the products
So, we have the following representation
0.5 (x + 3) = 0.5x + 1.5
Hence, the expression as a sum is 0.5x + 1.5
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Answer:
1. 0.5x + 1.5
2. are not
Heyy I need help please ^^. Could you also show me how to work this out as well? Thanks! (Both of those equations are supposed to be in 1 curly bracket btw.)
Which ordered pairs are solutions to this system of inequalities?
{5x−4y≥9
{6x+8y≤10
Answers
The ordered pair which is solution to this system of inequalities is (1.75, -0.0625).
The system of inequalities are 5x−4y≥9 and 6x+8y≤10.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The intersection consists of the elements that are contained in all of the intervals.
Here, 5x−4y≥9 -------(I) and 6x+8y≤10 -------(I)
Now, y ≤ 5/4 x+(-9/4); y ≤ -3/4 x+5/4
⇒ 5/4 x+(-9/4) ≤ -3/4 x+5/4
⇒ 5/4 x+3/4 x ≤ 5/4+9/4
⇒ 2x≤ 3.5
⇒ x≤ 1.75
Substitute x=1.75 in y ≤ 5/4 x+(-9/4), we get
y ≤ 1.25(1.75)-2.25
y ≤ 2.1875-2.25
y ≤ -0.0625
Two inequalities are intersect at (1.75, -0.0625)
Therefore, the ordered pair which is solution to this system of inequalities is (1.75, -0.0625).
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WILL GIVE BRAINLY
Henry has $150.00 to spend on a rental car for 2 days. It costs $39.90
per day plus $0.20 per mile to rent the car. Which inequality represents
how many miles, m, Henry can drive the car?
A. m ≤ 351
B. m ≥ 351
C. m ≤ 550.5
D. m ≥ 550.5
Answers
Answer:
The inequality that represents how many miles Henry can drive the car is "m <= 550.5". This inequality can be derived by first calculating the total cost of renting the car for 2 days at $39.90 per day and $0.20 per mile. This gives us a total cost of $79.80 for the rental plus $0.20 per mile for the number of miles Henry drives. Since Henry has $150.00 to spend, we can set up the following inequality to represent the maximum number of miles he can drive:
150.00 >= 79.80 + 0.20m
We can then solve for m by subtracting 79.80 from both sides of the inequality and dividing both sides by 0.20, which gives us:
m <= 550.5
Therefore, the inequality that represents how many miles Henry can drive the car is "m <= 550.5". This inequality states that Henry can drive the car for a maximum of 550.5 miles.
Step-by-step explanation:
in a database, a _____________ is a unit of information about one individual or item.
Answers
Answer: Record
Step-by-step explanation:
Graph the following function by moving the points to match two ordered pairs, including the x-intercept:
f(x) = log 1/8(x)
Answers
The graph of function f(x) = log 1/8(x) is shown in figure with x - intercept
(8, 0).
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The function is,
⇒ f (x) = log 1/8 (x)
Now,
Since, The function is,
⇒ f (x) = log 1/8 (x)
Hence, The x - intercept = (8, 0)
And, The graph is show in figure.
Thus, The figure is shown in figure.
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How do you dilate a figure by 2 3?
Answers
Dilate any given figure by a scale factor 2/3 represents the new image contracted by scale factor 2/3 or 0.667% times image get contracted.
Explanation :
Dilation represents the type of transformation which changes the size of the given image.To dilate any given figure first find the required scale factor and also center of dilation.In the given scale factor 2/3 the new image get changed by scale factor 2/3 or gets contracted by 0.667%.New image ( 2 / 3 ) times contracted in comparison of old image or 0.667% get reduced.Therefore, the dilate a given figure by scale factor 2/3 represents the figure gets contracted by 0.667%.
The complete question is:
How do you dilate a figure by scale factor 2/ 3?
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sara gets paid 1,500.00 per month plus 5.5% commission on all her sales. how much will sara get apid for the month of November if she sold $35,000 worth of merchandies
Answers
Answer: $1925 is the commission she gets from the merchandise, which means if you add 1,500 + 1925 = $3425. $3425 is what she got for that month.
Step-by-step explanation: if its wrong tell me
a woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, how tall is the tree?
Answers
A woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, 75 feet tall is the tree.
Let the tree height = x
From the question, we have
5/8 = x/120
x = (5*120)/8
x = 75 feet
Tree height = 75 feet
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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y=-6x+3 y=6x+3 solve with subsititution
Answers
Answer:
the answer is
-3/2
I hope that helps
Find the value of x.
(2x+6)
38°
x = [?]°
Answers
The value of x from the expression 2x + 6 = 38 is 16.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2x + 6 = 38
Subtracting 6 on both sides.
2x = 38 - 6
2x = 32
Divide both sides by 2.
x = 16
Thus,
The value of x is 16.
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question 31 pts for the data given below, we construct a 90% confidence interval for the population mean. 42.3 59.2 45.4 55.8 49.0 39.7 56.2 54.6 45.8 60.6 55.7 46.1 58.3 44.4 find the upper bound (round off to first decimal place)
Answers
the upper bound is 54.2.
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
31 pts for the data given below, we construct a 90% confidence interval for the population mean.
42.3 59.2 45.4 55.8 49.0 39.7 56.2 54.6 45.8 60.6 55.7 46.1 58.3 44.4 .
MEAN = 50.94
varience = 48.55
s.d = √48.55 = 6.96.
C=0.90,α= 1-0.90=0.10
t=ta/2.df = 1.771 (using t value table)
90% confidence interval
(47.6378,54.2336)
Hence the upper bound is 54.2.
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Need help with this problem
Answers
By using some exponent properties, we will see that the equivalent expression to √(x⁵*y⁶) is:
x²*y³*√x
So the correct option is the first one.
How to simplify the given expression?
Here we need to remember 3 properties about exponents that we will need to use.
These are:
√x = x¹´²
Also remember that:
(xⁿ)ᵃ = xⁿ*ᵃ
And that:
√(a*b) = √a*√b
Well, our expression is:
√(x⁵*y⁶)
We can rewrite this as:
√x⁵*√y⁶
And using the first and second properties we can rewrite.
√x⁵ = x⁵´² = x⁴´²*x¹´² = x²*√x
√y⁶ = y⁶´² = y³
Replacing all that we get:
√(x⁵*y⁶) = x²*y³*√x
Thus, the correct option is the first one.
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