Determine whether each function is continuous at x=5. Justify your answer using the continuity test.
Answers
Answer:
2. [tex]f(x)=\frac{x^2}{x+5}[/tex]
Step-by-step explanation:
When you replace x=5 into those functions you obtain:
[tex]1. f(x)=\sqrt{x^2-36} = \sqrt{5^2-36} = \sqrt{-11} \\2. f(x)=\frac{x^2}{x+5}=\frac{5^2}{5+5}=\frac{25}{10}[/tex]
We can see that the function number 1, when the x=5 is replaced, falls into the imaginary numbers or complex domain, so the function is not continuous in the real domain.
On the other hand, the second function falls into the real domain whe x=5 is replaced, so the function is continuous in the real domain!
I hope you understand!
Related Questions
What is 40.302 in word form
Answers
Answer:
Forty and three hundred two thousandths.
Step-by-step explanation:
40 = forty
300 = three hundred
.02 = two thousandths
Hope this helps.
Answer:
Step-by-step explanation:
Forty and three hundred two thousandths.
Saiges spaceship traveled 588 kilometers in 60 seconds. Determine whether or not each spaceship trip below has the same speed as saiges spaceship
Answers
Answer:
Part 1) 441km in 45s --> Has the same speed as Saige's spaceship
Part 2) 215km in 25s --> Does not have the same speed as Saige's spaceship
Part 3) 649km in 110s --> Does not have the same speed as Saige's spaceship
Step-by-step explanation:
The complete question is
Saige's spaceship traveled 588 kilometers in 60 seconds.
Determine whether or not each spaceship trip below has the same speed as Saige's spaceship.
441km in 45s
215km in 25s
649km in 110s
we know that
The speed is equal to divide the total distance traveled by the total time
In this problem we have that
The speed of Saiges spaceship is equal to
[tex]\frac{588}{60}=9.8\ \frac{km}{sec}[/tex]
case 1) we have
441km in 45s
Find out the speed of the spaceship trip
[tex]\frac{441}{45}=9.8\ \frac{km}{sec}[/tex]
Compare the speed of the spaceship trip with the speed of Saiges spaceship
[tex]9.8\ \frac{km}{sec}=9.8\ \frac{km}{sec}[/tex]
therefore
Has the same speed as Saige's spaceship
case 2) we have
215km in 25
s
Find out the speed of the spaceship trip
[tex]\frac{215}{25}=8.6\ \frac{km}{sec}[/tex]
Compare the speed of the spaceship trip with the speed of Saiges spaceship
[tex]8.6\ \frac{km}{sec}\neq 9.8\ \frac{km}{sec}[/tex]
therefore
Does not have the same speed as Saige's spaceship
case 3) we have
649km in 110s
Find out the speed of the spaceship trip
[tex]\frac{649}{110}=5.9\ \frac{km}{sec}[/tex]
Compare the speed of the spaceship trip with the speed of Saiges spaceship
[tex]5.9\ \frac{km}{sec}\neq 9.8\ \frac{km}{sec}[/tex]
therefore
Does not have the same speed as Saige's spaceship
at 8 a.m. the temperature was -14 degrees by noon the tempature was 12 degrees. Find the change did it rise or drop?
Answers
An architect draws a blueprint of a house. He draws the living room on the blueprint as 4.5 in. long by 6 in. wide with a scale of 1 in. for every 4
ft. He draws a second copy of the blueprint with a scale of 1 in. for every 3 ft. How many inches long should the living room be in this second
blueprint?
Answers
Answer:
the answer is 8.5
Step-by-step explanation:
yeet
Answer:
I think the closest would be 8 :3
Hello need it asap I will give you 5 star for all answer
Answers
Answer:x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2 f(2) = 2.5(2) - 10.5 g(2) = 64(0.5*2)
f(2) = 5 - 10.5 g(2) = 64(1)
f(2) = -5.5 g(2) = 64
3 f(3) = 2.5(3) - 10.5 g(3) = 64(0.5*3)
f(3) = 7.5 - 10.5 g(3) = 64(1.5)
f(3) = -3 g(3) = 96
4 f(4) = 2.5(4) - 10.5 g(4) = 64(0.5*4)
f(4) = 10 - 10.5 g(4) = 64(2)
f(4) = -0.5 g(4) = 128
5 f(5) = 2.5(5) - 10.5 g(5) = 64(0.5*5)
f(5) = 12.5 - 10.5 g(5) = 64(2.5)
f(5) = 2 g(5) = 160
6 f(6) = 2.5(6) - 10.5 g(6) = 64(0.5*6)
f(6) = 15 - 10.5 g(6) = 64(3)
f(6) = 4.5 g(6) = 192
The hypotenuse of a right triangle is 13 inches. If the long leg is 7 inches longer than the short leg, find the lengths of the leg using the Pythagorean theorem
Answers
Answer:
The length of the short leg is 5 inches and the leg of the long leg is 12 inches
Step-by-step explanation:
Let
a -----> the long leg of a right triangle
b ----> the short leg of a right triangle
c ----> the hypotenuse of a right triangle
we know that
Applying the Pythagoras Theorem
[tex]c^{2} =a^{2}+b^{2}[/tex] -----> equation A
we have that
[tex]a=b+7[/tex] -----> equation B
[tex]c=13\ in[/tex] ----> equation C
Substitute equation B and equation C in equation A and solve for b
[tex]13^{2} =(b+7)^{2}+b^{2}[/tex]
[tex]169=b^2+14b+49+b^2[/tex]
[tex]2b^2+14b+49-169=0[/tex]
[tex]2b^2+14b-120=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]b=5\ in[/tex]
see the attached figure
Find the value of a
[tex]a=b+7[/tex] ----> [tex]a=5+7=12\ in[/tex]
therefore
The length of the short leg is 5 inches and the leg of the long leg is 12 inches
The lengths of the leg : 12 and 5
Further explanationQuadratic function is a function that has the term x²
The quadratic function forms a parabolic curve
The general formula is
[tex]\large {\boxed {\bold {f (x) = ax ^ 2 + bx + c}}}[/tex]
where a, b, and c are real numbers and a ≠ 0.
There are 3 ways to solve quadratic equations
a. factoring b. perfect squared c. quadratic formula
We use the factoring method
Quadratic equation x² + bx + c = 0 is equivalent to quadratic equation
[tex]{\displaystyle {x ^ 2 + (p + q) \times \: pq}}[/tex]
where p + q = b and px q = c
for a = 1, the result of factoring is (x + p) (x + q)
If at an angle there is an angle of 90 degrees, this triangle is said to be a right angle
There is a hypotenuse in this triangle which is the sum of the two sides
c² = a² + b²where c = hypotenuse
This formula is known as the Pythagorean theorem which states that:
the hypotenuse or the longest side in a right triangle equal to the sum of the squares of the other sides.
The hypotenuse of a right triangle is 13 inches
then c = 13
If the long leg is 7 inches longer than the short legthen a = b + 7
Then the phytagorean equation becomes:
(b + 7)² + b² = 13²
49+14b+b²+b²=169
49+14b+2b²=169
2b²+14b-120=0
b²+7b-60=0
factoring
(b-5)(b+12)=0
b=5 or b=-12
we use positive number ⇒5
So :
the long leg = b+7=5+7=12
the short leg = b = 5
Learn more
the triangle angle
brainly.com/question/1611320
Prove the converse of the Pythagorean Theorem
brainly.com/question/1597216
Use Pythagoras' theorem
brainly.com/question/10488367
Keywords : Pythagorean Theorem , hypotenuse, the long leg
Find the percent of each number.
1. 32% of 60 =
Answers
Answer:
Step-by-step explanation:
Answer:
19.2
Step-by-step explanation:
Is this statement true or false?
According to the graph, during periods of recession, the number of people in poverty increases.
True
False
Answers
Answer: The Statement is true
Step-by-step explanation: the lines in the graph are constantly parallel to each other, showing that when one increases, so does the other
Answer:
The given statement is true.
Step-by-step explanation:
We are given the following graph in the picture:
On the x-axis years are shown from 1959 to 2005.
The y axis shows the poverty rate and the number of people in poverty.
The blue strips in the graph are the recession time.
Now, for each blue strip, we could see the line for poverty rate and the number of people in poverty increases. There is an upward trend in the line in the blue strip.
In other words we could say that the slope increases for all the blue strips which actually represents that the number of people in poverty increases in recession.
Thus, the given statement is true.
what values of y will make the expression true? 10 - y = y - 10
Answers
Answer:
y = 10
Step-by-step explanation:
Given
10 - y = y - 10 ( subtract y from both sides )
10 - 2y = - 10 ( subtract 10 from both sides )
- 2y = - 20 ( divide both sides by - 2 )
y = 10
Which is greater, 9 x 10-2 or 3 x 10-4? How many times
greater is the number you chose than the other number?
Explain your reasoning.
Answers
Final answer:
[tex]9 \times 10^{-2 }(0.09)[/tex] is greater than [tex]3 \times 10^{-4} (0.0003)[/tex], and is 300 times greater.
Explanation:
To determine which is greater between [tex]9 \times 10^{-2 }[/tex] and [tex]3 \times 10^{-4}[/tex]we need to understand how to interpret numbers in scientific notation. The expression [tex]9 \times 10^{-2 }[/tex] means 9 times 1 following 2 zeroes to the left, resulting in 0.09. In the case of [tex]3\times 10^{-4}.[/tex] it means 3 times 1 following 4 zeroes to the left, producing 0.0003.
Comparing these values, [tex]9 \times 10^{-2 }[/tex] is clearly the larger number because 0.09 is greater than 0.0003. To find out how many times greater it is, we divide the larger number by the smaller one: 0.09 / 0.0003 equals 300. Therefore, [tex]9 \times 10^{-2 }[/tex]is 300 times greater than [tex]3\times 10^{-4}.[/tex]
i need help with a math problem right now it says A car rental agency advertised renting a car for $23.95 per day and $0.25 per mile. If Trevor rents this car for 3 days, how many whole miles can he drive on a $100 budget?
Answers
The distance remaining for a road trip over several hours is shown in the table. Use information to find the constant rate of change in miles per hour.
Answers
What square roots of 10 lies between which two whole numbers?
Answers
The square root of 10 lies between two whole numbers, 3 and 4. This concept can be understood using number sense and geometry.
The square root of 10 falls between two whole numbers. To determine these two numbers, we need to consider the closest perfect square numbers to 10. These are 9 (the square root of 9 is 3) and 16 (the square root of 16 is 4). Hence, the square root of 10 must be somewhere between 3 and 4. Using a calculator, we find the approximate square root of 10 to be around 3.16. So, the square root of 10 lies between 3 and 4.
This kind of problem is related to number sense and geometry, especially when it comes to understanding square roots.
Learn more about Square Roots here:https://brainly.com/question/3120622
#SPJ2
emade
There are 666 students
going to a trivia
competition. If each school
van can hold 6 students,
how many vans will they
need?
Answers
Answer:
666 divided by 6 is 111. So, they would need 111 vans.
Subtraction fraction answer for 13 3/16 Subtract 2 1/4
Answers
Answer:
10.9
Step-by-step explanation:
So you add or subtract the number, leaving the bottom number the same and then simplify if you need to.
If a flagpole that is 20 feet tall casts a 6 foot
shadow, how long a shadow would a building that
is 15 feet tall cast at the same time of day?
Answers
Answer:
4.5 foot shadow
Step-by-step explanation:
By looking at this you can make a ratio that very every 5 feet there is a 1.5 foot shadow.
So 1.5 x 3 = 4.5 foot shadow
(Very sorry If it is incorrect Good luck!)
Find the distance between (3,4) and (-5,7)
Answers
Answer:
(x+7, y-3)
Step-by-step explanation:
7 units to the right and 3 units down
7 3/4% as a fraction in simplest form
Answers
this probably isn't right but this is what the internet says 31/400
To convert 7 3/4% to a fraction in simplest form, add the whole number and the fractional part together, find a common denominator, and simplify if necessary.
Explanation:To convert 7 3/4% to a fraction in simplest form, we first need to convert the mixed number to an improper fraction. The whole number part, 7, can be written as 7/1. Adding the fractional part, we have (7/1) + (3/4). To add fractions, we need a common denominator, which in this case is 4. So, we rewrite the fractions as (28/4) + (3/4). Adding the numerators, we get 31/4. Since we want the fraction in simplest form, we can simplify 31/4 by dividing both the numerator and the denominator by their greatest common factor, which is 1. Therefore, 7 3/4% as a fraction in simplest form is 31/4.
Learn more about Converting percentages to fractions here:
https://brainly.com/question/35291109
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Round your answers to the nearest whole number.
The fasted train in the world can travel 300 feet per second. How fast is this in miles per hour?
(1 mile = 5280 feet)
Answers
Answer:
205 miles per hour.
Step-by-step explanation:
1 mile = 5280 feet so:
300 ft / second = 300/ 5280 miles/second.
There are 3600 seconds in an hour so
this converts to 300 * 3600 / 5280 miles per hour
= 204.55 miles per hour.
Hey!
-----------------------------------------------
Solution:
Let's use dimensional analysis!
[tex]= \frac{1mi}{5280ft} * \frac{3600}{1hr} * \frac{300ft}{1sec}[/tex]
[tex]= \frac{1,080,000}{5,280}[/tex]
[tex]= 204.454545...[/tex]
[tex]= 205[/tex]
-----------------------------------------------
Answer:
205
-----------------------------------------------
Hope This Helped! Good Luck!
Gary says that 3 - 1 1/3 will be more than 2, since 3 – 1 is 2. Draw a picture to prove that Gary is wrong.
Answers
Answer:
It makes 5/3 it is less than two!
Step-by-step explanation:
Topic: Fractions and Mixed Numbers
You have to remember the concept of fractions, let's represent by cake diagrams, it says that Gary says that 3, let's say it's 3 cakes, as the fractions are represented in terms of thirds, let's draw the cakes each one divided in 3.
and the statement says that taking away 1 and 1/3 it will make more than 2.
As you can see in the picture below, we take away 1 cake and we will take away another third of a second cake represented by the brown region of the cakes. it means that the yellow region is what's left after taking the 1 and 1/3. as you can see it doesn't make two, makes less than two exactly 5/3.
PS: Try and do it mathematically now!
What inequality is graphed below?
x < -6
x ≤ -6
x ≥ -6
Answers
Answer:
x ≥ -6
Step-by-step explanation:
How many real solutions does the function shown on the graph have?
No real solutions
One real solution
Two real solutions
Cannot be determined
Answers
Answer:
0 because it doesn't cross the x-axis
Step-by-step explanation:
Interpreting the graph, it is found that the function has no real solutions.
The number of different real solutions that a function has is given by the number of times it crosses the x-axis(also known as the horizontal axis) on the graph.
In this problem, the function never crosses the x-axis, thus, it has zero real solutions.
A similar problem, in which the real solutions are taken from a graph, is given at https://brainly.com/question/16349072
Suppose that the length of a rectangle is 4 times the width. If the area is 900 square feet, then what is the width of the rectangle, in feet?
Answers
Answer:
Width 15 feet
Step-by-step explanation:
Use formula
[tex]A_{rectangle}=\text{Width}\cdot \text{Length}[/tex]
Let x feet be the width of the rectangle.
If the length of a rectangle is 4 times the width of the rectangle, then the length is 4x feet.
The area of the rectangle is 900 square feet, so
[tex]900=x\cdot 4x\\ \\900=4x^2\\ \\x^2=225\ [\text{Divided by 4}]\\ \\x=\pm 15[/tex]
The width cannot be negative, then x=15 feet and 4x=60 feet.
Final answer:
To find the width of the rectangle when the length is 4 times the width and the area is 900 square feet.
Explanation:
To find the width of the rectangle:
Let the width be w feet.
Since the length is 4 times the width, the length is 4w feet.
Given that the area is 900 square feet, we can set up the equation w * 4w = 900 to solve for w.
4w² = 900
w² = 225
w = 15 feet
Therefore, the width of the rectangle is 15 feet.
Q. Saline IV fluid bags cost $64.20 for 24, 1000 ml bags from one supplier. A new supplier sells 500 ml bags for $2 each
The hospital uses about 10,000, 1000 ml bags each month. Nurses report that about half of the bags are more than half
full when they are discarded. If you are going to use only one supplier, which size bag provides the best deal, and how
much will you save each month? Compare the cost of the new supplier to the current one.
Answers
Answer:
The 1000 ml bags, over $3000
Step-by-step explanation:
First, determine how many bags you need from each vendor. Then find the cost per bag with each vendor. Remember, the bags are reported to be only half full when discarded, therefore you need the equivalent of 5,000 1,000 ml bags and 5,000 500ml bags.
Answer:100ml bag is 3000
Step-by-step explanation:
two numbers are in the ratio of 2to 3 if the smaller number is 18 what is the larger number
Answers
Answer:
27
Step-by-step explanation:
Solve -2(t+2)+5t=6t+11
Answers
Answer:
t=-5
Step-by-step explanation:
Answer:
t = -5
Step-by-step explanation:
Distribute by multiplication -2(t + 2), obtaining
-2t - 4 + 5t = 6t + 11.
Combine the t terms; this yields -4 = 3t + 11. Solving for 3t, we get
3t = -4 -11, or 3t = -15. Thus t must be -5.
Which point is not on the graph of the function y = x + 5?
(2, 7)
(6, 11)
(220, 225)
(10, 5)
Answers
Answer:
(10, 5 )
Step-by-step explanation:
To determine which points lie on the graph or not.
Substitute the x- coordinate of the point into the equation and if the value agrees with the y- coordinate of the point then the point is on the graph.
(2, 7 )
y = 2 + 5 = 7 ← True thus point is on the graph
(6, 11 )
y = 6 + 5 = 11 ← True thus point is on the graph
(220, 225 )
y = 220 + 5 = 225 ← True thus point is on the graph
(10, 5 )
y = 10 + 5 = 15 ≠ 5 ← Point is not on the graph
Jessica's home town is a mid-sized city experiencing a decline in population. The following graph models the estimated population if the decline continues at the same rate. Select the most appropriate unit for the measure of time that the graph represents. A. hours B. years C. weeks D. days
Answers
Answer:
C on Plato
Step-by-step explanation:
Raymond buys bottles of water at 2 dollars each and a large pizza at 13 dollars. The total costar 21 dollars. How many bottles of water did Raymond buy?
Answers
Answer:
4
Step-by-step explanation:
$21-$13=$8
$8÷$2=4 bottles
What is negative 5 5/6–2 3/5
Answers
Answer:
the answer is -8 13/30
Step-by-step explanation: