For what interval is the function f(x) = (20 + \sqrt{x}) / (\sqrt{20 + x}) continuous?
Answers
1. according to the condition
[tex] \left \{ {{x \geq 0} \atop {20+x\ \textgreater \ 0}} \right. \ =\ \textgreater \ \ x \geq 0.[/tex]
2. for more details see the attached graph.
Answer: [0;+oo)
Related Questions
Help!
Could it be...??
a. /_ A
b. /_ BCA
c. /_ b
d. /_ CBA
Answers
A truck has total of a pounds of fruit in each of n boxes. How many pounds of fruit are on the truck?
Answers
Answer:
a x n
Step-by-step explanation:
There are a pounds in n identical boxes. That means you would have to multiply to get the answer.
An equipment rental company charges a flat rate of $25, plus $13 per day for insurance. Kyle has $121. Write an inequality to represent the number of days, d, for which he can rent equipment
Answers
Final answer:
The inequality to represent the number of days, d, Kyle can rent equipment with $121 is 25 + 13d ≤ 121. After solving, the result is d ≤ 7, meaning Kyle can rent the equipment for at most 7 days.
Explanation:
To represent the number of days, d, that Kyle can rent equipment given he has $121, we set up an inequality taking into account the flat rate and the daily insurance cost. The equipment rental company charges a flat rate of $25 plus $13 per day for insurance. Therefore, the cost for d days would be $25 + $13d. Since Kyle has $121, we can write the inequality as:
25 + 13d ≤ 121.
This inequality shows that the total cost of renting the equipment for d days, which includes the flat rate and the per-day insurance cost, must be less than or equal to the amount Kyle has.
To solve for d, subtract 25 from both sides:
13d ≤ 121 - 25
13d ≤ 96
Now, divide both sides by 13 to find the maximum number of days Kyle can rent the equipment:
d ≤ 96 / 13
d ≤ 7
Thus, Kyle can rent the equipment for at most 7 days.
Kyle can rent equipment for at most 7 days with $121, considering a flat rate of $25 and a $13 per day insurance charge, as represented by the inequality 25 + 13d ≤ 121.
Explanation:To find the inequality that represents the number of days, d, for which Kyle can rent equipment given that he has $121, we need to consider both the flat rate and the per day insurance charge.
The flat rate for renting equipment is $25, and the daily insurance charge is $13 per day. So, the cost for d days would be the flat rate plus the daily charge times the number of days, which can be represented by the following equation:
Cost = Flat rate + (Insurance charge per day × Number of days)
Cost = 25 + 13d
Since Kyle only has $121, he can spend up to that amount. Therefore, the inequality would be:
25 + 13d ≤ 121
To solve for d:
13d ≤ 121 - 25
13d ≤ 96
d ≤ 96/13
≤ 7.38
Since Kyle can't rent equipment for a fraction of a day, we take the whole number part of the division result. This means that Kyle can rent the equipment for at most 7 days.
Can anyone help me on this question?:) tysm ily
Answers
V=25*40*40+25*35*40=40*1875=75000 cm³
answer: 75000 cm³.
Find three consecutive odd integers such that the sum of the smallest and 7 times the largest is 68
Answers
x = smallest
y = middle
z = largest
x + 7z = 68 ← This equation represents the given information
We can assume that "z" is less than 11 because 7*11 = 77, which is greater than 68.
Our possible consecutive odd integers could be:
a) 1, 3, 5
b) 3, 5, 7
c) 5,7, 9
Lets to plug in the "x" and "z" values
a) 1 + 7(5) = 1+ 35 = 36 This is incorrect, because 36 ≠ 68
b) 3 + 7(7) = 3 + 49 = 52 This is incorrect as well, because 52 ≠ 68
That leaves our final choice. Let's check to be certain
c) 5 + 7(9) = 5 + 63 = 68
5, 7, 9 is the 3 consecutive integers such that the sum of the smallest and 7 times the largest is 68.
The three consecutive odd integers such that the sum of the smallest and 7 times the largest is 68 are: Integers 5, 7 and 9.
Let;
x = smallest odd integer(x+2) = middle odd integer(x +4) = largest integerThe question however suggests that;
The sum of the smallest number and 7 times the largest number is 68.
Therefore;
x + 7(x+4) = 688x + 28 = 688x = 40x = 5.In essence,
the smallest number is x = 5.the middle number is x+2 = 7.the largest number is x+4 = 9Read more:
https://brainly.com/question/18473365
two angles are supplementary. One angle measures at 75° more than twice the measure if the other. What are the measurements of the two angles?
Answers
a + b = 180 (because supplementary angles means their sum is 180)
a = b + 75
substitute the value of a (b+75) into the first equation to get:
b + 75 + b = 180
simplify to get:
b = 52.5
use this value to substitute into any of the 2 equations to get the value of a:
52.5 + 75 = a
a = 127.5
So, the measurements of the two angles are 52.5° and 127.5°
say they are x and y
x+y=180
and one meauses 75 more than twice the other
x=75+2y
solve
subsitute 75+2y for x in other equation
75+2y+y=180
75+3y=180
minus 75 from both sides
3y=105
divide both sides by 3
y=35
sub back
x=75+2y
x=75+2(35)
x=75+70
x=145
the angles are 145° and 35°
High statement is true? Y=log10^x is not a logarithmic function because the base is greater than 0
Answers
Just took the test!!
Sorry I didn't see this earlier
Answer:
Option 3 - [tex]y=\log_{1}x[/tex] is not a logarithmic function because the base is equal to 1.
Step-by-step explanation:
To find : Which statement is true?
Solution :
As the function defined in all statement is logarithmic function.
So, The definition of logarithmic function is defined as
[tex]y=\log_bx\Rightarrow b^y=x[/tex] where, b>0 and b ≠ 1.
Now, The following statement
1) [tex]y=\log_{10}x[/tex] is not a logarithmic function because the base is greater than 0.
The statement is False as by definition, the base of a log must be greater than zero but cannot equal one.
2) [tex]y=\log_{\sqrt3}x[/tex] is not a logarithmic function because the base is a square root.
The statement is False as by definition, the base [tex]\sqrt3[/tex] is a positive number not equal to one.
3) [tex]y=\log_{1}x[/tex] is not a logarithmic function because the base is equal to 1.
The statement is True as by definition log cannot have a base of one.
4) [tex]y=\log_{\frac{3}{4}}x[/tex] is not a logarithmic function because the base is a fraction.
The statement is False, as 3/4 is a legitimate base, just like any other positive number other than one.
Therefore, Option 3 is true.
How many ways are there to choose eight coins from a piggy bank containing 100 identical pennies and 80 identical nickels?
Answers
There are 9 ways to choose eight coins from a piggy bank.
Total number of ways =
(Combinations of 8 pennies) + (Combinations of 7 pennies and 1 nickel) + ... + (Combinations of 0 pennies and 8 nickels)
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9 ways
Jane has $10000 to invest in AAA and AA bonds. The AAA bond yields a 5% and requieres a minimum investment of $1000. The AA bond yields an average of 8% and requires a minimum investment of $2000. Jane requires that at least three times as much money should be invested in the AAA bond as in the AA bond
Answers
$10,000 to invest
AAA bonds - minimum of $1,000 yields 5%
AA bonds - minimum of $2,000 yields 8%
Jane requires that at least three times as much money should be invested in the AAA bond as in the AA bond
Let x represent the investment in AA bond.
x + 3x = 10,000
4x = 10,000
x = 10,000 / 4
x = 2,500
Jane should invest 2,500 to AA bond.
Jane should invest 7,500 to AAA bond. This amount is 3 times the amount invested in AA bond.
2,500 * 8% = 200
2,500 + 200 = 2,700
7,500 * 5% = 375
7,500 + 375 = 7,875
Jane's $10,000 investment will earn $575 interest for a total of $10,575.
which of the following is equivalent to the polynomial below
Answers
We have then:
x ^ 2-10x + 61
(x- (5 + 6i)) (x- (5-6i))
Checking:
(x- (5 + 6i)) (x- (5-6i))
x ^ 2 - x * (5-6i) - (5 + 6i) x + (5 + 6i) * (5-6i)
x ^ 2 - 5x + 6ix - 5x- 6ix + 25 - 30i + 30i + 36
x ^ 2 -10x + 61
Answer:
(x- (5 + 6i)) (x- (5-6i))
Given ΔJKL : ΔXYZ, find the scale factor.
6 8
---- ----
9 x
Answers
Multiply means and extremes
6x = 72
x = 12
6/9 = 8/12
The scale factor is 4/3 or 1 and 1/3
Hope this helps =)
Answer:
it is 16
Step-by-step explanation:
find the sum and express it in simplest form.
[tex](b - 3x) + ( - 5b + 6x - 5)[/tex]
Answers
= b - 3x - 5b + 6x - 5
= b - 5b - 3x + 6x - 5
= -4b + 3x - 5
If 9 is added to twice a number and this sum is multiplied by 6 the result is the same as if the number is multiplied by 7 and 14 is added to the product. What is the number?
Answers
Therefore, let that number be y.
"if 9 is added to twice a number" = 2y + 9
"this sum is multiplied by six" = (2y + 9) x 6
"the number is multiplied by 7" = 7y
"14 is added to the product" = 7y + 14
Now combine the expressions and solve away!
(2y + 9) x 6 = 7y + 14
Expand.
12y + 54 = 7y + 14
Shift all the y to a side and all the pure numbers to another side.
12y - 7y = 14 - 54
Group them.
5y = - 40
Divide 5 on both sides.
y = - 8
Therefore, the number is - 8.
how to erite a sequence of 1/4 , 1/2,3 write a rule for the sequence 1/4 1/2 3/4
Answers
a1= 1/4
d= 1/4
an= 1/4 + (n-1)(1/2) - First you need to distribute the 1/2 to both the n and -1 to get: an= 1/4 + 1/2n -1/2.
Then you need to add like terms (1/4-1/2) to get an=1/2n-1/4. Hope this helps!
The sequence 1/4, 1/2, 3/4 increases by 1/4 for each subsequent term, defining it as an arithmetic sequence with a common difference of 1/4.
To find a rule for the sequence 1/4, 1/2, 3/4, we can examine the pattern and observe that the sequence consists of fractions that increase by 1/4 each step. Starting with 1/4, when we add 1/4, we get 1/2, and adding another 1/4 to 1/2 gives us 3/4. So the rule of the sequence can be written as 'start at 1/4 and add 1/4 each step'. This pattern is an arithmetic sequence with a common difference of 1/4.
The area of a circle (A) is given by the formula A=pi*r2
where r is the circle's radius. The formula to find r is . If and , r is centimeters.
Answers
The area of a circle is calculated with the formula A = πr², where pi is the mathematical constant approximately equal to 3.14159 and r represents the circle's radius. Considering significant figures is crucial for maintaining precision, as demonstrated in rounding the calculated area of a circle with radius 1.2 m to 4.5 m², based on the initial data's precision.
Explanation:The area of a circle is calculated using the formula A = πr², where π (pi) is a constant approximately equal to 3.14159, and r is the radius of the circle. When calculating the area with a given radius, it's important to consider the significance of figures in your final answer. For instance, if a circle's radius is given as 1.2 meters (with two significant figures), and you calculate the area to be 4.5238934 square meters using a detailed value of pi, you need to round your final answer to maintain the precision of your initial data, resulting in an area of 4.5 m².
It's also valuable to note how ancient civilizations, like the Greeks, approximated mathematics related to circles and how such estimations have evolved into our modern understanding, where the concept of significant figures plays a critical role in ensuring accuracy across varying fields of study and applications.
An urn initially contains 5 white balls and 7 black balls. each time a ball is selected, its color is noted and it is replaced in the urn along with 2 more balls of the same color. what is the probability that of the first 2 balls selected, one is white and one is black?
Answers
Rosalia passed out fliers that say, “Vote for Rosalia!” She gave out 85 fliers on Monday, 66 fliers on Tuesday, and 99 fliers on Wednesday. What fraction of the fliers did she give out on Wednesday? Use a diagonal fraction bar in your answer. Explain how you found the answer.
Answers
Answer:
She gave out a total of 250 fliers and 99 of them were given out Wednesday. The fraction for that would be 99/250.
Step-by-step explanation:
Consider the provided information.
She gave out 85 fliers on Monday 66 fliers on Tuesday, and 99 fliers on Wednesday.
Now, calculate the total number of fliers she give:
She give 250 fliers in total.
We need to find the fraction of the fliers she give out on Wednesday.
On Wednesday she give 99 fliers and total she give 250 fliers.
99/250
Hence, she give out 99/250 fraction of fliers on Wednesday.
what are the zeros of the function below?
f(x) = x(x-1)(x+11)/(x+12)(x-13)
a. 0,1, and -11
b. 0, -1, and 11
c. 13 and -12
d. -13 and 12
Answers
[tex]x(x-1)(x+11)=0[/tex]
A product is equal to zero whenever one of the factors is equal to zero.
That means that zeros of our functions are:
1)[tex]x=0[/tex]
2)[tex]x-1=0[/tex]
[tex]x=1[/tex]
3)[tex]x+11=0[/tex]
[tex]x=-11[/tex]
The final answer is a. Function has zeros at (0, 1, -11).
A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 3 weeks, the sheet is only 1.25 meters thick. Let S(t) denote the ice sheet's thickness S (measured in meters) as a function of time t (measured in weeks). Write the function's formula.
Answers
Answer: The required function formula is,
S(t) = 2 - 0.25 t
Step-by-step explanation:
Here, the initial thickness of the ice sheet = 2 meters,
After 3 weeks, the thickness of ice sheet = 1.25 meters
Total changes in the thickness in 3 weeks = 2 - 1.25 = 0.75 meters,
⇒ Total changes in the thickness in 1 weeks = 0.75/3 = 0.25 meters,
Since, the ice is melting with the constant rate.
⇒ The rate of ice decreasing = 0.25 meters per week.
⇒ Total changes in t weeks = 0.25 t meters
The new thickness of ice after t weeks = Initial thickness - Total changes in t weeks.
⇒ S(t) = 2 - 0.25 t
Which is the required function's formula.
The function's formula for the ice sheet's thickness as a function of time is S(t) = -0.25t + 2.
Explanation:To write the function's formula, we can use the slope-intercept form of a linear equation, which is given by the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope represents the rate at which the ice thickness decreases over time. From the given information, we know that the thickness decreases by 0.75 meters over 3 weeks. Therefore, the slope is -0.75/3 = -0.25 meters per week.
Since the ice thickness is 2 meters in the beginning, the initial point on the graph is (0, 2). Using the slope-intercept form, we can write the formula for the ice sheet's thickness as a function of time as:
S(t) = -0.25t + 2
Learn more about Arctic Circle lake ice thickness here:https://brainly.com/question/15739889
#SPJ2
Y=10x
Graph the function
Answers
since it doesn't say anything after the 10x, the y-intercept is at (0, 0)
1. What is the area of this figure?
Enter your answer in the box.
? cm²
2. What is the measure of angle x?
Enter your answer in the box.
x = °
Answers
Enter your answer in the box.
A = (5x5) + 1/2(4)(5)
A = 25 + 10
A = 35
answer
35 cm²
--------------
2. What is the measure of angle x?
Enter your answer in the box.
x = 90° - 47
x = 43°
Answer:
The area if this figure is 35cm2
Step-by-step explanation:
divide -2x^3-5x^2+4x+2 by x+2
Answers
We shall perform the division with two methods: long division and synthetic division.
Long Division:
-2x² - x + 6
-----------------------------
x+2 | -2x³ - 5x² + 4x + 2
-2x³ - 4x²
------------------------------
- x² + 4x + 2
- x² - 2x
---------------------
6x + 2
6x + 12
---------------
- 10
Answer: [tex]-2x^{2}-x+6- \frac{10}{x+2} [/tex]
Synthetic Division:
-2 | -2 -5 4 2
4 2 -12
-------------------
-2 -1 6 -10
Answer: [tex]-2x^{2} - x + 6 - \frac{10}{x+2} [/tex]
To divide the given polynomial by x + 2, use polynomial long division, which involves dividing the leading term, multiplying the divisor, subtracting, and repeating the process until all dividend terms are addressed.
To divide the polynomial -2x^3 - 5x^2 + 4x + 2 by x + 2, we can use the process of polynomial long division. This method is similar to long division with numbers, where we divide, multiply, subtract, bring down the next term, and repeat the process until we have gone through all terms of the dividend.
The process would look like this:
Divide the first term of the dividend (in this case, -2x^3) by the first term of the divisor (x), yielding -2x^2.Multiply the entire divisor (x + 2) by this quotient (-2x^2) and subtract the result from the dividend.Bring down the next term of the dividend and repeat the process until there are no terms left to bring down.The final result would be the quotient of the division, which may or may not have a remainder.
The glass container is filled to a height of 2.25 inches. What percent of the container is filled with sand?
Answers
Part A) How much sand is currently in the container?
[sand currently in the container]=(5)*(4 1/2)*(2.25)-----> (5)*(4.5)*(2.25)
[sand currently in the container]=50.625 in³
the answer Part a) is 50.625 in³
Part B) How much more sand could the container hold before?
[sand could the container hold before]=[5*4.5*3]-[50.625]
[sand could the container hold before]=[67.5]-[50.625]------> 16.875 in³
the answer Part B) is 16.875 in³
Part C) What percent of the container is filled with sand?
the volume of container is [5*4.5*3]=67.5 in³
the volume filled with sand=50.625 in³
therefore
if 100%----------------> 67.5 in³
X---------------------> 50.625 in³
X=(50.625*100)/67.5=75 %
the answer Part C) is 75%
Which of these is equivalent to 92 + 42? (9 + 4)2 (9 × 4)2 (9 × 9) + (4 × 4) (9 + 9) + (4 + 4)
Answers
9 ^ 2 + 4 ^ 2.
We have then that the equivalent expression for this case is:
(9 × 9) + (4 × 4)
Both expressions give the same result 97
Answer:
(9 × 9) + (4 × 4)
why does 16 to the power of 0 equal 1?
Answers
hope this helps
Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should the length of the third side be). Write the inequalities for each case. 8 and 13
Answers
5 < third side < 21
Final answer:
The length of the third side of a triangle with side lengths of 8 and 13 must be greater than 5 units and less than 21 units according to the triangle inequality theorem.
Explanation:
To find the range for the length of the third side of a triangle given two sides with lengths of 8 and 13, we can use the triangle inequality theorem.
This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the absolute value of their difference.
The inequalities for the third side, let's call it c, are:
c < 8 + 13c > |13 - 8|Therefore, we can say:
c < 21c > 5So the length of the third side must be greater than 5 units and less than 21 units.
y - 5 = 0.5x2 + 6x - 3 How many x-intercepts does the graph of this quadratic have?
Answers
Y - 5 = 0.5x2 + 6x - 3--------------- > y=0.5x2 + 6x -3+5=0.5x2 + 6x+2
y=0.5x2 + 6x +2
using a graphic tool
see the attached figure
the graph have two x-intercepts----------> (-11.657,0) and (0.343,0)
Answer:
its (A)
Step-by-step explanation:
Question 7 plz help me saner this question
Answers
[tex] \frac{8}{4000} * 100 [/tex]
1/5 %
= 0.2%
I hope this helps!
Find the measure of the major arc if its central angle is 35
Answers
[tex] \left[\begin{array}{ccc}\boxed{\boxed{360-35=325}}\end{array}\right] [/tex]
That major arc would be [tex]325[/tex]° [tex]degrees[/tex].
Hope this helps you boy!
The pyramid shown has a square base that is 1212 centimeters on each side. The slant height is 1818 centimeters. What is the surface area of the pyramid?
Answers
Answer : Surface area of pyramid = 4406832 square cm.
Explanation :
Since we have given that
Side of square base = 1212 cm
Slant height of pyramid = 1818 cm
As we know that ,
[tex]\text{Surface area of pyramid }=\frac{1}{2}\times perimeter\times \text{ slant height}[/tex]
[tex]\text{ Since, perimeter of square }=4\times side\\=4\times 1212\\=4848 cm[/tex]
Now,
[tex]\text{ Surface area of pyramid }= \frac{1}{2}\times 4848\times 1818\\\\\text{ Surface area of pyramid }=4406832\text{ square cm}[/tex]
Hence, surface area of pyramid = 4406832 square cm.