If f(x)= x^2-25 and g(x)= x-5, what is the domain of (f/g) (x)
The domain of the compound function (f/g)(x) is all real numbers except x = 5, where the function g(x) would cause a division by zero.
To find the domain of the compound function (f/g)(x), we need to consider the domains of both f(x) and g(x), as well as where g(x) is not equal to zero, since we cannot divide by zero.
The function f(x) = x^2 - 25 is a quadratic function and its domain is all real numbers because a quadratic function is defined for every real number.
The function g(x) = x - 5 is a linear function, and its domain is also all real numbers. However, for the quotient (f/g)(x), we must exclude the value where g(x) = 0. Solving g(x) = 0 gives us the value x = 5.
Therefore, the domain of (f/g)(x) is all real numbers except x = 5, since at x = 5, the denominator g(x) would be zero, making the division undefined.
Lin parachutes from a plane at a height of 22,000 ft above sea level. Several minutes later she notes from an instrument on her wrist that she had dropped 10,000 ft. How far above sea level is she now?
–12,000 ft
6000 ft
10,000 ft
12,000 ft
Lin is 12000 ft far above sea level.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, the initial height of Lin is 22000 ft.
Now, the height of Lin is dropped by 10000, therefore, the new height is:
22000 - 10000
= 12000
Hence, Lin is 12000 ft far above sea level.
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A sporting goods store pays $120 for a rubber raft. The percent of markup is 45%. Find the raft’s selling price.
A daycare center charges a $75 enrollment fee plus $100 per week. Write a function, C, for the cost of daycare after a certain number of weeks. w.
the equation would be:
C = 75+100w
Answer: Our required function would be
[tex]C=75+100w[/tex]
Step-by-step explanation:
Since we have given that
Charges of daycare = $175
Enrollment fee = $100 per week
Let C be the cost of daycare after a certain number of weeks.
Let w be the number of weeks.
So, function would be
[tex]C=75+100w[/tex]
Hence, our required function would be
[tex]C=75+100w[/tex]
$48 decreased by 25%
In England, mass is measured in units called stones. One pound equals 1/14 of a stone. A cat weighs 3/4 stone. How many pounds does the cat weigh?
Compatible numbers are numbers in a problem that are easy to compute ---------------(it is blank. help me find the answer and i will give you 40 points!!!!!!) please find the blank!PLEASE!!!!!!!!!!
Compatible numbers are numbers in a problem that are easy to compute is a correct statement.
How to perform mathematical operations mentally ?To perform mathematical operations like addition, subtraction,division and multiplication break the numbers into parts such that they are near to the multiple of 10 by subtracting or adding such values to those numbers.
According to the given question compatible are easy to compute it is true.
Compatible numbers are easy for addition, subtraction,division and multiplication and these operations can easily done by mentally without pen and paper.
For example - If we have to add 430 and 760.First we will add 400 and 700 that is 1100 and 30 added to 60 is 90 so the answer is 1190.
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Triangle ABC is an isoceles right triangle inscribed in a circle. the center of the circle is point D and the diameter of the circle is AC. Which of the following would NOT be true for the right triangle and circle described above?
The measure of arc AC is equal to the measure of arc AB
AD is congruent to DC and to BD
The measure of arc AB is equal to the measure of arc BC
the measure of angle B is 90 degrees
Solve x = log9(4)
**Round your answer to the nearest hundredth.
How many centigrams are there in 24 grams?
A. Restate the question: 24 grams=____centigrams
B. Use the place value chart to determine the multiplication factor,and solve.
Given: ∠KJL and ∠KML intercept arc KL. Prove: m∠KJL = m∠KML
The Prove of m∠KJL = m∠KML is shown below.
What is Arc?An "arc" is a smooth curve that connects two points in mathematics. In general, an arc is a section of a circle. It is essentially a portion of a circle's circumference. An arc is a type of curve.
We have,
KJL and ∠KML intercept arc KL.
Now, Angle made by arc at center is double the angle made on any point on the circle other than arc.
So, m <KJL = 1/2 < ( KL)
m <KML = 1/2 (KL)
By comparing the above statement
m <KML = m <KJL
Hence proved.
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How to add 3.4 plus 40
The difference of the squares of twenty and thirteen
Jacob is training for a marathon. His plan is to run the same distance for 3 days a week, then increase that distance by the same amount each week of training. During week 6, Jacob runs 14 miles per day, which is 1.5 miles more per day than he ran during week 5. Which equation represents the daily running distance, in miles, as a function of time, t, in weeks?
f(t) = 0.5t + 7
f(t) = 0.5t + 11
f(t) = 1.5t + 5
f(t) = 1.5t + 12.5
it is C hope this helps
solve the system of equations {3x-y=6 { 6x+y=21 explain the steps on how to do this please
What is the degree of the polynomial c^4+7c^2
Use the LCD to rewrite 1/6 and 3/8 with the same denominator
The two fractions expressed using lowest common denominator (LCD) is written as [tex]\frac{4}{24} \ and \ \frac{9}{24}[/tex]
The given fractions;
1/6 and 3/8
LCD is the lowest common denominator. To express the given fraction using LCD, we will consider the common multiples of the denominators.
The common multiples of 8 and 6 include the following;
first multiple = 24second multiple = 48With the first common multiple, we will rewrite the two fractions to have the same denominator as shown below;
[tex]\frac{1}{6} = \frac{4}{6\times 4} = \frac{4}{24} \\\\\frac{3}{8} = \frac{3\times 3}{8\times 3} = \frac{9}{24}[/tex]
Thus, the two fractions with the same denominator is written as [tex]\frac{4}{24} \ and \ \frac{9}{24}[/tex]
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What is 19.2×108 minutes in hours? 1.152×1011 h 1.152×107 h 3.200×109 h 3.200×107 h
Answer:
3.200×107 h
Step-by-step explanation:
How do you solve the cubic square root of 80
to get to work truman waited 11 minutes for the bus, then travled 21.78 miles on the bus at a speed of 33 miles per hour how much time passed from the time Truman left for work to the time he arrived at work
Truman took approximately 51 minutes to get to work.
Explanation:To calculate the total time it took Truman to travel to work, we need to consider the time he waited for the bus and the time it took to travel the distance.
A _______ is a set of characters that uses the same typeface.
Final answer:
A font is a complete set of characters with the same typeface or design, crucial for typographic identity in various industries. Typefaces can be serif, conveying classical vibes, or sans serif, appearing modern. Digital advancements have made typefaces more accessible and diverse for designers.
Explanation:
Understanding Typeface in Typography
A font is a complete set of characters that uses the same typeface or design. This uniformity is a vital aspect of typographic identity and conveys different meanings and vibes, which can be crucial to a corporate image, for instance. The selection of an appropriate typeface is influenced by its use case; businesses might choose a typeface that reflects their industry and brand values. The character of a font can be greatly affected by factors such as whether it is serif or sans serif. A serif typeface, which includes small decorative lines at the end of the strokes that form the letters, like Times New Roman or Garamond, often conveys a classical or refined feeling. In contrast, sans serif typefaces, like Helvetica, lack these lines and therefore appear more modern.
The evolution from physical typesetting to digital design has vastly increased the availability and variety of typefaces, making them accessible and affordable, some even for free. In addition, digital typefaces can be created and distributed worldwide with minimal cost. This evolution has led to a proliferation of typefaces for designers to choose from in creating distinct and visually engaging texts.
Two angles form a linear pair. the measure of one angle is 26∘26∘ greater than the measure of the other angle. find the measure of each angle.
Final answer:
To find the measures of two angles forming a linear pair, where one angle is 26° greater than the other, set up an equation with the sum equal to 180°. Solving the equation reveals that the angles measure 77° and 103°.
Explanation:
When two angles form a linear pair, they are adjacent (share a common side) and supplementary, meaning their measures add up to 180°. If one angle is 26° greater than the other, we can set up the following equations to represent the relationship between the two angles:
Then x + 26° is the measure of the larger angle.
Since they form a linear pair, x + (x + 26°) = 180°.
Combining like terms gives us 2x + 26° = 180°. To find the value of x, subtract 26° from both sides, yielding 2x = 154°. Divide by 2 to get x = 77°. Therefore, the smaller angle measures 77°, and the larger angle measures 77° + 26° = 103°.
Summarily, the measures of the two angles forming a linear pair are 77° and 103° respectively.
What is the mode of this data set? {8, 11, 20, 10, 2, 17, 15, 5, 16, 15, 25, 6} 12.5 13 15 25 nextreset?
Four friends paid a total of 32 dollars for movie tickets. What is the ratio 32 dollars for4 people written as a unit rate
What is the value of x
24
9
21
14
we know that
[tex](5x+15)\°+(3x-3)\°=180\°[/tex] -----> by consecutive interior angles
so
Solve for x
[tex](5x+15)+(3x-3)=180\\ 8x+12=180\\8x=180-12 \\x=168/8 \\x=21\°[/tex]
therefore
the answer is
[tex]x=21\°[/tex]
On Monday, a local hamburger shop sold a combined total of 426 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Monday?
Explain how you would order from least to greatest three numbers that include a positive a negative number and zero
Which property is illustrated by the following equation?
- 8 ( - 5 + 3 ) = - 8 ( - 5 ) + ( - 8 )(3)
Which of the following is an advantage to using tables? A.Tables make the most difficult problems much easier. B.Tables can help to see patterns in data. C.All problems require tables to solve them.
The correct answer is that tables can help to identify patterns in complex data sets, particularly when multiple variables are involved. They provide a linear organization that simplifies finding specific data points and can facilitate the calculation of conditional probabilities in regard to dependent variables.
Explanation:Selecting the correct advantage of using tables among the given options, the correct response would be option B: Tables can help to see patterns in data. Tables are indeed important tools when dealing with data and statistical information. They organize data in a linear way, making it easier to locate specific points. They're capable of breaking down complex data points that might be hard to convey through written explanation or through other graphical data representation formats.
Furthermore, tables are particularly useful when displaying data associated with multiple variables - for example in Contingency Tables or Two-way tables. These tables simplify the process of calculating probabilities, especially when the variables involved are dependent on each other. These tables can facilitate calculating conditional probabilities easily by decisively organizing the data.
While tables are advantageous in their own right, it's not accurate to say, as in option A, that they automatically make the most difficult problems much easier, nor, as in option C, that all problems require tables to solve them. Instead, they represent a powerful, but specific tool among many others available for data analysis.
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The woods behind Adam’s house has a length of 15 m and is 4 m wide. What is the perimeter of the woods(in m)?
The perimeter of the woods behind Adam’s house, which is shaped as a rectangle, is calculated by the formula 2(length + width), substituting the given values we get 38 m.
Explanation:The subject of this question involves calculating the perimeter of a rectangle, in this case, the size of the woods. Perimeter is calculated by adding all the sides of a figure, and for a rectangle, you can calculate it using the formula: 2(length + width).
Given that the length of the woods is 15 m and the width is 4 m, we can substitute these values into the formula like this: 2(15m + 4m) = 2(19m) which gives us a total perimeter of 38 m.
To visualize this, if an average male is about two meters tall, around 19 men laid end to end would cover the total perimeter of the woods.
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