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.
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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Can someone answer questions 8-14 asap and show their work on a piece of paper thanks
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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write a two column proof
Answer:
Step-by-step explanation:
Explain how you would order from least to greatest three numbers that include a positive a negative number and zero
A 6ft tall person casts a shadow that is 10 ft long. A nearby statue casts a 16 ft shadow. How tall is the statue?
How do you solve the cubic square root of 80
Geometry proofs - paragraph proofs to formal proofs! Prove RS = TU
To prove RS = TU, we can use the congruence of corresponding parts of congruent triangles. By the side-angle-side (SAS) congruence postulate, if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Therefore, RS = TU.
Explanation:To prove that RS = TU, we need to show that the lengths of RS and TU are equal. In order to do this, we can use the congruence of corresponding parts of congruent triangles. Let's assume that triangles RST and TUV are congruent.
By the side-angle-side (SAS) congruence postulate, if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Since RST and TUV are congruent, we can conclude that RS and TU are congruent as well. Therefore, RS = TU.
what is 3.69 divided by 0.3 step by step please
What is the degree of the polynomial c^4+7c^2
Solve x = log9(4)
**Round your answer to the nearest hundredth.
solve the system of equations {3x-y=6 { 6x+y=21 explain the steps on how to do this please
Evaluate 4m+23+np−3, when m=7, n=2, and p=8. enter your answer in the box.
The value of expression 4m + 23 + np - 3 for m = 7, n = 2, and p = 8 is 64.
To solve the given expression, we substitute the given values of m, n, and p into the expression:
4m + 23 + np - 3
Given m = 7, n = 2, and p = 8, we substitute these values into the expression:
4(7) + 23 + (2)(8) - 3
28 + 23 + 16 - 3
28 + 23 = 51
51 + 16 = 67
67 - 3 = 64
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?
The stage manager of a school play creates a rectangular acting area of 42 square yards. String lights will outline the acting area. To the nearest whole number, how many yards of string lights does the manager need to enclose this area?
transform y=k(x) by translating it down 3 units. label the new function p. what happens to the y-coordinate in each new ordered pair? ( ignore the pen and pencil )
Find the length of a rectangular lot with a perimeter of 120 meters if the length is 6 meters more than the width
Answer:
The length is 33 and the Width is 27.
Step-by-step explanation:
So I made it easier by only looking at half of the rectangle. 120 divided by 2 is 60. So out of the length and width, it had to add to equal 60. I plugged in a few numbers and determined 27 and 33. SO, if you add those together it equals 60 while 33 is 6 more meters than 27 and two 27 and two 33 equals 120 for the whole rectangle
Shiloh has to earn at least $200 to meet her fundraising goal. She has only 100 cakes that she plans to sell at $5 each. Which inequality shows the number of cakes, x, Shiloh can sell to meet her goal?
20 ≤ x ≤ 200
40 ≤ x ≤ 100
100 ≤ x ≤ 200
20 ≤ x ≤ 100
Answer:
b
Step-by-step explanation:
40*5 is 200 which would meet her goals
and 100 is the maximum number of cakes she has, she would make $500 dollars and it's the maximum since she can't sell cakes she doesn't have.
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]
Look at the table showing different prices for cans of soup. Prices for Soup Price A Price B Price C $3.87 for 3 $2.38 for 2 $8.75 for 7 Which gives the prices in order, from greatest to least unit rate?
Answer with Step-by-step explanation:
Prices for Soup
Price A Price B Price C
$3.87 for 3 $2.38 for 2 $8.75 for 7
Price A=$3.87/3 for 1
=$ 1.29 for 1
Price B=$2.38/2 for 1
=$ 1.19 for 1
Price C=$8.75/7 for 1
=$ 1.25 for 1
Prices in order, from greatest to least unit rate is:
Price A=$ 1.29
Price C=$ 1.25
Price B=$ 1.19
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?
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
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.
ABCD is a parallelogram. A is the point (2,5), B is the point (8,8) and the diagonals intersect at (3.5, 2.5). What are the coordinates of C and D? How do I work this out?
Midpoint of diagonals: [tex]\( (3.5, 2.5) \)[/tex]. Using midpoint formula, [tex]\( C(5, 0) \) and \( D(-1, -3) \)[/tex].
Since [tex]\(ABCD\)[/tex] is a parallelogram, its diagonals bisect each other. So, the midpoint of the diagonals gives the center of the parallelogram, which is the midpoint of [tex]\(AC\) and \(BD\)[/tex].
Given that the midpoint of the diagonals is [tex]\((3.5, 2.5)\)[/tex], we can find the midpoint of [tex]\(AC\) and \(BD\)[/tex].
The midpoint formula is given by [tex]\(\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\).[/tex]
For the midpoint of [tex]\(AC\)[/tex]:
[tex]\[\left(\frac{2+x_C}{2}, \frac{5+y_C}{2}\right) = (3.5, 2.5)\][/tex]
From this, we get:
[tex]\[2+x_C = 7 \quad \text{and} \quad 5+y_C = 5\][/tex]
which gives [tex]\(x_C = 5\) and \(y_C = 0\)[/tex].
For the midpoint of \(BD\):
[tex]\[\left(\frac{8+x_D}{2}, \frac{8+y_D}{2}\right) = (3.5, 2.5)\][/tex]
This yields:
[tex]\[8+x_D = 7 \quad \text{and} \quad 8+y_D = 5\][/tex]
which results in [tex]\(x_D = -1\) and \(y_D = -3\)[/tex].
So, the coordinates of [tex]\(C\) are \((5, 0)\)[/tex] and the coordinates of [tex]\(D\) are \((-1, -3)\)[/tex].
If m <5=42 what is m <4
42
48
128
138
Answer:
48° or 138°
Step-by-step explanation:
[tex]\displaystyle Complementary\:Anlges\:[Sum\:up\:to\:90°] \\ Supplementary\:Angles\:[Sum\:up\:to\:180°][/tex]
[tex]\displaystyle 90° = 42° + m∠4 \: \: \: \: \: 180°= 42° + m∠4[/tex]
[tex]\displaystyle 48° = m∠4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 138° = m∠4[/tex]
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Which of the following is a step in constructing a circle circumscribed about a triangle? (6 points)
Select one:
a. Use a compass to locate the intersection of the midpoint of each side.
b. Use the perpendicular bisectors to find the center of the circle.
c. Use a compass to locate the intersection of the altitude of each side.
d. Use the angle bisectors to find the center of the circle.
The correct step in constructing a circle circumscribed about a triangle is: Use the perpendicular bisectors to find the center of the circle.
The correct answer is an option (c)
What is a circumscribed triangle?"A triangle is a circumscribed triangle when a circle passes through all three vertices of the triangle."
What is perpendicular bisector?"A line that intersects another line segment perpendicularly and divides it into two parts of equal measurement."
For given question,
Steps to construct a circle circumscribed about a triangle:
- Construct the perpendicular bisector of one side of triangle.
- Construct the perpendicular bisector of another side of the triangle.
- The point at which they intersect inside the triangle would be the center of the circumscribed circle
- Place compass on the center point, adjust its length to reach any corner of the triangle, and draw the circle.
Therefore, the correct step in constructing a circle circumscribed about a triangle is: Use the perpendicular bisectors to find the center of the circle.
The correct answer is an option (c)
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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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$48 decreased by 25%
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: