We are given the functions:
f(x) = 6x + 8
g(x) = x – 2
The first step in solving this problem is to find for the value of (f / g) (x) given the two functions above. Now finding for (f / g) (x), we can see that if we distribute x inside (f / g) we get f (x) / g(x)
therefore,
(f / g) (x) = f (x) / g (x)
= (6 x + 8) / (x – 2)
Substituting x = -3 will give us:
(f / g) (- 3) = [6 (- 3) + 8] / (- 3 -2)
(f / g) (- 3) = 2
Answer:
D: 2
how to find the midpoint using coordinates A(-1,5), B(2,-3)
One of the UK lottery systems consists of selecting six numbers from forty-nine for a one-pound stake. The winning numbers are drawn at random and the order is not important. Determine the probability that a randomly selected set of six numbers will win the lottery.
4.167 × 10-6
8.63 × 10-7
5.467 × 10-6
7.15 × 10-8
The answers is D.)7.15 × 10-8
Answer:
7.15 × 10-8 0 or 7.15 * 10^-8
Step-by-step explanation:
(6!(49 - 6)!)/49!
720/10068347520
= 7.15 * 10^-8
I hope this answer gives you an idea of the process used to find the answer.
A couple has 2 children. what is the probability that both are girls if the older of the two is a girl?
Find the measure of each interior angle
Decagon in which the measures of each interior angles are x + 5, x + 10, x + 20, x + 30, x + 35, x + 40, x + 60, x + 70, x + 80, and x + 90
To find each interior angle of a decagon given as expressions with x, we sum the expressions and set equal to 1440 degrees, the total sum of interior angles. Solving for x, we find x=100 and then substitute to find each angle.
To find the measure of each interior angle of a decagon where the angles are given as expressions involving x, we must use the fact that the sum of interior angles in a polygon is (n-2)180 degrees, where n is the number of sides in the polygon. For a decagon, which has 10 sides, the sum would be (10-2)180 = 1440 degrees.
x + 5 + x + 10 + x + 20 + x + 30 + x + 35 + x + 40 + x + 60 + x + 70 + x + 80 + x + 90 = 1440
Combining like terms, we find that:
10x + 5 + 10 + 20 + 30 + 35 + 40 + 60 + 70 + 80 + 90 = 1440
10x + 440 = 1440
10x = 1440 - 440
10x = 1000
x = 100
Once x is found, we substitute back into each angle expression to find the measure of each interior angle:
x + 5 = 105 degrees
x + 10 = 110 degrees
x + 20 = 120 degrees
x + 30 = 130 degrees
x + 35 = 135 degrees
x + 40 = 140 degrees
x + 60 = 160 degrees
x + 70 = 170 degrees
x + 80 = 180 degrees
x + 90 = 190 degrees
Simplify.
3 square root of -27n^27
A. 3n^3
B. -3n^3
C. -3n^9
The diameter of a circle is 8 centimeters. a central angle of the circle of the circle intercepts an arc of 12 centimeters. what is the radian measure of the angle?
The radian measure of the angle is 1.5 radians.
Explanation:To find the radian measure of the angle, we need to determine the length of the arc intercepted by the angle. We know that the diameter of the circle is 8 centimeters, so the radius is half of that, which is 4 centimeters. The circumference of the circle is given by the formula C = 2πr, where r is the radius.
In this case, the arc length intercepted by the angle is 12 centimeters. We can use the formula for the circumference to find the radian measure of the angle.
C = 2πr
12 = 2π(4)
12 = 8π
Dividing both sides of the equation by 8, we get:
π = 1.5 radians
David drives 210 miles a week for work. He fills his petrol tank twice a week. Each fill up is for 42 litres. Assuming he uses all of the petrol each week and only uses the car to travel to and from work, what is the mileage per litre of his car?
Point P has coordinates (1, –3). Point W is symmetric to point P with respect to the line y = –x. What are the coordinates of point W?
(3,0)
(3, –1)
(3, –3)
(–3, 1)
Sammy borrowed $10,000 to purchase a new car at an annual interest rate of 11%. She is to pay it back in equal monthly payments over a 5-year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar.
In your lab, a substance's temperature has been observed to follow the function T(x) = (x + 5)3 + 7. The turning point of the graph is where the substance changes from a liquid to a solid. Explain to your fellow scientists how to find the turning point of this function?
Mr. Brown owned a house, which he rented for $60 a month. The house was assessed at $9000. In 1975 the rate of taxation was increased from $25 to $28 per $1000 assessed valuation. By what amount should the monthly rent have been raised to absorb the increase in that year's taxes?
What is the slope of any parallel line to the line 8x + 9y = 3 in the standard (x,y) coordinate plane?
I REALLY NEED YOUR HELP!!! PLEASE!!!!!
A store is selling two mixtures of nuts in 20-ounce bags. The first mixture has 15 ounces of peanuts combined with five ounces of cashews, and costs $4.25. The second mixture has five ounces of peanuts and 15 ounces of cashews, and costs $6.75. How much does one ounce of peanuts and one ounce of cashews cost?
Select one:
a. $0.40 for peanuts and $0.15 for cashews
b. $0.15 for peanuts and $0.40 for cashews
c. $0.12 for peanuts and $0.49 for cashews
d. There is no solution.
The cost of one ounce of peanuts is $ 0.15 and the cost of one ounce of cashews is $ 0.40. Then the correct option is B.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
A store is selling two mixtures of nuts in 20-ounce bags.
The first mixture has 15 ounces of peanuts combined with five ounces of cashews and costs $4.25.
The second mixture has five ounces of peanuts and 15 ounces of cashews and costs $6.75.
Let the cost of one ounce of peanuts be x and one ounce of cashews cost be y. Then we have
15x + 5y = 4.25 ...1
5x + 15y = 6.75 ...2
By solving equations 1 and 2, Then we have
x = $ 0.15 and y = $ 0.40
Then the cost of one ounce of peanuts is $ 0.15 and the cost of one ounce of cashews is $ 0.40.
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What is the value stored at x, given the statements: int x; x = 3 / static_cast(4.5 + 6.4);?
The value stored at x will be 0.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ x = 3 / static_cast(4.5 + 6.4)
Now,
Since, The expression is,
⇒ x = 3 / static_cast(4.5 + 6.4)
Hence, The value of x is find as;
The operands 4.5 and 6.4 are added as;
⇒ 4.5 + 6.4 = 10.9
So, When this value is cast to int datatype, it becomes 10.
So, We get;
⇒ x = 3/10
= 0.3
Since, x in a variable of type int.
So, when a value of 0.3 is assigned to x, it is stored as 0.
Thus, The value stored at x = 0.
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Create a list of the odd numbers between 1 and n (include 1 as well as n -- if it's odd-- in the list). Associate the list with the variable odds.
If a triangle is equilateral then it has 3 congruent angles proof
Allow ABC to be an
equilateral triangle so AB = AC = BC. Let X be the midpoint of BC, AX is the
median of BC, and BX = CX. Look at triangles BAX and CAX. Obviously, AX = AX since
AB = AC and BX = CX, subsequently by SSS Congruence Test, we have that
triangles BAX and CAX are congruent. Therefore, corresponding angles are
congruent so <ABX = <ACX. Because <ABX and <ABC are the same angle,
they are obviously congruent, and then <ABX = <ABC. Likewise, <ACX and
<ACB are the same angles so <ACX = <ACB. Then, <ABC = <ACB. Please
note that <ABC = <B and <ACB = <C. Therefore, <B = <C.
At present, disregard AX and let Y be the midpoint of AC.
Then BY is the median of AC. Then AY = CY. Evidently, BY = BY. Because AB = BC, we see that triangles ABY
and CBY are congruent by SSS. Then corresponding sames are congruent so <BAY
= <BCY. Since <BAY and <BAC are the same angles then <BAY =
<BAC. Similarly, <BCY = <BCA since they are the same angles. Then
<BAC = <BCA. Note that <BAC = <A and <BCA = <C. Therefore,
<A = <C.
Thus, <A = <C = <B. So all the angles are congruent.
Write logbx + logby - logbz as a single logarithm.
If f(x) = 3x – 2 and g(x) = 6 – 4x, find f(x) + g(x). A. 7 + 4x B. 4 – x C. –x – 4 D. –4 – 7x
When you are doing an experiment that will have multiple trials, how do you handle averages?
whats the answer to this?
14/112 =0.125
2600*0.125 = 325
c) 325
what rotation will map the figure onto itself?
The correct answer is 180° about the center.
To map the given figure onto itself, we need to find the rotational symmetry. Let’s analyze the “X” shape:
A 90° rotation would not work because it would overlap the arms of the “X.”
Similarly, a 270° rotation would also result in overlapping arms.
A 45° rotation would not preserve the original shape due to the asymmetry of the “X.”
However, a 180° rotation about its center will bring each arm of the “X” back to a position occupied by another arm, effectively mapping it onto itself. An “X” has rotational symmetry at 180°; every half turn gives us an identical view.
The correct answer is 180° about the center. This specific degree of rotation is required due to the symmetrical nature of an “X” shape where each arm aligns with another after being rotated by this angle.
find the area of one segment formed by a square with sides of 6 inches inscribed in a circle (hint: use the ratio of 1:1:square root of 2 to find the radius of the circle)
To find the area of a segment formed by a square inscribed in a circle, calculate the circle's radius from the square's diagonal, then find the circle's area and divide by 4. The area of one segment is approximately 14.14 square inches.
Explanation:Finding the Area of a Segment in an Inscribed Circle
To find the area of one segment formed by a square with sides of 6 inches inscribed in a circle, we first need to determine the radius of the circle. The given ratio of 1:1:square root of 2 is key here. In a right-angled triangle with sides of equal length (1:1), the hypotenuse will be the square root of 2, according to the Pythagorean theorem. Since the diagonal of the square is the diameter of the circle, and the square has sides of 6 inches, we can calculate the diameter (d) of the circle as:
d = 6 inches × square root of 2
Therefore, the radius (r) is half of that:
r = (6 inches × square root of 2) / 2 = 4.24 inches (approximately)
With the radius, we can calculate the area (A) of the circle:
A = πr² = 3.1415927… × (4.24 inches)²
A ≈ 56.55 square inches (to two significant figures)
Now, the area of one segment is the area of the circle divided by the number of segments, with this particular scenario having 4 equal segments:
Area of one segment = Total area / 4
Area of one segment ≈ 56.55 square inches / 4 = 14.14 square inches (approximately)
The area of one segment formed by the inscribed square in the circle is approximately 14.14 square inches.
The area of one segment of a circle formed by an inscribed square with sides of 6 inches is approximately 14.14 square inches, calculated by first finding the radius of the circle using the 1:1:√2 ratio and then using the area formula A = πr².
Explanation:To find the area of one segment formed by a square with sides of 6 inches inscribed in a circle, we first need to calculate the radius of the circle using the given ratio of 1:1:√2. In an inscribed square, the diagonal is equal to the diameter of the circle. The diagonal of the square can be found using the Pythagorean theorem (a² + b² = c²) where a and b are the sides of the square and c is the diagonal. In this case, the diagonal is √(6² + 6²) = √(36 + 36) = √72 = 6√2 inches, which is also the diameter of the circle.
Thus, the radius (r) of the circle is half of the diameter, r = 6√2 / 2 = 3√2 inches. Now we can compute the area (A) of the circle using the formula A = πr². Plugging our radius into this formula gives us A = π(3√2)² = π(18) ≈ 56.55 square inches.
The circle is divided into four equal segments by the square, so the area of one segment is one-fourth of the total area of the circle. Therefore, the area of one segment is approximately 56.55 / 4 = 14.14 square inches.
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What is the slope of the line that contains the points (9, –4) and (1, –5)?
The slope of the line that contains the given point is the rise/run, which is: 1/8.
How to Find the Slope of a Line?The slope of a line = rise / run = change in y / change in x.
Given the points on a line as (9, –4) and (1, –5):
Change in y = (-4 -(-5) = 1
Change in x = (9 - 1) = 8
Slope of the line = change in y/change in x = 1/8.
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Evaluate the following expression.
153^0
0
1
153
Answer:
The answer is B = 1
Step-by-step explanation:
The exponent zero rule states that any number raised to the power of zero equals to 1 or mathematically:
x^0 = 1 for any real number x
So applying this rule
153^0 = 1 with x =153
Two horses are ready to return to their barn after a long workout session at the track. The horses are at coordinates H(1,10) and z(10, 1). Their barns are located in the same building, which is at coordinates B(-3,-9). Each unit/grid on the coordinate plane represents 100 meters. Which horse is closer to the barn? Justify your answer.
Angle 1 and angle 2 form a linear pair. if m angle 2 = 67. what is m angle 1
Final answer:
The measure of angle 1 can be found by using the fact that angle 1 and angle 2 form a linear pair. By setting up an equation and solving, we find that angle 1 measures 113 degrees.
Explanation:
To find the measure of angle 1, we need to understand that angle 1 and angle 2 form a linear pair. A linear pair of angles is formed when two adjacent angles are supplementary, meaning they add up to 180 degrees. So, angle 1 + angle 2 = 180 degrees. Given that angle 2 measures 67 degrees, we can substitute this value into the equation to find angle 1: angle 1 + 67 degrees = 180 degrees. Solving for angle 1, we get angle 1 = 180 degrees - 67 degrees = 113 degrees.
What is the area of the trapezoid?
Amy purchased 17 pencils and 18 pens for a fund-raiser at school and spent $61.50. Jocelyn purchased 10 pencils and 21 pens and spent $57. How much does each pencil cost?
How many microliters are in a two liter bottle of soda?