help pls with explanation maybe?
The domain of this function can be expressed as (-∞,0) U (0,∞).
The interval on which the function is decreasing is
(-∞,0) U (0,∞).
The interval on which the function is increasing is none.
The interval on which the function is constant is (0,0).
What is domain?The domain of a function is the set of all acceptable inputs for the function. In other words, it is the set of all values for which the function is defined.
The domain of the given function is all real numbers, excluding 0.
This can be seen by observing that the denominator in the fraction is the absolute value of t, which is always positive.
Therefore, the domain of the function is all real numbers except 0, which can be expressed as (-∞,0) U (0,∞).
The function is decreasing over all intervals in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.
Therefore, the interval on which the function is decreasing is
(-∞,0) U (0,∞).
The function is constant over the interval (0,0) since the absolute value of 0 is 0 and thus, the denominator in the fraction is equal to 0.
Therefore, the interval on which the function is constant is (0,0).
Finally, the function is not increasing over any interval in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.
Therefore, the interval on which the function is increasing is none.
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The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted. The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules.
Answer:
The constant of variation in the given problem is 9.8
GIVEN
w = 2,116.8
m = 120
h = 1.8
SOLUTION
w=kmh
2116.8 = k(120)(1.8)
2116.8=216k
9.8=k
I need help plsssssssssssssss
Answer:3.14sq^2
Step-by-step explanation:b x c x a = 3.14
Eric rents a bounce house for his son's birthday. There is a rental fee of $85 and a fee of $8 per hour. Eric only has $125 to spend on the bounce house. Write an equation to find the number of h, hours, that Eric can rent the bounce house.
please help, I need an answer and fast!
Answer:
[tex]85 + 8h = 125[/tex]
20 points!!! Pleaseee help
T3=R1
T4=R2}==>TUR=TSR
RT=RT
so: S=U
Write the equation in standard form for the circle with center (3,0) and radius 5.
The equatiοn οf the circle will be [tex]x^{2}+y^{2} -6x-16=0[/tex]
What is circle?A clοsed rοund shaped figure which cοntains nο cοrners is called circle. It has center called (h, k) and radius r. Rοund clοck, car tire, wheels are the examples οf circle.
If the center and radius is given then the equatiοn οf circle is:
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex] ------------- (1) where (h, k) centre and r radius.
Here center οf the circle is (3,0) and radius οf the circle is 5
putting h= 3 , y=0 and r=5 in equatiοn (1) we get
[tex](x-3)^{2} + (y-0)^{2} =5^{2}[/tex]
⇒ (x²- 6x+9) +y²=25
⇒ x²+y²-6x+9-25=0
⇒x²+y²-6x-16=0
Hence the equatiοn οf circle is x²+y²-6x-16=0.
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What's the area of a regular triangle with a side length of 15? (Explanations step-by-step are appreciated!)
the area of the equilateral triangle with a side length of 15 is approximately 97.4279 square units.
A regular triangle is also known as an equilateral triangle, which means all of its sides are equal in length. To find the area of an equilateral triangle with a side length of 15, we can use the following formula:
Area = (√(3) / 4) × side²
where "side" is the length of one side of the triangle.
Let's plug in the given value of side length, which is 15, into the formula:
Area = (√(3) / 4) × 15²
Area = (√(3) / 4) × 225
Area = 97.4279 (rounded to 4 decimal places)
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tell whether the ratios form a proportion 4:14 and 12:40
Answer:
NO
Step-by-step explanation:
First, we should simplify both fractions to the most simple form.
4/14=2/7
12/40=6/20=3/10
A proportion means that it is equal. 2/7 does not equal 3/10, so the answer is no.
A big box store decreased the price of a computer from $399 to $349. What is the approximate percentage that the price of the computer was reduced?
Responses
12.5%
14.3%
25%
35%
The approximate percentage that the price of the computer was reduced is 12.5%.
what is a percentage?A number can be expressed as a fraction of 100 using a percentage. The letter "%" stands for it. We may compare numbers of various sizes quickly and efficiently using percentages to compare a quantity to its entire or total.
To find the approximate percentage that the price of the computer was reduced, we can use the following formula:
percentage decrease = (original price - new price) / original price x 100%
Substituting the given values, we get:
percentage decrease = (399 - 349) / 399 x 100%
percentage decrease = 50 / 399 x 100%
percentage decrease ≈ 12.5%
Therefore, the approximate percentage that the price of the computer was reduced is 12.5%.
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A town with a population of 80,250 people has 500 city blocks. Each block is one-tenth mile long by one-tenth mile wide. Find the population density of the town in the people per square mile.
Answer:
First, we need to find the area of one block:
Area of one block = length x width = (1/10) mile x (1/10) mile = 1/100 square mile
Since there are 500 blocks in the town, the total area of the town is:
Total area of town = 500 blocks x (1/100) square mile/block = 5 square miles
To find the population density, we divide the population by the total area:
Population density = population / total area
Population density = 80,250 / 5 = 16,050 people per square mile
Therefore, the population density of the town is 16,050 people per square mile.
Please help with graph problem. Thank you loads!!!
Answer:
a. 250,000
b. 450,000
Step-by-step explanation:
Construct a polynomial function of least degree possible using the given information.
Real roots: −1, 1, 3 and (2,
f(2)) = (2, 7)
The polynomial function of least degree possible using the given information is: f(x) = -7/3 (x+1)(x-1)(x-3)
What is polynomial function?
A polynomial function is a type of mathematical function that consists of one or more terms, each of which is a constant multiplied by a variable raised to a non-negative integer power.
To construct a polynomial function of least degree possible using the given information, we need to use the fact that the function has real roots at -1, 1, and 3. This means that the function can be factored as follows:
f(x) = a(x+1)(x-1)(x-3)
where a is a constant coefficient that we need to determine.
Next, we need to use the fact that the function passes through the point (2, 7) to determine the value of a. We substitute x=2 and f(x)=7 into the above equation and solve for a:
7 = a(2+1)(2-1)(2-3)
7 = -3a
a = -7/3
Therefore, the polynomial function of least degree possible using the given information is:
f(x) = -7/3 (x+1)(x-1)(x-3)
Note that this function has real roots at -1, 1, and 3, and passes through the point (2, 7).
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I got through with part A but not part B, it's really confusing.
Therefore, the coordinates of A are (1, 3) and (2, 4). Therefore, the area of the shaded region is (1/2) square units.
What is area?In mathematics, area is the measure of the amount of surface enclosed by a two-dimensional shape or object. It is the size of a surface, and is typically measured in square units such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²).
Here,
First, we need to find the coordinates of the point where the line and the curve meet (point A).
Substituting y = x(4 – x) into y + 2x = 5, we get:
x(4 – x) + 2x = 5
Simplifying and rearranging, we get:
x² – 3x + 2 = 0
Factoring, we get:
(x – 1)(x – 2) = 0
Therefore, x = 1 or x = 2.
When x = 1, y = 3, and when x = 2, y = 4. Therefore, the coordinates of A are (1, 3) and (2, 4).
To find the area of the shaded region, we need to find the integral of the curve y = x(4 – x) between x = 1 and x = 2, and subtract the area under the line y + 2x = 5 between the same limits.
The equation y + 2x = 5 can be rewritten as y = -2x + 5.
Integrating y = x(4 – x) between x = 1 and x = 2, we get:
∫(1 to 2) x(4 – x) dx = (8/3) – (2/3)
= 2
Integrating y = -2x + 5 between x = 1 and x = 2, we get:
∫(1 to 2) (-2x + 5) dx = (3/2)
Therefore, the area of the shaded region is:
=2 - (3/2)
= (1/2) square units
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Hi I don’t understand help
The exact value of x is 12.97.
Describe Bisector?In geometry, a bisector refers to a line or plane that divides a geometric figure into two equal parts. Specifically, a bisector divides an angle into two equal angles, a line segment into two equal parts, or a plane figure into two equal areas.
There are two types of bisectors:
Angle bisector: A line or ray that divides an angle into two equal angles is called an angle bisector. The point where the bisector intersects the angle is known as the vertex of the angle.
Segment bisector: A line, ray, or line segment that divides a line segment into two equal parts is called a segment bisector. The point where the bisector intersects the line segment is known as the midpoint of the line segment.
We can use the angle bisector theorem to find the value of x. According to the angle bisector theorem, the length of the segment bisecting an angle in a triangle is proportional to the lengths of the two sides adjacent to that angle.
Let's call the point where ST intersects QS point U. Then, by the angle bisector theorem, we have:
QU / QR = SU / SR
Substituting the given values, we get:
QU / 20 = x / 16
Multiplying both sides by 20, we get:
QU = (20x) / 16 = (5x) / 4
Similarly, we have:
SU / QS = TU / TR
Substituting the given values and simplifying, we get:
SU / 12 = x / 20
Multiplying both sides by 12, we get:
SU = (12x) / 20 = (3x) / 5
Now, we can use the fact that QRS is a triangle to find the remaining side length:
QR + RS = QS
20 + 16 = 12 + SU + QU
36 = 12 + (3x/5) + (5x/4)
Multiplying both sides by 20, we get:
720 = 240 + 12x + 25x
720 = 37x + 240
37x = 480
x = 480/37
So the value of x is approximately 12.97 (rounded to the nearest hundredth).
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the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 22 minutes and a standard deviation of 6 minutes. find the probability that a randomly selected athlete uses a stairclimber for (a) less than 18 minutes, (b) between 22 and 31 minutes, and (c) more than 30 minutes.
The probability that a randomly selected athlete uses a stair climber for,
(a) P(X < 18) = 0.2514
(b) P(22 < X < 31) = 0.4332
(c) P(X > 30) = 0.0918
Let X be the amount of time an athlete uses a stair climber. Then, X ~ N(22, 6^2) represents a normal distribution with mean 22 and standard deviation 6.
(a) To find the probability that a randomly selected athlete uses a stair climber for less than 18 minutes, we need to calculate P(X < 18).
Z-score for 18 minutes = (18 - 22) / 6 = -0.67
Using a standard normal table or calculator, we find that P(Z < -0.67) = 0.2514.
Therefore, P(X < 18) = P(Z < -0.67) = 0.2514.
(b) To find the probability that a randomly selected athlete uses a stair climber for between 22 and 31 minutes, we need to calculate P(22 < X < 31).
Z-score for 22 minutes = (22 - 22) / 6 = 0
Z-score for 31 minutes = (31 - 22) / 6 = 1.5
Using a standard normal table or calculator, we find that P(0 < Z < 1.5) = 0.4332.
Therefore, P(22 < X < 31) = P(0 < Z < 1.5) = 0.4332.
(c) To find the probability that a randomly selected athlete uses a stair climber for more than 30 minutes, we need to calculate P(X > 30).
Z-score for 30 minutes = (30 - 22) / 6 = 1.33
Using a standard normal table or calculator, we find that P(Z > 1.33) = 0.0918.
Therefore, P(X > 30) = P(Z > 1.33) = 0.0918.
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to bake a cake , raffy needs 3 cups of sugar for 5 cups of flour. if he uses 35 cups of flour, how much sugar doe he need and how many cakes will he bake
Answer: 21 cups of sugar, 7 cakes
Solve the following proportion:
3/5=x/35
Cross multiply:
5x=35(3)
5x=105
x=21 cups of sugar
3 cups of sugar= 1 cake
21 cups of sugar= x cakes
Cross multiply:
3x=21
21/3
7 cakes
Use a trigonometric ratio to solve for y. Round to two decimals places as necessary giving brainliest to whoever gets the correct answer. Image is below
Check the picture below.
[tex]\sin(43^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{18}}\implies 18\sin(43^o )=y\implies 12.28\approx y[/tex]
Make sure your calculator is in Degree mode.
In 2002 a company's sales revenue was $540,000 and its marketing expenses were $97,200. Marketing expenses are what percentage of total sales?
Answer:
18%
Step-by-step explanation:
first you divide 97,200 from 540,000= 0.18 x 100=18%
Ms. Maynard grates 23/30 of a block of cheese. Mr. Connor then eats another 3/30 of the cheese. What fraction of the cheese is left over?
Ms. Maynard grates 23/30 of a block of cheese, leaving the fraction of 7/30 of the cheese. Mr. Connor then eats 3/30 of the cheese, leaving the fraction of 4/30 of the cheese remaining.
Let us suppose the total block of cheese as 1.
If Ms. Maynard grates 23/30 of a block of cheese, then the fraction of cheese left is:
Remaining cheese = 1 - 23/30 = 7/30
After Mr. Connor eats 3/30 of the cheese, the fraction of cheese left is:
Remaining cheese = 7/30 - 3/30 = 4/30
Therefore, 4/30 of the cheese is left over after grating by Ms. Maynard and Mr. Connor respectively.
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Help don’t understand
Thank you geometry 10tg grade
The surface area of a cylinder is given by the formula:
A = 2πrh + 2π[tex]r^{2}[/tex]= 2*3.14*4.8*19.1= 575.504 square ft.
What is surface area?Surface area is the measure of the total area that the surface of an object occupies. It is the sum of all the areas of the individual faces or surfaces of the object. For example, if you have a cube, the surface area would be the sum of the areas of all six faces of the cube. The surface area is usually measured in square units, such as square meters, square centimeters, or square feet, depending on the system of measurement used. Surface area is an important concept in many fields of study, including mathematics, physics, chemistry, and engineering.
by the question.
The surfaces area of a cylinder is given by the formula:
[tex]A = 2πrh + 2πr^2[/tex]
where r is the radius of the circular base of the cylinder, and h is the height of the cylinder.
If a=9.6ft and b=19.1ft, we need to determine the values of r and h before we can calculate the surface area.
Since the cylinder has a circular base, we know that the diameter of the base is equal to b, or 19.1ft. Therefore, the radius of the base is half the diameter, or:
r = b/2 = 19.1/2 = 9.55ft
we know that the radius of the cylinder is = diameter/2
= 9.6/2
= 4.8
The surfaces area of a cylinder= [tex]A = 2πrh + 2πr^2[/tex]
A = 2πrh + 2π[tex]r^{2}[/tex]= 2*3.14*4.8*19.1= 575.504 square ft.
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Jim has only 5p coins and 10p coins.The ratio of the number of 5p coins to the number of 10p coins 2:3 work out the ratio of total value of the 5p coin : the total value of the 10p coin give your answer in its simplest form
Answer: required ratio is 1;3
Step-by-step explanation:
Since we have given that
Ratio of the number of 5 p coins to the number of 10 p coins = 2:3
So, the number of 5p coins be '2x'
Let the number of 10p coins be '3x'.
Value of 5p coins = 5p x 2x =10px
Value of 10p coins = = 10p x 3px=30px
So, the ratio of value of 5p coins to the value of 10p coins is given by
10px:30px
1:3
can someone please help me:(
The equation, (x - 10)² + (y - 5)² = 144, represents a circle with center (10, 5) and radius 12.
Determining the center and radius of a circleFrom the question, we are to determine the center and radius of the circle represented by the given equation
From the given information, the given equation is
(x - 10)² + (y - 5)²= 144
To determine the center and the radius of the circle we will compare the given equation to the standard form of the equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
The equation
(x - 10)² + (y - 5)²= 144
can be written as
(x - 10)² + (y - 5)²= 12²
By comparison,
h = 10, k = 5 and r = 12
Hence, the center of the circle is (10, 5) and the radius is 12
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fizzfizz soda comes in two flavors, regular and diet. if a researcher has 7 boxes of each, how many ways can he select 4 boxes, consisting of 2 boxes of regular and 2 boxes of diet, for a quality control test?
Number of ways that the researcher can select 4 boxes, consisting of 2 boxes of regular and 2 boxes of diet, for a quality control test is 441
To select 4 boxes consisting of 2 regular and 2 diet from 7 boxes of each, we need to use combinations.
The number of ways to select 2 regular boxes out of 7 is
C(7,2) = 21
Similarly, the number of ways to select 2 diet boxes out of 7 is also 21.
Now we need to choose 2 regular boxes out of 2 and 2 diet boxes out of 2, which can only be done in one way.
So the total number of ways to select 4 boxes consisting of 2 regular and 2 diet is
21 x 21 x 1 x 1 = 441
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A new player joins the team and raises the mean to 22
A. The mean age of the team rounded to 1 decimal place is 20.9 years
B. The age of the new player is 23.1 years
A. How do i determine the mean age of the team?The mean age of the team can be obtained as illustrated below:
Age (x) = 19, 20, 21, 22, 23, Frequency (f) = 2, 3, 1, 4, 1Mean age =?Mean age = ∑fx / ∑f
Mean age = [(19 × 2) + (20 × 3) + (21 × 1) + (22 × 4) + (23 × 1)] / (2 + 3 + 1 + 4 + 1)
Mean age = 230 / 11
Mean age = 20.9 years
Thus, the mean age of the team is 20.9 years
B. How do i determine the age of the new player?The age of the new player can be obtained as follow:
Mean of previous player = 20.9 yearsNew mean = 22Age of new player =?New mean = (mean of previous + age of new player) / 2
22 = (20.9 + age of new player) / 2
Cross multiply
22 × 2 = 20.9 + age of new player
44 = 20.9 + age of new player
Collect like terms
44 - 20.9 = Age of new player
Age of new player = 23.1 years
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Complete question:
Pleas attached photo
A study found that 4 out of every 5 driver use seatbelts two cars are randomly stopped at a seat belt check what is the probability both drivers are wearing their seatbelt
I think we need to (4 divided by 5)+2
4 divided by 5= 0.8
0.8+2
=2.8
answer: 2.8
the probability that both drivers are wearing their seatbelts is 0.64, or 64%.
what is multiplication rule for independent events?P(A and B) = P(A) x P(B|A)
The probability of both drivers wearing seatbelts can be calculated as follows, assuming that one driver's use of a seatbelt has no effect on the other driver's use of a seatbelt and that the probability of a driver wearing a seatbelt is independent of the other driver:
Let P(S) be the probability that a driver wears a seatbelt, then P(not S) is the probability that a driver does not wear a seatbelt.
Given that 4 out of every 5 drivers wear seatbelts, we have P(S) = 4/5 = 0.8 and P(not S) = 1 - P(S) = 1 - 0.8 = 0.2.
Let A be the event that the first driver wears a seatbelt, and B be the event that the second driver wears a seatbelt. We need to find the probability of both A and B occurring, which is denoted as P(A and B).
he probability of the first driver wearing a seatbelt is P(A) = P(S) = 0.8,
and the probability of the second driver wearing a seatbelt given that the first driver is wearing a seatbelt is P(B|A) = P(S) = 0.8 because the two drivers are stopped at random.
Using the multiplication rule for independent events, we have:
P(A and B) = P(A) x P(B|A)
= 0.8 x 0.8
= 0.64
Therefore, the probability that both drivers are wearing their seatbelts is 0.64, or 64%.
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8 and 1/32 are powers of what number
Answer:
2
Step-by-step explanation:
Both 8 and 1/32 are powers of 2.
2³ is 8, since 2*2*2=8.
2^-5 is 1/32.
2^5 is 2*2*2*2*2, and the negative sign in front of the 5 flips the answer to be 1/32
What is the axis of symmetry of h(x) = 6x2 − 60x + 147?a. x=−5b. x=−3c. x=3d. x=5
The axis of symmetry of the function h(x) is x = 5. So, option D is correct.
The axis of symmetry of a quadratic function is a vertical line that divides the parabola into two symmetric parts. The axis of symmetry is always a vertical line passing through the vertex of the parabola.
In algebraic terms, the axis of symmetry of a quadratic function of the form [tex]f(x) = ax^2 + bx + c[/tex] is given by the equation:
[tex]x = -\frac{b}{2a}[/tex]
Where a and b are the coefficients of the quadratic expression.
Let's consider the given question:
To find the axis of symmetry of the quadratic function [tex]h(x) = 6x^2 - 60x + 147[/tex], we can use the formula [tex]x = -\frac{b}{2a}[/tex], where a and b are the coefficients of the quadratic expression.
In this case, a = 6 and b = -60, so the axis of symmetry is:
[tex]x = -\frac{(-60)}{2*(6)}[/tex]
[tex]x = 5[/tex].
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John borrows R3000 from the bank .he must repay the loan after 3 years . the bank changes compound interest at 10% per annum .how much interest will John pay over the three years
Answer:
Step-by-step explanation:
10 percent of 3000 = 300
3000+300=3300
3300+300=3600
3600+300=3900
interest = 3900-3000
= R900
he will pay R900 interest over 3 years.
i think this is the answer.
Numbers that are greater than 11 over 16 and less than 15 over 16
Any number that is strictly greater than 11/16 and strictly less than 15/16 belongs to this interval.
What is the inequalities?In mathematics, inequalities are statements that cοmpare twο values and indicate whether οne value is greater than, less than, οr equal tο the οther value.
Tο find the numbers that are greater than 11/16 and less than 15/16, we need tο cοnsider all numbers between these twο values, excluding the endpοints. That is,
11/16 < x < 15/16
where x represents the number we are looking for. We can also write this using interval notation as:
(11/16, 15/16)
Hence, any number that is strictly greater than 11/16 and strictly less than 15/16 belongs to this interval.
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which congruency theorem can be used to prove that △abd ≅ △dca?
a. SAS
b. Not enough information
c. SSS
d. AAS
the correct answer is a. SAS congruency theorem can be used to prove that ABD =DCA.
In this question we accept two angles is given that is:
two triangles ∠ABD and
In this, an angle is common that is,
AD = AD
AB = CD
∠A is equal = ∠A (which is given)
That is the reason the SAS rule is right.
SSS is a geometric term that stands for "side-side-side." It refers to a congruence condition in which three sides of one triangle are equal to three corresponding sides of another triangle, making the two triangles congruent. Congruent triangles have the same size and shape, so if two triangles are congruent, all corresponding angles and sides are equal.
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the complete question is:
Which congruency theorem can be used to prove
that ABD =DCA?
a. SAS
b. Not enough information
c. SSS
d. AAS