Given:
\(\begin{gathered} f(x)=x \\ and \\ g(x)=\frac{2}{9}x-2 \end{gathered}\)Graphing:
Where:
blue line = g(x)
green line = f(x)
So, this transformation is a translation and a rotation
Answer: the third one
The vertices of triangle ABC are given: A (0;-1) B(12; -10) C(10;4)
Find:
a) the equation of the median and bisector drawn from vertex A;
b) the equation of the altitude from vertex B;
c) the point of intersection of the median and height;
d) the coordinates of the center of mass (the point of intersection of the medians).
Elliot bought a bicycle which cost $600. In addition, he had to pay 3% sales tax. How much did he pay for the bicycle?
Answer:
$618
Step-by-step explanation:
$600 is the base sale cost
Another 3% is required on top of the sale price:
$600 x 3/100 of $600 = $18.00 (or 3%)
$600 + $18 = $618
Hope that helps
functions that aren't invertible can be made invertible by restricting their domains. for example, the function $x^2$ is invertible if we restrict $x$ to the interval $[0,\infty)$, or to any subset of that interval. in that case, the inverse function is $\sqrt x$. (we could also restrict $x^2$ to the domain $(-\infty,0]$, in which case the inverse function would be $-\sqrt{x}$.) similarly, by restricting the domain of the function $f(x).
When the domain of x is restricted, the function x2 becomes one-to-one, and the inverse function is x.
It is true that limiting a function's domain might cause it to become invertible. Because it is not one-to-one in the example, the function x2 is not invertible across its complete domain of real numbers (i.e., it assigns multiple outputs to some inputs). However, x2 becomes one-to-one and invertible when the domain of x is constrained to or any subset of that interval. The range of x2, which is, is used to define the inverse function in this situation, which is
The function x2 becomes one-to-one when the domain of x is constrained, and the inverse function is
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If your heart rate is 155 beats per minute during strenuous exercise, what is the time per beat in units of seconds
Answer:
5 beats per second
Step-by-step explanation:
statistic operation depends
In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
25% percent of the females in Math town have brown eyes. To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes
what is percent ?
A percent is a way of expressing a number as a fraction of 100. The symbol for percent is %, which means "per hundred".
In the given question,
Let's assume that there are 100 people in Math town.
60% of them are males, so there are 60 males and 40 females.
Out of the 60 males, 30% have brown eyes, so there are 18 males with brown eyes.
28% of the entire population have brown eyes, so there are 28 people with brown eyes.
To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes:
28 - 18 = 10
So, there are 10 females with brown eyes.
Out of the 40 females in Math town, what percentage have brown eyes?
10 brown-eyed females out of 40 females is:
10/40 = 0.25 or 25%
Therefore, 25% of the females in Math town have brown eyes.
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Playing Dirty
Data is often kept about rules violations in sports games such as fouls in basketball, flags in football or penalty box minutes in hockey. Examining this data can provide insight into each sport. In this problem, you will examine some aspect of sporting rules violations using scatter plots, best fit lines, residuals and/or correlation coefficients to answer questions. You may choose to examine number of penalties (like number of flags thrown against a football team), severity of penalties (like penalty yards assessed against a football team), or another rules violation of your choice.
Before researching data, do you think the number of penalties a team gets in a season is correlated to the number of wins the team gets in that season? Do you think it is a positive or negative relationship? Do you think the relationship is weak or strong? Explain your reasoning.
I believe that the number of penalties a team gets in a season affects the number of wins due to if they get so many penalties that can get disqualified which can cause them to lose. I think its a positive relationship and a weak relationship because its different everytime.
Is there a relationship between the number of penalties a team gets in a season and the number of wins in that season? Show any mathematical work that leads to your answer.
Do penalties cause a change in wins or wins cause a change in penalties or neither? Explain your reasoning.
Record two new questions for the data that you research that are similar to questions (2) and (3), then answer these questions using mathematics.
To test penalties' effect on a team's wins, analyze the data and calculate the correlation coefficient. Penalties and wins may be correlated, but one does not necessarily cause the other.
Other factors like team skill and strategy may influence penalties and wins.
The new questions using mathematics are
Is there a relationship between the gravity of penalties assessed against a football team (penalty yards) and their total points scored in a season?
Analyzing the correlation coefficient of penalty yards and points scored can help establish a possible connection between these two variables.Does the number of fouls committed by a basketball team in a season influence their shooting percentage?
You can investigate the possible connection between the number of fouls committed and the shooting accuracy by examining their correlation.What is the rules violations?By using the available data, one can conduct a statistical analysis to establish a potential correlation between the total number of penalties a team has accumulated throughout a season and their overall number of wins.
Although there is a correlation between fines and victories, it does not imply that one is the direct cause of the other. It is possible that there are other contributing elements, such as team abilities, tactics, etc.
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tanx(1+cos2x)=sin2x prove the identity
Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).
What is the prove of the given identity?To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.
Starting with the left-hand side (LHS):
tan(x)(1 + cos(2x))
We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:
LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))
Next, we can simplify the expression by expanding and combining like terms:
LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)
Simplifying further:
LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)
Now, let's work on the right-hand side (RHS):
sin(2x)
Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).
Now, let's compare the LHS and RHS expressions:
LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)
RHS = 2sin(x)cos(x)
To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:
LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)
Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:
LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)
= [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)
= 2sin(x) - 2sin³(x) / cos(x)
Now, using the identity 2sin(x) = sin(2x), we can simplify further:
LHS = sin(2x) - 2sin³(x) / cos(x)
Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.
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Select the correct answer.
If no denominator equals zero, which expression is equivalent to 15/x-6 + 7/x+6?
A.
OB.
OC.
OD.
22 +132
²36
22-48
236
22
C.36
22 +48
²36
The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).
Given expression is,
[15 / (x - 6)] + [7 / (x + 6)]
Cross multiplying the two fractional expressions,
= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]
= [15x + 90 + 7x - 42] / [x² - 6²]
= (22x + 48) / (x² - 36)
Hence the equivalent expression is D.
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-20 greater than or equal to 5w
Answer:
It depends is w is a negative or positive number
Step-by-step explanation:
5w could = 5 x 4 = 20 this is greater than -20
5w could = 5 x -4 = -20 this is equal to -20
hope this helps...
please help, it’s due today.
Use the quadratic formula to solve 2x^2-5x-5=0
Show all your work
Answer:
https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php try this website, it shows a step by step solution, and is a calculator for your problem <3
Step-by-step explanation:
Can yall help me with this one please? ✊ :(
(The problem is in the picture)
Answer:
Hey there!
Length: \(l\\\)
Width: \(1/3l-1\)
Expression to find the area: \(l(1/3l-1)\), or \(1/3l^2-l\).
Expression to find the perimeter: \(2l+2(1/3l-1)\), or \(8/3l-1\).
Perimeter divided by area: \(\frac{\frac{8}{3}l-1 }{1/3l^2-l}\)
Let me know if this helps :)
Please help, I will give brainliest. I am struggling badly.
Answer:
2nd awnser i had that exact question the other day
Step-by-step explanation:
14\4139 what is the answer
Answer:
14 divided by 4139 is 0.0033824595312878
Step-by-step explanation:
The number of unique visitors to the college website can be approximated by the formula N(t)=410(1.32)t where t represents the number of years after 1997 when the website was created. Approximate to the nearest integer the number of unique visitors to the college website in the year 2020.
Answer:
243212
Step-by-step explanation:
Substitute the given value of t into the given formula. To find t, subtract 1997 from 2020.
2020−1997=23
Now substitute 23 into the equation for t and calculate.
N(t)N(23)==≈410(1.32)t410(1.32)23243,212
The number of unique visitors to the college website in the year 2020 was approximately 243,212.
Suppose the distributor charges the artist a $40.00 cost for distribution, and the streaming services pay $4.00 per unit. (Note: One unit = one thousand streams)
Model the profit for the total number of streams by answering the questions below:
Use the cost for distribution to build your y-intercept. What is the y-intercept?
Hint: the y-intercept is a point on the y axis, so your answer should be an ordered pair.
Hint: you have to keep in mind that any time you pay for something, you are SPENDING money, if your y-intercept is incorrect, all your numbers will be off.
Use the payment per unit to build your slope. What is the slope?
Use the slope-intercept format (y = mx + b) to give the equation of the line. What is the equation of this line?
Graph the line by adjusting the sliders below. Show your line by attaching an image below.
After how many streams will you pay for the distributor charges? (Hint: this is where the line crosses the x-axis, round to the nearest thousand)
How many streams would it take to profit $750,000? (Hint: Remember one unit = one thousand streams)
Challenge Question: In 2020, Puerto Rican rapper Bad Bunny claimed the top spot of most-streamed artists globally on SPOTIFY, with more than 8.3 billion streams (8,300,000,000) this year from fans around the globe. His album YHLQMDLG—released in late February 2020, featuring collaborations with Sech, Anuel AA, and Daddy Yankee—is the number one streamed album as well. Calculate the profit earned using these numbers. (Hint: Use the slope-intercept format to build this equation. Also, remember one unit = one thousand streams).
The question is an illustration of a linear equation
The y-intercept is 40The slope is 4The equation of the line is \(y =4x + 40\)You pay the distributor after 1 chargeYou pay $750,000 for 177.5 streams(a) How to calculate the y-interceptFrom the question, we have the following parameters:
Cost of distribution: $40.00Rate = $4.00 per unitThe cost of distribution represents the y-intercept, while the rate represents the slope.
Hence, the y-intercept is 40
(b) How to calculate the slopeIn (a), we have:
The rate represents the slope.
Hence, the slope is 4
(c) The equation of the lineA linear equation is represented as:
\(y = mx + b\)
Where:
m represents the slopeb represents the y-interceptUsing the results in (a) and (b), the linear equation is:
\(y =4x + 40\)
See attachment for the graph of the equation
(c) The number of streams you pay the distributorFrom the graph, we can see that the line touches the x-axis at the negative x-axis.
This means that, you pay the distributor after 1 charge
(d) The number of streams to pay $750,000This means that: y = 750.
So, we have:
\(y =4x + 40\)
\(750 = 4x + 40\)
Subtract 40 from both sides
\(4x = 710\)
Divide both sides by 4
\(x = 177.5\)
Hence, you pay $750,000 for 177.5 streams
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create a model or equation that will represent to the amount of relief each family will receive bearing in mind that the number of families will vary.
Missing Information
Suppose the officials conducted a survey for 4 days to determine the actual number of families residing in the barangay and the secretary constructed a tableto keep track of the data.
Day 0:
Number of families: 850
Amount of relief each family will receive: 520
Answer:
f(x) = 442000/x
Step-by-step explanation:
Given
The data in the above table
Required
Determine a model or equation
First, we need to determine the amount of relief for all families.
Using data in day 0.
Total Amount = 850 * 520
Total Amount = 442000
Next, we determine the function of equation.
Let the number of families he represented by x
The function or equation is gotten by dividing the total amount by the number of families.
Hence:
f(x) = Total Amount ÷ x
Substitute values for total amount and x
f(x) = 442000/x
Hence, the model that satisfies the given information is:
f(x) = 442000/x
Review the graph.
On a coordinate plane, a circle has center (4, 0) and radius 4. Another circle has center (2, negative 3) and radius 6. The area inside of the first circle and outside of the second circle between the 2 circles is shaded.
Which system of inequalities is shown in the graph?
36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
36 < (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
Answer:
36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²
Step-by-step explanation:
This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.
A
X
Find the value of x.
D
X+2
x = [?]
B
3
E
2
C
Answer:
x = 4
Step-by-step explanation:
if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.
DE is such a line , then
\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\) ( substitute values )
\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )
3x = 2(x + 2)
3x = 2x + 4 ( subtract 2x from both sides )
x = 4
what a subcategory of a polygon
Three or more line segments that only intersect at their ends form closed, two-dimensional shapes known as polygons.
What is a polygon?A polygon is a closed, two-dimensional shape with straight sides that is flat or plane. It has straight sides. Polygons are a different category that belongs to the category of two-dimensional figures because two-dimensional (2D) figures are flat because they lack volume.
Polygons are flat 2D shapes that have straight lines and all lines are closed, meaning that they don't have any disconnected lines. Polygons are a subcategory of 2D figures because they carry all traits of 2D figures but also have special ones of their own. Examples of polygons are squares, rectangles, and triangles. Examples of nonpolygons but still are 2D figures are circles, ovals, and any other flat shape.
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Complete question
How can polygons be considered a subcategory of two-dimensional figures?
Overdraft protection can be set up to which of the following accounts?
a. Savings account
b. Credit Card
c. A line of credit
d. All of the above
2(34 + 12) > 5b This inequality contains a variable, b. Choose ALL numbers that make this inequality true. A) 16 B) 18 C) 19 D) 20 E) 22
Answer:
A and B
Step-by-step explanation:
A triangle has sides with lengths 8, 15, and 17.
1. Verify this is a Pythagorean Triple
2. Approximate the acute angles in this triangle
Yes, the given set of the sides of a triangle follows the Pythagorean Triple and the acute angles are 61.92° and 28.08°.
What is the Pythagorean Triple?Pythagorean triples are a²+b² = c² where a, b and c are the three positive integers. These triples are represented as (a, b, c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.
Given that, A triangle has sides with lengths 8, 15, and 17.
1) Checking for Pythagorean triples;
17² = 289
8²+15² = 225+64 = 289 = 17²
∴ 17² = 8²+15²
Since, they are following the Pythagoras theorem so, they are Pythagorean triples.
2) Calculating the acute angles:- [please refer to attached figure]
Let 15 be the perpendicular, 8 be the base and 17 is the hypotenuse,
sinC = 15/17 (sine of an angle is ratio of perpendicular to hypotenuse)
∠ C = sin⁻¹(15/17)
∠ C = 61.92°
∠ A = 90°-61.92°
∠ A = 28.08°
Hence, the given set of the sides of a triangle follows the Pythagorean Triple and the acute angles are 61.92° and 28.08°.
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Recall that with base-ten blocks: 1 long 10 units, 1 flat 10 longs, and 1 block 10 flats. What is the fewest number of multibase blocks that can be used to represent the corresponding numeral in the given base?
a. 20 longs in base seven
b. 10 longs in base three
a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.
In base seven, we have the following conversions:
1 long = 1 unit
1 flat = 10 units
1 block = 10 flats
To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.
So, the fewest number of multibase blocks required would be 2 flats.
Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.
In base three, we have the following conversions:
1 long = 1 unit
1 flat = 3 units
1 block = 3 flats
To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.
So, the fewest number of multibase blocks required would be 3 flats and 1 unit.
Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
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Each volleyball set costs $63.74.
Which equation represents the cost, c, of n sets?
The equation that represents the cost, c, of n sets is c = 63.74n
Which equation represents the cost, c, of n sets?from the question, we have the following parameters that can be used in our computation:
Each volleyball set costs $63.74.
Let the total number of sets be n
So we have
Cost of n = 63.74 * n
This gives
c = 63.74n
Hence, the equation is c = 63.74n
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simplify 8+3{x-2[x+5(x3)]}
the correct answer is negitive one hundred eighty (-180)
Which expressions are equivalent to?
Answer:
-6(b+2) +8
= -6b -12 +8
= -6b -4
Step-by-step explanation:
14. What is the equation of a circle with a center at (4,−9) and a radius of 5?
A) (x+4)^2+(y−9)^2=5
B) (x+4)^2+(y−9)^2=25
C) (x−4)^2+(y+9)^2=25
The equation of a circle with a center at (4,−9) and a radius of 5 is
(x−4)^2+(y+9)^2=25. The correct Option C.
How to find equation of a circle?A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.
The equation of a circle with center (h, k) and radius r units is
(x−h)^2+(y−k)^2=r^2 .
where h = 4
k = -9
r = 5
The equation of the circle
(x−4)^2+(y−(-9))^2 = 5^2
The equation of the circle
(x−4)^2+(y+9)^2 = 25
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Choose the sentence that is equivalent to the following statement:
Among any two consecutive positive integers, there is at least one integer that is not prime.
a. If x and y are positive integers, then x is not prime and y is not prime.
b. If x and y are positive integers, then x is not prime or y is not prime.
c. If x is a positive integer, then x is not prime and x 1 is not prime.
d. If x is a positive integer, then x is not prime or x 1 is not prime.
Answer:
bbbbbbbb
Step-by-step explanation:
bbbbbbbbb;bbbbbbbvvvbbbbb;vvvvvvvvvvvvvv
Carla asked students at a lunch table what their main course they liked. Out of these students, 28n liked pizza, 15 liked chicken nuggets, and 8 liked both. what is the probability that a randomly selected student will like pizza but not chicken nuggets?
The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.
To find the probability that a randomly selected student will like pizza but not chicken nuggets.
Let P = the number of students who like pizza but not chicken nuggets
Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets
P = 28n - 8
So, the probability that a randomly selected student will like pizza but not chicken nuggets is:
P(Pizza but not nuggets) = P/(Total number of students)
We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:
Total number of students = 28n + 15 - 8 = 28n + 7
So, the probability that a randomly selected student will like pizza but not chicken nuggets is:
P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)
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The Kaumajet Factory produces two products - table lamps and desk lamps. It has two separate departments - Finishing and Production. The overhead budget for the Finishing Department is $550,000, using 500,000 direct labor hours. The overhead budget for the Production Department is $400,000 using 80,000 direct labor hours.
The Kaumajet Factory will allocate $7.20 of factory overhead to each unit of table lamp using the multiple production department factory overhead rate method with an allocation base of direct labor hours.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Predetermined overhead rate for Finishing Department = $550,000 / 500,000 direct labor hours = $1.10 per direct labor hour
Predetermined overhead rate for Production Department = $400,000 / 80,000 direct labor hours = $5.00 per direct labor hour
For one unit of table lamp, 2 hours of finishing and 1 hour of production are required, so the total direct labor hours for one unit of table lamp is 2 + 1 = 3 hours.
Finishing Department overhead cost per unit of table lamp = 2 hours * $1.10 per direct labor hour = $2.20
Production Department overhead cost per unit of table lamp = 1 hour * $5.00 per direct labor hour = $5.00
Total factory overhead cost per unit of table lamp
$2.20 + $5.00 = $7.20
Therefore, the Kaumajet Factory will allocate $7.20 of factory overhead to each unit of table lamp using the multiple production department factory overhead rate method with an allocation base of direct labor hours.
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The Kaumajet Factory produces two products-table lamps and desk lamps. It has two separate departments - Finishing and Production. The overhead budget for the Finishing Department is $550,000, using 500,000 direct labor hours. The overhead budget for the Production Department is $400,000 using 80,000 direct labor hours.
If the budget estimates that a table lamp will require 2 hours of finishing and 1 hour of production, how much factory overhead will the Kaumajet Factory allocate to each unit of table lamp using the multiple production department factory overhead rate methods with an allocation base of direct labor hours?
a. $4.91
b. $6.33
c. $7.20
d. $5.00