The formula for the equation of y, the number of units sold as a function of x is y = 0.00625x + 250
How to illustrate the equation?From the information given, when the company spends no money on advertising, it sells 250 units and for each additional $4000 spent, an additional 25 units are sold.
The formula for y will be:
y = (25/4000)x + 250
y = 0.00625x + 250
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Name the corresponding part if polygon WXYZ ≅ polygon PQRS.
Question: QP =
The corresponding part of PQ is WX
How to determine the corresponding parts?The congruent statement is given as:
polygon WXYZ ≅ polygon PQRS.
This means that the corresponding points are:
W and P, X and Q, Y and R, Z and S
When two points Q and P are joined together, we have:
polygon WX ≅ polygon PQ
Hence, the corresponding part of PQ is WX
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Which statement is true about the graphs of the two lines y= -4/5x + 2 and y = - 5/4x - 1/2?
They have no relation, except for the fact that they intersect.
We have given that,
The graphs of the two lines y= -4/5x + 2 and y = - 5/4x - 1/2
If the equations were instead y = +5/4x - 1/2 and
What is the slope of the perpendicular line?Vertical lines and horizontal lines are perpendicular to each other. The slope of the perpendicular line in this case would be the slope of a horizontal line which would be 0. The slope of the parallel line is undefined and the slope of the perpendicular line is 0.
y = -4/5x + 2, or
y = +4/5 + 2 and
y = -5/4x -1/2,
Then they would be perpendicular.
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HELP ASAP
8. The tubes on the frame of this road bike form a triangle. The owner's manual
identifies some of the angle measures formed by the bike frame. Based on the
information in the diagram below, determine which tube is the longest.
top tube
seat tube
top tube
30%
7
55
C
down tube
Part I: Classify the triangle formed by the three bike frame tubes as equilateral,
isosceles, or scalene. Find the measure of ZB and explain your classification. (3
points; 1 point for classification, 1 point for the angle measure, and 1 point for
explanation)
seat tube
down tube
Answer:
See below
Step-by-step explanation:
Longest is the down tube.....it is opposite the largest angle (95°) angle in the triangle . This is a SCALENE triangle ( all sides of different length)
The longest tube that we have here is the down tube. The triangle that is formed id the scalene triangle
What is the scalene triangle
A scalene triangle is a type of triangle where all three sides have different lengths. In other words, no two sides of a scalene triangle are equal in length. Additionally, the angles of a scalene triangle are also different from each other.
The term "scalene" comes from the Greek word "skalenos," which means "uneven" or "unequal." This name reflects the defining characteristic of the scalene triangle, which is the absence of any equal sides or angles.
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( Math ) Please explain how you got this answer! Please use substitution method!
Answer:
y = 1
x = -2
Step-by-step explanation:
During the substitution method, you are substituting one function into another. Because both functions are set equal to "x", you can make the functions equal each other. This allows you to 'get rid' of the "x" variable and simplify to find the value of "y".
5A) x = -2y
5B) x = 2 - 4y
-2y = 2 - 4y <----- Set both equations equal
2y = 2 <----- Add 4y to both sides
y = 1 <----- Divide both sides by 2
Now that you know what "y" equals, you can plug that value into the "y" variable into one of the equations. This will allow you to then simplify and find the answer for "x".
x = -2y <----- Equation 5A
x = -2(1) <----- Plug 1 into "y"
x = -2 <----- Multiply -2 and 1
a
b
c
or d
question is in picture
A, -9 ≤ -3X -6 ≤ 6
What is inequality?Inequality is an algebraic statement that shows that two quantities are unequal.
Analysis:
From the above, only A, is the correct inequality represented above.
solving for x in A, we have,
-9 ≤ -3x - 6 ≤ 6
splitting,
-9 ≤ -3x -6
-3 ≤ -3x
1 ≥ x
x ≤ 1
-3x-6 ≤ 6
-3x ≤ 12
x ≥ 12/-3 ≥ -4
-4 ≤x ≤1, A
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There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does this situation represent a linear or non-linear function, and why?
Answer:
Step-by-step explanation:
It represents a linear function because there is a constant rate of change.
Step-by-step explanation:
Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.
Here, number of hours represents input value and minutes represents the output value,
Now, By the given table,
The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),
Also,
⇒ The rate of change output value with respect to input value remains constant,
Hence, It represents a linear function because there is a constant rate of change.
Solve the quadratic equation numerically (using tables of x- and y- values). x squared + 7 x + 12 = 0 a. x = -1 or x = -1 c. x = -3 or x = -3 b. x = -4 or x = -3 d. x = 2 or x = -1 Please select the best answer from the choices provided
Answer:
b. x = -4 or x = -3
Step-by-step explanation:
[tex]x^{2} +7x+12[/tex]
To factor this, come up with two numbers that can be multiplied together to get 12, but add to get 7.
We get 4 and 3.
4 + 3 = 7
4 x 3 = 12
Now we can factor with these two numbers:
[tex](x+4)(x+3) = 0[/tex]
Now, solve for x by separating the factors:
[tex]x + 4 = 0[/tex]
[tex]x = -4[/tex]
And,
[tex]x + 3 = 0[/tex]
[tex]x = -3[/tex]
So, the answers are -4 and -3.
A chord AB divides a circle of radius 8 cm into two segments. If AB subtends a
central angle of 45, find the area of the minor segment.
Answer:
Area of the minor segment = 2.505324230749 cm²
Step-by-step explanation:
Area of the minor segment
= Area of the sector ABC - Area of the triangle ABC
……………………………………………………………………………………
• Area of the sector ABC
= Area of the whole circle ÷ 8
= (π×8²) ÷ 8
= 8π
______
•• Area of the triangle ABC
= (1÷2) × CA × CB × sin(45)
= (1÷2) × 8 × 8 × (√2/2)
= 16√2
______
Thus
Area of the minor segment
= 8π - 16√2
= 2.505324230749
If 80% of a number is 288 and 95% of the same number is 342, find 15% of that
number.
Answer:54
Step-by-step explanation:
There are quicker ways to solve this but a simple and easy way to do this would be by dividing your number by the percent so 288/80 and with this, you would get your number for 1 percent or 3.6. Now you can multiply that number by the percent your need to find so 15. And 15 x 3.6 is = 54.
The diagram shows a line joining O to P.
The gradient of the line is 2
The length of the line is √2645
Work out the coordinates of P.
Answer: (23, 46)
Step-by-step explanation:
The equation of the line is y = 2x, and we can thus represent point P as (x, 2x)
Substituting into the distance formula,
[tex]\sqrt{2645}=\sqrt{(x)^{2}+(2x)^{2}}\\\\2645=x^2 + (2x)^2\\\\2645=x^2 + 4x^2\\\\2645=5x^2\\\\529=x^2\\\\x=23[/tex]
Thus, the coordinates of P are (23, 46)
Could someone answer the rest please!
Much appreciated if you do (:
Answer:
shown below
Step-by-step explanation:
4 x 2 = 8
1 x 2 = 2
a⁸b²
(a⁵b²)(a²b⁶)
a⁷a⁵b⁶b²a²b⁸
a¹⁴b¹⁶
8 - 14 = -6
2 - 16 = -14
a^-6 b^-14
next one
25^3x-21
/
25^2x+14
1^x-35
(04.01, 04.02 HC)
Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he plays volleyball.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Eric plays basketball (x) and the number of minutes he plays volleyball (y) every day. (5 points)
Part B: How much time does Eric spend playing volleyball every day? Show your work. (3 points)
Part C: Is it possible for Eric to have spent 35 minutes playing basketball if he plays for a total of exactly 95 minutes and plays basketball for 25 minutes longer than he plays volleyball? Explain your reasoning. (2 points)
Eric spend 60 minutes for basketball and 35 minutes for volleyball.
What is Linear Equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.
Here, let Eric plays basketball for x minutes.
and volleyball for y minutes.
Total time spend on playing basketball and volleyball everyday = 95 minutes.
Duration of Basketball 25 minutes more than volleyball
Now, according to question,
x + y = 95 ..........(i)
x - 25 = y ...........(ii)
On solving equation (i) and (ii), we get
x + x - 25 = 95
2x = 95 + 25
2x = 120
x = 120 / 2
x = 60
put value of x in equation (ii), we get
60 - 25 = y
y = 35
Yes, it is possible and clearly described in above calculation.
Thus, Eric spend 60 minutes for basketball and 35 minutes for volleyball.
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A cone has a volume of 350 cubic meters. The area of the base is 70 square meters. What is the height of the cone? Show work
Answer: The height is 15
Step-by-step explanation:
Vcone = pi * r^2 * h / 3
Area of the base = pi*r^2 = 70 so...
350 = 70 * h / 3
350 = (70/3) * h multiply both sides by 3/70
350 (3/70) = h = 15 m
find the midpoint of each line segment
Answer:
([tex]\frac{7}{2}[/tex],[tex]\frac{1}{2}[/tex])
Step-by-step explanation:
For this you use the midpoint formula
[tex](\frac{x_{2} +x_{1} }{2} ,\frac{y_{2} +y_{1} }{2} )[/tex]
the points would be (2,1) and (5,2)
The midpoint would be ([tex]\frac{7}{2}[/tex],[tex]\frac{1}{2}[/tex])
Suppose you work 45 hours at a rate of 7.25 per hour pluse overtime pay for any hours over 40. You also received a 2% commission on the $800 of chinatableware you sold. Your paycheck lists 324.25 as your gross earnings is that correct
No, your paycheck is incorrect. The gross salary will be 342.25.
What is the gross salary?The amount of money paid to any employee without any deductions of the taxes or anything is called as gross salary.
The gross salary will be calculated as follows:-
40x 7.25= $290.00 (base salary)
5x 7.25 = 36.25 (overtime)
.02x 800= 16.00 (commission)
Gross salary will be = 36.25 + 16 + 290 = $324.25
Therefore your paycheck is incorrect. The gross salary will be 342.25.
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answer? To this question please
Answer: The second table.
Step-by-step explanation: The y coordinates are getting smaller over time, so I believe the second one would be the correct answer. I hope this helps! :)
Choose the letter of the equation for
the graph.
Using translation concepts, the equation for the graph is given as follows:
b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we have a cosine function(zero at pi/2, this is zero at the origin), shifted pi/2 units to the right and 1 unit up(as the standard amplitude is between -1 and 1, here is between 0 and 2).
Hence the rule is given by:
b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].
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What is the horizontal and vertical shift for the absolute value function below f(x)=3[x+9]+6
We will see that we have a shift of 9 units to the left and 6 units upwards
How to identify the translations?For any given function H(x), we define a vertical shift of N units as:
g(x) = H(x) + N.
If N > 0, the shift is upwards.If N < 0, the shift is downwards.While a horizontal shift is written as:
g(x) = H(x + N).
If N > 0, the shift is to the left.if N < 0, the shift is to the right.Here we know that:
f(x) = 3*|x + 9| + 6
If the original function was:
H(x) = 3*|x|
Then we can write:
f(x) = H(x + 9) + 6
So we have a shift of 9 units to the left and 6 units upwards.
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You buy a CD for $9000 that earns $172.92 in interest every 2 months. What is the
annual yield on your investment?
Answer:
$4,000.343
Step-by-step explanation:
Divided the months of the year and caculate the intrest.
Which expression simplifies to 2 divided 15 ?
Answer: 4/30
Step-by-step explanation:
it does
Please help and show the steps.
How do you figure out the equation to graph it
g(x)=(x-1)^2-1
Answer:
Graph of the given equation is a opening up parabola passing through origin (0,0) and (2,0) and having vertex (1,-1)
Step-by-step explanation:
parabola - it is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.
vertex - The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.
the given equation can be resolved as:
[tex]g(x)=(x-1)^2-1\\g(x) = x^2 -2x +1 -1\\g(x) = x^2 - 2x[/tex]
now substituting x = 0,
[tex]g(x) = x^2 - 2x\\g(x) = (0)^2- 2(0)\\g(x) = 0[/tex]
therefore the equation satisfies the point (0,0)that is origin.
now putting g(x) = 0,
[tex]g(x) = x^2 - 2x\\0 = x^2- 2x\\2x = x^2\\2=x[/tex]
so when y coordinate is 0 x coordinate is 2,
therefore the equation also satisfies the (2,0)
general equation of a parabola is
[tex]f(x) = ax^2 + bx + c[/tex]
and the vertex of the parabola is given by [tex]\frac{-b}{2a}{,}{f{(}\frac{-b}{2a}{)}}[/tex]
given equation of parabola [tex]g(x) = x^2 - 2x[/tex]
here a = 1 and b= -2
substituting in the vertex formula,
vertex of the parabola is [tex]{(}{1}{,}{f{(}{1}{)}}{)}[/tex]
[tex]f(1) = 1 - 2 = -1[/tex]
therefore the vertex is (1,-1).
so the parabola is passing through origin(0,0) and (2,0) with vertex (1,-1).
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Rewrite without parentheses.
-9²x4 (7x²-6w+2)
Simplify your answer as much ac
Answer:
2268x²-1944w+648
-9² = 81
81×4 =324
use the 324 to remove the bracket
HELP me find percentage qwq
Answer:
option B or 40%
Step-by-step explanation:
Well if 14/35 of the class is male. You divide 14 by 35. And after using calculator I see the answer is 40% of the class is male.
Thank
What is the solution set for the following inequality? 4x – 3 + 6x > 5x + 7
Answer:
you got that
Step-by-step explanation:
wet wet wet
Answer:
{ x : x > 2 }
Step-by-step explanation:
4x - 3 + 6x > 5x + 7 , that is
10x - 3 > 5x + 7 ( subtract 5x from both sides )
5x - 3 > 7 ( add 3 to both sides )
5x > 10 ( divide both sides by 5 )
x > 2
Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation and in set
builder form using a compound inequality.
Note: To type in the sign, type <= or use the Math Quill by clicking the yellow arrow.
Answer:
Domain: Interval notation is [tex](-3, 4][/tex], set builder is [tex]\{x|-3 < x\leq4 \}[/tex]Range: Interval notation is [tex][0, 3)[/tex], set builder is [tex]\{y|0\leq y < 3\}[/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
which function has an asymptote at x=5 and an x-intercept of (6,0)?
The function is f(x) = log(x - 5).
What is Asymptotes?A line or curve that acts as the limit of another line or curve.
The complete question is
Which function has an asymptote at x = 5 and an x-intercept of (6,0)? a. f(x) = log(x − 5) b. f(x) = log(x 5) c. f(x) = log x − 5 d. f(x) = log x 5
let us take,
f(x) = log(x - 5)
y = 0, then
0 = log(x-5)
x - 5 = [tex]e^{0}[/tex]
x - 5 = 1
x = 6
So, it can be conclude that the x-intercept is at (6, 0)
Hence, the function is f(x) = log(x - 5).
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Find the radius of this sphere. Then calculate the volume of a sphere
Answer:
Since we want to find radius and the diameter is 28 we will divide by two = ²⁸/2 which gives a radius of 14
since the radius is 14cm. we move on to the volume .
WE SUBSTITUTE
⁴/3× ²²/7× 14 equals 58.2cm²
therefore radius; 14cm
volume; 58.2cm
calculus piecewise function.
Part A
The notation [tex]\lim_{x \to 2^{+}}f(x)[/tex] means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.
So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc
We don't actually arrive at x = 2 itself. We simply move closer and closer.
Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2
Therefore f(x) = (x/2) + 1
Plug in x = 2 to find that...
f(x) = (x/2) + 1
f(2) = (2/2) + 1
f(2) = 2
This shows [tex]\lim_{x \to 2^{+}}f(x) = 2[/tex]
Then for the left hand limit [tex]\lim_{x \to 2^{-}}f(x)[/tex], we'll involve x < 2 and we go for the first piece. So,
f(x) = 3-x
f(2) = 3-2
f(2) = 1
Therefore, [tex]\lim_{x \to 2^{-}}f(x) = 1[/tex]
===============================================================
Part B
Because [tex]\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)[/tex] this means that the limit [tex]\lim_{x \to 2}f(x)[/tex] does not exist.
If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.
===============================================================
Part C
You'll follow the same type of steps shown in part A.
However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.
So you'd only involve the second piece f(x) = (x/2) + 1
You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.
===============================================================
Part D
As mentioned earlier, since [tex]\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3[/tex], this means the limit [tex]\lim_{x \to 4}f(x)[/tex] does exist and it's equal to 3.
As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.
probability of independent events: decimal answers (probability and counting)
The probability that both are smokers is 6903/180000
How to determine the probability?The given parameters are:
Male smoker = 177
Female smoker = 78
Total student = 78 + 522 = 600
The probability of a male smoker is
P(Male) = 177/600
The probability of a female smoker is
P(Female) = 78/600
The probability that both are smokers is
P(Smoker) =P(Male) *P(Female)
So, we have:
P(Smoker) = 177/600 * 78/600
Simplify
P(Smoker) = 177/600 * 39/300
Evaluate the product
P(Smoker) = 6903/180000
Hence, the probability that both are smokers is 6903/180000
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Solve for u. -5/6u = 15
Answer:
u = -18
Step-by-step explanation:
[tex]\frac{-5u}{6} =15[/tex]
Multiply both sides by 6.
-5u = 15 × 6
-5u = 90
Divide both sides by -5.
u = -18