Answers
Answer:
n = 3(1, 1/6), (-2, 7/6), (5, -7/6)2x + 6y = 3Step-by-step explanation:
A graphing program can help a lot in this case. Even without the program, it seems clear from a graph that only the first three points will lie on the same line.
The slope of the line can be found from the first two points as ...
∆y/∆x = (7/6 -1/6)/(-2 -1) = (6/6)/-3 = -1/3
Then the point-slope form of the equation can be written as
y -1/6 = -1/3(x -1)
Multiplying by 6 gives ...
6y -1 = -2x +2
Adding 2x+1 puts the equation into standard form:
2x + 6y = 3
Related Questions
Can you help me with this question?
Answers
Sure. To make an equilateral triangle we make any segment AB, which is already done, then we draw one circle (or an arc from the circle) with center A and radius AB, and one circle with center B and radius AB. The two circles intersect at two points; we call either one of them C and ABC is equilateral.
Answer: C
Write an expression to represent: Four less than the quotient of a number x and 5
Answers
The mathematical representation of the expression 'Four less than the quotient of a number x and 5' is 'x/5 - 4'. This involves division and subtraction of the number x.
Explanation:The subject of this question is Mathematics, particularly algebraic expressions. In this case, you are being asked to express the phrase 'Four less than the quotient of a number x and 5' as an algebraic expression. The 'quotient of a number x and 5' implies division of the number x by 5, which is represented as 'x/5'. 'Four less than' signifies a subtraction of four from the preceding expression. Therefore, the whole expression can be written as 'x/5 - 4'.
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What is the common factor of the numerator and denominator in the expression [tex]\frac{(2x+3)(x-4)}{(x-4)(x+4)}[/tex]
Enter your answer as a binomial, like this: x + 7
Answers
Answer:
Step-by-step explanation:
(x - 4)
What you are being asked to do is find the exact same binomial in the top as is in the bottom.
But there's a small catch. You must stipulate that x cannot equal 4. If it does, then you will get 0/0 which is undefined. You can't have that happening -- not at this level.
Any other value for x is fine.
Please help - will mark brainlest
Answers
Answer:
C 294
Step-by-step explanation:
We can use proportions to solve. Put number of miles over gallons
202 miles x miles
--------------- = ----------------
11 gallons 16 gallons
Using cross products
202*16 = 11 x
Divide by 11 on each side
202*16/11 = 11x/11
293.81818181818 =x
To the nearest whole number
294 miles =x
Match the function with its graph.
1) y= tan x
2) y= cot x
3) y= -tan x
4) y= -cot x
Answers
Answer:
Option a. 1C, 2A, 3B, 4D.
Step-by-step explanation:
1) We know that tan(x)=sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=0. For that reason, we know that the graph passes through the point (0,0).
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus tan(45)=1. The only graph that passes through the point (0,0) and is possitive when x=45 is the graph C.
2) We know that cot(x)=cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=+∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus cot(45)=1. The only graph that has an asymptote in y=0 and is possitive when x=45 is the graph A.
3) We know that -tan(x)=-sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then -tan(x)=0. For that reason, we know that the graph passes through the point (0,0).
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -tan(45)=-1. The only graph that passes through the point (0,0) and is negative when x=45 is the graph B.
) We know that -cot(x)=-cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=-∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -cot(45)=-1. The only graph that has an asymptote in y=0 and is negative when x=45 is the graph D.
The correct matches of the functions with their graphs are as follows: 1) y = tan(x) matches with graph C, 2) y = cot(x) matches with graph A, 3) y = -tan(x) matches with graph B, and 4) y = -cot(x) matches with graph D.
1) y = tan(x) matches with graph C:
- The tangent function has a period of π (180 degrees) and is undefined at odd multiples of π/2 (90 degrees). This is why it has vertical asymptotes at x = π/2, 3π/2, etc.
- The graph of y = tan(x) passes through (0, 0) because tan(0) = 0.
- It has a repeating pattern where it increases to positive infinity as it approaches the vertical asymptotes and decreases to negative infinity as it approaches the odd multiples of π/2.
2) y = cot(x) matches with graph A:
- The cotangent function is the reciprocal of the tangent function: cot(x) = 1/tan(x). It is undefined at even multiples of π/2 (0, π, 2π, etc.), which is why it has vertical asymptotes at x = 0, π, 2π, etc.
- The graph of y = cot(x) never crosses the y-axis, and it has an asymptote at y = 0.
- It has a repeating pattern where it approaches 0 as it approaches the vertical asymptotes.
3) y = -tan(x) matches with graph B:
- The negative tangent function, -tan(x), is the reflection of the positive tangent function y = tan(x) about the x-axis.
- The graph of y = -tan(x) passes through (0, 0) because -tan(0) = 0.
- It has a repeating pattern similar to the positive tangent but is reflected about the x-axis.
4) y = -cot(x) matches with graph D:
- The negative cotangent function, -cot(x), is the reflection of the positive cotangent function y = cot(x) about the x-axis.
- The graph of y = -cot(x) never crosses the y-axis, similar to the positive cotangent, and it has an asymptote at y = 0.
- It has a repeating pattern similar to the positive cotangent but is reflected about the x-axis.
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SureFire Distribution Company sells phone systems to businesses. On September 1, they began with a balance of 193 digital phones. It received shipments of 23 and 45 phones on September 15 and 30 respectively. It sold 45 phones on September 8 and 100 phones on September 19. How many were on hand as of September 30?
146
145
165
116
Answers
I think 145 but I’m not quite sure
Answer:
116. add all and subtract respective to the date.
Step-by-step explanation:
Ken ate 2?7 of the chocolate bar one day and 8?14 the next day. How much of the chocolate bar did Ken eat?
Answers
Answer:
6/7
Step-by-step explanation:
8/14 simplified is 4/7.
So 2/7+4/7=6/7.
Identify the area of the rhombus. PLEASE HELP! I'm desperate!!
Answers
Area = 1/2(diagonal) * √4*side^2 - diagonal^2
Area = 1/2(16)*√(4*17^2 - 16^2)
Area = 8 * √(4*289-256)
Area = 8 *√900
Area = 8 * 30
Area = 240 m^2
Let's illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The given population is the scores of ten female students in a class. Student 0 1 2 3 4 5 6 7 8 9 Weight 136 99 118 129 125 170 130 128 120 147 The parameter of interest is the mean weight in pounds ???? in this population. The sample is an SRS of size ????=4 drawn from the population. Because the students are labeled zero to nine, a single random digit from Table A chooses one student for the sample. (a) Find the mean of the ten weights in the population. This is the population mean ???? . (Enter your answer rounded to one decimal place.)
Answers
Answer:
a: sample mean: 130.2 pounds
This is not the population mean
Step-by-step explanation:
To find the mean weight of the sample, add up all the values and divide by the total number of values entered. In this case, 10, so we have...
mean: (136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147)/10 =
1302/10 = 130.2
This is not the population mean. It is the mean of the sample. We would have to know more information to make a conjecture about the population mean.
Final answer:
The population mean of the students' weights is determined by summing all the weights and dividing by the number of students, resulting in 130.2 pounds.
Explanation:
To find the population mean (denoted as μ), we add up all the weights of the ten students in the population and divide it by the total number of students. Let's do the calculation:
The weights of the students are 136, 99, 118, 129, 125, 170, 130, 128, 120, and 147 pounds.
The sum of these weights is 136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147 = 1302 pounds.
Since there are 10 students in the population, we divide the total weight by 10 to find the mean:
μ = ΣX / N = 1302 / 10 = 130.2 pounds
Therefore, the population mean (μ) is 130.2 pounds.
A rectangular piece of stained glass has the dimensions shown in the diagram. What is the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid?
Answers
Answer:
The correct option is D) [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Consider the provided figure.
We need to find the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid.
For this first find the total area as shown:
The given figure is a rectangle.
The area of rectangle is [tex]l\times b[/tex]
Where, l = 6 cm + 3 cm = 9 cm and b = 5cm
Therefore the area of the rectangle is;
Area of rectangle = [tex]9cm\times 5cm=45cm[/tex]
Now find the area of trapezoid.
The area of trapezoid is: [tex]\frac{a+b}{2}h[/tex]
Where h is the height and a and b are the parallel sides.
Area of trapezoid = [tex]\frac{9+3}{2}\times 5=30[/tex]
Thus, the area of trapezoid is 30 cm.
Therefore, the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid is:
[tex]Probability=\frac{\text{Area of trapezoid}}{\text{Area of rectangle}}[/tex]
[tex]Probability=\frac{30}{45}=\frac{2}{3}[/tex]
Hence, the correct option is D) [tex]\frac{2}{3}[/tex]
Answer:
2/3
Step-by-step explanation:
I got it right
Ben drove 350 miles in 6 1/2 hours Marcie drove 520 miles on 12 1/4 hours who drove faster
Answers
Answer:
Ben drove faster
Step-by-step explanation:
BEN:350 miles / 6.5 hours = 53.84 miles per hour
MARCIE:520 miles / 12.25 hours = 42.44 miles per hour
53.84 is faster than 42.44 therefore Ben is faster.
If 2/3x + 4 less than or equal to 14 what is the largest possible value of 7x - 2
Answers
⅔x+4≤14
⅔x≤10
2x≤30
x≤15
Max value of x is 15
7x-2≤?
7(15)-2=105-2=103
7x-2≤103
Greatest value for 7x-2 is 103
A division problem can be written out using repeated subtraction. Which division problem is solved below? 40 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4
Answers
Answer:
The problem that is getting solved is 40 divided by zero
Answer:
Step-by-step explanation:
This is a faulty way of showing it. What you are solving here is
40 - 10*4 which is 0. What is transcribed is not equivalent to any division that I can see.
Perhaps 0/40
If you have answers, please list them.
The function f(x)=x^2-4x+4 is shifted 3 units to the right to create g(x). What is g(x)
Answers
Answer:
g(x) = x² - 7x + 16Step-by-step explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
===================================
f(x) = x² - 4x + 4 shifted 3 units to the right. Therefore g(x) = f(x - 3):
g(x) = (x - 3)² - (x - 3) + 4 use (a - b)² = a² - 2ab + b²
g(x) = x² - 2(x)(3) + 3² - x - (-3) + 4
g(x) = x² - 6x + 9 - x + 3 + 4 combine like terms
g(x) = x² + (-6x - x) + (9 + 3 + 4)
g(x) = x² - 7x + 16
Can someone help on 3 vertex, parabola questions real quick?
1. Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.
y = 1/28x^2
x = 1/28y^2
-28y = x^2
y^2 = 14x
2. Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -4).
y = -1/4x^2
y^2 = -4x
y^2 = -16x
y = -1/16x^2
3. Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.
y = -1/9x^2
y^2 = -36x
y = -1/36x^2
y^2 = -9x
Answers
Answer:
lol
Step-by-step explanation:
Write and equation of the translated or rotated graph in general form (picture below)
Answers
Answer:
The answer is ellipse; 3x² + y² + 6x - 6y + 3 = 0
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
* 3x² + y² = 9
∵ A = 3 , B = 0 , C = 1
∴ B² - 4 AC = (0)² - 4(3)(1) = -12
∴ B² - 4AC < 0
∴ The graph is ellipse or circle
* If A and C are nonzero, have the same sign, and are not
equal to each other, then the graph is an ellipse.
* If A and C are equal and nonzero and have the same
sign, then the graph is a circle.
∵ A and C have same signs with different values
∴ It is an ellipse
* Now lets study T(-1 , 3), that means the graph will translate
1 unit to the left and 3 units up
∴ x will be (x - -1) = (x + 1) and y will be (y - 3)
* Lets substitute the x by ( x + 1) and y by (y - 3) in the equation
∴ 3(x + 1)² + (y - 3)² = 9
* Use the foil method
∴ 3(x² + 2x + 1) + (y² - 6y + 9) = 9
* Open the brackets
∴ 3x² + 6x + 3 + y² - 6y + 9 = 9
* Collect the like terms
∴ 3x² + y² + 6x - 6y + 12 = 9
∴ 3x² + y² + 6x - 6y + 12 - 9 = 0
∴ 3x² + y² + 6x - 6y + 3 = 0
* The answer is ellipse of equation 3x² + y² + 6x - 6y + 3 = 0
I f(x)= square root x-3 which inequality can be used to find the domain of f(x)
Answers
Answer:
[tex]x\ge3[/tex]
Step-by-step explanation:
The given function is [tex]f(x)=\sqrt{x-3}[/tex].
The domain of this function refers to all values of x, for which the function is defined.
This square root function is defined when the expression under the radical sign is greater or equal to zero.
That is; the domain of the function is [tex]x-3\ge0[/tex]
This implies that [tex]x\ge3[/tex]
Can someone help please?!? ):
Answers
Answer:
5, 6, 11, 17, 28Step-by-step explanation:
[tex]a_1=5,\ a_2=6,\ a_n=a_{n-1}+a_{n-2}\\\\a_3=a_2+a_1\\a_4=a_3+a_2\\a_5=a_4+a_3\\\\\text{first term:}\ 5\\\text{second term:}\ 6\\\text{third term:}\ 6+5=11\\\text{fourth term:}\ 11+6=17\\\text{fifth term:}\ 17+11=28[/tex]
Im on a time limit! could someone help me with this?
Answers
Answer:
B is the answer because the other equations have real numbers
Step-by-step explanation:
Answer:
B is the correct answer
Step-by-step explanation:
What number represents the same amount as 2 hundreds ++plus 14 tens ++plus 3 ones?
Answers
343 is the answer because 14 tens is 1 hundred and 4 tens
The number that represents 2 hundreds, 14 tens, and 3 ones is 343, by adding each place value: 200 + 140 + 3.
Explanation:The student asks how to represent the quantity consisting of 2 hundreds, 14 tens, and 3 ones in a single number.
To solve this, we can convert each quantity to its respective place value in the decimal system and sum them.
Two hundreds is equal to 200 (2 x 100), 14 tens equals 140 (14 x 10), and 3 ones equals 3 (3 x 1).
Adding them together gives us 200 + 140 + 3 = 343.
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 5x − 6y = 3 10x − 12y = 6 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Answers
Final answer:
The system of equations has infinitely many solutions because they represent the same line. The solution can be written in terms of the parameter t as (x, y) = ((3 + 6t)/5, t).
Explanation:
The student's question involves determining the type of solution a system of two linear equations has and finding the solution if it exists. The given system of equations is:
5x - 6y = 3
10x - 12y = 6
Notice that the second equation is just the first equation multiplied by 2. This means the system has infinitely many solutions because the two equations are actually the same line. To find these solutions in terms of a parameter t, we can solve the first equation for x as follows:
Choose t to represent y (i.e., let y = t).
Substitute y = t into the first equation to get 5x - 6t = 3.
Solve for x to find x = (3 + 6t)/5.
Therefore, the solutions to the system can be expressed as (x, y) = ((3 + 6t)/5, t), where t is any real number.
If they are going 12 miles per 1/3 hour . What is the average speed per hour in miles
Answers
Answer:
12 miles per (1/3) hour equals
36 miles per hour
Step-by-step explanation:
If f( x ) = x - 5, then match each of the following.
1 .
-6
2 .
-4
3 .
-5
4 .
3
5 .
0
6 .
-3
f(-1)
f(0)
f(1)
f(2)
f(5)
f(8)
Answers
Answer:
1. f(-1)
2.f(1)
3.f(0)
4.f(8)
5.f(5)
6.f(2)
Step-by-step explanation:
[tex]f(-1)-------------\ \ \ \ -6\\\\f(0)-------------\ \ \ \ \ \ \ -5\\\\f(1)-------------\ \ \ \ \ \ \ -4\\\\f(2)-------------\ \ \ \ \ \ \ -3\\\\f(5)-------------\ \ \ \ \ \ \ \ \ 0\\\\f(8)-------------\ \ \ \ \ \ \ \ \ 3[/tex]
Step-by-step explanation:We are given a function f(x) by:
[tex]f(x)=x-5[/tex]
It is a linear function with positive slope i.e. 1.
Also, now we will calculate the value of the function at different values of x and match the function to it's corresponding value.
a)
[tex]f(-1)[/tex]
[tex]f(-1)=-1-5\\\\i.e.\\\\f(-1)=-6[/tex]
b)
[tex]f(0)[/tex]
Now when x=0 we have:
[tex]f(0)=0-5\\\\i.e.\\\\f(0)=-5[/tex]
c)
[tex]f(1)[/tex]
when x=1
[tex]f(1)=1-5\\\\i.e.\\\\f(1)=-4[/tex]
d)
[tex]f(2)\\\\f(2)=2-5\\\\i.e.\\\\f(2)=-3[/tex]
e)
[tex]f(5)[/tex]
when x=5 we have:
[tex]f(5)=5-5\\\\i.e.\\\\f(5)=0[/tex]
f)
[tex]f(8)[/tex]
Put x=8
[tex]f(8)=8-5\\\\i.e.\\\\f(8)=3[/tex]
The length of an intercepted arc of a central angle of a circle is 4 cm. If the radius of the circle is 5 cm, what is the measurement of the central angle to the nearest whole degree?
A) 35°
B) 41°
C) 46°
D) 50°
Answers
Answer:
C
Step-by-step explanation:
The formula we use here is:
Length of arc = [tex]\frac{\theta}{360}*2\pi r[/tex]
Where
[tex]\theta[/tex] is the central angle
r is the radius
Putting the given information into the formula we can solve for the central angle:
[tex]LengthOfArc=\frac{\theta}{360}*2\pi r\\4=\frac{\theta}{360}*2\pi(5)\\4=\frac{\theta}{360}*10\pi\\\frac{4}{10\pi}=\frac{\theta}{360}\\\theta=\frac{4*360}{10\pi}\\\theta=45.84[/tex]
rounded to nearest degree, we have 46 degree
C is the right answer.
Answer: OPTION C
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
- Use the following formula for calculate the measure fo the central angle:
[tex]\theta=\frac{s}{r}[/tex]
Where s is the arc length and r is the radius.
- Know the lenght of the arc and the radius, you can substitute values.
Therefore, you obtain;
[tex]\theta=\frac{4}{5}=0.8\ radians[/tex]
Convert to degrees:
[tex]\frac{(0.8)(180\°)}{\pi}=45.83\°[/tex]≈46°
a cube has a side length of 4 feet what is the volume of the cube
Answers
Answer:
V=64
Step-by-step explanation:
What you do is go based off the volume formula of a cube which is V=a^3.
You have a side length of 4.
V=4^3.
V=64.
Jimmy is selling used books at a yard sale. A customer buys 9 books at a cost of $0.75 each and pays with a $20.00 bill. Jimmy must determine c, the amount of change in dollars he should give the customer. Which equation represents c? 20-0.75c=9 20-0.75=9c 0.75(9)+c=20 0.75c+9=20
Answers
Answer:
Step-by-step explanation:
You need to multiply .75 and 9 you'll get 6.75 .. then you need to take 20 and subtract 6.75 and you'll get 13.25
Answer:
C is the correct choice.
What is the recursive rule for this geometric sequence?
-64,-16,-4,-1, ...
Enter your answers in the boxes
An= __ •an-1
A1= __
Answers
A1(nilai sebutan pertama)=-64
Answer:
1/4
-64
Step-by-step explanation:
Write an inequality to represent "7 less than the product of a number, n, and 16 is at most 45."
Answers
What is the length of the missing side of the triangle in simplest radical form? The figure is not drawn to scale.
Answers
Answer:
4√34
Step-by-step explanation:
the question asks for the value of the hypotenuse
Applying the Pythagorean equation
a²+b²=c² where a=12cm, b=20cm and c?
substituting values to equation
12²+20²=c²
144+400=c²
544=c²
√544=c
√16 × √34 =c
4×√34
4√34
ANSWER
[tex] 4 \sqrt{34} cm[/tex]
EXPLANATION
The missing side is the hypotenuse of the right triangle.
According to the Pythagoras Theorem, the length of the square of the hypotenuse is equal to the sum of the length of the squares of the two shorter legs.
Let the hypotenuse be x.
Then,
[tex] {x}^{2} = {20}^{2} + {12}^{2} [/tex]
[tex]{x}^{2} = 400 + 144[/tex]
[tex] {x}^{2} = 544[/tex]
Take positive square root of both sides.
[tex]x = \sqrt{544} [/tex]
[tex]x = 4 \sqrt{34} [/tex]
Find sec x if tan^2 x= 1/2
(picture provided)
Answers
Answer: option d.
Step-by-step explanation:
Based on the information given in the problem, you know that:
[tex]tan^2x=\frac{1}{2}[/tex]
You also know that:
[tex]sec^2(x)=tan^2(x)+1[/tex]
Substitute values. Then, you obtain:
[tex]sec^2(x)=\frac{1}{2}+1\\\\sec^2(x)=\frac{3}{2}[/tex]
Apply square root to both sides. Therefore, you obtain:
[tex]\sqrt{sec^2(x)}=\±\sqrt{\frac{3}{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3(2)}}{2}\\\\sec(x)=\±\frac{\sqrt{6}}{2}[/tex]
Answer:
D
Step-by-step explanation: