Answer:
[tex]3\, x + (-1)\, y = 1[/tex].
Step-by-step explanation:
Both the slope of this line and the coordinates of a point on this line are given. Therefore, start by finding the point-slope equation of this line: if the slope of a line in a plane is [tex]m[/tex], and this line goes through a point at [tex](x_{0},\, y_{0})[/tex], the point-slope equation of this line will be [tex](y - y_{0}) = m\, (x - x_{0})[/tex].
The slope of the line in this question is [tex]m = 3[/tex]. It is given that this line goes through the point [tex](2,\, 5)[/tex], where [tex]x_{0} = 2[/tex] and [tex]y_{0} = 5[/tex]. Substitute in these values to find the point-slope equation of this line:
[tex](y - y_{0}) = m\, (x - x_{0})[/tex].
[tex](y - 5) = 3\, (x - 2)[/tex].
Rewrite this point-slope equation in the requested format:
[tex]y - 5 = 3\, x - 6[/tex].
[tex]3\, x - 6 = y - 5[/tex].
[tex]3\, x = y + 1[/tex].
[tex]3\, x - y = 1[/tex].
[tex]3\, x + (-1)\, y = 1[/tex].
Dude my sister posted this one
Answer:
do i need to do the right or wrong answer
im pretty sure that there is 12
Step-by-step explanation:
OPTION ONE GRAGH A GRAGH B OPTION TWO APPERAS TO INCREASE LESSAPPERAS TO INCREASE MOREIS LESSINCREASES MOREINCREASES LESS
To emphasize the slow increase in profits, it would be best for Bradley to use Graph A for his presentation.
Bradley should use this graph for his presentation because the profit appears to increase less on this graph (regardless both graphs show the same information)
7x+19 (less than or equal too) 12
Answer:
x [tex]\leq[/tex] 17/7
Step-by-step explanation:
7x + 19 [tex]\leq[/tex] 12
Is the inequality you are trying to solve.
When solving an inequality, we solve it like a regular equation and do inverse operations by looking at the number and doing the opposite of whatever its operation is. Whatever happens on one side happens to the other. So you would first subtract 19 on both sides.
1. 7x + 19 [tex]\leq[/tex] 12
-19 -19
7x [tex]\leq[/tex] -17
the reason we subtracted was because the opposite operation to addition is subtraction as the number 19 had had a plus sign behind it
--
We would now divide as the operation opposite to multiplication is division and 7x is 7 times x
2. 7x [tex]\leq[/tex] -17
÷7 ÷7
x [tex]\leq[/tex] [tex]\frac{17}{7}[/tex] OR 2 [tex]\frac{3}{7}[/tex]
--
The answer is:
x [tex]\leq[/tex] 17/7
Hope this helped!
Find all of the zeros of this function and use them to sketch a rough graph.
The zeroes of the function f(x) = x⁵ - 8x³ - 9x are x = 0, 3, - 3, i, and - i.
Consider the function,
f(x) = x⁵ - 8x³ - 9x
x⁵ - 8x³ - 9x = x( x⁴ - 8x² - 9 )
Factoring: x⁴ - 8x² - 9
The coefficient of x⁴ is 1, the coefficient of -8x² is - 8, and - 9 is the constant term.
x⁴ - 8x² - 9 = x⁴ - 9x² + x² - 9 = x²( x² - 9 ) + 1( x² - 9 )
x⁴ - 8x² - 9 = ( x² - 9 ) ( x² + 1 )
So,
x⁵ - 8x³ - 9x= 0
x( x⁴ - 8x² - 9 ) = 0
x( x² - 9 ) ( x² + 1 ) = 0
x( x - 3 )( x + 3 ) ( x² + 1 ) = 0
Therefore, the zeroes of the function are:
x = 0, x = 3, x = - 3, and
x² + 1 = 0
x² = - 1
x = ± √( - 1 ) = ± i
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Is 2x-y=44x-2y=6 A Consistent and dependent?
Solution
We are given the two equations
[tex]\begin{gathered} 2x-y=4\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ 4x-2y=6\ldots\ldots\ldots.\ldots\ldots\text{.}(2) \end{gathered}[/tex]Now, equation (1) x 2
[tex]\begin{gathered} 4x-2y=8\ldots\ldots.\ldots\ldots\ldots\ldots\ldots(1) \\ 4x-2y=6\ldots\ldots\ldots\ldots\ldots\ldots.\ldots(2) \end{gathered}[/tex]Equation (1) - equation (2)
[tex]\begin{gathered} (4x-4x)+(-2y-(-2y))=8-6 \\ 0+0=2 \\ 0=2 \end{gathered}[/tex]Which is never possible!
Therefore, the system of equation is NOT consistent.
Note:
Let us also draw the graph of the eqautionm given
Therefore, the system of equation is Inconsistent and Independent
Larissa invested $19,000 in an eleven-year CD giving 7.5% interest, but needed to withdraw $2,500 after four years. If the CD’s penalty for early withdrawal was one year’s worth of interest on the amount withdrawn, how much money did Larissa have when the CD reached maturity, not including the amount she withdrew?
Answer:
$32190
Step-by-step explanation:
19,000 x 1.3 = 24700
24700-2500=22200
22200 x 1.45 = 32190
What line gets the proportionality between y and x of 4/3
Help needed! please help math
The Mercury is 5.745 × 10^9 kilometers closer to the sun.
In this question, we have been given the approximate average distance from the sun to Neptune and Mercury.
Mercury : 5.79 × 10^9 kilometers
Neptune : 4.5 × 10^7 kilometers
We need to find how much Mercury is closer to the sun.
To find the distance by which Mercury is closer to the sun, consider the difference (5.79 × 10^9) - (4.5 × 10^7)
In the above difference the exponents of 10 are different.
So, we consider the 10^7
we write 5.79 × 10^9 as 579 × 10^7
So the difference would be,
(579 × 10^7) - (4.5 × 10^7)
= (579 - 4.5) × 10^7
= 574.5 × 10^7 km
= 5.745 × 10^9 km
Therefore, the Mercury is 5.745 × 10^9 kilometers closer to the sun.
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there is a .9987 probability that a randomly selected 27-year old male lives through a year. a life insurance company charges $154 for insuring that the male will live through the year. if the male does not survive the year, the policy pays out $100,000 as a death benefit
Using probability we know that the expected value of the insurance company is $141.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.So, the expected value of the insurance company:
Probability = 0.9987So, 1.0000 - 0.9987 = 0.0013Now, get the expected value as follows:
E(x) = 0.9987 × 154 + 0.0013(-9987)E(x) = 153.7998 + (-12.9831)E(x) = 153.7998 - 12.9831E(x) = 140.8167Rounding off: $141
Therefore, using probability we know that the expected value of the insurance company is $141.
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The complete question is given below:
There is a .9987 probability that a randomly selected 27-year-old male lives through a year. a life insurance company charges $154 for ensuring that the male will live through the year. if the male does not survive the year, the policy pays out $100,000 as a death benefit.
What is the expected value for the insurance company?
Sorry the picture is a little tight I can't find the value of A and I keep getting the wrong answer which is really frustrating. I think I just need a little assistance.
The slope of the line can be calculated using the points (2,2) and (6,10):
[tex]\begin{gathered} m=\frac{10-2}{6-2} \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]Since the point (a,8) should belong to the same line, the slope should be the same using the points (a,8) and any other point. Since the slope is 2, use the points (a,8) and (2,2):
[tex]\begin{gathered} 2=\frac{8-2}{a-2} \\ =\frac{6}{a-2} \end{gathered}[/tex]We got this expression for a:
[tex]2=\frac{6}{a-2}[/tex]Take the reciprocal of both sides of the equation:
[tex]\frac{1}{2}=\frac{a-2}{6}[/tex]Multiply both sides by 6:
[tex]\begin{gathered} \frac{6}{2}=a-2 \\ \Rightarrow a-2=3 \end{gathered}[/tex]Add 2 to both sides of the equation:
[tex]a=5[/tex]Therefore, a=5.
Find the coordinates of the midpoint of a segment with the given endpoints.C(0,5) and D(-4,-5)
We have the following:
[tex]m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})_{}[/tex]resolving:
[tex]\begin{gathered} m=(\frac{0+(-4)_{}}{2},\frac{5+(-5)_{}}{2})_{} \\ m=(-\frac{4}{2},\frac{0}{2}) \\ m=(-2,0) \end{gathered}[/tex]Therefore, the midpoint is:
[tex]m=(-2,0)[/tex]help me please
thank you
Part (a)
[tex]P(0)=0.7166(0)^2+6.267(0)+1.344 \approx 1.3[/tex]
Part (b)
[tex]P(5)=0.7166(5)^2+6.267(5)+1.344 \approx 50.6[/tex]
Part (c)
[tex]P(10)=0.7166(10)^2+6.267(10)+1.344 \approx 135.7[/tex]
Assume the point (10,20) belongs to the graph of f(x) what point belongs to the graph of y = f( x - 5 )(15,20) (10,25) (5,20) (10,15)
Answer:
(15, 20)
Explanation:
If the point (10,20) belongs to the graph of f(x), a function that satisfies this point for example could be:
[tex]f(x)=2x[/tex]When x is replaced with x-5, we have:
[tex]\begin{gathered} f(x-5)=2(x-5) \\ =2x-10 \end{gathered}[/tex]Therefore, when x=15
[tex]\begin{gathered} f(x-5)=2(15)-10 \\ =30-10 \\ =20 \end{gathered}[/tex]A point that belongs to the graph of y = f(x-5) is (15, 20).
You can make 8 pancakes with 5g of butter. How much butter do you need for 12 pancakes.
Determine the constant of proportionality for the relationship.
p equals 2 over 150
p = 0.0133
p = 75
p = 150
The constant of proportionality for the relationship is p = 75.
How to express proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
In other words, a proportional relationship is one in which two quantities vary directly with each other.
It can be represented as follows:
y = px
where
p = constant of proportionalityx and y are the variablesTherefore, when we are given the variables the constant of proportionality can be found as follows:
where
y = 150
x = 2
p = y / x
p = 150 / 2
Therefore,
p = 75
Complete question: Determine the constant of proportionality for the relationship: y = px where y = 150 and x = 2
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The table shows Mr. Blackwell's total earnings as a car salesman for different sale amounts.
Graph the points on the coordinate plane and connect them with a straight line.
A graph of the points on the coordinate plane with a straight line is shown in the image attached below. An equation in slope-intercept to represent the relationship is y = 125x + 500.
How to calculate the slope of a line?In order to determine the equation of this line in slope-intercept, we would first of all calculate its slope. Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope, m = (3,000 - 1,750)/(20 - 10)
Slope, m = 1,250/10
Slope, m = 125.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.c represents the intercept.At point (10, 1,750), we have;
y - 1,750 = 125(x - 10)
y - 1,750 = 125x - 1,250
y = 125x - 1,250 + 1,750
y = 125x + 500
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Answer:
Step-by-step explanation:
3k-18 written as a product of 3
The answer is 6
If you divide 18 by 3 it's 6
Joe has 3/4 cup of paint in a container. He uses 1/3 cup on a project and then adds another 1/2 cup. How much paint does he have now?
Answer:
Step-by-step explanation:
The cup of paint he has now is 11/12.
What is the amount of paint he has now?We are basically going to add or subtract the quantity of cup added or used respectively.
Initially, he has 3/4 cup of paint.
He uses 1/3 cup out of the 3/4 cup of paint, so we subtract 1/3 from 3/4:
= 3/4 - 1/3 = 5/12
He adds another 1/2 cup, so we add 1/2 to what we have left previously (5/12):
= 5/12 + 1/2 = 11/12
Therefore, the amount of paint he has now is 11/12 cup
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A bookstore sells 6 books for $82.50. Which table represents the relationship
between number of books and the total price?
Answer: A
Step-by-step explanation: to find the base price, you would do 82.5 to give you a rate of 0.0727 (repeating) book per dollar. then if you do that with 7 and 8 in the same table, t gives you the same rate so A would be the answer.
Answer:
A
Step-by-step explanation:
We don't actually need to do any math to figure this out. We can use process of elimination and logical thinking.
we know it's not B because the prices are too close to each other, there is also the fact that 3 books should cost half of 82.50, and 15.75 isn't half of 82.50.
it's not D because 21 books cannot cost 33.75 dollars if 6 books cost 82.50.
it's not c because 12 books should be double the cost of 82.50, which it isn't.
therefore it must be A
hope this helps :D
A solid figure is composed of rectangular prism and a right triangular prism. The figure and some of its dimensions are sown in this diagram.
Whats the volume of the figure? (5 ft, 5ft, 2 ft, 4 ft, and 7ft.)
Answer:
volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length.
Step-by-step explanation:
Last semester, Jim earned an A in his 4-credit MATH 128 class, a B+ in his 3-credit ENG 152 class, a C- is his 2-credit COM 210 class, and a A- in his 5-credit HIST 151 class. What was his GPA for the semester? Be sure to use the following grade values in your calculation.
Jim's GPA for the last semester was 3.41.
What is the GPA?The Grade Point Average (GPA) is the summary of academic achievement in an academic period (semester).
GPA is computed as course unit value multiplied by grade points, divided by the sum of course units.
The Grade Point Average (GPA) may also be described as the cumulative GPA, that is, the sum of the grade points divided by the sum of the units.
Determining a student's GPA helps the school administrators to ascertain the student's academic progress, verifying areas for further improvement.
Class Course Grade Credit Hours Grade Value Total Grade
MATH 128 A 4 4.0 16 (4 x 4)
ENG 152 B+ 3 3.3 9.9 (3 x 3.3)
COM 210 C- 2 1.7 3.4 (2 x 1.7)
HIST 151 A- 5 3.7 18.5 (5 x 3.7)
Total 14 47.8
GPA = 3.41 (47.8/14)
Thus, for last semester, Jim's GPA was 3.41.
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i need help with mat equation
[tex]\qquad \textit{power of a complex number} \\\\\ [\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)] \\\\[-0.35em] ~\dotfill\\\\ z=2[\cos(104^o)~~ + ~~i\sin(104^o)] \\\\\\ z^2=2^2[\cos(2\cdot 104^o)~~ + ~~i\sin(2\cdot 104^o)] \\\\\\ z^2=\underset{polar}{4[\cos(208^o)~~ + ~~i\sin(208^o)]}~\hfill \implies ~\hfill z^2\approx \underset{rectangular}{\stackrel{4\cos(208^o)}{-3.532}~~,~~\stackrel{4\sin(208^o)}{-1.878} i}[/tex]
calculate the the population standard division of the data set 5,4,5,3 to 6 round to the nearest hundred
Do you have a picture of your question?
Which of the following is the simplified form of the expression 15z-9-3z-z+8?
Answer:
11z - 1
Step-by-step explanation:
Which graph best represents this system of equations and its solution? 2x = 6 − y 5x − 4y = 28
18 red marbles; 6 to 9
27 blue marbles are there in the bag.
How to find the number of blue marbles?Given,
A bag contains 18 red marbles.
The ratio of red marbles to blue marbles is 6:9
Solution:
From the given ratio of 6:9,
If 6 part is red marble, then 1 part = 18/6 =3
Therefore,
The number of blue marbles is 9*3 = 27
Thus, there are 27 blue marbles in the bag.
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Does the point(1, 1)satisfy the in equality 11x + 8y ≥ 20?
Answer:
Step-by-step explanation:
Find the x -intercept and the y-intercept of the graph of the equation.-x+2 y=-7Good evening I am having a hard time getting this math is there any way you can help me?
Answer:
• x-intercept =7
,• y-intercept = -3.5
Explanation:
Given the linear equation
[tex]-x+2y=-7[/tex]x-intercept
The x-intercept is the value where the line crosses the x-axis.
We calculate this by setting y=0
[tex]\begin{gathered} \text{When y=0} \\ -x+2y=-7 \\ -x+2(0)=-7 \\ -x=-7 \\ x=7 \end{gathered}[/tex]The x-intercept is 7.
y-intercept
The y-intercept is the value where the line crosses the y-axis.
We calculate this by setting x=0
[tex]\begin{gathered} \text{When x=0} \\ -x+2y=-7 \\ -0+2y=-7 \\ 2y=-7 \\ Divide\text{ both sides by 2} \\ \frac{2y}{2}=-\frac{7}{2} \\ y=-3.5 \end{gathered}[/tex]The y-intercept is -3.5.
Josh opens a savings account with a $300 deposit. He won't add or withdrawal any money. The
account earns 2% simple interest. What is the total amount that Josh will have on his savings at
the end of 5 years?
O $6
O $306
O $30
O $330
The most appropriate choice for simple interest will be given by-'
Amount of money Josh have at the end of 5 years = $330
Fourth option is correct
What is simple interest?
Simple interest ( SI) is the interest earned on a certain principal at a certain rate over a certain period of time,
If P is the principal, rate is r %, time is t years,
SI = [tex]\frac{p \times r \times t}{100}[/tex]
Adding Principal and simple interest will give the amount
Here,
Principal deposited by Josh= $300
Rate of interest = 2%
Time = 5 years
Simple interest = [tex]\frac{300 \times 2 \times 5}{100}\\[/tex]
= $30
Amount of money Josh have at the end of 5 years = $(300 + 30)
= $330
Fourth option is correct
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Graph they given functions FNG in the same rectangular coordinate system describe the graph of G is related to the graph of F
Functions given:
[tex]f(x)=4x[/tex][tex]g(x)=4x-4[/tex]Using a graphing calculator, we can find the graph of both functions:
The red line is representing f(x) graphically, while the blue line is representing g(x) graphically.
As they have the same slope, then f(x) is parallel to g(x).
Answer:
The functions are parallel.
