Answer:
(3, -5) or x=3, y=-5
Step-by-step explanation:
Systems of Equations:In a systems of equation, we're looking for what pair of (x, y) values make both equations true. When a pair of (x, y) makes an equation true, that just means it's on the line of the graph. So a pair of (x, y) values that makes both equations true, is simply when both lines intersect.
Solving Systems of Equations:
There are multiple methods to solve a systems of equation including: elimination, substitution, and graphing.
Each way has their advantages, and I'll show to to apply substitution and elimination
Elimination Method:In this method we want to manipulate one of equations (or possibly both) so that they each have a variable with the "same coefficient" but different sign (one positive, one negative).
In the equations given, you may notice that the "y" variables each have the same coefficient, so we could multiply either of the equations by negative one, so one has positive y and another has negative y.
The reason we want the equations set up in this way, is so that we can add the equations which results in one of the variables being "eliminated" so that we can solve for a single value for the other variable.
So we start with:
[tex]x+y=-2\\2x+y=1[/tex]
let's multiply the top equation by -1 (remember to apply this to both sides so you don't actually change the equation)
[tex]-(x+y)=-(-2)\implies -x-y=2[/tex]
So now from here we have the two equations
[tex]-x-y=2\\2x+y=1[/tex]
If we add the two equations we get the following
[tex](-x+2x)+(-y+y)=(2+1)[/tex]
Notice how the -y and y cancel each other out? This is the entire point of the elimination method, so now we can solve for x
[tex]x=3[/tex]
This actually simplifies in our favor since -x + 2x = x, and the right side is just some constant, so we don't need to manipulate the equation anymore to solve for x.
Now that we know what the x-value is, we can plug this into either equation to solve for y. For simplicity I'll use the x + y = -2 equation.
[tex]3+y=-2\\y=-2-3\\y=-5[/tex]
So we know the solution is (3, -5) or [tex]x=3,\ y=-5[/tex]
Substitution MethodThe substitution method has the same goal as the elimination method, that is, get a one-variable equation so we can solve for one value. In this method, we want to define one variable in terms of the other variable, that way we can substitute this into the other equation, giving us a new equation with only one variable.
So let's just start with the top equation:
[tex]x+y=-2[/tex]
From here we can define "y" in terms of x, by subtracting x from both sides.
[tex]y=-2-x[/tex]
Now let's look at our other equation
[tex]2x+y=1[/tex]
Notice how it has a y variable, well we have one way of defining it: y = -2 - x. If we plug this into the bottom equation, now we only have x terms, giving us a one-variable equation.
[tex]2x+(-2-x)=1[/tex]
Now let's add 2 to both sides to cancel out the -2, and simplify 2x - x
[tex]x=3[/tex]
From here we essentially do the same thinkg we did in elimination method, except it may be a bit easier since we already have "y" solved for, we just need an x-value, which we now have!
[tex]y=-2-x\\\text{we know that x = 3}\\y=-2-(3)\\y=-5[/tex]
so now we have our solution: [tex](3, -5)\text{ or }x=-3, y=-5[/tex]
If cos of Ф = 2/5, find sin Ф/2 and cos Ф/2. Assume the angles are in the 1st quartile
a. The trigonometric ratio sin(Ф/2) = +√(3/10)
b. The trigonometric ratio cos(Ф/2) = +√(7/10)
What are trigonometric ratio?Trigonometric ratios are the ratios of the sides of a right-angled triangle. They include
sinФ, cosФ, tanФ etcwhere Ф is the angle between the sides
a. How to find the trigonometric ratio sin(Ф/2)?Given that cosФ = 2/5, we use the trigonometric identity
cosФ = 1 - 2sin²(Ф/2)
Making sin(Ф/2) subject of the formula, we have
sin(Ф/2) = ±√(1 - cosФ)/2
So, susbstituting the value of cosФ = 2/5 into the equation, we have
sin(Ф/2) = ±√(1 - cosФ)/2
sin(Ф/2) = ±√(1 - 2/5)/2
sin(Ф/2) = ±√[(5 - 2)/5]/2
sin(Ф/2) = ±√(3/[5 × 2])
sin(Ф/2) = ±√(3/10)
Since Ф is in the first quartile, sin(Ф/2) = +√(3/10)
b. How to find the trigonometric ratio sin(Ф/2)?Given that cosФ = 2/5, we use the trigonometric identity
cosФ = 2coss²(Ф/2) - 1
Making sin(Ф/2) subject of the formula, we have
coss(Ф/2) = ±√(1 + cosФ)/2
So, susbstituting the value of cosФ = 2/5 into the equation, we have
coss(Ф/2) = ±√(1 + cosФ)/2
cos(Ф/2) = ±√(1 + 2/5)/2
cos(Ф/2) = ±√[(5 + 2)/5]/2
cos(Ф/2) = ±√(7/[5 × 2])
cos(Ф/2) = ±√(7/10)
Since Ф is in the first quartile, cos(Ф/2) = +√(7/10)
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638 divided by 34 long division
Answer:
18 R26
Step-by-step explanation:
[tex]\ \ \ \ \ \ \,\,\, 18 \textrm{ R}26\\{34\ \overline{\smash{)}\ 638}}\\\textrm{ } \ \ \ \underline{-34}\\\textrm{ } \ \ \ \ \ \, 298\\\textrm{ } \: \, \ \ \underline{-272}\\\textrm{ } \ \ \ \ \ \ \: \, 26[/tex]
The lines passing through which pairs of points have a positive y-intercept? Select all that apply. A (- 3, 10) and (1, 2) B (- 1, 6) and (0, 2) C (1, 2) and (3, 4) D (0, - 4) and (3, - 2) E (3, 1) and (5, 2)
The lines passing through points A (- 3, 10) and (1, 2) , B (- 1, 6) and (0, 2) , and C (1, 2) and (3, 4) has positive y-intercept.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
As we know, the slope formula is:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
A (- 3, 10) and (1, 2)
m = (2-10)/(1+3)
m = -8/4 = -2
y = mx + c
y = -2x + c
Plug (- 3, 10)
10 = -2(-3) + c
c = 10 - 6 = 4 (positive y-intercept)
Similarly, for the other points:
B (- 1, 6) and (0, 2)
y = -4x + 2 (positive y-intercept)
C (1, 2) and (3, 4)
y = x + 1 (positive y-intercept)
D (0, - 4) and (3, - 2)
y = 0.667x - 4 (negative y-intercept)
E (3, 1) and (5, 2)
y = 0.5x -0.5 (negative y-intercept)
Thus, the lines passing through points A (- 3, 10) and (1, 2) , B (- 1, 6) and (0, 2) , and C (1, 2) and (3, 4) has positive y-intercept.
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can someone help me please?
let's consider two numbers for this case, hmmm say
x = 13
y = 17
so yes, 13 < 17
also true, 13 + 2 < 17 + 2
also true that 2(13) < 2(17)
now, -13 < -17? well, not quite
reason being, the on the negative side of the number line, the closer to 0, the larger the number, for that case, -1 is much much larger than -1,000,000.
What is the probability that a point chosen at random in the triangle is also in the blue square?
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Divide the area of the square by the area of the triangle.
[tex]\dfrac{A_{\textrm{square}}}{A_{\textrm{triangle}}} = \dfrac{3^2}{(9\times 6)\div 2}[/tex]
And simplify.
[tex]= \dfrac{9}{54 \div 2}[/tex]
[tex]= \dfrac{9}{27}[/tex]
[tex]=\dfrac{1}{3}[/tex]
Avery earned a score of 310 on Exam A that had a mean of 350 and a standard deviation of 20. She is about to take Exam B that has a mean of 550 and a standard deviation of 40. How well must Avery score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally disturbed.
The score that Avery must get on Exam B is given as follows:
470.
What is the z-score formula?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.
For exam A, the mean and the standard deviation are given as follows:
[tex]\mu = 350, \sigma = 20[/tex]
She scored 310, hence the z-score of her grade is given as follows:
Z = (310 - 350)/20
Z = -2.
For exam B, the mean and the standard deviation are given as follows:
[tex]\mu = 550, \sigma = 40[/tex]
To do as well as on exam A, she needs a z-score of -2, hence the grade X is obtained as follows:
-2 = (X - 550)/40
X - 550 = -80
X = 470.
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I need your help please with this problem of math.
(14+8²)÷2-10
Answer: 29
Step-by-step explanation: your welcome
2x^2 – 4x + 3 = 0 Solve using the quadratic formula
Please help i tried twice im so confused, nobody has the answer.
Answer: d = -8
Step-by-step explanation: look at the attached link
A college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.
x > 0 and y > 0
0 < x ≤ 100 and 0 < y ≤ 400
0 < x ≤ 100 and y > 400
0 < x and y < 100
The constraints to represent the incoming students at the college are -
0 < x ≤ 100 and 0 < y ≤ 400
What is an Inequality? What is a expression? What is a mathematical equation?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have a college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students
Now -
[x] = the number of out-of-state students
[y] = the number in-state students
y = 4x
0 < x ≤ 100
and the range of [y] will be -
0 < y ≤ (4 x 100)
0 < y ≤ 400
Therefore, the constraints to represent the incoming students at the college are -
0 < x ≤ 100 and 0 < y ≤ 400
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A coordinator will select 7 songs from a list of 11 songs to compose an event's musical entertainment lineup. How many different lineups are possible?
Answer:
Step-by-step explanation:
= 604800
What is the solution to the equation?
1/2n+3=6
n = 18
n = 9
n = 6
n=3/2
start by plugging them in to thr problem
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
Write F ∩ H and F ∩ H using interval notation. If the set is empty, write ∅.
The final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
What is the interval notation?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.
We have,
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
F is the set of all real numbers that are less than or equal to 4. H is the set of real numbers greater than 7.
F U H is the union (or combination) of the two sets, so it is the set of all real numbers that are less than equal to 3 or greater than 6:
F ∩ H is the set of real numbers that are in both sets; but since F is less than or equal to 4 and H is greater than 7, there are no numbers that are in both sets. Hence the answer is the empty set, Ø:
F ∩ H = Ø
F ∩ H = [7, 4]
F ∪ H = [-∞, ∞]
Hence, the final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
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What is the rate of change of the function?
Enter your answer as a number, like this: 42
Answer:
-2
Step-by-step explanation:
1. Identify two points with integer (not fraction or decimal) coordinates:
Ex: (0,5) and (3,-1)
2. subtract the y-coordinates: -1-5 = -6
and the x- coordinates (IN THE SAME ORDER): 3-0 = 3
3. divide the difference in y (-6) by the difference in x (3): -6/3 = -2
Solve the equation without using a calculator
[tex]\bf\\x^{x^2-2x+1}=2x+1[/tex]
The value of the variable x in the equation xˣ²⁻²ˣ⁺¹ = 2x + 1 is 1 + √2
Exponential EquationsAn equation is a mathematical statement that shows that two mathematical expressions are equal.
An equation combines two expressions connected by an equal sign. These two expressions on either side of the equals sign are called the “left-hand side” and “right-hand side” of the equation. We generally assume the right-hand side of an equation is zero.
Basically, an equation is a statement that equate or says two expressions are equal to one another.
The problem given may be assumed as an exponential equation
xˣ²⁻²ˣ⁺¹ = 2x + 1
Solving for x by isolating the variable;
x = 1 + √2
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Answer:
x = 1 ±√2
Step-by-step explanation:
You want to solve the exponential equation ...
x^(x² -2x +1) = 2x +1
without using a calculator.
GuessThere are no algebraic methods for solving such an equation.
We can solve quadratic equations, so we can guess that the exponent of x is 2:
x² -2x +1 = 2
x² -2x -1 = 0
Using 2 as an exponent, the given equation becomes ...
x² = 2x +1 . . . . . . . exponent on the left is 2
x² -2x -1 = 0
That is, the exponent being 2 is consistent with the requirements on x.
QuadraticThe solution to the quadratic can be found using the quadratic formula:
x² -2x -1 = 0
x = (-(-2) ±√((-2)² -4(1)(-1))/(2(1)) = (2±2√2)/2
x = 1±√2
Either of these values will make the exponent of x be 2, so both are solutions to the equation. The negative solution is not found by the graphing calculator (attached).
sorority has 35 members, 25 of whom are full members and 10 are pledges. Two persons are selected at random from the membership list of the sorority. Find the requested probabilities The second person selected is a pledge if the first person selected was a full member.
(a) The probability that the first person selected is a pledge is; 10/35
(b) The probability that the first person selected is not a pledge is; 25/35
(c) The probability that the second person selected is a pledge if the first person selected was also a pledge is; 9/34
How to find the probability of selection?We are given;
Total number of members in the Sorority = 35
Number of full members = 25
Number of members that are pledges = 10
Formula for probability is;
Probability = Number of Favorable Outcomes / Total Number of Outcomes.
1) Probability that the first person selected is a pledge = number of pledges/total number of members = 10/35
2) Probability that the first person selected is not a pledge = 1 - (Probability that the first person selected is a pledge)
= 1 - 10/35 = 25/35
3) If the first person selected was also a pledge, then for the second pledge, one pledge is out, so we have 9 pledges in 34 people.
P = number of pledges / total = 9/34
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Complete question is;
A sorority has 35 members, 25 of whom are full members and 10 are pledges. Two persons are selected at random from the membership list of the sorority. Find the requested probabilities. (Enter the probabilities as fractions.)
(a) The first person selected is a pledge.
(b) The first person selected is not a pledge.
(c) The second person selected is a pledge if the first person selected was also a pledge.
20. ASSESS REASONABLENESS Your friend says that when the pool in Exercise 19 is more than 8 feet deep, you will win the race. Is your friend's claim reasonable? Explain your reasoning. pls hurry
Answer:
Step-by-step explanation:
No because the deepness of an pool doesnt affect how fast you will swim during the race
No because the deepness of an pool doesnt affect how fast you will swim during the race.
What is the depth?
Depth refers to a type of vertical distance, where vertical distance is the difference between two vertical positions. One of the most common everyday examples of depth is its use in reference to water.
Here given that,
Your friend says that when the pool in Exercise [tex]19[/tex] is more than [tex]8[/tex] feet deep, you will win the race.
Our swimming speed will never change it does not depend on the depth of the pool.
Hence, depth of the pool does not effect the speed of swimmer.
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What two ways could you describe the shape pattern below?
ΔΟΔΟΔΟ
Answer:
The pattern is a repeated triangle and circle.
So, the next shape would be a triangle and a circle.
Step-by-step explanation:
5. Gary has walked 5 miles
already and continues
walking at a pace of 2
miles per hour. Write an
expression to represent
how many miles he has
walked.
Answer:210 miles
Step-by-step explanation:Gary walking in opposite directions will calculate how long it takes for him to be a given distance apart.
Four scenarios of statistical studies are given below. Decide which study uses a sample statistic.
Based on the four scenarios of statistical studies given, a study which uses a sample statistic is: D. As part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election, 39 said yes.
What is a sample statistic?In Mathematics and Statistics, a sample statistic can be defined as a small piece of statistical information that is obtained by a researcher or scientist from the sample of a population.
This ultimately implies that, a sample statistic simply refers to any numerical quantity (figure) or data that is generated from the sample of a population by a researcher or scientist.
In this context, we can reasonably infer and logically deduce that 84 of Kaisa's classmates represent the sample of the total population while the 39 classmates who answered yes represent the sample statistic.
In conclusion, the statistical study that was conducted by Kaisa is a study that represent the sample statistic.
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Complete Question:
Four scenarios of statistical studies are given below. Decide which study uses a population parameter.
The average finish time for the Ironman, Kona was 11:32 for the 1883 finishers, with an average swim time of 1:14, an average bike time time of 4:14.
Lakeside Family Dentistry reported that 6 of the 15 patients who came in for a regular cleaning one day had at least one cavity.
Of 351 dog owners who were surveyed, 70 reported owning two dogs.
As part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election, 39 said yes.
here is the image of triangle ABC and its dilation using Center D and scale factor 2. Why is B'C' on the same line as its corresponing side segment BC
Since only the lengths increase by scale factor, B'C' on the same line as its corresponding side segment BC .
What is the Dilation?
Math definition of dilation Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.
The following are the properties of dilation of the triangle:
1)measures of the angles will not change
2)The sides of the image of the triangle are multiplied by the scale factor 2.
So,
A'B'=2AB
B'C'=2BC
A'C'=2AC
Since only the lengths increase by scale factor, B'C' on the same line as its corresponding side segment BC .
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pythagorean theorem number search activity
Step-by-step explanation:
1). Red
x² = 98² - 44² = 9604 - 1936 = 7668
x =√7668 = 6√213
2) orange
X² = 31²+30² = 1861
x = √1861
How many solutions does the system of equations have?
Answer: IT can have simultaneous solutions
Step-by-step explanation:
You need to go through the cubic units and count them to get the answer
Answer:
2 solutions
Step-by-step explanation:
The solutions of the system of equations are the points of intersection of the two graphs, the red line and the blue parabola. Since there are two points of intersection, there are 2 solutions.
Answer: 2 solutions
Levi invested $8,500 in an
account paying an interest rate of 3.4%
compounded continuously. Assuming no deposits or withdrawals are
made, how much money, to the nearest ten dollars, would be in the
account after 18 years?
The amount of money after 18 years when the interest is compounded continuously is $15725.
What is compound interest?The process of calculating interest and reinvesting it in an account's balance over an infinite number of periods is known as continuous compounding.
Given that Levi invested $8,500 in an account paying an interest rate of 3.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars?
The compound interest will be calculated as
[tex]P(t) = P_oe^{rt}[/tex]
[tex]P(t) = 8500\times e^{0.034\times 18}[/tex]
P(t) = 8500 x 1.85
P(t) = $15725
Therefore, the amount of money after 18 years when the interest is compounded continuously is $15725.
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Answer:15670
Step-by-step explanation:
y = 3x + 2
y = 2x + 2
One solution
No solution
Infinite solutions
Answer:
The answer would be One solution.
Step-by-step explanation:
Solving by substitution.y=3x+2;y=2x+2
Step: Solve y=3x+2 for y:
y=3x+2
Step: Substitute 3x+2 for y in y=2x+2:
y=2x+2
3x+2=2x+2
3x+2+−2x=2x+2+−2x(Add -2x to both sides)
x+2=2
x+2+−2=2+−2(Add -2 to both sides)
x=0
Step: Substitute 0 for x in y=3x+2:
y=3x+2
y=(3)(0)+2
y=2(Simplify both sides of the equation)
Answer:
x=0 and y=2
If it was no solution you would not be able to solve. If it was infinite then there would be infinite solutions, but there is not so One Solution is the answer.
Find the missing angle:
RPQ:________
The missing angle RPQ between the intersected chord is 115 degrees.
How to find the angle between intersected chord?The intersecting chords theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle
If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore,
∠RPQ = 1 / 2 (arc angle RQ + arc angle SA)
arc angle RQ = 175 degrees
arc angle SA = 55 degrees
Hence,
∠RPQ = 1 / 2 (175 + 55)
∠RPQ = 1 / 2 (230)
∠RPQ = 115 degrees.
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How do you simplify the square ro
ot of 180 and how do you know that it is in simplest form?
Step-by-step explanation:
[tex] \sqrt{180 } = 6 \sqrt{5} [/tex]
because 6² = 36 and 36×5 = 180
I don't think there's any simple way to do it
Divide €45 between Sharon and Louise in the ratio of 4: 5.
Answer:
€20 for Sharon
€25 for Louise
Step-by-step explanation:
For a ratio of 4:5, you add 4+5 = 9.
You need 4 out of 9 parts for Sharon, and 5 out of 9 parts for Louise.
4/9 × €45 = €20 for Sharon
5/9 × €45 = €25 for Louise
I really need help on this!
The common ratio of given geometric sequence is r = - (1/2)
What is geometric sequence?A geometric sequence is a set of integers that follows a pattern where each term is multiplied by a fixed number called the common ratio, or r, to find the following term.
solution:
a3 = - (3/8)
a8 = 3/256
common ratio = a3 / a8
= - (3/8) / 3/256
common ratio = - (1/32)
a8/a3 = (ar^7) / (ar^2)
= r^5
r^5 = - (1/32)
r = - (1/2)
Hence the common ratio of given geometric sequence is r = - (1/2)
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What is the r2 value for the following data to three decimal places?
0.783 0.278 0.611 0.885
Answer:
0.783
Step-by-step explanation: got it right :)
help meeeeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee
Answer:
The quickest answer is to take the number 72 and divide it by the rate of interest. In this case, it would take approximately 72/6, or 12 years to double.
Step-by-step explanation: