Calculate the coordinates of the points where the line y = 1 - 2x cuts the curve x^2+ y^2 = 2
Answers
Answer:
[tex](1, -1)[/tex] and [tex](-\frac{1}{5}, \frac{7}{5})[/tex]
In decimal form this would be (1, -1) and (-0.2, 1.4)
Step-by-step explanation:
Basically here we are trying to solve a system of 2 equations. The first one is a straight line and the second is a circle. This can be done graphically and graph is attached. There will be two points where the line cuts the circle so two solution sets
The equations are
Line Equation [tex]y = 1 - 2x[/tex] (1) and
Circle Equation [tex]x^2+ y^2 = 2[/tex] (2)
[tex]y=1-2x[/tex]
Plug this value of y into the second equation for the circle
[tex]x^2 + (1-2x)^2= 2[/tex]
Apply the perfect squares formula [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]
[tex](1-2x)^2 = 1^2-2\cdot \:1\cdot \:2x+\left(2x\right)^2\\= 1-4x+4x^2\\\\[/tex]
So equation (2) becomes
[tex]1-4x+4x^2 +x^2 = 2 \\\\\\5x^2 -4x - 1 = 0[/tex]
Solve using the quadratic formula
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a is the coefficient of x ², b is the coefficient of x and c is the constant
So
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)}}{2\cdot \:5}[/tex]
Now,
[tex]\sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)} = \sqrt{\left(-4\right)^2+4\cdot \:5\cdot \:1}[/tex]
= [tex]\sqrt{16+20} = \sqrt{36} = 6[/tex]
Therefore
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \:6}{2\cdot \:5}[/tex]
[tex]x_1=\frac{-\left(-4\right)+6}{2\cdot \:5}[/tex] = [tex]\frac{-\left(-4\right)+6}{2\cdot \:5} =[/tex] [tex]\frac{10}{2\cdot \:5}[/tex] [tex]= 1[/tex]
[tex]x_2 = \frac{-\left(-4\right)-6}{2\cdot \:5}[/tex] [tex]= \frac{4-6}{2\cdot \:5}[/tex] = [tex]-\frac{1}{5}[/tex]
To find corresponding values for [tex]y_1 y_2[/tex] plug these values of [tex]x_1, x_2[/tex] into the line equation
[tex]y_1 = 1- 2(1) = -1[/tex]
[tex]y_2 = 1 - 2(-\frac{1}{5}) = 1 + \frac{2}{5} = \frac{7}{5}[/tex]
So the two points of intersection are
[tex](1, -1)[/tex] and ([tex](-\frac{1}{5}, \frac{7}{5})[/tex].
In decimal form this would be (1, -1) and (-0.2, 1.4)
See attached graph
Related Questions
I am thinking of a decimal number less than one. The hundredths digit is four times more than the tenths digit. The sun of the tenths and hundredths digit is 10. What number am I thinking of?
Answers
Answer:
The number would be 0.28.
here, in tenths position is 2 and in hundredths position is 8.
so, 8 = 4 x 2
and 8 + 2 = 10.
Round 468.113 to the nearest tenth.
Answers
Answer:
468.1
Step-by-step explanation:
good luckkk
Answer:
468.1
Step-by-step explanation:
rounding to the nearest tenth
The blue prints (scale drawing) of a new strip mall are 2 feet by 9 feet. The actual strip mall is 200 feet by 900 feet. What is the scale factor from the blue prints to the actual mall?
Answers
The scale factor from the blue prints to the actual mall is 1:100.
How to calculate the value?From the information, the blue prints (scale drawing) of a new strip mall are 2 feet by 9 feet and the actual strip mall is 200 feet by 900 feet.
Therefore, the scale factor from the blue prints to the actual mall will be:
= 200 / 2
= 100
Therefore, the scale factor from the blue prints to the actual mall is 1:100.
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Can Σx² be negative? Why or why not
Answers
A marine biologist collects coral species from the bottom of a coral reef. The biologist swims to depths of 314 meters, 258 meters, and 412 meters below sea level.
A scuba diver holding a speciment on coral is shown.
Question 1
Part A
Represent these depths as rational numbers, in order from shallowest to deepest.
Part B
Graph these depths and their opposites on the number line.
Answers
Answer:
PA The biologist swims to depths of 3 1/4 meters. 2 5/8 meters, and 4 1/2 meters below sea level.
Order the well depths from deepest to shallowest. Strategy. Write the depths as negative numbers . Compare the negative numbers .
Step-by-step explanation:
Which number is rational and a real number, but not an integer?
OA. -5
O B. 9/
517
C. There is no such number.
OD. √
Answers
517 is real because it can be plotted on a number line.
What in math is an integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.Which a real number?
Both rational and irrational numbers are considered to be real numbers. Real numbers include all rational and irrational numbers, including integers (-2, 0, 1), fractions (1/2, 2.5), and the number 3.9/517 is real because it can be plotted on a number line,
Its rational because it can be written as a fraction of 2 integers
But it is not an integer.
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Thor travels 49 miles per hour. How long does it take him to travel 294 miles? Your answer should be in Miles, accurate to at least the nearest tenth.
Answers
Answer: I think it's 6 hours. If you do 294 divided by 49 which will give you 6 which means you traveled 294 miles in 6 hours.
Find the missing number.
Number of toffees
2
Your answer
4
6
8
Number of children
12
X
36
48
5 points
Answers
Answer:
24
Step-by-step explanation:
Each no. of toffee is multiplied by 6 to get the no. of children to have a toffee.
█░█░█ █░█ ▄▀█ ▀█▀ █▀ ▀█ ▄█▄ ▀█ ▀█
▀▄▀▄▀ █▀█ █▀█ ░█░ ▄█ █▄ ░▀░ █▄ ░▄
Answers
Answer: 54
Step-by-step explanation:
52 + 2 = 54
Write the following expression using a single exponent.
5^0 x 5^5
Answers
Way 1: because if 2^a*2^b then it equals 2^(a+b) making sure that the bases are equal meaning 2
Another way: 5^0 equals one because anything raised to the power zero is one so it literally just says 5^5*1 which equals 5^5
On the last three physics exams a student scored 85, 87, and 91. What score must the student earn on the next exam to have an average of at
Least 90?
Answers
If you want to have an average of at least 90, the score that you need to get in the last exam is at least 97 points.
What score must the student earn on the next exam to have an average of at least 90?
We know that the scores on the first 3 exams are 85, 87, and 91.
If the score in the fourth exam is x, then the average of the 4 exams will be:
(85 + 87 + 91 + x)/4
If we want to have an average of at least 90, then we need to solve:
(85 + 87 + 91 + x)/4 = 90
Solving that for x we will get:
(263 + x) = 90*4
x = 90*4 - 263 = 97
The score that you need to get in the last exam is 97 points.
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It's possible to build a triangle with side lengths of 3,3,and 9
Answers
It's not possible to build a triangle with side lengths of 3,3,and 9.
How to illustrate the information?It should be noted that to compute a triangle, the addition of the shortest sides must be longer than the longest side.
In this case, 3 + 3 = 6
But the longest side is 9 and it's longer than 6.
Therefore, it's not possible to build a triangle with side lengths of 3,3,and 9.
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It's possible to build a triangle with side lengths of 3,3,and 9
True or false?6. Solve the inequality.
-10 ≤ 2x-4<8
о
-8
-3
-3≤x<6
-1
Answers
Answer:
Step-by-step explanation:
(2ax2a)+(3bx3b)-(2x2ax3b)
Answers
Step- by-step
(2a*2a)+(3b*3b)-(2*2a*3b)
Remove parenthese
2a(2a) + 3b(3b) - (2(2a) (3b))
4a^2 + 9b^2 - (4a•(3b))
4a^2 + 9b^2 - 12ab
6 + 4|2x + 6| = 14
Solve for x
Answers
Answer:
x = -1
Step-by-step explanation:
6+4 = 10
14-10 = 4
2x + 6 = 4
2x (-2) = -2
-2 + 6 = 4
Find the values of x and y.
PLEASE HELP ME I DONT GET THIS
Answers
What is -(9) fourth power
Answers
Answer:-9 to the fourth power is -6561
Step-by-step explanation: You would have to do 9 times 9 times 9 times 9 and that would equal 6561 then you would add the negative.So therefore the answer is -6561.
Please give brainliest if right.
Answer:
-6561
Step-by-step explanation:
[tex]-9^4 = -9 \times -9 \times -9 \times -9 = -6561[/tex]
Choose all expressions that are equal to 16.02. #1 16 +0.02, #2 3.42 +8+4.6, #3 16.01 +1, #4 12.06 +3.14, #5 7.36 +8.66
Answers
Expression number #1, #2 and #5 are equal to 16.02 in the given question.
As per the question statement, we have to choose all expressions that are equal to 16.02
The options are
[tex]16+0.02[/tex][tex]3.42+8+4.6[/tex][tex]16.01 +1[/tex][tex]12.06+3.14[/tex][tex]7.36+8.66[/tex]Lets verify #1
[tex]16+0.02 = 16.02[/tex]
Hence verified.
Lets verify #2
[tex]3.42+8+4.6=16.02[/tex]
Hence verified
#3
[tex]16.01+1=17.01\neq 16.02[/tex]
#4
[tex]12.06+3.14=15.2\neq 16.02[/tex]
#5
[tex]7.36 +8.66=16.02[/tex]
Hence verified
Therefore from the above, conclusion can be made that Expression number #1, #2 and #5 are equal to 16.02 in the given question.
Algebraic expressions: In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)To learn more about number system, click on the link given below:
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Which phrase best completes the diagram?
Globalization
?
A. More unequal distribution of natural resources
B. Improved incomes for poor people in all countries
C. Decreased competition for small businesses
OD. Decreased demand for natural resources
Answers
The phrase that best relates to the term "Globalization" is "Improved incomes for poor people in all countries".
As per the question statement, we are provided with the term of "Globalization" and we are required to match it with the best possible phrase from the four options provided.
Option (A) is "More unequal distribution of natural resources" which is incorrect because unequal distribution does not depend on globalization but on the size of the company and their effects on the environment.
Option (C) is "Decreased competition for small businesses" which is incorrect because this will increase the competition for small business.
Option (D) is "Decreased demand for natural resources" which is incorrect, since globalization speeds up the exchange of capital-labor production which requires more natural resources rather than their decrease.
Option (B) is "Improved incomes for poor people in all countries" which is the correct match, because globalization's main character is economic growth which directly affects the totally population of a country including the poor as the country becomes open to trade and then tends to work faster than the time when it was not open to trade, and this creates job opportunity for the people and helps in increasing the living standard of the people.
Hence, the best possible match to the term "Globalization" is "Improved incomes for poor people in all countries".
Globalization: As the name itself suggests, Globalization is the process of interaction and integration among people, companies, and governments worldwide for the development of international trade, economy and harmony.To learn more about Globalization, click on the link below.
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Answer:
More unequal distribution of natural resources
Step-by-step explanation:
Write 7.83 x 10-3 in standard notation
Answers
Answer:
0.00783
Step-by-step explanation:
7.83 × 10^-3
Move the decimal point 3 places to the left.
7.83 × 10^-3 = 0.00783
Evaluate the expression ab, for a = 4 and b = 7.
Answers
Answer:
28
Step-by-step explanation:
4 x 7 = 28
Find the perimeter and the area of a figure pls help urgent
Answers
The perimeter and the area of the figure are 36 meters and 48 square meters
How to find the perimeter and the area of the figure?Perimeter
This is the sum of the side lengths of the figure
So, we have
Perimeter = 7m + 6m + 7m + 6m + 5m + 5m
Evaluate
Perimeter = 36 meters
Area
This is the sum of the areas of the shapes that makes up of the figure
So, we have
Area = Area of rectangle + Area of triangle
This gives
Area = 7 * 6 + 0.5 * (6/2) * (11 - 7)
Evaluate
Area = 48 square meters
Hence. the perimeter and the area of the figure are 36 meters and 48 square meters
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PLEASE HELP ASAP WILL GIVE BRAINLIST 11!
The approximate weights of two animals are 5.36 x 10^4 lbs. and 6.2 x 10^4 lbs. Find the total weight of the two animals. Write the final answer in scientific notation with the correct number of significant digits.
12 x 10^4 lbs.
5.9 x 10^4 lbs.
1.22 x 10^5 lbs.
1.2 x 10^5 lbs.
Answers
1. 120,000 lbs
2. 59,000 lbs
3. 122,000 lbs
4. 120,000 lbs
Answer: 1.156 × 10^5
Step-by-step explanation:
5.36 x 10^4
6.2 x 10^4
5.36+6.2=11.56
11.56 x 10^4 = 1.156 × 10^5 (scientific notation)
36. THOUGHT PROVOKING
Draw a different figure that
has the same perimeter as
the triangle shown. Explain
why your figure has the
same perimeter.
x+3
3x
2x + 1
Answers
A possible figure that has the same perimeter as the given triangle is a rectangle with side lengths, x + 1, x + 1, 2•x + 1, 2•x + 1
Please find attached the drawing of the figure of the rectangle, that has the same perimeter (6•x + 3) as the triangleHow can the perimeter of the triangle be calculated?The perimeter of a two dimensional geometric figure is its total boundary length.
The perimeter is given by the addition of the lengths of all the sides of the figure.
The perimeter, P, of the given triangle is therefore;
P = x + 3 + 2•x + 1 + 3•x = 6•x + 3
The perimeter, P = 6•x + 3
A different figure, drawn, that has the same perimeter as the given triangle (6•x + 3) is a rectangle that has side lengths of x + 1, 2•x + 1, x + 1, and 2•x + 1.
Please find attached the drawing of a rectangle that has a perimeter of 6•x + 3, which is the same as the perimeter of the triangle.
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=* When the stock market fell, Hayes lost 18% of the value of his stocks. The
stock was worth $2,486.95 before the loss. What was the stock worth after
?the loss
Answers
Answer:
Approximately $2,039.30
Step-by-step explanation:
Original value = $2,486.95
Value lost = 18%
100% value = $2,486.95
100% - 18% = 82% value remaining
.82 x 2,486.95 = 2039.299 or $2,039.30
T
Introduction to permutations and combinations
Suppose we want to choose 3 letters, without replacement, from the 4 letters A, B, C, and D.
(a) How many ways can this be done, if the order of the choices is relevant?
0
(b) How many ways can this be done, if the order of the choices is not relevant?
0
X
Answers
we get that if choices matter then there is only 1 way and if the choices do not matter, then there are 24 ways to choose from the given 4 letters by using permutation.
We are given four letters:
A, B, C and D
We need to choose 3 letters from it without replacement.
(a) If the order of choices matter, then there would only be 1 way to choose the letters.
(b) If the order of choices do not matter , then by permutation, we get that:
The number of ways of choosing = 4 × 3 × 2
Ways = 24 ways.
Therefore, we get that if choices matter then there is only 1 way and if the choices do not matter, then there are 24 ways to choose from the given 4 letters by using permutation.
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What value of x makes this equation true?
F 3
G-9
H -1
J 27
X/3−3 = x/9+
3
Answers
Fractions represent parts of a whole or collection of objects. In the above question the value of x is equals to 9
What is a fraction?Fractions represent parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called numerator. It tells how many equal parts of whole or collection are taken. The number below line is called denominator. It shows total number of equal parts the whole is divided into or the total number of the same objects in a collection.
When whole is divided into equal parts, the number of parts we take makes up a fraction.
In the mathematics, there are three major types of fractions. They are the proper fractions, improper fractions and mixed fractions. Fractions are those terms which have the numerator and denominator. Fractions are the terms used to determine parts of a whole object.
[tex]\frac{x}{3}-3= \frac{x}{9} + 3[/tex]
[tex]\frac{x}{3}- \frac{x}{9} = 3+3[/tex]
[tex]\frac{3x}{9}-\frac{x}{9} = 9[/tex]
[tex]\frac{2x}{9}= 9[/tex]
[tex]x=\frac{9*9}{2}[/tex][tex]=9[/tex]
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13. Higher Order Thinking Olivia has $20 to spend. She wants to buy a visor and magnet. The sales tax is $2.21. 1. Use estimation to find out if Olivia has enough money for her purchase. 2. Explain how to find the exact amount of change she will receive. 3. Find the exact amount of change. Show your work.
Answers
Answer:
Step-by-step explanation:
$20-$2.21=0.21
There are 63 students going on the trip, and you want to divide them up between 15 chaperones with 4 or 5 students in each group. How many groups will have 4 students, and how many will have 5?
Answers
There are 12 groups with 4 students and 3 groups with 5 students
How many groups will have 4 students, and how many will have 5?Represent the students as follows:
Group with 4 students = x
Group with 5 students = y
So, we have the following system of equations
4x + 5y = 63
x + y = 15
Make x the subject in x + y = 15
x = 15 - y
Substitute x = 15 - y in 4x + 5y = 63
4(15 - y) + 5y = 63
Expand
60 - 4y + 5y = 63
Evaluate
y = 3
Substitute y = 3 in x = 15 - y
x = 15 - 3
This gives
x = 12
Hence, there are 12 groups with 4 students and 3 groups with 5 students
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7) If a = 2, b = 3, c = 4, and d = 12, evaluate 6c-4b
Answers
Answer:
12
Step-by-step explanation:
Step1:- substitute the values of a and b in the equation
6(4)-4(3)
Step2:- solve the expression
6(4)=6×4=24
4(3)=4×3=12
so 6(4)-4(3)=24-12= 12