Calculate the coordinates of the points where the line y = 1 - 2x cuts the curve x^2+ y^2 = 2
Answers
Answer:
\((1, -1)\) and \((-\frac{1}{5}, \frac{7}{5})\)
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 \(y = 1 - 2x\) (1) and
Circle Equation \(x^2+ y^2 = 2\) (2)
\(y=1-2x\)
Plug this value of y into the second equation for the circle
\(x^2 + (1-2x)^2= 2\)
Apply the perfect squares formula \(\left(a-b\right)^2=a^2-2ab+b^2\)
\((1-2x)^2 = 1^2-2\cdot \:1\cdot \:2x+\left(2x\right)^2\\= 1-4x+4x^2\\\\\)
So equation (2) becomes
\(1-4x+4x^2 +x^2 = 2 \\\\\\5x^2 -4x - 1 = 0\)
Solve using the quadratic formula
\(x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)
Here a is the coefficient of x ², b is the coefficient of x and c is the constant
So
\(x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)}}{2\cdot \:5}\)
Now,
\(\sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)} = \sqrt{\left(-4\right)^2+4\cdot \:5\cdot \:1}\)
= \(\sqrt{16+20} = \sqrt{36} = 6\)
Therefore
\(x_{1,\:2}=\frac{-\left(-4\right)\pm \:6}{2\cdot \:5}\)
\(x_1=\frac{-\left(-4\right)+6}{2\cdot \:5}\) = \(\frac{-\left(-4\right)+6}{2\cdot \:5} =\) \(\frac{10}{2\cdot \:5}\) \(= 1\)
\(x_2 = \frac{-\left(-4\right)-6}{2\cdot \:5}\) \(= \frac{4-6}{2\cdot \:5}\) = \(-\frac{1}{5}\)
To find corresponding values for \(y_1 y_2\) plug these values of \(x_1, x_2\) into the line equation
\(y_1 = 1- 2(1) = -1\)
\(y_2 = 1 - 2(-\frac{1}{5}) = 1 + \frac{2}{5} = \frac{7}{5}\)
So the two points of intersection are
\((1, -1)\) and (\((-\frac{1}{5}, \frac{7}{5})\).
In decimal form this would be (1, -1) and (-0.2, 1.4)
See attached graph
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1+6 pls help me nowwwwwww
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Answer:
7
Step-by-step explanation:
Hurricane Katrina dropped about 14 inches of rain over a 48 hour period. How much rain is this per hour?
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Answer:
Step-by-step explanation:
Set of whole numbers from 1 to 10 inclusive greater than seven and odd
Answers
Answer:
{7, 9}
(Numbers from 1 to 10 equal to or greater than 7 are 7 and 9)
Step-by-step explanation:
We have to find the set of whole number greater than and equal to 7 from 1 to 10,
Now, From 1 to 10, the odd numbers are, 1,3,5,7,9,
And of these, 7 and 9 are equal to or greater than 7
So, we get the set,
{7, 9}
A pet store has both dogs and cats. The sum of the numbers of dogs and cats is 56. The difference of the numbers of dogs and cats is 10.
There are more dogs than cats.
How many dogs and how many cats are in the pet store?
Answers
In the store, the number of dogs are 33 and cats are 23.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
The sum of the number of dogs and cats is 56. The difference of the numbers of dogs and cats is 10.
Let x be the number of dogs and y is the number of cats.
So x+y = 56
x-y = 10
2x = 66
x = 33
y = 56-33 = 23
Hence In the store, the number of dogs are 33 and cats are 23.
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Help please!! Thank you :)
Answers
Answer: 5:3, 5/3, 5 to 3
Step-by-step explanation:
It takes Alicia 1/2 hour to wash, comb her hair and put on her clothes, and 1/4 hour to have her breakfast. How much time does it take Alicia to be ready for school?
Answers
Answer:
3/4 hour
Step-by-step explanation:
Answer:
1 hour + 8 =575
Step-by-step explanation:
add tow answer 768
Based on the information in the two-way table, what is the probability that a person
selected at random both bikes and runs?
Round your answer to the nearest tenth of a percent.
Answers
Answer:
Step-by-step explanation:
David made an error when determining the product of (–2.5)(–8.3). Step 1: (–2.5)(–8.3) = (–8.3)(–2.5) Step 2: = (–8.3)(–2) + (–8.3)(–0.5) Step 3: = (–16.6) + (–4.15) Step 4: = –20.75 In which step did David make his first error?
Answers
Answer:
David make his first error at Step 3
Step-by-step explanation:
We need to determine the error David made when finding the product of (-2.5)(-8.3)
He did the following steps
Step 1: (–2.5)(–8.3) = (–8.3)(–2.5)
Step 2: = (–8.3)(–2) + (–8.3)(–0.5)
Step 3: = (–16.6) + (–4.15)
Step 4: = –20.75
David made a mistake in Step 3
When we multiply (-1) with (-1) we get + instead of - sign. The correct step 3 would be:
Step 3: =(16.6)(4.15)
Step 4: =20.75
So, David make his first error at Step 3
graph f(x)=-0.25 + 4
Answers
Answer:
4.25 I think but I hoped that helped
can someone help me please?????
Answers
Answer:
Step-by-step explanation:
16 cm
Find all numbers whose absolute value is 3 . If there is more than one, separate them with commas. If there are no such numbers, click on "None".
(This is not negative 3)
Answers
Answer:
3, and -3
Step-by-step explanation:
Because absolute value is the distance away from zero, |3| and |-3| would both be 3 units away from 0. Be sure to have the negative on the inside if you're trying to make something positive, otherwise -|3| means that the absolute value of 3 would then become negative since the negative sign isn't a part of the absolute. hope this helps!
The numbers whose absolute values is 3 are : 3 and - 3
The absolute value of a number is the distance from zero a number is on the number line. Absolute values measures the distance from zero ignoring whether the distance is to the right or left of the number line.
Three units to the right of Zero = 3
Three units to left of Zero = -3
The absolute value of - 3 represented as |-3| = 3
Hence, The numbers whose distance from zero is 3 on the number line are : 3 and - 3
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2/3x -4= -2
A.-3
B.-4
C.-9
D.3
Answers
Answer:
D
Step-by-step explanation:
mark me as brainliest?
Answer:
D. 3
Step-by-step explanation:
if you were trying to find the value of x, heres how i got the answer:
2/3x - 4 = -2
- add 4 to both sides
2/3x = 2
- divide both sides by 2/3
x = 3
YO PLEASE HELPP
Mai enlarges a triangular sign by a multiple of 4
creating similar triangles. The bottom of the original
sign is side EG. Which side of the enlarged sign
corresponds to side EG?
If she wanted to turn the sign so that side JK was on
the bottom, what side of the original sign would this
correspond to?
Answers
The side of the enlarged triangle corresponding to side EG is JK.
The side of the original triangle that corresponds to JK is EF.
Which side of the enlarged sign corresponds to side EG?Similar triangles are triangles that have the same shape but may have different sizes. This means that corresponding angles of similar triangles are equal, and corresponding sides are in proportion.
In other words, if two triangles are similar, their corresponding sides are proportional, and their corresponding angles are congruent.
Given ΔEFG and ΔJKL, the side of the enlarged triangle corresponding to side EG is JK.
The side of the original triangle that corresponds to JK is EF.
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Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
Answers
The total cost of the pita bread and hummus dips will be $305.00.
To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:
Cost of pita bread:
Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates
Cost of each crate = $15.00
Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00
Cost of hummus dips:
Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes
Cost of each box = $20.00
Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00
Therefore, the expressions Toula can use to determine the costs are:
Cost of pita bread = 3 crates × $15.00/crate
Cost of hummus dips = 13 boxes × $20.00/box
The total cost will be the sum of the costs of pita bread and hummus dips:
Total cost = Cost of pita bread + Cost of hummus dips
Total cost = $45.00 + $260.00
Total cost = $305.00
Therefore, the total cost of the pita bread and hummus dips will be $305.00.
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7).
2. Hot Text: For each graph, choose the correct sentence to describe the graph.
The graph represents a proportional relationship.
The graph does not represent a proportional relationship.
Answers
a. The graph represents a proportional relationship.
b. The graph does not represent a proportional relationship.
c. The graph does not represent a proportional relationship.
d. The graph represents a proportional relationship.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:
y = kx.
Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.
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Name the triangle as described
Answers
Answer:
scalene triangle
Step-by-step explanation:
what is the population of the Emperor penguin rounded to the nearest ten thousand and to the nearest hundred thousand
Answers
Answer:
130,000 to 250,000
Step-by-step explanation:
This problem refers to triangle ABC. If A = 80°, B = 60°, and b = 15 cm, find a. (Round your answer to the nearest whole number.)
a = ? cm
Answers
a/sin(A) = b/sin(B)
Substituting the given values:
a/sin(80°) = 15/sin(60°)
a = (15 sin(80°))/sin(60°)
a ≈ 17 cm (rounded to the nearest whole number)
Therefore, side a is approximately 17 cm.
Answer:
Step-by-step explanation:
We can use the law of sines to find the length of side a. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. In other words:
a/sin A = b/sin B = c/sin C
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides.
We are given that A = 80°, B = 60°, and b = 15 cm. We can substitute these values into the law of sines and solve for a as follows:
a/sin 80° = 15/sin 60°
Multiplying both sides by sin 80°, we get:
a = 15*sin 80°/sin 60°
Using a calculator, we can evaluate sin 80° and sin 60° as follows:
sin 80° ≈ 0.9848
sin 60° = √3/2 ≈ 0.8660
Substituting these values, we get:
a ≈ 15*0.9848/0.8660
a ≈ 17.06
Rounding this to the nearest whole number, we get:
a ≈ 17
Therefore, the length of side a is approximately 17 cm.
bella answered 33 questions on her math test. she earned a 92% on the test. how many questions did she answer correct
Answers
Answer: 30.36
Step-by-step explanation:
92% of 33 is 30.36. I don't know how Bella got 30.36 questions correct, but that is what I got.
whats 5x5? Maybe will mark brainiest
Answers
Answer:
25
Step-by-step explanation:
5x5 = 25
Answer:
25
Step-by-step explanation:
Let's go through our times tables really quick!
5x1 = 5 (5 + 0)
5x2 = 10 (5 + 5)
5x3 = 15 (5 + 5 + 5 [10 + 5])
5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)
As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5
So, 5x5 is 25
Hope this helped!
What is the equation of the line that passes through the point (7,6) and has a slope of 0
Answers
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
Given,
The points which the line passes, (x₁, y₁) = (7, 6)
Slope of the line, m = 0
We have to find the equation of the line:
We know that,
y - y₁ = m(x - x₁)
So,
y - 6 = 0(x - 7)
y - 6 = 0
y = 6
That is,
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
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What is the total weight of the bags that weighed /8 pound each?
Answers
The total weight of Rice that Mark buys is given as follows:
2.5 pounds.
How to obtain the total weight?The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.
The weight of each bag is given as follows:
5/8 pounds = 0.625 pounds.
The number of bags is given as follows:
4 bags.
Hence the total weight of Rice that Mark buys is given as follows:
4 x 0.625 = 2.5 pounds.
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Somebody please help me ITS URGENT
Answers
Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.
What is the equation?Equation is a mathematical statement that expresses two expressions as equal. It consists of two expressions separated by an equal sign (=). An equation is used to solve for a unknown value by using known values and following the rules of algebra and arithmetic. Equations can be used to solve for a single unknown, multiple unknowns, and even non-numeric values.
Given that the total cost for parking and four tickets to a baseball game is $175.00.
$25 is the parking fee.
4 tickets cost $175 - $25.
Suppose that each ticket costs t.
t =($175 - $25)/4
Each ticket costs $37.5.
The equation follows.Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.
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If the triangle above is translated two units to the right, what is the correct coordinate for A'?
Answers
Answer: 0, 5
Step-by-step explanation: a translation is just like sliding the object in this case a triangle/point on the triangle. so the point it is at now is -2, 5 because it is 2 to the left and 5 up. and if you go to the right 2. then you are adding 2 to the x value. so -2 +2 = 0. which is how you get 0, 5
Marie is calculating an annuity payment. Her mortgage of $200,000 compounds monthly for 30 years. What is the nt value she will use in her formula?
Answers
Based on the annuity payment that Marie will make and the number of years, the nt value that she will use in her formula is 360 months.
How to find the nt value?The nt value is the number of periods that Marie will need to pay her annuity payment. This value can be yearly, monthly, weekly and even daily.
As the mortgage compounds monthly in this instance, the nt value will need to be monthly as well.
To find the nt value, the formula is:
= Number of years x number of compounding periods per year
= 30 x 12 times a year
= 360 months
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Answer:
360
Step-by-step explanation:
i did that and i got it right
Find the equation of the line with slope –5/2
and y-intercept (0,0).
Answers
Answer:
y= -5/2X
.....................
Suppose the prices of a certain model of new homes are normally distributed with a mean of 150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid between $149,000 and $151,000 if the standard deviation is $1000
Answers
The percentage of buyers is approximately 68.26% of buyers of new houses paid between \($149,000\) and \($151,000\) .
We are given that the prices of the new homes are normally distributed with a mean of \($150,000\) and a standard deviation of $1000.
Using the 68-95-99.7 rule, we know that: approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the data falls within two standard deviations of the mean, approximately 99.7% of the data falls within three standard deviations of the mean.
In order to determine the proportion of customers who spent between $149,000 and , we must first determine the z-scores for these values:
z1 = (149,000 - 150,000) / 1000 = -1 z2 = (151,000 - 150,000) / 1000 = 1
Now, we can determine the proportion of data that falls between z1 and z2 using the z-table or a calculator. The region to the left of z1 is 0.1587, and the area to the left of z2 is 0.8413, according to the z-table. Thus, the region bounded by z1 and z2 is:
0.8413 - 0.1587 = 0.6826
We can get the percentage of consumers who spent between by multiplying this by 100% is \($149,000\) and \($151,000\):
0.6826 x 100% = 68.26%
Therefore, the standard deviation of customers who paid between is \($149,000\) and \($151,000\) for this model of new homes.
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Find the slope of (-3, -3 ) and (2 , 3)
Answers
Answer:
6/5
Step-by-step explanation:
rise/run
4. What is Probability?
(ii) State the axioms of probability
(iii)Two fair dice are thrown, what is the probability of getting
(a) the sum of 9
(b) two odd numbers
(c) two prime numbers
(d) two factors of 12
4c. What is Statistics?
Answers
(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.
(ii) The axioms of probability are:
the non-negativity (that the probability of an event is greater than or equal to zero), and
the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).
(iii) When two fair dice are thrown the probability of getting:
a) The sum of 9 = 1/9
b) Two odd numbers = 1/4
c) two prime numbers = 1/9
d) two factors of 12 = 1/9
(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.
How to find probability when two dice are thrown?To find probability when two dice are thrown, we have:
(a) The sum of 9:
We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways
A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.
(b) Two odd numbers:
We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).
possible outcomes = 9,
So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.
(c) Two prime numbers
We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)
possible outcomes = 4,
So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.
(d) Two factors of 12:
We count the number of ways and divide by the total possible outcomes.
The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways
possible outcomes = 6
Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12
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i dont understand how this question works so therefeore i dont know how to do it, can anyone help?
Answers
is simply changing from percentage form to a decimal form usually, but the fractional form works the same. Check the picture below.
