y= x +2
x^2 +y^2=10
solve using any method
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
(-3, -1) and (1, 3)
»»————- ★ ————-««
Here’s why:
I have graphed the two equations given on a graphing program.When graphed, they pass at points (-3, -1) and (1,3). Therefore, they are the solutions to the system.⸻⸻⸻⸻
See the graph attached.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
[tex]{ \tt{y = x + 2 - - - (a)}} \\ { \tt{ {x}^{2} + {y}^{2} = 10 - - - (b) }} \\ substitute \: for \: y \: in \: (b) : \\ { \tt{ {x}^{2} + {(x + 2)}^{2} = 10 }} \\ { \tt{ {x}^{2} + {x}^{2} + 4x + 4 = 10 }} \\ { \tt{2 {x}^{2} + 4x - 6 = 0}} \\ { \tt{ {x}^{2} + 2x - 3 = 0 }} \\ { \boxed{ \bf{x = 1 \: and \: - 3}}} \\ in \: (a) : \\ y = x + 2 \\ { \boxed{ \bf{y = 3 \: and \: - 1}}}[/tex]
Related Questions
If y = 8 cm, what is the area of the blue section of this shape?
Answers
Answer:
56 cm squared
Step-by-step explanation:
First things first: Cop one triangle off the rectangle, and attach it to the other one, so the shape looks like a L
Now I can actually solve this:
The left side is 8 cm (because y = 8 cm)
The top is 10 cm
The middle is 6 cm
The inside left is 3 cm
And the very bottom is 2 cm
First, we'll solve for the newly constructed rectangle: 3 x 2. That equals 6.
Next, solve for the longer rectangle: 10 x 5. That's 50.
Now, add the two areas, and we get 56. So the area of the whole thing is 56 cm squared.
(Please keep in mind that I could be wrong, so double check it for me, thanks!)
Assume that both populations are normally distributed.
a. Test whether u1≠ u2 at the alpha=0.05 level of signifigance for the given sample data. (u= population mean, sorry couldnt insert the symbol). Determine p value. Should the null hypothesis be rejected?
b. Construct a 95% confidence interval about μ1−μ2. at the alphα=0.05 level of significance for the given sample data.
Population 1 Population 2
n 18 18
x 12.7 14.6
s 3.2 3.8
Answers
Answer:
Fail to reject the null hypothesis
[tex]CI = (-4.278, 0.478)[/tex]
Step-by-step explanation:
Given
[tex]n_1=n_2 = 18[/tex]
[tex]\bar x_1 = 12.7[/tex] [tex]\bar x_2 = 14.6[/tex]
[tex]\sigma_1 = 3.2[/tex] [tex]\sigma_2 = 3.8[/tex]
[tex]\alpha = 0.05[/tex]
Solving (a): Test the hypothesis
We have:
[tex]H_o : \mu_1 - \mu_2 = 0[/tex]
[tex]H_a : u1 - u2 \ne 0[/tex]
Calculate the pooled standard deviation
[tex]s_p = \sqrt\frac{(n_1-1)\sigma_1^2 + (n_2-1)\sigma_2^2}{n_1+n_2-2}}[/tex]
[tex]s_p = \sqrt\frac{(18-1)*3.2^2 + (18-1)*3.8^2}{18+18-2}}[/tex]
[tex]s_p = \sqrt\frac{419.56}{34}}[/tex]
[tex]s_p = \sqrt{12.34}[/tex]
[tex]s_p = 3.51[/tex]
Calculate test statistic
[tex]t = \frac{x_1 - x_2}{s_p*\sqrt{1/n_1 + 1/n_2}}[/tex]
[tex]t = \frac{12.7 - 14.6}{3.51 *\sqrt{1/18 + 1/18}}[/tex]
[tex]t = \frac{-1.9}{3.51 *\sqrt{1/9}}[/tex]
[tex]t = \frac{-1.9}{3.51 *1/3}[/tex]
[tex]t = \frac{-1.9}{1.17}[/tex]
[tex]t = -1.62[/tex]
From the t table, the p value is:
[tex]p = 0.114472[/tex]
[tex]p > \alpha[/tex]
i.e.
[tex]0.114472 > 0.05[/tex]
So, the conclusion is that: we fail to reject the null hypothesis.
Solving (b): Construct 95% degree freedom
[tex]\alpha = 0.05[/tex]
Calculate the degree of freedom
[tex]df = n_1 + n_2 - 2[/tex]
[tex]df = 18+18 - 2[/tex]
[tex]df = 34[/tex]
From the student t table, the t value is:
[tex]t = 2.032244[/tex]
The confidence interval is calculated as:
[tex]CI = (x_1 - x_2) \± s_p * t * \sqrt{1/n_1 + 1/n_2}[/tex]
[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/18 + 1/18}[/tex]
[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/9}[/tex]
[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * 1/3[/tex]
[tex]CI = -1.90 \± 2.378[/tex]
Split
[tex]CI = (-1.90 - 2.378, -1.90 + 2.378)[/tex]
[tex]CI = (-4.278, 0.478)[/tex]
The in center is the center of the circle of a triangle
1) circumscribed
2) centralized
3) cocentric
4) inscribed
Answers
Answer:
inscribed
Step-by-step explanation:
For any given triangle, the circle inside of it is called the Inscribed circle
Plz help i need a correct answer
Answers
Answer:-244
Step-by-step explanation:
I think you subtract -290 from -46.
Sorry If I am wrong.
========================================================
Explanation:
Imagine reflecting everything so that location A is above location B. Effectively all you're doing is erasing the negative signs.
That would place A at 290 feet and B would be at 46 feet. The difference in elevation is 290-46 = 244 feet
Instead of reflecting, you can turn the page upside down and just ignore the negative signs, and then subtract like normal.
This trick only works if both elevations A and B are below sea level.
--------
Or you could subtract like so:
|A-B| = |-290-(-46)| = |-290+46| = |-244| = 244
The absolute value is used to ensure the result is not negative. A negative difference makes no sense. In this case, "difference" and "distance" mean the same thing more or less.
Marlene is trying to estimate v 42. She uses this table of values:
Square 6.02 6.12 6.22 6.32 6.42 6.52
Value
36.0 37.2 38.4 39.7 41.0 42.3
Square 6.62 6.72 6.82 6.92 7.02
Value
43.6 44.9 46.2 47.6 49.0
What should she do next to find 42 to the nearest hundredth?
A. She should find the squares of numbers between 6.4 and 6.5.
ООО
B. She should find the average of 6.4 and 6.5.
C. She should find the squares of numbers between 6.5 and 6.6.
O D. She should estimate that 42 is 6.50,
Answers
Answer:
A
Step-by-step explanation:
Did the quiz
Which score is better in terms of percentages: 12 out of 15 or 23 out of 26?
Answers
Answer:
23/26 is a greater percentage, it equals around 88% while 12/15 equals 80%
Step-by-step explanation:
James made 20 basketball shots in 15 minutes.
What is the number of basketball shots James can make in 45 minutes?
А
60
B
45
С
34
D 7
Answers
A
60
Because if he made 20 basketballs shots in 15 and 15 multiplied by 3 is 45, then you have to multiply 20 by 3 to get 60
tammy buys candy that cost 5 dollars per pound. she will spend more than 40 dollars on candy. what are the possible numbers of pounds she will buy
Answers
Answer:
Step-by-step explanation:
x = number of pounds
5x<30
x<30/5
so she can buy X<6 pounds
1. Calculate the variance of the set of data to two decimal places.
{ 1,2,4,4,5,6,6}
a. 22
b. 4
c.3.14
d. 1/7
e.2
Answers
============================================================
Explanation:
First we need the arithmetic mean
Add up the values to get 1+2+4+4+5+6+6 = 28
Divide this over the number of values (n = 7) to get 28/n = 28/7 = 4
The mean is 4.
Next, we subtract the mean from each data value and square the difference
(1-4)^2 = 9(2-4)^2 = 4(4-4)^2 = 0(4-4)^2 = 0(5-4)^2 = 1(6-4)^2 = 4(6-4)^2 = 4Add up those results: 9+4+0+0+1+4+4 = 22
Lastly, we divide over the number of items (n = 7) to get the population variance: 22/n = 22/7 = 3.14 approximately
----------
Side note:
If you wanted the sample variance, then you divide over n-1 = 7-1 = 6
22/(n-1) = 22/6 = 3.67 is the approximate sample variance
What is the domain of the function graphed below?
Answers
Answer:
x < 7
Step-by-step explanation:
the domain of a function defines the valid x values for the function.
as we go from left to right through all possible values of x, we see all values incl. x=-1 are creating a valid function result (y) for this function. until we reach x=7.
the empty ball indicates that there is no y value defined here. and for any value x>7 there is no y value defined.
so, x < 7 is the right one.
Answer: A
Step-by-step explanation:
I need help comment please
Answers
Answer:
41
Step-by-step explanation:
The angle were looking for is on the other side of the figure. It is also on the inside so we would divide 82 in half giving us 41.
Evaluatef(x) = 2.5x-11 when x = 4
Answers
Answer:
-1
Step-by-step explanation:
f(4) = 2.5(4) -11
f(4) = 10 -11
f(4) = -1
The height of a triangle is 4 m more than twice the length of the base. The area of the triangle is 35 m^2 . Find the height of the triangle
Answers
Answer:
Step-by-step explanation:
Let the Base of the △ be x
Then the Height will be 2 x + 4
Area of △ = 1 2 b h
Where, b = b a s e , h = h e i g h t , A r e a = 35
(in this case)
Substitute the values into the equation → 35 = 1 2 ( 2 x + 4 ) ( x ) → 35 = ( 2 x + 4 ) 2 ( x ) →
35 = ( x + 2 ) ( x ) → 35 = x 2 + 2 x
Subtract 35 both sides
→ 0 = x ^2 + 2 x − 35
Rewrite the equation in the Standard form
x ^2 + 2 x − 35 = 0
Factor the equation
→ ( x + 7 ) ( x − 5 ) = 0
So we have
x = − 7 , 5
numbers So x = 5
They have asked us to find the Height
So, ⇒ H e i g h t = 2 x + 4 = 2
Allison works at a Bank. Her employer offers her a retirement pension plan which will be 1.75% of her average salary for the last five years of employment for every year worked. Allison is planning on retiring after working at the Credit Union for 32 years. Her salaries over the last five years are $70,000; $73,100; $75,200; $77,500; and $79,000. Calculate Allison's annual pension.
Answers
9514 1404 393
Answer:
$41,977.60
Step-by-step explanation:
Allison's average salary for the last 5 years is ...
(70 +73.1 +75.2 +77.5 +79)/5 = 74.96 . . . . thousand dollars
Then her annual pension is ...
1.75% × $74,960 × 32 = $41,997.60
A randomized control trial comparing the efficacy of two drugs showed a difference between the two (with a P value <0.05). Assume that in reality, however, the two drugs do not differ. This is an example of:
Answers
Answer:
Type I error (alpha error)
Step-by-step explanation:
Given that a TYPE 1 ERROR is a type of research error often referred to as false positive or alpha error and happens when a researcher wrongly rejects a true null hypothesis. This action by the researcher verifies a statistically significant difference even though there is no difference.
Hence, considering the situation described in the question above, the correct answer to the question is "TYPE 1 ERROR"
Evaluate:
Σ21(2n + 8) = [?]
HELP ME PLS
Answers
Answer:
42n+108
Step-by-step explanation:
21(2n+8)
42n+108
Ann bought 8 bottles of water and 4 sports drinks for $25. Blake bought 2 bottles of water and 9 sports drinks for $32.25. What was the cost of each bottle of water and each sports drink.
Answers
it think it is 10 or so but like just read or it and you will get it :)
what is the solution
Answers
Answer:
c 13 over 12
Step-by-step explanation:
it help I makeit
Point A is located at (-23, -2). Point B is located at (-23,23). What is the distance
between point A and point B?
Answers
Answer:
25
Step-by-step explanation:
Since the x values are the same
the distaance is simply the difference in the y values
23 - (-2) = 25
In ΔIJK, the measure of ∠K=90°, KJ = 65, IK = 72, and JI = 97. What is the value of the cosine of ∠J to the nearest hundredth?
Answers
Answer:
[tex]\cos(J) = 0.67[/tex]
Step-by-step explanation:
Given
[tex]\angle K = 90^o[/tex]
[tex]KJ = 65[/tex]
[tex]IK = 72[/tex]
[tex]JI = 97[/tex]
Required
[tex]\cos(J)[/tex]
The question is illustrated with the attached image.
From the image, we have:
[tex]\cos(J) = \frac{KJ}{JI}[/tex]
This gives:
[tex]\cos(J) = \frac{65}{97}[/tex]
[tex]\cos(J) = 0.67010309278[/tex]
[tex]\cos(J) = 0.67[/tex] --- approximated
Question 2 of 20
Which of the following sets represents the range of the diagram below?
Answers
Answer:
D. {3, 5, 7}
Step-by-step explanation:
Sets of y-values or outputs of a relation of a function = the range
The outputs/y-values of the relation mapped above are what we have on our right hand, which area {3, 5, 7}
Therefore,
Range = {3, 5, 7}
What is the value of f(6) in the function below?
fx) = 2x
Answers
Answer:
substitute that (6) in X so f(6) = 2(6) which is = 12
What is one way to determine if two fractions are equivalent?
Answers
Answer
Two fractions are equivalent fractions when they represent the same part of a whole. Since equivalent fractions do not always have the same numerator and denominator, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator.
A pyramid with a square base, where the side length of the base is 7.2 cm and the height of the pyramid is 10.4 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answers
Answer:2647.5
Step-by-step explanation:
What is the pattern?
2x = 3.5
3x = 2.5
4x = 2
5x = ?
6x = 1.6666
7x =
8x =
9x =
10x =
11x =
12x = 1.4166
Answers
Answer:
I don't know sorry for your right question ok
Can you help me with this question? 15 points and brainliest if right!
Answers
Answer:
3/4
Step-by-step explanation:
because it is a linear function it means it has the same slope in every point
so you have to take 2 points and find the slope
I take points (0,1) and (4,4)
m = (y2-y1) / (x2-x1)
note that it does not matter which points you chose to be second or first
m = (4-1) / (4-0) = 3/4
you can solve it from the graph too 3/4 is y/x it means for every 4 unit right move 3 units up
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is −4h.
Explain what the inequality −4h ≤-14 represents.
Answers
9514 1404 393
Explanation:
-4h ≤ -14
in this context is a relation that would tell how many hours it would take for the temperature to be at or below -14 degrees.
What is the greatest common
factor of the expression?
2x^2y^3+4x^2y^5
Answers
Answer:
[tex]2x^2y^3[/tex]
Step-by-step explanation:
The given expression is :
[tex]2x^2y^3+4x^2y^5[/tex]
We need to find the greatest common factor of the expression.
The first term is [tex]2x^2y^3[/tex]
The other term is [tex]4x^2y^5[/tex]
[tex]2x^2y^3[/tex] is common in both terms. So,
[tex]2x^2y^3(1+2y^2)[/tex]
Hence, the greatest common factor of the expression is equal to [tex]2x^2y^3[/tex].
At the beginning of the year, the odometer on an SUV read 37,532 miles. At the end
of the year, it read 52,412 miles. If the car averaged 24 miles per gallon, how many
gallons of gasoline did it use during the year?
Answers
He used 620 gallons of gas
To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of credits for the course. Suppose a student had these grades: 3.7 in a 5 credit Math course 1.8 in a 3 credit Music course 2.8 in a 5 credit Chemistry course 2.8 in a 4 credit Journalism course What is the student's GPA for that term
Answers
Answer:
2.89, rounded to the nearest hundredth
Step-by-step explanation:
Given that GPA is weighted by credits, we must first multiply each grade by its credit amount and sum those up to weigh the credits. Then, we divide by the total amount of credits to get the GPA per credit.
So, we start with math,
3.7 *5 + 1.8 *3 + 2.8 * 5 + 2.8 * 4 = 49.1 as the total GPA weighted per credit.
Then, to find the average per credit, we divide by the total amount of credits, which is 5 + 3 + 5 + 4 = 17.
Our answer is 49.1/17 = 2.89, rounded to the nearest hundredth