Answers
Two
Explanation:
The solution of a system of equations is defined as the values which satisfies both equations.
Graphically, the solutions are represented by the points of intersection between the two equtaions.
In the given graph, we have a circle and a line, we can note that these two intersect in two points.
This means that the system has two solutions
Hope this helps :)
Related Questions
What is the quadratic function with the given vertex and through the given point? Write the equation of the parabola in vertex form and describe how the function was transformed from the parent function y = x2.
vertex (0, 0), point (−2, 2)
Answers
y = A(x - h)² + k
Where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
The coefficient A may be found when you have another point of the quadratic function.
2) Therefore, being the vertex (0,0), h = 0 and k = 0, and the equation is
y = Ax²
3) Replacing the coordinates of the point (-2,2) into the equation you get:
2 = A (-2)² ⇒ A = 2/4 = 1/2
4) The resulting equation is y = (1/2)x² ← answer
Since, the system is giving me an error, I had to put the second part of the answer in a separate file. Please, see the attached pdf file.
The quadratic function with vertex (0, 0) and passing through the point (-2, 2) is y = 0.5x^2. This is a transformation of the parent quadratic function y = x^2 with a vertical stretch by a factor of 0.5.
Explanation:The quadratic function with the given vertex (0, 0) and going through the point (-2, 2) can be written in the form of the vertex form of a quadratic function i.e. y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Since the vertex given is (0,0), the function becomes y = ax².
Now, to find the value of 'a', we can substitute the x and y coordinates of the given point (-2,2) into the equation. So, 2 = a(-2)², this simplifies to 2 = 4a. Solving for 'a', we get a = 0.5. So, the function is y = 0.5x².
This function is a transformation of the parent function y=x². The 0.5 in front of x² means that the graph of the function stretches vertically by a factor of 0.5. Thus, the parabola opens upwards and is narrower than the parent function.
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what integer and 9 have the product of -135
Answers
-15 times 9 equals -135
:) Have a nice day and maybe consider grading this answer brainliest? <3
a bucket contains 50 lottery balls numbered 1-50.one is drawn at random.Find p(multiple of 6/2-digit number)
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P(B | A) = P(A ∩ B) / P(A)
We know that:
- between 1 and 50 there are 41 two-digit numbers, therefore
P(A) = 41/50 = 0.82
- between 1 and 50 there are 8 multiples of six, therefore
P(B) = 8/50 = 0.16
- between 1 and 50 there are 7 two-digits mutiples of six, therefore
P(A ∩ B) = 7/50 = 0.14
Now, we can calculate:
P(B | A) = P(A ∩ B) / P(A)
= 0.14 / 0.82
= 0.17
Therefore, the probability of getting a multiple of 6 if we draw a two-digit number is 17%.
hey can you please help me posted picture of question
Answers
Method 1:
The given function is a cubic function. And inverse of a cubic function is also a function.
Method 2:
Since the function is one-to-one function i.e it passes the horizontal line test, its function will pass the vertical line test which is a test if a relation is a function or not.
So, yes the inverse of G(x) will be a function.
Cross section of a metal ingot is a trapezoid the cross section has an area of 39 square cm the top base of the cross section is 12 CM the length of the bottom base is 2 cm greater than the top base how tall is the Metal Ingot explain
Answers
A = (1/2)(b₁ +b₂)×h
Fill in the given information and solve for h.
39 cm² = (1/2)(12 cm +(12 cm +2 cm))×h
39 cm²/(13 cm) = h = 3 cm
The height of the metal ingot is 3 cm.
Determine the number of solutions the following system of equations will have: 1/3 y - 5 = 2x y = 15 + 6x
Answers
1/3 y - 5 = 2x
y = 15 + 6x
The equations are linearly dependent, that is, there is a scalar that allows us to write an equation as a linear combination of the other.
We multiply the equation (1) by a scalar, which will be 3:
3 * (1/3 y - 5) = 3 * (2x)
Rewriting:
y-15 = 6x
y = 15 + 6x
Answer:
Therefore, if there is a solution, then there are infinite solutions.
10 cm^3 of a normal specimen of human blood contains 1.2 g of hemoglobin. How many grams does 39 cm^3 of the same blood contain?
39 cm^3 of blood contains
............. grams of hemoglobin.
Answers
Therefore;
10 cm^3 of blood ---------- 1.2 g of hemoglobin
39 cm^3 of blood ---------- x g of hemoglobin
The,
x = (39*1.2)/10 = 4.68 g of hemoglobin.
That is, 39 cm^3 of blood contains 4.68 grams of hemoglobin.
Which of the following options represeWrite the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.nts the form of a linear equation that should be used to write the equation of a line when the slope and a point on the line are given? general form standard form factored form point-slope form
Answers
y-yo = m (x-xo)
Where,
m = (y2-y1) / (x2-x1)
m = (1-6) / (- 6-6)
m = (- 5) / (- 12)
m = 5/12
We choose an ordered pair:
(xo, yo) = (6, 6)
Substituting values:
y-6 = (5/12) (x-6)
y = (5/12) x - 2.5 + 6
y = (5/12) x + 3.5
y = (5/12) x + 7/2
Answer:
the equation of the line is:
y = (5/12) x + 7/2
y-yo = m (x-xo)
m = (y2-y1) / (x2-x1) m = (1-6) / (- 6-6) m = 5/12
y-yo = 5/12 (x-xo)
use (6,6) as(xo,yo)
y-6 = (5/12) (x-6)
y = (5/12) x + 7/2
How many fluid ounces in 8 ounces and 5 cups?
Answers
which of the following is the converse of the statement "If it is my birthday, then it is September"?
Answers
If p ( x ) = 8 + 6 x − 4 x 2 p(x)=8+6x-4x2 represents the profit in selling x x thousand boombotix speakers, how many speakers should be sold to maximize profit?
Answers
Final answer:
To maximize the profit from selling Boombotix speakers, the company should sell 0.75 thousand speakers, or 750 speakers, which is determined by finding the vertex of the profit function p(x) = 8 + 6x - 4x2.
Explanation:
The function p(x) = 8 + 6x - 4x^2 represents the profit from selling x thousand Boombotix speakers. To find the number of speakers that should be sold to maximize profit, we need to find the vertex of the parabola represented by this quadratic function, which is a downwards opening parabola because the coefficient of x^2 is negative (-4).
The vertex form of a quadratic function is p(x) = a(x-h)2 + k, where (h, k) is the vertex of the parabola. The x-coordinate of the vertex (h) can also be found using the formula h = -b/(2a) where a is the coefficient of x2 and b is the coefficient of x in the standard form of the quadratic function. In this case, a = -4 and b = 6. Applying the formula:
h = -b/(2a) = -6/(2 * -4) = -6 / -8 = 0.75
Hence, the company should sell 0.75 thousand speakers, or 750 speakers, to maximize profit.
hey can you please help me posted picture of question
Answers
it has a slope equal to 1 and passes through the origin. All the other linear functions are derived from this parent function.
So, the correct answer to this question is option B
Hey can you please help me posted picture of question
Answers
We can get:
Head, Head
Head, Tail
Tail, Head
Tail, Tail
So, tossing 2 coins, result in 4 possible outcomes which make the sample space.
So correct answer is option B
11beehshahbaz
answer gl
Pablo randomly picks three marbles from a bag of eight marbles (four red ones, two green ones, and two yellow ones).
How many outcomes are there in the sample space?
Answers
The sample space for drawing 3 marbles from a bag of 8 marbles is 56. This is determined using the combinations formula in statistics and probability, which takes into account the number of items and the number of draws.
Explanation:The question you're asking relates to the concept of combinations in probability and statistics. When Pablo picks three marbles from a bag of eight marbles without replacement, he changes the number of possibilities with each draw. The sample space of his experiment consists of all possible outcomes he could get when drawing the three marbles.
The number of outcomes is determined by calculating the combination of 8 items taken 3 at a time. The formula for combinations is:
C(n, r) = n! / r!(n - r)!
Substituting the given values:
C(8, 3) = 8! / 3!(8 - 3)!
C(8, 3) = 8! / 3!5! = (8 x 7 x 6) / (3 x 2 x 1) = 56
So, the sample space for this experiment contains 56 possible outcomes.
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The question is about calculating combinations in combinatorics, a topic in mathematics. For a bag containing 8 marbles and picking 3 at a time, there are 56 possible outcomes or ways in which the marbles can be drawn from the bag.
Explanation:The number of outcomes in the sample space can be found by multiplying the number of choices for each marble. In this case, Pablo is picking three marbles from a bag of eight marbles. The number of outcomes is determined by the combination formula: nCr = n! / (r! * (n - r)!). So, for Pablo picking three marbles from eight marbles, the number of outcomes in the sample space is:
nCr = 8! / (3! * (8 - 3)!)
nCr = 8! / (3! * 5!)
nCr = 8 * 7 * 6 / (3 * 2 * 1) = 56.
Therefore, there are 56 outcomes in the sample space.
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Hey can you please help me posted picture of question
Answers
So, vertical stretch will result in:
14x
Flipping over y-axis means changing the sign of x.
So, the resultant function will be:
G(x) = -14x
Thus, the A option is the correct answer
y varies inversely x and y =-4 when x =7 . find the constant of variation and use it to write the equation that relates the variables
Answers
y = kx
k = constant of variation
To find k, plugin the values for y = -4 and x = 7 and then solve for k
y = kx
-4 = k7
-4 / 7 = k7/7
-4 / 7 = k
k = -4 / 7
Now that we found k, we write the equation that relates the variables like below
[tex]y = -\frac{4}{7}x[/tex]
you are painting a room that is 18 ft long, 14 ft wide and 8 ft high. find the area of the four walls that you are going to paint.
Answers
(14)(8)*2
+(18)(8)*2
equals 512.
Final answer:
The total area to be painted is 512 square feet, calculated by summing up the areas of the two longer walls (288 sq ft) and the two shorter walls (224 sq ft). For time estimation, the linear equation would be t = 4 + (512/1000), resulting in approximately 4.51 hours of painting time.
Explanation:
To calculate the area of the four walls in a room for painting, you will be finding the surface area of the sides not including the floor or ceiling. First, you need to calculate the area of the two longer walls and the two shorter walls separately.
For the longer walls, the area for one wall is 18 ft (length) times 8 ft (height), which gives you 144 square feet for one long wall. There are two such walls, so multiply by 2, which equals 288 square feet for both long walls.
For the shorter walls, the calculation is similar. The area for one short wall is 14 ft (width) times 8 ft (height), which gives 112 square feet for one short wall. With two short walls, the total is 224 square feet.
Add the area of the long walls and the area of the short walls together to get the total painting area: 288 sq ft + 224 sq ft = 512 square feet.
To express this as part of a linear equation for time estimation given in the scenario, if it takes one hour per 1,000 square feet, we would use the equation t = 4 + (A/1000), where t is the total time in hours and A is the area in square feet. Since the painting area is 512 square feet, the painting time is t = 4 + (512/1000), giving 4.512 hours, which rounds up to approximately 4.51 hours.
The sum of Andy and Brett's ages is 44. Andy's age is 8 more than twice Bret's age. Find the solution.
Answers
The ages of Andy and Brett can be determined by setting up two equations from the given information and solving for their ages. Andy is 32 years old, and Brett is 12 years old.
Explanation:The subject of this question is Mathematics. The question falls under algebraic problem-solving typically taught in middle school. To find Andy and Brett's ages, we can set up two equations based on the given information.
Let A represent Andy's age, and B represent Brett's age. According to the problem, we have:
A + B = 44 (since the sum of their ages is 44)A = 2B + 8 (since Andy's age is 8 more than twice Brett's age)We can substitute the second equation into the first:
(2B + 8) + B = 443B + 8 = 443B = 36B = 12Brett is 12 years old. Now, we can find Andy's age using the second equation:
A = 2(12) + 8A = 24 + 8A = 32 years oldSo, Andy is 32 years old, and Brett is 12 years old.
The sum of Andy and Brett's ages can be found using a system of equations. We can solve the equations to find Andy's age is 32 and Brett's age is 12.
Explanation:The problem can be solved using a system of equations.
Let's assume Andy's age is 'x' and Brett's age is 'y'.
We are given that the sum of their ages is 44, so the equation is: x + y = 44.
Additionally, Andy's age is 8 more than twice Brett's age, so we have another equation: x = 2y + 8.
Now we can solve this system of equations to find the values of x and y.
Substituting the value of x from the second equation into the first equation, we get (2y + 8) + y = 44. Simplifying this equation gives us 3y + 8 = 44. Subtracting 8 from both sides, we have 3y = 36. Dividing both sides by 3, we get y = 12. Substituting this value back into the first equation, we find x = 32.
Therefore, Andy is 32 years old and Brett is 12 years old.
PLZ HELP ASAP CIRCLES
Answers
[tex] x^{2} -10x+ y^{2}-10y=-25 \\ \\ x^{2} -2(x)(5)+25 +y^{2}-2(y)(5)+25=-25+50 \\ \\ (x-5)^{2}+(y-5)^{2}=25 [/tex]
So, the center of the circle is (5,5) with radius equal to 5.
So, Draw the circle placing the center at (5,5) and with radius equal to 5.
The mean for your data set is 13. The standard deviation is 2.5. What is the z-score for 10? Note 1: If necessary, round your answer to 3 decimal places
Answers
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
thus the z-score for the data set with mean 13 and standard deviation of 2.5 will be:
z=(10-13)/2.5
z=-1.2
Kelly estimates it will take her 35 minutes to make the punch and 45 minutes to set up. Will Kelly finish before the guests arrive if she starts at 11:45 a.m? Explain your answer. (Kelly's guests will arrive at 1:30)
Answers
use the product-to-sum identities to rewrite the following expression
sin 14° cos50°
Need help with hw, willing to give $$
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[tex]sin(x) cos(y) = \frac{1}{2} (sin(y+x) - sin(y-x))[/tex]
In this example, x = 14, y = 50
Answer: D
[tex]\frac{1}{2} (sin(64) - sin(36))[/tex]
Solve the systems x ≡ 1 (mod 2), x ≡ 2 (mod 3). x ≡ 2 (mod 5), 2x ≡ 3 (mod 7), 3x ≡ 4 (mod 11). x ≡ 31 (mod 41), x ≡ 59 (mod 26).
Answers
We know that '[tex]x=1(mod 2)[/tex]' means 2 divides '[tex]x-1[/tex]'. Keep in mind I can't add a three line "equality" symbol in Brainly...
The previous can be written with this statement:
[tex]x-1=2k[/tex]
In which '[tex]k[/tex]' is any integer.
From the previous equation is very easy to see that '[tex]x=2k+1[/tex]'.
We write the remaining congruence modulo relations as equations and solve for them in similar fashion:
[tex] x_{1}-2=3k [/tex]
[tex] x_{2}-2=5k [/tex]
[tex] 2x_{3}-3=7k [/tex]
[tex] 3x_{4}-4=11k [/tex]
[tex] x_{5}-31=41k [/tex]
[tex] x_{6}-59=26k [/tex]
Now we solve for the x's, remember, k is any integer!
[tex] x_{1} =3k+2[/tex]
[tex] x_{2} =5k+2[/tex]
[tex] x_{3} = \frac{7k+3}{2} [/tex]
[tex] x_{4} = \frac{11k+4}{3} [/tex]
[tex] x_{5} =41k+31[/tex]
[tex] x_{6} =26k+59[/tex]
the angle of the first hill of a roller coaster is 55 degrees. if the length of the track from the beginning of the ascent to the highest point is 98 feet, what is the height if the roller coaster when it reaches the top of the first hill?
Answers
sin θ=opposite/hypotenuse
θ=55°
opposite=h
hypotenuse=98 ft
thus the height will be:
sin 55=h/98
solving for h we get:
h=98×sin55
h=80.28 ft
Thus the height is 80.28 ft
Find an equation of the line described. Write the equation in slope-intercept form when possible. Slope 1, through (-4,3)
Answers
[tex]y=mx+b[/tex]
The point-slope form of the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]
We have:
[tex]m=1\ and\ A(-4;\ 3)\to x_1=-4\ and\ y_1=3[/tex]
Substitute:
[tex]y-3=1(x-(-4))\\\\y-3=x+4\ \ \ |+3\\\\\boxed{y=x+7}[/tex]
julie will build a rectangular pen for her dog against a barn. A wall from the barn will from one side of the pen. She has 32m of fencing to form the other three sides. She plans to build the pen so that it has its maximum possible area. What will be the dimensions of julie's pen?
Answers
the answer is 8 and 16
name a pair of fractions that use the least common denominator and are equivalent to 9/10 and 5/6
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Given the following sets:
A={ 2, 4, 6, 8, 10}
B={ 3, 5, 7, 9}
C={ 2, 3, 5, 7}
N={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Match the following Unions and intersections to the correct set.
1.
What is A U C?
2.
What is A ∩ B?
3.
What is A ∩ N?
4.
What is B ∩ N?
5.
What is B U C?
{2, 3, 4, 5, 6, 7, 8, 10}
{2, 3, 5, 7, 9}
{ }
{3, 5, 7, 9}
{2, 4, 6, 8, 10}
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B = {3, 5, 7, 9}
C = {2, 3, 5, 7}
N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
1. A ∪ C = {2; 3; 4; 5; 6; 7; 8; 10}
2. A ∩ B = { } =Ø
3. A ∩ N = {2; 4; 6; 8; 10} = A
4. B ∩ N = {3; 5; 7; 9} =B
5. B ∪ C = {2; 3; 5; 7; 9}
Can you please help me with this math problem
Answers
Area Trapezoid = (b1 + b2) * h / 2
b1 = 8
b2 = 12
h = 5
Area Trapezoid = (8 + 12 ) * 5 / 2
Area Trapezoid = 20 * 5/2
Area = 50 square feet.
The problem is that no lumber yard will cut that for you without charging you. The practical answer is 12 * 5 = 60 square feet is what you will have to buy. Then you cut out the triangles for yourself.
This question is nasty. It sounds like you should be finding area of the figure you see. I'll do that first, although I don't think it's the right answer. (But it might be).
Area Trapezoid = (b1 + b2) * h / 2
b1 = 8
b2 = 12
h = 5
Area Trapezoid = (8 + 12 ) * 5 / 2
Area Trapezoid = 20 * 5/2
Area = 50 square feet.
The problem is that no lumber yard will cut that for you without charging you. The practical answer is 12 * 5 = 60 square feet is what you will have to buy. Then you cut out the triangles for yourself.
how does the division look for 8.43206 ÷ 26
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Have a great day!