What are the ordered pairs of the solutions for this system of equations? y=x^2-2x+3
y=-5x + 1
Answers
The ordered pairs of the solutions for this system of equations is (-2,11) and (-1,6)
Two integers written in a certain order make up an ordered pair. As a result, we may define an ordered pair as a pair of components that appear in brackets and in a specific order.
These equations are composed of a line and a parabola. The intersection points between them must be located:
\(y=x^2-2x+3\)
y=-5x+1
Thus,
\(x^2-2x+3=-5x+1\)
\(x^2-2x+5x+3-1=0\)
\(x^2+3x+2=0\)
\(x^2+x+2x+2=0\)
\(x(x+1)+2(x+1)=0\)
x+2=0, x=-2
x+1=0, x=-1
Since the quadratic expression may be factored out, the following x-values represent the system's solution:
x=-2 and x=-1
Now, we may obtain the corresponding y values using either of the system's original equations. We decide to use a linear equation as an illustration:
When x =-2,
y=11
x=-1,
y=6
Thus the two points solution us (-2,11) and (-1,6)
To learn more about ordered pairs refer the link:
https://brainly.com/question/23922144
#SPJ9
Related Questions
Given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
True
False
Answers
It is true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
A parabola is a quadratic function graph .A parabola is a curve equation in which a point on the curve is equidistant from a fixed point and a fixed line.
The fixed point is known as the parabola's focus, and the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie on the fixed line.
A parabola is a locus of any point that is equidistant from a given point (focus) and a given line (directrix). The parabola is a significant curve of the coordinate geometry's conic sections.
The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h,k) denotes the vertex.
The standard equation of a regular parabola is y² = 4ax.
It's true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
Learn more about Parabola here:
brainly.com/question/21685473
#SPJ4
The points (4,1), (2, -2), and (-3, -3) are vertices of a polygon.
right triangle acute triangle isosceles triangle obtuse triangle
Answers
Answer:
obtuse
Step-by-step explanation:
or acute triangle
is the answer
Draw am arc with a radius of 2 inches and a measure of 220 degrees.
Please explain how to do this.
And no links.
Answers
Answer: you cant draw an arc with a radius, are you sure the question is right
Step-by-step explanation:
40th term of 2,7,12,17
Answers
So we can infer that the n = 5.
But we also have to add a number after that because right now the sequence would be 5,10,15,20. We need to find out how we get to 2 from 5n.*
*2 is the first number in the sequence
And to get 2 from 5 you simply subtract the number 5 by 3. So you end up with 5n - 3
Now that you have the nth term just substitute the term you want to find out so in this instance it is 40. 40 * 5 = 200 and then you take away 3 so It the answer must be 197. Hope this helps
In the diagram below, triangle lmn is congruent to cba. What is the length of segment ln?
Answers
Answer:
this is step by step explenation
see more...
Jessica made an ice cream with a radius of 4.5 centimeters and a height of 9 centimeters. Find the volume of the cone in cubic centimeters. Show your work and include the units. Round to the nearest whole number if necessary.
Please help me
Answers
The volume of the cone is approximately 191 cubic centimeters.
What is the volume of a cone?
The formula for the volume of a cone is:
V = (1/3) * π * r² * h
where "r" is the radius of the base, "h" is the height, and "π" is pi (approximately equal to 3.14).
Substituting the given values, we get:
V = (1/3) * π * (4.5 cm)² * 9 cm
V = (1/3) * π * 20.25 cm² * 9 cm
V = (1/3) * π * 182.25 cm³
V ≈ 191.36 cm³
Rounding to the nearest whole number, we get:
V ≈ 191 cm³
Therefore, the volume of the cone is approximately 191 cubic centimeters.
To know more about volume of a cone visit:
brainly.com/question/1578538
#SPJ1
An insurance agent earns a base salary of $32,000, and a commission of 3% of his sales. He also receives an additional fee of $16. 00 for each home policy he sells. The agent has sold a total of $89,000 and 8 home policies this month. Find the commission and fees he has earned
Answers
To find the commission and fees the insurance agent has earned, we need to first calculate the 3% commission from the $89,000 in sales. This is equal to $2,670. Next, we need to calculate the additional fees from the 8 home policies sold. This is equal to $128. Thus, the total commission and fees the agent has earned this month is $2,798 ($2,670 + $128).
This commission and fees amount is in addition to the base salary of $32,000. Thus, the total earned this month by the insurance agent is $34,798 ($32,000 + $2,798). This figure is obtained by adding the base salary and the commission and fees. Note that this figure does not include any bonuses or other incentives that the agent may receive.
To learn more about commission:
https://brainly.com/question/26283663
#SPJ4
let [a; b] be a non-degenerate closed interval in r, and let f : [a; b] ! r. for ant x 2 [a; b] and any t 2 [a; b] s.t. t 6
Answers
According to the given data the non - degenerated closed interval in r is calculated as \(\int\limits^t_s\)f(t) - f(s).
What is the degenerated interval?Any set that only contains one real number is known as a degenerate interval (i.e., an interval of the form [a,a]). an interval is measured in terms of numbers. An interval is any integer that falls between two specific numbers. This range encompasses all real numbers between those two. Real numbers can be any number anyone can think of. A degenerate interval is any set that contains only one real number (i.e., an interval of the form [a, a]). The empty set is included in this definition by some authors. A suitable interval is one that is either empty or degenerate and has an infinite number of elements.
According to the given data:f(x\(_r\)) - f(x\(_r\)₋₁) = F' (e\(_r\))(x\(_r\) - x\(_r\)₋₁)
By summating the equation it becomes.
f(t) - f(s) \(\int\limits^t_s\) f < = f(t) - f(s) --------->
\(\int\limits^t_s\) ts < = f(t) - f(s) ------------->2
From 1 and 2
\(\int\limits^t_-s < ={f(t) - f(s) < = \int\limits^t_d {f}\)
So, it finally becomes
\(\int\limits^t_s\)f < = f(t) - f(s)
To learn more about non - degenerated closed interval visit:
https://brainly.com/question/10071979
#SPJ4
Two rectangles with the same side length are always congruent
Answers
Answer:
no
Step-by-step explanation:
the length and the width in one rectangle are the same as the length and width in a second rectangle, then yes those rectangles must be congruent. If you just mean the lengths of 2 rectangles are equal, but their widths are different, then no those rectangles are not congruent.
Forty percent of a number is greater than one-half the number decreased by 15. Which inequality can be used to determine the number?A 40x > x /2 - 15B 40x > 2x - 15C 0.40x > x/2 - 15D 0.4x < x/2 - 15
Answers
Answer: 12
Step-by-step explanation: 21-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1=12
Are the following Triangles Similar? Why or Why Not?
Answers
Answer:
Yes, they are.
Step-by-step explanation:
They are both obtuse triangles. They may be different sizes but they are the same.
The anterior cruciate ligament (acl) is one of the ligaments that help stabilize the knee. surgery is often recommended if the acl is completely torn, and recovery time from the surgery can be lengthy. a medical center developed a new surgical procedure designed to reduce the average recovery time from the surgery. to test the effectiveness of the new procedure, a study was conducted in which 210 patients needing surgery to repair a torn acl were randomly assigned to receive either the standard procedure or the new procedure. based on the design of the study, would a statistically significant result allow the medical center to conclude that the new procedure causes a reduction in recovery time compared to the standard procedure, for patients similar to those in the study? explain your answer
Answers
A statistically significant result will allow the medical center to conclude that the new procedure causes a reduction in recovery time.
What is a Statistically significant result?A result is statistically significant if there's a very low probability that it could have occurred by chance.
What this means is that the reduction in the recovery time was truly as a result of the new procedure which is why it will be adopted by the medical center.
Read more about Statistically significant result here https://brainly.com/question/15848236
I need help on these three questions I’m so confused on how to answer them
Answers
Answer:
1. S(1) = 1; S(n) = S(n-1) +n^2
2. see attached
3. neither
Step-by-step explanation:
1. The first step shows 1 square, so the first part of the recursive definition is ...
S(1) = 1
Each successive step has n^2 squares added to the number in the previous step. So, that part of the recursive definition is ...
S(n) = S(n-1) +n^2
__
2. See the attachment for a graph.
__
3. The recursive relation for an arithmetic function is of the form ...
S(n) = S(n-1) +k . . . . . for k = some constant
The recursive relation for a geometric function is of the form ...
S(n) = k·S(n-1) . . . . . . for k = some constant
The above recursive relation is not in either of these forms, so it is neither geometric nor arithmetic.
Which of the following factors does NOT control the stability of a slope?
the angle of repose for intact bedrock
whether the slope is rock or soil
the amount of water in the soil
the orientation of fractures, cleavage, and bedding
Answers
The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.
Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.
The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.
To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.
know more about Bedrock.
https://brainly.com/question/2948854
#SPJ11
Dilate rectangle
A
B
C
D
using center
P
and scale factor 1/2
. Either draw the image, take a picture, and upload the dilation or type a detailed description of the new rectangle.
Answers
Answer:
The coordinates of the points of the rectangle A'B'C'D' are;
The coordinates of the point A' = (-2, -1)
The coordinates of the point B' = (-2, 1)
The coordinates of the point C' = (2, 1)
The coordinates of the point D' = (2, -1)
Step-by-step explanation:
Placing the point P as the origin of the chart, we have;
The coordinates of the points are given as follows;
The coordinates of the point B = (-4, 2)
The coordinates of the point C = (4, 2)
The coordinates of the point A = (-4, -2)
The coordinates of the point D = (4, -2)
Given that the sides are parallel to the axis, we have;
The length of the segment AB = 2 - (-2) = 4
The length of the segment BC = 4 - (-4) = 8
The length of the segment CD = 2 - (-2) = 4
The length of the segment AD = 4 - (-4) = 8
Therefore, a dilation by 1/2 will give;
The length of the segment A'B' = AB/2 = 4/2 = 2
The length of the segment B'C' = BC/2 = 8/2 = 4
The length of the segment C'D' = CD/2 = 4/2 = 2
The length of the segment A'D' = AD/2 = 8/2 = 4
The coordinates of the point A' = The coordinates of the point A/2 = (-4, -2)/2 = (-2, -1)
The coordinates of the point A' = (-2, -1)
The coordinates of the point B' = The coordinates of the point B/2 = (-4, 2)/2 = (-2, 1)
The coordinates of the point B' = (-2, 1)
The coordinates of the point C' = The coordinates of the point C/2 = (4, 2)/2 = (2, 1)
The coordinates of the point C' = (2, 1)
The coordinates of the point D' = The coordinates of the point D/2 = (4, -2)/2 = (2, -1)
The coordinates of the point D' = (2, -1).
An equation is shown 3/5k=225. what is the value for k that makes the equation true?
Answers
Answer:
.0024
Step-by-step explanation:
3 = 225 x 5k
3/255 = 5k
5k = 0.117
k=0.0024
What are the solution(s) of -1/2X+4= X+ 1?
O-1 and 8
О 1 and 4
O 2
O 3
Answers
Answer:
X = 2
Step-by-step explanation:
-1/2X+4= X+ 1
Add 1/2X to each side
-1/2X+ 1/2 X+4= X+ 1 + 1/2 X
4 = 3/2 X +1
Subtract 1 from each side
4-1 = 3/2 X +1-1
3 = 3/2 X
Multiply each side by 2/3 to isolate x
3 * 2/3 = 3/2 X * 2/3
2 =X
three people are sitting on a bus sebastian is seated 3 feet directly behind abdul and 4 feet directly left of harold how far is abdul from harold
Answers
Answer:
7 feet
Step-by-step explanation:
All you have to do since he's sitting 3 feet directly behind Abdul and 4 feet directly left of Harold it would be 7 just by adding them up.
Hope this helps.
The following table provides a probability distribution for the random variable y. a. Compute E(y) (to 1 decimal). b. Compute Var(y) and σ (to 2 decimals). Var(y)
Answers
The expected value of the random variable y is computed to be 3.8.The variance of y is calculated to be 4.06, and the standard deviation is approximately 2.02.
To compute the expected value of the random variable y, we multiply each value of y by its corresponding probability and sum them up. In this case, we have:
E(y) = (2)(0.2) + (4)(0.1) + (5)(0.3) + (8)(0.2) + (10)(0.2) = 0.4 + 0.4 + 1.5 + 1.6 + 2 = 3.8.
To calculate the variance of y, we first need to compute the squared deviations from the expected value for each value of y, multiply them by their corresponding probabilities, and sum them up. Then, subtracting the squared expected value of y gives us the variance. Using the formula:
Var(y) = \(E[(y - E(y))^2],\)
we have:
Var(y) = \([(2 - 3.8)^2](0.2) + [(4 - 3.8)^2](0.1) + [(5 - 3.8)^2](0.3) + [(8 - 3.8)^2](0.2) + [(10 - 3.8)^2](0.2),\)
Var(y) = 0.36 + 0.04 + 0.36 + 4.84 + 36,
Var(y) = 4.06.
Finally, the standard deviation (σ) is the square root of the variance:
σ = √Var(y) ≈ √4.06 ≈ 2.02.
Therefore, the variance of y is 4.06, and the standard deviation is approximately 2.02.
Learn more about probability here:
https://brainly.com/question/32117953
#SPJ11
PLEASE HELP ME I CANT GET IT RIGHT
Answers
Answer:
I believe the answer is 760 ft²
Step-by-step explanation:
16×39/2=312
(17+39)(16)/2=448
448+312=760ft²
let me know if it was right. good luck!
Can someone help me solve this pls
Answers
Answer: that’s an acute angle
Step-by-step explanation:
What is x in this equation?
3x + 1 = 10
Answers
Answer:
x=3
Step-by-step explanation:
I NEED HELP PLEASE!!!!!!!
1) How long is it from 9:15 am to 4:48 pm? h
2) Find the value of 4n if n=7
3) Solve the equation 3y=21
4) Change the index notation of a⁴ to its factors
Answers
2) 28
3) y = 7
4) a times a times a times a
Explain what was wrong with EACH graph you picked.
(why does the graph NOT represent a proportional relationship)
Answers
Find the next three terms in the geometric sequence: 72, 36, 18,... (sorry for bothering a lot)
Answers
Answer:
18 / 2 = 9
9 / 2 = 4.5
4.5 / 2 = 2.25
The next three terms are 9,4.5,2.25
Hope this helps
Step-by-step explanation:
Convert y-8.25=(x-3) into slope intercept form
Answers
Answer:
y = x + 5.25
Step-by-step explanation:
y - 8.25 = (x - 3)
y - 8.25 = x - 3
y = x + 5.25
Could you please give me brainliest for this? Thank you!
Answer:
y = x + 5.25
Step-by-step explanation:
y - 8.25 = x - 3 Add 8.25 to both sides of the equation
y = x + 5.25
O GRAPHS AND FUNCTIONSGraphing a function of the form f(x) = ax + b: Integer slopeGraph the function g(x)=-3x-1.ywww.6-4-Хv5
Answers
this is:
x g(x)
-3 8
-2 5
-1 2
0 -1
1 -4
2 -7
3 -10
then this value we locate them in the graph, each ordered pair
\(\begin{gathered} \text{if x = -1} \\ g(-1)=-3(-1)-1 \\ g(-1)=3-1 \\ g(-1)=2 \end{gathered}\)then we have the coordinate (-1, 2) and place it on the Cartesian plane
\(\begin{gathered} \text{if x=0} \\ g(0)=-3(0)-1 \\ g(0)=-1 \end{gathered}\)we have the coordinate (0, -1)
\(\begin{gathered} \text{if x = 1} \\ g(1)=-3(1)-1 \\ g(1)=-3-1 \\ g(1)=-4 \end{gathered}\)we have the coordinate (1, -4)
Find the area of the trapezoid.A trapezoid with the top base labeled six meters and the bottom base labeled four meters. The height is labeled six meters.
Answers
Given: The dimension of a trapezoid as shown below
\(a=6m,b=4m,h=6m\)To Determine: The area of the given trapezoid
Solution
The formula for finding the area of a trapezoid is
\(A_{\text{rea}}=\frac{1}{2}(a+b)h\)Substitute the given into the formula
\(\begin{gathered} A_{\text{rea}}=\frac{1}{2}(4+6)\times6 \\ A_{\text{rea}}=\frac{1}{2}(10)\times6=30m^2 \end{gathered}\)Hence, the area of the trapezoid is 30m²
A rectangle has a width of 2.45 feet and a length of 6.5 feet. how will the area of the rectangle change if each side is increased by a factor of 5? the area will be one-fifth the original. the area will be startfraction 1 over 25 endfraction the original. the area will be 25 times the original. the area will be 5 times the original.
Answers
The area of the new rectangle will be 25 times that of the original
Area of a rectangleA rectangle is a 2D shape that has 4 sides and equal interior angles
If rectangle has a width of 2.45 feet and a length of 6.5 feet, then;
Width = 2.45 feet
Length = 6.5feet
A = 2.45 * 6.5
A = 15.925 square feet
If each side of the rectangle is increased by a factor of 5, hence;
W1 = 5(2.45) = 12.25feet
L1 = 5(6.5) = 32.5 feet
Determine the area of the new rectangle
A = 12.25 * 32.5
A = 398.125 square feet
Ratio of the area
A1/A = 398.125/15.925
A1 = 25A
Hence the area of the new rectangle will be 25 times that of the original
Learn more on area of rectangle here: https://brainly.com/question/2607596
#SPJ1
the surface area of a cylinder is 140 pie square feet, and its height is 9 feet. find its radius
Answers
Answer:
the radius is 2.02
Step-by-step explanation:
use the formula to solve the radius of a cylinder