The graphs intersect at the points (3, 13) and (-2, -7).
How to determine the intersection of 2 graphsGiven the following equations:
y₁ = x² + 3x - 5 (quadratic equation)
y₂ = 4x + 1 (linear equation)
To find the intersection point(s) of the two graphs, we need to solve their equations simultaneously. By so doing, we'll set the equations equal to each other:
y₁ = y₂
x² + 3x - 5 = 4x + 1
collect the like terms
x² - x - 6 = 0
Now we'll factor the quadratic expression:
(x - 3)(x + 2) = 0
x - 3 = 0 or x + 2 = 0
x = 3 or x = -2
Now we have the points of intersection on the x-axis.
To get the corresponding values on the y-axis, we'll plug each value of x into either of the original equations.
Let's use the first equation:
y₁ = x² + 3x - 5
When x = 3:
y₁ = 3² + 3(3) - 5 = 13
When x = -2:
y₂ = 4x + 1 = 4(-2) + 1 = -7
So the first intersection point is (3, 13) and the second intersection point is (-2, -7).
Therefore, the graphs intersect at the points (3, 13) and (-2, -7).
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Christie's Auction sold a painting for
$24,500. It charges all buyers a 15%
premium of the final bid price. How much
did the bidder pay Christie's?
The price that bidder pays to Christie's is $2130.4.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
And to convert a fraction or a decimal into percentage, they are multiplied by 100.
Given that,
The price for which painting is sold is $24,500.
The percentage of premium price of the final bid is 15%.
Suppose the price paid by the bidder be x.
Then, as per the question the following equation can be written for the price of painting,
x + 15% of x = 24500
=> x + (15/100)x = 24500
=> 115x/100 = 24500
=> x = (24500 × 100) ÷ 115
=> x = 2130.43
Hence, the amount paid to Christie's is $2130.4.
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Allison collected books to donate to different charities. The following expression can be used to determine the number of books each charity received.
(12 + 4 • 5) ÷ 2
Based on this expression, how many books did each charity receive?
What is the length of missing side X? Options are on photo
Help ASAP
Answer:
it should be 5 because its a rectangle
Answer:
x = 5cm
Step-by-step explanation:
Remember opposite sides of a rectangle are congruent
The opposite side of side "x" is equal to 5 cm therefore x = 5 cm
Important note! : The triangle does not change the side length as it is formed using it.
Given the angles in the diagram below, what is mZ2?
Answer:
98
Step-by-step explanation:
Hello There!
The angle that has a measure of 82 degrees and the angle labeled "2" are supplementary angles.
This meaning that the sum of the two angles is 180
So to find the missing angle (2) we subtract the given angle (82 in this case) from 180
so ∠2 = 180 - 82
180 - 82 = 98
Hence, the answer is 98°
Which is a better deal on a $345 item: 40% off original price or 30% off and additional 15% at the register?
Answer:
345 - 40% = 207$
Step-by-step explanation:
(345 - 30%) - 15% = 205.3 (Better deal)
Answer:
30% off and additional 15% at the register
Step-by-step explanation:
Deal 1
$345 × 40% = $138
$345 - $138 = $207
Deal 2
$205.30
DO NOT PRANK!! I NEED HELP PLS (will give brainly)
Use the diagram below for this question. The angle bisectors of triangle ABC meet at G.
If m∠ ABC = (4x + 12) degrees and m∠ GBA = (3x – 4) degrees , find m∠ GBC.
A.26 degrees
B.44 degrees
C.52 degrees
D.36 degrees
Answer:
b
Step-by-step explanation:
hiiii
Which statement about the data is true and find the median and range.
Answer:
I think it's D
its either A or D because the median is definitely 4
Find the slope and the y intercept
The radius of a cylindrical construction pipe is 1.5 ft. If the pipe is 15 ft long whats the volume
Answer:
Step-by-step explanation:
r = 1.5 ft
h = 15 ft
π = 3.14
Volume = πr²h
= 3.14 * 1.5 *1.5 *15
= 1.5.975 cubic feet
The radius of a cylindrical construction pipe is 1.5 ft. If the pipe is 15 ft long, what's the volume ?
Answer:-Given:-[tex] \bullet [/tex] Radius (r) of a cylindrical construction pipe is 1.5 ft.
[tex] \bullet [/tex] Height (h) of a cylindrical construction pipe is 15 ft.
To Find:-Volume of a cylindrical construction pipe.
Solution:-We know,
Formula of Volume of cylinder is πr²h.
So, Volume = 3.14 × (1.5)² × 15
Volume = 3.14 × 1.5 × 1.5 × 15
Volume = 105.975 cubic ft.
The volume of a cylindrical construction pipe is 105.975 cubic ft. [Answer]In a clothing store, 65% of the customers buy a shirt, 30% of the customers buy a pair of pants, and 20% of the customers buy both a shirt and a pair of pants. I’m f a customer is chosen at random, what is the probability that he or she buys a shirt or a pair of pants?
Answer:
The Answer will be (0.75)
POSSIBLE POINTS: 5
Taina found the area of a table in the shape of a trapezoid. The height of the trapezoid is 10 ft, base one is 6 ft and base two is 5 ft. Taina says the area of the figure
is 110 square foot inches. What mistake did Taina make? What is the actual answer?
9514 1404 393
Answer:
wrong formulawrong unitsStep-by-step explanation:
The formula for the area of a trapezoid is ...
A = 1/2(b1 +b2)h
A = (1/2)(6 ft +5 ft)(10 ft) = 55 ft²
The numerical value of the answer would be 110 if we "forgot" to multiply by 1/2.
The area units would be "square foot inches" if inch dimensions crept into the problem somewhere.
It looks like Taina made two mistakes:
didn't correctly use the correct formuladidn't pay attention to area units2 1/2 ft x 1/4 ft
please help
Step-by-step explanation:
0.0580644 m2 hope this helps
Step-by-step explanation:
Here,
[tex] \frac{21}{2}ft \: \times \: \frac{1}{4} ft[/tex]
[tex] = \frac{21}{8} {ft}^{2} [/tex]
OR :
[tex]2 \frac{5}{8} {ft}^{2} \: \: also \: \: \: 2.625 {ft}^{2} [/tex]
Solve for x.
2
8
4
X
Answer:
Impossible
Step-by-step explanation:
This diagram is not correctly stating the question
Which of the following is a factor of 2x2 - x-6?
O (x+2)
O (2x - 3)
o (x – 3)
O (2x + 3)
answer of the question
Answer:
The number of milk chocolate pieces is between 115 and 120 pieces.
Step-by-step explanation:
Please help me fast i need help please
Answer:
30
Step-by-step explanation:
because I find the lcm for each number
А Campus athletics is interested in the proportion of registered students living on campus who play basketball recreationally during the semester. They take a random sample of 198 registered students listed as living in campus housing and ask each whether or not they do so. A 95% confidence interval is correctly calculated from this data as (0.12, 0.18). Which of the following is the correct interpretation of this confidence interval ?
a. None of these are correct.
b. We are 95% confident that the proportion of the 198 sampled students that actually play basketball is between 0.12 and 0.18
c. We are 95% confident that, among the population of students that play basketball recreationally, the proportion who live on campus is between 0.12 and 0.18.
d. The sample proportion of on-campus students that play basketball will be between 0.12 and 0.18 in 95% of samples of size 198
Answer:
c. We are 95% confident that, among the population of students that play basketball recreationally, the proportion who live on campus is between 0.12 and 0.18.
Step-by-step explanation:
According to the question, it is mentioned that there is 95% confidence interval and it is calculated (0.12,0.18)
So the correct interpretation is that they are 95% confident that the students who play basketballs the proportion should lies between 0.12 and 0.12
So, the option C is correct
The rest of the options are wrong
What is the answer please I need help if you send a link I will report because your just trying to scam someone
Answer:
The median is 6.
Step-by-step explanation:
Decide whether 2x+8 and 2(x+4)+4 are equivalent expressions. Explain how you know
Answer:
2x+8 and 2(x+4)+4 are not equivalent expressions
Step-by-step explanation:
Firs we need to expand 2(x+4)+4 using the distributive law as shown;
2(x+4)+4
=2(x) + 2(4) + 4
= 2x + 8 + 4
= 2x + 12
Since the result is not equivalent to 2x+8 hence 2x+8 and 2(x+4)+4 are not equivalent expressions
HS: Algebra 2A [M] (Prescriptive) (GP)/ 5 Quadratic Functions
2. Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
y=(x - 5)(5x+4)-5x?
linear function
linear term: 15x
constant term: -25
quadratic function
quadratic term: 5x?
linear term: 15x
constant term: -25
quadratic function
quadratic term: -5x?
linear term: -21%
constant term: -20
linear function
linear term: -21x
constant term: -20
Congratulations! You have shown o
completing one or more activities. I
unchack Hide excused activities
Answer:
Linear, the linear term is -21x and the constant term is -20. Last option is the answer
Step-by-step explanation:
We are given the following function:
[tex]y = (x - 5)(5x + 4) - 5x^2[/tex]
First we have to simplify y, before solving the question:
[tex]y = (x - 5)(5x + 4) - 5x[/tex]
Applying the distributive property:
[tex]y = 5x^2 + 4x - 25x - 20 - 5x^2[/tex]
[tex]y = 0x^2 - 21x - 20[/tex]
[tex]y = -21x - 20[/tex]
No quadratic term, so it is linear.
The linear term is -21x and the constant term is -20.
Rewrite 2/5 and 4/11 so that they have a common denominator
Answer:
22/55 and 20/55
Step-by-step explanation:
multiply 2 and 5 by 11 to get 22/55, and multiply 4 and 11 by 5 to get 20/55
Ariel takes 3 pages of notes during each hour of class. In all, how many hours will Ariel
have to spend in class before she will have a total of 36 pages of notes in her notebook?
Answer:
12 hours
Step-by-step explanation:
36 divide that by 12 and she has 12 hours to write on 36 pages
can anyone help me with this please! Serious plz lol
I hope this helps you
Which of the following is a true statement?
o & >
o = }
Os <
Answer:
the last one Denise, is the only one that is true
Step-by-step explanation:
Answer:
last one
Step-by-step explanation:
Squares are Rhombus but not rectangles true or false
Answer:
True
Step-by-step explanation:
Rhombus is a sideways SQUARE
Answer: True
if you turn a square 45 degrees to the side it is a rhombus
solve the equation f/3+22=17
Answer:
f = -15
Step-by-step explanation:
f/3 + 22 - 22 = 17 - 22
f/3 + 0 = -5
f/3 = -5
f = 3 × (-5)
f = -15
Thus, The answer is -15
-TheUnknownScientist
a plate moves at a sped of 45 mm/yr. How far will the plate move in 100 years?
Answer:
4,500 millimeters per year.
Step-by-step explanation:
brainliest?
Answer:
4500 mm or 4.5 m
Step-by-step explanation:
45 mm/yr x 100 yr = 4500 mm = 4.5 m
PAST DUE DATE NEED DONE NOW! NO LINKS! HELP ME FIND THE EQUATION
To write an equation for this line, you first need to understand how to derive it.
Let's utilize slope-intercept form, as it's the easiest to understand compared to any other form for line functions:
y = mx + b
m: The slope of the line
b: The y-intercept (The point where the line is at the y-axis)
Now that we've defined our variables, how do we go about making the actual equation? Let's start off with the slope, m.
The slope is a measure of how high or low the line is. The number is a ratio between the rise and run of a slope. In other words, it is essentially [tex]\frac{rise}{run}[/tex]
Let's look back at the graph. In the time interval from 1 to 2 seconds, we see that the line rises by 22 feet. Because the time interval is only 1 second, the run is 1 second.
Therefore:
m = [tex]\frac{rise}{run}[/tex]
m = [tex]\frac{22}{1}[/tex]
m = 22
We now have the first variable of the equation.
y = 22x + b
What about b? As we established earlier, b is the value of coordinate y at the y-intercept. Essentially, to find b we need to know what the value of y is when the coordinate x is 0.
As you can see from the graph you made, the value of y when x is 0 is also 0. This makes sense, too. How can the cheetah travel distance at 0 seconds when it obviously hasn't started moving? We now know b = 0. Now, we have gotten all of the variables we need to make a full equation:
y = 22x + 0
y = 22x
If you'd like me to explain how I did anything, just ask!
- breezyツ
Answer:
Equation: y=22x + 0 (you can put 0 if you want)
Step-by-step explanation:
Okay, so this is set up as a y=mx+b equation meaning that m=rate of change and b=y-intercept. If a cheetah runs 22 feet per second which is x, that means that m=22. And if 1 second is equal to 22 feet then in 0 seconds they run 0 feet, which is your y-intercept. Another way to find the rate of change (m) is by using the equation y2-y1/x2-x1 or 44-22/1 in this case. This equation is usually written as y=22x. Hope this helps!
6 cm
6 cm
1
6 cm
9 cm
-6 cm
-15 cm
Answer:
180 cm^2
Step-by-step explanation:
Remark
If you put the slices that have been removed back into the figure, and figure out the resulting rectangle and subtract the slices, you get an answer that is easily calculated.
Note
The square on the upper right is 6 cm high. That makes the width of the rectangle 9 + 6 = 15. The length is already known as 15. So this square is 15 by 15 = 225
The lower right triangle is a little harder to handle. The total width is 15. The height of the triangle is 6 + 6. The first 6 comes from the square that was removed. The total with is 15. So the height of the lower right triangle is 15 - 12 = 3
Answer
The answer to the square on the upper left that was removed = 6*6 = 36
The answer to the triangle on the lower right is 1/2 * 6 * 3 = 9
The total of the removed figues is 36 + 9 = 45
The area of the figure with both figures removed is 225 - 45 = 180 cm^2
HELP!!! FIRST TO ANSWER GETS BRAINIEST!!!Which of the following equations was used to graph the line shown?
Answer:
Which Equations???
Step-by-step explanation:
Also for coordinates its
([tex]6,6[/tex])
And I think I answer is A
Hope this helps.. Have a nice day :)
Answer:
y=-x+6
Step-by-step explanation:
A negitive line faces down so this becomes y=-x. so in y=mx+b, b is the point where the line crosses the y axis. So that crosses at 6, so your eqation is y=-x+6
