Which represents the solution(s) of the graphed system of equations, y = x2 2x – 3 and y = x – 1? (1, 0) and (0, –1) (–2, –3) and (1, 0) (0, –3) and (1, 0) (–3, –2) and (0, 1)
Answers
Answer: the second choice: (0, - 2) and (1, 0).
Explanation:
1) The solution of a graphed system of equations is the points of intersection of the equations.
2) Hence, this method requires to graph each function in one Cartesian coordinate system.
3) To graph the function y = x² + x - 2, you can follow these steps
draw the perpendicular x(horizontal)-axis, and y(vertical)- axismark the divisions in each axis (1 unit is a good scale for this case)notice that y = x² + x - 2 is a parabolawrite y = x² + x - 2 in its vertex form following these steps:y = (x² + x) - 2
y + 1/4 = (x² + x + 1/4) - 2
y + 1/4 = (x + 1/2)² - 2
y = (x + 1/2)² - 2 - 1/4
y = (x + 1/2)² - 9/4
Compare with the vertex form y = (x + h)² + k, where the coordinates of the vertex are (h,k). Therefore, the vertex is (1/2, - 9/4).
The parabola open upwards (because the coefficient of the quadratic term is positive).Find the y-intercept (x =0) and x-intercepts (y = 0), and write a table with some values:x y = (x + 1/2)² - 9/4-2 0-1 - 2-1/2 -2.250 - 21/2 -1.251 02 44) To graph the function y = 2x - 2, you can follow these steps:
Use the same Cartesian coordinate systemNotice it is a lineThe slope is 2 (the coefficient of x)The y-intercept is - 2( the constant term)Build a table (use the same x-values used for the first graph)x y = 2x - 2-2 - 6-1 - 4-1/2 - 30 - 21/2 - 11 02 2The tables show that these points are common to the two functions: (0, - 2) and (1,0).
The graphs are shown in the figure attached.
You can see that the parabola (blue curve) and the line (purple line) intercept each other at those two points ( 0, - 2) and (1,0).
Related Questions
If a recipe requires 1/4 pounds of ground beef
to make 6 servings of chili, how many servings
can be made with 1 1/2 pounds of ground beef?
Answers
Answer:
36 servings
Step-by-step explanation:
1/4p = 6s
6(1/4p) = 6(6s)
1 1/2p = 36s
Eugene's grandmother is teaching him how to make her salsa recipe. Each batch of salsa requires 1/4 of a cup of red onions. If they have 1 1/2 cups of red onions, how many batches of salsa can they make
Answers
Answer:
6
Step-by-step explanation:
6 times 1/4 is equal to 6/4, which is 1 1/2 :)
1 1/2 = 3/2
3 • 4
- - =
2 1
12
— =
2
6
5. During a field trip, 168 students were
divided into 14 equal groups. How
many students were in each group?
Answers
Answer:
so, 168 divided by 14 = 12
Step-by-step explanation:
14 x 12 =168
Answer:
168÷14=12
12 multiplied by 14 is 168.
If the number of equally likely sample outcomes of a single stage of an experiment is 4, what is the total number of elements in the sample space if the experiment has 3 stages?
Answers
Answer
64
Step-by-step explanation:
4 x 4 x 4
so it's like you take 4 and 3 stage = 4 x 4 x 4
Hope it helped !
Have a nice day studying ! Mark me as Brainliest too Ty !
if f(x)=7x-3, what is the value of x when f(x)=1
Answers
1 = 7x - 3
Add 3 to both sides:
7x = 4
Divide both sides by 7:
x = 4/7
Hope this helps!
17 of 3017 of 30 Questions
Question 1
Rectangle PQRS is graphed on the coordinate plane.
Part A
Rectangle PQRS is rotated 90° counterclockwise about the origin to create rectangle P'Q'R'S' (not shown). What are the coordinates of point R'?
Answers
a) When rotating 90 degrees clockwise, (x,y) maps onto (-y,x), meaning R(6,-7) maps onto (7, 6).
The price of a camera is $ 9810 inclusive of sales tax. If the rate of sales tax is 9%, find the printed price of the camera.
Answers
Answer:
$8927.1
Step-by-step explanation:
printed price is the actual price without including tax price
tax price= 9/100×9810
tax price= 0.09×9810= $882.9
printed price of the camera= 9810-882.9= $8927.1
Question 9 of 30
Find the surface area of the polyhedron below. The area of each base is 65
cm-.
7 cm
cm
12 cm
cm
cm
Please help asap
Answers
Answer:
A
Step-by-step explanation:
12×4=48cm²
12×3=36cm²
12×2×2×2=96cm²
therefore is 270cm² + 65cm² + 65cm²
=370cm²
a group of 12 people must pay $435 to rent a chalet. to have access to 3 canoes, they must also pay a rental fee of $15 per boat.
how much did each people had to pay?
Answers
Answer: Each person had to pay $40
Step-by-step explanation:
435 + 15*3
435+45 = 480
480/12 = 40
Each person had to pay $40
The rule is 8,9 what is the 100th number
Answers
The hundredth number in the series as defined in the task content is; 107.
What is the 100th Number?According to the task content;
The first term of the sequence of numbers is; 8 and evidently, the common difference of the sequence is; 9-8 = 1.
On this note it follows that the 100th number is;
T(100th). = 8 + 99(1) = 107.
Read more on terms in sequence;
https://brainly.com/question/7882626
#SPJ1
170 over 360 simplify
Answers
Answer: 17/36
Step-by-step explanation:
Help me on this math problem! DUE TONIGHT!! Please read the instructions so you can include all the answers needed!
Answers
Answer:
x=10, first angle is 107, second angle is 73
Step-by-step explanation:
A semi- circle has an area of 35cm . What is its diameter?
Answers
Answer:
Area Semicircle = 1/2 πr²where
r radius of semicircle
→ ½ * 22/7 * r² = 35
→ 11/7 * r² = 35
→ r² = 35*7/11
→ r² = 245/11
→ r² = 22.77
→ r = √22.77
→ r = 4.77
Therefore,
Diameter = 2*4.77
= 9.54 cm
Select two values that can replace \square□\square to make the equation true. \square=5. 40
Answers
Answer and Explanation:
x= 5.04
so, as this is a multiple choice question, the two values are
A - five ones and forty thousands
and
C - (5x1) + (4 x 1/100)
and as they both equal 5.04 (the value of "x"), those two would be the correct answers out of the four options given, hope this helps!!
find the surface area of the figure. round to the nearest hundredth when necessary.
Answers
Answer:
in terms of pi: 112.5pi mm squared
substituting pi for 3.14: 353.25 mm squared
Step-by-step explanation:
Surface area cone equation:
Πr2 + π*r*s
4.5^2 = 20.25pi
400 + 20.25 = 420.25
sqrt(420.25) = 20.5
20.25pi + 92.25pi = 112.5pi
Roger is sixteen years old and eats granola bars. He attends P.R. Walker High School. In this example, is the independent variable.
Roger's age
Roger's school
Roger's diet
Answers
Answer:
Since the Independent variable is something that is modified or controlled in a scientific experiment, it is his age.
What is a possible value for the missing term of the geometric sequence?
54, ___, 1944, ...
Answers
Answer:
324
Step-by-step explanation:
The missing term in this geometric sequence is the geometric mean of 54 and 1944.
[tex] \sqrt{54 \times 1944} = \sqrt{104976} = 324[/tex]
Answer:
324
Step-by-step explanation:
The formula for the missing term in a geometric sequence is the square root of x times y.
What is the third term of the sequence described by the following explicit formula? an = 9 + (n - 1)8
Answers
Answer: Solve for a: a = [tex]\frac{8n+1}{n}[/tex]
Solve for n: [tex]n=\frac{1}{a-8}[/tex]
Step-by-step explanation:
solve for n: Move all terms to the left side and set them equal to zero. Then set each factor equal to zero.
solve for a: Divide each term in an = 9 + (n−1) ⋅ 8 by n and simplify.
What is the surface area of this figure?
Answers
Answer:
582 ft squared
Step-by-step explanation:
15*9*2 = 270
15*4*2 = 120
6*6*2 = 72
9*4*2 = 72
6*4*2 = 48
270 + 120 + 72 + 72 + 48 = 582
In a test (+5) marks are given for every correct answer and (-2) marks are given for every incorrect answer. Smitha answered all questions and scored (-15) marks though he got 3 correct answers. How many incorrect answer had she attempted?
Any one help I will mark u as BRAINLIEST ANSWER if u help me plssssss! I will not accept wrong answer pls
Answers
Answer:
15 answers
Step-by-step explanation:
To solve this question we need to set up an equation.
Let's name the number of incorrect answers x.
We can set up an equation that's essentially:
(Points for correct answer)*(number of correct answers)+(points for incorrect answer)*(number of incorrect answers)=final score
When we plug in our numbers and variables it looks like this:
5(3)+(-2x)=-15
Simplify
15-2x=-15
Subtract 15 from both sides
-2x=-30
Divide both sides by -2
x=15
This means Smitha attempted 15 wrong answers, and that there were 18 questions in total.
peter drove 1.5 hours at an average speed of 40 mph. He then drove for another 40km.
5 miles=8 kilometers
how far did peter drive?
give your answer in miles
Answers
Answer:
john drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour.
Step-by-step explanation:
answer Number 3 please
Answers
Answer:
It is reasonable
Step-by-step explanation:
23 degrees Fahrenheit converts directly to -5 degrees Celsius
Ryan and Patrick are eating together. They spent a total of
18 dollars on pizzas and calzones. Each pizza is 3 dollars
and each calzone is 2 dollars. They spent 2 minutes
eating each pizza and spent 5 minutes per calzone. It
took them 23 minutes to eat their food.
Help me
Answers
Answer:
Will you be my friend? please answer
Step-by-step explanation:
what do you need to find ?
the number of pizzas and calzones they were eating ?
if so :
p = number of pizzas
c = number of calzones
3p + 2c = 18
2p + 5c = 23
let's multiply the first equation by 2 and the second squadron by 3, and then subtract the second from the first :
6p + 4c = 36
- 6p + 15c = 69
-------------------------
0 -11c = - 33
c = 3
2p + 5c = 23
2p + 5×3 = 23
2p + 15 = 23
2p = 8
p = 4
so, they were eating 4 pizzas and 3 calzones.
I don't understand can anyone help me pls
Answers
180-140 = 40 so that’s ur central angle and the central angle always is the same as the arc
6x - 8 = 40
6x = 48
x = 8
Cooper has a points card for a movie theater. • He receives 70 rewards points just for signing up. • He earns 8.5 points for each visit to the movie theater. • He needs at least 260 points for a free movie ticket. Which inequality can be used to determine v, the minimum number of visits Cooper needs to earn his first free movie ticket?
FIRST TO ANSWER CORRECTY WILL BE MARK AS BRILLIANT !!!!
Answers
Answer:
The correct answer is 70+8.5V > 260
Step-by-step explanation:
The equation of this is that instead of getting 260 points instantly he can get to 23 movies and earn the points each visits. So
8.5x23+70=265.5
Hence the correct answer is C
3) If the speed limit on a highway in the UK is 70 miles per hour and
it is 120km per hour in Canada, which country has the higher speed
limit for highways? What is the difference between them?
Answers
Step-by-step explanation:
for this we need to know the conversion rate between miles and kilometers :
1 mile = 1.60934 km
which means
1 km = 0.621371 miles
so,
70 m/h = 70×1.60934 km/h = 112.6538 km/h
compared to the 120 km/h limit in Canada, it is clear that the speed limit in Canada is higher.
the difference is
7.3462 km/h = 7.3462×0.621371 = 4.56471564 m/h
a figure has 2 pairs of parallel sides, 2 pair of sides of equal length, and 4 right angles what quadrilateral best describes this figure
Answers
given the following exponential function identify whether the change represents growth or decay y= 56(0.91)^x
Answers
Answer:
Decay
Step-by-step explanation:
Any "r" value between 0 and 1 indicates an exponential function in decay. The "r" value is the one in the parentheses and raised to the exponent. In this case, the value is 0.91. This number falls within the "r" value boundaries of a decaying exponential function.
My age is twice what my age was 15 years ago . what was my age 15 years ago ?
Answers
Answer:
two times less than your age is now
The function C(t)=100*e^-0.000121t describes how to find the percentage of carbon-14, C(t), remaining in an object after t years. According to this information, what was the percentage of carbon-14 remaining in an object after 55 years? (Round your answer to the nearest hundredth.)
Answers
Answer:
99.34 years
Explanation:
Given function:
[tex]\sf C(t)=100*e^{-0.000121t}[/tex]
Insert t = 55:
[tex]\sf C(55)=100*e^{-0.000121(55)}[/tex]
Simplify following:
[tex]\sf C(55)=99.3367[/tex]
Round to nearest hundredth:
[tex]\sf C(55)=99.34[/tex]
