Find the solution(s) of the system of equations:
y = –x2 + 4x + 5
y = x2 + 2x + 1
a. (–1,2) and (2,17)
b. (1,0) and (–2,9)
c. (1,4) and (2,9)
d. (–1,0) and (2,9)
Answers
The easiest way to find the solutions is to graph the equations then observe the coordinate intersections of each graph :)
The solution to the equation are (2, 9) and (-1, 0)
Given the functions as shown below:
y = –x2 + 4x + 5 y = x2 + 2x + 1Equating both equations will give;
–x^2 + 4x + 5 = x^2 + 2x + 1
Collect the like terms to have:
–x^2 + 4x + 5 –x^2 - 2x - 1 = 0
-2x^2 + 2x + 4= 0\
2x^2 - 2x - 4 = 0
x^2 - x - 2 =0
Factorize to have:
x^2 - x - 2 =0
x^2 - 2x + x - 2 = 0
x(x-2)+1(x-2) = 0
x = 2 and -1
If x = 2
y = 2^2 + 2(2) + 1
y = 9
If x = -1
y = (-1)^2 + 2(-1) + 1
y = 1 - 2 + 1
y = 0
Hence the solution to the equation are (2, 9) and (-1, 0)
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Related Questions
True or false? A figure that has opposite sides with equal lengths and equal slopes and diagonals with slopes that are negative reciprocals must be a square.
Answers
Answer:
False.
Step-by-step explanation:
The diagonals are at right angles ( because of the negative reciprocal slopes)
so it could be a square or a rhombus.
The given figure can be a rhombus or square.
What is square?The square is a 4 - sided figure, each side of the square is equal and makes a right angle.
The area of a square having sided a unit can be given by a² square unit.
Given that,
A figure has equal length of opposite sides.
Also, slopes and diagonals are equal with negative reciprocals.
Since, The square and rhombus both have equal sides and equal diagonals,
But a square makes right angle on sides.
In the given question, right angle is not given.
Therefore, the figure can be square or rhombus.
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Recommendations Skill plans A Math FL Standards Algebra 1 > J.10 Solve one-step and two-step equations: word problems UFG You have prize On a sunny fall day, Raymond and his family go to an orchard to pick apples for their famous apple pies. First, they pick enough Golden Delicious apples to fill a bag. Then, they pick enough Honeycrisp apples to fill another bag. The bag of Honeycrisp apples weighs 20 pounds. In all, Raymond's family picks 44 pounds of apples. Which equation can you use to find the weight w of the Golden Delicious apples? W + 20 = 44 20w = 44 W - 20 = 44 = 44 20 Solve this equation for w to find the weight of the Golden Delicious apples. pounds Submit
Answers
(a) The equation for estimating the weight W of the Golden Delicious apples is W + 20 = 44.
(b) The weight of the Golden Delicious apples is 24 pounds.
Let the weight of the Golden Delicious apples = WWeight of the Honeycrisp apples = 20 lbTotal weight of the apples = 44 lb
The equation for estimating the weight W of the Golden Delicious apples is calculated as follows;
Weight of Golden delicous apples + Weight of Honeycrisp = Total weight of the apples
W + 20 = 44
The weight of the Golden Delicious apples is calculated as follows;
W + 20 = 44
collect similar terms together;
W = 44 - 20
W = 24 lb
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What is the sine rule
Answers
Answer:
Sine, in a right triangle, is the side opposite to the angle divided by the hypotenuse.
Law of sines (on any triangle) is
[tex]\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}[/tex]
where A, B, and C are angles and a, b, and c are side lengths opposite to the angles.
Answer:
sine rule states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.
Step-by-step explanation:
In a triangle with sides a,b,c:
a/sin A = b/sin B = c/sin C
A recipe that makes 24 cupcakes calls for 5 1/2 cups of flour. How much flour is needed to make 30 cupcakes?
A. 5 7/8 cups
B. 6 1/2 cups
C. 5 3/4 cups
D. 6 7/8 cups
Answers
Answer: D hope this helps
At which x-value does the cosine function attain a maximum value?.
Answers
Answer:
cos(x) = ???
so the maximum cosine can be is 1 and that happens when x = 0
I'm pretty sure that's what you meant...
The value of x where the cosine function attains a maximum value is 0.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
Cosine function.
The value of cos 90° is 0.
The value of cos 0° is 1.
The value of cos 30° is √3/2.
The value of cos 60° is 1/2.
We see that the cosine function has the maximum value at zero degrees.
Thus,
Cos x has the maximum value at x = 0.
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There are 93 calories in 3 cups of popcorn. How many calories are in 4.5 cups of popcorn?
Answers
Answer: I think its 106 calories
Step-by-step explanation:
sorry if im wrong
Write an equation of the line passing through point A(6,-1) that is perpendicular to line y= -2x + 8. what does Y equal? Y=?
Answers
Answer:
y = [tex]\frac{1}{2}[/tex] x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 2x + 8 ← is in slope- intercept form
with slope m = - 2
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (6, - 1 ) into the partial equation
- 1 = 3 + c ⇒ c = - 1 - 3 = - 4
y = [tex]\frac{1}{2}[/tex] x - 4 ← equation of perpendicular line
Pleaseee help meeee
Answers
Answer: A.
Step-by-step explanation:
This is the only option in which the terms are ordered from least to greatest.
Therefore, A is the correct answer.
???????? Helppppppppp
Answers
In ∆RAM and ∆REP
m<E=m<ALet's check ratio
[tex]\\ \sf{:}\longrightarrow \dfrac{AR}{RE}=\dfrac{4}{12}=\dfrac{1}{3}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{RM}{RP}=\dfrac{2}{6}=\dfrac{1}{3}[/tex]
Hence
option B is correct
Answer:
[tex]second \: one \: is \: correct[/tex]
what is the least common denominator of 10 and 14
Answers
Answer:
70
Step-by-step explanation:
Given -
the least common denominator of 10 and 14 is - *70*
Prime factor of 14 are 2 and 7
14 = 2 * 7
Prime factor of 10 are 2 * 5
10 = 2 * 5
Now Multiplying the highest exponent prime factor to calculate the LCM of 14 and 10
LCM (10,14) = 2 * 5 * 7
LCM (10,14) = 70
Martin has read 40% of a book. He has 48 more pages to finish. How many pages are there in the book?
Answers
Answer: There are 80 pages in Martin's book.
48 pages = 60%
divide by six
8 pages = 10%
mulitiply by 10
80 pages = 100%
Hope this helps :)
Answer the following for 10 points
Answers
Answer:
Regional metamorphism
Step-by-step explanation:
(all definitions below are NOT my own definitions, but burrowed from trustworthy informational sites)
It is not Sediment Layering because Sediment Layering is sedimentary rocks layers are piled one on top of the other.
It is not Cooling of Magman because Cooling of Magman is elements within the magma combine and crystalize into minerals that form an igneous rock.
It is not Contact Metamorphism because Contact Metamorphism is metamorphism due to contact with or proximity to an igneous intrusion.
It IS regional metamorphism because it is metamorphism affecting rocks over an extensive area as a result of the large-scale action of heat and pressure.
50 Point Question Answer ASAP giving brainliest
Answers
Answer:
the reminder is 5 and the quotient is 2x+4
Please help me fill in the blanks :)
Answers
Answer:
Absolute value is the distance from numbers on a number line. The absolute value of -7 is 7 b/c it is 7 units from 0. The absolute value of 5 is 5 b/c it is 5 units from 0.
A negative number is a number that is negative. On a horizontal number line negative numbers are to the left.
A positive number is a number that is positive. On a horizontal number line positive numbers are to the right.
I don't understand the last paragraph though. Hope this helped :D
Step-by-step explanation:
please help dont want to fail final exam
How much does she earn if she does not make any sales on a given day?
Question 7 options:
$75
$175
$0
$25
Answers
Answer:
$75 I think. Not 100% sure but like 95% sure :)
Marcus dropped a ball from a height of 400 cm. The sequence below shows the height of the ball, in cm, during its first four bounces.
240, 144, 86.4, 51.84,
Which formula could be used to determine the height of the ball after n bounces?
A. h(n) = 400(0.60)^n
B. h(n) = 400(0.60)^(n-1)
C. h(n)= 240(0.60)^n
D. h(n) - 240(0.60)^(n-1)
(nvm, I figured it out. sorry lol)
Answers
Answer: The answer is C.
solve inequalities by using transformation rules? 7(x-2)<4x-8
Answers
Answer:
x < 2
Step-by-Step Explanation:
A lady is 5 years younger to her husband and he is 5 times as old as his daughter. If the daughter was 5 years old 3 years back, what is the present age of the lady? 25
45
35
30
Answers
Answer:
35
Step-by-step explanation:
5x (5+3)=40-5=35
Awnser please jsjshshshdh
Answers
Answer:
No
Step-by-step explanation:
A function cannot have two of the same x values (3 and 3)
I hope this helps!
*log x raised to n is the same as log n divide log x *
a. False
b. True
Answers
what is the correct answer to: 0.9 x (8.2 x 20.35)
Answers
Answer:
150.183
Step-by-step explanation:
0.9 x (8.2 x 20.35) =
0.9 x (166.87) =
150.183
Which of the following is a true statement?
A. A number is divisible by two and three if the number ends in a 0, 2, 4, 6, or 8.
B. A number is divisible by three and nine if the sum of the digits is divisible by three.
C. A number is divisible by nine if the last two digits are divisibly by nine.
D. A number is divisible by six if the number is divisible by both two and three.
Answers
na me back. She says I'm mister r00000-
mantic, call me fantastic. Touch me na me
back. She says I'm Mr. Ro- Smooooth" - Biggie
Cheese
WILL GIVE BRAINLYIST
Andre is in charge of cooking broccoli and zucchini for a large group. He has to spend all $17 he has and can carry 10 pounds of veggies. Zucchini costs $1.50 per pound and broccoli costs $2 per pound. One graph shows combinations of zucchini and broccoli that weigh 10 pounds and the other shows combinations of zucchini and broccoli that cost $17.
Graph
A combination of veggies that costs $17 but does not weigh 10 pounds.
Select all that apply.
Group of answer choices
D. 10 pounds of zucchini and 1 pound of broccoli
B. 4 pounds of zucchini and 6 pounds of broccoli
A. 6 pounds of zucchini, and 4 pounds of broccoli
C. 2 pounds of zucchini and 7 pounds of broccoli
Answers
Answer:
its A
Step-by-step explanation:
Jan has a piece of yarn that is 6 1/2 feet long. She cuts off a piece that is 2 5/12 feet long. How much yarn does she have left?
A. 3 3/4 feet
B. 4 1/12 feet
C. 4 3/4 feet
D. 8 7/12 feet
Please keep answer simple, and no absurd, out of context answers, thank you!
Answers
Select the graph of the equation y + x + 3 = 0.
Answers
Answer:
C.
Step-by-step explanation:
The picture I took is underneath.
A diver dove from a board that was 6 3/4 feet above the water's surface, and descended until he was 8 1/3 feet below the water's surface. What was the total distance that the diver desceded?
Answers
Answer:
15 1/12 feet
Step-by-step explanation:
Well if he descended 8 1/3 feet below the water, that means he must've went from board to water which is 6 3/4 feet then down 8 1/3 feet
6 3/4 + 8 1/3
= 6 9/12 + 8 4/12
=15 1/12 feet
PLEASE HELP ME RNNNNN!!!!!! I NEED THE ANSWERS
I really need help don’t answer if your not giving the correct answer don’t respond
Answers
Answer:
pretty sure its A
Step-by-step explanation:
Rewrite the linear equation 2x = 13y – 9 in slope-intercept form
Answers
Answer:
[tex]y \: = \: \frac{2}{13} x \: + \: \frac{9}{13} [/tex]
Step-by-step explanation:
we need to write it in the form y = mx + c where m is the slope(gradient) and y is the y intercept
1) add 9 to both sides
2x = 13y - 9
2x + 9 = 13y
2)divide 13 on both sides
2x + 9 = 13y
2/13x + 9/13 = y
final equation is
[tex]y \: = \: \frac{2}{13} x \: + \: \frac{9}{13} [/tex]
100 Point question answered ASAP for brainliest!
Answers
Step-by-step explanation:
that is really easy too easy for that many points.
it is truly simple :
the graph (and with it the function) is shifted down by 3 units.
that means everything of the function stays the same, just the functional results are consistently lowered by 3.
so, g(x) = f(x) - 3 = -2x² - 7 - 3 = -2x² - 10
that is really all there is to it.
For a new neighborhood, 100 acres of land will be split into 10 lots.How many acres of land will each lot have?
Answers
10
Step-by-step explanation:
I think it's 10 my bad if I'm wrong
