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)
Learn more on equations here: https://brainly.com/question/16863577
Related Questions
Help...? Thanks! No links
Answers
Answer: C) Move it 3 places to the left
Explanation:
We're dividing the number [tex]34.62[/tex] by [tex]10^3[/tex], which is the same as dividing by 1000.
The exponent 3 tells us how many spots to move the decimal point. We move to the left because the number gets smaller. If we multiplied by [tex]10^3[/tex], then we'd move the decimal point 3 spots to the right.
So, [tex]34.62 \div 10^3 = 34.62 \div 1000 = 0.03462[/tex]
Can anyone please answer number 6.
Answers
Answer:
Step-by-step explanation:
Exact Form:
2
√
2
+
3
√
5
−
2
2
2
+
3
5
-
2
Decimal Form:
7.53663105
…
Answer:
28
Step-by-step explanation:
2(√2+3)² -3(√2+3*√2-2)
expand collect like terms
2(2+6√2+9)-3(4√2-2)
2(2+6√2+9)-3(4√2-2)
calculate remove parentheses
2(11+6√2)-12√2+6
remove parentheses
22+12√2-12√2+6
remove opposite and calculate
solution= *28*
was this helpful???!
Please answer number 3???
Answers
8cm * 2.5 = 20cm per side
compare 8/11 to 3/5
PLEASE HELP !!!
Answers
Rewrite both fractions with a common denominator:
8/11 x 5 = 40/55
3/5 x 11 = 33/55
40/55 is greater than 33/55 so 8/11 is greater than 3/5
Find the area of an equilateral triangle with side length 4.6 cm. Round your answer to 1 DP.
Answers
The areas of a triangle is b*h / 2
4.6*4.6 = 21.16
21.16/2 = 10.58
This is because it is an equilateral triangle so all side lengths are the same
Answer:
A = 9.2 cm²
Step-by-step explanation:
A = 1/2 bh, you know the base = 4.6 and you need to find the height of the triangle.
Drawn the attitude of the equilateral triangle to the base and use a² + b² = c²
c = side of the triangle = 4.6 , b = 1/2 0f 4.6 = 2.3 . the attitude to the base ÷ the base in half.
a² + (2.3)² = (4.6)²
a² + 5.29 = 21.16
a² = 21.16 - 5.29
a² = 15.87
[tex]a = \sqrt{15.87}[/tex]
Now we know the height of the triangle = [tex]\sqrt{15.87}[/tex] , the base = 4.6
A = 1/2bh
A = 1/2 (4.6)([tex]\sqrt{15.87}[/tex] )
A = 9.1625
A = 9.2 cm² or the A of any equilateral triangle = [tex]\frac{\sqrt{3} }{4} s^2[/tex]
A = [tex]\frac{\sqrt{3} }{4} (4.6)^2[/tex]
A = 9.1625
A = 9.2
a sweater was on 20% discount. the amount of discount was $7 what was the original price?
Answers
Answer:
$35
Step-by-step explanation:
if $7 is only 20% of the original price multiply 7×5
-20%×5=100%
same thing as 7×5=35
just switch the percent by its worth
someone pls pls help
Answers
Answer:
4√2 cm
Step-by-step explanation:
ABCD is a square.
Each side measures 8 cm.
So,
AB = BC = CD = AD = 8 cm
P, Q, R, and S are mid - points of ABCD.
P is the mid - point of AB.
So,
AP = PB
AP + PB = AB
AP + AP = AB
2AP = 8
AP = 8 / 2
AP = 4 cm
S id the mid - point of AD.
So,
DS = SA
DS + SA = AD
SA + SA = AD
2SA = 8
SA = 8 / 2
SA = 4 cm
Property of a square : The angle between two sides is 90°.
So,
The angle between side SA and AP is 90°.
So,
SA, AP and SP forms a right angled triangles.
By Pythagoras theorem,
( SP)² = ( SA )² + ( AP )²
( SP )² = 4² + 4²
= 16 + 16
( SP )² = 32
SP = √32
SP = 4√2 cm
Since PQRS is also a square.
In square, all sides are equal.
So,
PQ = QR = RS = SP
Since SP = 4√2 cm
Hence,
PQ = 4√2 cm
Therefore,
the length of PQ is 4√2 cm.
Answer: 5.7
Step-by-step explanation:
Midpoint means the middle of line. So to find the middle of the line I just need to divide the line by 2.
So the midpoint of AB is:
8/2=4 = BP
Since Q is also a midpoint so BQ is equal to 4.
We know BP=BQ=4. Looking at the diagram we can tell PBQ is a triangle.
The hypotenuse of the triangle is PQ.
Pythagoras's theorem helps us to find the hypotenuse. So we just plug in the values to find PQ.
P's Theorem : a²+b²=c²
basically in the case of this question it means:
(BP)²+(BQ)²=(PQ)²
now we just subsiture the values and solve for PQ:
4²+4²=(PQ)²
16+16=(PQ)²
32=(PQ)²
PQ=5.65...
= 5.7(rounded to one decimal place)
Drag and drop the answers to the boxes to correctly complete the proof.
Given: Rhombus JKMH with diagonals intersecting at point P
Rhombus J K M H with diagonals J M and H K intersecting at P
Prove: JM⎯⎯⎯⎯⎯⊥HK⎯⎯⎯⎯⎯⎯
By the definition of Response area, JK⎯⎯⎯⎯⎯≅KM⎯⎯⎯⎯⎯⎯ and by the reflexive property of congruence, KP⎯⎯⎯⎯⎯≅KP⎯⎯⎯⎯⎯ . Because the diagonals of a rhombus bisect a pair of opposite angles, ∠JKP≅∠MKP , making △JKP≅△MKP by the Response area. Because Response area, ∠JPK≅∠MPK, and these angles are right angles because two angles that form a linear pair are congruent, thereby making JM⎯⎯⎯⎯⎯⊥HK⎯⎯⎯⎯⎯⎯ by the definition of perpendicular segments.
Response area means blank
The answers are Congruent segments, a rhombus, a parallelogram, SSS congruence postulate, ASA congruence postulate, SAS congruence postulate, CPCTC, they are adjacent, and vertical angles are congruent
Answers
The completed proof is presented as follows;
By definition of a rhombus [tex]\overline{JK} \cong \overline{KM}[/tex] and by the reflexive property of
congruence [tex]\overline{KP} \cong \overline{KP}[/tex], because the diagonals of a rhombus bisect a pair
of opposite angles, ∠JKP ≅ ∠MKP, making ΔJKP ≅ ΔMKP by the SAS
congruency postulate, because CPCTC, ∠JPK ≅ ∠MPK, and these angles
are right angles because two angles that form a linear pair are congruent,
thereby making, [tex]\overline{JK} \perp \overline{KM}[/tex] by definition of perpendicular segments.
Reasons:
Please find attached the drawing of the given rhombus JKMH, that show
the point of intersection of the diagonals JM and HK at point P.
A rhombus is an equilateral quadrilateral, therefore, the adjacent sides [tex]\overline{JK} \ and \ \overline{KM}[/tex] are congruent.The SAS congruency postulate states that if a triangle has two sides and an included angle that are congruent to two sides and an included angle of another triangle, then the two triangles are congruent.CPCTC is an acronym for Congruent Parts of Congruent Triangles are Congruent.Learn more about the properties of a rhombus here:
https://brainly.com/question/10618409
Please I really need help I’ll give brainliest
Based on the information in the diagram, which triangle
congruence property can be used to justify that triangle ABC is congruent to triangle FGH?
Answers
Answer:
In this I would choose C
Step-by-step explanation:
PLZ HELP
Given the side lengths, determine whether the triangle is acute,right, obtuse, or not a triangle.
15,17,21
Not a triangle
A cute
Right
Obtuse
3,9,10
Not a triangle
Acute
Right
Obtuse
Answers
Answer:
It is an acute scalene triangle
Step-by-step explanation:
All angles are acute, making it an acute triangle
scalene because all sides are different lengths
John is a mechanic with a technical license. He has worked 40 hours at minimum wage
this week. How much is his gross wage for the week?
Answers
Answer:
$290
Step-by-step explanation:
if minimum wage is $7.25
7.25×40= 290
5) So far you have a MP3 Player with 0.5 GB of music already stored on the MP3 player and know that each song is about 0.002 GB of memory. What are the possible numbers of additional songs that you can put on the MP3 player if it holds at most 2 GB?
Answers
Answer: Any whole number between 0 and 750, including both endpoints.
One example could be 700 additional songs.
==================================================
Explanation:
x = number of additional songs, some nonnegative whole number
1 song takes up 0.002 GB, so x of them take up 0.002x GB of memory.
Add on the 0.5 GB already used to get the expression 0.002x+0.5 to represent the total amount of storage taken up. We want this expression to be 2 or smaller.
[tex]0.002x + 0.5 \le 2\\\\0.002x \le 2-0.5\\\\0.002x \le 1.5\\\\x \le 1.5/0.002\\\\x \le 750\\\\[/tex]
This says the most songs we can add are 750.
Because x is the number of songs, it doesn't make sense to have x be negative. This means [tex]x \ge 0[/tex] or [tex]0 \le x[/tex] is the case as well.
Combining [tex]0 \le x[/tex] and [tex]x \le 750[/tex] produces the compound inequality [tex]0 \le x \le 750[/tex]
The number of additional songs is any whole number between 0 and 750, including both endpoints.
The roster notation of this set could look like this: {0, 1, 2, ..., 748,749,750}
The triple dots indicate "keep this pattern going". That way we don't have to fill in all 751 values which would be a tedious process.
So you can add on something like 700 songs because it's between those endpoints mentioned, but cannot add something like 800 songs.
Answer:
0 - 750 additional songs
Step-by-step explanation:
current: 0.5 mb
remaining: 2-0.5=1.5 mb
each song: 0.002 gb
take remainig amount of space: 1.5 mb and divide by how much space each song takes: 0.002 mb to find out how many songs can fit in 1.5 mb of space
work:
(total amount of storage-used amount of storage)/storage per song
(2.0-0.5)/0.002
= 1.5/0.002
= 750 songs
what are the possible number of additional songs?
anything up until 750.
The difference between a number and 16 is 49.
ANYBODY KNOW THE ANSWER?~
Answers
Hey there!
GUIDE
• The word “sum” means add
• The word “difference” means subtract
• The word “product” means multiply
• The word “quotient” means divide
• The word “is” means equal to
• The “unknown number” is a variable that is not known. So people usually label it as a variable until they figure out what the unknown value is.
Now that we have that information out the way we can solve for your given question.
“The [DIFFERENCE] between [a number] & 16 [is] 49
Lets break it down
• DIFFERENCE (between) = subtract☑️
• A NUMBER = UNKNOWN (so we will label it is as “n”]☑️
• 16 will stay the same because NOTHING was done to it!
• IS = is equal to☑️
We have the key terms out of the way so now we met our answer
ANSWER:
“n - 16 = 49”
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
a number decreased by 23% equals 123
Answers
Answer:
100 is inital value of that decrease
Pete grabbed 18 mixed nuts, StartFraction 2 Over 9 EndFraction of which were almonds. Which equation shows how to determine the number of almonds Pete grabbed?
Answers
Answer:
Thats one heck of a whole lot nuts
Step-by-step explanation:
Two vehicles are moving, one with the velocity of 20 m/s towards east and another with 10 m/s towards west. Calculate the distance between them after 20 minutes they are started from the same place and the same time.
Answers
Answer:
12 km
Step-by-step explanation:
20 minutes = 20 * 60 = 1200 second
distance = velocity * time
car 1 = 1200 * 20 = 24000 m = 24km
car 2= 1200 * 10 = 12000 m = 12km
so distance between them after 20 minutes is 24 -12 = 12 km
Solve and show your work for each question...
Answers
[tex]0.\overline{36} = \dfrac{36-0}{99} = \dfrac{36}{99} = \dfrac{4}{11}\\\\\\0.3\overline{6}= \dfrac{36-3}{90} = \dfrac{33}{90} = \dfrac{11}{30}\\\\\\0.36 = \dfrac{36}{100} = \dfrac{9}{25}[/tex]
Jim’s backyard is rectangular with dimensions of 80 feet by 120 feet. He is planning to designate part of the yard to plant a vegetable garden. The garden will be a similar rectangle, using a scale factor of 3/4. How much fencing will he need if he wants to enclose the garden on all four sides?
How many feet does he need?
Answers
Step by step solution:
3/4=0.75
(80*0.75)(120*0.75)
(60)(90)
5400
5,400 feet^2
Hope that helps :)
Interpreting Composite Functions in the Real World
Try it
The volume of air in a balloon is represented by the function von = = nr?, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function rt) = 42
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements
Answers
Answer:
Answer is A and C on edge
Step-by-step explanation:
The composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.
What is composite function?When the two or more than two functions are written in the form of single function. Then such function is called the composite function.
Let suppose there is a function f(x) and another function g(x). Then the composite function can be given as,
[tex]f[g(x)][/tex]
The volume of air in a balloon is represented by the function,
[tex]V(r)=\dfrac{4}{3}\pi r^3[/tex]
Here, r is the radius of the balloon, in inches.
The radius of the balloon increases with time, in seconds, by the function,
[tex]r(t) = \dfrac{1}{4}t^2[/tex]
The composite function that can be used to determine the volume of the balloon after t seconds is,
[tex]V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{4}t^2)^3\\V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{64}t^6)\\V(r(t))=\dfrac{1}{48}\pi t^6[/tex]
After the 6 seconds,
[tex]V(r(6))=\dfrac{1}{48}\pi (6)^6\\V(r(6))=\dfrac{1}{48}\pi \times46656\\V(r(6))=972\pi[/tex]
Thus, the composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.
Learn more about the composite function here;
https://brainly.com/question/10687170
#SPJ2
Malachi is practicing math fluency. He has 100 math operation flashcards with 42 addition problem cards, 56 subtraction cards, and 2 multiplication cards. He will time himself to see how fast he can solve the problems on two cards. He chooses his two cards and they are both multiplication cards. Is choosing two multiplication cards likely? Explain by running a simulation.
Part A: State the problem or question and assumptions. (2 points)
Part B: Describe the process for one repetition, including possible outcomes, assigned representations, and measured variables. (3 points)
Part C: Use digits from a table of random digits or use your calculator to perform one repetition. Submit the list of random digits and indicate those that represent multiplication cards. (3 points)
Part D: Suppose there were 5 times when both cards selected were multiplication cards after 1,500 repetitions of the simulation. State your conclusions from these results. (2 points)
Essay Submission
Answers
Answer: It is highly unlikely to get both multiplication cards on the first try.
Part A The question asked is: there are two multiplication cards out of one hundred cards including forty-two addition problem cards and fifty-six subtraction cards.What are the odds of getting just the multiplication cards.The assumption is this we are talking about the first try.
Part B You make the multiplication cards, card#1 and card#2. All other cards are #3-100. Then you use the random number generator to see odds of two numbers out of one hundred, which is 0.02%. as I did 2/100 x 1/99 then multiply by 100 so.02
Part C I got 83 and 27as my first two numbers with my random number generator, So Malachi didn't get a multiplication card in this random test. card #1 and card #2 are the multiplication cards
Part D The percentage of the time that you'd expect both multiplication cards to be picked is 0.002 or .2%. The proportion of the time that it happened here is 5/1500=.00333 or .33%, which means that this is pretty much in line with what you'd expect
Step-by-step explanation: I got a 10/10 on 3.07 essay test for honors statistics.
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P′Q′R′ has vertices P′(4, 0), Q′(3, 1), and R′(−1, −2).
Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)
Answers
Answer:
Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4
Part B:
P''(-1, 0)
Q''(0, -1)
R''(2, -1)
Part C:
The two Triangles PQR and P''Q''R'' are not congruent.
(sin^2(0)) I really need help with this asap
Answers
Answer:
Asapa
[tex] (sin2(0) [/tex]
Solve -2.5n + 8.7 > 5.45.
Answers
Answer:
Solved for n: n < 1.3
Step-by-step explanation:
Are there answer choices included?
If TU = 6 units, what must be true?
O SU + UT = RT
O RT + TU = RS
© RS + SU = RU
TU + US = RS
Answers
Answer:
SU + UT = RT
Step-by-step explanation:
Given that TU = 6 units, RT = 12 units and RS = 24 units.
So,
For finding US, we will subtract the length of RT and TU from RS.
US = RS - RT - TU
US = 24 - 12 - 6
US = 6 units
Putting all the given values in the given conditions, we get the first option right, which is:
SU + UT = RT
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807If you don’t answer it correctly then don’t mind answering
Answers
The answers are underneath each problem. The reason this makes sense is due to the distributive property.
27. GCF of 27 and 12 is 3
3(4+9)
28. GCF of 12 and 36 is 12
12(1+3)
29. GCF of 16 and 20 is 4
4(4+5)
30. GCF of 2x and 8 is 2
2(x+4)
31. GCF of 30 and 12x is 6
6(5+2x)
32. GCF of 42x and 49 is 7
7(6x+7)
To do this, find the GCF and then divide each number by so. Then, add them in parenthisis and multiply it by the GCF
triangle ABC rotated 90 degress clockwise about point P to create triangle DEF. Determine the correct orientation and location of triangle DEF
Answers
When a triangle is rotated, it must be rotated through a center.
The location of the triangle would be above point P, and the orientation is triangle DEF (the first triangle)
The triangle is given as: triangle ABC.
And the degree of rotation is 90 degrees clockwise.
Given that the triangle is rotated about point P, then the new location after 90 degrees rotation would be above point P.
And the orientation would point to the right of point P.
Hence, the location of the triangle would be above point P, and the orientation is triangle DEF (the first triangle).
Read more about rotation at:
https://brainly.com/question/1616371
A grocery store sells 25 crates of peaches for $125. How much does 1 crate cost?
Answers
Answer: One crate of peaches is $5
Step-by-step explanation:
All you do for this question is divide 125 by 25 gives us 5
Answer:
5
Step-by-step explanation:
Just decide 125 by 25 and get the answer :)
May I please receive help?
Answers
Answer:
a = 19.6 (rounded to the nearest tenth)
Step-by-step explanation:
a^2 + b^2 = c^2
Hypotenuse - 35 m, Legs - 29 m, x
a^2 +29^2 = 35^2
a^2 + 841 = 1225
Subtract 841 from both sides
a^2 = 384
Square root both sides
√a^2 = √384
a = 19.595
Find the difference.
17 minus 2 and one-third equals what number?
A. 15 and one-third
B. 15 and two-thirds
C. 14 and two-thirds
D. 14 and one-third
Answers
Answer:
C. 14 and 2/3
Answer:
C
Step-by-step explanation:
17 - 2 1/3
17 -2 -1/3
15 -1/3
14 2/3
The sum of Alyssa's age and her sister's age is 48 years. Alyssa's age is 6 years less than twice her sister's age. What is Alyssa's age, and what is her sister's age?
Answers
Answer:
Alyssa's Sister = 18, Alyssa = 30
Step-by-step explanation:
48 = 2x-6 + x
54 = 2x + x
54 = 3x
18 = x
2(18) - 6
36 - 6
30
48 = 2(18) - 6 + 18
48 = 36 - 6 + 18
48 = 30 + 18
48 = 48