How many solutions does the system have?
{y = −2x + 2
y = x^2 − 3x
Enter your answer in the box.
________
Answers
Answer:
The system has two solution
Step-by-step explanation:
we have
[tex]y=-2x+2[/tex] ----> equation A
[tex]y=x^{2}-3x[/tex] ----> equation B
Solve the system of equations by graphing
Remember that
The solution of the system of equations is the intersection point both graphs
There are two point of intersection between the two graphs
see the attached figure
therefore
The system has two solution
Related Questions
The table shows the snack preferences of 50 shoppers at the mall. What is the probability that one shopper, selected at random from the 50 surveyed, preferred the potato chips or pretzels? Fruitsnacks/9 shoppers, Potatochips 12 shoppers, Apple 3 shoppers, pretzels 14 shoppers, Water 12 shoppers ---> are the answers for the question---> A. one over five B. thirteen over twenty-five C. one over ten D. eighteen over twenty five
Answers
A sphere has a radius of 2x + 5. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4pir2 for surface area of a sphere.
Answers
[tex] S = 4 \pi r^2 [/tex]
Now substitute 2x + 5 in for r, the radius.
Then simplify the expression and write it in standard form.
[tex] S = 4 \pi (2x + 5)^2 [/tex]
[tex] S = 4 \pi (4x^2 + 20x + 25) [/tex]
[tex] S = 16 \pi x^2 + 80 \pi x + 100 \pi [/tex]
Divide. 5x3y3z - 6x4y2z2 + 4xy3z xyz
Answers
Final Answer:
The result of dividing [tex](5x^3y^3z - 6x^4y^2z^2 + 4xy^3z)[/tex] by xyz is [tex](5x^2y^2 - 6x^3yz + 4y^2z).[/tex]
Explanation:
To divide [tex](5x^3y^3z - 6x^4y^2z^2 + 4xy^3z)[/tex] by xyz, we'll divide each term in the polynomial by xyz separately.
First, let's divide [tex]5x^3y^3z by xyz: (5x^3y^3z) / (xyz) = 5x^2y^2.[/tex]
Then, divide [tex]-6x^4y^2z^2 by xyz: (-6x^4y^2z^2) / (xyz) = -6x^3yz.[/tex]
Lastly, divide [tex]4xy^3z by xyz: (4xy^3z) / (xyz) = 4y^2z.[/tex]
Thus, the resulting polynomial after division is [tex]5x^2y^2 - 6x^3yz + 4y^2z.[/tex]This is derived from individually dividing each term in the polynomial by xyz, simplifying each term, and collecting like terms together to obtain the final result.
In this process, division by xyz means dividing each term of the polynomial by the factors x, y, and z, and simplifying the expression. By doing so, we obtain a simplified form of the polynomial where each term is reduced by the common factors x, y, and z, resulting in the expression [tex](5x^2y^2 - 6x^3yz + 4y^2z)[/tex] as the quotient.
Complete question:
Divide [tex](5x^3y^3z - 6x^4y^2z^2 + 4xy^3z)[/tex] by xyz.
Use the complex zeros(1/2, -3+7i, -3-7i) to factor f(x)=-2x^3 - 11x^2 -110x +58
Answers
P(x)=-(2x^3+11x^2+110x-58)
P(1/2)=-(2*1/8+11*1/4+110*1/2-58)=0
P(x)=(1/2-x)(2x²+12x+116) (using synthetic division)
P(x)=(1-2x)(x²+6x+58)=(1-2x)(x+3+7i)(x+3-7i)
one may note that it could also be simplified to
[tex]\bf f(x)=(1-2x)(x+3+7i)(x+3-7i) \\\\\\ f(x)=(1-2x)[(x+3)+(7i)][(x+3)-(7i)] \\\\\\ f(x)=(1-2x)~~[\stackrel{\textit{difference of squares}}{(x+3)^2-(7i)^2}] \\\\\\ f(x)=(1-2x)[(x^2+6x+9)-(7^2i^2)] \\\\\\ f(x)=(1-2x)[(x^2+6x+9)-(49\cdot -1)] \\\\\\ f(x)=(1-2x)[(x^2+6x+9)-(-49)] \\\\\\ f(x)=(1-2x)[(x^2+6x+9)+49] \\\\\\ f(x)=(1-2x)(x^2+6x+58)[/tex]
A certain species of fish require 1.5 1.5 cubic feet of water per fish to maintain a healthy environment. find the maximum number of fish you could put in a tank measuring 6 6 feet by 3 3 feet by 4 4 feet.
Answers
A _____________ is a three-dimensional form that has length and width but minimum thickness.
Answers
Find the absolute maximum and minimum values of the following function on the given interval. If there are multiple points in a single category list the points in increasing order in x value and enter N in any blank that you don't need to use.
f(x)=9x^3−27x+9, [0,3],
Answers
Help me solve this math problem
Answers
If you want the graph of f(x), perhaps it looks like this one.
Ben is repacking a 45-pound bag of rice into 8 smaller bags. How much rice is going to be in each smaller bag/11008924/c50ec7f7?utm_source=registration
Answers
1 bag = 45 ÷ 8
1 bag = 5.625 pound
------------------------------------------------------------
Answer: 1 bag = 5.625 pound of rice
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please help me with algebra 2?! i am so lost on how to do this!
1.Multiply and simplify if possible.
four square root of eleven•four square root of ten
(1 point)
11four square root of ten
11
10
four square root of one hundred ten
2.What is the simplest form of the expression?
cubed root of twenty four times a to the tenth times b to the sixth
(1 point)
3a3b2cubed root of two a
2a3bcubed root of a
2a3b2cubed root of three a
none of these
Answers
- both squared roots are multiplied by 4, therefore you can regroup: 4·(√11·√10)
- since they are both squared roots, you can multiply the two numbers: 4·√(11·10)
- therefore the answer is: 4·√110
Question 2:
- first thing, you need to factorize the number: 24=2³·3
- then, highlight the exponents multipes of 3: ∛(2³·3·a^9·a·b^6)
- now you can take outside the cubic root everything that has an exponent multiple of 3, dividing the exponents by 3: 2·a³b²·∛3·a
find A if 17th and 18th terms in the expansion of (2+A)^50 are equal.
Answers
The 18th term is 50C17*2^33*a^17
The ratio of these two terms is (17th term)/(18th term) = 1/a. We want the value of this to be 1, so
.. A = 1
_____
My calculator says
.. 50C16 = 4,923,689,695,575
.. 50C17 = 9,847,379,391,150
the latter being exactly 2 times the former.
PLEASE ANSWER ASAP.
Find the area of the triangle QRS.
Area = square units
Answers
Answer:area is 140
Step-by-step explanation:
Answer:
Area= 140 square units
Step-by-step explanation:
q(-9, 5). r(6,10). s(2,-10).
find the area of the triangle QRS.
Area=140 square units
A negative correlation means that ________. select one:
a. high values of one variable are associated with low values of the other
b. high values of one variable are associated with high values of the other
c. low values of one variable are associated with low values of the other
d. there is no relationship between the two variables
Answers
Negative correlation is a relationship between two variables wherein if the value of one variable increases, the value of the other variable decreases, and vice versa.
A negative correlation means that high values of one variable are associated with low values of the other. This suggests that as one variable increases, the other decreases respectively and vice versa, which can be seen in various real-world scenarios such as the relationship between time spent studying and number of mistakes made on a test.
Explanation:In the context of statistics and data analysis, a negative correlation means that high values of one variable are associated with low values of the other. This implies that as one variable increases, the other decreases correspondingly and vice versa. For instance, if we were examining the relationship between time spent studying and number of mistakes made on a test, a negative correlation might indicate that the more time a student spends studying, the fewer mistakes they make on the test. This is indicative of a negative correlation because as the value of one variable (study time) increases, the value of the other variable (mistakes) decreases.
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Solve for x.
[tex]cos x= \frac{ \sqrt{3} }{2}[/tex]
A: 0.15°
B: 0.87°
C: 30°
Answers
[tex] \frac{ \sqrt{3} }{2} = 30[/tex]
John and Matt are going to fill a pool with 2 different sized hoses. John can fill the pool in 5 hours, while Matt can complete it in 10 hours. Explain each step in solving this equation.
Answers
John and Matt are going to fill a pool with 2 different sized hoses. John can fill the pool in 5 hours, while Matt can complete it in 10 hours.How long will it take both to fill the pool? Explain each step in solving this equation.
we know that
John can fill the pool in --------------> 5 hours
therefore
I calculate the amount of pool that John fills in one hour
if John can fill 100% of the pool in----------------> 5 hours
X--------------------------------------> 1 hour
X=1/5=0.20 pool/hour
Matt can fill the pool in --------------> 10 hours
therefore
I calculate the amount of pool that Matt fills in one hour
if Matt can fill 100% of the pool in----------------> 10 hours
X--------------------------------------> 1 hour
X=1/10=0.10 pool/hour
adding both amounts
(0.20+0.10)=0.30 -----------> 30% pool/hour
then
if both can fills 30% of the pool in----------------> 1 hour
100%-------------------------------> X
X=100/30=3.33 hours----------> 3 hours + 19 minutes+ 48 sec
the answer is 3.33 hours (3 hours + 19 minutes+ 48 sec)
The equation to determine the amount of pool filling (y) according to time (t) in hours is given by
y=0.30*t
Use the given point on the terminal side of angle 0 to find the value of the trigonometric function indicated.
1)tan0;(10,-18)
2)tan0;(4,3)
Answers
2 is tan 0 = 3/4
In general, an angle with a terminal side on the point (x, y) the tan of that line is the fraction y/x
Simplify the expression. w5(w2)–4
Answers
By simplifying this expression, we would first have to (find the roots which would be polynomial).
We would have to find the the polynomial root of [tex] \boxed{F(w) = w7-4}[/tex]
After resolving this, we would then have to find the leading coefficient and also the trailing constant.
[tex]LC \Longrightarrow[/tex] = (1)
_________
[tex]TC \Longrightarrow[/tex] = (1,2,4)
This would be the result of the simplification of this expression listed above.
Therefore, your correct answer would be [tex]\boxed{w^7-4}[/tex]
I hope this helps you!
Answer:
[tex]\frac{1}{w^{3} }[/tex]
The engine of a car has a displacement of 305 cubic inches. what is the displacement in cubic feet? round your answer to 2 decimal places.
Answers
1 inch = 2.54 centimeters
Therefore, to convert to cubic measurements
(1 in)³ = (2.54 cm)³
Thus;
1 in³ = 16.387 cm³
Hence 305 cubic inches will be equivalent to
305 × 16.387
= 4998.035 cm³
Answer:
0.18 cubic feet (in 2 decimal places)
Step-by-step explanation:
The relationship between the unit of measurement inches and the unit of measurement feet may be expressed mathematically as
12 Inches = 1 feet
finding the cube of both sides i.e both sides to the power of 3,
1728 cubic inches = 1 cubic feet
therefore,
305 cubic inches
= 305/1728 cubic feet
= 0.1765 cubic feet
Kendall says the sum of (6x^2+4xy+2y^2) and (4x^2-2xy-3y^2) is (10x^2+2xy-5y^2) what error did Kendall make
Answers
=
(10x^2 + 4xy - y^2)
Kendall assumed the 2y^2 was negative and not positive leading her to create the error of -5y^2
Hope this helps :)
The error made was in the summation of the y^2 terms in each expression, leading to an incorrect final sum of the two expressions.
Explanation:Kendall's error lies in incorrectly adding the terms that contain y^2. Specifically, Kendall summed 2y^2 from the first expression and -3y^2 from the second expression, but mistakenly calculated the result as -5y^2 instead of the correct -y^2. Remember, when performing operations with similar terms, you must carry the correct sign along with each term.
So, the correct sum of (6x^2+4xy+2y^2) and (4x^2-2xy-3y^2) is (10x^2+2xy-y^2).
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PLEASE I NEED MAJOR HELP (PICTURE IS DOWN BELOW)
Answers
You simply read the table on this one
To solve this problem, you need to put it into a proportion.
Since you want to find how many high school students will have an art major out of 1,000 people, you will want to find the current ratio of art majors to all majors, so we can solve the proportion.
Add all the values together.
26+24+16+21+18+20= 125
26/125 <-- art majors over all majors
[tex] \frac{26}{125} = \frac{x}{1000} [/tex]
Cross multiply.
125*x= 1000*26
125*x= 26,000
x= 208
208 out of the 1,000 students will most likely want to pursue an art major.
Hope this helps!
What's the probability of getting at least k heads in n coin flips?
Answers
Two planes start from the same airport and fly in opposite directions. the second plane starts 1/2 hour after the first plane, but its speek is 50 miles per hour faster. find the air speed of cach plan, if 2 hours after the first plante departs, the plans are 2000 miles apart
Answers
t = 2 hours.
r = r
Second plane
t = 1.5 hours
(30 minutes = 1/2 hour. the second plain has been in the air 2 - 1/2 hour = 1.5 hours. )
r = r + 30
Equation
2 * r + 1.5(r + 50) = 2000
2r + 1.5r + 75 = 2000
3.5r = 2000 - 75
3.5r = 1925
r = 1925 / 3.5
r = 550
the first plane was going 550 mph
the second plan was going 600 mph
Factor the common factor out of 8x3 + 12x.
Answers
The factor of this is 4x(2x² + 3)
So the common factor is 4x
I hope this helps~!
As always, it is my pleasure to help students like you.
A metronome uses a pendulum to keep time. The table gives the angular displacement of a pendulum as it swings back and forth. What is the period of its oscillations?
Time Angle
0.0 15.0
0.1 2.55
0.2 -14.4
0.3 -7.35
0.4 11.6
0.5 11.3
Answers
The period is the length of one complete cycle of the pendulum. That mean that is will start positive go negative and return to positive.
If we assume that time 0 is the start with an angle of 15 degree, then we are looking for the point in the graph where it returns to about 15 degrees.
If you create a scatter plot of the data, it would appear that it would reach 15 between 0.4 and 0.5 seconds. At 0.4 it is at 11.6, then it moves up. At 0.5, it is on it's way down at 11.3.
It is safe to assume that it reached 15 between these points to complete one period.
A slice is made parallel to the base of a triangular pyramid. What is the shape of the resulting two-dimensional cross-section? Drag and drop the word to correctly complete the sentence. The cross-section is in the shape of a . rectangletriangletrapezoid
Answers
Thank you for posting your answer at Brainly! Feel free to ask some more questions!
Your answer is Triangle
This is your answer becuase if you split a pyramid in half you will get two Identical triangle shapes.
Hope this has helped :)
Aldo drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Aldo drove home, there was no traffic and the trip only took 5 hours. If his average rate was 21 miles per hour faster on the trip home, how far away does Aldo live from the mountains? Do not do any rounding.
Answers
8x = 5x +105
3x = 105
x = 105 /3
x = 35
8 x 35 = 280 miles away
The distance of Aldo's house from the mountains when calculated using the parameters is; 280 miles
How to Solve Algebra Word Problems?We know that distance is given by;
Distance = speed * time
Distance with traffic = 8x
Distance without Traffic plus average rate = 5(x + 21)
Thus;
8x = 5(x + 21)
8x = 5x + 105
3x = 105
x = 105/3
x = 35
Thus;
Distance from his house = 5(35 + 21) = 280 miles
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Wyatt's dog is tethered to a post in his yard. If the rope tied to the dog is 12 feet long, how many square yards does the dog have access to? (Use 3.14 for π.)
https://clackamasweb.owschools.com/media/g_mat08_ccss_2016/7/img_circle_quiz.gif
452.16 yd 2 50.24 yd 2 75.36 yd 2 25.12 yd 2
Answers
Solution:
Wyatt's dog is tethered to a post in his yard.
The rope tied to the dog is 12 feet long.
we have been asked to find
How many square yards does the dog have access to?
when Wyatt's dog is tethered to a post in his yard, then that dog can move along that post only and the area covered will be a circle with radius 12ft.
So Area access to dog in ft^2 [tex] = \pi r^2=\pi 12^2=144 \pi [/tex]
But it ask for area in yards, so we will have to use conversion formula
[tex] 1ft=0.33333yard [/tex]
Area access to dog in yards[tex] =144*3.14*(0.33333)^2=50.24 \ Yards [/tex]
Answer:
Wyatt's dog is tethered to a post in his yard.
The rope tied to the dog is 12 feet long.
we have been asked to find
How many square yards does the dog have access to?
when Wyatt's dog is tethered to a post in his yard, then that dog can move along that post only and the area covered will be a circle with radius 12ft.
So Area access to dog in ft^2
But it ask for area in yards, so we will have to use conversion formula
Area access to dog in yards
Step-by-step explanation:
A cube 3 1/2 inches long V = _____ cubic inches
Answers
The side of cube is given as 3 1/2 inches.
converting 3 1/2 into mixed fraction we have 7/2 inches.
on dividing 7 by 2 we get 3.5 inches
Formula to find volume of cube is given by:
[tex] V = a^{3} [/tex]
where "a" is length of side.
Plugging the value of a in the formula we have,
[tex] V = (3.5)^{3} [/tex]
Volume of cube is 42.875 cubic inches.
Please help thank you!
Answers
answer is B
Manny Brought a brand new car in 2012 for $28750. if the car depreciates by 12% each year, write n exponential function to model the situation, then find the value of the car in 2018
Answers
[tex]y=a(1-r)^{x} [/tex]
where a is the initial value (28750)
r is the rate of decrease (0.12)
x is the time, in this case in years (6 . 2018-2012 = 6 years)
[tex]y=28750(1-0.12)^{6} [/tex]
y ≈ 13351.62
Value of the car in 2018 after depreciation by 12% each year is equals to $13351.5
What is exponential decay?" Exponential decay is the decrease in the value of the product at a constant rate over a period of time interval."
Formula used
y = a (1 - r)ⁿ
a = Initial value
r =rate of depreciation
n = time
y = exponential function
According to the question,
Cost of new car 'a' = $28750
Rate of depreciation 'r' = 12%
2018 - 2012 = 6years
n = 6
Substitute the given values in the formula we get,
Exponential function
y = 28750 [1 - (12 / 100)]⁶
⇒ y = 28750 ( 1 - 0.12)⁶
⇒ y = 28750 ( 0.88)⁶
⇒ y = 28750 (0.4644) ( up to four decimals)
⇒ y = $13351.5
Hence, value of the car in 2018 after depreciation by 12% each year is equals to $13351.5
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