On solving the system of equations by substitution method , the solution is x = 0 , y = 1 and x = 4 , y = 9 .
In the question ,
it is given that
the system of equation is
y = x² - 2x + 1
y = 2x + 1
by using substitution method ,
Substituting y = 2x + 1 in y = x² - 2x + 1
we get
2x [tex]+[/tex] 1 [tex]=[/tex] x² - 2x [tex]+[/tex] 1
x² - 2x [tex]+[/tex] 1 - 2x - 1 [tex]=[/tex] 0
x² - 4x = 0
x(x-4) = 0
So , x=0 or x = 4
for x=0 , y = 2x+1 = 1
for x = 4, y = 2(4) + 1 = 9
Therefore, the solution for the system of equations is x=0 , y=1 and x=4 , y=9 .
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Factorise a squared - a -20
Answer:
(a-5)(a+4)
Step-by-step explanation:
[tex]a^{2}[/tex]-a-20
[tex]a^{2}[/tex]+4a-5a-20
a(a+4) -5(a+4)
(a-5)(a+4)
b. Which of these products has the same value as 4(12)? Select all that apply.
A.
8(6)
B.
76
C.
316
D.
12(4)
E.
124
Answer:
A and D
Step-by-step explanation:
8(6) means 8x6 so that's 48
and 12(4) is the same as 4(12) so that should be simple enough
3 (2− k) = −3k + 2
I need this for class
The value of k for the expression, 3 (2− k) = −3k + 2, does not exist.
According to the question,
We have the following expression:
3 (2− k) = −3k + 2
Now, we will multiply 3 into the bracket:
6-3k = -3k+2
Now, moving -3k from the left hand side to the right hand side will result in the change of the sign from minus to plus:
6-3k+3k = 2
Now, 3k will get subtracted from 3k. So, we do not have any variable left for this equation.
Hence, the value of k for the expression, 3 (2− k) = −3k + 2, does not exist.
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i took a sample of the grade point averages for students in my class. for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89. the standard error for the sample was:
The standard error for the sample was 0.13 when "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89."
What is standard error?The standard deviation of a statistic's sampling distribution, or an estimate of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean. By dividing the standard deviation by the square root of the sample size, the standard error is determined. By taking into account the sample-to-sample variability of the sample means, it provides the precision of a sample mean.
Here,
The standard error=standard deviation/√number of samples
=0.65/√25
=0.65/5
=0.13
When "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89," the standard error for the sample was 0.13.
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David picked 15 pears. Jenna picked p fewer pears than David. Write an expression that shows how many pears Jenna picked.
Answer:
15-p
Step-by-step explanation:
15-p
if saint cloud is growing according to the equation pn= 200(1.03)n where n is years after 2010, and the population is measured in thousands. find when the population will be 400 thousand.
In 2267 year, this population would be 400000.
From the question, we have
population is growing as Pn = 200*(1.03)n
substituting the value, we get
400000 = 200*(1.03)n
2000 = 1.03n
ln(2000) = n*ln(1.03)
n = ln(20000) / ln(1.03)
n = 257.15
2010 + 257.15 = 2267 year , this population would be 400000.
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
mandy begins bicycling west at 30 miles per hour at 11:00 a.m. if liz leaves from the same point 20 minutes later bicycling west at 36 miles per hour, when will she catch mandy?
The time at which Liz will catch up with Mandy is 1 pm.
Here we have to find the time when Mandy and Liz meet.
Let t be the time taken by Liz to meet Mandy
Given:
Speed of Mandy = 30mile/hr
Speed of Liz = 36 miles/hr
Formula:
Speed = Distance/ time
Distance by Mandy = 30t
Distance by Liz = 36( t - 20/60)
As the distance covered by both is the same. So we have
30t = 36( t - 1/3)
6t = 12
t = 2
2 hours past 11 am is 1 pm.
Therefore Liz catch Mandy at 1 pm.
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(30 x 5) + (9 x 5) =
150 + 45 = 195
Answer:
thats correct
Step-by-step explanation:
super bowl xlvi was played between the new york giants and the new england patriots in indianapolis. due to a decade-long rivalry between the patriots and the city's own team, the colts, most indianapolis residents were rooting heartily for the giants. suppose that 90% of indianapolis residents wanted the giants to beat the patriot. what is the probability that, of a sample of 100 indianapolis residents, at least 15% were rooting for the patriots in super bowl xlvi?
The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.
By using the normal distribution method, a mean u and standard deviation σ,
The ratio of people who wants the Giants to eat patriots is p = 0.90,
The assumed sample size denoted by n is 100,
and their distribution's mean is u = 0.90,
by using the standard deviation formula is
σ = √(p(1 - p) ÷ n),
σ = √(0.90(1 - 0.90) ÷ 100),
σ = 0.03,
we get that the standard deviation is σ = 0.03
Here the probability that at least 15% of 100 Indianapolis residents encouraged the Patriots in the gaint match Super Bowl XLVI is
P(X > 0.15) = 1 - P((X - u) ÷ σ) > (0.90 - 0.15) ÷ 0.03))
The significant value of X,
X - u ÷ σ = Z
we get,
P(X > 0.75) = (Z<5)-1
P(X < 0.75) = 1.293 - 1
P(X < 0.75) = 0.293
By solving we get, The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.
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Find the value of x.
79
118°
109
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Find the value of x ?y = 180 -71 = 109
x = 360 - (81+100+71)
x = 360 -252
x = 108
answer is B
x = 108 and y = 109
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The value of X is 108 and the value of y is 109. The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division.
Find the value of x ?Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
y = 180 -71 = 109
x = 360 - (81+100+71)
x = 360 -252
x = 108
Therefore the value of x and y is x = 108 and y = 109
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Which of the following is(are) the solution(s) to |5x + 2| = 8 ?
Answer:
x = -2 ; x = 6/5
Step-by-step explanation:
5x + 2 >=0
5x >= -2
5/5 x >= -2/5
x >= -2/5
if x >= -2/5
5x +2 = 8
5x = 8 -2
5x = 6
5/5 x = 6/5
x = 6/5
if x < -2/5
-5x -2 = 8
-5x = 8+2
-5x = 10
-5/-5 x = 10/-5
x = -2
Describe in words where cube root of 24 would be plotted on a number line.
100 points and brainliest
Answer: the square root of twenty-four would be plotted (A) between 4 and 5, but closer to 5 on a number line.
Step-by-step explanation:
79 ala decena mas cercana
Answer:
80
Step-by-step explanation:
the mpg (miles per gallon) of a certain compact car is normally distributed with a mean of 31 and a standard deviation of 1.2. what is the probability that the mpg for a randomly selected compact car would be more than 30?
The probability that a compact car's randomly chosen mpg would be higher than 30 is 0.797.
Given data;
A certain compact car's mpg (miles per gallon) has a mean of 31 and a standard deviation of 1.2 and is regularly distributed.
We need to get the probability that the mpg for a randomly selected compact car would be more than 30.
Therefore;
Mean = μ = 31
Standard deviation = σ = 1.2
Let;
P(X > 30) = P(X - 31/1.2 > 30 - 31/1.2)
= P(Z > -0.833)
= 0.797
Hence, the probability that the mpg for a randomly selected compact car would be more than 30 is 0.797.
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Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
6, (2, 8) 7, (2,10)
The equation of the straight lines are:
For m = 6 and (x1, y1) = (2, 8) => y = 6x - 4
For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4
We know that the equation of a line with gradient m and y-intercept is:
y = mx + c.
We need to find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
We know the point-slope form of equation of line,
(y - y1) = m(x - x1)
For m = 6 and (x1, y1) = (2, 8)
(y - 8) = 6(x - 2)
y - 8 = 6x - 12
y = 6x - 4
For m = 7 and (x1, y1) = (2, 10)
(y - 10) = 7(x - 2)
y - 10 = 7x - 14
y = 7x - 4
Therefore, the equation of the straight lines are:
For m = 6 and (x1, y1) = (2, 8) => y = 6x - 4
For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4
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Area and Circumference of Circles
All circles have the same ratio of circumference to (fill in the blank)
constant . Using this ratio, an exact formula was determined for the distance around a circle: (fill in the blank)
Pi([tex]\pi[/tex]) is the ratio of circumference to diameter for any circle.
Perimeter is the distance around a circle.
Circumference of circle [tex]C = \pi d[/tex].
Perimeter of circle [tex]= 2 \pi r[/tex]
What is circle ?
A circle is a spherical shape without boundaries or edges.
A circle is a closed, curved object with two dimensions in geometry.
Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.
For smaller values of θ, the arc length AB is almost equal to the length of the line segment [tex]\bar{AB}[/tex]. Similarly, arc CD ≅ [tex]\bar{CD}[/tex].
Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.
Circumference = [tex]\pi \times[/tex] diameter or circumference = 2[tex]\pi \times[/tex] radius if this constant equals some value.
So it was proved.
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A baseball diamond is a square that measures 90ft on each side. Write and expression for the distance from 2nd base to home plate in square root form using a^2+b^2=c^2, then give the answer rounded to the nearest tenth
If a baseball diamond is a square that measures 90ft on each side. The expression for the distance from 2nd base to home plate in square root form isc =√ (90)² + (90)² and the distance is 127ft.
How to find the distance?Using the Pythagoreans theorem formula
c= √ a²+b²
Where:
c = length of hypotenuse
a and b = length of the sides of the right triangle
Let plug in the formula
c =√ (90)² + (90)²
c =√ 8100 +8100
c =√16200
c = 127.3
c = 127 ft (Approximately)
Therefore the distance is 127ft.
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in 1950, the world population was 2560 million people. in 1960, the population was 3040 million people. assume that world population grows in constant relative proportion. (a) what is the relative growth rate, k? [3p] (b) use the model to predict the population in 2020.
(i) Relative growth rate, k = 48 million people/ year
(ii) Population in 2020 is given by 5920 million people.
Given that in 1950, the population of world was 2560 million.
In 1960, the population of world was 3040 million people.
Also it is mentioned that, world population grows in constant relative proportion.
So, the difference between time = 1960 – 1950 = 10 years
The growth in population = 3040 mil – 2560 mil = 480 million
So the relative growth rate of population is = 480/10 = 48 million/year
Now N be the new population, k be the relative population growth rate, all figures in millions. And t be the time in years passes since 1950.
Then the mathematical model is,
N = 2560 + kt
So for 2020, t = 2020-1950 = 70
k = 48
So, N = 2560+48*70 = 5920
So the population in 2020 is 5920 million people.
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when a certain unfair die is rolled, an even number is times as likely to appear as an odd number. the die is rolled twice. what is the probability that the sum of the numbers rolled is even?
The probability that the sum of the numbers rolled on the dice is even =1/2.
What is referred as probability?A probability is a measure of the magnitude of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages including several from 0% to 100% can be used to describe probabilities.For the given question,
A fair dice is rolled twice.
Six different results are available with a single roll of the dice (1,2,3,4,5,6)
Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².
Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]
Total sample space for sum of even = 18
For the probability that the sum of the numbers rolled is even is -
probability (sum is even) = 18 / 36 = 1/2
Thus, the probability that the sum of the numbers rolled is even is 1/2.
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Solve for the roots in simplest form using the quadratic formula:
2x²-28x= -116
Round to the nearest hundredth. 44.242
Answer:
44.24
Step-by-step explanation:
The 2 in the thousandths place is lower than 5 therefore it does not round the 4 to a 5
Answer:
44.24
Step-by-step explanation:
hopes this helps please mark brainliest
a dart board is a regular octagon divided into regions as shown. suppose that a dart thrown at the board is equally likely to land anywhere on the board. what is the probability that the dart lands within the center square?
The probability that the dart lands in centre is = √2-1.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
Let the side of octagon be rexterior angle of octagon = 360/8 = 45So interior angle = 180 -45 = 135So all the triangles will have 45-90-45 combinationsc sides of triangles = r/2√r/2 Calculate the total area of octagon and the area of central squareProbability = area of square /area of octagon = r2/(r2+r2+22√+r2)r2/(r2+r2+22+r2)= 1/(2+22√)take 2 common and multiply and divide byhence,The probability that the dart lands in centre is = √2-1.
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Need help ASAP find the value of x in the triangle below
Answer:
x = 12
Step-by-step explanation:
Creating an equationAngles in a triangle add up to 180 degrees.
This means that 6x - 19 + 3x + 7 + 84 = 180
Solving for x6x - 19 + 3x + 7 + 84 = 180
==> combine like terms
9x + 72 = 180
==> subtract 72 from both sides
9x = 108
==> divide both sides by 9
x = 12
Miguel's class just held a class election. 70% of the 30 students in the class voted. How many students voted?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 30}}{\left( \cfrac{70}{100} \right)30}\implies 21[/tex]
Answer: 21
Step-by-step explanation:
70% of 30 students is 21
Hope this helped :)
Factor the expression using the GCF.
The expression $32z-48$ factored using the GCF is
Answer:
16(2z-3) or GCF: 16
Step-by-step explanation:
32z-48 has a GFC of 16
16(2z-3)
Answer:
$16(2z-3)
Step-by-step explanation:
Prime factorization:
32: 2*2*2*2*2
48: 2*2*2*2*3
Notice any similarities:
2*2*2*2=16
$32z-$48 = $16(2z-3)
Separate 25 into two parts so that one part is 13 less than the other part.
NEED HELP QUICKLY!!
Answer:
One number is 19 and the other is 6
Step-by-step explanation:
25 = x + (x- 13)
25 = x + x - 13
38 = 2x
19 = x
x = 19
25 - 19 = 6
7
Oliver makes a plan to be healthier, starting with exercising more often. He signs up for a karate class, thinking this will be a cool way to get active.After three weeks, Oliver finds himself dreading karate class. He would much rather stay home and play RPG with his friends. Since Oliver has already made the decision, what is the BEST path for him to take?
It a because i told the tese
Jenna and Becca were both selling cookies door to door. Jenna sold 8 boxes of cookies for every 3 boxes of cookies Becca sold. Combined,they sold a total of 385 boxes of cookies. How many boxes did each girl sell?
the sum of the number of factors of n and n2 is 34. how many such distinct numbers such that n<150 exist?
The total 18 numbers such that n<150 exist, if the sum of the numbers of factors of N and N^2 is 34
Let me give you an example. 12. Both 2- 2 times and 3- 1 times are factors of 12.
Factors in total (2+1)*(1+1)=6
It will have 2- 4 times and 3-2 times for 122.
15 total factors of 5*3
Situation 1: N = xy
attempting a reverse strategy for N*N Factors in 35=5*7 are x-4 times and y-6 times.
Regarding N-x-2 and Y-3 timings.
There are a total of (2+1)*(3+1)=12 factors.
Situation 2
Since N2 has 34 factors if N2 is raised to the power of 34, there are 17 factors for N.
Consequently, 17+1 = 18 factors in total.
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