Answers
The solutions to the system of equations formed by the linear equation 9 · x + 9 · y - 79 = 0 and the quadratic equation x² + 5 · x - y - 4 = 0 are (x₁, y₁) = (5 / 3, 64 / 9) and (x₂, y₂) = (- 23 / 3, 148 / 9).
How to solve a system of equations
Herein we find a system of equations formed by a linear equation and a quadratic equation. This system must be resolved by means of algebra properties. First, write the system of equations:
9 · x + 9 · y - 79 = 0
x² + 5 · x - y - 4 = 0
Second, clear the variable y in the first equation:
9 · x + 9 · y - 79 = 0
9 · y = 79 - 9 · x
y = 79 / 9 - x
Third, substitute y on the second equation:
x² + 5 · x - (79 / 9 - x) - 4 = 0
x² + 6 · x - 115 / 9 = 0
Fourth, use the quadratic equation to find the solutions of x:
x₁ = 5 / 3, x₂ = - 23 / 3
Fifth, calculate the solutions of y:
y₁ = 79 / 9 - x₁
y₁ = 64 / 9
y₂ = 79 / 9 - x₂
y₂ = 148 / 9
The solutions are (x₁, y₁) = (5 / 3, 64 / 9) and (x₂, y₂) = (- 23 / 3, 148 / 9).
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Related Questions
9. A water tank is filled at a constant rate.
After 36 minutes, there are 648 gallons of
water in the tank. How many gallons of
water flowed into the tank each minute?
Use the model.
36
כp
648
regist
the upc
has 49 vor
the same nu
voters will
Answers
Answer: 18 gallons
Step-by-step explanation:
648/36 = 18
Use the quadratic function to predict y if x equals 7.
y=2x²-3x+3
y=-77
y=-80
y=80
y=77
Answers
Answer: C. y=80
Step-by-step explanation:
1. Based on the given conditions, formulate: x=7
2. Calculate: Substitute x=7 into y=2x(to the power of) - 3x+3
y=80
3. Then find the correct option: C
Ahmed earns $450/week. He receives a 4% increase in pay.
What is Ahmed’s weekly pay after his increase?
Answers
Sydney’s fitness app says she has completed `70\%` of her goal for the week. Her goal is `50` miles. How far has she biked?
Answers
Sydney has biked `35` miles.
9(2n+1) help please brooooooo
Answers
Answer:
18n + 9
Step-by-step explanation:
Distribute 9 into the expression.
9*2n = 18n
9*1 = 9
18n + 9
What percentage of 2000 is 1200
Answers
= 60%
I WILL GIVE BRAINLY TO WHOEVER HELPS!!
Select all the equations that represent the bar diagram.
Answers
Answer:
A and C
Step-by-step explanation:
Does the table represent a
function? Explain.
x
-3 -2 0 -3 -2
y 9 4 0 -9 -4
Answers
keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.
I need help with this Please been struggling all day
Answers
Answer:
x-intercepts: -0.16 and 3.16
vertex: (1.5, 5.5)
Step-by-step explanation:
The weather report suggested that your city’s temperature increased from -10 degree celsius to 20 degree celsius. What is the rise in temperature?
Answers
Answer:
The temperature increased in 30 degrees Celsius
Step-by-step explanation:
What is [tex]\sqrt{x-3} -\sqrt{x} =3[/tex]
Answers
Answer:No solution
Step-by-step explanation:
The solution of the equation is 4. Once you plug in 4, you will find that it does not fit
1-2 does not equal to 3
solve -x+y=6 and 2x+5y=-12 using substitution method
Answers
x=-6 and y=0 are solutions for the equations 2x+5y=-12.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given equations,
-x+y=6...(1)
2x+5y=-12 ...(2)
From equation 1
y=6+x
Now put y value in 2
2x+5(6+x)=-12
2x+30+5x=-12
7x+30=-12
Subtract 30 on both sides
7x=-12-30
7x=-42
Divide both sides by 7
x=-6
Now plug in x value in equation 1
-(-6)+y=6
6+y=6
y=0
Hence, x=-6 and y=0 for the equations 2x+5y=-12.
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In an animal rescue facility are 21 animals.14 cats and 7 dogs. During the day 5 animals were adopted.what is the probabity that 3 cats and 2 dogs were adopted? Review ch 7 on probability
Answers
Answer:
0.3756
Step-by-step explanation:
I believe this is a combinatorics probability problem.
We first figure out in how many ways we can choose 3 cats out of 14 cats
Then we figure out how many ways we can choose 2 dogs out of 7 dogs
The total number of ways to select 3 cats and 2 dogs will be the product of these two
We then figure out in how many ways we can select 5 animals out of a total of 21 animals
The product we computed divided by the above number will give the probability
The number of ways we can choose k items out of n items is given by nCk i.e n Choose k
The formula is rather complicated but almost all calculators should be able to compute this given n and k
Let's deal with the selection of 3 cats from the population of 14 cats
This is given by 14C₃ which works out to 364
Number of ways for selecting 2 dogs from 7 dogs = 7C₂ = 21
Number of ways of selecting 5 animals from 21 = 21C₅ = 20349
The probability of selecting 3 cats and 2 dogs is therefore:
[tex]\dfrac{364 \times 21}{20349} = 0.3756[/tex]
That, I believe is the answer. Please let me know if it is correct and if you need more info.
I need assistance on This question
Answers
Answer: it would be A.
Step-by-step explanation: I did the quiz
Graph the equation. y = -(x-4)^2+4
Answers
2x-3y=-9
x-5y=-29 solve by substitution
Answers
Answer:x=6
y=7
Step-by-step explanation:
x=5y-29
2(5y-29)-3y=-9
7y=49
y=7
x=5(7)-29
x=6
Give the degree of the polynomial.
Answers
Answer: 7
This is a seventh degree polynomial.
Step-by-step explanation:
The degree of the polynomial is the highest exponent.
Step-by-step explanation:
7 is the degree of the polynomial
7 is the highest exponent.
please mark brainliest
THE ONE PIECE IS REAL
Answers
Answer: im going to be king of the pierates
Step-by-step explanation: :)
HELP ME PLEASE THANKS
Answers
Answer: Answer choice B
Step-by-step explanation:
Can you guys awnser the questions in the boxes below
Answers
Answer:35 divide by 10.50= 3.33 = 4 hrs
Step-by-step explanation:
given the slope of the line and one point the passage through (2,-1) m=5/4
Answers
Answer:
slope intercept form:
y = [tex]\frac{5}{4}[/tex] x - [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
m = 5/4
x = 2 from the point (2,-1)
y = -1 from the point (2,-1)
y = mx + b
-1 = [tex]\frac{5}{4}[/tex] ([tex]\frac{2}{1}[/tex]) + b
-1 = [tex]\frac{10}{4}[/tex] + b
-1 = [tex]\frac{5}{2}[/tex] + b Subtract [tex]\frac{5}{2}[/tex] from both sides
[tex]\frac{-2}{2}[/tex] -+ [tex]\frac{-5}{2}[/tex] = b
[tex]\frac{-7}{2}[/tex] = b
y = mx + b
y = [tex]\frac{5}{4}[/tex] x - [tex]\frac{7}{2}[/tex]
Answer:
if you need the equation: y + 1 = [tex]\frac{5}{4}[/tex] (x-2) or y + 1 = [tex]\frac{5}{4}[/tex] x [tex]-\frac{5}{2}[/tex]
the answer: y = [tex]\frac{5}{4}[/tex] x [tex]-\frac{7}{2}[/tex]
Step-by-step explanation:
Kind of explanatory you have a slope and a point, your formula is going to be y-y₁ = m(x-x₁)
Find the values of x, y, and z in the triangle.
(Image attached.)
Answers
3x=171
x= 57
Z: 2x-9+x=180
3x=189
x= 63
X: 180=63+57+c
180= 120+x
60=x
So Y= 57 Z= 63 X= 60
68. A researcher wants to know if the mean
times (in minutes) that people watch their
favorite news station are the same. Suppose
that Table 13.24 shows the results of a
study.
CNN
45
12
18
38
23
35
Table 13.24
FOX
15
43
68
50
31
22
Local
72
37
56
60
51
Assume that all distributions are normal, the
four population standard deviations are
approximately the same, and the data were
collected independently and randomly. Use a
level of significance of 0.05.
Answers
By using the concept of mean and standard deviation, it can be inferred that
The the drug stays in the system for more than 397 minutes
What is mean and Standard Deviation?
Suppose there is a data set and the average of the data set has to be calculated. To calculate the average of the data set, mean is used
To know about Standard Deviation, it is important to know about Variance
Variance is the sum of the square of deviation from mean.
Square root of the variance gives the standard deviation
Given n = 35,
Population mean = 397
Population Standard Deviation = 18
Here the sample size is large. So the distribution is approximately normal
To test :
Test statistic t =
= 1.97
p value at = 0.0244
Since 0.0244 < 0.05, the null hypothesis is rejected
So the the drug stays in the system for more than 397 minutes
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pls help me with this question
Answers
Answer:
[tex]\frac{13}{30}[/tex]
Step-by-step explanation:
You have saved $16,000 for a down payment on a house. Your bank requires a minimum down payment of 15%.
What is the maximum price you can offer for a home in order to have enough money for the down payment?
Answers
(16000 x 100) / 15
This equals $106666.67.
The exponential form of log5 25 = 2 when written exponentially is 25 = 25.
False
True
Answers
Answer: never mind
Step-by-step explanation:
74 % of 315
estimate using the rate per 100
Answers
Answer:
23.4920634921
Step-by-step explanation:
74/315 x 100% = 23.4920634921
I will mark brainliest, kinda urgent
Answers
The quadratic function that models the graph on the image is given as follows:
y = (x - 1)² - 1.
What is the quadratic function?The features of the quadratic equation given from the graph are given as follows:
The vertex.The y-intercept.The equation of a quadratic function with vertex (h,k) is defined as follows:
y = a(x - h)² + k.
In which a is the leading coefficient of the function.
From the graph, the coordinates of the vertex are given as follows:
(1,1).
As the vertex is the turning point of the function.
Hence the parameters h and k have values of:
h = 1, k = 1.
Hence:
y = a(x - 1)² + 1.
The y-intercept of the function is of:
y = 2.
This means that when x = 0, y = 2, hence the leading coefficient a is obtained as follows:
2 = a(0 - 1)² + 1
a = 1.
Hence the equation is of:
y = (x - 1)² - 1.
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6. The table shows the number of goals scored by a soccer team in 20 matches.
4
1
1
2
2
1
1
3
0
4
0
3
1
2
2
2
3
4
(a) Represent the data on a dot diagram.
(b) Find
(i) the mean,
(ii) the median,
2
(iii) the mode, of the distribution.
3
Answers
a) The dot plot of the data-set is given by the second image shown at the end of the answer.
b - i) The mean of the distribution is of: 1.6 goals.
b - ii) The median of the distribution is of: 1.
b - iii) The mode of the distribution is of: 1 goal.
What are the measures?The mean is given by the sum of all observations of the data-set, hence it is of:
Mean = (0 x 5 + 1 x 6 + 2 x 4 + 3 x 3 + 4 x 1 + 5 x 1)/20 = 1.6.
The median of the distribution is the middle value of the distribution, which is the value of which half the distribution is less than and half is greater than.
Adding in the frequency table given at the end of the answer, it is found that the middle term is of 1, as the sum of the frequencies reaches 10, which is half of the cardinality of 20, at a number of 1.
The mode is the term with the highest absolute frequency, hence it is also of one goal, as it has the highest absolute frequency, which is of 6.
The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as the table, in a different format.
Missing InformationThe table is given by the first image shown at the end of the answer.
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The diagram shows a shape with all side lengths measured in centimetres. All the angles are right angles.
Write an expression, in terms of
x, for the total shaded area.
Answers
The expression for the total shaded area is in terms of x is
Area = (x + 5)(x - 3)
How to find the total shaded areaThe top side of the diagram shows that the dimension for the shaded area has length = x + 5
The width of the shaded area is x - 3
Area of a rectangle is given by the formula
Area = Length * width
Area = (x + 5) * (x - 3)
Area = x² - 3x + 5x - 15
Area = x²+ 2x - 15
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