Answer:
stuff and more stuff
Step-by-step explanation:
Topic: Nonlinear Systems of EquationsCreate a system of equations that includes one linear equation and one quadratic equation.Show all work in solving your system of equations algebraically.
Answer:
• Equations
[tex]y=x+2[/tex][tex]y=x^2[/tex]• Solutions (2, 4) and (–1, 1)
Explanation
System of equations
• Linear equation
[tex]y=x+2[/tex]• Quadratic equation
[tex]y=x^2[/tex]We have to set both equations to 0 and equalize them:
• 1. Setting them to 0:
[tex]0=x+2[/tex][tex]0=x^2[/tex]• 2. Equalizing them:
[tex]x+2=x^2[/tex]To solve the system using the General Quadratic Formula, we have to set the equation in the form ax² + bx+ c = 0:
[tex]x^2-x-2=0[/tex]Thus, in this case a = 1, b = -1 and c = -2. Using the formula:
[tex]x_{1,2}=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-2)}}{2(1)}[/tex][tex]x_{1,2}=\frac{1\pm\sqrt{1+8}}{2}[/tex][tex]x_{1,2}=\frac{1\pm\sqrt{9}}{2}[/tex]Finding both solutions:
[tex]x_1=\frac{1+3}{2}=\frac{4}{2}=2[/tex][tex]x_2=\frac{1-3}{2}=\frac{-2}{2}=-1[/tex]Finally, replacing these values in the linear equation to find y:
[tex]y_1=2+2=4[/tex][tex]y_2=-1+2=1[/tex]Therefore, the solutions are (2, 4) and (–1, 1).
1. Ali collects comic books. He buys 2
comic books a week. This year after 5
weeks he has 17 comic books in his
collection. Write an equation relating
the number of comic books c to the
number of weeks w.
xw + 5w - 17 = 0 is the required equation.
How to find the required related equation?Given,
Ali buys 2 comic books a week.
After 5 weeks he has 17 comic books this year.
Solution:
Let w be weeks and c be comic books.
Since Ali buys 2 comic books a week.
1w = 2c
For 5 weeks, he would have,
5w = 10c, if he bought 2books per week.
But he had 17 books,
i.e, he would have collected some books last year.
Let x be the no of unknown weeks last year.
(x + 5)w = 17c
(x+5)w-17c= 0
xw + 5w - 17 = 0 is the required equation.
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The question is clearly in the pic
A) The slope represents the probability of winning for each rank.
B) The y-intercept means the probability of winning for an unranked school.
C) The probability of winning for a school ranked number 4 is; 78%
How to Interpret Linear Equation Graphs?The formula representing the general form of an equation in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
A) From the given graph, we see that the y-axis represents the probability of winning for each rank while the x-axis represents the ranks of the schools. Thus;
Slope unit = Probability of winning/Rank
B) The y-intercept is the point at which the graph crosses the y-axis. In this case, it means no ranked school and that is the probability of winning for an unranked school.
C) The linear equation is given by the formula;
y = -6.4x + 103.8
Thus, for a rank of 4, we have;
y = -6.4(4) + 103.8
y = 78.2 ≈ 78%
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Which number line shows the points −125 and –2.8?
A. Alternative Text
B. Alternative Text
C. Alternative Text
D. Alternative Text
The number line having -2.4 and -2.8 is attached below
What is number line?Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. We refer to these as closed number lines. Number lines may alternatively be left empty or blank. A number ladder is a vertical number line.
Given number: −12/5 and –2.8
As, we can write -12/5 in decimal form= -2.4
Now, we have to put the number on the number line
As, -2.4 lies between -2 and -3 on the left side of zero.
and, -2.4 lies between -2.5 and -3.0 on the left side of zero.
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2. Write in standard form: one hundred dollars and fourteen cents
1
4. Which statement is NOT true about the diagram below?
O AD = DC
O m<CDB =92
O m<ADB =88
O DB is a perpendicular of AC
Answer:
DB is a perpendicular of AC
u/3 = -51 solve for u simplify your answer as much as possible
Answer:
u = -153
Step-by-step explanation:
u/3 = -51
multiply both sides by 3:
3(u/3) = 3(-51)
u = -153
Select the lesser of the two given numbers.
-5, -11
Which is the lesser of the two numbers?
Find the derivative of the function with solutions.y = In( e^(3 - x^2 ) + 9 ))
Answer:
[tex]\frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9}[/tex]Explanation:
We were given the function:
[tex]y=\ln\left(e^{3-x^2}+9\right)[/tex]We are to find the derivative of this function, we have it shown below:
[tex]\begin{gathered} y=\operatorname{\ln}(e^{3-x^{2}}+9) \\ If:y=ln(u) \\ Then:y^{\prime}=\frac{u^{\prime}}{u} \\ y^{\prime}=\frac{dy}{dy} \\ u=e^{3-x^2}+9 \\ u^{\prime}=-2xe^{3-x^2} \\ y^{\prime}=\frac{u^{\prime}}{u} \\ \Rightarrow y^{\prime}=\frac{-2xe^{3-x^2}}{e^{3-x^2}+9} \\ But:y^{\prime}=\frac{dy}{dx} \\ \frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9} \\ \\ \therefore\frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9} \end{gathered}[/tex]an office ceiling is 9 feet high file boxes are each 3/4 feet tall. what is the greatest number of these file boxes that can be stacked in the office? Show how you know.
Answer:
12
Step-by-step explanation:
Equation:
[tex]9 /\frac{3}{4}[/tex] [tex]=x[/tex]
[tex]12=x[/tex]
Check!
[tex]12(\frac{3}{4} )=9[/tex]
Therefore, the greatest number of file boxes that can be stacked is 12.
The population of City A is 8.59 x 10^4. The population of City B is 3.2 x 10^3 Select all of the values that show the difference in population of City A and City B
The difference of population in these two cities are 85900- 3200
= 82,700
How do you calculate difference?
Subtract the largest number from the lowest number to determine the difference between two integers. The difference between the two numbers is the product of this sum. As a result, there are 55 between the numbers 45 and 100.
Given: Population of city A= 8.59 x 10^4
and population of city B = 3.2 x 10^3
This can also be written as :
Population of city A= 85,900
and population of city B = 3200
Thus the difference of population in these two cities are 85900- 3200
= 82,700
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The price of an item yesterday was $140. Today, the price rose to $357. Find the percentage increase.
Answer: 70% is percentage increase
Step-by-step explanation:
230-140/140 x 100 =90/140 x100 =0.7 x 100=70
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
HELP PLS Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line is the ratio of the rise to the run, or rise divided by the run. slope of line is 4/3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (3,0) and (0,-4)
y₂=-4, y₁=0, x₁=3, x₂=0
Substitute values in formula
m=-4-0/0-3
m=4/3
Hence slope of line is 4/3.
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help me its so hard !!!
For the rectangle given, considering its diagonal properties, the value of x=4, while the angle VUR=36°
Angles and properties of plane shapesTo answer this question, let us recall the following:
The diagonals of a rectangle bisects each other into four eqaul length.The base angles of an Isosceles triangle are equal.Complementary angles add up to give a total of 90°.Hence;
the lengths RV and SV are
so, 3x+8=6x-4
6x-3x=8+4 [collecting like terms]
3x=12
when we divide both sides of the equation by 3, we have the value of x=4.
the angles VRS and VRU are complementary
so, 54°+VRU = 90°
VRU = 90°-54°
VRU = 36°
The triangle RUV is an Isosceles
so, angles VRU and VUR are equal, therefore angle VUR = 36°.
We can reduce from our workings that the value of x = 4 and the angle VUR is 36°.
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Find the value of x that makes A || B.
B
2
42= 3x20 and 25 = x + 20
x = [?]
Helpppppppssssss hehe
Answer:
Step-by-step explanation:
a. From 4 to 7 is 3 units. 7-10 is another 3 units and so on. The constant 3 units is the common difference.
The formula for a arithmetic sequence is
[tex]a_{n}=a_{1}+d(n-1)[/tex]
Where d is the common difference and a_1 is the first term.
[tex]a_{1}=4[/tex] and [tex]d=3[/tex]. Thus the equation of the nth term is
[tex]a_{n}=4+3(n-1)[/tex]
The single inequality y > |x + 2| is equivalent to which of the following systems?
Answers:
1.y > x + 2
y > –x + 2
2.y > x + 2
y > –x – 2
3.y > x + 2
y < –x + 2
4.y > x + 2
y < –x – 2
The single inequality y > |x + 2| is equivalent to:
4. y > x + 2
y < –x – 2
What is an inequality?It should be noted that an inequality is simply used to show the relationship between the expressions that aren't equal.
The non-negative value of a real number x, regardless of its sign, is its absolute value or modulus | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think about a number's absolute value is as its distance from zero on the real number line.
It should be noted that based on the information, the inequality is:
y > |x + 2|. This is the positive part of the modulus.
This is the same as y < –x – 2 when the signs are changed. This is the negative part of the modulus.
In conclusion, the correct option is 4.
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6. Select the operations that would increase the value of a given number.
A. Multiply the number by 10.
B. Multiply the number by 0.1.
C. Divide the number by 10.
D. Divide the number by 0.1.
7.Select the operations that would decrease the value of a given number.
A. Multiply the number by 10.
B. Multiply the number by 0.1.
C. Divide the number by 10.
D. Divide the number by 0.1.
The operations that would increase the value of a given number include the following:
A. Multiply the number by 10.
D. Divide the number by 0.1.
The operations that would decrease the value of a given number include the following:
B. Multiply the number by 0.1.
C. Divide the number by 10.
How to increase the value of a number?Multiplication is a mathematical operation which can be used to increase the value of a given number, especially by multiplying the number by a value that is greater than 1. Similarly, the value of a given number can also be increased by dividing it by a number that is lesser than 1 such as 0.1
How to decrease the value of a number?Multiplication is a mathematical operation which can be used to decrease the value of a given number, especially by multiplying the number by a value that is lesser than 1. Similarly, the value of a given number can also be decreased by dividing it by a number that is greater than 1 such as 10.
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Aldo has 61 miles remaining after 48 minutes of driving. How many miles will
be remaining after 60 minutes of driving?
Answer:
76.25
Step-by-step explanation:
61:48 = x:60
48x=3660
3660/48 = 76.25
So the answer is 76.25 miles are left.
Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 61 people is taken.What is the probability that the mean IQ score of people in the sample is less than 98? Round your answer to 4 decimal places, if necessary.
To find the probability that the mean IQ score of people in the sample is less than 98, first we need to convert the value into z-score by using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Then, when x=98:
[tex]\begin{gathered} z=\frac{98-100.0}{15.0} \\ z=\frac{-2.0}{15.0} \\ z=-0.1333 \end{gathered}[/tex]By checking in a standard normal table z=-0.1333 has a p-value=0.4471.
Then the probability is 0.4471 that also can be expressed as 44.71%
suppose arya stark draws a sample of 10 observations with a mean of 50 and a population standard deviation of 4. she would like to establish a 95% confidence interval. which formula would you tell her to use?
The formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.
What is termed as the confidence interval?A confidence interval shows the likelihood that a parameter would then fall between two values near the mean.The amount of uncertainty as well as certainty inside a sampling method is measured by confidence intervals.They are also used to test hypotheses and perform regression analysis.For the given question, the data is-
Mean μ = 50Standard deviation σ = 4Confidence interval 95%Sample size n = 10.Sample mean = xThe formula for finding the 95% confidence interval is normal approximation of the distribution.
z = (x - μ)/s
Where, s = σ/√n
The corresponding value of z for 96% is taken from the z score table.
Thus, formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.
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y = 3x + 5
y = 4x² + x
The system of equations has two solutions, these are:
(-0.89, 2.33) and (1.4, 9.2)
How to solve the system of equations?Here we have the following system of equations:
y = 3x + 5
y = 4x² + x
We can see that y is already isolated in both equations, so we can write the equation:
3x + 5 = y = 4x² + x
3x + 5 = 4x² + x
now we can solve this for x, this is just a quadratic equation:
3x + 5 - 4x² - x = 0
-4x² + 2x + 5 = 0
Using the quadratic formula, we can see that the two solutions are:
[tex]x = \frac{-2 \pm \sqrt{2^2 - 4*(-4)*5} }{2*-4} \\\\x = \frac{-2 \pm 9.17}{-8}[/tex]
So the solutions are:
x = (-2 +9.17)/-8 = -0.89
x = (-2 - 9.17)/-8 = 1.4
Evaluating the linear equation in these values, we get:
y = 3*(-0.89) +5 = 2.33
y = 3*(1.4) + 5 = 9.2
So the solutions of the system are:
(-0.89, 2.33) and (1.4, 9.2)
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I just need help solving this problem.
Answer:
see below
Step-by-step explanation:
sum of angles in right triangle is 180
90 + 50 = 140
b = 180 - 140 = 40 deg
find c
cos(50) = 20/ c
c = 20/cos(50) = 31.1
find a
tan(40) = 20/a
a = 20/tan(40) = 23.8
3y+2x=-1 solve for x
Answer:
Answer down below!
Step-by-step explanation:
Your answer would be -3/2y + (-1/2)
If you need the steps, refer to the image below!
I DONT KNOW PLS HELPP
7:8:9 = .... : 12 : ....
Answer:
7:8:9=21/2:12:27/2
Step-by-step explanation:
12/8=3/2
3/2*7=21/2
3/2*9=27/2
Pls brainliest
A farmer harvested 250 fruits. 82 were oranges and there were twice as many sapodillas as paw paws. What percentage of the fruits were paw paws? ||giving 30 points
Answer:
22.4%
Step-by-step explanation:
There were twice as many sapodillas as paw paws--take the sapodillas as 2 units and paw paws as 1 unit.
Form an equation.
2u + 1u + 82 = 250
Simplify and solve for 1 unit.
3u = 168
1u = 56
Number of paw paws is 56.
Formula for finding percentage of an object is given as (number of object/total number of items) x 100.
Percentage of paw paws
= (56/250) x 100
= 22.4%
Jane wants to buy a CD for $12. She has saved $7. How much money does she still need if 6% sales tax will be added to the cost of the CD.
Using the sales tax, the amount of money she still needs is $5.72
What is sales tax?A sales tax is a consumption tax imposed by the government on the sale of goods and services.
Jane wants to buy a CD for $12. She has saved $7.
The amount she needs if 6% sales tax is added to the cost can be calculated as follows;
Let's find the sales tax,
sales tax = 6% of 12
sales tax = 6 / 100 × 12
sales tax = 72 / 100
sales tax = $0.72
Therefore,
amount she needs to save = 12 + 0.72 - 7
amount she needs to save = 12.72 - 7
amount she needs to save = $5.72
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If F(n) = -n Then F(-6)= ?
Answer: 6
Step-by-step explanation:
-n plug -6 in so -(-6)=6
Answer:
boo ba loob
Step-by-step explanation:
sweating in saucy bbq sauce