Solve the following system of equations. Show all work and solutions.
y = 2x^2 + 6x + 1
y = −4x^2 + 1
Answers
Make the equations equal and solve for x
2x²+6x+1=-4x²+16x²+6x=06x(x+1)=06x=0 or x+1=0x=0 or x=-1For x=0
y=-4(0)+1=1For x=-1
y=-4(1)+1=-3The solutions are
(0,1) and (-1,-3)Graph attached
Related Questions
Which are the solutions of x2 = –7x – 8?
StartFraction 7 Over 2 EndFraction minus StartFraction StartRoot 17 EndRoot Over 4 EndFraction comma StartFraction 7 Over 2 EndFraction + StartFraction StartRoot 17 EndRoot Over 4 EndFraction
StartFraction negative 7 Over 2 EndFraction minus StartFraction StartRoot 17 EndRoot Over 4 EndFraction comma StartFraction negative 7 Over 2 EndFraction + StartFraction StartRoot 17 EndRoot Over 4 EndFraction
StartFraction 7 minus StartRoot 17 EndRoot Over 2 EndFraction comma StartFraction 7 + StartRoot 17 EndRoot Over 2 EndFraction
StartFraction negative 7 minus StartRoot 17 EndRoot Over 2 EndFraction comma StartFraction negative 7 + StartRoot 17 EndRoot Over 2 EndFraction
Answers
The solutions of the given quadratic equation are:
[tex]x = \frac{-7 + \sqrt{17} }{2} \\\\x = \frac{-7 - \sqrt{17} }{2}[/tex]
How to get the solutions of the quadratic equation?
Here we have the quadratic equation:
[tex]x^2 = -7x - 8[/tex]
To solve it, we can rewrite it as:
[tex]x^2 + 7x + 8 = 0[/tex]
Now if we use Bhaskara's formula, we get the solutions:
[tex]x = \frac{-7 \pm \sqrt{(7)^2 - 4*1*(8)} }{2} \\\\x = \frac{-7 \pm \sqrt{17} }{2}[/tex]
Then the two solutions are:
[tex]x = \frac{-7 + \sqrt{17} }{2} \\\\x = \frac{-7 - \sqrt{17} }{2}[/tex]
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4 < x < 7
Please give me a proper explanation.
Answers
An explanation for 4 < x < 7 is that 4 is less than and x is less than 7.
How to explain the information?The mathematical expression that is given is 4 < x < 7. It should be noted that this implies that 4 is less than and x is less than 7.
In this case, the appropriate values that can fit x in this situation will be 5 and 6.
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Latoya bought 8 pounds of potatoes at a local wholesaler for $18. Her friend Herman bought 6 pounds of potatoes at the supermarket for $15. Herman thinks he got the better deal because $15 is less than $18.
Answers
Answer:
Herman is wrong. Latoya got the better deal.
Step-by-step explanation:
Latoya bought 8 pounds of potatoes for $18.
► 18 / 8 = $2.25 per pound
Herman bought 6 pounds of potatoes for $15.
► 15 / 6 = $2.50 per pound
Cheaper per pound is better!
Consider the function f(x) = x3 − 4x2 + 2. Calculate the limit of the difference quotient at x0 = 3 for f(x).
Answers
The answer is -5
Step-by-step explanation:
i know that because i just did this problem
55 POINTS!!!!!! WILL GIVE BRAINLIEST!!!!!!! PLS HELP ASAP!!!!!
Danielle is trying to solve the equation [tex]8^x=\frac{1}{64}[/tex]. Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answers
Answer:
x=-2
Step-by-step explanation:
Given equation:
8^x= 1/64
Ensure both sides of the equation are in power format by changing 1/64
1/64 = 64^-1
8^x = 64^-1
2^3(x) = 2^6(-1)
The bases will cancel out each other
3(x) = 6(-1)
3x = -6
x = -6/3
x = -2
Check
8^x = 1/64
x = -2
8^-2
= 1/8²
= 1/8*8
= 1/64
Rhombus RSTU is congruent to rhombus
WXYZ. Could rhombus RSTU be a
translation image of rhombus WXYZ?
Why or why not? Can you be sure that
rhombus RSTU is a translation image of
rhombus WXYZ? Why or why not?
Answers
Rhombus RSTU is congruent to WXYZ, and are translational images of each other because all their sides and angles are equal
What are the properties of a rhombus?Some of the properties of a rhombus are;
The sides are congruent.All the opposite sides are parallel to each other.Diagonals bisect each other perpendicularly.The angles are supplementary, that is, they add up to 180°If Rhombus RSTU is congruent to WXYZ, then they are both translation images of each other because all their sides and angles are equal.
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1. If mPQ = 130°, find mRQ.
Answers
Answer:
mRQ = 50
Step-by-step explanation:
180-130=50
create an Ordered pair located on the X axis using -6,-2,0,3,5
Answers
Answer:(-6,0)
Step-by-step explanation:
Distribute and simplify these radicals.
√12-(-1+√5)
O-4√3
0-2√3+2√15
O 4√3
06√3
K
Answers
[tex] \sqrt{12} + 1 - \sqrt{5} \\ = \sqrt{4} \times \sqrt{3} + 1 - \sqrt{5} \\ = 2 \sqrt{3} + 1 - \sqrt{5} [/tex]
For positive acute angles A and B, it is known that sin A = 24/25 and cos B = 11/61
Find the value of cos(A + B) in simplest form
Answers
Answer:
Rounded to 0.42. Not rounded: 0.41729656785
Step-by-step explanation:
24/25 = 0.96
11/61 = 0.180327869
Add those together.
Answer for that: 1.14032787
Find the cos for the answer.
Which is 0.41729656785 to 0.42
Which scatter plot shows a negative linear association?
A.
B.
C.
D.
Answers
Answer:
D
Step-by-step explanation:
If you imagine the dots continued in a connected line, (imagining where the data points will likely go), the line's slope informs you if it is a negative (going down/negative slope) linear association or if it's a positive (going up/positive slope) linear association.
For A, it has a positive slope [as it increases].
For B, it also has a positive slope
For C, there is no correlation, the dots are not showing any trends
For D, there is a negative slope.
This means that the scatter plot D shows a negative linear association.
Option (D) shows a negative linear association between the variables is the correct answer.
A scatter plot is a type of data visualization that shows the relationship between different variables. Scatter plots are used to plot data points on a horizontal and a vertical axis in an attempt to show how much one variable is affected by another.
For the given situation,
The graph shows the data points on a horizontal and a vertical axis.
A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.
Among graphs, in option (D) when one variable tends to increase in the x-axis, the other variable decreases in the y-axis.
Hence we can conclude that option (D) shows a negative linear association between the variables is the correct answer.
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anyone can help please and quickkkk
Answers
The values of x, y, and z are 1, 2, and 3 respectively after using the substitution method.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a linear equation in three variable:
2x + 3y - z = 5 ...(1)
4x - y - z = -1 ...(2)
x + 4y + z = 12 ...(3)
[tex]\rm \mathrm{Substitute\:}x=\dfrac{5-3y+z}{2}[/tex] (from the equation 1 and 2)
After solving:
[tex]\rm \begin{bmatrix}-7y+z+10=-1\\ \dfrac{5y+3z+5}{2}=12\end{bmatrix}[/tex]
From the above, two equations:
y =2
z =3
Plug the above values in equation 1
x = 1
Thus, the values of x, y, and z are 1, 2, and 3 respectively after using the substitution method.
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If m∠2 = 137 and m∠P = 22, what is m∠O?
Answers
Answer:
The answer is 21
Step-by-step explanation:
This should help you
A survey was conducted by a pet store to find the number of cats and dogs owned by people in a neighborhood block. The results of the survey are represented in this Bar Graph. Which statement describes why the Bar Graph is not properly drawn? A. The vertical scale is too high. B. The vertical scale should not start at zero. C. The bars are not the same width. D. The bars are not the same height.
Answers
Answer: C
Step-by-step explanation:
Justin rides his bicycle 2.5 kilometers to school.
Luke walks 1,950 meters to school. How much
farther does Justin ride to school than Luke
walks to school?
Answers
Answer:
1 kilometre = 1000 metres
2.5km = 2.5 × 1000m = 2500m
2500 - 1950 = 550m
Therefore Justin rides 550m farther than Luke walks to school.
A polygon is shown. What is the area of the polygon ?
Answers
Answer:
C
Step-by-step explanation:
Lower rectangle = 4 * 12 = 48 in^2
Upper trapezoid 1/2 ( 5 + 12 ) * 6 = 51 in^2
total = 48 + 51 = 99 in^2
F(x)=2x^2+6x-4
G(x)=5x^3-6x^2-3
Find (f+g)(x)
Answers
A function assigns the values. The value of (f+g)(x) is (5x³ - 4x² - 6x - 7).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given F(x)=2x²+6x-4 and G(x)=5x³-6x²-3, therefore, the value of (f+g)(x) is,
(f+g)(x) = f(x) + g(x)
= 2x²+6x-4 + 5x³-6x²-3
= 5x³ - 6x² + 2x² - 6x - 4 - 3
= 5x³ - 4x² - 6x - 7
Hence, the value of (f+g)(x) is (5x³ - 4x² - 6x - 7).
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which statement best describes the polynomial?
Answers
PLEASE HELP! PIC ATTACHED
Answers
Answer:
x = 25
Step-by-step explanation:
First turn this into an equation:
[tex]\frac{4}{5}[/tex] times x = 20
Now divide both sides by [tex]\frac{4}{5}[/tex]. You can't divide by a fraction, instead you multiply by flipping the fraction. So now you're multiplying both sides by [tex]\frac{5}{4}[/tex].
20 times 5 = 100. Next you divide [tex]\frac{100}{4}[/tex]. This is equal to 25. You have completed the equation and now have the answer:
x = 25
Have a great day!
Ari said there are three possible outcomes when you spin this spinner twice: two reds, a yellow and a red, or two yellows.
So, the probability of getting two yellows is 1/3
Do you agree or disagree? Explain your thinking.
Answers
Answer:
I disagree.
Step-by-step explanation:
The reasoning may be wrong but I believe it is disagree.
I am going to keep it simple.
On the spinner there are 4 options, 3 for red and 1 for yellow.
Therefore, we have a 1/4 chance to get a yellow once.
If we get a yellow again, it is another. 1/4 chance.
1/4 x 1/4 is 1/16, considerably smaller than 1/3.
Answer:
From inspection of the diagram, we can see that the spinner is divided into 4 equal parts, where 3 parts are red and 1 part is yellow.
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Therefore,
[tex]\implies \textsf{Probability of getting a red} = \sf \dfrac{3}{4}[/tex]
[tex]\implies \textsf{Probability of getting a yellow} = \sf \dfrac{1}{4}[/tex]
Multiplication Rule for Independent Events
For independent events A and B:
[tex]\sf P(A\:and\:B)=P(A) \times P(B)[/tex]Therefore,
[tex]\begin{aligned}\implies \sf P(yellow\:and\:yellow) & = \sf P(yellow) \times P(yellow)\\\\ & = \sf \dfrac{1}{4} \times \dfrac{1}{4}\\\\ & = \sf \dfrac{1}{16}\end{aligned}[/tex]
ConclusionAri is incorrect. The spinner is divided into 4 parts, where only one part is yellow. Therefore, the probability of spinning a yellow is 1/4. As the events are independent, the Multiplication Rule should be used to calculate the probability of spinning 2 yellows. So the probability of spinning 2 yellows is 1/4 x 1/4 = 1/16.
Help! I need to finish but I'm stuck! Will give brainliest!
The shaded figure below is composed of a trapezoid and a semicircle on a coordinate plane.
Which of the following expressions represents the area of the shaded figure?
2(18 + π)
2(12 + π)
4(9 + 2 π)
8(3 + π)
Answers
Answer:
2(12 + π)
Step-by-step explanation:
This will get you about 30and even by just counting squares you will get the closest to this answer.
Quadrilateral ABCD is a rhombus. What conditions must be true?
Answers
Answer: B, C, D
Step-by-step explanation:
A rectangle must have at least one right angle, not a rhombus. So, A is wrong.This is a specific property of a rhombus, so B is correct.This is a specific property of a rhombus, so C is correct.Since all rhombi are parallelograms, and diagonals of a parallelogram bisect each other, D is also correct.A rental car company charges $63.41 per day to rent a car and $0.05 for every mile driven. Ella wants to rent a car, knowing that: She plans to drive 275 miles. She has at most $200 to spend. What is the maximum number of days that Ella can rent the car while staying within her budget?
Answers
Answer:
2 days
Step-by-step explanation:
275 miles times 0.05 = $13.75 for mileage
200-13.75=186.25 left
186.25/63.41(daily fee)= 2.93
She can rent it for 2 days
scientist wants to estimate the puffin population on puffin island
Answers
Answer:
The cliffs are home to many seabirds. Despite its name, there are few puffins (around 50 pairs during the April-July breeding season).
Step-by-step explanation:
A student looked at the diagram below and concluded x=y.
The student justified that conclusion by saying that both angles are subtended by arc AB.
What is the students error?
What are the values of X and y?
Answers
Answer:
[tex]y = 85[/tex]
[tex]x = 95[/tex]
Find x??? Please help asappppp
Answers
Answer:
It's at the beginning of x+4, the 2nd symbol of 4x-4, and the beginning of X+1.
Step-by-step explanation:
No explanation for you! Just choose them! It's right!
help please i need the answer.
Answers
i think you just have to do 3 + 14+2+2+3and then solve i guess
Find the values of x in the following figures.
Please help
Answers
Answer:
1) x = 15°2) x = 60°Step-by-step explanation:
1)(2x + 4x + 6x) * 2 = 360*
2x + 4x + 6x = 180°
12x = 180°
x = 180 : 12
x = 15
2)(2x + x) * 2 = 360
2x + x = 180
3x = 180
x = 180 : 3
x = 60°
Smallville High School scored more than 30 points in their last football game entirely from safeties and field goals. (In
football, a safety counts as 2 points and a field goal counts as 3 points.)
1. Write an inequality for this scenario in standard form.
2. Write the inequality in slope-intercept form.
3. Graph the inequality.
Answers
Inequalities help us to compare two unequal expressions. The inequality for this scenario in standard form is 2x + 3y > 30.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Let the safety counts be represented by x, while the field goal count is represented by y.
Part A: The inequality for this scenario in standard form.
2x + 3y > 30
Part B: The inequality in slope-intercept form.
2x + 3y > 30
3y > 30 - 2x
y > 10 - (2/3)x
y < (2/3)x - 10
PartC: The inequality is represented below.
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A grab bag contains 2 football cards and 8 basketball cards. An experiment consists of taking one card out of the bag, replacing it, and then selecting another card. Determine whether the events are independent. What is the probability of selecting a football card and then a basketball card? Express your answer as a decimal.
Answers
The events are not independent.
The probability of selecting a football card and a basketball card is 0.16.
What is the probability?Probability is the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of selecting a football card and a basketball card = (number of football cards / total number of cards) x (number of basketball cards / total number of cards)
2/10 x 8/10 = 0.16
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