Answers
The given system of equations is:
[tex]\begin{gathered} x^2+y-3=0 \\ x^2-y+1=0 \end{gathered}[/tex]Add the two equations to eliminate the variable y:
[tex]\begin{gathered} 2x^2-2=0 \\ 2x^2=2 \\ x^2=1 \\ \text{ Therefore,} \\ x=\pm1 \end{gathered}[/tex]Substite x = 1 into the first equation:
[tex]\begin{gathered} (-1)^2+y-3=0 \\ 1+y-3=0 \\ y=3-1=2 \end{gathered}[/tex]Subtitute x=-1 into the second equation:
[tex]\begin{gathered} (1)^2+y-3=0 \\ 1+y-3=0 \\ y=3-1=2 \end{gathered}[/tex]Therefore, the points (-1, 2) and (1, 2) are solutions of the system.
The graph of the system is:
Related Questions
Write out the Harmonic Sequence
Answers
Answer:
Step-by-step explanation:
maybe try to add pollyonxies
What is the measure of ∠ 1 if ∠ 1 is (2x-3) and ∠is (8x)
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We know that:
[tex]\angle1+\angle2=180\degree[/tex]Then we have:
[tex]\begin{gathered} (2x-3)\degree+(8x)\degree=180\degree \\ (10x)\degree-3\degree=180\degree \\ (10x)\degree=183\degree \\ x=\frac{183\degree}{10} \\ x=18.3\degree \\ \angle1=2\cdot18.3\degree-3\degree \\ \angle1=33.6\degree \end{gathered}[/tex]a ceiling fan makes 1/8 of a full rotation in 2/5 seconds how many rotations per seconds does the fan make?
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The Solution:
The question says a ceiling fan makes 1/8 of a full rotation in 2/5 of a second. That is,
[tex]\begin{gathered} \frac{1}{8}r=\frac{2}{5}s \\ where\text{ r=a full rotation} \\ s=\text{ a second} \end{gathered}[/tex]We are asked to find how many rotations per second the fan makes. By making s the subject of the formula in the above equation, we get
[tex]\begin{gathered} \frac{1}{8}r=\frac{2}{5}s \\ \text{Cross multiplying, we get} \\ 16s=5r \end{gathered}[/tex]Dividing both sides by 16, we get
[tex]\begin{gathered} \frac{16s}{16}=\frac{5r}{16} \\ \\ s=\frac{5r}{16} \end{gathered}[/tex]So, the fan makes 5/16 of a full rotation in every second.
The firm Bosox and Yankee has a monopoly on the production of baseball memorabilia. The firm faces the following demand curve for its product:The firm has a fixed cost of $1,000.00 and a constant marginal cost of $14 for producing units of baseball memorabilia.1. Assume the firm cannot price discriminate. How may units will the firm produce in order to maximize theprofits? a. 25 b. 50 c. 100 d. 290
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Answer:
Step by step
Suposse you ran 2 km in 10 min. With what speed did you run?
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Answer:
12km/h
Step-by-step explanation:
10*6=60min=1hr
2*6=12km
Simplify: 21 + 14 + (-18) + (-3) +4
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Answer:
Step-by-step explanation:
21 + 14 + (-18) + (-3) +4= 18
21+14=35
35+-18=17
17+-3=14
14+4=18
Hopefully this Helped! :)
please answer the following questions. the first one is answered
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Since we have a table for the function, every time we have a value for x, we look for it on the x column and the f(x) value will be the value in the samr row on the f(x) column.
Similarly, if we have a value of f(x), we look for it in the column f(x) and get the corresponding x.
So, if we have f(x) = 1, we see that this value is in the 7th row, and the corresponding x is 6, so x = 6.
For f⁻¹(x) we do the same but switching the columns.
So, to find f⁻¹(9), we would normally look for x = 9, but since it is f⁻¹ we look for f(x) = 9, which is in the 6th row and the corresponding x is 5, so f⁻¹(9) = 5.
For f⁻¹(x) = 6, we would look for 6 on f(x), but since it is f⁻¹ we look for x = 6, which is in the 7th row and the corresponding f(x) is 1 so x = 1.
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
Answers
An equation for S in terms of n representing Dianelys' salary after working n years for the company is equal to S = 40000 + 2500(n-1).
As given in the question,
Dianelys' first year salary is equal to $40000.
Raise given to Dianelys' every year is $2500
Table to represent the value for different years
First year = $40000
Second year = 40000 + 2500(1)
= $42500
Third year = 42500 + 2500
= 45000
= 40000 + 2500(2)
Fourth year = 45000 +2500
= $47500
= 40000 +2500(3) .....
An equation for S in terms of n years
S = 40000 + 2500(n -1)
Therefore, an equation for S in terms of n representing Dianelys' salary after working n years for the company is equal to
S = 40000 + 2500(n-1).
The complete question is:
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S, in terms of n, representing Dianelys' salary after working n years for the company.
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Name the reference angle in radians for an angle of -315 degree
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The angle of -315 degree means angle of 315 degree in clockwise direction from the positive x-axis.
The angle -315 degree means that angle lies in first quadrant as,
So measure of reference angle is,
[tex]360-315=45[/tex]Reference angle in radians is,
[tex]45\cdot\frac{\pi}{180}=\frac{\pi}{4}[/tex]So reference angle of -315 degree in radians is,
[tex]\frac{\pi}{4}\text{ radians}[/tex]How do I find the inserting the missing values? at the rows? How can I Write the rule ,in terms of s and t, to show how t is related to s?
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Find: the missing value in the table
Expalantion: i)
[tex]52[/tex][tex]1+\frac{3}{4}\times52[/tex][tex]40[/tex]ii)
[tex]\begin{gathered} 1+(\frac{3}{4}\times x)=55 \\ x=\frac{54\times4}{3} \\ x=72 \end{gathered}[/tex]so the answer of second part will be
[tex]72[/tex][tex]1+(\frac{3}{4}\times72)[/tex]The equation y = 8z + 50 models the cost y for 2 members of the art club to go to a museum,including the shared cost of hiring a tour guide for $50. Which statement must be true?АIt will cost $240 altogether it 30 members go.BIt will cost $130 altogether it 10 members go.8 members of the art club will go to the museum.D50members of the art club will go to the museum.
Answers
According to the information given, the equation allow us to know the cost for x members to go to the museum not how many will go. For that reason option C and D cannot be true unless a fix cost was given too.
Then using the equation we can find the cost for 30 and 10 members and select the statement that is true.
[tex]\begin{gathered} y=8\cdot(30)+50 \\ y=240+50 \\ y=290 \end{gathered}[/tex][tex]\begin{gathered} y=8\cdot(10)+50 \\ y=80+50 \\ y=130 \end{gathered}[/tex]The statement that is true is b, the costr for 10 members is $130.
Find sin 2x, cos 2x, and tan 2x if cosx= 5/13 and x terminates in quadrant IV.
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Consider the following expression:
[tex]\cos(x)=\frac{5}{13}[/tex]this expression can be represented in the following right triangle:
To find y, we can apply the Pythagoras theorem as this:
[tex]y=\sqrt{13^2\text{ - 5}^2}\text{ = 12}[/tex]but since x terminates in quadrant IV, we have that
[tex]y=\text{ - 12}[/tex]and thus
[tex]\sin(x)=\text{ -}\frac{12}{13}[/tex]and
[tex]\tan(x)=\text{ -}\frac{12}{5}[/tex]now, using this data in the following formulas:
we can conclude that the correct answer is:
Answer:[tex]\sin(2x)=\text{ -}\frac{120}{169}[/tex][tex]\cos(2x)=\text{ - }\frac{119}{169}[/tex][tex]tan(x)=\frac{120}{119}[/tex]please help me do this i think i’mdoing it right but i’m not sure The graph shows a parabola and its focus. Write the equation of the parabola in vertex form.
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Step 1
Write the parabola in vertex form eqaution
[tex](x-h)^2=-4a(y-k)[/tex]where
[tex]\begin{gathered} h=0=x-\text{coordinate of the vertex} \\ k=1=y-\text{coordinate of the vertex} \end{gathered}[/tex]Step 2
Find the required equation
The distance between the vertex and the focus = a
Therefore,
[tex]\begin{gathered} \text{The vertex=(0,1)} \\ \text{The focus= (0,-2)} \end{gathered}[/tex]Hence with the formula for the distance between two points we have
[tex]\begin{gathered} D=\sqrt[]{(0-0)^2+(-2-1)^2}^{}_{} \\ D=\sqrt[]{0^2+(-3)^2} \\ D=\sqrt[]{0+9} \\ D=\sqrt[]{9} \\ D=3 \\ a=D=3 \end{gathered}[/tex]Step 3
Get the required equation by substitution
[tex]\begin{gathered} (x-h)^2=-4(a)(y-k) \\ (x-0)^2=-4(3)(y-1) \\ x^2=-12(y-1) \end{gathered}[/tex]Hence in vertex form, the equation of the parabola will be
[tex]y=-\frac{1}{12}x^2+1[/tex]The answer is written as;
[tex]y=-\frac{1}{12}x^2+1[/tex]1. Tina is getting ready to take the final exam for MAT 143. Her averages before the final exam are given.
Test average-68 Hand-in-Assignment average = 75
MML average 90
The Test is 60% of the grade, Hand-in Assignment is 10% of the grade, MML is 10% of the grade
and the Final exam is 20% of the grade.
a) What should she score in the final exam to make a B (minimum 80) in the class? Note that the
maximum you can earn in the final exam is 100 points. Use PCC grading scale.
b) What should she score in the final exam to make a C (minimum 70) in the class? Note that the
maximum points you can earn in the final exam is 100 points. Use PCC grading scale.
Answers
Using the weighted mean, the minimum scores needed are given as follows:
a) To earn a B: Not possible.
b) To earn a C: 63.5.
How to obtain the weighted mean?The weighted mean is obtained by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
If these weights are proportions, then the weighted mean is given by the sum of each grade multiplied by it's proportion.
In the context of this problem, Tina grades are given as follows:
68 with a weight of 0.6.75 with a weight of 0.1.90 with a weight of 0.1.x with a weight of 0.2.Hence her final grade is given as follows:
G = 68 x 0.6 + 75 x 0.1 + 90 x 0.1 + 0.2x = 57.3 + 0.2x.
For a grade of B, the minimum score is given as follows:
57.3 + 0.2x = 80
0.2x = 22.7
x = 22.7/0.2
x = 113.
Hence it is not possible to earn a B, as the maximum possible score is of 100.
For a grade of C, the minimum score is given as follows:
57.3 + 0.2x = 70
0.2x = 12.7
x = 12.7/0.2
x = 63.5.
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Heather is considering purchasing an item that costs $9. The sales tax in Heather's area is set at 5.9%. What is the total purchase price that Heather would be charged on this purchase?
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The total purchase price that Heather would be charged on this purchase is $10.
Solution:
Total charge = $9 x (1 + 0.059)
Total charge = $9 x 1.059
Total charge = $9.531
Total charge ≈ $10.
To calculate sales tax multiply the purchase price by the sales tax rate. Don't forget to convert the sales tax rate from percentage to decimal. When sales tax is calculated, it will be added to the purchase price. The result is the total cost and these are paid by the customer. Most states impose sales tax on top of the cost of each item you purchase.
The total amount you actually pay for the purchase is called the gross price and the price before tax is called the net selling price. To calculate the sales tax on an item, you must first convert the pre-tax cost of the item to a decimal and then multiply it by the sales tax percentage. Once sales tax is calculated, it must be added to the pre-tax value to determine the total cost of the item.
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Just wondering how I would get the area of the middle part, I have both the triangles and one square down, I just can’t get the middle one.
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The total area = Area of a right angle triangle + rectangle
The area of triangle = 1/2 x b x h
base = 11
Height = 8
Area of a triangle = 1/2 x 8 x 11
Area = 8 x 11 / 2
Area = 88/2
Area = 44 square inches
For the first rectangle
Area = Length x width
Length = 11 inches and width = 9 inches
Area = 11 x 9
Area = 99 square inches
Which statement is true of this function?
f(x) = (1) ² - 2
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..........................................
Round 9.948 to the nearest whole number.
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Answer: 9.900
i had this before the answer is right.The length of a shadow of a building is 26 m. The distance from the top of the building to the tip of the shadow is 35 m. Find the height of the building. If necessary, round your answer to the nearest tenth.
Answers
Using the length of shadow, the height of the building to the nearest tenth is 23.4 metres.
How to find the height of the building?The length of a shadow of a building is 26 m.
The distance from the top of the building to the tip of the shadow is 35 m.
The height of the building can be found as follows:
This situation forms a right angle triangle.
Therefore, the length of the shadow is the adjacent side and the distance from the top of the building to the tip of the shadow is the hypotenuse side.
Hence, using Pythagoras theorem,
c² = a² + b²
35² - 26² = b²
1225 - 676 = b²
b² = 549
b = √549
b = 23.4307490277
Therefore, the height of the building is 23.4 m.
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WILL GIVE BRAINS HELP ME OUT
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Answer:
First translation: Horizontal Translation
Second Translation: Reflection over horizontal line
Step-by-step explanation:
Reflection over a line creates a mirror image of the original image relative to the line
Horizontal translation shifts the image to the right or left only relative to the original position and along the x-axis only
Actually, first translation =reflection over horizontal line and second translation of horizontal translation will also result in the same.
Could any one help me figure out the last two parts? Thanks
Answers
Given the equation of a quadratic function:
[tex]f(x)=x^2-3x-28[/tex]First, we will find the x-intercepts to find the largest x-intercept
So, substitute f = 0, then solve for x as follows:
[tex]\begin{gathered} x^2-3x-28=0 \\ (x-7)(x+4)=0 \\ x-7=0\rightarrow x=7 \\ x+4=0\rightarrow x=-4 \end{gathered}[/tex]So, The largest x-intercept = 7
Second, we will find the y-coordinate of the y-intercept
So, substitute x = 0
[tex]f(x)=(0)^2-3(0)-28=-28[/tex]So, The y-coordinate of the y-intercept = -28
the difference between 9 thirty-seven and 8 thirty sevens
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100 is the difference between 9 thirty-seven and 8 thirty sevens.
Define subtraction.To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction. For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches. Wikipedia
Given Data
difference between 9 thirty-seven and 8 thirty sevens
Converting into numerical:
937 and 837
Subtraction:
937 - 837
100
100 is the difference between 9 thirty-seven and 8 thirty sevens.
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Lisa has 1/3 of a chocolate bar. Minah on the other hand, has 2/3 more. They both calorie wise equal 3020. How much calories do Lisa have? How much calories do Minah have?
Does this question make sense? If so, what's the answer?
HELP.
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Answer: lisa should have about 1006 cal minah should have 2014 cals thequestion has some spelling errors like "How much calories do Lisa have?" and "How much calories do Minah have?"
[tex]5 ( a - 5 ) 25[/tex]5 ( a - 5 ) 25
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The value of the variable a in the equation is a = 10
What is a linear equation?A linear equation is any equation with a constant rate
How to evaluate the equation?The equation is given as
5(a - 5) = 25
Open the brackets in the above equation
So, we have the following equation
5a - 5 * 5 = 25
Evaluate the products in the above equation
So, we have the following equation
5a - 25 = 25
Add 25 to both sides of the equation
So, we have the following equation
5a - 25 + 25 = 25 + 25
Evaluate the sum in the above equation
So, we have the following equation
5a = 50
Divide both sides by 5
So, we have
5a/5 = 50/5
Evaluate the quotient
a = 50/5
Evaluate the quotient
a = 10
Hence, the solution to the equation is a = 10
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Graph the solution set.-10x≤2y
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To be able to determine the graph of this inequality, we'll start rearranging the inequality putting the "y" variable at the left side of the equation.
[tex]\begin{gathered} -10x\leq2y \\ \frac{-10x}{2}\leq\frac{2y}{2} \\ -5x\leq y \\ or \\ y\ge-5x \end{gathered}[/tex]Since the inequality here is greater than or equal to, this means that the shade is above the solid line.
This equation also has a slope of -5 and y-intercept of 0.
Therefore, the graph of this equation looks like this:
what is the first step to solving 3.7x-15.9=2.79
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The first step to solving the expression:
[tex]3.7x\text{ - 15.9 = 2.79}[/tex]We need to transfer that term that doesn't have "x" from the left side to the right side. To do this we need to invert its signal as shown below:
[tex]3.7x=2.79+15.9[/tex]The second step is to sum the terms with similar letters or no letters at all.
[tex]3.7x\text{ = }18.69[/tex]The third step is to isolate the "x" variable by switching the constant that is multiplying it from the left side to the right side. To do that the constant needs to divide on the right.
[tex]\begin{gathered} x\text{ = }\frac{18.69}{3.7} \\ x\text{ = }5\text{.}05 \end{gathered}[/tex]10, 11, 12, 14, 12, 11, 13, 12, 14, 11 find the mean
Answers
Answer:
12
Step-by-step explanation:
Add all the numbers up. Then, you divided the answer by the number of values. So, its 120 divided by 10. which equals 12.
Directions: Solve each system of equations algebraically. Verify the solution using the graph of the system. 1. y=-x-4 y = 3x у I o X
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Directions: Solve each system of equations algebraically. Verify the solution using the graph of the system.
y=-x-4 (I)
y = 3x (II)
________________________
Using the substitution method
y = 3x
Substituting (II) in (I)
y=-x-4
3x =-x-4
3x +x = -4
4x= -4
x= -1
_____________________
Replacing in one of the equations
y = 3x
y= 3*-2
y= -3
___________
Verify the solution using the graph of the system
_____________________
Answer x= -1, y = -3
Victoria is purchasing a futonmattress for $223.80,including tax. She gives thesales clerk 2 fifty-dollar bills, 3twenty-dollar bills, and 13five-dollar bills. How muchshould she receive in change?T
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According to the given data we have the following:
Victoria is purchasing a futon mattress.
futon mattress price=$223.80
Victoria would pay the futon mattress with 2 fifty-dollar bills, 3 twenty-dollar bills, and 13 five-dollar bills.
So, 2 fifty-dollar bills would be=2*50=$100
Jill claims that for positive fractions a/b+a/c= a/b+c because the fractions have a common numerator. How do you respond?
Answers
Answer:
Jill is incorrect.
Step-by-step explanation:
To add fractions, you need a common denominator, not a common numerator, so Jill is incorrect and her sum of fractions is incorrect.
The correct addition is:
[tex] \dfrac{a}{b} + \dfrac{a}{c} = \dfrac{ac}{bc} + \dfrac{ab}{bc} = \dfrac{ac + ab}{bc} [/tex]
