The given equation can be converted into a system of equations by setting each side of the given equation to equal zero separately. The system of equations will then be x² - x + 2 = 0 and x² + 3x + 1 = 0.
Explanation:The given equation, x²+3x+1=2x²+2x+3, can be set as a system of equations by getting each side of the equation to equal zero. Begin by subtracting the entire left-hand side of the equation from the right-hand side which gives us:
2x² + 2x + 3 - (x² + 3x + 1) = 0
This simplifies to x² - x + 2 = 0. That's your first equation.
Now, take the left-hand side of the original equation and set it equal to zero: x² + 3x + 1 = 0. That's your second equation. So the system of equations from the original equation are:
x² - x + 2 = 0 x² + 3x + 1 = 0Learn more about System of Equations here:
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A teacher took a survey and found that 16 of 25 students liked a certain snack item best. Make a prediction of how many students liked the snack item best if there are 225 students.
Zachary used the calculations shown to find how much he would spend on 16 ounces of pistachios. 6 ounces of pistachios cost $7.50 mc022-1.jpg Unit price = $0.80 per ounce mc022-2.jpg What was his first error? The price per ounce should have been $45.00 per ounce. The price per ounce should have been $1.25 per ounce. The final cost should have been $20.00. The final cost should have been $16.80.
15 POINTS I REALLY NEED HELP!!!!!!!!!!!!!!!!!!!!!The solution to 16x = 48 is x = ___. (Only input the number.) Numerical Answers Expected! Answer for Blank 1:
What is 40,630 written in scientific notation?
Answer:
4.063 x 10*4
Step-by-step explanation:
take the big number and move it from the exponent then bwa
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What is the area of a parallelogram that has a base of 6 cm and a height of 4 mm
When flying at an altitude of 5 miles, the lines of sight to the horizon looking north and south make about a 173.7 degree angle. how much of the longitude line directly under the plane is visible from 5 miles high?
Final answer:
The visible portion of the longitude line under the plane from an altitude of 5 miles is approximately 320.38 kilometers, using the formula D = 112.88 km √h where h is the altitude in kilometers.
Explanation:
The question asks how much of the longitude line directly under the plane is visible from an altitude of 5 miles high. To find this distance, we can use the formula given for horizon distance: D = 112.88 km √h, where h is the altitude in kilometers. Since 5 miles is approximately 8.05 kilometers, we can calculate the distance to the horizon by taking the square root of the altitude and multiplying by 112.88 kilometers.
First, calculate the square root of the altitude:
√8.05 ≈ 2.838.
Then, we multiply by the constant:
D ≈ 112.88 km × 2.838 ≈ 320.38 km.
Therefore, from an altitude of 5 miles, the visible portion of the longitude line directly under the plane is approximately 320.38 kilometers long.
Kim is a single woman in her mid-20s working while taking college credits to earn a bachelors degree. She is financing her education herself through both her income and taking out student loans. Her earnings in 2010 were $30,000 before taxes. She paid $5000 intuition and paid $350 interest on her student loan. In filing her state tax return form Kim takes a deduction for tuition paid and the interest paid on the loan. In taking these two deductions by how much did she lower taxable income? What is her taxable income now? What is her marginal tax rate? What will she owe in taxes for 2010?
he table below shows 10 data values: What values of minimum, Q1, median, Q3, and maximum should be used to make a box plot for this data? (1 point) 301 345 305 394 328 317 361 325 310 362 Minimum = 300, Q1 = 345, median = 330, Q3 = 317, maximum = 362 Minimum = 300, Q1 = 317, median = 330, Q3 = 345, maximum = 362 Minimum = 301, Q1 = 310, median = 326.5, Q3 = 361, maximum = 394 Minimum = 301, Q1 =361, median = 326.5, Q3 = 310, maximum = 394
Answer:
the third one its 100% verified
Step-by-step explanation:
What is the ratio of 5 gallons blue paint to 9 gallons of yellow paint?
How many ways can you choose 3 of of 7
please answer the question in the picture above
Hey can you please help me posted picture of question
PLZ HELP ASAP INSCRIBED QUADRILATERALS
Evaluate the expression 2x - (4y - 3) + 5xz, when x = -3, y = 2, and z = -1
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A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the orange.
a
By what percentage is the grapefruit heavier than the apple?
PLS answer this soon... before an hour at most.
Which algebraic expression represents “the bagels were divided equally into fifteen bags”?
15 + b
157b
Which algebraic expression represents “the bagels were divided equally into fifteen bags”?
a. 15 + b
b. 157b
c. 15/b
d. b/15
Answer:
Option D [tex]\frac{b}{15}[/tex]
Step-by-step explanation:
Let
b-----> the number of bagels
we know that
To find the algebraic expression of "the bagels were divided equally into fifteen bags" , divided the number of bagels by fifteen
so
[tex]\frac{b}{15}[/tex]
The sum of three numbers is 12. The sum of twice the first number, 5 times the second number, and 6 times the third number is 59. The difference between 8 times the first number and the second number is 23. Find the three numbers.
The question requires solving a system of linear equations which results from given conditions on three unknown numbers. The unknowns can be represented by the letters x, y, and z which need to be solved for by leveraging the knowledge of algebra.
Explanation:The question given is a classic example of a system of linear equations. Let's represent the first number as x, the second number as y, and the third number as z. From the question, we have the following equations:
[tex]x + y + z = 12 \\2x + 5y + 6z = 59 \\8x - y = 23[/tex]
Solving this system, we can find the values for x, y, and z which represent the three numbers. One of the methods for solving such a system is substitution or elimination method. Nevertheless, the solving such system requires a strong understanding of basic algebra including addition, subtraction, multiplication, and division of numbers and algebraic expressions.
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You have been asked to calculate the break-even point for a new line of souvenir t-shirts. the selling price will be $25 per shirt. the labor costs will be $5 per shirt. the administrative costs of operating the company are estimated to be $60,000 annually and the sales and marketing expenses are $20,000 a year. additionally, the cost of materials will be $10 per shirt. what is the break-even quantity?
In rotation, which point is moved the greatest?
Find the slope of the line.
Answer:
The slope of the line is [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
To know the slope of a line we can have the equation or to know points of the line. In this case from the graph we can get to points (-4,-1) and (0,-3). Having this and using the equation to calculate the slope, we have:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Defining:
[tex](x1=-4,y1=-1)[/tex] and [tex](x2=0,y2=-3)[/tex]
Replacing this values in the initial equation, this is:
[tex]m=\frac{-3-(-1)}{0-(-4)}[/tex]
[tex]m=\frac{-2}{4} =-\frac{1}{2}[/tex]
The slope of the line is [tex]-\frac{1}{2}[/tex]
Find a cartesian equation for the curve. r = 9 sin(θ)
If prices increase at a monthly rate of 0.5%, by what percentage do they increase in a year?
What is the formula to solve?
We have been given that prices increase at a monthly rate of 0.5%.
Number of months in a year = 12
Let us suppose the item cost $1, then the percentage is given by
[tex]P=P_0(1+r)^n\\ \\ P=1(1+0.005)^{12}\\ \\ P=1.062[/tex]\\
Therefore, increase in a year is
[tex]1.062-1\\ =0.062[/tex]
Therefore, the required percentage in a year is 6.2%
a weightlifter uses 45 pound plates and 10 pound plates to lift 260 pounds .let x represent the number of 45 pounf weights and y represents the number of 10 pound weights .
part 1 Rights an equation is standard form that represents the situation.
part 2. if the weightlifter uses eight 10 pound weights, how many 45 pound weights did he use???????
A standard form equation representing the weightlifting situation is 45x + 10y = 260. If eight 10-pound plates are used, the number of 45-pound plates used is 4.
Explanation:The situation given can be translated mathematically to an equation in standard form as follows: 45x + 10y = 260. This equation signifies that the total weight lifted (260 pounds) is equal to the sum of the weight of the 45
pound plates
(which each weighs 45 pounds multiplied by the number of plates, represented by x) and the 10 pound plates (which each weighs 10 pounds multiplied by the number of plates, represented by y). In the second part of the question, we're told that the weightlifter uses eight 10-pound weights, so y=8. Substituting y=8 into the equation from above, it simplifies to 45x + 80 = 260, which solves to x = 4. So, if the weightlifter uses eight 10 pound plates, then he uses four 45 pound plates.
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Which of the following comparisons is False
A..... 5.c is Warner than 5.F
B......15.c is cooler than 60.F
C........30.c is Warner than 90.F
D.......35.c is cooler than 100.F
Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6).
describe how you shaded bars to show data
1A. Nan and Soto are designing a coffee table using four inch tiles Nan uses 30 tiles and soto uses half as many how many total tiles did they use
1B. If the area of the table is 36 inches by 24 inches will they have enough towels to cover the table if not how many more will they need
2 different questions
But they are related
Nan and Soto used a total of 45 tiles. However, to cover a coffee table that has an area of 36 inches by 24 inches, they need 54 tiles, so they will need to acquire 9 more tiles.
1A. Nan uses 30 tiles and Soto uses half as many, which means Soto uses 15 tiles. So, they used a total of 45 tiles (30 + 15).1B. The area of the coffee table is 36 inches by 24 inches, which equals 864 square inches (36 x 24). Each tile is a four-inch square, so it covers an area of 16 square inches (4 x 4).
To find out how many tiles are needed, we divide the total area of the table by the area of one tile: 864/16 = 54 tiles. Since Nan and Soto have only 45 tiles, they need an additional 54 - 45 = 9 more tiles to cover the table.
Find the amount of annuity.
Amount of each deposit: $295
deposited: quarterly
Rate per year: 10%
Number of years: 6
Type of annuity: due
We need to find the future value of annuity due with the following given values :-
Payment, Pm = 295 dollars.
N=4 (for quarterly)
Rate at 10%, r = 0.10/4 = .025
Time for 6 years, T = 6x4 = 24.
Future Value formula is :-
[tex]FV_{ad}=P_m*(1+r)*[\frac{(1+r)^T-1}{r} ] \\\\ FV_{ad}=295*(1+0.025)*[\frac{(1+0.025)^{24}-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{(1.025)^{24}-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{(1.80872595)-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{0.80872595}{0.025} ] \\\\ FV_{ad}=295*(1.025)*(32.34903798) \\\\ FV_{ad}=9,781.54 \;dollars[/tex]
Hence, the final answer is 9,781.54 dollars.