y\(y = {2x}^{2} + 6 - 10 \\ y = - x + 5\)find the solution to the system of equations
Answers
1) Solving the system of equations:
y=2x²+6-10 ⇒ y =2x² -4
y=-x+5 x (-1)
1.2 Rewriting it and Subtracting
y =2x²- 4
-y =+x-5
----------------------
0=2x²+x -9
2) Now solving that quadratic equation 2x²+x -9=0, using the Resolutive formula:
\(\begin{gathered} \Delta=b^2-4ac \\ \Delta=(1)^{2}-4(2)(-9) \\ \Delta=1+72 \\ \Delta=73 \end{gathered}\)\(\begin{gathered} x=\frac{-b\pm\sqrt[]{\Delta}}{2a} \\ x=\frac{-1\pm\sqrt[]{73}}{4} \\ x_1=\frac{-1-\sqrt[]{73}}{4} \\ x_2=\frac{-1+\sqrt[]{73}}{4} \end{gathered}\)3) Now plugging in back into the II equation y=-x+5
\(\begin{gathered} y=-(\frac{-1-\sqrt[]{73}}{4})+5 \\ y=\frac{1+\sqrt[]{73}}{4}+5 \\ y=\frac{21+\sqrt[]{73}}{4} \end{gathered}\)3.1Plugging the x solutions into y=2x²-4
\(\begin{gathered} y=2(\frac{-1-\sqrt[]{73}}{4})^2-4 \\ y=\frac{21+\sqrt[]{73}}{4} \\ y=2(\frac{-1+\sqrt[]{73}}{4})^2-4\text{ =}\frac{21-\sqrt[]{73}}{4} \end{gathered}\)After checking in both of the original equations, there is only one valid x solution.
So the solution to that system is
\(x=\frac{-1-\sqrt[]{73}}{4}\text{ and }y=\frac{21+\sqrt[]{73}}{4}\)Related Questions
Kon'nichiwa, everyone! just to make sure you are correct if you answer this question make sure you have a explaination, and a good one with that.
ex; you took the test and have proof you took it.
ex; explaining how you got your answer
also if you happen to need this "⎯⎯" you can just copy paste that and put it in the answer
that's all, thanks for reading this :D
Answers
Answer:
Hey there i see that you are doing scientific notation things well i will help you
Step-by-step explanation:
so 5.2 X 10 to the 5th power = 520000
3.9 X 10 to the 8th power = 390000000
and 4.7 X 10 to the 5th power = 470000
so on that info the answer is
4.7 x 10(5), 5.2 x 10(5), 3.9 x 10(8)
hope you have a nice day
Answer and work is all shown in the provided screenshot! I hope this helps! :)
Company B calculates the earnings of an employee, E, for working h hours using the equation E = 8.25h
Answers
The earning οf an emplοyee is 8.25 dοllars per hοur and hοurly pay rate is 8.25 dοllars.
What is pay rate?Pay rate refers tο the amοunt οf mοney an emplοyer pays an emplοyee fοr their wοrk, typically expressed as an hοurly, weekly, οr mοnthly rate. It is the rate at which an emplοyee is cοmpensated fοr their time and labοr, and can be influenced by a number οf factοrs, such as jοb skills, experience, industry, lοcatiοn, and market demand fοr the particular rοle. The pay rate may alsο be subject tο deductiοns fοr taxes, insurance, and οther benefits prοvided by the emplοyer.
Here,
The hοurly pay rate οf the emplοyee can be calculated by dividing the earnings by the number οf hοurs wοrked. Using the given equatiοn, we can rewrite it as E = 8.25h
Dividing bοth sides by h,
E/h = 8.25
Therefοre, the hοurly pay rate οf the emplοyee is 8.25 dοllars per hοur.
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Which equation calculates the number of 1/8 foot pieces you can cut from 5 feet of ribbon
Answers
Answer:
40
Step-by-step explanation:
The number ribbons cut from the 5 feet long one is 40 ribbons, the equation is n = 5÷1/8
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x - 5 = 16 is an equation.
Given that, a ribbon of 5 feet long ribbon is cut into n 1/8-foot-long ribbons, we need to determine the equation calculates the number of 1/8 foot pieces,
So, the equation =
n = 5÷1/8
n = 40
Hence the number ribbons cut from the 5 feet long one is 40 ribbons, the equation is n = 5÷1/8
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what percentage of 60 is 21
Answers
The solution goes thus:
\(\begin{gathered} =\frac{21}{60}\text{ x 100 } \\ =\frac{2100}{60} \\ =\frac{210}{6}=\text{ 35\%} \end{gathered}\)Hence , 35% of 60 is 21
Please see my question in the attachment, thanks
Answers
As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.
In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;
As x → -1⁻, f(x) → ∞.
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Student Enrollment
The enrollment at a local college has been decreasing linearly. In 2004, there where 975 students enrolled. By
2009, there were only 730 students enrolled. Determine the average rate of change of the school's enrollment
during this time period, and write a sentence explaining its meaning.
The average rate of change=
The enrollment at the college has been [Select an answer at a rate of
Select an answer v
Answers
The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.
To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:
Average rate of change = (Change in enrollment) / (Change in time)
The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.
Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:
Change in enrollment = 730 - 975 = -245 students
The change in time can be calculated as:
Change in time = 2009 - 2004 = 5 years
Now we can calculate the average rate of change:
Average rate of change = (-245 students) / (5 years) = -49 students per year
Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.
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Solve the problem:
Kiram has 5 ziploc bags. He puts an equal number of marbles (X). Then he realized that he
needed to add 2 more marbles for each bag. If the total number of marbles is 30 how many
marbles in each bag?
Answers
Answer:
Step-by-step explanation:
ohfpifpijpijsfpjspijpsijfpsjfpsjfpisjfpijsfpsijf
how many numbers lie between 101 the square and 102 the square
Answers
Answer:
203
Step-by-step explanation:
Square of 101 = 101^2= 10201
Square of 102 = 102 ^2=10404
No. of numbers between both of them =10404-10201=203
Answer:
203
Step-by-step explanation:
✓101 kare = 10.201
✓102 kare = 10.404
✓ 10.404- 10.201 = 203
#Başarılar
#Türkiye
The peaches are priced at three for $2. How much does one dozen cost? Write an equivalent ratio to find the answer. Show your work.
Answers
Answer:
12:8
Step-by-step explanation:
3:2
12:x
12÷3=4
2×4=8
12:8
Calcular los 3/5 de los 2/3 de las 3/4 de 560
Answers
For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.
How to solve fractions?To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:
Step 1: Calculate 3/4 of 560:
3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420
Step 2: Calculate 2/3 of the result from Step 1:
2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280
Step 3: Calculate 3/5 of the result from Step 2:
3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168
Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.
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50 POINTS and BRAINLIEST-- A pattern of shaded and unshaded squares is shown below:
Answers
Answer:
The number of shaded squares changes by 2 in each figure
Therer will be 90 squares shaded in the 50th figure
Step-by-step explanation:
Brainliest PLS
Answer:
1. I'm not exactly sure but I would say that you add two to every square.
2. 90
Step-by-step explanation:
To find the first answer, you just add and count the squares.
To find the second answer, you just add two to every square, up to 50 squares.
A student is given the triangle attached. The student claims that sin(20°)=x/5in. Explain why this reasoning is incorrect.
Answers
The reasoning of the student is wrong because the claim doesn't abide by the sine rule and formula.
What is a sine rule and formula?The sine rule states that in a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.
That is;
a/sinA= b/sinB = c/sinC
Therefore, the proper equation to find X = 5/sin98° = X/sin20°
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-3z-z I need help pleeeaaassseee
Answers
Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$300/week for 9 1/2
years at 5.5%/year compounded weekly
Answers
Answer: $227,226.51
Step-by-step explanation:
First, we need to convert the period to weeks.
9 1/2 years = 9.5 years
1 year = 52 weeks
9.5 years = 494 weeks
Next, we can use the formula for the future value of an annuity:
FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)
where:
PMT = payment amount per period
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values:
PMT = $300
r = 0.055 (5.5% expressed as a decimal)
n = 52 (compounded weekly)
t = 9.5 years = 494 weeks
FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)
FV = $227,226.51
Therefore, the future value of the annuity is approximately $227,226.51.
Can I please get some help I’ve been stuck on this question for a while!
Answers
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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T
Radius i den store sirkelen er r.
Vis at summen av arealet til de fire hvite feltene kan skrives A = r²(2 – 2 ).
Løs oppgaven her.
Answers
Thank you :)
\(\pink{ \rule{1pt}{90000000pt}}\color{blue}{ \rule{1pt}{90000000pt}}\color{yellow}{ \rule{1pt}{90000000pt}}\purple{ \rule{1pt}{90000000pt}} \green{\rule{1pt}{90000000pt}}
\)
I need Help please!!!
Answers
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
Please help me with this
Answers
Answer:
Option 2 Andrew and Jason rode bikes to the park after Andrew finished his morning chores
Please help me with both I’ll mark your answer brainly
Answers
Answer: i can say the first one is teenagers watch more movies than parents but have one causle equal movie subject (documationy)
Step-by-step explanation: sorry if this did't help
Solve 20% of blank = 40
Answers
Answer: 200
Step-by-step explanation:
Let the unknown number be x.
Therefore, 20%*x = 40
20% as a fraction is 1/5.
Therefore x*(1/5) = 40
Multiply both sides by 5:
x = 200
Drag each inequality to the column which is labeled with its solution.
( look at photo for reference )
Answers
Drag the solution of each inequality as shown below:
3(x - 5) + x < 13 : x<7
2(x + 8) > 4x + 2 : x<7
3x + 2(x - 8) > x : x > 4
2(x + 6) < 3x + 8 : x > 4
How to solve the inequalities?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4
3(x - 5) + x < 13
3x -15 + x < 13
4x -15 < 13
4x < 13 + 15
4x < 28
x < 28/4
x < 7
2(x + 8) > 4x + 2
2x + 16 > 4x + 2
2x - 4x > 2 - 16
-2x > -14
x < -14/(-2) (Note: Sign will change if you divide with negative numbers)
x < 7
3x + 2(x - 8) > x
3x + 2x -16 > x
5x - 16 > x
5x - x > 16
4x > 16
x > 16/4
x > 4
2(x + 6) < 3x + 8
2x + 12 < 3x + 8
2x - 3x < 8 - 12
-1x < -4
x > -4/(-1)
x > 4
Therefore, drag the solution of each inequality accordingly.
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In the diagram figure PMNO is the image of figure ABCD
What is the name of the image of AD?
○ MP
○ PO
○ DA
○ ON
Answers
The name of the figure illustrated in the image of AD is Side B. PO.
How to illustrate the diagram?From the diagram in the question, Figure ABCD is the Image of PMNO, that is each vertex is a corresponding pair of the other image. This implies that P with AM with BN with CO with D
The same can be applied to the sides in the two images ABCD correspond with PMNO, also each corresponding side will be AD to PO. In this case, AB to PMBC to MNDC to ON.
Therefore, the image of side AD must be PO.
In conclusion, the correct option is B.
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Solve w=1/2x^2y for x
Answers
Answer : x= \(\sqrt{2wy}\)/ y
Step-by-step explanation:
Which of the following is the correct graph of the linear equation below?
y+3 = -(x-4)
=-
PRII
A.
5 -4 -3
-2.1
2
3
4
-1
-2
+-3
-4
T'
Answers
A triangle has an area of 36 cm². The base and height are scaled by a factor of 5.
What is the area of the resulting triangle?
Enter your answer in the box.
Answers
Answer:
900
Step-by-step explanation:
The area of the final triangle would be 900 cm².
What is scale factor?Scale factor is used to compare the final and initial dimensions of the figure. Mathematically, we can write scale factor -
{K} = {final dimensions/initial dimensions}
Given is that a triangle has an area of 36 cm². The base and height are scaled by a factor of 5.
Assume the initial dimensions of the triangle be {x} and {y} respectively. So, we can write the initial area as -
{1/2}{x}{y} = 36
{x}{y} = 72
After the scaling, we can write the final area as -
A = {1/2}{5x}{5y}
A = {25/2}{x}{y}
A = 12.5 x 72
A = 900 cm²
Therefore, the area of the final triangle would be 900 cm².
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evaluate 7 - (-19) - 18 + (-19) + 18
Answers
= 26 - 18 + (-19) + 18
= 8 + (-19) + 18
= - 11 + 18
= 7
Remember:
• follow BEDMAS or PEDMAS
• always go from left to right
• 2 negatives = positive
• 2 positives = negative
• negative and a positive = negative (and vice versa)
Select the equivalent expression (7^2 x 5^6)^4
Answers
Answer:
x (12 y + 4)
good luck
Ammonia is a compound consisting of a 1:3 ratio of nitrogen and hydrogen atoms. If a sample contains 1983 hydrogen
atoms, how many total atoms are present?
Answers
Answer:
2644 atoms
Step-by-step explanation:
1983/3 = 661
1983 + 661 = 2644 atoms
Answer:
2644 total N and H atoms
Step-by-step explanation:
N/H is 1/3
N/H = 1/3
N/(1983) = 1/3
N = (1983/3)
N = 661 N atoms
1983 + 661 = 2644 total N and H atoms.
Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 100 subjects has a distribution that agrees with the distribution of state populations.
Answers
Answer:
Step-by-step explanation:
H₀ : The distribution of the sample agrees with the population distribution.
H₁ : the distribution of the does not agree with the population distribution.
Using the Chi-square test statistics
we will compute the expected frequencies
Now expected frequency for Washington will be
Fe = Npi = 1000×51% = 5100
expected frequency for Oregon
Fe = Npi = 1000×30% = 300
expected frequency for Idaho
Fe = Npi = 1000×11% = 110
expected frequency for Montana
Fe = Npi = 1000×8% = 80
The Chi=square test statistics is;
x² = ∑ [ (Fo - Fe)² / Fe )
now we substitute
Given our Fo ( 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana) from the question
x² = (450-510)²/510 + (340-300)²/300 + (150-110)²/110 + (60-80)²/80
x²= 31.9376
so the chi-square test statistics is 31.9376
Now the chi-square critical value
first we compute for degree of freedom
d.f = k -1 = 4 - 1 = 3
So from the critical value table, degree of freedom 3 and significance level 0.05,
the chi-square critical value is 7.8147
Therefore chi-square test statistics 31.9376 is greater than the chi-square critical value 7.8147, so NULL HYPOTHESIS IS REJECTED at 5% significance.
There is sufficient evidence to warrant rejection of the claim that the distribution of the sample agrees with the distribution of the state populations.
Chicago, Illinois has an elevation of 600 feet. Seely, California is -200 feet. What does 0 represent in the context of this situation?
Answers
Answer:
Sea level
Step-by-step explanation:
In geography, 'Elevation' is measured in relation to sea level, so sea level would be zero.
Thus, Chicago is 600 feet above sea level and Seely, California is 200 feet below sea level.
If there were nothing but flat land all the way from Seely to the ocean, sea water would come in and cover Seely. Fortunately for the people in Seely. California's coastal mountain range is between the town and the ocean, so that does not happen.
Answer:
It represents the "SEA LEVEL"