Solve the following system of equations for x to the nearest hundredth : y + 2x + 1 = 0; 4y - 4x ^ 2 - 12x = - 7
Answers
Answer:
We can start by solving the first equation for y:
y + 2x + 1 = 0y = -2x - 1We can then substitute this expression for y into the second equation:
4y - 4x^2 - 12x = -74(-2x - 1) - 4x^2 - 12x = -7-8x - 4 - 4x^2 - 12x = -7-4x^2 - 20x + 3 = 0We can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2awhere a = -4, b = -20, and c = 3.
x = (-(-20) ± sqrt((-20)^2 - 4(-4)(3))) / 2(-4)x = (20 ± sqrt(400 + 48)) / (-8)x = (20 ± sqrt(448)) / (-8)x = (20 ± 4sqrt(7)) / (-8)x ≈ -0.85 or x ≈ -2.93Verification:To verify these solutions, we can substitute them back into the original equations:
For x ≈ -0.85:
y + 2x + 1 = 0y + 2(-0.85) + 1 = 0y ≈ 0.74y - 4x^2 - 12x = -74(0.7) - 4(-0.85)^2 - 12(-0.85) = -7-2.8 - 2.89 + 10.2 = -7This checks out, so x ≈ -0.85 is a valid solution.
For x ≈ -2.93:y + 2x + 1 = 0y + 2(-2.93) + 1 = 0y ≈ 4.864y - 4x^2 - 12x = -74(4.86) - 4(-2.93)^2 - 12(-2.93) = -719.44 - 33.45 + 35.16 = -7.85This does not check out, so x ≈ -2.93 is not a valid solution.
Therefore, the only solution to the system of equations to the nearest hundredth is x ≈ -0.85, and the corresponding value of y is y ≈ 0.7.
We can start by isolating y in the first equation:
y + 2x + 1 = 0
y = -2x - 1
Then, we can substitute this expression for y into the second equation:
4y - 4x^2 - 12x = -7
4(-2x - 1) - 4x^2 - 12x = -7
-8x - 4 - 4x^2 - 12x = -7
-4x^2 - 20x - 3 = 0
We can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = -4, b = -20, and c = -3. Substituting these values, we get:
x = (-(-20) ± sqrt((-20)^2 - 4(-4)(-3))) / 2(-4)
x = (20 ± sqrt(400 - 48)) / (-8)
x = (20 ± sqrt(352)) / (-8)
x = (20 ± 18.78) / (-8)
So the solutions are:
x ≈ -0.11 or x ≈ -4.39
Therefore, the system of equations has two solutions for x: x ≈ -0.11 and x ≈ -4.39 (rounded to the nearest hundredth).
Related Questions
North Dakota has 465 campgrounds over 12 counties while West Virginia has 711 campgrounds. If North Dakota was proportional to West Virginia in the number of campgrounds to counties, how many counties would West Virginia be expected to have? Round to the nearest whole number.
Answers
Number of countries would west Virginia be expected to have is 18 countries
The number of campgrounds that North Dakota has = 465 campgrounds
The number of countries = 12 countries
The number of campgrounds that West Virginia has = 711 campgrounds
Given that the North Dakota was proportional to West Virginia in the number of campgrounds to counties.
The proportion will be
465 / 12 = 711 / x
Divide the terms
38.75 = 711 / x
x = 711 / 38.75
Divide the terms
x = 18.4
x ≈ 18 countries
Hence, number of countries would west Virginia be expected to have is 18 countries
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Find the value of x. Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
9. sin 18 = x/21
x = 21* sin 18
x = 6.5
10. tan 55 = 29/x
x* tan 55 = 29
x = 29/tan 55
x = 20.3
11. sin 23 = x/25
x = 25 * sin 23
x = 9.8
12. sin 47 = 33/x
x * sin 47 = 33
x = 33/sin 47
x = 45.1
please fast if could
Answers
Answer:9/41
SOH = opposite over hypotenuse
Step-by-step explanation:
please help me..thx!
Answers
Answer:
x=25
Step-by-step explanation:
X=180-125-30
x=25
given vector u equals open angled bracket negative 10 comma negative 3 close angled bracket and vector v equals open angled bracket 4 comma 8 close angled bracket comma what is projvu? open angled bracket negative 640 over 109 comma negative 192 over 169 close angled bracket open angled bracket negative 256 over 109 comma negative 512 over 109 close angled bracket open angled bracket negative 8 comma negative 3 close angled bracket open angled bracket negative 16 over 5 comma negative 32 over 5 close angled bracket
Answers
The correct answer is open angled bracket negative 16 over 5 comma negative 32 over 5 close angled bracket, as it is the vector u.
The projection of vector u onto vector v is given by the formula:
projv(u) = (u . v/||v||^2) * v
where u . v is the dot product of vectors u and v,and ||v|| is the magnitude of vector v
Given that u = <-10, -3> and v = <4, 8>, we can substitute these values into the formula and find projv(u)
projv(u) = ( (-10)(4) + (-3)(8) )/ (4^2 + 8^2) * <4,8>
projv(u) = ((-40 - 24)/ (16 + 64))* <4,8>
projv(u) = (-64/80) * <4,8>
projv(u) = (-4/5) * <4,8>
projv(u) = <-16/5,-32/5>
The vector u is already parallel to the vector v, that's why the projection of vector u on vector v is equal to vector u itself.
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Sonya carried all the books weighing 2 1\4 pounds and 2 3/8 pounds to the library. How many pounds of books did Sonya carry?
Answers
Pluto has been hard to measure from Earth because of its atmosphere. In 2007 Young, Young, and Buie measured Pluto as having a diameter of 2322 km. In 2017 new measurements were taken and Pluto is now believed to be 2376.6 km in diameter. Since the older measurement is now considered incorrect, what was the percent error of the 2007 measurement? [enter your answer as a percentage without the % sign] Round to two decimals.
Answers
Answer:
The percent error of the 2007 measurement is 2.30
Step-by-step explanation:
To determine the percent error of the 2007 measurement,
Percent error is given by
Percent error = \(\frac{|True value - Observed value| }{True value} \times 100%\)%
Observed measurement in 2007 = 2322 km
True value (observed in 2017) = 2376.6 km
∴ Percent error = \(\frac{|2376.6 - 2322| }{2376.6} \times 100%\)%
Percent error = \(\frac{54.6 }{2376.6} \times 100%\)%
Percent error = 0.022974 × 100%
Percent error = 2.2974%
Percent error ≅ 2.30%
Since the answer is required to be entered without the % sign, then
Percent error = 2.30
Hence, the percent error of the 2007 measurement is 2.30.
how many ft is equal to 1.66m
Answers
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
explain why the statement x < 3 or > 5 cannot be written 5 < x < 3
Answers
Answer:
This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.
Step-by-step explanation:
x < 3 or x > 5
This means, x is less than 3, but greater than 5.
Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.
Which equation applies the associative property of multiplication?
Responses
(−14−53)−35=−14−(53−35)
, open parenthesis fraction negative 1 over 4 end fraction minus fraction 5 over 3 end fraction close parenthesis minus fraction 3 over 5 end fraction equals fraction negative 1 over 4 end fraction minus open parenthesis fraction 5 over 3 end fraction minus fraction 3 over 5 end fraction close parenthesis,
−512⋅(65⋅13)⋅92=(−512⋅65)⋅(13⋅92)
, fraction negative 5 over 12 end fraction times open parenthesis fraction 6 over 5 end fraction times fraction 1 over 3 end fraction close parenthesis times fraction 9 over 2 end fraction equals open parenthesis fraction negative 5 over 12 end fraction times fraction 6 over 5 end fraction close parenthesis times open parenthesis fraction 1 over 3 end fraction times fraction 9 over 2 end fraction close parenthesis,
−67⋅811⋅13=811⋅(−67)⋅13
, fraction negative 6 over 7 end fraction times fraction 8 over 11 end fraction times fraction 1 over 3 end fraction equals fraction 8 over 11 end fraction times open parenthesis fraction negative 6 over 7 end fraction close parenthesis times fraction 1 over 3 end fraction,
(−78⋅25)+(−78⋅35)=−78⋅(25+35)
Answers
The equation applies the associative property of multiplication is −512⋅(65⋅13)⋅92=(−512⋅65)⋅(13⋅92).
What is associative property of multiplication?The associative property of multiplication can be described as the law that is been used in making calculation that involves using the multiplication operation.
When using the associative property of multiplication law, we will need to associate, which means we will join together the given terms which can be done in different ways irrespective of how it is been grouped together and this can be seen in the option B , because the result of the multiplication using the distributive property gives us (−512⋅65)⋅(13⋅92).
Therefore, option B is correct.
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If you bought something in Texas for $52.00, you would be charged $3.25 in state sales tax. What is the state sales tax rate in Texas? Round your answer to the nearest hundredth of a percent
Answers
Answer:6.25%
Step-by-step explanation:
3.25 / 52 = 0.0625
A certain forest covers an area of 2100 km^2. Suppose that each year this area decreases by 5.25%. What will the area be after 6 years
Answers
Answer:
The area after 6 years is \(1519.49km^2\)
Step-by-step explanation:
Given
\(a = 2100\) --- Initial Value
\(r = 5.25\%\) --- Rate
Required
Determine the area after 6 years
Because the area reduces,, the following formula will be used to solve the question.
\(y = a*(1 - r)^t\)
Here
\(t = 6\)
So, we have:
\(y = 2100*(1 - 5.25\%)^6\)
Convert percentage to decimal
\(y = 2100*(1 - 0.0525)^6\)
\(y = 2100*(0.9475)^6\)
\(y = 1519.47866516\)
\(y = 1519.49\) -- approximated
The area after 6 years is \(1519.49km^2\)
Given that 4x – 5y = 12 Find y when x = -3 Give your answer as an improper fraction in its simplest form.
Answers
Step-by-step explanation:
4(-3)-5y=12
-12-5y=12
-5y=12+12
-y= 24/5
y= -24/5
y= -4⅕
hope it helps
Help me out please please
Answers
Answer:
490000
Step-by-step explanation:
Substituting \(x=40\),
\(I=-425(40)^2 + 45500(40) - 650000=490000\)
using d= rt, find r if d= 350 miles and t= 5 hours
Answers
Answer:
70 miles /hour = r
Step-by-step explanation:
d=rt
Substitute d=350 miles and t = 5 hours
350 miles = r* 5 hours
Divide each side by 5 hours
350 miles = 5 hours = r
70 miles /hour = r
Eniki has a sequence of numbers given by the formula t (n) = 4(5^n). a. What are the first three terms of Eniki's sequence? Hint (a):
b. Chelita thinks the number 312.500 is a term in Eniki's sequence. Is she correct? Justify your answer by either giving the term number or explaining why it is not in the sequence. Hint (b):
c. Elisa thinks the number 94.500 is a term in Eniki's sequence. Is she correct? Explain. Hint (c):
Answers
a) The first three terms of Eniki's sequence are 20, 100, and 500.
b) The number 312,500 is the 7th term in Eniki's sequence.
c) The number 94,500 is not a term in Eniki's sequence since it does not correspond to any whole number value of 'n'.
The term 'n' in the formula represents the position of the number in the sequence, starting from the first term.
Enoki's also has a sequence of numbers, which is given by the formula (n) = 4(5ⁿ). Let's break down this formula to understand what it means.
a. To find the first three terms of Eniki's sequence, we substitute the values 1, 2, and 3 for 'n' in the formula. This gives us:
n = 1: 4(5¹) = 20
n = 2: 4(5²) = 100
n = 3: 4(5³) = 500
Therefore, the first three terms of Eniki's s sequence are 20, 100, and 500.
b. Chelita thinks that the number 312,500 is a term in Eniki's sequence. To determine whether she is correct or not, we need to find the value of 'n' that corresponds to this number. We can rearrange the formula to solve for 'n' as follows:
n = log base 5 (312,500/4)
Using a calculator, we find that n is approximately equal to 7. Therefore, the number 312,500 is the 7th term in Eniki's sequence.
c. Elisa thinks that the number 94,500 is a term in Eniki's sequence. To verify this, we can once again solve for 'n' in the formula:
n = log base 5 (94,500/4)
Using a calculator, we find that n is approximately equal to 6. Therefore, the number 94,500 is not a term in Eniki's sequence since it does not correspond to any whole number value of 'n'.
In summary, Eniki's sequence is defined by the formula
=> f(n) = 4(5ⁿ),
where 'n' represents the position of the number in the sequence.
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Please help i had this for three days and still cannot figure it out im slow heh
Answers
The radius is the segment from the circle’s center to the end of the circle. So, you’re looking for a segment which goes halfway across the circle. This would be segment FE.
Hope this helps! :)
A football team has attempted 6 running plays. The change in field position resulting from each play is shown in the table. Running Play Outcomes Play 1 –3 yards Play 2 2 yards Play 3 –1 yard Play 4 –2 yards Play 5 –3 yards Play 6 1 yard What is the average change in field position per running play? –6 yards per play –1 yard per play 0 yards per play 1 yard per play Mark this and return
Answers
Answer:
Step-by-step explanation:
-3 +2 +-1 +-2 +-3 +1 = -6 yards total
-6 / 6 = -1 yard per play average
The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range of the transformed function is the same as the parent function, but the domains of the functions are different. The domain of the transformed function is the same as the parent function, but the ranges of the functions are differe
Answers
Both the domain and range of the transformed function are the same as those of the parent function.
What are Range and Domain?
The collection of all potential output values that a function can generate given its domain is known as its range.
The set of all potential input values for which a function is specified is referred to as its domain.
The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.
Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.
A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.
Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.
A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well
So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.
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Anna’s average running speed is 3 times faster than her walking speed. Since time=distancerate, the time it takes Anna to run 16km is 163x and the time it takes Anna to walk 16km is 16x. Find the difference between Anna’s walking time and running time for 16km.
Answers
The velocity or speed is the ratio of distance and time thus the difference between Anna’s walking time and running time for 16km is 32/(3x).
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
Average velocity = total distance / total time taken
Units of velocity are given by ⇒ meter/second
Let's say Anna's walking speed is x.
Given that, Anna’s average running speed is 3 times faster than her running speed is 3x
Since,time = distance/speed
The walking time = 16/x
Running time = 16/3x
Difference = 16/x - 16/3x
⇒ (1-1/3)16/x
⇒ (2/3)(16/x)
⇒ 32/(3x).
Hence "The velocity or speed is the ratio of distance and time thus the difference between Anna’s walking time and running time for 16km is 32/(3x)".
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Emilia and Joshua shared some money in the ratio 1:6.
Emilia received £15.
How much did Joshua receive?
Answers
Answer:
15x6
Step-by-step explanation:
do 15x6 and what that is, is the answer
HELP 10 MIN LEFT!!!!
Answers
Answer:
To one decimal place,
y = 16.3 m
Step-by-step explanation:
Using SOHCAHTOA,
In this case we need to use CAH,
WE know the angle = 25 and the hypotenuse H = 18,
so,
y = adjacent
\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)
Answer: 16.3 in.
Step-by-step explanation:
use SOH CAH TOA
cos x = adj/hyp
cos 25 = y/18
18 cos 25 = y
y= 16.3
which is greater? no links pls. 0.04 or -0.39? and -0.6 or 0.5?
Answers
Answer:
0.04 and 0.5
Step-by-step explanation:
Answer:
1. 0.04
2. 0.5
Step-by-step explanation:
The positive choice will be greater.
a quadratic function is defined by f(x) = x*2 - 8x - 4.
Which expression also defines f and best reveals the max and mini of the function?
a) (x-4)*2 - 20
B) (x-4)*2 + 12
c) x(x-8) -4
d) (x-4)*2 + 20
Answers
The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4 is (x - 4)^2 - 20.\) Option A
How to find the expressionThe vertex form of a quadratic function is given by\(f(x) = a(x - h)^2 + k\) where (h, k) represents the coordinates of the vertex.
In the given quadratic function \(f(x) = x^2 - 8x - 4\), we can rewrite it in the vertex form by completing the square:
\(f(x) = (x - 4)^2 - 16 - 4\\f(x) = (x - 4)^2 - 20\)
From this expression, we can see that the vertex of the quadratic function is at the point (4, -20).
The term\((x - 4)^2\) tells us that the vertex is at x = 4, and the constant term -20 indicates the y-coordinate of the vertex.
The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4\) is \((x - 4)^2 - 20.\)
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You dive 21 feet from the surface of a lake in 7 seconds. What is the mean change in your position in feet per second?
Answers
Answer:
Unit rate: 21feet / 7seconds = 3 feet per second.
3 feet per second * 5 seconds = 15 feet
21 feet + 15 feet =36 feet
You are 36 feet from the surface.
Step-by-step explanation:
I need help please with this activity is
F(x)=(x+2)^2-1
Answers
Answer: (4,35); (3,24); (2,15); (1,8)
Step-by-step explanation:
Emily volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go.
On Saturday, 416 people went to The Youth Wing, 448 people went to Social Issues, and 341 went to Fiction and Literature. On Sunday, the library had 500 total visitors.
Based on what Emily had recorded on Saturday, about how many people should be expected to go to Social Issues? Round your answer to the nearest whole number.
Answers
We may predict that, when rοunded tο the clοsest whοle number, 185 persοns οught tο be present at Sοcial Prοblems οn Sunday.
What in mathematics is a whοle number?Detailed numbers the set οf integers that cοntains zerο and the natural numbers. nοt a decimal and fractiοn. Integer 0 thrοugh 2, 3, 4, 5, 6, 7, 8, 9, 10, and sο οn. a cοunting number, a negative number, οr zerο.
The library saw a sum οf 416 + 448 + 341 = 1205 visitοrs οn Saturday. By dividing the entire number οf visitοrs by the number οf visitοrs whο visited Sοcial Prοblems, and then multiplying the result by 100% tο represent the results as a percentage, we can determine what percentage οf these visitοrs visited Sοcial Issues:
Percentage οf visitοrs whο went tο Sοcial Issues = (448 ÷ 1205) x 100%
Percentage οf visitοrs whο went tο Sοcial Issues ≈ 37.18%
We may assume that a similar percentage οf Saturday's visitοrs will return οn Sunday in οrder tο estimate the number οf persοns whο can be expected tο attend Sοcial Prοblems οn that day. Tο determine hοw many peοple will visit Sοcial Prοblems οn Sunday, we can utilize the prοpοrtiοn mentiοned abοve:
Estimated number οf visitοrs tο Sοcial Issues οn Sunday = (37.18% οf 500 visitοrs)
Estimated number οf visitοrs tο Sοcial Issues οn Sunday ≈ 185
We may calculate that, if we rοund tο the next whοle number, 185 persοns shοuld be anticipated tο attend Sοcial Prοblems οn Sunday.
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4a + 3a Please solve I will give brainliest to first answer!
Answers
Answer:
7a
Step-by-step explanation:
Find the volume of the cone. Use 3.14 for π. Remember that there is a formula for calculating the volume of a cone.
Answers
The volume of the cone is 314cm³
What is volume of a cone?A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.
The volume of the cone is 1/3πr²h
h²= 13²-5²
h = √169 - 25
h = √144
h = 12 cm
V = 1/3πr²h
V = 1/3 ×3.14 × 5² × 12
V = 942/3
V = 314 cm³
therefore the volume of the cone is 314cm³
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Find the value of x when 5 - x = 12x + 4
Answers
Answer:
5-4=12x+x
1=13x
1/13=×