What is the solution to this system of linear equations? 3x – 2y = 14 5x + y = 32
Answers
Answer:
work is shown and pictured
Answer:
Answer B. (6, 2)
Hope it works!
Step-by-step explanation:
Related Questions
Use Newton's method to estimate the requested solution of the equation. Start with given value of X0 and then give x2 as the estimated solution.
x3 + 5x +2 = 0; x0 = -1; Find the one real solution.
Answers
Answer:
-0.3913Step-by-step explanation:
Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;
[tex]y = f(x_0) + f'(x_0)(x-x_0)[/tex]
[tex]x_n = x_n_-_1 - \frac{f(x_n_-_1 )}{f'(x_n_-_1 )}[/tex]
If [tex]x_0 = 1\\[/tex]
We will iterate using the formula;
[tex]x_1 = x_0 - \frac{f(x_0 )}{f'(x_0 )}[/tex]
Given f(x) = x³ + 5x +2
f(x0) = f(-1) = (-1)³ + 5(-1) +2
f(-1) = -1 -5 +2
f(-1) = -4
f'(x) = 3x²+5
f'(-1) = 3(-1)²+5
f'(-1) = 8
[tex]x_1 = -1+4/8\\x_1 = -1+0.5\\x_1 = -0.5\\\\x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\\x_2 = -0.5 - \frac{f(-0.5)}{f'(-0.5)}[/tex]
f(-0.5) = (-0.5)³ + 5(-0.5) +2
f(-0.5) = -0.125-2.5+2
f(-0.5) = -0.625
f'(-0.5) = 3(-0.5)²+5
f'(-0.5) = 3(0.25)+5
f'(-0.5) = 0.75+5
f'(-0.5) = 5.75
[tex]x_2 = -0.5 - \frac{(-0.625)}{5.75}\\x_2 = -0.5 + \frac{(0.625)}{5.75}\\x_2 = -0.5 + 0.1086957\\x_2 = -0.3913[/tex]
The estimated solution is -0.3913 (to 4dp)
if 1/u=1/f-1/v is the formula Express f as the subject of the formula
Answers
Answer:
[tex]f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }\\[/tex]
Step-by-step explanation:
[tex]1/u=1/f-1/v\\\frac{1}{f} = \frac{1}{u} +\frac{1}{v}\\Divide- both- sides- by; 1\\\frac{1}{f} \div \frac{1}{1} = ( \frac{1}{u} +\frac{1}{v}) \div \frac{1}{1}\\\\f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }[/tex]
This expression gives the solutions to which quadratic equation?
Answers
Answer:
Hey there! Your answer would be: [tex]3x^2+4=x[/tex]
The quadratic formula is (-b±√(b²-4ac))/(2a), and helps us find roots to a quadratic equation.
All quadratic equations can be written in the [tex]ax^2+bx+c[/tex] form, and a, b, and c, are numbers we need for the quadratic equation.
Our given quadratic equation is 1±√(-1)²-4(3)(4)/2(3)
We can see that b is -1, as -b is positive 1.
That gives us [tex]ax^2+-1x+c[/tex], which can be simplified to [tex]ax^2-x+c[/tex].
We can see that a is 3, because 2a=6, so a has to be 3.
That gives us [tex]3x^2-x+c[/tex]
Finally, we see that 4 is equal to b, clearly shown in the numerator of this fraction.
Which gives us a final answer of [tex]3x^2-x+4[/tex], or [tex]3x^2+4=x[/tex]
Which is the dependent variable in 4x^2-5/6x-9=y if y=f(x)
Answers
Answer:
y
Step-by-step explanation:
The expression
y = f(x)
tells you that y is the dependent variable, and that it depends on x, the independent variable. The independent variable is always the function argument. Any variable that depends on that is the dependent variable.
On a piece of paper, graph y + 2 ≤ -2/3x +4. Then determine which answer choice matches the graph you drew.
Answers
Answer:
B
Step-by-step explanation:
You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).
The shading is below the line because y-values are less than (or equal to) values on the line.
Choice B matches the attached graph.
Answer:
it is graph b
Step-by-step explanation:
An inverse variation includes the point (-8,-19). Which point would also belong in this inverse variation? A. (-19,-8) B. (-8,19) C. (-19,8) D. (8,-19)
Answers
Answer:
(A) (-19,-8)
Step-by-step explanation:
Given that the graph is an inverse variation.
The equation of variation is:
[tex]x=\dfrac{k}{y}[/tex]
Since point (-8, -19) is on the graph
[tex]-8=\dfrac{k}{-19}\\k=152[/tex]
Therefore, the equation connecting x and y is:
[tex]x=\dfrac{152}{y}[/tex]
[tex]\text{When y=-8},x=\dfrac{152}{-8}=-19\\\\\text{When y=19},x=\dfrac{152}{19}=8\\\\\text{When y=8},x=\dfrac{152}{8}=19\\\\\text{When y=-19},x=\dfrac{152}{-19}=-8[/tex]
Therefore, the point that is also on the graph is:
(A) (-19,-8)
Identify a pair of vertical angles in the figure
A. Angle ADE and Angle ADB
B. Angle EDC and angle DBA
C. angle ADE and angle EDC
D. Angle ADE and angle BDC
Answers
Answer:
A pair of vertical angles are ADE and BDC. Vertical angles are located across from each other.
Answer:
D. Angle ADE and angle BDC
Step-by-step explanation:
Vertically opposite angles are equal.
Angle ADE and angle BDC are a pair of vertical angles.
3. Given the polynomial p(x) = x^4 - 2x^3 -7x^2 + 18x – 18 a. Without long division, find the remainder if P is divided by x+1. b. If one zero of P is 1-i, find the remaining zeros of P. c. Write P in factored form.
Answers
Answer:
(a) remainder is -40
(b) The remaining zeroes are (x+3) and (x-3)
Step-by-step explanation:
p(x) = x^4 - 2x^3 -7x^2 + 18x – 18
(a) Remainder of P(x) / (x+1) can be found using the remainder theorem, namely
let x + 1 = 0 => x = -1
remainder
= P(-1)
= (-1)^4 - 2(-1)^3 -7(-1)^2 + 18(-1) – 18
= 1 +2 -7-18-18
= -40
remainder is -40
(b)
If one zero is 1-i, then the conjugate 1+i is another zero.
in other words,
(x-1+i) and (x-1-i) are both factors.
whose product = (x^2-2x+2)
Divide p(x) by (x^2-2x+2) gives
p(x) by (x^2-2x+2)
= (x^4 - 2x^3 -7x^2 + 18x – 18) / (x^2-2x+2)
= x^2 -9
= (x+3) * (x-3)
The remaining zeroes are (x+3) and (x-3)
Find the 55th term of the following arithmetic sequence.
7, 10, 13, 16, ...
Answers
The 55th term of the 7, 10, 13, 16, ... arithmetic sequence is a(55) = 169.
This is an arithmetic sequence since there is a common difference between each term. In this case , adding 3 to the previous term in the sequence gives the next term.
a(n) = a(1) + d( n- 1)
d = 3
This is the formula of an arithmetic sequence.
an = a(1) + d( n- 1)
Substitute in the values of
a(1) = 7 and
d = 3
a(n) = 7 + 3 ( n- 1)
Simplify each term.
a(n) = 7 + 3n- 3
Subtract 3 from 7.
a(n) = 3n + 4
The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.
Substitute in the value of n to find the nth term.
a(55) = 3 (55) + 4
Multiply 3 by 55 .
a(55) = 165 + 4
Add 165 and 4.
a(55) = 169
Thus , The 55th term in the arithmetic progression of 7, 10, 13, 16,... is a(55) = 169.
To learn more about Aritmetic sequence
https://brainly.com/question/6561461
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what happens to the value of the expression n+15n as n decreases? answer
Answers
Answer:
The value will decrease.
Step-by-step explanation:
What is the y-intercept of the line given by the equation below? y = 4x – 6 A. (4, 0) B. (–6, 0) C. (0, –6) D. (0, 4)
Answers
Hey there! :)
Answer:
C. (0, -6).
Step-by-step explanation:
In slope-intercept form ( y = mx + b), the 'b' value represents the y-intercept.
In this instance:
y = 4x - 6
The 'b' value is equal to -6. This means that the y-intercept is at (0, -6).
-------------------------------------------------------------------------------------------
The y-intercept can also be solved for by substituting in 0 for x:
y = 4(0) - 6
y = 0 - 6
y = -6.
Answer:
C. (0, –6)
Step-by-step explanation:
y = 4x - 6
The equation is:
y = mx + b
where b is the y-intercept.
In this case, - 6 is the vertical intercept.
Do not confuse from (-6, 0) because that represents an x-intercept.
if 2 1/5 of a number is 5. what is the number
Answers
Answer:
2
Step-by-step explanation:
5÷2 1/5 = 2
Answer:
2 3/11
Step-by-step explanation:
To find the original number, we need to divide 5 by 2 1/5.
5/ 2 1/5
Convert 2 1/5 to an improper fraction:
11/5
5/ 11/5
When dividing fractions, we can multiply the first number by the reciprocal of the second one to get the answer.
5*5/11
25/11
2 3/11
Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1). g
Answers
Complete Question:
Find the directional derivative of g(x,y) = [tex]x^2y^5[/tex]at the point (1, 3) in the direction toward the point (3, 1)
Answer:
Directional derivative at point (1,3), [tex]D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]
Step-by-step explanation:
Get [tex]g'_x[/tex] and [tex]g'_y[/tex] at the point (1, 3)
g(x,y) = [tex]x^2y^5[/tex]
[tex]g'_x = 2xy^5\\g'_x|(1,3)= 2*1*3^5\\g'_x|(1,3) = 486[/tex]
[tex]g'_y = 5x^2y^4\\g'_y|(1,3)= 5*1^2* 3^4\\g'_y|(1,3)= 405[/tex]
Let P = (1, 3) and Q = (3, 1)
Find the unit vector of PQ,
[tex]u = \frac{\bar{PQ}}{|\bar{PQ}|} \\\bar{PQ} = (3-1, 1-3) = (2, -2)\\{|\bar{PQ}| = \sqrt{2^2 + (-2)^2}\\[/tex]
[tex]|\bar{PQ}| = \sqrt{8}[/tex]
The unit vector is therefore:
[tex]u = \frac{(2, -2)}{\sqrt{8} } \\u_1 = \frac{2}{\sqrt{8} } \\u_2 = \frac{-2}{\sqrt{8} }[/tex]
The directional derivative of g is given by the equation:
[tex]D_ug(1,3) = g'_x(1,3)u_1 + g'_y(1,3)u_2\\D_ug(1,3) = (486*\frac{2}{\sqrt{8} } ) + (405*\frac{-2}{\sqrt{8} } )\\D_ug(1,3) = (\frac{972}{\sqrt{8} } ) + (\frac{-810}{\sqrt{8} } )\\D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]
3. A tunnel is 300 feet deep and makes an angle of 30° with the ground, as shown below.
30°
300 feet
Tunne
How long is the tunnel?
Answers
Answer:
173.20 ft
Step-by-step explanation:
[tex] \tan \: 30 \degree = \frac{length \: of \: tunnel}{depth \: of \: tunnel} \\ \\ \frac{1}{ \sqrt{3} } = \frac{length \: of \: tunnel}{300} \\ \\ length \: of \: tunnel \\ \\ = \frac{300}{ \sqrt{3} } \\ \\ = \frac{300 \sqrt{3} }{3} \\ \\ = 100 \sqrt{3} \\ \\ = 100 \times 1.7320 \\ \\ = 173.20 \: ft[/tex]
Ms. Stone decided to purchase 2 reusable bottles instead. When she got to the counter, she realized she had $10.15, only ⅝ of the money she needed for the purchase. How much does 1 bottle cost?
Answers
Answer:
The price of one reusable bottle is $8.12
Step-by-steetp explanation:
Ms stone wanted to purchase two reusable bottles but discovered she had only ⅝of the Mone and that ⅝ is equal to $ 10.15.
So the cost of what she wants to purchase will be called x.
Mathematically
⅝ * x = 10.15
X = (10.15*8)/5
X = 81.2/5
X= 16.24
The price of the two bottles is $16.24
So the price if one bottle will be calculated as follows.
2 bottles=$ 16.24
One bottle= $16.24/2
One bottle= $8.12
The price of one reusable bottle is $8.12
please help me, i will give you brainliest
Answers
Answer:
4
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
JN* NK = LN * NM
3x = 2*6
3x = 12
Divide by 3
3x/3 =12/3
x =4
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 30 meters cubed A sphere with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? 10 meters cubed 20 meters cubed 30 meters cubed 40 meters cubed
Answers
Answer:
30 m^3
Step-by-step explanation:
Answer:
B. 20m3
Step-by-step explanation:
i dont know if its correct, hope it is tho
x=-4
Tell whether it’s graph is a horizontal or a vertical line
Answers
Answer:
Vertical Line
Step-by-step explanation:
A vertical line is x = [a number]
A horizontal line is y = [a number]
Answer:
vertical line
Step-by-step explanation:
A vertical line is of the form
x =
All the x values are the same and the y value changes
x = -4 is a vertical line
Simplify the algebraic expression: 7x2 + 6x – 9x – 6x2 + 15. A) x2 + 15x + 15 B) x2 – 3x + 15 C) 13x2 + 3x + 15 D) x4 – 3x + 15
Answers
Answer:
B) [tex]x^2-3x+15[/tex]
Step-by-step explanation:
[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]
A) [tex]x^2+15x+15[/tex]
B) [tex]x^2-3x+15[/tex]
C) [tex]13x^2 + 3x + 15[/tex]
D) [tex]x^4-3x + 15[/tex]
━━━━━━━☆☆━━━━━━━
▹ Answer
B. x² - 3x + 15
▹ Step-by-Step Explanation
7x² + 6x - 9x - 6x² + 15
Collect like terms
x² + 6x - 9x + 15
Subtract
x² - 3x + 15
Final Answer
x² - 3x + 15
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Hi, can someone help me on this. I'm stuck --
Answers
Answer:
a) Fx=-5N Fy=-5*sqrt(3) N b) Fx= 5*sqrt(3) N Fy=-5N
c) Fx=-5*sqrt(2) N Fy=-5*sqrt(2) N
Step-by-step explanation:
The arrow's F ( weight) component on axle x is Fx= F*sinA and on axle y is
Fy=F*cosA
a) The x component and y component both are opposite directed to axle x and axle y accordingly. So both components are negative.
So Fx = - 10*sin(30)= -5 N Fy= -10*cos(30)= -10*sqrt(3)/2= -5*sqrt (3) N
b) Now the x component is co directed to axle x , and y component is opposite directed to axle y.
So x component is positive and y components is negative
So Fx = 10*sin(60)= 5*sqrt(3) N Fy= -10*cos(60)= -10*1/2= -5 N
c)The x component and y component both are opposite directed to axle x and axle y accordingly. So both components are negative.
So Fx = - 10*sin(45)= -5*sqrt(2) N
Fy= -10*cos(45)= -10*sqrt(2)/2= -5*sqrt (2) N
Ann's $6,900 savings is in two accounts. One account earns 3% annual interest and the other earns 8%. Her total interest for the year is $342. How much does she have in each account?
Answers
Answer:
x=4200, y=2700
Step-by-step explanation:
let x be first account
y the second
x+y=6900
0.03x+0.08y=342
solve by addition/elimination)
multiply first equation by 0.03
0.03x+0.03y=207 subtract from second
0.03x+0.03y-0.03x-0.08y=207-342
0.05y=135
y=2700, x=4200
Q4. A simple random sample of size n=180 is obtained from a population whose size=20,000 and whose population proportion with a specified characteristic is p=0.45. Determine whether the sampling distribution has an approximate normal distribution. Show your work that supports your conclusions.
Answers
Answer:
np = 81 , nQ = 99
Step-by-step explanation:
Given:
X - B ( n = 180 , P = 0.45 )
Find:
Sampling distribution has an approximate normal distribution
Computation:
nP & nQ ≥ 5
np = n × p
np = 180 × 0.45
np = 81
nQ = n × (1-p)
nQ = 180 × ( 1 - 0.45 )
nQ = 99
[tex]Therefore, sampling\ distribution\ has\ an\ approximately\ normal\ distribution.[/tex]
If 8 Superscript y Baseline = 16 Superscript y + 2, what is the value of y? –8 –4 –2 –1
Answers
Answer:
-8
Step-by-step explanation:
8ʸ = 16ʸ⁺²
(2³)ʸ = (2⁴)ʸ⁺²
2³ʸ = 2⁴ʸ⁺⁸
3y = 4y + 8
y = -8
Answer:
A. -8
Step-by-step explanation:
edge 2021
What is the length of Line segment B C?
Answers
Answer:
given,
AB= 17
AC= 8
angle BCA =90°
as it is a Right angled triangle ,
taking reference angle BAC
we get,h=AB=17
b=AC=8
p=BC=?
now by the Pythagoras theorem we get,
p=
[tex] \sqrt{h { }^{2} - b {}^{2} } [/tex]
so,p=
[tex] \sqrt{17 {}^{2} - 8 {}^{2} } [/tex]
[tex] = \sqrt{225} [/tex]
=15 is the answer....
hope its wht u r searching for....
help one more for my friend lollllll well maybe 2 more
Answers
Answer:
8 : 1
Step-by-step explanation:
The graph shows a point at the location corresponding to 8 cups of raspberry juice and 1 cup of lemon-lime soda. So the ratio is ...
raspberry juice : lemon-lime soda = 8 : 1
Answer:
D
Step-by-step explanation:
raspberry : lemon lime soda::8:1
Find the cost to asphalt a circular racetrack if asphalt costs $90 per 100 f2. (Use 3.14 for it. Round to the nearest dollar.) r = 80 ft R = 145 ft
Small circle in a large circle
r= 80 ft
R=145 ft
Y
R
(Use 3.1 4 for a.)
Answers
Answer:
$41,330
Step-by-step explanation:
To find the cost to asphalt a circular path, first, calculate the area of the circular path:
Area of circular path = area of big circle (A1) - Area of small circle (A2)
Area of circle = πr²
Radius of big circle (R) = 145 ft
Area of big circle (A1) = 3.14*145²
= 3.14*21,025
A1 = 66,018.5 ft²
Radius of small circle (r) = 80ft
Area of small circle (A2) = 3.14*80²
= 3.14*6,400
A2 = 20,096 ft²
=>Area of path = 66,018.5 - 20,096 = 45,922.5 ft²
If 100ft = $90
45,922.5 ft = x
Cross multiply and find x (cost to asphalt the circular path)
100*x = 45,922.5*90
100x = 4,133,025
Divide both sides by 100
x = 4,133,025/100
x = $41,330.25
To the nearest dollar, $41,330 is needed to asphalt the circular path
help please & thank u love u
Answers
Because the ratio between x increase and y increase stay the same in a proportional graph and the line is straight
Find the volume of the solid generated by revolving the region enclosed by the triangle with vertices (1 comma 0 ), (3 comma 2 ), and (1 comma 2 )about the y-axis. Use the washer method to set up the integral that gives the volume of the solid.
Answers
Answer: Volume = [tex]\frac{20\pi }{3}[/tex]
Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be
V = [tex]\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx[/tex]
For this case, the region generated by the conditions proposed above is shown in the attachment.
Because it is revolting around the y-axis, the formula will be:
[tex]V=\pi \int\limits^a_b {(R(y))^{2} - (r(y))^{2}} \, dy[/tex]
Since it is given points, first find the function for points (3,2) and (1,0):
m = [tex]\frac{2-0}{3-1}[/tex] = 1
[tex]y-y_{0} = m(x-x_{0})[/tex]
y - 0 = 1(x-1)
y = x - 1
As it is rotating around y:
x = y + 1
This is R(y).
r(y) = 1, the lower limit of the region.
The volume will be calculated as:
[tex]V = \pi \int\limits^2_0 {[(y+1)^{2} - 1^{2}]} \, dy[/tex]
[tex]V = \pi \int\limits^2_0 {y^{2}+2y+1 - 1} \, dy[/tex]
[tex]V=\pi \int\limits^2_0 {y^{2}+2y} \, dy[/tex]
[tex]V=\pi(\frac{y^{3}}{3}+y^{2} )[/tex]
[tex]V=\pi (\frac{2^{3}}{3}+2^{2} - 0)[/tex]
[tex]V=\frac{20\pi }{3}[/tex]
The volume of the region bounded by the points is [tex]\frac{20\pi }{3}[/tex].
Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an answer does not exist, enter DNE.) f(x) = x4 − 8x3 + 7
Answers
Answer:
D
Step-by-step explanation:
units digit of the number[tex]2^{4000}[/tex]
Answers
Answer:
6
Step-by-step explanation:
We want to find the units digit of [tex]2^{4000}[/tex]. Let's first look for a pattern:
[tex]2^{1}=2[/tex]
[tex]2^{2}=4[/tex]
[tex]2^{3}=8[/tex]
[tex]2^{4}=16[/tex]
[tex]2^{5}=32[/tex]
[tex]2^{6}=64[/tex]
[tex]2^{7}=128[/tex]
[tex]2^{8}=256[/tex]
...and so on
Notice the units digits: 2, 4, 8, 6, 2, 4, 8, 6, ... It repeats every four!
This means that for every exponent of 2 that is a multiple of 4 (like 4000 in the problem), the units digit will always be the fourth number in the repeating pattern: 6.
The answer is thus 6.
~ an aesthetics lover