Graph the equations to solve the system Y equals 1/3 X +6 and why equals 1/3 X +4
Answers
y = (1/3) x + 6
y = (1/3) x + 4
We note that both lines have the same slope in this case given by:
m = 1/3
Therefore, the lines are parallel. As they are parallel, they are not cut at any point.
Thus, the system of equations has no solution.
Answer:
The system has no solution (parallel lines)
Following the formula: y=mx+b,
where:
m= slope
b=y-intercept
As observed in the given equations, they have the same slope which is equal to 1/3 but each have different y-intercept which is 6 and 4.
Note that two lines are parallel if their slopes are equal and they have different y-intercepts.
Upon graphing, it had seen that the two functions are parallel.
See attached picture for the graph.
Related Questions
Use the intercept form to find the equation of the line with the given intercepts. the intercept form of the equation of a line with intercepts (a, 0) and (0,
b.is
Answers
b-0
m = -------- = -b/a
0-a
Then y-0 = (-b/a)(x-a), or y = (-b/a)(x-a) (answer)
peter put $8,000 into a savings account that pays 6% interest, compounded continuously. what will he have after 5 years?
Answers
[tex] Pe^{rt} [/tex]
P is Principal Amount
r is Rate
t is Time
P is 8000
r is 6%
t is 5
Therefore, you get $10,798.86.
Help me solve this please!
Answers
a) The calculator shows 5 solutions:
{5π/23, 5π/17, 25π/23, 25π/17, 45π/23}
These have approximate decimal values of
{0.6830, 0.9240, 3.4148, 4.6200, 6.1466}
b) The calculator shows 2 solutions with approximate decimal values of
{1.2925, 4.4341}
c) The calculator shows 2 solutions with approximate decimal values of
{1.3694, 4.9137}
_____
This (desmos) calculator displays intercepts to 3 decimal places. Since you want 4 decimal places, some additional refinement of the answer was necessary. That was accomplished using Newton's method iteration. The details are not shown. A suitable graphing calculator (for example, a TI-84) will supply the intercept coordinates to full calculator accuracy.
A local movie theater charges $12 for an adult ticket and $10 for a child's ticket. a group of eight people spent a total of $86 on tickets to a movie. how many adults and how many children were in the group? write a system of linear equations based on the description. use x to represent the number of adults and y to represent the number of children.
Answers
You can get this by setting up the following system of equations.
x + y = 8 (number of people)
10x + 12y = 86 (cost)
Which of these is equal to 50 + 21? 20 + 21 60 - 30 20 + 11 60 - 61
Answers
50 + 21 is equal to d. 11+ 60.
What is simplificarion?Simplification or simplifying fractions means simplifying a complicated mathematical expression to get a single or direct solution.
the value of 50 + 21 = 71 is option C.
a. 20 + 21
b. 60 - 30
c. 20 - 61
d. 11+ 60
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Final answer:
None of the provided options (20 + 21, 60 - 30, 20 + 11, 60 - 61) are equal to the sum of 50 + 21, which is 71. Each option computes to a different number, all of which are not equal to 71.
Explanation:
The question asks which of the given options is equal to the sum of 50 + 21. To solve this, we can compute each of the options to see which one equals 71, since 50 + 21 equals 71. Let's calculate:
20 + 21 = 41, which is not equal to 71.60 - 30 = 30, which is also not equal to 71.20 + 11 = 31, again not equal to 71.60 - 61 equals -1, which is not equal to 71.None of the provided options are equal to the sum of 50 + 21. The correct answer should be a number that when calculated results in 71, but none of these options do.
Express answer in exact form.
A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.
Answers
Please, see the attached file.
Thanks.
What are the foci of the hyperbola with equation 5y^2-4x^2=20?
Answers
divide each term by 20
(5y^2)/20-(4x^2)/20=20/20
simplifying gives us:
y^2/4-x^2/5=1
This follows the standard form of the hyperbola
(y-k)²/a²-(x-h)²/b²=1
thus
a=2, b=√5 , k=0, h=0
Next we find c, the distance from the center to a focus.
√(a²+b²)
=√(2²+(√5)²)
=√(4+5)
=√9
=3
the focus of the hyperbola is found using formula:
(h.h+k)
substituting our values we get:
(0,3)
The second focus of the hyperbola can be found by subtracting c from k
(h,k-c)
substituting our values we obtain:
(0,-3)
Thus we have two foci
(0,3) and (0,-3)
When he was 40 Keefer began investing $150 per month in various securities for his retirement savings. His investments averaged a 4.5% annual rate of return until he retired at age 70. What was the value of Keefer's retirement savings when he retired? Assume monthly compounding of interest.
Answers
Monthly saving, P = $150, Annual rate of return, R = 4.5% = 0.045.
Therefore, future value (FV) at the time of retirement will be;
FV = P*[1+(R/12)^12*30]/(R/12)
Substituting all the parameters;
FV = 150*[1+(1+0.045/12)^360]/(0.045/12) = $113.907.92
write an equation of an ellipse in standard form with the center at the origin and a height of 3 units and width of 1 unit
Answers
The equation of an ellipse with the specified attributes, using the center as the origin, is x2/0.25 + y2/2.25 = 1.
Explanation:The question asks for the equation of an ellipse with the center at the origin and a height of 3 units and width of 1 unit. In an ellipse, the center is the midpoint of both the major and minor axes. The major axis can be the horizontal (width) or vertical (height) axis, and the minor axis is the other one.
Given that the height of the ellipse is 3 units, this determines the major axis and its length of 2a=3, which means a=1.5. The width of the ellipse is 1 unit, this determines the minor axis and its length of 2b=1, which means b=0.5.
Using these values, the equation of such an ellipse, centered at the origin, in standard form is x2/0.25 + y2/2.25 = 1
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The equation of an ellipse in standard form with the center at the origin, a height of 3 units and width of 1 unit is [tex]\(4x^2 + (y^2/2.25) = 1\).[/tex]
Explanation:The equation of an ellipse in standard form with the center at the origin can be given by [tex]\(rac{{x^2}}{{a^2}} + rac{{y^2}}{{b^2}} = 1\)[/tex], where a is the semi-major axis and b is the semi-minor axis. Based on the information given in yourquestion, the height of the ellipse is 3 units which means the semi-major axis b is 1.5 units (since it's half the height). Similarly, the width of the ellipse is 1 unit which means the semi-minor axis a is 0.5 units (since its half the width). Substituting these values into the standard form of the ellipse we get: [tex]\(4x^2 + (y^2/2.25) = 1\)[/tex]
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on Sunday Mary pay $6 each on two tickets to a movie theater movies for $9.58 each Mary paid with 3 $20 bills how much changed
Answers
hjdjdjdjdbdhshssjdjdjdjdj
giving brainliest please help, and give steps if possible. Im trying to learn this.
Answers
(fg)(x) = (6-5x)(6x^2+x = 36x^2 + 6x - 30x^3 - 5x^2
and then you must combine like terms: (fg)(x) = -30x^3 + 31x^2 + 6x
Answer:
[tex]f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]
Step-by-step explanation:
[tex](fg)(x) \\ (fx) = 6 - 5x \\ g(x) = {6x}^{2} + x \\ substitute \: and \: calculate: \\ f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]
The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency
Answers
A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute. To the nearest tenth of an inch, what is the diameter of each car wheel? (Note: 1 mile = 5,280 feet)
Answers
Answer: 21.8 inches
Given:
A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute.
To get the diameter of each car wheel
Get first the length of revolution (circumference of the wheel) in inches.
Speed=50 miles/hr
=50miles/60 minutes
= 0.833333 miles/minute
=.833/5280=4400ft= 52,800 inches/minute
Since there are 770 revolutions per minute, per revolution (circumference of the wheel) =
=52,800/770
=68.57 inches
Formula of diameter given the circumference is:
D=C/π
D=68.57/3.14
D= 21.8 inches
Answer:
21.8
Step-by-step explanation:
just took test
What is the point-slope equation of the line with a slope 4/3 that goes through the point (-4,6)?
Answers
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})~\hspace{10em}slope = m\implies \cfrac{4}{3}\\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-6=\cfrac{4}{3}[x-(-4)]\implies y-6=\cfrac{4}{3}(x+4)[/tex]
Answer:
The point-slope form of the equation is y - 6 = 4/3(x + 4), which is answer B.
Step-by-step explanation:
In order to find the point-slope form of any equation, start with the base form of the equation.
y - y1 = m(x - x1)
Now input the slope given as m, and the point in for x1 and y1.
y - y1 = m(x - x1)
y - 6 = 4/3(x - -4)
y - 6 = 4/3(x + 4)
A gym has an inclined treadmill for joggers, as shown in the figure.
What is θ, the treadmill's angle of elevation?
Round your answer to the nearest degree.
Answers
in a right triangle
cos θ=adjacent side angle θ/hypotenuse
in this problem
adjacent side angle θ=38 in
hypotenuse=40 in
cos θ=38/40
θ=arc cos (38/40)-------> 18.19°-------> 18°
the answer is
18 degrees
What is the equation of a circle whose center is (4 6) and whose radius is 4 cm?
Answers
The h part in with the x is your x coordinate and the k part in with the y is your y coordinate. The r stands for the radius but be careful you have to square it.
so:
(x-(4))^2 +(y-(6)^2 = 16
I like to add the parenthesis around the "plugged in" numbers to help me remember negatives if I have any.
Simplify the square root of 864.
I cant remember this, please tell me how you got the answer.
Answers
[tex] \sqrt{864} [/tex]
[tex] \sqrt{4 \times 216} [/tex]
[tex] \sqrt{4 \times 4 \times 54} [/tex]
[tex] \sqrt{4 \times 4 \times 2 \times 27} [/tex]
[tex] \sqrt{4 \times 4 \times 2 \times 9 \times 3} [/tex]
now take out the pairs.
[tex]4 \sqrt{2 \times 9 \times 3} [/tex]
take out any of the square roots like 9
[tex]4 \times 3 \sqrt{2 \times 3} [/tex]
Now put it all back together.
[tex]12 \sqrt{6} [/tex]
I believe that is the answer.
What is the simplified form of sqrt 400x100? 200x50 200x10 20x50 20x50
Answers
√40,000 = 200
So your answer is 200 x 10.
Hope this Helps!!
Answer: The required simplified form is 20 × 10.
Step-by-step explanation: We are given to find the simplified form of the following radical expression :
[tex]E=\sqrt{400\times 100}.[/tex]
We will be using the following property of radicals :
[tex](i)~\sqrt{x}=x^\frac{1}{2}\\\\(ii)~\sqrt{a\times b}=\sqrt a\times\sqrt b.[/tex]
Therefore, we have
[tex]E\\\\=\sqrt{400\times 100}\\\\=\sqrt{400}\times\sqrt{100}\\\\=\sqrt{20^2}\times\sqrt{10^2}\\\\=((20)^2)^\frac{1}{2}\times(10^2)^\frac{1}{2}\\\\=20^{2\times\frac{1}{2}}\times(10)^{2\times\frac{1}{2}}\\\\=20\times10.[/tex]
Thus, the required simplified form is 20 × 10.
My brother owes me $10. I already have $10. My dads friend gave me and him $20 to split in half. He gave me the $20 and took my $10. Does he still owe me. Explain plz
Answers
your brother is supposed to give you $10
he gives you the money the friend told him to and you would have $20 PLUS the ten that he owes you. That would make you have $30. He took youre ten and gave you 20 but you were supposed to have 20 in the first place. He needs to give you the ten back he owes you.
The difference of a number and 8 is the same as 34 less the number. find the number.
Answers
8 - x = x -34
2x = 8 + 34
2x = 42
x = 21
Answer: The number is 21.
12x2 = 18x
i need someone to explain this
Answers
12x² = 18x------> 12x²-18x=0-----> divided by 12----> x²-(3/2)*x=0
this is the equation of a vertical parabola
x²-(3/2)*x=0-----> x*(x-1.5)=0
the x-intercepts of the parabola are
x=0
x=1.5
using a graph tool
see the attached figure
The angle of elevation to the top of a building in chicago is found to be 11◦ from the ground at a distance of 1000 feet from the base of the building. find the height of the building.
Answers
Ron and kathy are ticket sellers at their class play. ron handles student tickets that sell for $2.00 each, and kathy handles adult tickets that sell for $4.50 each. if their total income for 364 tickets was $1,175.50, how many tickets did ron sell?
Answers
You can get this by setting up a system of equations and solving by substitution.
x + y = 364 (number of tickets)
2x + 4.5y = 1175.50 (Cost)
for v=4i-8j, find unit vector u in the direction of v
a. u= 1/3i - 2/3j
b. i-j
c. sqrt3/3 i - 2 sqrt3/3 j
d. sqrt5/5 i - 2 sqrt5/5 j
Answers
u = v / lvl
The module of v is:
lvl = root ((4) ^ 2 + (-8) ^ 2)
lvl = root (16 + 64)
lvl = root (80)
lvl = 4 * root (5)
Substituting:
u = 4i-8j / (4 * root (5))
Rewriting:
u = i-2j / root (5)
u = root (5) / 5 i - 2 * root (5) / 5 j
Answer:
The unit vector in the direction of v is:
d. sqrt5 / 5 i - 2 sqrt5 / 5 j
PLEASE HELP 50 point will give brainlyest
Evaluate 81000−−−−√3 .
1/125
6/500
8/500
2/10
Answers
A recipe for fruit punch calls for cranberry juice and sparkling water. The ratio of cups of cranberry juice to cups of sparkling water is 6:24. According to the recipe, how many cups of cranberry juice are needed for every 1.5 cup of sparkling water? Write your answer as a fraction in simplest form.
Answers
6 / 24, or more fittingly, sparkling water / cranberry juice.
We can simplify the fraction to find an easy point of reference.
6 / 24 = 1 / 4
So if we're being asked for every one and a half cups, we'll get this fraction: 1.5 / 6.
It's about 6 cups of cranberry juice for every one and a half cups of sparkling water. Or was it the other way around? I only know the ratio, you figure out the rest.
Hope this helps!(i tried)
A shell fits into a golden rectangle with a length of 8 in. What is the shell's width? write your answer is simplified radical form and rounded to the nearest tenth of an inch.
Select one:
a. About 4.9 inches
b. About 4.1 inches
c. About 5.3 inches
Answers
l / w = (1 + root (5)) / 2
Where,
l: length of the rectangle
w: width of the rectangle
Clearing the width we have:
w = (2 / (1 + root (5))) * (l)
Substituting values:
w = (2 / (1 + root (5))) * (8)
Rewriting:
w = 4.94427191 inches
Rounding off we have:
w = 4.9 inches
Answer:
the shell's width is:
w = 4.9 inches
a. About 4.9 inches
The correct answer is option(a) about 4.9 inches.
To find the width of a golden rectangle with a given length, we will use the golden ratio formula that is
l / w = (1 + √5) / 2
Where, l = length of rectangle & w = width of rectangle
By applying the above formula we get the golden ratio, which is ≈ 1.618.
The formula for a golden rectangle is length(l) = 1.618 × width.
Given that length is 8 inches, we set up the equation:
8 = 1.618 × width
Solving for width:
width = 8 / 1.618 = 4.948...
The simplified radical form of 4.948... is ≈ 4.9 inches.
Thus, the correct answer is about 4.9 inches or option (a).
HELP!! PLEASE, 19 POINTS!! The equation (X squared + Y squared - 6x + 4y = d) describes a circle.
1. Determine the Y-coordinate of the center of the circle. (Hint.... Complete the square)
2. The radius of the circle is 6 units. What is the value of "d" in the given equation?
Answers
x²-6x+y²+4y=d
Group terms that contain the same variable
(x²-6x)+(y²+4y)=d
Complete the square twice. Remember to balance the equation by adding the same constants to each side
(x²-6x+9)+(y²+4y+4)=d+9+4
Rewrite as perfect squares
(x-3)²+(y+2)²=d+13the center of a circle is (3,-2)
the radius r²=d+13---------> 6²=d+13---------> d=36-13------> d=23
the answer is
the Y-coordinate of the center of the circle is -2
d is equal to 23
For this case we have the following equation:
x ^ 2 + y ^ 2 - 6x + 4y = d
By completing squares we have:
x ^ 2 + y ^ 2 - 6x + 4y + (-6/2) ^ 2 + (4/2) ^ 2 = d + (-6/2) ^ 2 + (4/2) ^ 2
Rewriting we have:
x ^ 2 + y ^ 2 - 6x + 4y + (-3) ^ 2 + (2) ^ 2 = d + (-3) ^ 2 + (2) ^ 2
x ^ 2 + y ^ 2 - 6x + 4y + 9 + 4 = d + 9 + 4
(x ^ 2 - 6x + 9) + (y ^ 2 + 4y + 4) = d + 13
(x-3) ^ 2 + (y + 2) ^ 2 = d + 13
Answer:
The y coordinate of the center of the circle is:
y = -2
Part 2:
For the value of d we have:
d + 13 = 6
d = 6 - 13
d = -7
Answer:
The value of d is:
d = -7
"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1% of examinees, what is the cutoff score on the test for admission?"
Answers
let the cutoff be x
but
P(x>0.01)=1-P(x<0.01)=1-0.01=0.99
the z value corresponding to 0.99% is z=2.33
thus
2.33=(x-600)/60
solving for x we get:
139.8=x-600
x=739.8
Before simplifying, how many terms are there in the expression -2x + 8 - 6y + 8x + 11?
Answers
Final answer:
The expression contains five terms before simplifying. We simplify by combining like terms to get a simplified result of 6x - 6y + 19 and then confirm the simplification by checking if the answer is reasonable.
Explanation:
The student has asked how many terms are in the expression -2x + 8 - 6y + 8x + 11 before simplifying. A term is a single mathematical expression that may consist of constants and/or variables, sometimes multiplied together but not added or subtracted to another term. In the given expression, there are a total of five terms: -2x, +8, -6y, +8x, and +11.
To simplify the algebra, we can combine like terms. Like terms are terms that contain the same variables to the same power. Here, -2x and +8x are like terms. When we combine them, we get 6x. The constants +8 and +11 are also like terms and can be added together to get +19. So, the simplified expression is 6x - 6y + 19.
Finally, we check our answer to ensure it is reasonable. Combining like terms -2x and +8x should result in +6x, and adding constants +8 and +11 should give us +19, which is our simplified result, confirming the reasonableness of our simplification.