How many solutions does this system of equations have?
y = -1/3x+7
y = -2x3 + 5x2 + x - 2
O A.
no solution
OB
1 solution
O C.
2 solutions
OD
3 solutions
Answer:
1 solution
Step-by-step explanation:
the two equations only cross once
The system of equations may have either 2 or 1 solution, but we cannot determine the exact number of solutions without further information or analysis.
We have,
The given system of equations consists of two equations in two variables:
y = (-1/3)x + 7 _______(1)
y = -2x³ + 5x² + x - 2 _______(2)
To find the solutions of the system, we need to find the values of x and y that satisfy both equations simultaneously.
Since both equations are in the form y = ...,
we can set the expressions on the right-hand sides of the equations equal to each other:
(-1/3)x + 7 = -2x³ + 5x² + x - 2
Rearranging and simplifying, we get:
2x³ - 5x² - (2/3)x + 9 = 0
To solve for x, we can use factoring or the rational root theorem.
However, the polynomial on the left-hand side of the equation does not appear to have any rational roots or easily factorable forms.
Therefore, to determine the number of solutions,
we can use Descartes' rule of signs to find the possible number of positive and negative roots of the polynomial:
The number of positive roots is either equal to the number of sign changes in the coefficients or less than it by an even integer.
There are two sign changes in the coefficients, so there can be either 2 or 0 positive roots.
The number of negative roots is either equal to the number of sign changes in the coefficients or less than it by an even integer.
There is one sign change in the coefficients, so there can be either 1 or 0 negative roots.
Since the sum of the possible number of positive and negative roots is either 2 or 1, the total number of solutions is either 2 or 1.
Therefore,
The system of equations may have either 2 or 1 solution, but we cannot determine the exact number of solutions without further information or analysis.
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Fourteen boys and 21 girls will be equally divided into groups. Find the greatest number of groups that can be created if no one is left out.
Answer:
7 groups can be made each with five people :)
Question 14(Multiple Choice Worth 5 points)
Find all polar coordinates of point P where P = negative pi divided by 6.
(1, negative pi divided by 6 + (2n + 1)π) or (-1, negative pi divided by 6 + 2nπ)
(1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ)
(1, negative pi divided by 6 + 2nπ) or (1, pi divided by 6 + (2n + 1)π)
(1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + (2n + 1)π)
Answer:
Find all polar coordinates of point P where P = (5 , -pi+%2F6 ).
There are two sets of possibilities.
(1) Same (positive) magnitude and an angle that is the same as the given angle, or differs from the given angle by an even multiple of pi:
P = (5, -pi%2F6%2B2n%2Api )
(2) Opposite (negative) magnitude and an angle that differs from the given angle by an odd multiple of pi:
(-5, -pi%2F6%2B%282n%2B1%29pi)
answer is: (5,-pi%2F6+%2B+2n%2Api) or (-5, -pi%2F6%2B%282n%2B1%29pi)
Answer:
negative pi divided by 6 + (2n + 1)π) or (-1, negative
A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 12t + 74, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?
The company earned 74 billion dollars from 2008 to 2018.
The company earned 12 billion dollars from 2008 to 2018.
The company earned 74 billion dollars in 2008.
The company earned 12 billion dollars in 2008.
Answer:
C) The company earned 74 billion dollars in 2008.
Answer:
C
Step-by-step explanation:
The person above me is correct give branliest
Nine million, twenty-seven thousand, four hundred and forty-eight
9,027,448
9027448
9027448
9027448
Express using exponents and simplify any numerical coefficients.
Answer:
2×2×y¹+¹+¹+¹
that is 4y⁴
marke as brainliest pls
I believe that the answer would be to count up the y's and the 2's. so in this case it would be 4 • 4y
Three measurements are made on each of three individuals in a random sample from a population. X 1 = 2, X2 = 8
and
1
1
187
X3 = 4. The distances d(X1, X2)between X1, X, and d(X2, X3) between X2, X3 respectively are (Use Euclidean inner
L5.
product)
Step-by-step explanation:
here is the answer hope it helps
Find the equation of the midline of the function y = 2 sin(1∕4x) – 3.
A) y = –3
B) y = 3
C) y = 2
D) y = 1∕4
Explanation:
The general sine equation is
y = A*sin(B(x-C)) + D
where the D variable directly determines the midline. In this case, D = -3, so that corresponds to a midline of y = -3
The sine curve oscillates going up and down, passing through this middle horizontal line infinitely many times. See the graph below.
Answer:
A) y = –3
Step-by-step explanation:I took the test
I need help really bad
Answer:
1 ???????
Step-by-step explanation:
The probability of A is 7/20, the probability of A intersection B is 49/400 what is the probability of B?
Answer:
n(A)+n(B)-49/400=n(AUB)
n(B)=1-7/20+49/400
n(B)=(400+49-140)/400
n(B)=309/400
2. About how much is 123.1 do you weigh in pounds? Estimate if you don't know☺ Find an online converter and find out how many kilograms that is.
Answer:
123.1 pounds is vary long, and I don't want to repeat, so 55.8372207 repeat.
Step-by-step explanation:
If you have any questions regarding my answer, tell me them in the comments, and I will come answer them for you. Have a good day.
evaluate the expression
Convert 413 in base 5 to base 10
Answer:
108
Step-by-step explanation:
4×5² + 1×5¹ + 3×5⁰
4×25 + 5+ 3×1
100+5+3
What is 40 % of 50?????????????????????????????????????/
Answer:
20
Step-by-step explanation:
Of means multiply
40% * 50
Change to decimal form
.40 * 50
20
Q12 A baker wants to order enough flour for 10 loaves of bread weighing 750g each. She has a recipe for a 500g loaf of bread which needs 480g of flour. How many kilograms of flour does the baker need? Show your working
Answer:
7.2kg of flour
Step-by-step explanation:
Total weight of bread = 10 x 750g
= 7500g = 7.5kg
500g of bread = 480g of flour
0.5kg of bread = 0.48kg of flour
7.5kg of bread = 7.2kg of flour
Reflect the given triangle over
the y-axis.
[3 6 3 ]
[-3 3 3]
Answer:
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}x_{1} &x_{2} &x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex] ---------> [tex]\left[\begin{array}{ccc}-x_{1} &-x_{2} &-x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-3&-6&-3\\-3&3&3\end{array}\right][/tex]
Pamela is 8 years older that Jiri. The sum of their age is 102. What is Jiri's age?
Answer:
Step-by-step explanation:
102-8= 94
94/2= 47
Jiri is 47 years old.
If the diameter of a hockey rink is 250 ft what is the surface area of the sphere?
Answer:
62,500 pi
Step-by-step explanation:
diameter = radius + radius
d = 2r
r = d/2
A = 4pi r^2
= 4 pi (d/2)^2
= 4pi d^2/4
= 4pi* 250^2/4
= 4pi * 62,500/4
= 4pi * 15625
= 62,500 pi
Please find the volume
Answer:
27/4 units^3
Step-by-step explanation:
V= area of the base × length
V= 3 3/8 × 2
= 27/4 units^3
Answer:
6 1/4 units ^3
Step-by-step explanation:
The volume is given by
V = Bh where B is the area of the base and h is the height
V = 3 3/8 *2
Changing to improper fractions
V = (8*3+3)/8 *2
= 27/8 *2
= 27 * 2/8
=27/4
Changing back to a mixed number
= 6 1/4
PLZ HELP ME AND IF U CAN XPLAIN
Answer:
B. 1/2
Step-by-step explanation:
Slope formula = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
[tex]\frac{(-4)-(-8) }{(6)-(-2)}[/tex]
[tex]\frac{4}{8}[/tex]
[tex]\frac{1}{2}[/tex]
Find the length of side
x
x in simplest radical form with a rational denominator.
Thanks In advance.
Answer:
Sorry I dont really understand wish I could help:(
Step-by-step explanation:
Answer:
[tex]\sqrt{10}[/tex]
[tex]\sqrt{5 } ^{2} + \sqrt{5 } ^{2} = x^{2}[/tex]
[tex]x^{2} =10[/tex]
Step-by-step explanation:
1. Look at the figure. Which construction is illustrated?
N
IR
H
a line perpendicular to
H3
through point N
a line parallel to
HU
through pointly
The construction illustrated in the figure is that of a line parallel to [tex]\overrightarrow{HJ}[/tex] through point N.
Given: Figure containing illustration of the construction
To find: The construction illustrated in the figure
It can be seen that the figure contains a straight line passing through H and J, a straight line passing through H and N, and a straight line passing through N which seems to be parallel to [tex]\overrightarrow{HJ}[/tex].
The figure also contains arcs made by a compass that measures the angle between [tex]\overrightarrow{HJ}[/tex] and [tex]\overrightarrow{HN}[/tex]. These arcs have been replicated at the point N on the straight line [tex]\overrightarrow{HN}[/tex].
This implies that the straight line through N has been constructed in such a way, so that the angle between that straight line and [tex]\overrightarrow{HN}[/tex] is equal to the angle between [tex]\overrightarrow{HJ}[/tex] and [tex]\overrightarrow{HN}[/tex]. This makes these angles, corresponding angles and [tex]\overrightarrow{HN}[/tex] as the transversal. Thus, the new straight line is constructed parallel to [tex]\overrightarrow{HJ}[/tex].
A strong counterargument that this illustration is not that of a line perpendicular to [tex]\overrightarrow{HJ}[/tex] through point N is that the figure does not contain any straight line perpendicular to [tex]\overrightarrow{HJ}[/tex].
Thus, the construction illustrated in the figure is that of a line parallel to [tex]\overrightarrow{HJ}[/tex] through the point N.
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- Olivia skates twice as far as Stephanie. This sum of their distances is 96 miles per month. How many
miles per month does Olivia skate?
A.32 miles
B.64 miles
C.48 miles
D.24 miles
Answer:
B.64 miles
Step-by-step explanation:
Let Oliver's be x
Let Stephanie's be y
[tex]x = 2y - - - (a) \\ x + y = 96 - - - (b)[/tex]
substitute for x in (b):
[tex]2y + y = 96 \\ 3y = 96 \\ y = 32[/tex]
find x in (a):
[tex]x = (2 \times 32) \\ x = 64[/tex]
Ellen makes $20 per hour in her job as a kiental assistant. She works 8 hours per day and 40 hours per week. How much does Ellen make in a day before taxes?
Ellen makes $20 per hour in her job as a kiental assistant. She works 8 hours per day and 40 hours per week. How much does Ellen make in a day before taxes?
Answer:-Money earned by Ellen per hour = $20.
Number of hours she works per day = 8 hours.
Money she'll make per day = 20×8 = 160
Hence, the answer is $160.
83. For what value of K will the points (1, 4), (-3, 16) and (k, -2) lie on one straight line.
Answer:
I don't know
Step-by-step explanation:
I don't know
Answer:
k = 3
Step-by-step explanation:
If the points lie on the same line then the slope between the points will be equal.
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (- 3, 16)
m = [tex]\frac{16-4}{-3-1}[/tex] = [tex]\frac{12}{-4}[/tex] = - 3
Repeat the process and equate to - 3
with (x₁, y₁ ) = (1,4) and (x₂, y₂ ) = (k, - 2)
m = [tex]\frac{-2-4}{k-1}[/tex] = [tex]\frac{-6}{k-1}[/tex] , then
[tex]\frac{-6}{k-1}[/tex] = - 3 ( multiply both sides by k - 1 )
- 6 = - 3(k - 1) ← divide both sides by - 3
2 = k - 1 ( add 1 to both sides )
3 = k
A computer parts company wants to make a rectangular memory board that has a perimeter of 14 cm and a diagonal of length 5 cm. What are the dimensions of the board?
Answer:
A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.: Call the two sides L & W: the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution
Step-by-step explanation:
==========================================================
Explanation:
x = width
y = length
both x and y are positive real numbers, and the units of which are in cm.
The perimeter of any rectangle is found by saying
P = 2*(length+width)
P = 2*(x+y)
Plugging in P = 14 leads us to
P = 2*(x+y)
14 = 2*(x+y)
14/2 = x+y
7 = x+y
Solve for one of the variables. Let's say we solve for y. That should get us y = 7-x which we'll use a bit later.
--------------
Notice how the diagonal forms two identical right triangles. The legs of which are x and y as defined earlier. The hypotenuse is 5, which is the diagonal length.
Use the pythagorean theorem to help solve for x
a^2 + b^2 = c^2
x^2 + y^2 = 5^2
x^2 + (7-x)^2 = 25 ... plug in y = 7-x
x^2 + 49 - 14x + x^2 = 25 ... use FOIL rule
2x^2-14x+49 = 25
2x^2-14x+49-25 = 0
2x^2-14x+24 = 0
2(x^2-7x+12) = 0
x^2-7x+12 = 0
(x-3)(x-4) = 0
x-3 = 0 or x-4 = 0
x = 3 or x = 4
If x = 3, then y = 7-x = 7-3 = 4
If x = 4, then y = 7-x = 7-4 = 3
We have this symmetry going on. If x is one of 3 or 4, then y is the other of those values. Because x = 3 and y = 4, or vice versa, this means we have a 3-4-5 right triangle (well to be fair we have two identical copies of such a triangle to form the rectangle).
Therefore, the dimensions of the rectangular board is 3 cm by 4 cm. The order doesn't matter so you could easily say "4 cm by 3 cm" to mean the same thing.
--------------
Check:
P = perimeter
P = 2*(length+width)
P = 2*(x+y)
P = 2*(3+4)
P = 2*7
P = 14
That helps confirm the answer.
What is the value of x in |6| = x?
Answer:
6
Step-by-step explanation:
the | | are for absolute value, which means
|-6|=|6|= 6
mr. jones has a patio in the sahpe of a trapezoid. a round fountain having a circumference of 14 pi linear feet is placed in the corner as showin in the accompanying diagram. to the nearest square foot, how much of the patio s area ins not taken up by the fountanin? reall tha the circumferencie of a circle is calculated using c = 2
The area of the patio not taken up by the fountain is 241ft²
Please find attached an image of the patio
Area of the patio not taken up by the fountain = area of patio - area of fountain
The patio is in a shape of a trapezoid. Thus, the area of the patio can be determined by using the formula for the area of a trapezoid
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Characteristics of a trapezoid
It has 4 vertices It has 4 edges If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogramArea of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height
Taking a look at the image, we are not provided with the height of the trapezoid, just the parallel sides and the hypotenuse.
Pythagoras theorem can be used to determine the the height of the trapezoid
The Pythagoras theorem : a² + b² = c²
where a = height
b = base = 20 ft - 12 ft = 8ft
8ft / 2 = 4
c = hypotenuse
a² + 4² = 25²
a² = 625 - 16
a² = 609
√609 = 24.68 ft
Area of the trapezoid = 0.5 x (20 + 12) x 24.68 = 394.88 ft²
The fountain is in the shape of a circle.
Area of a circle = πr²
Where : = π = pi = 22/7
R = radius
The radius would have to determined from the circumference
circumference of a circle = 2πr
14π = 2πr
r = 14π / 2π
r = 7
Area of the circle = [tex]\frac{22}{7}[/tex] × 7²
[tex]\frac{22}{7}[/tex] × 49 = 154 ft²
Area of the patio not taken up by the fountain = 394.88 ft² - 154 ft² = 240.88ft²
To round off to the nearest square, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.
The tenth digit is greater than 5, so one is added to 0. The number becomes 241ft²
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Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB, find the location of point B.
The required coordinates of point B are (-3, 7) where point M is the midpoint of AB.
What is Midpoint?A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.
Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB
We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AB.
Let the coordinates of B would be (x, y)
Substituting the coordinates of points A into the midpoint formula gives us :
-1 = (x+1)/2 ; 6 = (y+5)/2
-2 = x +1 ; 12 = y + 5
x = -3; y = 7
Therefore, the required coordinates of point B are (-3, 7).
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The cost of producing pens with the company logo printed on them consists of a onetime setup fee of $265.00 plus $0.95 for each pen produced. This cost can be calculated using the formula C=265.00+0.95p, where p represents the number of pens produced and C is the cost. Use the formula to calculate the cost of producing 2900 pens.
