The argument using the components of the non zero vectors which are not parallel are as follow, sa1 + tb1 = c1
sa2 + tb2 = c2
sa3 + tb3 = c3
Geometric argument,
a and b are nonzero vectors that are not parallel.
A plane in three-dimensional space.
Any vector in this plane can be written as a linear combination of a and b.
Let c be any vector in this plane.
Construct a parallelogram with sides a and b, and the diagonal of the parallelogram passing through the point c.
This diagonal is the vector c written as a linear combination of a and b, say c = sa + tb for some scalars s and t.
Diagonal of a parallelogram bisects and is bisected by its opposite sides.
c lies on the line passing through the midpoints of a and b.
c can be expressed as a linear combination of a and b.
Argument using components,
a and b are nonzero vectors that are not parallel, they are linearly independent.
Any vector in the plane determined by a and b can be expressed as a linear combination of a and b.
Let c = (c1, c2, c3) be any vector in this plane.
Now, c as c = sa + tb, where s and t are scalars to be determined.
Writing a and b in terms of their components, we have,
a = (a1, a2, a3) and b = (b1, b2, b3)
Then, we can write c as,
c = (s a1 + t b1, s a2 + t b2, s a3 + t b3)
Values of s and t such that c has the components (c1, c2, c3).
Equating the components of c with those of (c1, c2, c3), to get the system of equations,
sa1 + tb1 = c1
sa2 + tb2 = c2
sa3 + tb3 = c3
Therefore, solution of the argument of non zero vectors solved using standard techniques such as Gaussian elimination or Cramer's rule.
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The above question is incomplete, I answer the question in general according to my knowledge:
Suppose that a and b are nonzero vectors that are not parallel and c is any vector in the plane determined by a and b. Give a geometric argument to show that c can be written as c=sa +tb for suitable scalars s and t. Then give an argument using components.
A store purchased a stylus for $22.00 and sold it to a customer for 20% more than the purchase price. The customer was charged a 6% tax when the stylus was sold. What was the customer’s total cost for the stylus?
Answer: $27.98
Step-by-step explanation:
22.00 × .2= 4.40
22 + 4.40 = 26.40
26.40 × .06 = 1.584
26.40 + 1.584 = 27.984
Round to the nearest hundred so the total paid by the customer would be 27.98
Part A
Use GeoGebra to graph points A, B, and C to the locations shown by the ordered pairs in the table. Then join each pair of
points using the segment tool. Record the length of each side and the measure of each angle for the resulting triangle.
Location
A(3,4), B(1,1).
C(5.1)
A(4.5), B(2.1).
C(7.3)
—————-
AB=
BC=
AC=
Answer:
Step-by-step explanation:
Answer:
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]
Step-by-step explanation:
Step 1Place points A, B and C on the coordinate grid.
Alternatively, type the following into the input field as 3 separate inputs:
Triangle 1
A = (3, 4)B = (1, 1)C = (5, 1)Triangle 2
A = (4, 5)B = (2, 1)C = (7, 3)Step 2Use the Segment tool to join each pair of points.
Alternatively, type Segment( <Point>, <Point> ) into the input field (replacing <Point> with the letter name of the point) to create a segment between two points.
Record the length of each side.
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]
Step 3Use the Angle tool to measure each angle in the resulting triangle.
Alternatively, type Angle(Polygon(A, B, C)) into the input field to create all interior angles.
Record the measure of each angle.
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]
Note: All measurements have been given to the nearest hundredth (2 decimal places).
In △ △ ABC, CJ = 18. If CG = BG, what is KJ? Triangle A B C is divided by 4 segments. A H is the height. C J extends from C to side A B. B I extends from B to side A C. H I extends from the height on B C to I on A C. C J and B I intersect at point K. A J and B J are congruent. A I and C I are congruent.
Solving for CI in terms of the given lengths, we get: [tex]Cl=\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }[/tex]
Substituting this expression for CI and the given value for CG into the expression for BI, we get: [tex]BI=CG-\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }[/tex].
What is triangle?A triangle is a three-sided polygon, which is a closed two-dimensional shape with straight sides. In a triangle, the three sides connect three vertices, or corners, and the angles formed by these sides are called the interior angles of the triangle. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified by their side lengths and angle measurements. For example, an equilateral triangle has three sides of equal length, and all of its angles are 60 degrees; an isosceles triangle has two sides of equal length, and its base angles are also equal; a scalene triangle has three sides of different lengths, and all of its angles are also different. Triangles are a fundamental shape in mathematics and geometry, and they have numerous applications in fields such as architecture, engineering, physics, and more.
Given by the question.
Based on the given information, we can start by drawing a diagram of triangle ABC and the segments AH, BJ, CI, CJ, and BI as described.
Since CG = BG, we can draw the perpendicular bisector of side AC passing through point G, which will intersect side AB at its midpoint M.
Now, we can see that triangle CGB is isosceles with CG = BG, so the perpendicular bisector of side CB also passes through point G. This means that G is the circumcenter of triangle ABC, and therefore, the distance from G to any vertex of the triangle is equal to the radius of the circumcircle.
Next, we can use the fact that AJ and BJ are congruent to draw the altitude from point J to side AB, which we will call JN. Similarly, we can draw the altitude from point I to side BC, which we will call IM.
Since AJ and BJ are congruent, the altitude JN will also be the perpendicular bisector of side AB, so it will pass through point M. Similarly, the altitude IM will pass through point G, which is the circumcenter of triangle ABC.
Now, we can use the Pythagorean theorem to find the lengths of JN and IM in terms of the given lengths:
[tex]JN^{2}= AJ^{2} -AN^{2} \\ = ( AH+HN)^{2} - AN^{2} \\=AH^{2} +2AH*HN+HN^{2}-AN^{2} \\[/tex]
[tex]IM^{2}= CI^{2} -CM^{2} \\=( CG-GM)^{2} -CM^{2} \\CG^{2}-2CG*GM+GM^{2} -CM^{2}[/tex]
Since CG = BG and GM = BM (since M is the midpoint of AB), we can simplify the expression for IM^2 as follows:
[tex]IM^{2}[/tex] = [tex]BG^{2}[/tex] - 2BG * BM + [tex]BM^{2}[/tex] - [tex]CM^{2}[/tex]
= [tex]BG^{2}[/tex] - [tex]BM^{2}[/tex] - [tex]CM^{2}[/tex]
Now, we can use the fact that BJ and CI intersect at point K to find the length of KJ:
KJ = BJ - BJ * (CK/CI)
= BJ * (1 - CK/CI)
= BJ * (1 - BM/CM)
To find BM/CM, we can use the fact that triangle BCI is isosceles with BI = CI, so the altitude IM is also a median of the triangle. This means that CM = 2/3 * BI. Similarly, we can find BJ in terms of JN using the fact that triangle ABJ is isosceles with AJ = BJ:
BJ = 2 * JN
Substituting these expressions into the equation for KJ, we get:
KJ = 2 * JN * (1 - 2/3 * BI/CM)
Now, we just need to find BI/CM in terms of the given lengths. Using the fact that triangle BCI is isosceles with BI = CI, we can find BI in terms of CG:
BI = CG - CI
Substituting this expression into the equation for [tex]IM^{2}[/tex]and simplifying, we get:
[tex]IM^{2}[/tex] =[tex]BG^{2}[/tex] - CG * CI
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Michelle and Robert constructed a wooden bridge for ATVs over a deep creek on the edge of their property. To recuperate the cost of the materials, they decided to charge an annual toll of $8 to each of the 120 members of a local club. A survey showed that for every $1 the toll is increased, 4 members wouldn't use the bridge anymore. What is the best toll charge to allow them to recuperate the cost of the materials the fastest?
Answer:
the answer is $10
Step-by-step explanation:
trust that
Q6) The diagram shows a pyramid. The apex of the pyramid is V.
Each of the sloping edges is of length 6 cm.
A
6 cm
2 cm
B
2 cm с
F
6 cm
The base of the pyramid is a regular hexagon with sides of length 2 cm.
O is the centre of the base.
B
2 cm
E
2 cm C
Calculate the height of V above the base of the pyramid.
Give your answer correct to 3 significant figures.
V is 5.92 centimetres above the pyramid's base at its highest point.
What is pyramid?A pyramid is a 3D pοlyhedrοn with the base οf a pοlygοn alοng with three οr mοre triangle-shaped faces that meet at a pοint abοve the base. The triangular sides are called faces and the pοint abοve the base is called the apex. A pyramid is made by cοnnecting the base tο the apex. Sοmetimes, the triangular sides are alsο called lateral faces tο distinguish them frοm the base. In a pyramid, each edge οf the base is cοnnected tο the apex that fοrms the triangular face.
Give the altitude the letter h. Next, we have:
tan(60) = h/2
Simplifying, we get:
h = 2 tan(60) = 2 √(3)
The Pythagorean theorem yields the following:
[tex]$\begin{align}{{V O^{2}+O F^{2}=V F^{2}}}\\ {{V O^{2}+1^{2}=6^{2}}}\\ {{V O^{2}=35}}\end{align}$[/tex]
Taking the square root of both sides, we get:
VO ≈ 5.92 cm
Rounding to three significant figures, we get:
VO ≈ 5.92 cm
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Graph the system of linear equations.
4x + 3y = 24
-2x + 6y = 18
Use the Line tool to graph the lines.
Helpp with these questions please
Solution In the Attachment Above
Hope It Helps :)
A photography student took portrait photos of people from his hometown. He wants to
develop 21 of the photos, 9 of which were photos of babies.
If he randomly chooses to make 4 of the photos black and white, what is the probability that
all of them are of babies?
Answer: The total number of ways the photography student can choose 4 photos out of 21 is given by the combination formula:
Step-by-step explanation: C(21, 4) = (21!)/((4!)(21-4)!) = 5985
Out of the 21 photos, 9 were photos of babies. The number of ways the student can choose 4 baby photos out of 9 is given by:
C(9, 4) = (9!)/((4!)(9-4)!) = 126
Therefore, the probability that all 4 photos chosen are of babies is:
P = (number of ways to choose 4 baby photos)/(total number of ways to choose 4 photos)
P = C(9, 4)/C(21, 4)
P = 126/5985
P ≈ 0.021
So, the probability that all 4 photos chosen are of babies is approximately 0.021 or 2.1%.
Find x, if √x +2y^2 = 15 and √4x - 4y^2=6
pls help soon
Step 1: Rearrange the equation √x +2y^2 = 15 to get x = (15 - 2y^2)^2.
Step 2: Substitute x = (15 - 2y^2)^2 in the equation √4x - 4y^2=6.
Step 3: Simplify the equation to get 4(15 - 2y^2)^2 - 4y^2 = 6.
Step 4: Solve for y^2 by rearranging the equation to get y^2 = (6 + 4(15 - 2y^2)^2)/8.
Step 5: Substitute y^2 = (6 + 4(15 - 2y^2)^2)/8 in the equation x = (15 - 2y^2)^2.
Step 6: Solve for x by rearranging the equation to get x = (15 - (6 + 4(15 - 2y^2)^2)/4)^2.
Step 7: Substitute y^2 = (6 + 4(15 - 2y^2)^2)/8 in the equation x = (15 - (6 + 4(15 - 2y^2)^2)/4)^2.
Step 8: Simplify the equation to get x = (15 - (6 + 60 - 8y^
3x + y = 6
Y + 2 = x
Answer: x = 2, y = 0
Step-by-step explanation:
Assuming you need help solving for x or y, and the capital Y is y, we have the system of equations:
3x + y = 6
y + 2 = x
Substituting x for y + 2 gives us
3(y + 2) + y = 6
3y + 6 + y = 6
4y = 0
y = 0
Plugging y = 0 in for the second equation gives us
x = 0 + 2, or x = 2
FILL IN THE BLANK ______ can creep into a study if subjects are picked (intentionally or not) according to some criterion and not randomly.
Selection bias can creep into a study if subjects are picked (intentionally or not) according to some criterion and not randomly.
Selection bias occurs when the selection of study participants is not random and is instead influenced by certain criteria. This can result in a non-representative sample that does not accurately reflect the population being studied, leading to inaccurate conclusions. For example, if a study on the effectiveness of a medication only enrolls participants who are already known to respond well to that medication, the results may overestimate its effectiveness in the general population. To minimize selection bias, researchers should use random sampling techniques and carefully consider the inclusion and exclusion criteria .
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Dish A had cells with a radius of 5.1 x10-10 cm. Dish B had cells that had a radius of 4.1 x 10-8 cm. What is the sum of the radii of the two types of cells, using scientific notation?
Answer:
Step-by-step explanation:
To find the sum of the radii of the two types of cells in scientific notation, we need to add the two radii together. However, the radii are given in different orders of magnitude (exponents), so we need to convert one of the radii to match the order of magnitude of the other radius.
The radius of dish A cells is 5.1 x 10^-10 cm.
The radius of dish B cells is 4.1 x 10^-8 cm.
We can convert the radius of dish A cells to match the order of magnitude of dish B cells by multiplying it by 100 (10^2), which gives us:
5.1 x 10^-10 cm x 10^2 = 5.1 x 10^-8 cm
Now that both radii have the same order of magnitude (10^-8), we can add them together to get the total sum of the radii:
5.1 x 10^-8 cm + 4.1 x 10^-8 cm = 9.2 x 10^-8 cm
Therefore, the sum of the radii of the two types of cells, in scientific notation, is 9.2 x 10^-8 cm.
Answer:9.2 x 10^-8 cm.
Step-by-step explanation:
The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
a) The domain of the function is [0, 7.1875], while the range is [0,23]. Considering the domain and the range, the graph of the function is given by the image presented at the end of the answer.
b) The trip had a duration of 5.1875 hours.
How to obtain the domain and the range of the function?The function for this problem is defined as follows:
g(t) = 23 - 3.2t.
The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the domain is given as follows:
23 - 3.2t = 0
3.2t = 23
t = 23/3.2
t = 7.1875 hours.
The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].
The graph is a linear function between points (0, 23) and (7.1875, 0).
At the end of the trip there were 6.4 gallons left, hence the length of the trip is obtained as follows:
23 - 3.2t = 6.4
t = (23 - 6.4)/3.2
t = 5.1875 hours.
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Fredericka Smith's account statement. Unpaid balance of $75.06. Periodic rate of 2 percent. What is the finance charge? New purchases of $432.11. What is the new balance?
Answer:
Step-by-step explanation:
$75.06×2%=$75.06×0.02=$1.50
The finance charge is the product of the unpaid balance and the periodic rate.
The coordinates of three vertices of a parallelogram are (3,-2), (5,2) and (0,2). What are the coordinates of the fourth vertex?
The coordinate of fourth point of a parallelogram is (2,0)
We need to remember that the diagonals of a parallelogram intersect each other at a halfway point and the midpoint of each diagonal is the same.
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram's adjacent angles add up to 180 degrees.
The midpoint formula
[tex]M=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]
AC=BD
We can find the coordinates of the fourth vertex (x,y) through this procedure:
For x
[tex]\frac{5-2}{2}=\frac{0+x}{2}\\\\x=2\\\\for\ y \\\frac{2-2}{2}=\frac{y+2}{2}\\\\y=0[/tex]
Hence the coordinate of fourth point is (2,0)
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What would the slope of X -2, -1, 0, 1, 2. Y -12, -7, -2, 3, 8.
Answer:
slope = 5
slope = (y2 - y1) / (x2 - x1)
Using this formula, calculate the slope between pairs of points in the given set of data. For example, the slope between the first two points (-2, -12) and (-1, -7) is:
slope = (-7 - (-12)) / (-1 - (-2)) = 5 / 1 = 5
Calculate the slope between each pair of points as follows:
Between (-2,-12) and (-1,-7): slope = 5
Between (-1,-7) and (0,-2): slope = 5
Between (0,-2) and (1,3): slope = 5
Between (1,3) and (2,8): slope = 5
question content area top part 1 use a triple integral to find the volume of the solid bounded below by the cone z
The volume of the solid bounded below by the cone z = √(x^2 + y^2) and bounded above by the sphere x^2 + y^2 + z^2 = 18 is 192π/3 cubic units
To find the volume of the solid bounded below by the cone z = √(x^2 + y^2) and bounded above by the sphere x^2 + y^2 + z^2 = 18, we can use a triple integral.
First, we need to determine the limits of integration. Since the solid is symmetric about the z-axis, we can use cylindrical coordinates.
The cone is given by z = √(x^2 + y^2), which in cylindrical coordinates becomes z = r. The sphere is given by x^2 + y^2 + z^2 = 18, which in cylindrical coordinates becomes r^2 + z^2 = 18.
Thus, the limits of integration are
0 ≤ r ≤ √(18 - z^2)
0 ≤ θ ≤ 2π
0 ≤ z ≤ √(r^2)
The integral to find the volume is
V = ∭ dV = ∫∫∫ dV
Using cylindrical coordinates, dV = r dz dr dθ, so the integral becomes
V = ∫₀²π ∫₀ᵣ√(18 - z²) ∫₀ᵣ r dz dr dθ
We can simplify this integral by first integrating with respect to z:
V = ∫₀²π ∫₀ᵣ√(18 - z²) r dz dr dθ
Using a trigonometric substitution u = z/√(18 - z²), we can simplify this to
V = ∫₀²π ∫₀¹ r√(18 - u²(18)) 18du dr dθ
V = 18∫₀²π ∫₀¹ r√(18(1 - u²)) du dr dθ
Using another substitution u = sin(θ), we can simplify this to:
V = 36∫₀²π ∫₀¹ r√(1 - u²) du dr dθ
This integral can be evaluated using the formula for the volume of a sphere of radius R
V = 36(4/3 π(√2)³)
V = 192π/3 cubic units
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The given question is incomplete, the complete question is:
Use a triple integral to find the volume of the solid bounded below by the cone z = √(x^2 + y^2 ) and bounded above by the sphere x^2 + y^2 + z^2 = 18
ges saved
1. A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is
h(t)=25²-81.
O t=3.24 seconds
O t=9 seconds
O t=1.8 seconds
O t=6.48 seconds
Answer: t = 1.8 seconds
Step-by-step explanation:
The function h(t) = 25t^2 - 81 gives the height of the rock (in feet) at time t seconds after it was dropped.
When the rock lands, its height is 0. So we can set h(t) = 0 and solve for t:
25t^2 - 81 = 0
Solving for t, we get:
t = ±√(81/25) = ±(9/5)
Since we are only interested in the time after the rock was dropped, we take the positive value:
t = 9/5 = 1.8 seconds
Therefore, the time between when the rock was dropped and when it landed is 1.8 seconds.
So the answer is: t = 1.8 seconds
Classify each statement according to whether it describes a regression or a coefficient of determination Regression Coefficient of determination represented as R models the relationship between two variables describes how well data points fit a line values range from 0 to 1 can be positive or negative can be described by the linear equation YmX + b
The claims under "Regression" are as follows: 1. can be described by the l
Regression is a statistical technique that connects one or more independent (explanatory) variables to a dependent variable. If there is a relationship between changes in one or more of the explanatory factors and changes in the dependent variable, it can be shown using a regression model.
Y = mx + b is how the slope-intercept form of the equation for a straight line is expressed.
In the equation y = mx + b, m denotes the slope of the line and b its intercept. The distance between the line and the x- and y-axes is denoted by the letters x and y, respectively.
The first of the following claims, "Is used to assess the fit of a model," is true.
b) By including more factors, the result may be overstated.
called the coefficient of determination.
d.) Indicates the proportion of the variation in y that the model can account for.
e.) It is equivalent to the correlation coefficient r2 in basic linear regression.
What is Regression Analysis?
A collection of statistical procedures known as regression analysis is used to estimate the correlations between a dependent variable and one or more independent variables.
SS(res) + SS(reg) = SS, R2 1 - SS(res) / SS(tot) (tot)
R2 is defined as (SS(reg)/SS(tot) = (SS(reg)/n)/(SS(tot)/n)
Where SS(tot) = (y - y(bar)), the total sum of squares (proportional to the variance of the data), 2 • The explained sum of squares, also known as the regression sum of squares, is SS(reg) = (f(i)-y(bar)). SS(res) = (y(i) - f(i))2 = e2 is the sum of squares of residuals, often known as the residual sum of squares (i)
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helps asap !!!!!
if the original price of a refrigerator is $3200 tiana buys the refrigerator at a sale for 20% off the original price she has a discount voucher that gives her a further $64 off the sale price
what percentage of the original price does tiana pay for the refrigerator ?
(can somebody show me how to do this step by step)
Answer:
she payed 78% of the origional price
Step-by-step explanation: ok so boom right 20% of 3200 is 640 so that would make 2% 64 which would be the discount voucher ( 20% = 640 take a away a 0 on both and it shows u) so u do the 20% plus the 2% and that would make 22% and 22-100 is 78%. :)
The cost white in dollars for X pounds of deli meat is represented by the equation Y equals 3.5 X graph the equation and interpret the slope
The graph is of the given equation is represented in the figure below.
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic.
By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude indicates that the price per pound of deli meat has changed by 3.5 units.
Given linear equation represents the cost measured in dollars, as a function of the amount of deli meat, measured in pounds:
[tex]y = 3.5x[/tex]
The graph is of that linear equation as plotted below diagram.
By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude denotes a change in the price per pound of deli meat of 3.5 units.
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The graph is of the given equation is represented in the figure below linear line: Y = 3.5x
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic.
By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude indicates that the price per pound of deli meat has changed by 3.5 units.
Given linear equation represents the cost measured in dollars, as a function of the amount of deli meat, measured in pounds:
Linear line: Y = 3.5x
The graph is of that linear equation as plotted below diagram.
By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude denotes a change in the price per pound of deli meat of 3.5 units.
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Jonathan says that the function represented by the graph is always decreasing. Is he correct? fI not, where is the function decreasing?
Explain your reasoning.
If the slope of the graph is increasing from positive x-axis to negative x-axis, then the function is not that decreasing. Therefore, Jonathan's statement is incorrect.
What is the graph function about?The function is decreasing on intervals where the slope is negative. In this case, since the slope is increasing from positive x-axis to negative x-axis, the function is decreasing on the interval where x is negative.
To determine this interval more precisely, we would need to find the x-value(s) where the slope changes sign from positive to negative. These x-values correspond to critical points, such as local maximums or minimums. The function is decreasing before a local maximum and after a local minimum.
Therefore, Jonathan's statement is not correct, and the function represented by the graph is decreasing on the interval where x is negative.
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find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 13xy.
The equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 13xy is y = e^(13x^2/2).
To find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 13xy, we can use the method of separation of variables. Let's start by separating the variables:
dy/dx = 13xy
We can then rewrite this equation as:
dy/y = 13x dx
Integrating both sides of the equation gives:
ln|y| = 13x^2/2 + C
where C is the constant of integration.
To find C, we can use the fact that the curve passes through the point (0, 1). Substituting x=0 and y=1 into the equation above, we get:
ln|1| = 0 + C
C = 0
Substituting this value of C back into the equation gives:
ln|y| = 13x^2/2
Solving for y gives:
|y| = e^(13x^2/2)
Since the curve passes through the point (0, 1), we can take the positive branch of the absolute value to get:
y = e^(13x^2/2)
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5x+6/1/3=3x/0.4 HELP RSM.
Answer:
x = 0.8
Step-by-step explanation:
5x+6/1/3=3x/0.4
5x + 2 = 3x/0.4
2x + 0.8 = 3x
x = 0.8
You are buying 30 acres of farm land at $12000 per acre. What is total cost?
360000 acres
Step-by-step explanation:
12000 x 30= 360000
write the equation for the relationship between x and y. x=1,2,4 y= 0,-5,-15
Answer:
y = -5x + 5
Step-by-step explanation:
y = mx + b
y = __x + __
To write the equation we need the slope (m) and the y-intercept (b).
Slope:
The is the change in y over the change in x. As the y is decreeing by 5, the x is increasing by 1. This gives us the slope -5/1 = -5
y-intercept:
The y intercept is the point (0,b). It is when x equals zero. If we start at 1 and go back to 0. That mean that the y increase by 5, so the intercept is at the point (0,5) which makes the y-intercept 5.
y = -5x + 5
Helping in the name of Jesus.
Estimate the product. Then find each product 3/4 8 1/2
PLEASE HELP
The product of the number 3/4 and 8 1/2 is 51/8.
What is mixed fraction and improper fraction?A mixed number is one that has a fraction and a whole number, separated by a space. An example of a mixed number is 8 1/2. Contrarily, an improper fraction is one in which the numerator exceeds or is equal to the denominator. For instance, 17/2 is a bad fraction. An improper fraction is a fraction in which the numerator is more than or equal to the denominator, as opposed to a mixed number, which combines a whole number with a proper fraction.
The given numbers are 3/4 and 8 1/2.
Convert the mixed number to an improper fraction:
8 1/2 = (8 x 2 + 1) / 2 = 17/2
Then, we can multiply the fractions:
3/4 x 17/2 = (3 x 17) / (4 x 2) = 51/8
Hence, the product of 3/4 and 8 1/2 is 51/8.
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A line that includes the points (n, 6) and (3, -2) has a slope of 8/5. What is the value of n?
Answer:
n = 8
Step-by-step explanation:
We can find the slope using the slope formula which, which is
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x2, y2, x1, and y1 are a pair of coordinates and m is the slope.
We can allow (3, -2) to represent x2 and y2, and (n, 6) to represent x1 and y1:
[tex]8/5=\frac{-2-6}{3-n}\\ 8/5=\frac{-8}{3-n}\\ 8/5(3-n)=-8\\24/5-8/5n=-8\\-8/5n=-64/5\\n=8[/tex]
Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 JQK
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.
The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.
Actual count of K = 12 - 2 = 10
Total count of 6 and K = 7 + 10 = 17
The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:
Experimental probability = (frequency of K or 6) / (total number of draws)
Experimental probability = 17 / 100
Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.
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7. Hal records the numbers of winners
of a contest in which the player
chooses a marble from a bag.
DA G
Game 1
Game 2
Game 3
Number of Number of
Players
Winners
123
52
155
63
172
65
Based on the data for all three
games, what is the experimental
probability of winning the contest?
Express the answer as a decimal.
Answer:0.40
Step-by-step explanation:
the experimental probability of winning the contest is 0.4 or 40%.
Define probabilityProbability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 denotes the impossibility of the occurrence and 1 denotes its certainty. An occurrence is more likely to occur the higher its probability.
Players: 123 + 155 + 172, or 450 total
52 plus 63 plus 65 winners make up the total of 180.
Experimental probability of winning the contest = Total number of winners / Total number of players
Experimental probability of winning the contest = 180 / 450 = 0.4
Hence, the experimental probability of winning the contest is 0.4 or 40%
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