Use the quadrilateral below to help answer the next two questions.
If L is (-2,-5) and M is (4,-1), what should the slope of NO be in order for LMNO to be a parallelogram?
Note: Enter negatives when necessary with no space between the negative sign and the number.
If the answer is a fraction, leave as an improper fraction in simplest form. Ex. 4/3 for 8/6
The required slope of the side NO is given as 2/3 and the Slope of the LO is given as -3/2.
Given that,
A figure shown of a quadrilateral in order to prove the quadrilateral as a rectangle, the slope of the sides LO and NO is to be determined.
The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.
here,
Because of the parallel sides,
The slope of the side NO is = Slope of the side LM
= [-1 + 5] / [4 + 2] = 2/3
Because of the perpendicular sides,
The slope of the side LO = - 1 / slope of the side LM
= -1 / 2/3 = -3/2
Thus, the required slope of the side NO is given as 2/3 and the Slope of the LO is given as -3/2.
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Write the equation of the line in slope-intercept form (y = mx + b) based on the given information. 11. Passes through (12,-6) and perpendicular to y = 3x + 1
The equation of the line that is perpendicular to y = 3x + 1, in slope-intercept, is: y = -1/3*x - 2.
How to Write the Equation of a Perpendicular Line in Slope-intercept Form?If we are given a line that passes a point (12, -6) and is perpendicular to y = 3x + 1, we can find the equation of the line in slope-intercept form following the steps below.
First, find the slope of y = 3x + 1. The slope is 3. Since both lines are perpendicular to each other, therefore, the slope of the line that passes through (12, -6) would be the negative reciprocal of 3, which is m = -1/3.
Substitute m = -1/3 and (a, b) = (12, -6) into y - b = m(x - a):
y - (-6)) = -1/3(x - 12)
y + 6 = -1/3(x - 12)
Rewrite in slope-intercept form:
y + 6 = -1/3*x + 4
y + 6 - 6 = -1/3*x + 4 - 6
y = -1/3*x - 2
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At $4.20 per yd^3, how much will it cost to fill a container with dimensions of 3yd X 5yd X 7 1/3 yd?
Cost to fill the container = $ 462
The volume of the rectangular container:The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Various forms have various volumes.
The formula for the volume of a rectangular container is given by
Volume = Length × Width × Depth
Here we have,
Dimensions of a container are 3yd × 5yd × 7 1/3 yd
Here 7 1/3 = 22/3 yd
From the given formula,
Area of the container = 3yd × 5yd × 22/3 yd
= [tex](3 \times 5 \times \frac{22}{3} )yd^{3}[/tex]
= [tex]( 5 \times 22 )yd^{3}[/tex]
= 110 yd³
Given the cost per 1 yd³ = $ 4.20
=> cost of 110 yd³ = 110 × $ 4.20 = $ 462
Therefore,
Cost to fill the container = $ 462
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find the area of 10x^2+9x+2 when the the width is 2x+1
The circumference of a tree at different heights above the ground is given in the table below. Assume that all horizontal cross-sections of the tree are circles. Estimate the volume of the tree.
Estimated volume of the tree as per given height and circumference using trapezoidal rule is equal to 30907.5 cubic inches.
As given in the question,
Given height 'x' and circumference 'y=f(x)',
Height (inches) 'x' : 0 15 30 45 60 75 90
Circumference (inches) 'y=f(x)': 31 28 21 17 12 8 2
Trapezoidal rule :
Δx = (b - a ) n
Here b = 90
a = 0
n =6
Δx = ( 90 - 0)/6
= 15
Substitute the value to get the volume using trapezoidal rule:
T₆=(Δx/2)[f(x₀)²+ 2{f(x₁)²+ f(x₂)²+f(x₃)² + f(x₄)²+f(x₅)²}+ f(x₅)²]
= (15/2)[ 31² + 2 (28² + 21² + 17² + 8²) + 2² ]
= ( 15/2) [961 + 2{ 784+ 441 + 289 + 64} + 4]
= 15 × 2060.5
= 30907.5 cubic inches
Therefore, the volume of the tree as per given given table using trapezoidal rule is equal to 30907.5 cubic inches.
The above question is incomplete , the complete question is:
The circumference of a tree at different heights above the ground is given in the table below. Assume that all horizontal cross-sections of the tree are circles. Estimate the volume of the tree using the trapezoid rule. There needs to be six subdivisions in the trapezoid rule.
Height (inches) : 0 15 30 45 60 75 90
Circumference (inches): 31 28 21 17 12 8 2
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The plane is perpendicular to the axis but does not go through the vertex.
The plane intersects the double cone at only the vertex.
The plane is not intersecting the vertex, not parallel to the axis, not perpendicular to the axis, not parallel to the side of the cone, and it intersects only one cone.
The plane is tangent to both of the cones.
answers:
line
point
circle
elipse
match these
The plane is perpendicular to the axis but does not go through the vertex. The plane intersects the double cone at only the vertex is ellipse.
What is an ellipse ?A planar curve with two focal points is called an ellipse if at every point on the curve the sum of the two distances from the focal points is constant. It generalises the shape of a circle, a unique variety of ellipse in which the two focus points coincide.The plane is not intersecting the vertex, not parallel to the axis, not perpendicular to the axis, not parallel to the side of the cone, and it intersects only one cone is circle.A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.To learn more about ellipse refer :
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For triangle ABC, tell what information is given (i.e. SAS, SSS, ASA, etc.) in Column A. Solve for the indicated angle or side in Column B. If there are two solutions, give both. Express answers to the nearest tenth.
1. A=52°, b=120, c = 160, find a
2. a=13.7, A=2543°, B=78°, find b
3. A=38°, B=63°, c=15, find b
4. a=1.5, b=2.3, c=1.9, find B
5. b=795.1, c=775.6, B=51.85°, find C
6. b=40, c=45, A=51°, find a
7. b=50, a=33, A=132°, find B
8. a=20, b=12, c=28, find C
9. a=125, A=25°, b=150, find B
10. b=15.2, A=12.5°, C=57.5°, find c
Using the laws of sines and cosines, answers to the questions are as follows,
1. A=52°, b=120, c = 160,
SAS property, a=128
2. a=13.7, A=25.43°, B=78°,
AAS property, b=31.21
3. A=38°, B=63°, c=15,
ASA property, b=14
4. a=1.5, b=2.3, c=1.9,
SSS property, B=84
5. b=795.1, c=775.6, B=51.85°,
SAS property, C=50
6. b=40, c=45, A=51°,
SAS property, a=37
8. a=20, b=12, c=28
SAS property, C=120
9. a=125, A=25°, b=150
SAS property, 2 solutions are there, B1=149, B2=30.4
10. b=15.2, A=12.5°, C=57.5°
SAS property, c=14
What are the laws of sine and cosine?
We can determine a triangle's one side's length or one of its angles' measurements using the laws of sine and cosine.
In most cases, the unknown sides or angles of an oblique triangle are calculated using the law of sines formula.
The equation that connects the lengths of the triangle's sides and the cosines of its angles is known as the law of cosine or cosine rule.
1. Given A=52°, b=120, c = 160.
If we construct the triangle, we see that it is satisfying the SAS property
By using the law of cosine we get,
[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{120^{2}+160^{2}-2.120.160.\cos 52}\\a=127.9[/tex]
2. Given, a=13.7, A=25.43°, B=78°
From angle A, angle B, and side a, we calculate side b, by using the Law of Sines,
[tex]\frac{b}{a}=\frac{\sin B}{\sin A}\\b=a.\frac{\sin B}{\sin A}\\b=13.7. \frac{\sin 78}{\sin 25.43}\\b=31.21[/tex]
3. A=38°, B=63°, c=15
From angle A and angle B, we calculate angle C,
[tex]A+B+C=180\\C=180-A-B\\C=180-38-63\\C=79[/tex]
Next, From angle A, angle C, and side c, we calculate side a, by using the Law of Sines
[tex]\frac{a}{c}=\frac{\sin A}{\sin C}\\a=c.\frac{\sin A}{\sin C}\\a=15. \frac{\sin 38}{\sin 79}\\a=9.41[/tex]
Calculation of the third side b of the triangle using a Law of Cosines,
[tex]b^{2}=a^{2} +c^{2}-2.a.c.\cos B\\b=\sqrt{a^{2}+c^{2}-2.a.c.\cos B}\\b=\sqrt{9.1^{2}+15^{2}-2.9.41.15.\cos 63}\\b=13.68[/tex]
4. a=1.5, b=2.3, c=1.9
Calculation of the inner angles of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{1.5^{2}+1.9^{2}-2.3^{2} }{2 . 1.5.1.9}\\B=84.15[/tex]
5. b=795.1, c=775.6, B=51.85°
From angle B, side c, and side b, we calculate side a. by using the Law of Cosines and quadratic equation:
[tex]b^2 = c^2 + a^2 - 2.c. a. {\cos B} \\ 795.1^2 = 775.6^2+a^2-2. 775.6. a . \cos 51\ \\ a > 0 \\ a = 989.175[/tex]
Calculation of angle C of the triangle using a Law of Cosines
[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{989.175^{2}+795.1^{2}-775.6^{2} }{2 . 989.795}\\C=50.5[/tex]
6. b=40, c=45, A=51°
Calculation of the third side a of the triangle using a Law of Cosines
[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{40^{2}+45^{2}-2.0.45.\cos 51}\\a=36.87[/tex]
8. a=20, b=12, c=28
Calculation of angle C of the triangle using a Law of Cosines
[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{20^{2}+12^{2}-28^{2} }{2 . 20.12}\\C=120[/tex]
9. a=125, A=25°, b=150
2 solutions are possible for this,
solution for B1:
From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:
[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 28.21[/tex]
Calculation of angle B of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+28.21^{2}-150^{2} }{2 . 125.28}\\B=149[/tex]
solution for B2:
From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:
[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 243.679[/tex]
Calculation of angle B of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+243^{2}-150^{2} }{2 . 125.243}\\B=30.28[/tex]
10. b=15.2, A=12.5°, C=57.5°
From angle A and angle C, we calculate angle B:
[tex]A+B+C=180\\B=180-A-C\\B=180-12.5-57.5\\B=110[/tex]
From the angle A, angle B, and side b, we calculate side a, by using the Law of Sines.
[tex]\ \\ \dfrac{ a }{ b } = \dfrac{ \sin A }{ \sin B } \\ a = b \cdot \ \dfrac{ \sin A }{ \sin B } \\ a = 15.2 \cdot \ \dfrac{ \sin 12.30 }{ \sin 110\degree } = 3.5[/tex]
Calculation of the third side c of the triangle using a Law of Cosines
[tex]c^{2}=a^{2} +b^{2}-2.a.b.\cos C\\c=\sqrt{a^{2}+b^{2}-2.a.b.\cos C}\\c=\sqrt{15.2^{2}+3.5^{2}-2.15.4.\cos 57.30}\\c=13.64[/tex]
Therefore, we have found the solutions of all of the above bits using the law of sine and cosine.
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Find the inverse function in slope-intercept form (mx+b): f(x)= -3x+3
The inverse function of f(x) = -3x + 3 in slope-intercept form is g(y) = (-1/3)y + 1.
What is the inverse function?
The inverse function of a function f(x) is a function g(x) such that g(f(x)) = x for all x in the domain of f.
The given function is f(x) = -3x + 3. To find the inverse function, we can solve for x in terms of y:
y = -3x + 3
0 = -3x + y + 3
-y = -3x + 3
x = (-y + 3) / -3
The inverse function is then g(y) = (-y + 3) / -3. Rewriting this in slope-intercept form gives:
g(y) = (-1/3)y + 1
Hence, the inverse function of f(x) = -3x + 3 in slope-intercept form is g(y) = (-1/3)y + 1.
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PLEASSEEEE HEELPPP ASAPPPPP!!! (FOR 10 POINTS!)
For each system of equations below, choose the best method for solving
and solve. Show your work.
a. 3x+y=24
-x-y=-10
The solution to the system of equations 3x+y=24 and -x-y=-10 is x = 7, y = 3
How to determine the solution to the system?The system of equations is given as
3x+y=24
-x-y=-10
Make x the subject in the second equation
So, we have the following representation
x = 10 - y
Substitute x = 10 - y in the equation 3x+y=24
3(10 - y) +y=24
Expand the bracket
30 - 3y + y = 24
Evaluate the like terms
-2y = -6
Divide by -2
y = 3
Recall that
x = 10 - y
So, we have
x = 10 - 3
x = 7
Hence, the solution is x = 7, y = 3
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Which answer choice correctly complete the sentence?
The Problem Solving Plan is a method to
OA) show all your work in math.
O B) give an example of a real-life problem.
OC) make solving a word problem easier.
OD) check to see if your answer is reasonable.
Answer: C
Step-by-step explanation:
The problem solving plan is a method to make solving a word problem easier.
Use the figure to find the missing angles
Answer:
Angel 5 is 73
Angel 1 is 37
Angel 2 is 42
Angel 3 is 132
Angel 4 is 73
Angel 6 is 30
Step-by-step explanation:
If A (2,2) and B is (-2, -2) what is the distance between AB?
The distance AB between the two points is 5.7 units
How to determine the distance AB between the two points?From the question, we have the following parameters that can be used in our computation:
A = (2, 2) and B =(-2, -2)
The distance between the two points can be calculated using the following distance equation
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where
(x, y) = (2, 2) and (-2, -2)
Substitute (x, y) = (2, 2) and (-2, -2) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
distance = √[(2 + 2)² + (2 + 2)²]
Evaluate
distance = 5.7
Hence, the distance is 5.7 units
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I need help with this
Step-by-step explanation:
If M is the midpoint of AB then,
AM = BB so we can write the following equation:
4x + 13 = 3x + 17
transfer like terms to the same side of the equation4x - 3x = 17 - 13
add/subtractx = 4
Now on to the length of BM, we can replace x with 4 to find it.
3*4 + 17 = 29
Let G(x) = -2(3x + 4)(x - 1)(x – 3)^2 be a polynomial function.
Find the Y intercept and state the end behavior of g(x).
The vertical intercepts is (4/3,0) (3,0) (1,0) and The horizontial intercepts is (0,72)
The end behavior is as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Given the G(x) = -2(3x + 4)(x - 1)(x – 3)^2 as a polynomial function.
Since all the exponets will equal 0. The constant will just add to the term.
The leading degree is even. Thus Even Degree Polynomials like Quadratics tend to go approach positive infinity vertically as x approaches positive infinity, and as x approaches negative infinity, it approaches positive infinity vertically.
Our leading coefficient is negative which means our quadratic will get reflected across the x axis.
The end behavior is as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.
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bro i need help so bad
its congruent angles and whatever
GEOMETRY 50 POINTSS
Answer:
x = 20°y = 70°Step-by-step explanation:
A man walks for 2 hours at a certain speed. He then cycles at three times that seed for
4 hours. He goes 77km altogether. Find the speed at which he walks.
5.5km/hr is the speed at which he walks.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given
w = walking speed
t = time walking = 2
Given, A man walks for 2 hours at a certain speed which is 2w
He then cycles at three times that seed for 4 hours.
We can form a equation by given data
2w + 3×w×4 = 77
2w+12w=77
14w = 77
Divide both sides by 14
w = 5.5 km/hr
Hence, 5.5km/hr is the speed at which he walks.
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does anyone know the answers?
Answer:
1. Supplementary
2. Alternate exterior
Step-by-step explanation:
1. ∠1 and ∠2 are complementary because they both lie on the same straight line. If you had the values of these angles, they would add up to 180°
2. ∠1 and ∠8 are alternate exterior angles because they are on opposite sides of the transversal (the diagonal line from the bottom left to the top right) and they are on the outsides of the parallel lines. (∠1 is above the top horizontal line and ∠8 is below the bottom horizontal line.)
In the diagram, the length of segment VS is 39 units. Line n is a perpendicular bisector of line segment T V. It intersects line segment T V at point R. Line n also contains points Q and S. Line segment Q V is 3 x + 4. Line segment R V is 2 x + 5. Line segment T S is 6 x minus 3. What is the length of segment TV? 14 units 19 units 38 units 50 units
On solving the provided question, by help of the Linear Equation we got that TV = 38 units.
what is linear equation?Any equation with a degree of 1 or above is considered linear. This shows that the exponent of the linear equation's variable is bigger than 1. A linear equation will always have a straight line as its graph.
RST and RSV, two equal right triangles, are shown in the illustration.
Notice that:
TS = VS
We know that,
TS = 6x - 3
VS = 39
6x - 3 = 39
6x = 42
[tex]x = \frac{42}{6}[/tex]
x = 7
Now, you can identify in the figure that:
RV = 2x + 5
The length of segment RV may be determined by substituting the above-calculated value of "x" into the equation and evaluating:
RV = 2(7)+ 5
RV = 19 units
Now,
TV = 19 + 19
TV = 38 units
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(2k^3)^2
answer should contain only positive exponents
a) The base of the pyramid is a Hexagon
b) The height of the pyramid is
c) The vertex of the pyramid is
Blank 1: Hexagon
Blank 2:
For the given hexagonal pyramid, the base of the pyramid is a Hexagon, The height of the pyramid is 13 units, and the vertex of the pyramid is 7.
What is a hexagonal pyramid?
A hexagonal pyramid features isosceles triangles as the faces that join the pyramid together at the top and a hexagonal-shaped base.
Given, for a hexagonal pyramid
a) The base of the pyramid is a Hexagon.
b) The height of the pyramid is 13 units.
c) The vertex of the pyramid is 7.
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Kaitlyn is trying to put in a water pipe underneath the
ground for her pool. The pipe will run from point G(c,6) to
point H(-5,d) on the coordinate grid. Which expression
represents the shortest distance between M and N in
units.
The shortest distance between the two points is √[(c + 5)² + (6 - d)²]
How to determine the shortest distance between the two points?From the question, we have the following points that can be used in our computation:
G = (c, 6) and H = (-5, d)
The distance between the two points can be calculated using the following distance equation
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where
(x, y) = (c, 6) and (-5, d)
Substitute (x, y) = (c, 6) and (-5, d) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
distance = √[(c + 5)² + (6 - d)²]
Hence, the distance expression is √[(c + 5)² + (6 - d)²]
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40 POINTS Use photo
Find BA.
determine each feature of the graph of the given function
f(x)= -5/2x-1
horizontal asymptote: y =
vertical asymptote: x =
y intercept: ( _, 0)
x intercept: (0, _ )
hole: ( _ , _ )
Answer:
Step-by-step explanation:
HORIZONTAL ASYMPTOTE
lim x-> oo -5/(2x-1)
-5/(oo-1)
-5/oo
0
y = 0
VERTICAL ASYMPTOTE
2x - 1 = 0
2x = 1
2/2 x = 1/2
x = 1/2
y INTERCEPT
-5/(0-1)
-5/-1
5
(5,0)
X INTERCEPT
-5 = 0
Impossible
no x intercept
B={x|x is an integer and -4
The resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.
What is roster form?In the set-builder form, a short, statement, or formula is written inside a pair of curly braces, as opposed to the roster form, where the listed items are enclosed in a pair of curly braces and separated by commas.
Roster or tabular form: In roster form, all of the components of a set are listed, with commas used to divide them and braces used to enclose them.
For instance, Z = the set of all integers = {…,−3,−2,−1,0,1,2,3,…}.
So, we have:
B = {x:x is an integer and -4 < x < 6}
B has numbers from -4 and 6.
Now, write B in roster form as:
B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}
Therefore, the resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.
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Complete question:
Write the following sets in roster form:
B = {x:x is an integer and -4 < x < 6}
opinion 1: coefficient of x, coefficient of y, constant term
opinion 2: divide -105 by 3, divide 165 by 3, write the equation in slope-intercept form
opinion 3: -55, -35, 35, 55
Answer:
Coefficient of x
Write in the slope intercept form
35
Step-by-step explanation:
165 - 105x + 3y = 0 Subtract 165 from both sides and and 105x to both sides
3y = 105x - 165 Divide all the way through by 3
y = 35x - 55
The slope is the coefficient of x when the equation is written in the slope intercept form of the line.
The slope is 35
What is the answer to -6v-1+v
Answer:
-6v-1+v
collect the like terms
-6v + v - 1
you have
-5v-1
Answer:
answer is 5v-1
Step-by-step explanation:
add the common varribles which are V,
what are two diffrent if-then statements implied by Theorem 2-13?
The two different if-then statements implied by Theorem 2-13 are:
If lines and are both not vertical then p || q if and only if the slope of the line p is equal to the slope of the line q.If lines p and q are both vertical then p || q.What is the Parallel Lines & Perpendicular Lines?
Parallel Lines :Two or more lines that lie in the same plane and never intersect or meet each other are known as parallel lines,
Perpendicular Lines are formed when two lines meet each other at the right angle or 90 degrees.
Given: The theorem 2-13 is given.
We have to find what are two different if-then statements implied by Theorem 2-13.
The two different if-then statements implied by Theorem 2-13 are:
If lines and are both not vertical then p || q if and only if the slope of the line p is equal to the slope of the line q.If lines p and q are both vertical then p || q.Hence, The two different if-then statements implied by Theorem 2-13 are:
If lines and are both not vertical then p || q if and only if the slope of the line p is equal to the slope of the line q.If lines p and q are both vertical then p || q.To learn more about the Parallel Lines & Perpendicular Lines visit,
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If R = {(x, y): y=x²-4 and y ≤5], then Find a) Domain and Range of R b) Inverse relation (R') c) Domain and Ranpe of R d) To Sketch the graphs of R. and Ro
a) The Domain is [-∞, 5]
And the range is [-∞, 3]
b) The area covered by a relation's inverse is the same as its domain. In other words, the relationship's x-values are its inverse's y-values.
c) The Domain is [-∞, 5]
And the range is [-∞, 3]
d) The graph of R is shown below:
What is meant by Domain?The set of inputs that a function will accept is referred to as the domain of the function in mathematics. It is important to note that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.
The function f can be plotted in the Cartesian coordinate system in the special case where X and Y are both subsets of R. In this example, the graph's x-axis shows the domain as the projection.
Given,
R = {(x, y): y=x²-4 and y ≤5]
For x=0, y=-4
For x=1, y=-3
For x=2, y=0
For x=3, y=5
Therefore, the Domain is [-∞, 5]
And the range is [-∞, 3]
The area covered by a relation's inverse is the same as its domain. In other words, the relationship's x-values are its inverse's y-values.
The graph of R is shown below:
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A study was made by a retail merchant to determine the relation between weekly advertising expenditures and sales. The following data were recorded: Advertising Costs ($) 40 Sales ($) 385 20 400 25 395 20 365 475 30 50 440 40 490 20 420 50 560 525 40 25 480 50 510 a) Plot a scatter diagram, you may use Excel. (5 marks) b) Find the equation of the regression line to predict weekly sales from advertising expenditures. (6 marks) c) Estimate the weekly sales when advertising costs are $35. (2 marks) d) Plot the residuals versus advertising costs. Comment. (5 marks) e) Using the t-test, test the hypothesis that 6 against the alternative that B< 6. Use a 0.025 level of significance. (10 marks) f) Construct a 95% confidence interval for the average weekly sales when $45 is spent on advertising. (5 marks) g) Construct a 95% prediction interval for the average weekly sales when $45 is spent on advertising (5 marks) h) What is the percentage of variations in weekly sales explained by the advertising costs? (2 marks)
For given data,
a) A scatter diagram is as shown below.
b) the coefficient of correlation is, r = 0.63
c) the linear regression equation (least-squares equation of the line) to predict weekly sales from advertising expenditures is : y = 3.2208x + 343.71, where x is the Advertising Costs and y be the Sales in dollars
d) when advertising costs are $32, the weekly sales would be 446.78 dollars.
In this question, we have been given that a retail merchant made a study to determine the relation between weekly advertising expenditures and sales.
The following data were recorded:
Advertising Costs, $ 40 20 25 20 30 50 40 20 50 40 25 50
Sales, $ 385 400 395 365 475 440 490 420 560 525 480 510
a) a scatter plot for the above data is as shown below.
b) the coefficient of correlation is:
r = √0.403
r = 0.63
c) the linear regression equation is:
y = 3.2208x + 343.71
where x is the weekly Advertising Costs and y be the Sales in dollars
d) the weekly sales when advertising costs are $32:
y = 3.2208(32) + 343.71
y = 446.78
So, when advertising costs are $32, the weekly sales would be 446.78 dollars.
Therefore, for given data:
a) A scatter diagram is as shown below.
b) the coefficient of correlation = 0.63
c) the linear regression equation: y = 3.2208x + 343.71
d) when advertising costs are $32, the weekly sales would be 446.78 dollars.
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I need help with this.
Answer:
Step-by-step explanation:
ax² + bx + c = 0
D = b² - 4ac
If D > 0 , then quadratic equation has 2 roots.
If D = 0 , then quadratic equation has 1 roots.
If D > 0 , then quadratic equation has No roots in the set of real numbers.
~~~~~~~~~~~~~~~~~~~~
2y² + 4y = 3
2y² + 4y - 3 = 0
a = 2 , b = 4 , c = - 3
D = 4² - 4(2)( - 3) = 40 > 0 ( 2 solutions )
[tex]y_{12}[/tex] = ( - 4 ± 2√10 ) ÷ 4
[tex]y_{1}[/tex] = [tex]\frac{-2+\sqrt{10} }{2}[/tex]
[tex]y_{2}[/tex] = [tex]\frac{-2-\sqrt{10} }{2}[/tex]