Answers
The linear equations and the values of the variables of the equations are;
(-2, 4)(0, 3)x = 1/3, y = 0x = 1. y = 5x = -2, y = -2x = 10, y = -3x = 8 GB, y = 88, B. Going with Company B is not a good ideax = 14, y = 42Cost of a shampoo = (147 - b·y)/x, cost of a conditioner = (147 - a·x)/yWhat is a linear equation?
A linear equation is an equation that can be presented as; y = mx + c, where m is the slope and c is the y-intercept.
1. Please find attached, the graph of the equations y = 2x and y = 3x + 2, created with MS Excel, showing the solution point (-2, 4)
The solution is x = -2, y = 4
2. Please find attached, the graph of the equations y = 2x and y = 3x + 2, created with MS Excel, showing the solution point (0, 3)
The solution is x = 0, y = 3
3. The equations are solved using substitution as follows;
y = 2 - 6·x
9·x + 2·y = 3
Therefore;
9·x + 2×(2 - 6·x) = 3
4 - 3·x = 3
3·x = 4 - 3 = 1
x = 1/3
y = 2 - 6·x
y = 2 - 6 × 1/3 = 0
y = 0
4. 8·x + 7·y = 43
2·x + y = 7
Therefore;
y = 7 - 2·x
8·x + 7·y = 43
8·x + 7 × (7 - 2·x) = 43
49 - 6·x = 43
6·x = 49 - 43 = 6
x = 6/6 = 1
x = 1
y = 7 - 2·x
y = 7 - 2 × 1 = 5
y = 5
5. y = 8 + 5·x
Therefore where 7·x + 9·y = -32, we get;
7·x + 9 × ( 8 + 5·x) = -32
52·x + 72 = -32
52·x = -32 - 72 = -104
x = -104/52 = -2
x = -2
y = 8 + 5·x
y = 8 + 5 × (-2) = -2
y = -2
6. x = 4 - 2·y
x = 1 - 3·y
Therefore; 4 - 2·y = 1 - 3·y
3·y - 2·y = 1 - 4 = -3
y = -3
x = 1 - 3·y
x = 1 - 3 × (-3) = 10
x = 10
7. The cost for Company is C = 5·x + 48
The cost for Company 2 is C = 11·x
Therefore; 5·x + 48 = 11·x
11·x - 5·x = 48
6·x = 48
x = 48/6 = 8
The amount of data in GB at which the cost of both options are the same is 8 GB
y = 11 × 8 = 88
B. The amount of data at which the cost of both options are the same indicates that when using a small data amount, the cost of Company 2 is much more affordable, however, after 8 GB, the cost of using Company 1 becomes more affordable, hence going with Company 2 is not a good idea
8. Let x represent the number of students who can ride in a van and let y represent the number of students who can right in a bus, we get;
5·x + 3·y = 196
x + 6·y = 266
x = 266 - 6·y
Therefore;
5·x + 3·y = 196
5 × (266 - 6·y) + 3·y = 196
1330 - 27·y = 196
1330 -196 = 27·y
1134
y = 1134/27 = 42
y = 42
x = 266 - 6·y
x = 266 - 6 × 42 = 14
x = 14
9. Let x represent the number of bottles the shampoo and let y represent the number of bottles of the conditioner bought, therefore;
x + y = 19
Let a represent the cost of a shampoo and let b represent the cost of a conditioner
a·x + b·y = 147
The cost of a shampoo, a = (147 - b·y )/x
Cost of a conditioner, b = (147 - a·x )/y
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Related Questions
PLEASE ANSWER ASAP
Find the equation of the exponential function represented by the table below:
x y
0 2
1 6
2 18
3 54
what does y= ??
Answers
The value of Y is givan as y = 2 * 3^x
How to solve for yThe general form is of
y = ab^x
where we have to define the terms as
'a' is the initial value, 'b' is the base, and 'x' is the exponent
Point (0, 2):
y = ab^x
2 = a * b^0
Since any non-zero number raised to the power of 0 is 1, we have:
2 = a * 1
a = 2
Point (1, 6):
y = ab^x
6 = 2 * b^1
6 = 2 * b
b = 6 / 2
b = 3
From the values that we have solve we would have
y = 2 * 3^x
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Ryan is a runner. He can run 100 meters in 13 seconds. He
frequently races against Juan, who can run at a speed of 15
miles per hour. Which runner is faster? (1 mile = 1609.34
meters)
Answers
Answer:
Ryan: (100/13)(1/1,609.34)(3,600) =
17.21 miles per hour
Ryan is faster than Juan, by about 2.21 miles per hour
Find the Surface Area of a cone that has a slant height of 14 in and a diameter of 6 in. Remember to use the symbol when you plug it into your calculator. Round the answers to the nearest tenth.
Surface Area = ___ in2
Answers
The surafce area of the cone with a slant height of 14 in and a diameter of 6 in is 160.2 in².
What is the surface area of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The surface area of a cone can be expressed as;
SA = πrl + πr²
Where r is radius of the base, l is the slant height of the cone and π is constant pi.
Given that:
Slant height l = 14 in
Diameter d = 6 in
Radius r = diameter/2 = 6/2 = 3in
S.A = ?
Plug the given values into the above formula and solve for the surface area.
SA = πrl + πr²
SA = ( π × 3in × 14in ) + ( π × (3in)² )
SA = 160.2 in²
Therefore, the surface area is 160.2 in².
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9. It is estimated that a certain model rocket will reach an altitude of 200 ft. A photographer is setting up a camera 50 ft away from the launch pad. At what angle should he set the tripod to get a picture at the maximum altitude?
Answers
The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.
We have,
We can use trigonometry to solve this problem.
C
/ \
/ \
/θ \
/ \
/ \
A-------------B
50 ft
In this diagram, A represents the launch pad, B represents the maximum altitude of the rocket, C represents the position of the photographer, and θ represents the angle at which the tripod should be set.
We want to find θ.
First, we can find the height of the triangle ABC using the Pythagorean theorem:
AB² = AC² + BC²
200² = AC² + 50²
AC² = 200² - 50²
AC = √(200² - 50²)
AC = 190.526 ft
Next, we can use the tangent function to find θ:
tan(θ) = opposite/adjacent = AB/BC = 200/50 = 4
Taking the arctangent of both sides, we get:
θ = [tex]tan^{-1}(4)[/tex]
θ = 75.96 degrees
Therefore,
The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.
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Solve the following systems of inequalities and select the correct graph: 2x − y < 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.
Answers
The solution to the system of inequalities 2x − y < 4 and x + y < −1 is the intersection of the shaded regions below the lines 2x - y = 4 and x + y = -1, labeled AB on the graph. Regions A and B represent the solutions to each individual inequality.
To solve the system of inequalities 2x − y < 4 and x + y < −1, we can use the following steps
Solve each inequality for y in terms of x
2x - 4 < y
-x - 1 < y
Plot the boundary lines for each inequality as dotted lines. To do this, we can use the equality signs instead of the inequality signs.
2x - 4 = y
-x - 1 = y
Shade the region that satisfies each inequality. To do this, we can test a point that is not on the boundary line in each inequality. For example, we can test (0,0) in the first inequality
2(0) - 0 < 4
0 < 4
Since (0,0) satisfies the first inequality, we shade the region below the line 2x - y = 4. Similarly, we can test (0,-2) in the second inequality
(0) + (-2) < -1
-2 < -1
Since (0,-2) satisfies the second inequality, we shade the region below the line x + y = -1.
The solution to the system of inequalities is the intersection of the shaded regions, which is labeled AB in the graph. The shaded region labeled AB is the region that satisfies both inequalities, which is the region below both lines.
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What would happen if you put the wrong place value of a specific number
Answers
Writing the correct number relies on what our number system calls the place value system. The 9, the 3, and the 1 are all located in different spots in the larger number, and each of them is called a digit.
Putting the digits in the wrong locations could result in disaster when dealing with money and in many other situations.
school administrators asked a group of students and teachers which of two school logo ideas logo A or logo B they prefer. Are beining a student and prefering logo A independent events? why or why not?
Answers
Being a student and preferring logo A are dependent events.
We have,
Being a student and preferring logo A are not independent events because they are related to each other.
If a student prefers logo A, then they belong to the group of students who prefer logo A.
On the other hand, if a student belongs to a different group, such as the group of students who prefer logo B or are undecided, then they cannot be said to prefer logo A.
In general, two events are considered independent if the occurrence of one event does not affect the probability of the other event occurring.
However,
In this case, knowing whether someone is a student does affect the probability of them preferring logo A.
Thus,
Being a student and preferring logo A are dependent events.
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From the 12 albums released by a musician the recording company wishes to release 10 in a boxed set. How many different boxes sets are possible?
Answers
Ask a dif site if this one dont have it
ind the area inside 2cos 3r
(tip: use6
and6
)
Answers
The area inside the polar curve R = 2cos(3θ) for three full rotations is 6π.
The polar curve R = 2cos(3θ) is symmetric about the x-axis, with three petals that extend from θ = 0 to θ = π/3, π to 4π/3, and 5π/3 to 2π. To find the area inside the curve, we need to integrate the expression for the area element in polar coordinates over the desired region:
dA = (1/2) [tex]R^{2}[/tex] dθ
The limits of integration for θ are from α = -6π to β = 6π, since we want to find the total area inside the curve for three full rotations. Thus, the integral for the area is:
A = ∫(β=6π, α=-6π) (1/2) [tex]R^{2}[/tex]dθ
= ∫(β=6π, α=-6π) (1/2) (2cos(3θ))^2 dθ
= 2∫(β=6π/3, α=-6π/3) cos^2(3θ) d(3θ) (using the identity cos^2(3θ) = (1 + cos(6θ))/2)
= ∫(β=6π/3, α=-6π/3) (1/2 + (1/2)cos(6θ)) d(3θ)
= (1/2)θ + (1/12)sin(6θ) ∣(β=6π/3, α=-6π/3)
= (1/2)(6π - (-6π)) + (1/12)(sin(36π) - sin(-36π))
= 6π
Correct Question :
Find The Area Inside R=2cos(3θ) (Tip: Use Α=−6π And Β=6π )
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pls help me with this questions quick! right answer lol pls
Answers
The function given in the table is an exponential function.
The function given in the table is clearly not linear, since the y value is changing rapidly.
Here we can see that the function value is changing as the multiplication of 7.
y = 7⁰ = 1, when x = 1
y = 7¹ = 7, when x = 2
y = 7² = 49, when x = 3
y = 7³ = 343, when x = 4
y = 7⁴ = 2401, when x = 5
So here the equation of the function can be written as,
y = 7ˣ⁻¹
Here the variable x is in the exponent.
So it is an exponential function.
Hence the given function is an exponential function.
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Find the volume of the shape below. Round to the nearest tenth. Use
the pi button on the calculator.
11 mi
5 mi
Volume =
mi3
Answers
The volume of the shape to the nearest tenth is equal to 138.4π m³.
How to calculate the volume of a sphere?In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):
Volume of a sphere = 4/3 × πr³
Where:
r represents the radius.
By substituting the given parameters into the formula for the volume of a sphere, we have the following;
Volume of a sphere = 4/3 × π × 4.7³
Volume of a sphere = 138.4π m³
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Please answer all these questions by today
Answers
The statement that is not true on the cube - shaped box is C. The volume of the box is 1 square foot.
The possible dimensions for the bottom layer would be :
Length = 1 unit , Width = 12 unitsLength = 2 units , Width = 6 unitsLength = 3 units , Width = 4 unitsHow to find the possible dimensions ?In answer to the rectangular prism inquiry, we know that the prism is made of 36 cubic units and has a height of 3 units. To discover all potential bottom layer dimensions, divide the total number of cubic units (36) by the height (3 units):
36 / 3 = 12
The possible dimensions of the bottom layer:
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
This means that the possible dimensions would be:
Length = 1 unit , Width = 12 units
Length = 2 units , Width = 6 units
Length = 3 units , Width = 4 units
A square foot is a unit of area, not volume. The volume should be measured in cubic feet.
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PLEASE HELP
Part A:
List the three different types of visuals we use to organize all the possible outcomes in a sample space
1
2
3.
Part B:
Leena is arranging 3 different books in a row on a shelf. A detective story (D), a mystery story (M), and a comic book (C)
1. Pick one of the three types of visuals you listed in Part A to create a sample space for the arrangement of all possible outcomes for arranging the 3 books on a shelf. (1 point)
Fill in the Blank I will choose to create a
for this scenario
2. Create your visual either by hand or using technology
Answers
There are 6 different possible arrangements as obtained using the factorial method and they are :
DMC, CMD, DCM, MDC, CDM, MCD
Given that:
DETECTIVE STORY = D
MYSTERY STORY = M
COMIC BOOK = C
Now, To use the factorial method, we find the factorial value of the number of books to be arranged
Number of different possible arrangements = (number of books)!
Number of books = 3
Hence,
3! = 3 x 2 x 1 = 6 ways
The sample space :
DMC
CMD
DCM
MDC
CDM
MCD
Therefore, there are 6 different samples on the SAMPLE SPACE.
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Complete question is,
Leena is arranging 3 different books in a row on a shelf. Create a sample space for the arrangement of a detective story (D), a mystery story (M), and a comic book (C).
Source
StylesNormal
AASAAAP. NEEDD HELLPPPPP
Answers
The coordinates of B'(6, 3) and C'(4, 4).
We have,
The point A (6, 8) is translated to A' (2, 5).
So, here the points are translated as
(x₁ - x₂ , y₁ - y₂)
= (6 -2, 8-5)
= (4, 3)
So, the coordinates of B'
= (8 -2, 8-5)
= (6, 3)
and, the coordinate of C'
= (6-2, 9-5)
= (4, 4)
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The resistance, R, of a wire varies as its length and inversly as the square of its diameter. If the resistance of a wire 700ft long with a diameter of 0.2inches is 15611ohms, what is the resistance of 1800ft of the same type of wire with a diameter of 0.45inches? (Leave k in fraction form or round to at least 3 decimal places. Round off your final answer to the nearest hundredths)
Answers
The resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.
How to find the resistance of 1800ft of the same type of wire with a diameter of 0.45inchesLet R be the resistance of the wire,
L be the length of the wire,
d be the diameter of the wire, and
k be a constant of variation.
Then we have the equation:
R = k * L / d^2
Solving for k to find the resistance of a wire of varying length and diameter.
We can create an equation using the information provided:
15611 = k * 700 / 0.2^2
Solving for k, we get:
k = 15611 * 0.2^2 / 700
k ≈ 0.1799
Using k to calculate the resistance of a wire with a length of 1800 feet and a diameter of 0.45 inches:
15037.45 ohms = 0.1799 * 1800 / 0.452 R
As a result, the resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.
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What is an equation of the line that passes through the points (-4, 8) and (6, 3)?
Answers
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 8 ) and (x₂, y₂ ) = (6, 3 )
m = [tex]\frac{3-8}{6-(-4)}[/tex] = [tex]\frac{-5}{6+4}[/tex] = [tex]\frac{-5}{10}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 4, 8 )
8 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )
6 = c
y = - [tex]\frac{1}{2}[/tex] x + 6 ← equation of line
what numbers should replace a b c to make 9
Answers
Answer:
I did the math in my head but please please trust me
It’s below
Step-by-step explanation:
C = 1 1/2
B = 2
A = 5
I’m going to try to explain as best as I can
First solve for C by subtracting the other numbers in its line going up to down from 9:
9 - 3 1/2 + 4 = C
9 - 7 1/2 = C
1 1/2 = C
now that w have C we can solve for b doing same steps:
9 - 5 1/2 + 1 1/2 = b
9 - 7 = b
2 = b
now we do A:
9 - 2 + 2 = a
9 - 4 = a
5 = a
Answer
A should be 5
B should be 2
c should be
[tex] 1\frac{1}{2 \\ } [/tex]
all should add up to 9
2+A(5)+b(2)= 9
a(5)+3 1/2+ 1/2=9
5 1/2+ b(2)+ 1 1/2= 9
3 1/2+ 1 1/2+ 4= 9
a solid with volume 8 cubic units is dated by a scale factor of k. find the volume of the image for each given value of
k = 1/2
k = 0.6
k = 1
k = 1.5
Answers
The volumes of the image for each given value of k are computed below
Find the volume of the imageFrom the question, we have the following parameters that can be used in our computation:
Volume = 8
Scale factor = k
The volume of the image is calculated as
Volume = 8k^3
Using the values of k, we have
Volume = 8(1/2)^3 = 1
Volume = 8(0.6)^3 = 1.728
Volume = 8(1)^3 = 8
Volume = 8(1.5)^3 = 27
Hence, the volumes are calculaed above
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PLEASE HELP ME!!!!!! I WILL APPRECIATE IT SO MUCH
Answers
Mean =sum of numbers/number of numbers
Mean=8+12+8+11+15+6+9+8+10+13 /10
Mean=100/10
Mean=10
What is the distance from (−18, −5) to (−18, 24)? −29 units −19 units 19 units 29 units
Answers
The distance from (-18, -5) and (-18, 24) is 29 units which is calculated with the formula of shortest distance between two coordinates.
Hence option d is the correct option.
The coordinates are given as, say P is (-18, -5) and Q is (-18, 24).
The distance between P and Q can be calculated with the formula of shortest distance between two coordinates as,
Shortest distance between P and Q, PQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }[/tex] units
⇒ PQ = [tex]\sqrt{((-18) - (-18))^2 + ((24) - (-5))^2 }[/tex] units
⇒ PQ = [tex]\sqrt{(-18 +18)^2 + (24 +5)^2 }[/tex] units
⇒ PQ = [tex]\sqrt{(0)^2 + (29)^2 }[/tex] units
⇒ PQ = [tex]\sqrt{29^2}[/tex] units
⇒ PQ = 29 units
Hence option d 29 units is the correct option.
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I noticed that people were giving the wrong answers for this question before so here is the correct answer.
In 34 pound of a spice mix, there is 56 cup of cinnamon.
How much cinnamon does the spice mix contain per pound?
ANSWER: 1 1/9
Answers
One pound of spice mix will have 1 1/9 cups of cinnamon.
Given that in 3/4 pound of a spice mix there are 5/6 cups of cinnamon,
we need to find the amount of cinnamon in a pound,
Since, 3/4 pound = 5/6 cinnamon
So,
1 pound = 5/6 x 4/3
= 20/18 = 10/9
= 1 1/9 cups
Hence, one pound of spice mix will have 1 1/9 cups of cinnamon.
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.
Answers
The correct options are:
[tex]8(x^2 + 2x) = -3\\\\8(x^2 + 2x + 1) = -3 + 8[/tex]
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
What Is Quadratic Equation?Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Now, We have the quadratic equation is:
[tex]8x^2 + 16x + 3 = 0[/tex]
We separate variables from constants
[tex]8x^2+16x = -3[/tex]
Taking the common factor 8
[tex]8(x^2+2x)=-3[/tex]
Completing squares in the brackets and balancing the equation in the right side
[tex]8(x^2+2x+1)=-3+8[/tex]
Factoring the perfect square
[tex]8(x+1)^2=5[/tex]
[tex](x+1)^2=\frac{5}{8}[/tex]
[tex](x+1)=[/tex] ± [tex]\sqrt{\frac{5}{8} }[/tex]
x = -1 ± [tex]\sqrt{\frac{5}{8} }[/tex]
The correct options are:
[tex]8(x^2 + 2x) = -3\\\\8(x^2 + 2x + 1) = -3 + 8[/tex]
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
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The given question is incomplete, complete question is:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot
8(x2 + 2x + 1) = 3 + 1
8(x2 + 2x) = –3
giselle has 40 prizes for raffle ticket winners. She gives away 2 prizes each day until she runs out of prizes
Answers
Answer:20
Step-by-step explanation:
40/2=20
20 days of giving away 2 tickets
The table below lists the masses and volumes of several pieces of the same type of metal. There is a proportional relationship between the mass and the volume of the pieces of metal. Volume (cubic centimeters) (cubic centimeters) Volume Mass (grams) Mass (grams) 2.5 2.5 10.15 10.15 4.4 4.4 17.864 17.864 13.6 13.6 55.216 55.216 Determine the mass, in grams, of a piece of metal that has a volume of 12.4 12.4 cubic centimeters. Round your answer to the nearest tenth of a gram
Answers
The mass of a piece of metal that has a volume of 12.4 cubic centimeters.
We can set up a proportion with the given masses and volumes:
Mass ₁ / Volume ₁ = Mass ₂ / Volume ₂
We can choose any two sets of masses and volumes from the table to use in the proportion. Let's use the first set of masses and volumes:
2.5 / 2.5 = Mass₂ / 12.4
We can solve for Mass 2 by cross-multiplying and simplifying:
2.5 x 12.4 = 2.5 Mass ₂
31 = Mass ₂
Therefore, the mass of a piece of metal with a volume of 12.4 cubic centimeters is 31 grams. We can round this answer to the nearest tenth of a gram, which gives us 31.0 grams.
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please help! maths functions (find the equation of the line…)
Answers
Answer:
a) y = -2x + 3
b) y = -3x + 7
c) y = -1/2x + 4
d) y = 2
Step-by-step explanation:
Gradient is also known as slope
a) y = mx + b
3 = (-2)0 + b
b = 3
y = -2x + 3
b) y = mx + b
1 = (-3)(2) + b
1 = -6 + b
b = 7
y = -3x + 7
c) Slope m = (y2 - y1)/(x2 - x1)
m = (2 - 3)/(4 - 2) = -1/2
y = mx + b
3 = -1/2(2) + b
3 = -1 + b
b = 4
y = -1/2x + 4
d) The x‐axis or any line parallel to the x‐axis has a slope of 0.
y = mx + b
2 = -3(0) + b
b = 2
y = 2
Answer:
a) The equation of this line is y = -2x + 3
b) The equation of this line is y = -3x + 7
c) The equation of this line is y = -1/2x + 4 or y = -0.5x + 4
d) The equation of this line is y = 2
Step-by-step explanation:
The equation of a line can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.
a) The equation of the line with a gradient of -2 and cutting the y-axis at 3 can be found using the point-slope form of a linear equation. The point-slope form is given by y - y1 = m(x - x1), where m is the gradient and (x1, y1) is a point on the line. Substituting m = -2 and (x1, y1) = (0, 3), we get:
y - 3 = -2(x - 0)
Simplifying the right-hand side gives:
y - 3 = -2x
Adding 3 to both sides gives the final equation:
y = -2x + 3
b) The equation of the line with a gradient of -3 and passing through the point (2, 1) can be found using the point-slope form again. Substituting m = -3 and (x1, y1) = (2, 1), we get:
y - 1 = -3(x - 2)
Simplifying the right-hand side gives:
y - 1 = -3x + 6
Adding 1 to both sides gives the final equation:
y = -3x + 7
c) To find the equation of the line passing through the points (2, 3) and (4, 2), we first need to find its gradient. The gradient is given by:
m = (y2 - y1)/(x2 - x1)
Substituting the coordinates of the two points, we get:
m = (2 - 3)/(4 - 2) = -1/2 or -0.5
Now, we can use the point-slope form again, this time with (x1, y1) = (2, 3) and m = -1/2:
y - 3 = (-1/2)(x - 2)
Simplifying the right-hand side gives:
y - 3 = (-1/2)x + 1
Adding 3 to both sides gives the final equation:
y = (-1/2)x + 4 or y = -0.5x + 4
d)The line is parallel to the x-axis and passes through the point (-3 ; 2). A line parallel to the x-axis has a gradient of 0. The general equation of a line is y = mx + c, where m is the gradient and c is the y-intercept. Since the gradient is 0, the equation becomes y = c. Since the line passes through the point (-3 ; 2), we can substitute y = 2 into the equation to find that c = 2. Therefore, the equation of this line is y = 2.
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. sin(11°) cos(49°) + cos(11°) sin(49°) and Find its exact value.
Answers
The exact value for the trigonometric function of numbers is derived to be √3/2.
What are trigonometric identitiesTrigonometric identities are equations that involve the trigonometric functions (such as sine, cosine, tangent, cosecant, secant and cotangent) and are true for all possible values of the variables involved. These identities can be used to simplify trigonometric expressions, solve equations, and prove other mathematical statements.
Then sum and difference identities states that:
sin(A ± B) = sinAcosB ± cosAsinB
cos(A ± B) = cosAcosB ∓ sinAsinB
so;
sin(11°) cos(49°) + cos(11°) sin(49°) = sin(11 + 49)
sin(11°) cos(49°) + cos(11°) sin(49°) = sin(60°)
sin(11°) cos(49°) + cos(11°) sin(49°) = √3/2.
Therefore, the exact value for the trigonometric function of numbers is derived to be √3/2.
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What is the value of x? (6x+30) 2x
Answers
The value of x after solving the given equation (6x+30) = 2x is equal to -7.5.
To solve for x in the equation (6x+30) = 2x, we need to isolate x on one side of the equation.
First, we can simplify the equation by subtracting 2x from both sides:
(6x+30) - 2x = 0
Simplifying this further gives:
4x + 30 = 0
To isolate x, we can subtract 30 from both sides:
4x = -30
Finally, we can solve for x by dividing both sides by 4:
x = -7.5
Therefore, the value of x in the equation (6x+30) = 2x is -7.5.
In general, when solving linear equations such as this, we want to manipulate the equation in such a way that we can isolate the variable on one side of the equation.
This can involve adding or subtracting terms, multiplying or dividing by constants, or taking square roots, among other techniques. The goal is to get the equation into a form that allows us to solve for the variable by itself.
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Complete question is:
What is the value of x? (6x+30) = 2x
The following information has been provided by Miller Company: Advertising expense $19,800 Interest expense $7,400 Rent expense for store $24,000 Loss on sale of property and equipment $11,400 Cost of goods sold $42,600 Depreciation expense $14,200 Prepaid insurance $2,000 What is the amount included in the Other Items section of Miller's income statement?
Answers
Answer:
To find the amount included in the Other Items section of Miller's income statement, we need to add up all the expenses and losses that are not related to advertising, interest, rent, cost of goods sold, depreciation, and prepaid insurance. These expenses and losses fall under the category of "Other Expenses" or "Other Items" in the income statement.
From the given information, the expenses and losses that are not included in the above categories are:
- Loss on sale of property and equipment = $11,400
Therefore, the amount included in the Other Items section of Miller's income statement is $11,400.
Step-by-step explanation:
The numbers 1, 2, 3 and 4 have weights 0.1, 0.2, 0.3 and 0.4 respectively.
What is the weighted mean?
2.5
2.8
3.0
3.2
Answers
Answer:
1(.1) + 2(.2) + 3(.3) + 4(.4)
= .1 + .4 + .9 + 1.6 = 3.0
Answer:
Step-by-step explanation:
To calculate the weighted mean, first multiply each number by its corresponding weight, then add-up the products and divide by the sum of the weights-
weighted mean = (1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4) / (0.1 + 0.2 + 0.3 + 0.4)
Then simplifying the numerator:-
weighted mean = (0.1 + 0.4 + 0.9 + 1.6) / (0.1 + 0.2 + 0.3 + 0.4)
Then adding up the numerator:-
weighted mean = 3 / 1So the weighted mean of the numbers 1, 2, 3, and 4 with weights 0.1, 0.2, 0.3, and 0.4 respectively is 3.
work out the area of the shaded shape 5m 13m 9m 11m area
Answers
Answer:
To calculate the area of the shaded shape, we need to first find the area of the two rectangles and then subtract the overlap.
The area of the rectangle with dimensions 5m and 13m is:
Area = 5m x 13m = 65 square meters
The area of the rectangle with dimensions 9m and 11m is:
Area = 9m x 11m = 99 square meters
To find the overlap, we need to calculate the width of the shaded region. We can do this by subtracting the length of one rectangle from the other:
13m - 9m = 4m
So the width of the shaded region is 4m.
Now we can find the area of the shaded region by multiplying the width by the length:
Area = 4m x 5m = 20 square meters
Finally, we can find the total area by subtracting the overlap from the sum of the two rectangle areas:
Total Area = (65 + 99) - 20 = 144 square meters
Therefore, the area of the shaded shape is 144 square meters.
Answer: 61m^2 would be the answer