To Graph the equation using the slope and the y-intercept is discussed below.
let us consider a equation of line slope intercept form is y= -1/2x - 1.
As, the general form of equation is
y= mx+ b
where m is the slope and b is y intercept
Here in the equation slope= -1/2 and intercept is -1.
To y intercept is value of y when x= 0 then the coordinate in the graph should be (0, -1).
Now, the slope show the change in y wrt to x here if 2 unit in x then 1 unit.
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Manuel bought a car for 65% of the original price of $7,000. How much did he pay for the car
Manuel bought a car for 65% (percentage) of the original price of $7,000, he must have paid $4,550 for the car.
What is the percentage?The percentage is a number or ratio that represents a fraction of a whole number or the sum of ratios.
The percentage is computed by dividing one number by another and multiplying the result by 100.
The original price of the car = $7,000
The discount factor = 65% (1 - 35%) or 0.65
The discounted price = $4,550 ($7,000 x 0.65)
Thus, by implication, for receiving a discount of 35% (100% - 65%), Manuel paid $4,550 for the car.
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Find the measure of the exterior angle 1
WILL mark as brainliest if you get correct
Answer: C: 144
Step-by-step explanation:
First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.
Next subtract this from 180 to find the exterior angle.
180- 36 = 144 degrees
thats the meaure of the exterior angle!
Answer:144
First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.
Next subtract this from 180 to find the exterior angle.
180- 36 = 144 degrees
Suppose f(x) =8^3x and g(x) =8^4x which of these function operations are correct select all that apply
Suppose [tex]f(x) =8^{3x[/tex] and [tex]g(x) =8^{4x[/tex], function operations that are correct include the following:
A. (f + g)(x) = [tex]8^{3x} + 8^{4x}[/tex]
B. (f × g)(x) = [tex]8^{7x}[/tex]
C. (f - g)(x) = [tex]8^{3x} - 8^{4x}[/tex]
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:
(f × g)(x) = [tex]8^{3x+ 4x}=8^{7x}[/tex]
(f ÷ g)(x) = [tex]8^{3x- 4x}=8^{-x}[/tex]
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Suppose we wish to factor 13b2 + 23b - 8 by grouping. What is the key number, ac?
The key number, ac, is -104.
What is key number ?
Key number is the product of the coefficients of the first and last terms. The right binomial factors for a quadratic expression can be determined with its assistance.
We must multiply the coefficient of the quadratic term by the constant term to obtain the key value, ac, which results in:
ac = 13(-8) = -104
Therefore, The key number, ac, is -104.
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The list represents the number of students who checked books out of the library in a 10-day period.
48, 63, 75, 40, 32, 52, 35, 68, 83, 40
Find the median and interpret its meaning as it relates to the number of students checking out books.
A. The median is 32, and it represents the difference in the lowest and highest number of students who checked books out.
B. The median is 83, and it represents the highest number of students who checked books out.
C. The median is 40, and it represents the most common number of books that students checked out.
D. The median is 50, and it represents the typical number of students who checked books out.
Solve the following for θ, in radians, where 0≤θ<2π.
4sin2(θ)−7sin(θ)−4=0
Select all that apply:
0.4
3.61
1.66
5.81
1.4
3.07
Answer:
3.615.81Step-by-step explanation:
You want solutions to the equation 4sin(θ)² -7sin(θ) -4 = 0 on the interval [0, 2π].
GraphA graph of the left-side expression shows it has a value of 0 at ...
θ ≈ 3.61 or 5.81.
CheckUsing a calculator to check the offered answer choices, we find the values of θ that best satisfy the equation are θ = 3.61 or 5.81. (For this purpose, ±0.02 ≈ 0.)
Algebraic solutionWe can let x = sin(θ). Then the equation is ...
4x² -7x -4 = 0
x² -7/4x = 1
(x -7/8)² = 1 +(7/8)² = 113/64
x = (7 ±√113)/8
The value (7+√113)/8 is greater than 1, so the only value of x that is useful here is x = (7-√113)/8. The angles in the desired range are ...
{π - arcsin((7 -√113)/8), 2π +arcsin((7 -√113)/8)} ≈ {3.61, 5.81} . . . radians
A foam cube, 5 in. in width has a mass of 62 g. What is the volume and density
The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, the volume of the foam cube is 5 in. x 5 in. x 5 in. = 125 cubic inches.
Density is calculated by dividing the mass of an object by its volume. In this case, the density of the foam cube is 62 g / 125 cubic inches = 0.496 g/cubic inch.
So, the volume of the foam cube is 125 cubic inches and its density is 0.496 g/cubic inch.
MARK ME BRAINLEISTI am unsure about how to do this problem, pictured below.
The time taken to reach a population of 500 is gotten from 500=50e^0.55t
What is the exponential growth?
Exponential growth is a process that increases quantity over time as in the bacterial culture here.
We know that from the question, we have;
P(t)=Poe^rt
P(t) = population at time t
Po= Initial population
r = growth rate
t = time taken
Then we have that;
150 = 50e^2r
3=e^2r
ln3 = 2r
r = ln3/2
r = 0.55
If the rate of growth is 0.55, then to reach a population of 500;
500=50e^0.55t
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A student is using wooden blocks to build two towers of different heights. All of the blocks are the same size and have a height of 3/4inch. The short tower is 5 blocks high and the tall tower is 9 blocks high. What is the difference in height, in inches, between the short tower and the tall tower?
The difference in height of short and tall tower is 3 inch.
We have,
length of each block = 3/4 inch
So, the length of 5 block
= 5 x 3/4
= 15/4 inch
and, the length of 9 blocks
= 9 x 3/4
= 27/4 inch
So, the difference in height of short and tall tower is
= 27/4 - 15/4
= 12/4
= 3 inch
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In circle R, find arc length of arc GH
The length of the arc GH is 13.3 cm
What is length of an arc?The length of an arc is the distance that runs through the curved line of the circle making up the arc.
The length of an arc is expressed as;
l = tetha/360 × 2πr
tetha = R
R = 360-( 170+80)
R = 360-250
R = 110°
l = 110/360 × 2 × 3.14 × 6.4
l = 4787.2/369
l = 13.3 cm (1.dp)
therefore the length of the arc GH is 13.3 cm
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Rachel works at a lemonade stand at the park on Monday she used 1 2/5 bags of lemons on Tuesday she use 1 1/4 times as many lemons as on Monday how many bags of lemons does Rachel have use on Tuesday
Answer:
1.75 Bags of Lemons
Step-by-step explanation:
1 2/5 = 1.4
1 1/4 = 1.25
1.4 * 1.25 = 1.75 Bags of Lemons
A company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year. If bonds are sold at par value, the issuer records the first semi-annual interest payment with a credit to in the amount of $ .
The first semi-annual interest payment with a credit to in the amount of $109.556.15
Given that, a company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year.
We need to find the amount,
[tex]A = P(1+r/2)^{2t}[/tex]
[tex]A = 50,000(1+0.08/2)^{2(10)[/tex]
[tex]A = 50,000(1.04)^{20[/tex]
[tex]A = 109,556.15[/tex]
Hence, the first semi-annual interest payment with a credit to in the amount of $109.556.15
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can you please help me with the answer?
The dimension is gioven as 69.26 feet
How to solve for the dimensionxy = 1836
This is the area
The cost of fence = 2x + 2y
cost of interior fencing
2x + 4y
C = 20.40(C1) + 12.00(C2)
We have to put the vakues in the formula above
C = 20.40(2x + 2y) + 12.00(2x + 4y)
= 40.80x + 40.80y + 24.00x + 48.00y
= 64.80x + 88.80y
from xy = 1836
y = 1836 / x
We have to put the value in C
C = 64.80x + 88.80(1836/x)
= 64.80x + 164236.80/x
Take the deriveative with respect to x
64.80 - 164236.80/x^2 = 0
x = √(164236.80/64.80)
= 69.26 feet
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A toy ball can be modeled as a sphere. Moussa measures its circumference as 56.3 cm. Find the ball’s volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
Answer:
3013.5 cm³
Step-by-step explanation:
Given a ball with a circumference of 56.3 cm, you want to know its volume.
RadiusThe formula for circumference is ...
C = 2πr
Solving for radius, we get ...
r = C/(2π) = 56.3 cm/(2π) ≈ 8.96042 cm
VolumeThe volume of a sphere is given by ...
V = 4/3πr³
V = 4/3π(8.96042 cm)³ ≈ 3013.5 cm³
The ball's volume is about 3013.5 cubic centimeters.
__
Additional comment
Alternatively, we could use the formula ...
V = C³/(6π²)
to get the same result.
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What is the sum of 3.0 x 4.1 x 5.5
Answer: 67.65
Step-by-step explanation:
Multiply 3.0*4.1 and you get 12.3
Then take that sum and multiply it by the 5.5
So 12.3*5.5=67.65
Question 4
A is at -6 and B is at 9. Find the point, T, so that T is three-fifths of the distance from A to B.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2 3 4 5 6 7 8 9 10
The location of point T on the number line is 3
Calculating the location of point TFrom the question, we have the following parameters that can be used in our computation:
A = -6
B = 9
T = three-fifths of the distance from A to B.
Using the above as a guide, we have the following:
T = A + 3/5 *(B - A)
Substitute the known values in the above equation, so, we have the following representation
T = -6 + 3/5 *(9 + 6)
Evaluate
T = 3
Hence, the location is 3
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I scored 414/800 marks convert into Gpa
Do the following using Matlab: Generate 10 numbers between 1 and 6, calculate the mean. Generate 100 numbers between 1 and 6. calculate the mean. Generate 1000 numbers between 1 and 6, calculate the mean. There is a command in Matlab to generate numbers. Do not include the numbers when you submit the project. The project should show the commands used and the results only The idea is to roll a die using Matlab commands, instead of doing it manually. Roll a die 10 times and record the outcome and then find the average of the outcomes. Then compare the means for the cases of 10, 100 & 1000. On page 2 of lecture 10, we found that the mean of rolling a die to be 3.5. Therefore, your answer will be close to 3.5 every time you repeat the experiment for larger numbers.
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
We have,
To generate numbers between 1 and 6 in Matlab, we can use the "randi" command.
To generate 10 numbers, we can use:
```matlab
numbers10 = randi([1, 6], [1, 10]);
mean10 = mean(numbers10);
disp(mean10);
```
To generate 100 numbers, we can use:
```matlab
numbers100 = randi([1, 6], [1, 100]);
mean100 = mean(numbers100);
disp(mean100);
```
To generate 1000 numbers, we can use:
```matlab
numbers1000 = randi([1, 6], [1, 1000]);
mean1000 = mean(numbers1000);
disp(mean1000);
```
After running these commands, we will get the means for generating 10, 100, and 1000 numbers between 1 and 6.
As mentioned in the question, the mean of rolling a die is 3.5.
Therefore,
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
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solve the inequality and graph the solution on the line provided.
5x - 15 < 10
Answer: x < 5, see attached for the graph.
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
5x - 15 < 10
Add 15 to both sides of the equation:
5x < 25
Divide both sides of the equation by 5:
x < 5
For the graph, we will use an open circle because this is only less than (<), not less than and equal to.
Then, since x is all values less than 5, we will shade our arrow to the left of 5. See attached.
How many cubic meters of dirt are there in a pile conical shape 9m in diameter and 4m high
The Volume of Cone is 84.8 m³.
We have,
d = 9 m
r= 4.5 m
H = 4 m
So, Volume of Cone
= 1/3 πr²h
= 1/3 (3.14) (4.5)² (4)
= 1/3 (3.14) (20.25) (4)
= 84.8 m³
Thus, the volume is 84.8 m³.
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answer:
3t^2i + 2tj is the correct answer.
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :) (Do the one highlighted)
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions.
Which of the following is not an exponential function?To determine which option is not an exponential function, we will apply general equation of an exponential function.
f(x) = aⁿ
where;
a is the base of the functionn is the exponentSo from the given options;
(³/₅)ˣ is an exponential function, because ³/₅ is the base while x is the exponent.
4ˣ is an exponential function, because 4 is the base while x is the exponent.
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions, so there is no one base.
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Which linear equation shows a proportional relationship?
y = 2x
y equals one third times x plus 2
y equals negative two fifths times x minus 1
y = 1
A linear equation which shows a proportional relationship include the following: A. y = 2x.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 2/1 = 4/2 = 6/3 = 8/4
Constant of proportionality, k = 2.
Therefore, the required linear equation is given by;
y = kx
y = 2x
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Coordinate Proof!
Given: Isosceles ∆ABC; M is the midpoint of AC-.
Prove: area ∆ABM = area ∆CBM
Proof
AM = √(x₂ − x₁)² + (y₂-y₁)²
= √(4-0)² + (0-0)²
= √4² = _
BM = √(x2-x₁)² + (1₂-y₁)²
= √(4-4)² + (6-0)2
= √6² = _
AM- ≅ CM- ____
AM = CM ____
CM = 4. Subst.
area ∆ABM
A = 1/2 bh
= 1/2 ___
= ___
area ∆CBM
A = 1/2 bh
= 1/2 ___
= ___
Therefore: Area ∆ABM = area ∆CBM by ___
The completed calculation with regards to the area of the congruent triangles can be presented as follows;
The distance formula indicates;
AM = √((x₂ - x₁)² + (y₂ - y₁)²)
Therefore, we get;
AM = √((4 - 0)² + (0 - 0)²) = √(4²)
AM = √(4²) = 4
BM = √((x₂ - x₁)² + (y₂ - y₁)²)
BM = √((4 - 4)² + (6 - 0)²) = √(6²)
BM = √(6²) = 6
AM ≅ CM Definition of the midpoint of AC
AM = CM Definition of congruent segments
CM = 4 Substitution property
Area ΔABM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Area ΔCBM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Therefore Area ΔABM = area ΔCBM by congruence
What are congruent triangles?Triangles are congruent if they have the same size and shape.
The details of the reasons for the calculation steps and values are presented as follows;
Definition of midpoint of a segment
The midpoint of a line segment is the point that divides the segment into two parts of the same length
Definition of congruence?
Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement
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Please help asap need it please
Answer:
Step-by-step explanation:
i think that you times the numbers
I needed help with this one can some help me
A graph of quadrilateral M'N'O'P' after a vertical translation is shown below.
What is a translation?In Mathematics and Geometry, the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
By translating the pre-image of quadrilateral MNOP vertically downward 4 units, the coordinates of quadrilateral M'N'O'P' include the following:
(x, y) → (x, y - 4)
M (-2, 5) → (-2, 5 - 4) = M' (-2, 1).
N (-3, 2) → (-3, 2 - 4) = N' (-3, -2).
O (-5, 2) → (-5, 2 - 4) = O' (-5, -2).
P (-6, 5) → (-6, 5 - 4) = P' (-6, 1).
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A curve, described by x2 + y2 + 6y = 0, has a point A at (−3, −3) on the curve.
Part A: What are the polar coordinates of A? Give an exact answer.
Part B: What is the polar form of the equation? What type of polar curve is this?
Part C: What is the directed distance when theta equals 4 pi over 3 question mark Give an exact answer.
a) The polar coordinates of point A are (√(18), π/4).
b) The curve is a circle centered at the origin with radius 6.
c) The directed distance is the value of r, which is 6 √(3).
To find the polar coordinates of point A on the curve, we need to convert the point from Cartesian to polar coordinates. The conversion formula is:
r = √(x² + y²)
θ = arctan(y/x)
Using the values of point A, we have:
r = √((-3)² + (-3)²) = √(18)
θ = arctan((-3)/(-3)) = arctan(1) = π/4
To find the polar form of the equation x² + y² + 6y = 0, we need to convert it from Cartesian to polar coordinates. The conversion formulae are:
x = r cos(θ)
y = r sin(θ)
Using these formulae, we can rewrite the equation as:
r² cos²(θ) + r² sin²(θ) + 6r sin(θ) = 0
Simplifying this equation, we get:
r = -6 sin(θ) / (1 - cos²(θ))
To find the directed distance when θ equals 4 π over 3, we need to substitute this value of θ into the polar equation we found in Part B. Doing so, we get:
r = -6 sin(4 π/3) / (1 - cos²(4 π/3))
r = -6(-√(3)/2) / (1 - (-1/2)²)
r = 6 √(3)
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Please help me solve question 19!
Answer:
Step-by-step explanation:
Michael solved the given problem. Determine whether Michael's work is correct. If not, which step is incorrect?
Responses
A Step 1
B Step 4
C Step 3
D Step 2
Based on the information, the incorrect step is C. step 3.
How to calculate the valueStep 1: 4(3x – 3y = 6) –3(4x – 7y = 2)
Step 2: 12x – 12y = 24 –12x + 21y = –6
Step 3: 9y = 18
Step 4: y equals 1 over 2
Correct calculation:
3x – 3y = 6 (1)
4x – 7y = 2 (2)
make x the subject in ....(1)
3x - 3y = 6
3x = 6 + 3y
x = 6 + 3y/ 3
x = 2 + y
substitute x = 2 + y into (2)
4x – 7y = 2 (2)
4(2 + y) - 7y = 2
8 + 4y - 7y = 2
8 - 3y = 2
8 + 2 = -3y
10 = -3y
y = 10/-3
y = -3 1/3
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Michael solved the system of linear equations and provided the solution. 3x – 3y = 6 4x – 7y = 2 Step 1 4(3x – 3y = 6) –3(4x – 7y = 2) Step 2 12x – 12y = 24 –12x + 21y = –6 Step 3 9y = 18 Step 4 y equals 1 over 2 In which step did Michael show his first error? Step 2 Step 3 Step 4
Andretti Company has a single product called a Dak. The company normally produces and sells 82,000 Daks each year at a selling price of $62 per unit. The company’s nit costs at this level of activity are given below: Direct materials $ 7.50 Direct labor 9.00 Variable manufacturing overhead 2.40 Fixed manufacturing overhead 7.00 ($574,000 total) Variable selling expenses 3.70 Fixed selling expenses 3.50 ($287,000 total) Total cost per unit $ 33.10
There is a financial advantage of $ 1,187,520.
Incremental Costs and Revenues will be as follows
Increment in sales = 82,000 units × 40% = 32,800 units
and, Selling Price
= (32,800 units × $62 per unit)
= $ 2,033,600
Direct materials
= $ 7.50 × 32,800 units
= 246,000
Direct labor
= $ 9.00 × 32800
= $295,200
and, Variable manufacturing overhead
= 2.40 x 32800
= $78, 720
So, the contribution is
= 2,033,600 - (246000 + 285200 + 78720)
= 1,423,680
Now, Variable selling expenses
= 32800 x 3.7
= 121,360
and, Fixed Selling Expenses
= 32800 x 3.5
= 114,800
So, Net income = 1, 187, 520
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