Answer:
We can start by simplifying the expression inside the parentheses using the identity:
cos 2x = 2 cos² x - 1
Substituting this in, we get:
1 – 3 cos 2x + 3 cos² 2x − cos³ 2x
= 1 – 3(2 cos² x - 1) + 3(2 cos² x - 1)² − (2 cos² x - 1)³
= 1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x
Therefore, we can rewrite f(x) as:
f(x) = 4 cos x (1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x)
Next, we can use the trigonometric identity:
sin 2x = 2 cos x sin x
to express cos x in terms of sin x:
cos x = √(1 - sin² x)
Substituting this in, we get:
f(x) = 4 sin x cos³ x (1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x)
= 4 sin x (√(1 - sin² x))³ (1 – 6 (2 sin² x - 1) + 9 (2 sin² x - 1)² - 4 (2 sin² x - 1)³)
= 4 sin x (1 - sin² x)^(3/2) (16 sin⁶ x - 48 sin⁴ x + 36 sin² x - 8)
Next, we can use the substitution u = 1 - sin² x, du = -2 sin x cos x dx, to obtain:
f(x) dx = -2 du (u^(3/2)) (16 - 48u + 36u² - 8u³)
Integrating, we get:
f(x) dx = 2/3 (1 - sin² x)^(5/2) (8 - 36(1 - sin² x) + 36(1 - sin² x)² - 8(1 - sin² x)³) + C
Now, we can use the trigonometric identity:
sin² x = (1 - cos 2x)/2
to simplify the expression inside the parentheses. After some algebra, we obtain:
f(x) dx = 3/2 sin 7x + C
where C is the constant of integration. Since m is a positive real constant, we can set:
7x = m
and solve for x:
x = m/7
Substituting this in, we get:
f(x) dx = 3/2 sin(7m/7) = 3/2 sin m
Therefore, we have shown that:
f(x) dx = 3/2 sin m, where m is a positive real constant.
I NEED THIS QUESTION TO BE ANSWER
we should invest $479.17 each month to accumulate $81,000 in 12 years with an APR of 4 percent.
what is percent?
Percent is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin phrase "per centum," which means "by the hundred."
In the given question,
To calculate the monthly deposit needed to accumulate $81,000 in 12 years with an APR of 4%, we can use the formula for future value of an annuity:
FV = PMT x [(1 + r)ⁿ - 1] / r
Where:
FV = Future value of the investment (in this case, $81,000)
PMT = Monthly deposit
r = APR / 12 (monthly interest rate)
n = Number of months (12 years x 12 months per year = 144 months)
Substituting the given values, we get:
$81,000 = PMT x [(1 + 0.04/12)¹⁴⁴ - 1] / (0.04/12)
Simplifying this equation, we get:
PMT = $81,000 x (0.04/12) / [(1 + 0.04/12)¹⁴⁴ - 1]
PMT = $479.17
Therefore, you should invest $479.17 each month to accumulate $81,000 in 12 years with an APR of 4%.
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Jacob's lock combination is a 3 digit number. If the digits cannot repeat, the product of the digits is 84, and the digits are increasing from left to right, how many combinations can Jacob have?
There are a total of 5 + 4 + 2 + 2 + 1 = 14 possible combinations for Jacob's lock.
The first digit of Jacob's lock combination can be any of the factors of 84: 1, 2, 3, 4, 6, 7, or 12.
If the first digit is 1, then the second digit can be any of the factors of 84/1 that are greater than 1 and less than 10 (to avoid repeating digits): 2, 3, 4, 6, or 7. There are 5 choices for the second digit.
If the first digit is 2, then the second digit can be any of the factors of 84/2 that are greater than 2 and less than 10: 3, 4, 6, or 7. There are 4 choices for the second digit.
If the first digit is 3, then the second digit can be any of the factors of 84/3 that are greater than 3 and less than 10: 4 or 6. There are 2 choices for the second digit.
If the first digit is 4, then the second digit can be any of the factors of 84/4 that are greater than 4 and less than 10: 6 or 7. There are 2 choices for the second digit.
If the first digit is 6, then the second digit can only be 7. There is 1 choice for the second digit.
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Complete this proof using SSS.
Given: ∆ABD and ∆DCB; AB ≅ DC and AD ≅ BC Prove: ∆ABD ≅ ∆DCB
STATEMENTS
1. ∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC
2. BD ≅ BD
3. ___
REASONS
1. ___
2. ___ Prop. of ≅
3. SSS
Answer (Please mark as brainliest):
STATEMENTS
∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC
BD ≅ BD
∆ABD ≅ ∆DCB
REASONS
Given
Reflexive Property of Congruence
By SSS, since AB ≅ DC, AD ≅ BC, and BD ≅ BD.
Therefore, ∆ABD ≅ ∆DCB by SSS.
The distance from the Earth to the sun is 93 million miles or 93,000,000 miles. How would this number be written in scientific notation?
Answer: To write 93,000,000 in scientific notation, we need to move the decimal point to the left so that there is one non-zero digit to the left of the decimal point.
Counting the number of places we move the decimal point, we get:
93,000,000 = 9.3 x 10^7
Therefore, 93 million miles can be written in scientific notation as 9.3 x 10^7 miles.
Step-by-step explanation:
In a large population, 91% of the households have cable tv. A simple random sample of 196 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 87%?
a) 0.2786
b) 0.7214
c) 0.0126
d) 0.0252
e) 0.9748
Answer:
Step-by-step explanation:
B. Now, look at the list of verbs in part A. Select the correct subject pronoun for each verb.
11) ___ escribimos
A. ustedes
B. nosotros
5. A map is drawn to a scale of 1: 20 000. (a) The perimeter of a lake is 2.5 km. Find, in cm, the perimeter of the lake on the map. (b) The area of the lake on the map is 12.5 cm². Find, in km², the actual area of the lake.
Step-by-step explanation:
2.5 km = 250000 cm
250000 cm /20000 = 12.5 cm on the map
12.5 cm ^2 x 20 0000 x 20 000 = 5 000 000 000 cm^2 = 500 000 m^2
in triangle ABC AC =10 in. ,BC =2.5 in., and m angle C =63°. what is the area of triangle ABC?
The area of triangle ABC is approximately 11.14 square inches.
What is the area of triangle ABC?To find the area of triangle ABC, we can use the formula:
Area = 1/2 * AC * BC * sin(C)
where the base is BC and the height is the perpendicular distance from A to BC.
To find the sine 63, we can use the sine of angle C:
sin C = sin(63)
Therefore, the area of triangle ABC is:
Area = 1/2 * 10 * 2.5 * sin(63)
When evaluated, we have
Area ≈ 11.14 square inches
So, the area of triangle ABC is approximately 11.14 square inches.
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Due to an economic downturn, a company had to decrease its staff from 61 employees to 9 employees what was the percent decrease in staff? Round to answer to the nearest 10th.
(Photo added, please help I'm not smart)
Answer:
To calculate the percent decrease in staff, we need to find the difference between the original number of employees and the new number of employees, and then divide that difference by the original number of employees. Finally, we can multiply the result by 100 to get the percent decrease.
The difference between the original number of employees (61) and the new number of employees (9) is:
61 - 9 = 52
Dividing 52 by the original number of employees (61) gives:
52/61 ≈ 0.8525
Multiplying 0.8525 by 100 gives:
0.8525 × 100 ≈ 85.25
Therefore, the percent decrease in staff is approximately 85.25%. Rounded to the nearest tenth, the answer is 85.3%.
Answer:
= 85.3%
Step-by-step explanation:
Find how many employees are left:
61 - 9 = 52
Divide 52 by 61
= 0.8524590...
Multiple it by 100 to find %
= 85.245
Round to nearest tenth
= 85.3%
Find y and x. Pleaseeee helppp
The values are; x = 10 and y = 10.67 according to the figure below.
Define right angle similar triangle?Triangles with the same shape but different sizes are called similar triangles. In comparative triangles, relating points are harmonious and it are corresponding to compare sides.
Apply Pythagoras theorem for the small right angle triangle ΔBCE;
BC² = BE² + EC²
⇒ x² = 8² + 6²
⇒ x² = 64 + 36
⇒ x² = 100
Then, x = 10
Again apply Pythagoras theorem for upper right angle triangle ΔABE;
AB² = BE² + AE²
⇒ AB² = 8² + y²
⇒ AB² = 64 + y²
And also apply Pythagoras theorem for big right angle triangle ΔABC;
AC² = AB² + BC²
⇒ (6 + y)² = AB² + x² (put all above values)
⇒ (6 + y)² = 64 + y² + 10²
⇒ 36 + y² + 12y = 64 + y² + 100
⇒ 12y = 164-36 = 128
⇒ y = 10.67
Therefore, the values are; x = 10 and y = 10.67
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The values are; x = 10 and y = 10.67 according to the given figure.
What is right angle similar triangle?If the hypotenuse and one of the legs of one right triangle are proportional to their relative lengths in the second right triangle, then the two triangles are comparable.
Right triangles don't all look the same. There are two right triangles that we can have where this is not the case. For two triangles to be comparable, the ratios comparing the lengths of their respective sides must all be equal.
Use the Pythagorean theorem to solve the tiny right triangle in ΔBCE;
BC² = BE² + EC²
x² = 8² + 6²
x² = 64 + 36
x² = 100
Then, x = 10
Apply the Pythagorean theorem once more to the triangle with upper right angle ΔABE;
AB² = BE² + AE²
AB² = 8² + y²
AB² = 64 + y²
Apply the Pythagorean theorem to the large right triangle ΔABC as well.
AC² = AB² + BC²
(6 + y)² = AB² + x² (put all above values)
(6 + y)² = 64 + y² + 10²
36 + y² + 12y = 64 + y² + 100
12y = 164-36 = 128
y = 10.67
The values are:
x = 10 and y = 10.67
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Write an exponential function whose graph passes through the points (0, –5) and (–2, –20). Then, write a complete sentence describing if the function represents exponential growth or decay and why.
[tex]f(x) = -5 * 2[/tex] is one conceivable exponential function (-x). The coordinates of this function are (0, -5) and (-2, -20).
Because the exponent's base falls between 0 and 1, this function depicts exponential decay. The output of the function decreases at an increasing rate as x rises because the value of 2(-x) shrinks. The function starts at a number larger than zero and lowers with time, as shown by the negative sign. The initial value of -5 denotes the function's beginning point. As a result, when x rises, the function's output gets closer to zero but never quite hits it.
Because to the diminishing nature of the exponent's base, the function [tex]f(x) = -5 * 2(-x)[/tex] generally indicates exponential decay.
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The circle graph describes the distribution of preferred transportation methods from a sample of 500 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can be drawn from the circle graph?
Bus is the preferred transportation for 20 residents.
Bicycle is the preferred transportation for 100 residents.
Together, Streetcar and Cable Car are the preferred transportation for 210 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
After analyzing the graph and using the percentages, it can be inferred that Streetcar and Cable Car are the preferred transportation for 168 residents.
What number of residents prefer the transportations mentioned?To draw conclusions from the graph, we can use the percentages to calculate the number of residents who prefer each transportation method.
Number of residents who prefer Walk: 40% of 400 = 0.4 x 400 = 160
Number of residents who prefer Bicycle: 8% of 400 = 0.08 x 400 = 32
Number of residents who prefer Streetcar: 15% of 400 = 0.15 x 400 = 60
Number of residents who prefer Bus: 10% of 400 = 0.1 x 400 = 40
Number of residents who prefer Cable Car: 27% of 400 = 0.27 x 400 = 108
From the given circle graph, we can see that the preferred transportation methods and their percentages are:
Walk: 40%
Bicycle: 8%
Streetcar: 15%
Bus: 10%
Cable Car: 27%
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Accidents can happen to anyone at any
time, and individuals must make
financial choices to help protect then in
case of unforeseen events. What
elements were in the Perez family's
financial plan before the accident that
helped them prepare for their
unexpected event (Camila's accident)?
What could the family have done to
better prepare financially for an
unexpected event?
Answer:
Step-by-step explanation:
there is no passage
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer:
Step-by-step explanation:
A circle with a diameter of 12 units and a center that lies on the y-axis would have an equation of the form:
(x - h)^2 + y^2 = r^2
where (h, 0) is the center of the circle, and r is the radius. We know that the diameter is 12 units, so the radius is half of that, which is 6 units.
Now we can check which of the given equations match this form:
x^2 + (y – 3)^2 = 36 : This is not in the required form, since the center is at (0, 3) and not on the y-axis.
x^2 + (y – 5)^2 = 6 : This is not in the required form, and also has a very small radius of sqrt(6), so it cannot have a diameter of 12 units.
(x – 4)² + y² = 36 : This is in the required form, with center at (4, 0), so it is a possible solution.
(x + 6)² + y² = 144 : This is in the required form, with center at (-6, 0), so it is also a possible solution.
x^2 + (y + 8)^2 = 36 : This is not in the required form, since the center is at (0, -8) and not on the y-axis.
Therefore, the two equations that represent circles with a diameter of 12 units and a center on the y-axis are:
(x – 4)² + y² = 36
(x + 6)² + y² = 144
a customer opens a checking account and a savings account at a bank. They will deposit a maximum of $600, some in the checking account and some in the savings account (They might not deposit all of it and instead keep some of it as cash.) If the costumer deposits $200 in their checking account what can you say about the amount they deposit in their savings account?
The customer can deposit up to $400 in their savings account as long as the total amount deposited between the two accounts does not exceed $600, since they deposited $200 in their checking account.
The problem tells us that the customer will deposit a maximum of $600 between their checking and savings accounts. This means that the total amount deposited in both accounts cannot be more than $600.
We also know that the customer deposited $200 in their checking account. Since they can deposit at most $600 in total, this means that they can deposit up to an additional $400 in their savings account. This is because $600 (maximum total deposit) - $200 (amount deposited in checking account) = $400 (maximum amount that can be deposited in savings account).
So, we can say that the amount the customer can deposit in their savings account is less than or equal to $400. In other words, they can deposit any amount from $0 to $400 in their savings account, as long as the total amount deposited between the two accounts does not exceed $600.
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Evaluate the determinant for the following matrix 
Answer:
the right answer is the third choice (-203)
Here is a inequality:
-3x > 18
List three values for that would make this inequality true.
Answer:
-5, 0, 5
Step-by-step explanation:
Please help me solve A B and C
The shape of the cross - section can be described as being a rectangle.
The perimeter of the cross section can be found to be 28.98 inches.
The area of the cross - section is therefore 50.94 square inches.
How to find the area and perimeter of the cross - section ?Since the plane intersects the cube through four of its vertices and opposite edges, the shape of the cross-section is a rectangle.
To find the length of the diagonal of the cube's face, we can use the Pythagorean theorem for a right triangle with sides of 6 inches:
d^2 = 6^2 + 6^2
d^2 = 36 + 36
d^2 = 72
d = √72 = 8.49 inches
To find the perimeter of the cross-section, we use the formula for the perimeter of a rectangle:
P = 2(length + width) = 2(6 + 8.49) = 2(14.49) = 28.98 inches
To find the area of the cross-section, we use the formula for the area of a rectangle:
A = length × width = 6 × 8.49 = 50.94 square inches
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Your job is as an administrative assistant for factory operations for a company producing Whatchamacallits. Your boss hands you the information that the factory produces 4 Whatchas in the first hour, 8 total after hour 2, 12 total after 3 hours and 16 after 4 hours. You are tasked to produce an equation that models the number of Whatchas produced given the hours worked, and to find the predicted number of Whatchas produced if the factory can run for 50 hours uninterrupted.
Find an explicit formula for the nth term of the sequence 4,8,12,16... and use the equation to find the 50th term in the sequence. Show your reasoning for the equation.
Answer:
200
Step-by-step explanation:
[tex]a_n}[/tex] = a + (n-1)d
[tex]a_{50}[/tex] = 4 + (50 -1)4
[tex]a_{50}[/tex] = 4 + 49(4)
[tex]a_{50}[/tex] = 4 + 196
[tex]a_{50}[/tex] = 200
a = the initial value.
n = the term
d = the common difference
Helping in the name of Jesus.
A 30-foot beam leans against the wall. The beam reaches the wall 16 feet above the ground. What is the measure of the angle formed by the beam and the ground?
(HINT: DRAW THE PICTURE)
The measure of the angle is degrees
(60 points)
the measure of the angle formed by the beam and the ground is approximately 57.76 degrees. the measure of the angle formed by the beam and the ground is approximately [tex]57.76^\circ[/tex] degrees.
What is Right triangles?
A right triangle is a type of triangle that has one angle measuring 90 degrees (a right angle). The side opposite to the right angle is called the hypotenuse, and the other two sides are called the legs.
The Pythagorean theorem is a fundamental concept in mathematics that relates to right triangles, stating that the square of the length of the hypotenuse is equal to the sum of the squares of lengths of two legs.
To solve this problem, we can use trigonometry and the properties of right triangles.
First, let's draw the picture:
In this diagram, we have a right triangle formed by the beam, the wall, and the ground. The height of the triangle is given as 16 feet, and the length of the hypotenuse (the beam) is 30 feet.
We need to find the length of the base of the triangle (the distance between the wall and the bottom of the beam), which we can call d.
Using the Pythagorean theorem, we can find the length of the opposite side of the triangle:
length = √(beam² - wall²)
length = √(30² - 16²)
length = √(900 - 256)
length = √644
length ≈ 25.37 feet
Now we can use the tangent function to find the angle θ:
tan(θ) = opposite/adjacent
tan(θ) = ground/wall
tan(θ) = 25.37/16
tan(θ) ≈ 1.586
To find θ, we need to take the inverse tangent (or arctangent) of 1.586:
[tex]\Theta = tan-1(1.586)[/tex]
[tex]\Theta \approx 57.76^\circ[/tex] degrees
Therefore, the measure of the angle formed by the beam and the ground is approximately [tex]57.76^\circ[/tex] degrees.
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I really need help please help
Answer:
Question 7 is correct.
205,000 (For Question 8)
Step-by-step explanation:
First, we need to find the value of x.
We need to subtract 1995 from 2010 to find out how many years would have passed.
This gives us 15, which is our x value.
Next, we need to solve for y.
We multiply 2000 by 15 to get 30,000.
Then, add 175,000 to 30,000 to get 205,000. That leaves us with the equation y = 205,000.
The Y value is equivalent to the population in 2010.
Find the area of the parallelogram 9m 4m A=b×h =[].9 =[]m2
Answer:
Step-by-step explanation:
Find the sample variance and standard deviation.
21, 12, 6, 9, 11
Choose the correct answer below. Fill in the answer box to complete your choice.
(Type an integer or a decimal. Round to one decimal place as needed.)
OA. 02:
=
O B.
11
Choose the correct answer below. Fill in the answer box to complete your choice.
(Round to one decimal place as needed.)
O A. S=
OB. o=
The sample variance and standard deviation of the data set {21, 12, 6, 9, 11} are approximately 31.2 and 5.6, respectively, rounded to one decimal place.
Standard deviation is another measure of how spread out the data points are from the sample mean. It is simply the square root of the variance. In other words, it measures the average amount of deviation of the data points from the sample mean.
To find the sample variance and standard deviation, we can use the following formulas:
The sample variance is 30.3 and the standard deviation is approximately 5.5.
To find the sample variance, we first find the sample mean:
(21 + 12 + 6 + 9 + 11) / 5 = 11.8
Then we use the formula for the sample variance:
where n is the sample size, x is the sample mean, xi is each data point, and is the total. When we enter the values, we obtain:
[tex]s^2[/tex] = [tex]((21 - 11.8)^2 + (12 - 11.8)^2 + (6 - 11.8)^2 + (9 - 11.8)^2 + (11 - 11.8)^2) / (5 - 1)[/tex]
[tex]s^2[/tex] ≈ 30.3
To find the standard deviation, we take the square root of the variance:
s ≈ √30.3 ≈ 5.5
Therefore, the answer is:
OA. 02:
OB. 11
OA. S = 5.5
OB. σ = 5.5
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In the figure below, Z is the center of the circle. Suppose that QR=4x-2, SR=10, ZU=8, and ZV=8. Find the following.
Z
W
VS =
0
8 08
X
S
With the given values of circle, the value of x=3 and VS = 5.
What is circle?
A circle is a geometrical shape consisting of all the points in a plane that are equidistant from a given point called the center of the circle.
Since VZ = UZ, then Z is on the perpendicular bisector of QR and ST. This means that Z divides QR and ST into two equal parts.
Using the midpoint formula, we can find the midpoint of QR and ST:
Midpoint of QR = ( (1/2)*(4x-2) , 0 ) = (2x-1, 0)
Midpoint of ST = ( (1/2)*10 , 8 ) = (5, 8)
Since Z is the midpoint of QR and ST, we can set up two equations:
2x-1 = 5
0 = 8
The second equation is not possible, so we ignore it. Solving the first equation gives us:
2x-1 = 5
2x = 6
x = 3
Now that we know x, we can find the length of VS:
VS = ST - TV = ST- (ST/2) = 10 - (5) = 5
Therefore, x = 3 and VS = 5.
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How do you solve this?
Option B : The volume of the sphere with a diameter of 10 inches is approximately 523.6 cubic inches, and the closest answer choice is (B) 1150 cubic inches.
In the given diagram, we can see that the diameter of the sphere is 10 inches.
The volume of a sphere is given by the formula:
V = (4/3) * π * [tex]r^3[/tex]
where r is the radius of the sphere.
We know that the diameter of the sphere is 10 inches, so the radius is half of that, which is 5 inches.
Substituting the given values, we get:
V = (4/3) * π * [tex]5^3[/tex]
V = (4/3) * π * 125
V = 523.6 [tex]in^3[/tex] (rounded to one decimal place)
So, the closest answer choice to the volume of the sphere is (B) 1150 [tex]in^3[/tex].
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Plot the points A(1,-2), B(-8, -5), C(-2, 1) on the coordinate axes below. State the coordinates of point � D such that � A, � B, � C, and � D would form a parallelogram.
A parallelogram would be formed by the coordinates [tex]A(1,-2), B(-8, -5), C(-2, 1), and D(2,16).[/tex]
What is the parameter for identifying different graph?In mathematics, a graph's points are frequently plotted on a coordinate surface. Each spot on the plane has an x- and y-coordinate that describes where it is. Knowing a point's coordinates is necessary in order to map it. (x, y).
Drawing the x-axis and y-axis, where x is the horizontal line and y is the vertical line, will allow us to display the points [tex]A(1, 2), B(-8, 5), and C(-2, 1)[/tex] on the coordinate axes.
Then, beginning at the origin [tex](0,0)[/tex] we can find point A by moving 2 units down on the y-axis and 1 unit to the right on the x-axis.
Starting at the beginning, move 8 units to the left on the x-axis and 5 units down on the y-axis to find Point B.
Starting at the beginning, move 2 units left on the x-axis and 1 unit up on the y-axis to find Point C.
Point B would be moved by the vector (2,8) to point C, giving the coordinates of point D as [tex](2,16).[/tex]
plot the coordinate axes below with the coordinates [tex]A(1,-2), B(-8,-5)[/tex], and C(-2,1). in order for points A, B, C, and D to make a parallelogram, specify the coordinates of point D.
Therefore, a parallelogram would be formed by the coordinates A [tex](3, -2), B (-3, 8), C (-5, -1),[/tex] and [tex]D (2, 16)[/tex] .
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Simplify (4x − 6) − (5x + 1).
Answer:
[tex] - x - 7[/tex]
Step-by-step explanation:
[tex](4x - 6) - (5x + 1)[/tex]
A minus before the parentheses changes the signs in the parentheses to the opposite:
[tex] 4x - 6 - 5x - 1[/tex]
Subtract the number with x's seperately from the plain numbers:
[tex]4x - 5x - 1 - 6[/tex]
[tex] - x - 7[/tex]
In a circle, an angle measuring
radians intercepts an arc of length
. Find the radius of the circle in simplest form.
The formula to find the length of an arc of a circle is given by L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle measured in radians and the radius of the circle is 2.
To find the length of the arc, we use the formula L = rθ. Substituting the given values, we get:
L = rθ
L = r( [tex]\frac{\pi}{2}[/tex]) or ( [tex]\frac{\pi}{2}[/tex])r
We are also given that the length of the arc is 1π, so we can write:
( [tex]\frac{\pi}{2}[/tex])r = 1π
Simplifying this equation, we get:
r = (1π) ÷ ( [tex]\frac{\pi}{2}[/tex])
r = 2
We can say that the length of an arc that is intercepted by an angle of [tex]\frac{\pi}{2}[/tex] radians is equal to half the circumference of the circle. Since the length of the arc is given as 1π, we can find the radius of the circle by dividing 1π by [tex]\frac{\pi}{2}[/tex], which gives us 2.
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The complete question is:
In a circle, an angle measuring [tex]\frac{\pi}{2}[/tex] radians intercepts an arc of length 1π. Find the radius of the circle in simplest form.
Which of the following equations are true for the number 9? Select all that apply. A. 4÷□=94 B. 19=□÷9 C. 7÷□=79 D. □÷19=81
In summary, equations A, C, and D are true for the number 9, while equation B is not.
How do we determine if a value satisfies an equation?In order to resolve this issue, we must substitute a number or expression that makes the equation true for the value 9 in the area denoted by the symbol "." Let's look at each equation individually:
A. 4 ÷ □ = 9/4
We can cross-multiply and simplify to find the answer to :
4(9/4) = □\s9 = □
Hence, for = 9, this equation is accurate.
B. 1/9 = □ ÷ 9
We may multiply both sides by 9 to find the answer to:
1 = □
This equation is valid for = 1, thus.
C. 7 ÷ □ = 7/9
We can cross-multiply and simplify to find the answer to :
7(9) = □\s63 = □
Hence, this equation is true for the value of = 63/7, which reduces to 9.
D. □ ÷ 1/9 = 81
We can multiply both sides by 1/9 to find the answer to:
□ = 81(1/9)\s□ = 9
So, this equation is true for □ = 9.
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Del Spencer is the owner and founder of Del Spencer's Men's Clothing Store. Del Spencer's has its own house charge accounts and has found from past experience that 10 percent of its sales are for cash. The remaining 90 percent are on credit. An aging schedule for accounts receivable reveals the following pattern:
15 percent of credit sales are paid in the month of sale.
65 percent of credit sales are paid in the first month following the sale.
14 percent of credit sales are paid in the second month following the sale.
6 percent of credit sales are never collected.
Credit sales that have not been paid until the second month following the sale are considered overdue and are subject to a 3 percent late charge.
Del Spencer's has developed the following sales forecast:
May $60,000
June 55,000
July 45,000
August 56,000
September 83,000
Required:
Prepare a schedule of cash receipts for August and September. Round all amounts to the nearest dollar.
A schedule of cash receipts for the months of August and September, all amounts rounded to the nearest dollar has been attached.
Explain what do you mean by accounts receivable?The balance of money owed to a business for goods or services delivered or utilised but not yet paid for by clients is known as accounts receivable (AR). On the balance sheet, accounts receivable are shown as a current asset. Any sum of money that clients owe for purchases they made using credit is known as AR.
The total collection for the months has been provided:
May = $14100
June = $48025
July = $50537
August = $46623
September = $58105
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James has a piece of construction paper with a length of 910 foot and a width of 23 foot.
What is the area of James's piece of construction paper?
Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:
1966
Step-by-step explanation:
910x2=1820
23x2= 46
1820=46=1966