The linear function f with the given values is f(x) = 2x + 2
How to determine the linear function f with the given values.From the question, we have the following parameters that can be used in our computation:
f(0) = 2 , f(-2) = -2
A linear equation can be represented as
f(x) = mx + c
Substitute the known values in the above equation, so, we have the following representation
m * 0 + c = 2
m * -2 + c = -2
Solving 0 * x + c = 2, we have
c = 2
So, we have
m * -2 + c = -2
This gives
-2 * m + 2 = -2
Evaluate
-2m = -4
Evaluate
m = 2
So, we have
f(x) = 2x + 2
Hence, the function is f(x) = 2x + 2
Read more about linear function at
https://brainly.com/question/4074386
#SPJ1
Can someone please answer and provide an explanation for these problems?
The distance between each pair of points include the following:
44. 2.8 units.
45. 5.8 units.
46. 12.0 units.
47. 16.6 units.
48. 7.1 units.
49. 4.5 units.
How to determine the distance between two end points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Question 44.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(3 - 1)² + (2 - 4)²]
Distance = √[(2)² + (-2)²]
Distance = √8
Distance = 2.8 units.
Question 45.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-2 + 7)² + (0 - 3)²]
Distance = √[(5)² + (-3)²]
Distance = √34
Distance = 5.8 units.
Question 46.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-6 - 2)² + (-2 - 7)²]
Distance = √[(-8)² + (-9)²]
Distance = √145
Distance = 12.0 units.
Question 47.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(1 - 8)² + (-8 - 7)²]
Distance = √[(-7)² + (-15)²]
Distance = √274
Distance = 16.6 units.
Question 48.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-5 - 2)² + (-4 + 5)²]
Distance = √[(-7)² + (1)²]
Distance = √50
Distance = 7.1 units.
Question 49.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(5 - 3)² + (5 - 1)²]
Distance = √[(2)² + (4)²]
Distance = √20
Distance = 4.5 units.
Read more on distance here: brainly.com/question/12470464
#SPJ1
Use ≈ 3.14 and round your answer
to the nearest hundredth.
10 ft
6 ft
square feet
The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.
We know that,
In geometry, a cylinder is one of the basic 3d shapes with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.
The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.
The surface area of this cylinder = (2π x r)h
We have given a radius of the base is 8 cm and the height of the cylinder is 10 cm.
The surface area of this cylinder = (2π x r)h
= (2π x 8)10
= (50.24)10
= 502.4
Thus, The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.
Learn more about the area;
brainly.com/question/11952845
#SPJ1
The complete question is attached below:
PLS HELP! What is the domain and Rage of the given below?
And is it a Function or not?
X /-2/-2 /-1 /-1 /0
Y/ 5/-5/ 3/-3/-1
In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.
Diagram of how a function relates two relations.
We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products.
We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded. For example, if a person has $100 to spend, he or she would need to express the interval that is more than 0 and less than or equal to 100 and write
(
0
,
100
]
. We will discuss interval notation in greater detail later.
Let’s turn our attention to finding the domain of a function whose equation is provided. Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers. Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero. Third, if there is an even root, consider excluding values that would make the radicand negative.
Before we begin, let us review the conventions of interval notation:
The smallest term from the interval is written first.
The largest term in the interval is written second, following a comma.
Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive.
Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive.
Please solve this question
The expression that represents a purely imaginary number is:
[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]
Option D is the correct answer.
We have,
A pure imaginary number is a number that does not have a real part and can be written in the form of bi, where b is a real number and i is the imaginary unit (√(-1)).
We have,
[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]
In this expression, we can simplify and rewrite it as:
[tex]3i^5 + i(2 - 4i^3) + 6 - 2i[/tex]
Now, let's evaluate the powers of i:
[tex]i^5 = i^{4 + 1} = i^4 \times i = 1 \times i = i\\i^3 = i^{2 + 1} = i^2 \times i = (-1) \times i = -i[/tex]
Substituting these values back into the expression:
[tex]3i^5 + i(2 - 4i^3) + 6 - 2i = 3i + i(2 - 4(-i)) + 6 - 2i[/tex]
= 3i + i(2 + 4i) + 6 - 2i
= 3i + 2i + 4i² + 6 - 2i
= 3i + 2i + 4(-1) + 6 - 2i
= 5i - 4 + 6 - 2i
= 5i - 2i - 4 + 6
= 3i + 2
The expression 3i + 2 represents a pure imaginary number, as it has no real part (the constant term is 2 and does not involve the imaginary unit i).
Thus,
The expression that represents a purely imaginary number is:
[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]
Learn more about imaginary numbers here:
https://brainly.com/question/6748860
#SPJ1
task1 part b evaluate
The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
We have to given that,
Expression to solve,
⇒ ∫ (0 to 10) (x + 1) dx
Now, We can simplify as,
⇒ ∫ (0 to 10) (x + 1) dx
⇒ ∫ (0 to 10) (x) dx + ∫ (0 to 10) dx
⇒ (x² / 2)₀¹⁰ + ((x)¹⁰₀
⇒ 1/2 (10² - 0) + (10 - 0)
⇒ 1/2 × 100 + 10
⇒ 50 + 10
⇒ 60
Therefore, The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
Learn more about integral at:
brainly.com/question/27419605
#SPJ1
a triangle is shown below, find the m
The value of angle L is 61°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
If angle A and B are interior angles and angle C is the exterior angle, what this theorem is saying is that;
A+B = C
Similarly,
angle L and angle E are the interior angles and 113 is the exterior angle, therefore;
113 = L + 52
L = 113 -52
L = 61°
Therefore angle L is 61°
learn more about exterior angle theorem from
https://brainly.com/question/17307144
#SPJ1
Show that the triangles are congruent for the given value in the variable.
5. GH= 3
HI= 3x-9 and x=4
HI= 3(4)-9=
= 12-9
= 3
so, GH = HI
Do the same for GJ and JI.
6. 36=2x
18=x
So, the angles are the same.
4x-11=61
4(18)-11=61
So, the sides are also the same meaning the triangles are congruent.
Ben records the time it took each person to complete a different event.
He is completing a table with information.
Note that in this case, the missing information which is the shortest time is 27 minutes. this is computed using the knowledge of the range.
What is range?The range of a collection of data in statistics is the difference between the highest and smallest values, calculated by subtracting the sample maximum and minimum. It's measured in the same units as the data.
Thus,
Range = Longest time - Shortest time
Since
Mean: 39 minutes
Range: 26 minutes
Longest time: 53 minutes
Shortest time = Longest time - Range
⇒ Shortest time = 53 - 26
= 27 minutes.
Learn more about range;
https://brainly.com/question/26098895
SPJ1
What is the height, in meters, of a cylinder with surface area 104π m2 and radius 4 m?
PLEASE SOMONE HELP
The height h of the cylinder is 9 meters.
What is the height of the cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The surface area of a cylinder is expressed as;
Surface Area = 2πrh + 2πr²
Given that; the surface area is 104π m² and the radius as 4 m.
We need to solve for the height (h).
Plug the values into the above formula:
Surface Area = 2πrh + 2πr²
104π = 2πrh + 2πr²
104π = 2π( rh + r² )
Divide through by 2π
52 = rh + r²
52 = ( 4 × h) + ( 4² )
52 = 4h + 16
Subtract 16 from both sides
52 - 16 = 4h + 16 - 16
52 - 16 = 4h
36 = 4h
4h = 36
h = 36/4
h = 9 meters
Therefore, the height is 9 meters.
Learn about volume of cylinder here: brainly.com/question/16788902
#SPJ1
Susie paid 2/5 of the price of her movie ticket. Her parents paid the remaining portion of the movie ticket price. What decimal is equivalent to the fraction of the price of the movie ticket Susie paid?
17 points!!
Thanks to the other user
To find the decimal equivalent of 2/5, you can divide the numerator (2) by the denominator (5):
2 ÷ 5 = 0.4
Therefore, the decimal equivalent to 2/5 is 0.4.
(Mines) Simple Equation2/5 which is know as 2 ÷ 5 is 0.4TipWhenever you see a fraction like 2/5 just divide and it will turn into decimal.
find the center and radius by completing the square x2+6x+y2-4y=3
Answer:
Center: (-3, 2)
Radius: 4
Step-by-step explanation:
x2 + 6x + y2 - 4y = 3
x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4
(x + 3)² + (y - 2)² = 16
(x + 3)² + (y - 2)² = 4²
Center: (-3, 2)
Radius: 4
(X-7)(x-7) multiply the binomials
The product of given two binomials which are (x-7)(x-7) is equal to x² - 14x + 49.
To multiply the binomials (x-7)(x-7), we use the distributive property of multiplication, which states that:
(a + b)(c + d) = ac + ad + bc + bd
Using this property, we can expand the expression as follows:
(x-7)(x-7) = x(x-7) - 7(x-7)
= x² - 7x - 7x + 49
= x² - 14x + 49
The distributive property of multiplication is a mathematical rule that states that when a number is multiplied by the sum of two or more numbers, it is equivalent to multiplying the number by each of the addends and then adding the products.
To learn more about binomials click on,
https://brainly.com/question/15934262
#SPJ1
i need some help on this please
Using the intersecting chord theorem, we can calculate the value of x as: 12
How to solve the Intersecting chord theorem?The intersecting chord theorem states that If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.
Applying the intersecting chord theorem to the two chords of the circle, we can say that:
3x = (9 * 4)
3x = 36
x = 36/3
x = 12
Read more about Intersecting Chord Theorem at: https://brainly.com/question/13950364
#SPJ1
Given m ∥ n, find the value of x.
The value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.
(2x - 13) + 123 = 180° {supplementary angles}
2x - 13 + 123 = 180°
2x + 110 = 180
2x = 180 - 110 {collect like terms}
2x = 70
x = 70/2 {divide through by 2}
x = 35
Therefore, the value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3
Read more about angles here:https://brainly.com/question/24607467
#SPJ1
The rear window of Alex's van is shaped like a trapezoid with an upper base
measuring 36 inches, a lower base measuring 48 inches, and a height of 21 inches.
An 18-inch rear window wiper clears a 150° sector of a circle on the rear window, as
shown in the diagram below.
36 in.
21 in.
150 degrees
18 in.
48 in.
a. What is the area, in square inches, of the entire trapezoidal rear window? Show or explain how you got your answer.
b. What fractional part of a complete circle is cleared on the rear window by the 18-inch wiper? Show or explain how you got your answer.
c. What is the area, in square inches, of the part of the rear window that is cleared by the wiper? Show or explain how you got your answer.
d. What percent of the area of the entire rear window is cleared by the wiper? Show or explain how you got your answer.
a) The area of the entire trapezoidal rear window = 882 sq.in.
b) The fractional part of a complete circle is cleared on the rear window by the 18-inch wiper = 5/12
c) The area of the part of the rear window that is cleared by the wiper = 424.12 sq. in.
d) The percent of the area of the entire rear window is cleared by the wiper = 48.09%
We know that the formula for the area of trapezoid,
A = ((a + b) / 2) × h
Here, a = 36 in., b = 48 in. and height of the trapezoid h=21 in
Using above formula, the area of the entire trapezoidal rear window would be,
A = ((36 + 48) / 2) × 21
A = 882 sq.in.
Here, the 18-inch rear window wiper clears a 150° sector of a circle on the rear window.
We know that the measure of entire circle = 360°
So, the fractional part of a complete circle is cleared on the rear window by the 18-inch wiper would be,
150° / 360° = 5/12
Now we need to find the area of the part of the rear window that is cleared by the wiper.
We know that the formula for the area of sector of a circle is:
A = (θ/360) × πr²
Here, the central angle θ = 150° and radius r = 18 in.
A = (θ/360) × πr²
A = (150/360) × π × 18²
A = 424.12 sq. in.
Now we need to find the percent of the area of the entire rear window is cleared by the wiper.
P = [(area of the part of the rear window cleared by the wiper) / (area of the entire trapezoidal rear window)] × 100
P = (424.12 / 882) × 100
P = 48.09%
Learn more about the area of trapezoid here:
https://brainly.com/question/15640807
#SPJ1
Help with number 8 please
The simplification of the expression, ∛8x⁴y⁸ / 125 is [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex].
How to solve an exponential expression?The exponential expression can be solved as follows:
Therefore, let's simplify the expression.
To simplify the expression we have to deal with the exponential by applying it laws and also the cube root.
∛8x⁴y⁸ / 125
let's solve them individually,
125 = 5³ = 5 × 5 × 5
8 = 2³ = 2 × 2 × 2
Therefore,
∛8x⁴y⁸ / 125 = [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex]
learn more on exponentials here: https://brainly.com/question/29296157
#SPJ1
elle can buy 2 quarts of milk for 3$ or 1 gallon of milk for 3$ which is the better deal
Answer:
Elle should buy 1 gallon of milk for $3.
Step-by-step explanation:
In one gallon of milk, there are four quarts. So we can multiply the number of gallons by four to convert it to quarts.
(1 gallon)x(4 quarts) = 4 quarts in one gallon
4 quarts is greater than 2 quarts so 1 gallon for $3 is a better deal than 2 quarts for $3.
What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box. radians
The measure in radians for the central angle is approximately 0.7 radians.
To find the measure in radians for the central angle of a circle, we can use the formula:
θ = s / r
where θ is the central angle in radians, s is the intercepted arc length, and r is the radius of the circle.
In this case, the radius is given as 8 cm and the intercepted arc length is 5.6 cm.
Plugging these values into the formula, we have:
θ = 5.6 cm / 8 cm
Simplifying the expression:
θ = 0.7
We may use the following formula to get the centre angle of a circle's measurement in radians:
= s / r
s is the length of the intercepted arc, r is the circle's radius and is the centre angle in radians.
The intercepted arc length in this instance is 5.6 cm, while the radius is specified as 8 cm.
When these values are plugged into the formula, we get:
θ = 5.6 cm / 8 cm
Condensing the phrase:
θ = 0.7
For similar questions on radians
https://brainly.com/question/29058626
#SPJ11
Make selections to complete the proof.
Given: ∠WXZ≅∠YXZ, ∠XZW≅∠XZY, WX⎯⎯⎯⎯⎯⎯≅YX⎯⎯⎯⎯⎯, WZ⎯⎯⎯⎯⎯⎯≅YZ⎯⎯⎯⎯⎯
Prove: ∆WXZ≅∆YXZ
The required angles are,
∠BAC = 73 degree
∠BCA = 17 degree
∠DCF = 17 degree
∠CDF = 80 degree
∠CFD = 95 degree
Since we can see that,
In triangle ABC
The angle B is right angled
Since we know that,
Sum of interior angles of triangle = 180 degree
Therefore, in triangle ABC
⇒ (9x -8 ) + (2x-1) + 90 = 180
⇒ 11x = 99
⇒ x = 9
Thus,
Angle BAC = 9x - 8
= 9x9 - 8
= 73 degree
Angle BCA = 2x - 1
= 2x9 - 1
= 17 degree
Now in triangle, CDF,
Angle C is alternate angle for both the triangles,
Therefore,
Interior angle C of triangle CDF = angle DCF = 17 degree
Angle CDF = 9y - 1
= 9x9 - 1
= 80 degree
Angle CFD = 11y + 4
= 11x9 - 4
= 95 degree
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
The graph shows the distribution of the amount of chicken (in ounces) that adults eat in one sitting. The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
A graph titled Chicken Consumption has amount (ounces) on the x-axis, going from 3.2 to 12.8 in increments of 1.2. The highest point of the curve is at 8.
What percentage of adults eat between 5.6 and 8 ounces of chicken in one sitting?
2.5%
34%
47.5%
95%
Using concepts of the normal and of the uniform distribution, it is found that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
In an uniform distribution, all outcomes are equally as likely, thus they have the same height.
In the normal distribution,
The outcomes with the highest likelihood are those closest to the mean, thus they have the highest height.
This means that the mean of this distribution is 8.
The standard deviation cannot be a negative value,
So in this problem, it is 1.2,
Which means that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
To learn more about statistics visit:
https://brainly.com/question/30765535
#SPJ1
Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15. (A reading above 140 is considered to be high blood pressure). Find the percentage of people with blood pressure below 133.
The percentage of people with blood pressure below 133 is 78.81%.
First, we need to calculate the Z-score for the value 133 using the formula:
Z = (X - μ) / σ
where X is the value (133), μ is the mean (121), and σ is the standard deviation (15).
Z = (133 - 121) / 15
Z = 12 / 15
Z = 0.8
Next, we can use a standard normal distribution table or a calculator to find the area under the curve to the left of the Z-score 0.8.
Looking up the Z-score of 0.8 in the standard normal distribution table, we find that the area to the left of 0.8 is 0.7881.
Therefore, the percentage of people with blood pressure below 133 is 78.81%.
Learn more about z score here:
https://brainly.com/question/31871890
#SPJ1
A company packs its fruit salad in
containers that hold 1 5/8 pounds
How many containers does it
need to hold 585 pounds of fruit
salad?
Answer: 360 containers
Step-by-step explanation: 1 5/8 in decimal form is 1.625 pounds. Divide 585 by 1.625 pounds you get 360. It takes 360 containers to hold 585 pounds of fruit
Convert from radians to degrees.
1/4π
1/4π radians is approximately equal to 45 degrees.
To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.
Degrees = Radians × 180/π.
Therefore, to convert 1/4π radians to degrees, we have:
Degrees = (1/4π) × (180/π) ≈ 45°
Hence, 1/4π radians is approximately equal to 45 degrees.
To know more about Conversion here
https://brainly.com/question/15743041
#SPJ1
please helppppppppppppppppppppppp
Answer:
last option
Step-by-step explanation:
let g = 3,
9/5 + 7/2(3)
9/5 + 21/2
adjust to a common denominator of ten to get;
18/10 + 105/10
= 123/10 = 12 3/10
so the last option !
.....................................................................................
Answer:
(-6,0)
Step-by-step explanation:
An equation of a line can be modeled as y = mx + b where m is slope and b is y-intercept.
For the line r, we can model the equation as y = mx + 3 since the line intersects y-axis at (0,3) as seen in the attachment.
For the line t, we can model the equation as y = mx - 6 as the problem gives y-intercept for line t equal to -6. Hence, the line t intersects y-axis at (0,6)
Next, we have to find the slope of line t by finding the slope of line r in the attachment. Apply the rise over run by counting the steps, you can see in the attachment that I put to learn how to count rise and run of a line. Also note that the value in attachment here is a scalar quantity, meaning only magnitude, no direction.
So we will have the slope of -1 since a line graph is heading down so the output decreases as input increases. Therefore, we know that m = -1 for both lines. Therefore, for the line t, we can model the new equation to:
[tex]\displaystyle{y=-x-6}[/tex]
Then we find the x-intercept of the line by letting y = 0. Thus,
[tex]\displaystyle{0=-x-6}\\\\\displaystyle{x=-6}[/tex]
Therefore, the x-intercept of line t is at (-6,0).
Answer:
(-6,0)
Step-by-step explanation:
We need to determine the equation of line r first to find the x-intercept of line t.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
[tex]slope = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
For line r passing through (3, 0) and (0, 3), the slope is:
[tex]slope = \frac{3 - 0}{0 - 3} = -1[/tex]
Since line t has the same slope as line r, its slope is also -1.
The equation of a line in slope-intercept form (y = mx + b) is determined by its slope (m) and y-intercept (b).
We know that the slope (m) of line t is -1, and the y-intercept (b) is -6. Substituting these values into the slope-intercept form, we get:
y = -x - 6
To find the x-intercept, we set y = 0 and solve for x:
0 = -x - 6
Adding x to both sides:
x = -6
Therefore, the x-intercept of line t is (-6,0).
What is the probability that either event will occur?
Now, find the probability of event A and event B.
A
B
6
6
20
20
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
Answer:
0.12
Step-by-step explanation:
Given the frequencies of occurrence in the diagram, you want to know the probability of A and B.
ProbabilityThe probability of an event is the ratio of the number of times it occurs to the total number of trials.
The diagram shows the event (A and B) occurs 6 times out of a total of 6+6+20+20 = 52 trials.
P(A and B) = 6/52
P(A and B) ≈ 0.12
<95141404393>
hey i have a question about this assignment and want to check if my answers are right
The lengths of the sides and angles of the triangles, obtained using Pythagorean Theorem and trigonometric ratios are;
D. 19.2
C. 5.3
F. 2·√5
G. √3
H. 8·√3
K. 18.9
O. 15.5
N. 14.5
M. 41.4°
I. 74.1°
What is the Pythagorean Theorem?The Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the triangle.
D. x = √(15² + 12²) ≈ 19.2
C. x = √(10² - 8.5²) ≈ 5.3
F. x = 2·√(5) (Special triangles)
G. tan (60°) = 30/x = √3
x = 30/√3 = 10·√3
H. x/16 = (√3)/2
x = 16 × (√3)/2 = 8·√3
x = 8·√3
K. tan(34°) = x/28
x = 28 × tan(34°) ≈ 18.9
O. cos(55°) = x/27
x = 27 × cos(55) ≈ 15.5
N. sin(16°) = 4/x
x = 4/(sin(16°) ≈ 14.5
M. x = arccos(9/12) ≈ 41.4°
I. x = arcsin(25/26) ≈ 74.1°
Learn more on Pythagorean Theorem here: https://brainly.com/question/343682
#SPJ1
A ferris wheel has a radius of 10 inches and is 2 inches off the ground. It makes a complete revolution every 10 seconds.
If a rider is directly horizontal to the center of the wheel and moving downward, find an equation that gives his height above the ground as a function of time .
Answer:
y = -10·sin(πt/5) +12
Step-by-step explanation:
You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.
EquationThe general form of the equation will be ...
y = A·sin(2πt/T) + B
where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.
HeightWe assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:
B = 2 + 10 = 12
Scale factorThe scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...
A = 10
PeriodThe period (T) is given as 10 seconds.
Height functionPutting these parameters together gives ...
y = -10·sin(2πt/10) +12
y = -10·sin(πt/5) +12
__
Additional comment
We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.
Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.
<95141404393>
2x+6 what would be its value if X=-3 *
Answer:0
Step-by-step explanation:
so if x = -3 that means u take -3 * 2 and u get -6 because a negative * A positive is negative so -6 + 6 is 0
Answer:
0
Step-by-step explanation:
Just substitute x=-3
2x+6 =
2(-3) + 6 =
-6 + 6 = 0
The following transactions were completed by the company:
The company completed consulting work for a client and immediately collected $5,600 cash.
The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
The company paid an assistant $1,450 cash as wages for the period.
The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.
The company paid $720 cash for this period's cleaning services.
In accounting, the accounting equation is a fundamental principle that describes the relationship between a company's assets, liabilities, and equity. This equation is represented as Assets = Liabilities + Equity. Every financial transaction that a company undertakes has an impact on at least two of the components of the accounting equation.
Transaction Analysis:
a. The company completed consulting work for a client and immediately collected $5,600 cash earned.
This transaction increases both cash and revenue. There is no impact on liabilities or equity.
Accounts Affected:
Cash: +$5,600
Revenue: +$5,600
b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
This transaction does not impact any account initially. Revenue will increase when payment is received.
Accounts Affected:
Accounts Receivable: +$4,100
Revenue: +$0
c. The company paid an assistant $1,450 cash as wages for the period.
This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.
Accounts Affected:
Cash: -$1,450
Expenses: +$1,450
d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.
This transaction increases cash and decreases accounts receivable. There is no impact on liabilities or equity.
Accounts Affected:
Cash: +$2,050
Accounts Receivable: -$2,050
e. The company paid $720 cash for this period's cleaning services.
This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.
Accounts Affected:
Cash: -$720
Expenses: +$720
To know more about Accounting Equation here
https://brainly.com/question/14689492
#SPJ1
Complete Question
The following transactions were completed by the company
a. The company completed consulting work for a client and immediately collected $5,600 cash earned.
b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
c. The company paid an assistant $1,450 cash as wages for the period.
d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b
e. The company paid $720 cash for this period's cleaning services Required: Enter the impact of each transaction on individual items of the accounting equation. (Enter decreases to account balances with a minus sign.)