Answers
The length of PQ is 3√5 and its slope is -2
The length of SR is 3√5 and its slope is -2
The length of SP is 5√2 and its slope is -7
The length of RQ is 5√2 and its slope is -1
So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.
Understanding QuadrilateralTo find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:
D = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
and the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
1. Length PQ:
Using the distance formula, the length PQ can be calculated as follows:
PQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((3 - 0)² + (-4 - 2)²)
= √(3² + (-6)²)
= √(9 + 36)
= √45
= 3√5
2. Length SR:
Using the distance formula, the length SR can be calculated as follows:
SR = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((1 - (-2))² + (-5 - 1)²)
= √((1 + 2)² + (-6)²)
= √(3² + 36)
= √(9 + 36)
= √45
= 3√5
3. Length SP:
Using the distance formula, the length SP can be calculated as follows:
SP = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((1 - 0)² + (-5 - 2)²)
= √(1² + (-7)²)
= √(1 + 49)
= √50
= 5√2
4. Length RQ:
Using the distance formula, the length RQ can be calculated as follows:
RQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((-2 - 3)² + (1 - (-4))²)
= √((-2 - 3)² + (1 + 4)²)
= √((-5)² + 5²)
= √(25 + 25)
= √50
= 5√2
Now, let's calculate the slopes of the sides:
1. Slope PQ:
The slope of PQ can be calculated using the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (-4 - 2) / (3 - 0)
= -6 / 3
= -2
2. Slope SR:
The slope of SR can be calculated using the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (-5 - 1) / (1 - (-2))
= -6 / 3
= -2
3. Slope SP:
The slope of SP can be calculated using the slope formula:
m =[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (-5 - 2) / (1 - 0)
= -7 / 1
= -7
4. Slope RQ:
The slope of RQ can be calculated using the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (1 - (-4)) / (-2 - 3)
= 5 / (-5)
= -1
Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:
Length PQ: 3√5
Length SR: 3√5
Length SP: 5√2
Length RQ: 5√2
Slope PQ: -2
Slope SR: -2
Slope SP: -7
Slope RQ: -1
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Related Questions
what is a Pythagoras theorem
Answers
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
What is mathematical representation of Pythagoras theorem?From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;
C² = a²+b²
Where:
'C' represents the hypotenuse which is the longest part of the triangle and is always diagonal connecting the two other points.'a' represents the perpendicular length that forms the angle 90° of the right angle triangle.'b' represents the base of the triangle.Learn more about Pythagorean formula here:
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What means killogram?
Answers
Answer:
1,000 grams
noun. a unit of mass equal to 1,000 grams: the basic unit of mass in the International System of Units (SI). Up until 2019 the kilogram was defined as equal to the mass of an international prototype, a platinum-iridium cylinder kept in Sèvres, France.
Graph the image of this quadrilateral after a dilation with a scale factor of 2 centered at the origin. Use the polygon tool to graph the quadrilateral.
Answers
The new coordinates of the quadrilateral ABCD after the dilation is:
A' = (-6, 6)
B' = (-8, -4)
C' = (4, -8)
D' = (0, 0)
We have,
To find the coordinates of the new quadrilateral after a dilation with a scale factor of 2 centered at the origin, we multiply the x and y coordinates of each point by the scale factor.
Given the original coordinates of the quadrilateral ABCD:
A = (-3, 3)
B = (-4, -2)
C = (2, -4)
D = (0, 0)
To dilate the coordinates with a scale factor of 2, we multiply each coordinate by 2:
A' = 2 x (-3, 3) = (-6, 6)
B' = 2 x (-4, -2) = (-8, -4)
C' = 2 x (2, -4) = (4, -8)
D' = 2 x (0, 0) = (0, 0)
Thus,
The new coordinates of the quadrilateral ABCD after the dilation is:
A' = (-6, 6)
B' = (-8, -4)
C' = (4, -8)
D' = (0, 0)
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What is (fg)(x)?
f(x)=2x
g(x)=2x2+3x
Write your answer as a polynomial or a rational function in simplest form
Answers
Given statement Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.
To find (fg)(x), we need to first find the product of f(x) and g(x) and simplify the expression.
f(x) = 2x
g(x) = [tex]2x^2[/tex] + 3x
To find (fg)(x), we substitute g(x) into f(x):
(fg)(x) = f(g(x)) = f([tex]2x^2[/tex] + 3x)
Now we substitute f(x) = 2x into the expression above:
(fg)(x) = 2([tex]2x^2[/tex] + 3x)
Distribute the 2:
(fg)(x) = [tex]4x^2[/tex] + 6x
So, (fg)(x) = [tex]4x^2[/tex] + 6x.
Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.
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A cheetah's speed was timed over a 50-yard distance. The cheetah was clocked running 60 miles per hour. Write an equation to represent this situation. (If your answering please show how you solved this)
Answers
The equation that represents this situation is:
⇒ 60t = 0.0284091
where t is the time in minutes.
We have to given that,
The speed of the cheetah is 60 miles per hour
The distance timed was 50 yards
Now, We have to convert the distance to miles, because the speed is in miles per hour.
Since, 1 yard = 0.000568182 miles
Hence, 50 yards = 50 x 0.000568182 miles
50 yards = 0.0284091 miles
Now we can use the formula:
distance = speed x time
We know that,
The distance is 0.0284091 miles, and the speed is 60 miles per hour.
Hence, the time it took the cheetah to run the 50-yard distance.
So, the speed from miles per hour to miles per minute, since we want the time in minutes:
60 miles per hour = 1 mile per minute
Now we can plug in the values we know:
0.0284091 miles = (1 mile per minute) x time
Solving for time:
time = 0.0284091 / 1
time = 0.0284091 minutes
time = 0.0284091 minutes x 60 seconds per minute
time = 1.704546 seconds
Thus, the equation that represents this situation is:
⇒ 60t = 0.0284091
where t is the time in minutes.
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What is the sum of 104, 25, -11 to come of it
Answers
Answer:
118
Step-by-step explanation:
104+25+(-11)
129-11
118
Therefore, our answer is 118
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Of(x) = -x +
Of(v)=-3y+4
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Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be
written using function notation?
42-
Answers
The function notation of 9x + 3y = 12 is given as follows:
f(x) = 4 - 3x.
How to write the function notation?The function in the context of this problem is given as follows:
9x + 3y = 12.
The format for the function notation is given as follows:
Hence we must isolate the variable y, as follows:
3y = 12 - 9x
y = 4 - 3x (each term of the expression is divided by 3).
f(x) = 4 - 3x.
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Decide whether pairs of angles <1 and <2, <6 and<1 , and <5 and <6 are alternate interior angles, same-side interior angles, corresponding angles, or alternate exterior angles. Question content area bottom Part 1 Choose the statement that correctly describes angles 1 and 2.
*PLEASE ANSWER EACH QUESTION. IN ALL 3 PICS. THANKS
Answers
<1 and <2 are same-side interior angles. Option D
<1 and <5 are same-side interior angles. Option B
<6 and <8 are corresponding angles. Option C
How to determine the anglesTo determine the angles, we need to know the following;
Corresponding angles are angles formed in matching corners with the transversal when two parallel lines are intersected by any other lineSame side interior angles are two angles that are found on the interior of two lines and exactly on the same side of the transversal. Adjacent angles are equalNow, from the information given, we have that;
1. <1 and <2 are same-side interior angles because they are found on the same side of the transversal
2. We can see that < 1 and <5 are also same-side interior angles because they are two angles found on the exact same side of the transversal
3. Since corresponding angles are angles on matching corners of a transversal, < 6 and < 8 are corresponding angles
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Acylinder has a volume of 400 cubic feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.14 for me and round to the nearest hundredth
adius hype your answer...
1
Answers
The radius of the cylinder is 2.25 feet.
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the volume V is 400 cubic feet and the height h is 25 feet, we can substitute these values into the formula and solve for the radius r.
400 = 3.14 r² x 25
Dividing both sides of the equation by (3.14 * 25) to isolate r^2, we have:
r² = 400 / (3.14 x 25)
r² ≈ 5.08
Taking the square root of both sides to solve for r, we get:
r ≈ √5.08
r ≈ 2.25
Therefore, the radius of the cylinder is 2.25 feet.
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The class had 7 tests, on which he scored 85, 93, 78, 90, 88, 97, and 88.
What is the mean?
Answers
George and Manuel had a roofing business George as owner of the materials received $3 for every $2 manual received on a job that paid $750 what amount did each receive
Answers
Manuel received $187.50, and George received $562.50 for the job.
Let's break down the information provided:
The job paid a total of $750.
George received $3 for every $2 that Manuel received.
To determine the amounts George and Manuel received, we can set up a ratio based on their earnings.
Let's assume Manuel's earnings as the base amount:
George's earnings : Manuel's earnings = $3 : $2
We can set up the following equation to solve for Manuel's earnings:
(Manuel's earnings / Manuel's earnings) = ($2 / $2)
Since the ratio is equivalent, we can say:
George's earnings / Manuel's earnings = $3 / $2
To find the amount each person received, we'll assign a variable to Manuel's earnings. Let's call it "x."
Therefore, George's earnings can be represented as "3x."
According to the given information, their total earnings should sum up to $750:
x + 3x = $750
Combining like terms, we have:
4x = $750
To solve for x, we divide both sides by 4:
x = $750 / 4
x = $187.50
Now, we can determine the amounts each person received:
Manuel's earnings = x = $187.50
George's earnings = 3x = 3 * $187.50 = $562.50
Therefore, Manuel received $187.50, and George received $562.50 for the job.
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The room is 20 feet by 25 feet. The walls are 8 feet tall. You will be painting all 4
walls, but not the ceiling.
The paint costs $13.98 per gallon and covers 400 square feet per gallon.
1. What are the dimensions of the 4 walls?
2. What is the total area to be covered? Show your computations here.
3. How many gallons of paint will you need? (remember each gallon covers 400 sq ft)
Answers
1) The dimensions of the 4 walls are:
Two walls are 20 feet long and 8 feet tall.
Two walls are 25 feet long and 8 feet tall.
2) Total area to be covered:
= 720 square feet.
3) You will need 1.8 gallons of paint to cover all four walls of the room.
Now, The dimensions of the 4 walls are:
Two walls are 20 feet long and 8 feet tall.
Two walls are 25 feet long and 8 feet tall.
And, The total area to be covered is:
For the two 20 feet long walls:
A = 20 feet x 8 feet
A = 160 square feet each.
And, For the two 25 feet long walls:
A = 25 feet x 8 feet
A = 200 square feet each.
Hence, Total area to be covered:
= (160 + 160 + 200 + 200) square feet
= 720 square feet.
For the number of gallons of paint needed, divide the total area to be covered by the area covered by one gallon of paint:
Number of gallons of paint needed = Total area to be covered / Area covered by one gallon of paint
Number of gallons of paint needed = 720 square feet / 400 square feet per gallon
Number of gallons of paint needed = 1.8 gallons
Therefore, you will need 1.8 gallons of paint to cover all four walls of the room.
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Which of the following shows a 90° counterclockwise rotation of the blue figure
Answers
11. Which one of the following is unique? b. mode a. Mean c. Median d. A and B
Answers
Among the mean, mode, and median, the unique one is the b. mode.
What is the mode?The mode is the data value that occurs many times more than other data values.
Unlike the mean that shows the average value of all the data values, the mode occurs more. While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.
Similarly, the median can be computed when two values occur as the middle values.
Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.
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Answer Question 11 please
Answers
Answer:
increasing exponential function.
Step-by-step explanation:
We can see from the table that the function is not increasing by the same amount as it goes up by 1 in x, so it is not linear.
It must be exponential.
It is increasing at it increases in x, so it is an increasing exponential function.
Joshua and Milap were having a contest flying
planes. Joshua's plane flew 125 feet. Milap's
plane flew 12 feet less than twice as far as
Joshua's. How far did Milap's plane fly?
A 137 feet
B 238 feet
C 250 feet
D 262 feet
Answers
i believe the answer is 238.
twice the feet is 250, ( 2 x 125)
his plane flew 12 feet less than that,
250 - 12 = 238
A 3-quart jug of water costs $3.48. What is the price per cup?
Answers
The calculated value of the price per cup is $1.16
How to calculate the price per cup?From the question, we have the following parameters that can be used in our computation:
A 3-quart jug of water costs $3.48
The price per cup is calculated as
Unit rate = Total cost/Size of the cup
Substitute the known values in the above equation, so, we have the following representation
Unit rate = 3.48/3
Evaluate
Unit rate = 1.16
Hence, the price per cup is $1.16
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pls help me with this
Answers
The term 9b represents the cost to rent a bike.
We have,
Rentals
Bike $9/h
Electric scooter $10/h
Kayak $18/h
Canoe $20/h
Paddleboard $22/h
Helmet Add $6
Here, the term 9b represents the cost to rent a bike.
In the provided rental options, the cost of renting a bike is $9 per hour.
The term "9b" indicates that the cost is calculated by multiplying the hourly rate of $9 with the number of hours (b) the bike is rented for.
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Linear equations linear equations
Answers
A graph of the linear equation y = 2x - 1 in slope-intercept form is shown in the image attached below.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Based on the information provided above, we have the linear equation:
y = 2x - 1
Lastly, we would use an online graphing calculator to plot the given linear equation as shown in the graph attached below.
In conclusion, the slope of this linear equation is equal to 2 and it does not represent a proportional relationship.
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Complete Question:
Plot the linear equation on the coordinate axis shown on the right.
The graph of � = ∣ � ∣ y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right by 4 44 units. What is the equation of the new graph? Choose 1 answer: Choose 1 answer: (Choice A) � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 A � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 (Choice B) � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 B � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 (Choice C) � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 C � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 (Choice D) � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4y, equals, vertical bar, x, minus, 9, vertical bar, plus, 4 D � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4
Answers
An equation of the new graph is: A. y = ∣x - 4∣ - 9.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:
g(x) = f(x - N)
Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:
g(x) = f(x) + N
Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:
y = ∣x - 4∣ - 9
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A merchant has 1500 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
Answers
Answer:
900 kg
Step-by-step explanation:
Let's assume the cost price (C.P.) of sugar is Rs. x per kg.
The total quantity of sugar is 1500 kg.
Let the quantity of sugar sold at 8% profit be represented by y kg.
The quantity of sugar sold at 18% profit would then be (1500 - y) kg.
Using the rule of alligation, we can set up the following proportion:
(8% profit) y kg
-------------- = ------
(18% profit) (1500 - y) kg
Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).
The ratio of these differences is 2:3.
This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.
Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:
(2 kg) * (3/2) = 3 kg
Therefore, the quantity sold at 18% profit is 900 kg.
HELLLLPPPPP!!!!!!!!!!!! AHHHHHHHHHHH!!!!!!!
kenji is raising baby kittens. their weights after three weeks are 12 ounces, 14 ounces, 15 ounces, 15, ounces and 14 ounces, what is the mean weight of the kittens????
Answers
Answer: 14 ounces
Step-by-step explanation:
To find the mean, we add up all the values and divide by the number of values.
[tex]\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces[/tex]
Need help with this equation 8x²+10x-3
Answers
Answer:
Step-by-step explanation:
You have to use the quadratic formula
x = -b +/- [tex]\sqrt{(b^{2} -4ac)/2a[/tex]
and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2
you usually have to reject an answer but since there is no equal sign in the question, you should be fine
De los 12 jugadores del equipo 2/8 son delanteros
Answers
There are a total of 3 forwards on the team.
How many forwards are there on the team?A fraction represents a part of the whole or group of objects.In a fraction, numerator and denominator are separated by a horizontal bar known as the fractional bar
Given:
2/8 of the players are forwards.
Total number of players on the team = 12
We will determine the total number of forwards on the team by multiplying the total number of players by the fraction representing the forwards.
Fraction representing the forwards:
= 2/8
= 1/4
Total forwards on the team:
= 12 * (1/4)
= 3.
Translated question:
Of the 12 players on the team, 2/8 are forwards. What are the total forward in the team?
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The sum of 18 and a number, x, equals negative 40. Part A Which equation represents this situation? x-18=-40. x-18-40 18+x=-40. 18 + x = 40
Answers
Answer:
18+x = -40
Step-by-step explanation:
The sum of 18 and a number x is translated to "18+x"
Equals means "="
Negative forty is "-40"
Put them all in order and you get 18+x = -40
what is the probability that either event will occur? ASAP
Answers
The probability that either event will occur is 0.67
What is the probability that either event will occur?From the question, we have the following parameters that can be used in our computation:
Event A = 3
Event B = 1
Other Events = 2
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 3 + 1 + 2
Evaluate
Total = 6
So, we have
P(A) = 3/6
P(B) = 1/6
For either events, we have
P(A or B) = 3/6 + 1/6 = 0.67
Hence, the probability that either event will occur is 0.67
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To solve the quadratic equation 3(x−7)2=27 , Diego and Mai wrote the following: Diego 3(x−7)2=27 (x−7)2=9 x2−72=92 x2−49=81 x2=130 x=130−−−√ and x=−130−−−√ Mai 3(x−7)2=27 (x−7)2=9 x−7=9 x=16 Identify the mistake(s) each student made. Solve the equation and show your reasoning.
Answers
Given statement solution is :- The correct solutions to the quadratic equation [tex]3(x-7)^2 = 27[/tex] are x = 10 and x = 4.
Diego made an error in the step where he simplified [tex](x-7)^2 = 9 to x^2[/tex] - 72 = 9. The correct expansion of [tex](x-7)^2 is x^2 - 14x + 49[/tex], not [tex]x^2 - 72.[/tex]Therefore, his subsequent steps and solution are incorrect.
Mai made an error in the step where she simplified [tex](x-7)^2 = 9[/tex] to x - 7 = 9. The square root of 9 is ±3, so the correct equation should be x - 7 = ±3, not x - 7 = 9. Therefore, her solution is incorrect.
To solve the equation correctly, we start with the equation [tex]3(x-7)^2 = 27.[/tex]
Dividing both sides by 3, we have:
[tex](x-7)^2 = 9[/tex]
Taking the square root of both sides, we get:
x - 7 = ±3
Now, we need to solve for x by adding 7 to both sides:
x = 7 ± 3
This gives us two possible solutions:
x = 7 + 3 = 10
x = 7 - 3 = 4
So, the correct solutions to the quadratic equation [tex]3(x-7)^2 = 27[/tex] are x = 10 and x = 4.
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These shapes are similar.
Find X.
5
X
5
30
24
30
Answers
The value of x is 4.
To determine the value of x, we can use the concept of similarity between shapes.
Similar shapes have corresponding sides that are proportional to each other.
Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:
5/x = 30/24
To solve for x, we can cross-multiply:
30 · x = 5 · 24
30x = 120
Dividing both sides of the equation by 30:
x = 120 / 30
x = 4
Therefore, the value of x is 4.
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Pls help
This other expression is equal to
Answers
reasoning:
coefficients (the # in front of the variable) gets divided by the 3, and the exponents essentially just get subtracted.
12x^4 divided by 3x^2 (divide 12 by 3 and subtract the exponents to reach 4x^2)
same for -3x^2 divided by 3x^2 (since these terms are the almost same, you would just end up with -1)
6x^2 divided by 3x^2 (divide 6 by 3 which equals two, and subtract the exponents. that leave you with just 2 since 2-2 = 0 for the exponents)
place it together back in standard form
4x^2 - x + 2
What is the circumference of the circle if the radius is 10 cm?
Answers
Answer for this question
The circumference of the circle is 62.8cm.
The Circumference of the circle is given by the formula,
Circumference = 2*[tex]\pi[/tex]*r cm.........equation 1
Given, r = 10cm
On substituting the radius value in equation 1
Circumference = 2*[tex]\pi[/tex]*10
Circumference = 62.8 cm
Therefore, the circumference of the circle is 62.8cm.
Learn how to calculate the Area,
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