A segment with endpoints X (6, 2) and Y (- 1, - 3) is rotated 90º about the origin. What are the coordinates of X Prime and Y Prime?
A segment with endpoints X (6, 2) and Y (- 1, - 3) when rotated 90 degrees about the origin will result in new endpoints X' (-2, 6) and Y' (3, -1).
Explanation:This problem deals with the concept of point rotation in a 2D coordinate plane around the origin. When any point (X, Y) is rotated 90 degrees counter-clockwise about the origin, the new position, let's say (X', Y'), can be calculated by using the formulas X' = -Y and Y' = X. Therefore, applying these rotations to the points X(6,2) and Y(-1,-3), we get X'(-2, 6) and Y' (3, -1). So, the endpoints X Prime and Y Prime of the rotated segment are (-2, 6) and (3, -1) respectively.
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After rotating a 90-degree rotation about the origin, the coordinates of X (6, 2) and Y (-1, -3) transform to X' (-2, 6) and Y' (3, -1) respectively.
Explanation:When a point (x, y) is rotated 90º counterclockwise about the origin, it transforms to (-y, x). Let's apply this rule to the endpoints X (6, 2) and Y (-1, -3).
The coordinates of X prime would be (-2, 6) that is, (-y, x).
The coordinates of Y prime would be (3, -1) that is, (-y, x).
Thus, the transformed coordinates for X and Y would be (-2, 6) and (3, -1) respectively after a 90-degree rotation about the origin.
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In a circle whose radius is 4cm find the arc length intercepted by 30 degree angle
As per the radius and given angle the length of the arc will be equal to 2.09 cm.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the given information in the question,
Radius, r = 4 cm
Angle, θ = 30°
The formula for an arc's length is stated as:
= 2πr(θ ÷ 360)
So,
The length of arc = 2π(4)(30/360)
The length of the arc = 2.09 cm.
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Which of the following describes the graph of {x | 1 < x < 2}? open circles on 1 and 2 open circles on 1 and 2, arrows pointing out open circles on 1 and 2, line segment between no solution
Answer:
open circles on 1 and 2
Solve for x. x/3≤−6
Answer:
Hence, the value of x is [tex]x\leq -18[/tex]
Step-by-step explanation:
Consider the provided inequity.
[tex]\frac{x}{3}\leq -6[/tex]
We need to solve the above inequity of x.
Multiply both the side by 3.
[tex]3\times\frac{x}{3}\leq 3\times -6[/tex]
[tex]x\leq -18[/tex]
Hence, the value of x is [tex]x\leq -18[/tex]
A 150° angle is an obtuse angle. What do you Notice about the statement below? What do you Wonder about the statement?
N is between M and P. if MP=12 and NP=8, then what is the length of MN?
Three (6‐sided) dice are thrown what is the probability that the same number appears on all three dice?
Finding the average values of the representative coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the _______________ formula.
If you live in Dallas, then you live in Texas, what is the contrpositive of this?
Erin is 8 years younger than twice Paula’s age. The sum of their ages is 40. How old is Erin
To solve this problem, we set up two linear equations based on the given information and solved them simultaneously. We found that Erin's age is 24 years.
Explanation:This problem is a classic example of a linear equation. We can set up two equations based on the information given:
Erin is 8 years younger than twice Paula’s age. This can be written as E = 2P - 8.The sum of their ages is 40. This can be written as E + P = 40.Upon substituting the value of E (Erin's age) from the first equation into the second, we get: 2P - 8 + P = 40. Simplifying this gives P = 16. Substituting P = 16 into the first equation, we find E = 24. Therefore, Erin is 24 years old.
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Is the relation a function? (3, 6) (10, 13) (11, 1) (13, 6)
Yes, Given relation is a function.
Here,
Points are given as,
(3, 6) (10, 13) (11, 1) (13, 6)
What is a function?
A function is defined as a relation between a set of inputs having one output each.
Now,
The given relation is a function because we don't have any repeated x values. Each input (x) leads to exactly one output (y). if we plotted all the points, then we would not be able to pass a single vertical line through more than one point. Hence, this graph complies vertical line test.
So, Given relation is a function.
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A student has to earn a total of at least 280 points on four tests in his math class to pass the class, and his total on the first three tests is 197 points. set up an inequality necessary to find the minimum number of points that he must earn on the fourth test to pass the class. then solve the inequality.
Jessica has two strings. the first string measures 80 cm and the second string measures 64cm. she wants to cut the strings into equal lengths. of the least number of strings equal length is 16 what is the length of each string
The sum of two numbers is 64 . the larger number is 22 more than the smaller number. what are the numbers?
64-22 = 42
42/2 = 21
21+22 = 43
21 + 43 = 64
the numbers are 21 & 43
The larger number is 43 and the smaller number is 21.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The numbers will be calculated as:-
Let the larger number be L and the smaller number be S.
L + S = 64
From the given data the larger number is 22 more than the smaller number
L = S + 22
Put L = S + 22 in the above equation.
S + 22 + S = 54
2S = 64 -22
2S = 42
S = 42 / 2 = 21
L = S +22 = 21 + 22 = 43
Therefore, the larger number is 43 and the smaller number is 21.
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You randomly select one card from a 52-card deck. find the probability of selecting a blackblack twotwo or a blackblack eighteight
A rectangle has a length of 9.00 inches and a width of 4.25 inches. What is the area in square inches? Round to the correct significant digits. DO I ADD UNITS?????
8.0 × 105 + 6.0 × 107 = A. 14,000,000,000,000 B. 140,000,000 C. 60,800,000 D. 68,000,000
Alexandra is two years older than brad. cecilia is three years younger than alexandra. all three ages added together gives a total of 37 years. how old is each student?
Let us say that:
x = age of brad
x + 2 = age of Alexandra
(x + 2) – 3 = age of Cecilia = x – 1
We are also given that:
x + x + 2 + x – 1 = 37
solving for x:
3x + 1 = 37
3x = 36
x = 12 = age of brad
x + 2 = 14 = age of Alexandra
x – 1 = 11 = age of cecilia
When is it helpful to round the quotient to the nearest hundredths?
What is a correct first step in solving the inequality-4(3_5×)>_6×+9?
Write the solution to the given inequality in interval notation
How much is 8% of 1249? round the answer to the nearest hundredth
7.1 + 16.04 – .2 = ?
Three member of a tug-of-war team weigh 163 pounds, 148 pounds. and 143 pounds. what must the fourth member weight if the average weight is 150 pounds?
Toni can carry up to 23 lb in her backpack. Her lunch weighs 1 lb, her gym clothes weigh 2 lb, and her books (
b. weigh 4 lb each. How many books can she carry in her backpack? The inequality is . Toni can carry up to books in her backpack.
Evaluate.
3+2⋅6
_____
3
Give the slope intercept form of the equation of the line that is perpendicular to 5x-3y=8
Brad makes his own snack mix using whole grain cereal and mixed nuts. One batch of his recipe makes 6 cups of snack mix. Brad uses 3 times as much cereal as mixed nuts. The system below can be used to find the number of cups of cereal and number of cups of mixed nuts Brad uses to make one batch of snack mix.
Which describes the ingredients Brad uses to make one batch of snack mix?
Answer:
The answer is 4.5 cups of cereal and 1.5 cups of mixed nuts
Step-by-step explanation:
Let 'c' be the number of cups of cereal.
Let 'n' be the number of cups of mixed nuts.
One batch of his recipe makes 6 cups of snack mix, so equation becomes:
[tex]c+ n=6[/tex] ..... (1)
Also given that Brad uses 3 times as much cereal as mixed nuts, so equation becomes:
[tex]c=3n[/tex] ......(2)
Substituting (2) in (1)
[tex]3n+n=6[/tex]
=> [tex]4n=6[/tex]
=> [tex]n=1.5[/tex]
Since c = 3n, then
[tex]c=3*1.5=4.5[/tex]
So, the answer is 4.5 cups of cereal and 1.5 cups of mixed nuts.
Harry's school is selling t-shirts to raise money for the archery team. The school will receive 35% of the total sales which can be modeled by the equation y = 0.35x, where x represents the total number of sales. What is the meaning of the x-intercept in the equation?
Answer:
X-intercept states that the graph crosses the x-axis.
Substitute y = 0 and solve for x.
As per the statement:
Harry's school is selling t-shirts to raise money for the archery team.
The school will receive 35% of the total sales which can be modeled by the equation:
y = 0.35x
where, x represents the total number of sales and y represents the total cost of sale.
By definition of x-intercept:
0 = 0.35x
⇒x = 0
Therefore, the x-intercept in the equation represents:
The number of sales when no money has been raised.
If 1 cm = 0.394 inches, how many inches are in 1 kilometer?
Answer: There are 39400 inches in 1 kilometers.
Step-by-step explanation:
Since we have given that
1 cm = 0.394 inches
As we know that
1 m = 100 cm
1 km = 1000 m
1000 m = 100×1000=100000 cm
1 km = 100000 cm
So, it becomes,
[tex]1\ km=0.394\times 100000\\\\1\ km=39400\ inches[/tex]
Hence, there are 39400 inches in 1 kilometers.