when the figure below is rotated 90 degrees counterclockwise about the origin what would be the new coordinates of point c?
a (-5,3)
b (3,-5)
c (5,-3)
d (5,3)
Answers
When a point is rotated 90 degrees counterclockwise about the origin, its new coordinates can be found by swapping the x and y coordinates and changing the sign of the new y coordinate. In this case, the new coordinates of point C would be (-3,-5).
Explanation:When a point is rotated 90 degrees counterclockwise about the origin, its new coordinates can be found by swapping the x and y coordinates and changing the sign of the new y coordinate.
In this case, point C has coordinates (5,-3). When we rotate it, the new x coordinate becomes -3 and the new y coordinate becomes -5. Therefore, the new coordinates of point C would be (-3,-5).
Related Questions
In a rhombus, an altitude from the vertex of an obtuse angle bisects the opposite side. Find the measures of the angles of the rhombus.
Answers
Drawing the altitude forms a right triangle. Let the side of the rhombus be x. The altitude bisects the opposite side, so the base of the triangle formed would be 1/2x. We have an expression for the side opposite this portion of the obtuse angle (cut by the altitude) and for the hypotenuse (the side length of the rhombus, x). opposite/hypotenuse is the ratio for sine. Our equation then looks like this:
[tex]\sin x=\frac{\frac{1}{2}x}{x} \\ \sin x=\frac{1}{2}x \div x \\ \sin x=\frac{1}{2}x \div \frac{x}{1} \\ \sin x=\frac{1x}{2} * \frac{1}{x}=\frac{1x}{2x}=\frac{1}{2}[/tex]
Now we take the inverse sine of both sides:
sin⁻¹(sin x)=sin⁻¹(1/2)
x=30
Since this portion of the triangle is 30, and the right angle is 90, the missing angle (an acute angle of the rhombus) is 180-30-90=60°. Since the acute angles and obtuse angles of a rhombus are supplementary, the obtuse angles must be 180-60=120°.
The angles of the rhombus determines the inclination of the sides of the
rhombus.
The correct response;The measures of the four angles of the rhombus are 60°, 60°, 120°, and 120°.Method used to arrive at the above response;Given;The altitude of the rhombus bisects the opposite side.
The angle of the rhombus at the vertex point of the altitude = An obtuse angle
Required:The measure of the angles of the rhombus
Solution:The length of the sides of a rhombus are equal.
The opposite angles of a rhombus are equal.
Let x represent the length of a side of the rhombus, we have;
The bisector from the vertex of the obtuse angle = An altitude
The angle the altitude forms with the side it bisects = 90°
Therefore;
The triangle formed by the altitude, half the bisected side and the side of the rhombus adjacent to the bisected side = A right triangle
The hypotenuse side to the right triangle = The side of the rhombus
Let θ represent the angle opposite the altitude, and between the sides of
the rhombus, in the right triangle by trigonometric ratios, we have;
[tex]\displaystyle cos(\theta) = \mathbf{\frac{Adjacent}{Hypotenuse}}[/tex][tex]\displaystyle cos(\theta) = \frac{0.5 \cdot x}{x} = 0.5[/tex]
θ = arccos(0.5) = 60°
Therefore, two acute (opposite) angles of the rhombus are 60°
The two obtuse angles of the rhombus are each = (360° - 2×60°) ÷ 2 = 120°
The angles of the rhombus are 60°, 60°, 120°, 120°.Learn more about trigonometric ratios here:
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what is the area of this parallelogram?
44cm^2
55cm^2
99cm^2
220cm^2
(I forgot to put the picture on this one)
D. (4cm) F. 5cm C.
(11cm)
A. 5cm E 4cm B.
~~~~~~~~~~~~~~~~~~
what is the area of this parallelogram?
10.35cm^2
12.5cm^2
20.25cm^2
30.6cm^2
Answers
A= bh
Where b is the length of base and h is the height.
Here b=2.3+4.5 = 6.8 cm
and h= 4.5 cm
Put values in formula.
A= 6.8 x 4.5
A=30.6 cm²
Answer: 30.6 cm²
Find the length of a rectangular prism having a volume of 2830.5 cubic meters , width of 18.5 meters, and height of 9 meters.
Answers
Answer:
l = 17 m
w = 18.5 m
h = 9 m
d = 26.688 m
S = 1268 m2
V = 2830.5 m3
What is the value of 60 tens?
Answers
[tex] {10}^{6} [/tex]
You would multiply 60 times 10.
Hope it helped!:)
Use the compound interest formula to find the future value A for the following values.
P= $ 1,500
i = 0.075
n= 26
Answers
Help me fast pleaseee
Answers
Since 9 is closer to 10 than 0, we round up.
Simplify this algebraic expression
Z-4/4+8
A. Z-7
B.z+7
C.z+9
D.z-3
Answers
Z - 1 + 8
Z + (-1 + 8)
Z + 7
Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
Answers
f(-1) = 3 - 4 + 13 - 16 + 4 = 0 This one works so one factor is (x + 1)
f(-1/3) = gives a 0. So another factor is 3x + 1
The last factor is found by dividing 3x^2 + 4x + 1 into the original equation. That's (3x + 1)(x + 1) expanded.
When you do that you find that the last factor is (x^2 + 1)
You can see how this is factored at Wolframalpha dot com
a round swimming pool has a circumference of 54 ft. Carrie wants to buy a rope to put across the diameter of the pool. the rope cost $0.85 per foot, and carrie need 3 feet more then the diameter of the pool. how much will carrie pay for the rope?
Answers
If the diameter of the pool is 54 feet, then you add 3 since Carrie needs 3 feet more than the diameter.
54 + 3 = 57
Last, you multiply the number of feet needed for the rope times the cost per foot of the rope:
57 x 0.85 = 45.9 <-----------
Carrie will pay $45.9 for the rope.
Hope this helps you.
Have a great day!
Assume c and d function independently. for the system to function, either c or d must function.
a. if the probability that c fails is 0.08 and the probability that d fails is 0.12, find the probability that the system functions.
b. if both c and d have probability p of failing
Answers
[tex]\mathbb P(C\cup D)=\mathbb P(C)+\mathbb P(D)-\mathbb P(C\cap D)[/tex]
but since [tex]C[/tex] and [tex]D[/tex] are independent,
[tex]\mathbb P(C\cup D)=\mathbb P(C)+\mathbb P(D)-\mathbb P(C)\mathbb P(D)[/tex]
We're given that [tex]\mathbb P(C^C)=0.08[/tex] and [tex]\mathbb P(D^C)=0.12[/tex], so
[tex]\mathbb P(C\cup D)=(1-0.08)+(1-0.12)-(1-0.08)(1-0.12)=0.9904[/tex]
If [tex]\mathbb P(C^C)=\mathbb P(D^C)=p[/tex], then
[tex]\mathbb P(C\cup D)=(1-p)+(1-p)-(1-p)^2=1-p^2[/tex]
The probability that the system functions is 1. In part b, the probability that the system functions is 2 - 2p.
Explanation:To find the probability that the system functions, we need to find the probability that either c or d functions. Since c and d function independently, we can use the addition rule of probability. The probability that c functions is 1 minus the probability that c fails, which is 0.08, so the probability that c functions is 1 - 0.08 = 0.92. Similarly, the probability that d functions is 1 - 0.12 = 0.88. Since either c or d must function, we can add the probabilities of c and d functioning: 0.92 + 0.88 = 1.80 (which exceeds 1 since it's not possible for both c and d to function simultaneously). Therefore, the probability that the system functions is 1.
In part b, if both c and d have a probability p of failing, then the probability that c functions is 1 - p, and the probability that d functions is also 1 - p. Again, using the addition rule of probability, the probability that the system functions is: (1 - p) + (1 - p) = 2 - 2p.
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Tomas wrote the equation y = 3x 3/4+. When Sandra wrote her equation, they discovered that her equation had all the same solutions as Tomas’s equation. Which equation could be Sandra’s?
Answers
Answer:
–6x + 2y = 3/2 is Sandra's equation.
Step-by-step explanation:
Given Equation of Tomas is
[tex]y=3x+\frac{3}{4}[/tex]
Solution of equation of Sandra is same as solution of Tomas Equation.
This only possible when ratio of the coefficients of the variable and constant term is equal.
So,
Multiply Tomas equation with 2.
2y= 6x + 3/2
This is one of the equation possible for Sandra's equation
Therefore, –6x + 2y = 3/2 is Sandra's equation.
Solve –19 = x – 4. A. x = –76 B. x = 25 C. x = –15 D. x = –23
Answers
Answer:
The answer is : -15 (C)
Step-by-step explanation:
–19 = x – 4
x - 4 = -19
x = -19 + 4
x = -15
Graph y=(x+2)^2-3
Show Vertex
Answers
Answer:
-3,2
Step-by-step explanation:
just took the test edge 2020
Shelley compared the number of oak trees to the number of maple trees as part of a study about hardwood trees in a woodlot. She counted 9 maple trees to every 5 oak trees. Later in the year there was a big problem and many trees died. New trees were planted to make sure there was the same number of trees as before the big problem. The new ratio of the number of maple trees to the number of oak trees is 3:11. After planting new trees, there were 132 oak trees. How many more maple trees were in the woodlot before the big problem than after the bug problem? Explain.
Answers
Prior to the major issue, the woodlot had 72 more maple trees than it had after.
To solve this problem
Assuming x is a positive constant, we can represent the initial number of oak trees as 5x and the initial number of maple trees as 9x.
Prior to the problem, the ratio of maple trees to oak trees was 9:5, which produced the following equation:
[tex](9x)/(5x) = 9/5[/tex]
Later, the new ratio changed to 3:11 after new trees were planted to replace the original amount of trees. After planting, 132 oak trees were reported to have been planted. We so established the equation:
11y = 132
Solving for y:
y = 132/11 = 12
Now, we can find the new number of maple trees:
3y = 3 * 12 = 36
There were 36 maple trees when new trees were planted.
Before the problem, there were 9x as many maple trees as there were.
9x = 9 * 12 = 108
The difference between the original and new number of maple trees is:
108 - 36 = 72
So, Prior to the major issue, the woodlot had 72 more maple trees than it had after.
The game of european roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. a ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. gamblers can place bets on red or black. if the ball lands on their color, they double their money. if it lands on another color, they lose their money.
Answers
Answer:
a) Expected amount of winnings = -$0.084
Standard deviation = $3.00
b) Expected amount of winnings = -$0.084
Standard deviation = $1.73
c) The expected winnings for both cases is exactly the same, but the spread of the wins about the expected value/mean is low in the case (b) compared to case (a).
So, with the expected winnings using the method in (a) and (b) the same, the risk associated with betting $3 dollar per game is higher because it has a higher standard deviation. This points to higher spread of losses and wins betting $3 once than betting $1 three different times.
Step-by-step explanation:
(a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings?
It's either one wins or not with a bet of $3.
We can then obtain the probability mass function.
Random variable X represents the amount of winnings.
- If one bets $3 and picks the right colour, the person wins $6.
X = amount of winnings = 6 - 3 = $3
probability of winning = (18/37) = 0.486
- If one bets $3 and picks the wrong colour, then the person wins $0.
X = amount of winnings = 0 - 3 = -$3
Probability of losing = (19/37) = 0.514
The probability mass function is then
X | P(X)
3 | 0.486
-3 | 0.514
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
E(X) = (3×0.486) + (-3×0.514) = -$0.084
Standard deviation = √(variance)
Variance = Var(X) = Σx²p − μ²
μ = E(X) = -0.084
Σx²p = (3²×0.486) + [(-3)² × 0.514] = 9
Variance = 9 - (-0.084)² = 8.993
Standard deviation = √8.993 = 2.999 = $3
(b) Suppose you bet $1 in three different rounds. What is the expected value and standard deviation of your total winnings?
With a bet of $1,
It's either one wins or not with a bet of $1.
We can then obtain the probability mass function.
Random variable X represents the amount of winnings.
- If one bets $1 and picks the right colour, the person wins $2.
X = amount of winnings = 2 - 1 = $1
probability of winning = (18/37) = 0.486
- If one bets $1 and picks the wrong colour, then the person wins $0.
X = amount of winnings = 0 - 1 = -$1
Probability of losing = (19/37) = 0.514
The probability mass function is then
X | P(X)
1 | 0.486
-1 | 0.514
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
E(X) = (1×0.486) + (-1×0.514) = -$0.028
For 3 rounds of $1, the expected amount of winnings = 3 × -0.028 = -$0.084
Variance = Var(X) = Σx²p − μ²
μ = E(X) = -0.028
Σx²p = (1²×0.486) + [(-1)² × 0.514] = 1
Variance = 1 - (-0.028)² = 0.999216
Variance for combining 3 independent distributions = Σ λᵢ²σᵢ²
Variance of 3 rounds of $1 bets = 3[1²× var(X)] = 3 × var(X) = 3 × 0.999216 = 2.997648
Standard deviation = √(variance) = √(2.997648) = $1.73
(c) How do your answers to parts (a) and (b) compare? What does this say about the riskiness of the two games?
The expected winnings for both cases is exactly the same, but the spread of the wins about the expected value/mean is low in the case (b) compared to case (a).
So, with the expected winnings using the method in (a) and (b) the same, the risk associated with betting $3 dollar per game is higher because it has a higher standard deviation. This points to higher spread of losses and wins betting $3 once than betting $1 three different times.
Hope this Helps!!!
In matrix T, what is the value of element t13?
Answers
in the matrix T the element t(13) refers to the element in row 1 and column 3
therefore
the answer is 7
Natalia paid $38.95 for three medium sized pizzas and a salad. Solve an equation to find the cost of one pizza,p, if Natalia paid $11.98 for the salad
Answers
The cost of each pizza is
[tex]8.99 \: dollars[/tex]
EXPLANATION
We were given that, Natalia paid $38.95 for three medium sized pizzas and a salad.
Let
[tex]p[/tex]
represent the cost of each pizza and
[tex]s [/tex]
be the price of a salad.
Then we can write the equation,
[tex]3p + s = 38.95...(1)[/tex]
But we were also told that Natalia paid $11.98 for a salad. This means the cost of a salad is $11.98.
This implies that,
[tex]s = 11.98...(2)[/tex]
We now put equation (2) into equation (1) to get,
[tex]3p + 11.98 = 38.95[/tex]
We now solve for p to obtain,
[tex]3p = 38.95 - 11.98[/tex]
This gives us,
[tex]3p = 26.97[/tex]
We divide through by 3 to get,
[tex]p = 8.99[/tex]
Therefore the cost of each pizza is $8.99.
The linear equation is defined as the equation, which can be represented in the form of y=mx+b.
The cost of one pizza is $ 8.99.
Given that,
Cost of salad = $ 11.98Let the cost of pizza be x.The three pizzas cost will be 3x. The total cost of the food items = $ 38.95Now, using the linear equation formula:
Total cost = Cost of three pizzas + Cost of Salad
Substituting the values, the equation becomes:
$ 38.95 = 3x + $ 11.98
$ 38.95 - $ 11.98 = 3x
$ 26.97 = 3x
x = [tex]\dfrac{26.97}{3}[/tex]
x = $8.99
Therefore, the value of each pizza is $8.99.
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WILL GIVE BRAINLIEST
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
Enter your answer in the box.
m∠B=
Answers
5x = 200
x = 40
<B = 4(40) - 20 = 160 - 20 = 140
answer
<B = 140
General Idea:
A cyclic quadrilateral has all its vertices on the circumference of the circle. The opposite angles of a cyclic quadrilateral are supplementary, that is it add up to get 180 degrees.
Applying the Concept:
Opposite angles B and D add up to give 180 degrees.
[tex] \angle B + \angle D=180\\ \\ 4x-20+x=180\\ Grouping \; like \; terms\\ \\ 4x+x-20=180\\ Combining \; like\; terms\\\\ 5x-20 =180\\ Adding \; 20 \; on\; both\; sides\\ \\ 5x-20+20=180+20\\ Combine\; like\; terms\\ \\ 5x=200\\ Divide\; 5\; on\; both\; sides\\ \\ \frac{5x}{5} =\frac{200}{5} \\ Simplify \; fraction\; on\; both\; sides\\ \\ x=40\\ \\ Substitute \; 40\; for\; x\; in\; the\; expression\; for\; \angle B \\ \angle B=4x-20=4(40)-20=160-20\\\\\angle B=140 [/tex]
Conclusion:
When Quadrilateral ABCD is inscribed in this circle, the measure of angle B for the given diagram is [tex] 140^{\circ} [/tex]
1. A/an _______ triangle has all three angles measuring less than 90°. A. right B. obtuse C. scalene D. acute
Answers
So, the answer is
D)
What is m∠KNL?
Enter your answer in the box.
Answers
Set up am equation to make them equal to each other.
5x+2 = 3(x+14)
Distribute 3 to the values in the parentheses
5x+2 = 3x+42
Subtract 3x from both sides
2x +2 = 42
Subtract 2 from both sides
2x = 40
Divide both sides by 2
X=20
Substitute 20 for x in the angle KLN
3(20+14)
Simplify parenthesis
3(34)
Multiply
KLN =102 degrees
There are several relationships between angles in a transversal.
The measure of KNL is 102 degrees.
From the figure,
Angles KNJ and JNM are corresponding angles
So, we have:
[tex]KNJ = JNM[/tex]
This gives
[tex]3(x + 14) = 5x + 2[/tex]
Open brackets
[tex]3x + 42 = 5x + 2[/tex]
Collect like terms
[tex]3x - 5x = 2 - 42[/tex]
[tex]-2x = -40[/tex]
Divide both sides by -2
[tex]x = 20[/tex]
Angle KNL is
[tex]\angle KNL =3(x + 14)[/tex]
Substitute 20 for x
[tex]\angle KNL =3(20 + 14)[/tex]
[tex]\angle KNL =3(34)[/tex]
[tex]\angle KNL =102[/tex]
Hence, the measure of KNL is 102 degrees.
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What is the constant of variation for the quadratic variation? 0.1y = 3x2
Answers
Answer:
The constant of variation for the given quadratic equation is, 30
Step-by-step explanation:
One of the form of a quadratic equation is written as:
[tex]y = kx^2[/tex] ....[1]
where k is the coefficient and for this case the constant of variation.
In order to obtain the answer for the given equation, we write the given equation to the form above.
[tex]0.1y=3x^2[/tex] or
[tex]y=(\frac{3}{0.1})x^2[/tex] or
[tex]y=30x^2[/tex]
Comparing this equation with equation [1], to get the value of k;
k=30.
therefore, the constant of variation is, 30.
The length of a rectangle is 8 cm more than 3 times its width. The perimeter of the rectangle is 64 cm. Show the equation that would be used to find the dimensions of the rectangle.
Answers
the length (l) is 8 more than 3 times the width (w) and the length plus the width is equal to half the perimeter
so the means that L= 3W+8 and L+W= 32
so you can plug in L to get 3W+8+W=32
Finally it would be 4W+8=32
To find the dimensions of a rectangle with length '8 cm more than 3 times the width' and a perimeter of 64 cm, form the equation 2(3W+8) + 2W = 64. Solving for W gives the width, which can be substituted into the equation 3W+8 to give the length.
Explanation:The subject of the question is algebra, specifically how to form equations based on word problems involving geometric shapes. The rectangle problem you've given can be solved using the formulas for the perimeter of a rectangle.
The perimeter 'P' of a rectangle is given by P=2(length) + 2(width). In the problem, the length 'L' is given as 8 cm more than 3 times the width 'W', or L=3W+8. The perimeter 'P' is stated as 64 cm, so substituting our equation for length into the perimeter equation, we get 2(3W+8) + 2W = 64. This equation will yield the width of the rectangle. To get the length, you simply substitute the width into the length equation.
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HELP!
Solve equation...
please show steps
Answers
Solve the exponential equation algebraically and use a graphing utility
400/1+e^-x= 350
Answers
[tex]400=350(1+e^{-x} )[/tex]
[tex]400=350+350e^{-x} [/tex]
[tex]50=350e^{-x} [/tex]
[tex]350e ^{-x} =50[/tex]
[tex]e^{-x} = \frac{50}{350} [/tex]
[tex]e ^{-x} = \frac{1}{7} [/tex]
[tex]ln(e ^{-x} )=ln( \frac{1}{7} )[/tex]
[tex]-x=ln( \frac{1}{7} )[/tex]
[tex]x=-ln( \frac{1}{7} )[/tex]
[tex]x=1.95[/tex]
Now to find the solution using a graphing utility, just type the equation and look for the point in which the graph intercepts the x-axis as shown in the picture. The point in which the graph intercepts the x-axis is a zero of the function, and therefore the solution.
Can you please help me ??
Answers
You have to apply the Phytagorean Teorem, which is:
c^2 = a^2 + b^2
c=√(a^2 + b^2)
"c" is the hypotenuse.
"a" and "b" are the legs of the triangle (10 inches and 15 inches).
Let's substitute those values in the equation:
c=√(a^2 + b^2)
c=√(10^2 + 15^2)
c=√325
c=18 inches
What is the smallest possible whole-number length of the unknown side?
It is the next largest integer greater: 19 inches.
what is the value of log5 125
Answers
[tex]log_bX=a <=>X=b^a[/tex]
This means that
[tex]log_5125=a <=>125=5^a[/tex]
but we know that 5^3=5*5*5=125
therefore
a=3, or
[tex]log_5125=3[/tex]
Solve the system of equations using the linear combination method.
{4x−3y=12
7x−3y=3
Enter your answers in the boxes.
x =
y =
Answers
-7x + 3y = -3
------------------
-3x + 0 = 9
x = -3
4(-3) - 3y = 12
-12 - 3y = 12
-3y = 12 + 12
-3y = 24
y = -8
Answer:
x = -3
y = -8
Step-by-step explanation:
I took the test
the set of points (2,3,), (9,3), (9, -2), and (2,-2) identifies the vertices of a quadrilateral. which is the most specific describtion to tell which figure the points form?
Answers
it has two parallel sides, is a parallelogram.
it also has 4 right-interior-angles, so is a rectangle as well.
Harrison High School has 768 students. In 6 years, it is projected to have 1,157 students. What is the projected average rate of change per year in students over this time period?
Answers
a store is going out of business everything is marked down 40% how much do you pay for an item that cost $150
Answers
x= sale price
x= $150 - ($150 * 40%)
x= 150 - (150 * 0.40)
x= 150 - 60
x= $90 sale price
CHECK:
=150*60%
=$90
You can also find the sale price this way. Multiply the original price by 100-sale percent).
ANSWER: The sale price is $90.
Hope this helps! :)