Answer:
A.The signs change from negative to positive.
Step-by-step explanation:
We are given that trapezoid in quadrant III rotates 180 degrees clockwise about the origin.
We have to find the effect of rotation on the sign of coordinates .
We know that the transformation rule of rotation 180 degrees about the origin is given by
[tex](x,y)\righatarrow (-x,-y)[/tex]
When a trapezoid lie in III quadrant then the coordinates of all four points are negative because in III quadrant x and y are both negative.
When the trapezoid rotates 180 degrees clockwise about the origin then by using the given rule the sign of coordinates from negative to positive.
Hence, option A is true.
The signs of both x and y coordinates of a trapezoid in Quadrant III change from negative to positive after a 180° clockwise rotation about the origin, resulting in a new position in Quadrant I.
When a trapezoid positioned in Quadrant III, where both x and y coordinates are negative, undergoes a 180° rotation clockwise about the origin, the signs of both coordinates change. This type of rotation is a half-circle and results in the figure being mirrored over the origin into the quadrant directly opposite Quadrant III, which is Quadrant I. Here, both the x and y coordinates become positive, as any point that was (-x, -y) in Quadrant III will become (x, y) in Quadrant I after a 180° rotation.
This transformation aligns with the properties outlined for rotational symmetry operations, reversing the direction of both the x and y vectors without altering their magnitudes. The correct answer to the student's question is therefore option A: The signs change from negative to positive.
Write the slope-intercept form of the equation of each line given the slope and y-intercept
1. slope = --1/2 y-intercrept = -2
2. slope = - 4/3, Y intercept = 1
3. Slope = 1/3, Y intercept = -1
4 slope = -1/2, Y intercept 4
If you can, please explain. Thanks!
To write the slope-intercept form of a linear equation, we use the formula y = mx + b, where m represents the slope and b represents the y-intercept.
Explanation:To write the slope-intercept form of a linear equation, we use the formula y = mx + b, where m represents the slope and b represents the y-intercept.
For the first equation, the slope is -1/2 and the y-intercept is -2. So the equation is y = -1/2x - 2.For the second equation, the slope is -4/3 and the y-intercept is 1. Therefore, the equation is y = -4/3x + 1.For the third equation, the slope is 1/3 and the y-intercept is -1. The equation is y = 1/3x - 1.For the fourth equation, the slope is -1/2 and the y-intercept is 4. The equation is y = -1/2x + 4.Learn more about Linear equations here:
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Carlos has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Answer:
25
Step-by-step explanation:
What does t equal ?
Answer:
t = 56.67
Step-by-step explanation:
Remark
If you are given a rhombus, what you are being told is that all 4 sides are equal. So WX = XY
Equation
6t - 82 = 3t + 88 Add 82 to both sides
Solution
6t - 82 + 82 = 3t + 88 + 82 Combine6t = 3t + 170 Subtract 3t from both sides6t - 3t = 3t - 3t + 170 Combine3t= 170 Divide by 3t = 170/3t = 56.67Which of the following equations is equivalent to 2/3x - 1/2y = 6?
2x - y = 6
2x - y = 36
4x - 3y = 36
Answer:
4x - 3y = 36
Step-by-step explanation:
2/3x - 1/2y = 6
Multiply each side by 6 to get rid of the fractions
6* (2/3x - 1/2y) = 6*6
Distribute the 6
12/3 x - 6/2y = 36
4x -3y = 36
simplify:
[tex] \sqrt[5]{3} + \sqrt{12} + \sqrt{32} [/tex]
[tex]\sqrt[5]3+\sqrt{12}+\sqrt{32}=\sqrt[5]3+\sqrt{4\cdot3}+\sqrt{16\cdot2}=\sqrt[5]3+\sqrt4\cdot\sqrt3+\sqrt{16}\cdot\sqrt2\\\\=\boxed{\sqrt[5]3+2\sqrt3+4\sqrt2}[/tex]
AB is dilated by a scale factor of 3 to form AB . Point O is the center of dilation, and point O lies on AB . If the slope of AB is 3, what can be said about line A'B' ?
A. The slope of is 6, but does not pass through O.
B. The slope of is 9, and passes through O.
C. The slope of is 9, but does not pass through O.
D. The slope of is 3, and passes through O.
E. The slope of is 3, but does not pass through O.
Option: D is the correct answer.
D. The slope of is 3, and passes through O.
Step-by-step explanation:It is given that:
AB is dilated by a scale factor of 3 to form AB .
Also, the line AB pass through the origin.
So, if AB pass through (0,0) and some point (x,y) then the slope of line AB is:
[tex]Slope=\dfrac{y-0}{x-0}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]
( Since, it is given the slope of AB is 3 )
Now , if AB is dilated to A'B' by a scale factor of 3 then
(0,0) → (0,0)
and
(x,y) → (3x,3y)
i.e. (0,0) and (3x,3y) will lie on A'B'.
Hence, the slope of line A'B' is given by:
[tex]Slope=\dfrac{3y-0}{3x-0}\\\\i.e.\\\\Slope=\dfrac{3y}{3x}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]
Hence, both have the same slope.
The answer is : Option: D
Answer:
Step-by-step explanation:
James cut three squares lasagnas so that each piece was 1/5 of a lasagna. How many pieces did James cut the lasagna into?
Final answer:
James cuts each of the three lasagnas into five equal parts, resulting in a total of 15 pieces of lasagna.
Explanation:
When James cuts each square lasagna into pieces that are each 1/5 of the lasagna, he's effectively dividing each whole lasagna into five equal parts. Since he has three whole lasagnas, each cut into 1/5-sized pieces, the total number of pieces he would end up with can be found by multiplying the number of pieces per lasagna by the number of lasagnas.
To calculate this, you multiply 5 (the number of pieces from one lasagna) by 3 (the number of lasagnas):
Multiply the number of pieces per lasagna (5) by the number of lasagnas (3).
5 pieces/lasagna × 3 lasagnas = 15 pieces
Thus, James cuts the lasagna into 15 pieces in total.
Find three ratios equivalent to 5/7
Answer:
10/14, 15/21
Step-by-step explanation:
WE are given a ratio 5/7
To find equivalent ratios it is sufficient to multiply both numerator and denominator by the same number
Let us take 2,3 for example.
When we multiply both numerator and denominator by 2, value does not change.
Hence we get equivalent fraction.
So 10/14 is one such fraction.
Next is multiply by 3
15/21 is another fraction.
The location of four game stops are on a coordinate grid are as follows:
Stop 1 at (−2,1)
Stop 2 at (−2, −7)
Stop 3 at (5,−7)
Stop 4 at (5, 1)
Paulo begins at Stop 1 and then walks to Stop 2, then Stop 3, and then Stop 4. Then he walks to Stop 1 again. The path between each stop is a straight line. One unit on the coordinate grid equals 125 feet.
What is the total distance Paulo walked?
Answer:
3750 feet
Step-by-step explanation:
Given that Paulo begins at Stop 1 and then walks to Stop 2, then Stop 3, and then Stop 4. Then he walks to Stop 1 again.
Where stops are given by coordinates:
Stop 1 at (−2,1)
Stop 2 at (−2, −7)
Stop 3 at (5,−7)
Stop 4 at (5, 1)
The path between each stop is a straight line. One unit on the coordinate grid equals 125 feet.
Now we need to find about what is the total distance Paulo walked.
So first we graph those points so that we can easily count the length of each side. then add each side to get the total length
length of rectangular path = 8+7+8+7=30
since one unit on the coordinate grid equals 125 feet. So to find the actual length we need to multiply 30 by 125 feet.
Hence final answer will be 125*30 = 3750 feet.
Which transformation changes triangle ABC to triangle A’B’C’?
Answer: rotation 180 degrees counterclockwise about the origin
Step-by-step explanation: the formula for rotating 180 degrees is (x , y) = (-x , -y). thus, an example of point A is (2 , -4), and it results in being (-2, 4), and so forth for the following points.
Answer:
Reflection about the y axis, and then about the x- axis
Step-by-step explanation:
When reflecting an object about the y- axis, the x-coordinates are multiplied with -1.
When reflecting an object about the x-axis, the y-coordinates are multiplied with -.
When reflecting about both axes, both coordinates are multiplied by -1.
Now looking at the coordinates of the two triangles:
A(2, -4) → A'(-2, 4)
B(5, -5) → B'(-5, 1)
C(4, -5) → C'(-4, 5)
All of the coordinates are multiplied by -1.
Which algebraic rule describes the transformation?
A) (x, y) → (x + 1, y − 3)
B) (x, y) → (x + 3, y − 1)
C) (x, y) → (x − 1, y + 3)
D) (x, y) → (x − 3, y + 1)
Answer:
B
Step-by-step explanation:
To get to to triangle Y'X'Z', you need to move triangle YXZ 3 units to the right (+3), and 1 unit down (-1). So (x+3,y-1)
Answer:
b
Step-by-step explanation:
athaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below. What are the solutions to the equation? x = –1, 6 x = –6, 1 x = –22, 27 x = –27, 22
Answer:
x = - 6 or x = 1
Step-by-step explanation:
given a quadratic equation in standard form : ax² + bx + c = 0 : a ≠ 0
then the equation can be solved using the quadratic formula
• x = ( - b ± [tex]\sqrt{b^2-4ac}[/tex]) / 2a
x² + 5x - 6 = 0 is in standard form
with a = 1, b = 5 and c = - 6
x = (- 5 ± [tex]\sqrt{5^2-(4(1)(-6)}[/tex]) / 2
= (- 5 ± [tex]\sqrt{25+24}[/tex]) / 2
= (- 5 ± [tex]\sqrt{49}[/tex]) / 2
x = [tex]\frac{-5-7}{2}[/tex] = [tex]\frac{-12}{2}[/tex] = - 6
or x = [tex]\frac{-5+7}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1
The solutions to the quadratic equation x² + 5x - 6 = 0 are x = 1 and x = -6.
Explanation:To solve the quadratic equation x² + 5x - 6 = 0, Nathaniel used the quadratic formula.
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c correspond to the coefficients of the quadratic equation.
In this case, a = 1, b = 5, and c = -6.
Substituting these values into the quadratic formula, we get x = (-5 ± √(5² - 4(1)(-6))) / (2(1)).
Simplifying further, we have x = (-5 ± √(25 + 24)) / 2.
This yields two solutions: x = (-5 + √49) / 2 and x = (-5 - √49) / 2.
Simplifying the square root, we get x = (-5 + 7) / 2 and x = (-5 - 7) / 2.
Therefore, the solutions to the quadratic equation are x = 1 and x = -6.
The selling price of a chair is Rs 980 with a loss of 20%. What is the cost price of the chair?
Answer:
1225
Step-by-step explanation:
a loss of 20% represents 80% ( 100 - 20) of the cost price
100% represents the cost price
To find the cost price divide the selling price by 80 to find 1% and multiply by 100 to find cost price
cost price = [tex]\frac{980}{80}[/tex] × 100 = 1225
Sally and her husband Jim left their house at the same time traveling in the same direction. Sally drove at 55mph and Jim drove at 65mph. How many hours was it before Jim was 100 miles ahead of Sally?
Answer:
It will take 10 hours.
Step-by-step explanation:
We know distance = rate * time
Sally's rate = 55
Jim's rate = 65
We want Jim to be 100 miles ahead of Sally
The time will always be the same.
d =Sally's distance
Sally
d = 55t
Jim
d+100 = 65 t
We know have 2 equations with 2 unknowns. Substitute d= 55t into Jim's equations
55t + 100 = 65t
Subtract 55t from both sides.
55t-55t + 100 = 65t-55t
100 = 10t
divide each side by 10
100/10 = 10t/10
10 = t
Answer:
It will take exactly 10 hours
Step-by-step explanation:
what is the factored for of the polynomial x2 - 16x + 48
Answer:
[tex](x-12)(x-4)[/tex]
Step-by-step explanation:
[tex]x^2 - 16x + 48[/tex]
In the given expression , the product is 48 and sum is -16
-4 times -12 gives us 48
-4 plus -12 gives us -16. So two factors are -4 and -12
Beak the middle term using factors
[tex]x^2 -4x-12x+48[/tex]
Group first two terms and last two terms
[tex](x^2 -4x)+(-12x+48)[/tex]
FActor out GCF from each group
[tex]x(x -4)-12(x-4)[/tex]
FActor out x-4 that is in common
[tex](x-12)(x-4)[/tex]
what is the answer to 4r + 9r - 11r + 7r
Answer:
9r
Step-by-step explanation:
Simplify:
4r + 9r - 11r + 7r
13r - 11r + 7r
2r + 7r
9r
The answer to the given expression i.e. 4r + 9r - 11r + 7r is 9r.
Given that,
The given expression is 4r + 9r - 11r + 7r.We need to solve the above expression.Based on the above information, the calculation is as follows:
= 4r + 9r - 11r + 7r
= 20r - 11r
= 9r
Therefore we can conclude that the answer to the given expression i.e. 4r + 9r - 11r + 7r is 9r.
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For f(x)=-2x-13, find f(x) when x=5
Can someone please help me?
Answer:
f(x) = -38
Step-by-step explanation:
well f(x) is the same thing as y so just write it as y so its easier to understand.
y = -2x -13
take the x value they give you which in this case is 5 and plug it in to the x in your equation.
y = -2(5) -13
now just use a calculator or something and find that
y = -25 - 13
and finally
y = -38
now just change y back to f(x) if needed
hope this helps :)
Ms. Valenzuela had her students design a snake house for the zoo. In the de3sign shown, the anaconda has 538 more square feet than the python. The python has twice as many square feet as the rattlesnake. How much area does each snake have?
Answer:
If the python has the area x sq. ft, they all have the area [tex]\dfrac{5x}{2}+538\ sq. ft.[/tex]
Step-by-step explanation:
Let x sq. ft be the area the python has.
1. If the anaconda has 538 more square feet than the python, then the anaconda has (x+538) sq. ft.
2. If the python has twice as many square feet as the rattlesnake, then the rattlesnake has the area [tex]\dfrac{x}{2}\ sq. ft.[/tex]
In total they have the area
[tex]x+(x+538)+\dfrac{x}{2}=\dfrac{5x}{2}+538\ sq. ft.[/tex]
What is 90/70
Simplified
As an improper fraction, the simplified answer would be 9/7 after you divide both top and bottom by 10
------------------------
If you need a mixed number, then 9/7 converts to 1 & 2/7 because
9/7 = 1 remainder 2
If you had 9 cookies and 7 friends, then each friend gets 1 whole cookie, and there will be 2 left over.
Answer:
The answer would be 9/7 as improper, but if you want the mixed number it would be 2 2/7. Glad I could help let me know if I can do anything else
Step-by-step explanation:
Use what you know about the sum of the angles of a triangle to find m
Answer:
Angle ABC is 22 degrees
Angle BAC is 68 degrees
======================================
Work Shown:
Because there are just 3 points, we can refer to "angle BAC" as "angle A" and "angle ABC" as "angle B". Focus on the middle letter of each three-letter sequence.
The three angles A, B, C add up to 180 degrees. This is true for any triangle.
A+B+C = 180
(6x+8) + (2x+2) + 90 = 180 ... substitution
6x+8 + 2x+2 + 90 = 180
8x+100 = 180
8x+100-100 = 180-100 ... subtract 100 from both sides
8x = 80
8x/8 = 80/8 ... divide both sides by 8
x = 10
If x = 10, then angle BAC is
angle BAC = 6x+8
angle BAC = 6*10+8
angle BAC = 60+8
angle BAC = 68
Use x = 10 to find angle ABC as well
angle ABC = 2x+2
angle ABC = 2*10+2
angle ABC = 20+2
angle ABC = 22
The three angles of this triangle are A = 68, B = 22, C = 90
As a check, the three angles must add to 180
A+B+C = 180
68+22+90 = 180
180 = 180
Answers are confirmed
Another thing to notice is that A+B = 90 meaning that A and B are complementary angles. A+B = 68+22 = 90.
Jason spends 3 1/12 hours biking and 2 1/3 hours at the mall. How much less time does Jason spend at the mall compared to biking?
We must find the difference between 3 1/12 and 2 1/3. So we can first subtract 3 from 2 and we earn 1 whole number. Next we must subtract 1/12 and 1/3. This is the same as 3/36-12/36, which is -9/36 or -1/4. Since we can't have -1/4 we must subtract 1/4 from 1 and earn 3/4 as our answer.
Hope this helps! <3
Mrs.Barkley has 75 feet ribbon. If each of the 18 students in her class gets an equal length of ribbon, how many inches of ribbon will each student get?
Answer:
Each student would get 4 inches of ribbon
Step-by-step explanation:
Mrs. Barkley has 75 inches of ribbon and is splitting it between 18 students so you would divide 75 by 18. When you divide you get 4.166666... etc. So the answer would be 4
Each of the 18 students in Mrs. Barkley's class will receive 50 inches of ribbon when 75 feet of ribbon are divided equally among them.
The student has asked how many inches of ribbon each student will get if Mrs. Barkley has 75 feet of ribbon and splits it equally among 18 students. To solve this problem, we first need to convert feet to inches because there are 12 inches in a foot. Then we divide the total inches of ribbon by the number of students.
Total length of ribbon for each student= 75/18
The total length of ribbon for each student≈4.1667
So, each student will receive approximately 4.1667 feet of ribbon.
To find out how many inches this is, we'll convert this value to inches. Since 1 foot is equal to 12 inches, we can multiply the total length of the ribbon for each student by 12:
The total length of ribbon for each student (in inches)=4.1667×12
The total length of ribbon for each student (in inches)≈49.9999
Therefore, each student will receive approximately 50 inches of ribbon.
Norah has 2/3 ton of stone to spread equally in 4 square yards. How many tons of stone will be spread in each square yard?
Answer:
The answer is 1/6.
In each square yard, Norah would spread 1 / 6 ton of stone.
Given that,
Norah has 2/3 tons of stone to spread equally in 4 square yards, how many tons of stone will be spread in each square yard is ot be determined.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Quantity if Stone = 2/3 ton
Area = 4 square yards
Quantity per yard = [2/3] / 4= 1 / 6
Thus, in each square yard, Norah would spread 1 / 6 ton of stone.
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Factor -.36 out of -1.8w+3.96
[tex]-1.8w+3.96=(-0.36)(5w)+(-0.36)(11)\\\\=\boxed{-0.36(5w+11)}[/tex]
Which of the following is an irrational number?
Answer:
7.25252525
Step-by-step explanation:
Irrational numbers are numbers that never end, therefore 7.25 is an irrational number. also, none of the other ones are never ending
The ratio of students who walk home from school to the students who ride the bus is 2:7
The number of bus riders is how many times the number of students who walk home?
Answer:
2.5 is the answer
Step-by-step explanation:
7/2 = 2.5
You need to divide the no of bus rider with no of students
A box contains10 pens, 5 of the pens are red, 4 are balck and 1 are bluem What is the probability of pulling out a black pen first, putting it back into the box, and then pulling a red pen ?
Final answer:
The probability of drawing a black pen first and then a red pen with replacement from a box of 10 pens is 20%.
Explanation:
To calculate the probability of drawing a black pen and then a red pen with replacement in a box that contains 10 pens, we should calculate the probability of each event separately and then multiply them since the events are independent.
There are 5 red pens, 4 black pens, and 1 blue pen, making a total of 10 pens. The probability of drawing a black pen is the number of black pens divided by the total number of pens: P(black) = 4/10 or 0.4.
Since the pen is replaced, the total stays the same. Therefore, the probability of then drawing a red pen is the number of red pens divided by the total number of pens: P(red) = 5/10 or 0.5.
To find the combined probability of both events happening in sequence (drawing a black pen and then a red pen), we multiply the two probabilities together: P(black and red) = P(black) × P(red) = 0.4 × 0.5 = 0.2 or 20%.
During a recent shopping trip, Erin bought six shirts that cost $15.95 each. How much change did Erin receive if she paid with a $100 bill?
Answer:
4 Dollars and 30 cents
Step-by-step explanation:
15.95 x 6 = 95.7
100-95.7= 4.30
Final answer:
Erin bought six shirts at $15.95 each, totaling $95.70. After paying with a $100 bill, she would receive $4.30 in change.
Explanation:
The question asks us to calculate the total cost of six shirts and then determine the change from a $100 bill. Erin bought six shirts that cost $15.95 each. To find the total cost, we multiply the price of one shirt by the number of shirts:
$15.95 × 6 = $95.70.
Next, we calculate the change Erin would receive if she paid with a $100 bill:
$100 - $95.70 = $4.30.
Therefore, Erin would receive $4.30 in change.
Please Help!
Write an inequality and solve each problem.
Two less than a number is less than 9.
Answer:
Step-by-step explanation:
Unknown number be 'x'
X-2<9
An explanation of solving an inequality where the number is two less than a number less than 9.
An inequality can be written as: x - 2 < 9, where x is the number.
To solve the inequality:
Add 2 to both sides: x < 11
So, the solution to the inequality is: x < 11
the equation of a circle is given below x^2 + (y+4)^2 = 64. What is its center? what is its radius?
The center of the circle described by the equation x^2 + (y+4)^2 = 64 is at the point (0,-4), and the radius is 8.
Explanation:In the context of a circle, the general equation form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Looking at your given equation x^2 + (y+4)^2 = 64, it is in this general format.
Here, the value of a is 0 (as there is no number being subtracted from x) and b is -4 (the y coordinate has been shifted 4 units down). Therefore, the center of the circle is at point (0,-4).
For the radius, since r^2 = 64, the radius r will be the square root of 64 which is 8.
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