Answers
Related Questions
Point Q with coordinates (4, –7) is rotated 270° clockwise about (5, 1) . What are the coordinates of its image?
Answers
Answer:
The coordinates of the image are [tex]Q'(x,y) = (13,0)[/tex].
Step-by-step explanation:
The rotation of point Q around a given point of reference is defined by:
[tex]Q'(x,y) = O(x,y) + r_{OQ}\cdot (\cos (\theta_{OQ}\pm \theta_{R}),\sin (\theta_{OQ}\pm \theta_{R}))[/tex] (1)
Where:
[tex]O(x,y)[/tex] - Point of reference.
[tex]r_{OQ}[/tex] - Magnitude of line segment OP.
[tex]\theta_{OQ}[/tex] - Direction of the point Q with respect to the point of reference, measured in sexagesimal degrees.
[tex]\theta_{R}[/tex] - Rotation angle, measured in sexagesimal degrees.
[tex]Q'(x,y)[/tex] - Rotated point.
Please notice that positive sign means counterclockwise rotation, whereas the negative sign represents clockwise rotation.
The magnitude and direction of the line segment are defined by the following expressions:
Magnitude
[tex]r_{OQ} = \sqrt{(x_{Q}-x_{O})^{2}+(y_{Q}-y_{O})^{2}}[/tex] (2)
Direction
[tex]\theta_{OQ} = \tan^{-1}\left(\frac{y_{Q}-y_{O}}{x_{Q}-x_{O}} \right)[/tex] (4)
Where:
[tex]x_{O}[/tex], [tex]y_{O}[/tex] - Coordinates of point of reference.
[tex]x_{Q}[/tex], [tex]y_{Q}[/tex] - Coordinates of the point Q.
If we know that [tex]x_{O} = 5[/tex], [tex]y_{O} = 1[/tex], [tex]x_{Q} = 4[/tex], [tex]y_{Q} = -7[/tex], then the magnitude and direction of the segment OQ are, respectively:
[tex]r_{OQ} = \sqrt{(4-5)^{2}+(-7-1)^{2}}[/tex]
[tex]r_{OQ} \approx 8.062[/tex]
[tex]\theta_{OQ} = \tan^{-1}\left(\frac{-7-1}{4-5} \right)[/tex]
[tex]\theta_{OQ} = \tan^{-1}\left(\frac{-8}{-1} \right)[/tex] (Which means that line segment OQ belongs to third quadrant)
[tex]\theta_{OQ} \approx 262.875^{\circ}[/tex]
If we know that rotation is clockwise, [tex]x_{O} = 5[/tex], [tex]y_{O} = 1[/tex], [tex]r_{OQ} \approx 8.062[/tex] and [tex]\theta_{OQ} \approx 262.875^{\circ}[/tex], then the rotated point is:
[tex]Q'(x,y) = (5,1) + (8.062\cdot \cos (262.875^{\circ}-270^{\circ}),8.062\cdot \sin (262.875^{\circ}-270^{\circ}))[/tex]
[tex]Q'(x,y) = (5,1) + (8, -1)[/tex]
[tex]Q'(x,y) = (13, 0)[/tex]
The coordinates of the image are [tex]Q'(x,y) = (13,0)[/tex].
what is Inequality Notation
Answers
Answer:
There are four inequality notations. They are. > means greater than. ≥ means greater than or equal to. < means less than.
Step-by-step explanation:
given logx 2=p and logx 7=q , express log7 4x² in terms of p and q
Answers
Answer:
[2(p + 1)]/q
Step-by-step explanation:
logx 2 = p
logx 7 = q
log7 4x² = log7 (2x)²
= (logx (2x)²)/(logx 7)
= (2 logx 2x)/(logx 7)
= (2 logx 2 + 2 logx x)/(logx 7)
= (2p + 2)/q
= [2(p + 1)]/q
In a triangle, PR is 12 more than twice PQ and QR is two more than 4 times PQ. If all three sides of the triangle have integer lengths, what is the largest possible value of x?
Answers
Answer:
x = 10
Step-by-step explanation:
In a triangle, PR is 12 more than twice PQ and If all three sides of the triangle have integer lengths, what is the largest possible value of x?
From the attached diagram, x = PQ
We have sides:
PQ, PR and QR
PR is 12 more than twice PQ
PR = 12 + 2PQ
PR = 12 + 2x
QR is two more than 4 times PQ.
QR = 2 + 4(PQ)
QR = 2 + 4x
Hence: we solve using Triangle Inequality
The triangle inequality states that the sum of the lengths of two sides of a triangle must be greater than the length of the third side.
Based on this property, if you know the lengths of two sides of a triangle and are trying to find the range of lengths of the third side, you can add the two known side lengths together and subtract the smaller one from the bigger one. The third side must be greater than the sum of the other two sides and less than their difference.
PQ > PR + QR
PQ < PR - QR
Therefore:
x + 12 + 2x > 2 + 4x
3x + 12 > 2 + 4x
12 - 2 > 4x - 3x
10 = x
Albert makes 20 kg of sweets in 5 weeks. If he continued to make sweets, how much would he have after 10 weeks?
Answers
Answer:
he will have 40 kg
Step-by-step explanation:
10:5=2
20 x 2 = 40
C=
5
9
(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
ANSWER EXPLANATION: Think of the equation as an equation for a line
y=mx+b
where in this case
C=
5
9
(F−32)
or
C=
5
9
F−
5
9
(32)
You can see the slope of the graph is
5
9
, which means that for an increase of 1 degree Fahrenheit, the increase is
5
9
of 1 degree Celsius.
C=
5
9
(F)
C=
5
9
(1)=
5
9
Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of
9
5
degrees Fahrenheit.
C=
5
9
(F)
1=
5
9
(F)
(F)=
9
5
Since
9
5
= 1.8, statement II is true.
The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of
5
9
degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:
C=
5
9
(F)
C=
5
9
(
5
9
)
C=
25
81
(whichis≠1)
An increase of
5
9
degree Fahrenheit leads to an increase of
25
81
, not 1 degree, Celsius, and so Statement III is not true.
Answers
Answer:
final answer is D
UwU
D okakkakakakakkakakakkakakakaka
Is the equation a function?
Answers
Answer:
I do so believe the equation is a function
Step-by-step explanation:
if im wrong im so sorry
:) hope this helps!!
A boat traveled 240 miles downstream, then 240 miles back upstream. The trip downstream took 20 hours. The trip back upstream took 60 hours. Use this information to fill in the following blanks. Note: Express your answers as integers.
The speed of the boat in still water is [answer]
miles per hour.
The speed of the current is [answer]
miles per hour.
Answers
Answer:
it takes longer for the boat to get back because it's moving against the current. to see how fast the boat is moving, you divide the amount of miles traveled, by how long it took.
240/20 = 12
in still water the boat travels it's 12 miles per hour
240/ 60 = 4
against the current, the boat travels 4 miles per hour
if you need to find the speed of the current, you need to find the resistance that's going against the boat making it slow down. you do that by doing 12 - 4 = 8 miles per hour is the speed of the current.
Step-by-step explanation:
I hope this helps :)
What is the value of KL
Answers
Answer:
40.5
Step-by-step explanation:
Since the centroid (the point of concurrency of the sides of a triangle) divides the 3 medians into the ratios from the point to the centroid to the centroid to the side into the ratio of 2:1. To find PK divide 27 by 2
27/2=13.5
Then add 27 and 13.5 to get KL
27+13.5=40.5
If a scale factor of One-fifth is used to make a reduction, what is the base of the original triangle?
Original triangle
Reduced triangle
Height
3
Base
5
1
10
15
25
Answers
Answer: the answer is d
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she descended 41.6 feet. How many feet had she been below sea level, if she was 102 feet below sea level after she descended?
Answers
Answer:
143.6 below sea level
Step-by-step explanation:
Given that:
Initial altitude of the submarine = 102 feet below sea level
Distance descended over the next 10 minutes = 41.6 minutes
To find:
The altitude below sea level after she descended ?
Solution:
To find the resultant altitude below sea level, we need to subtract the altitude descended in the next ten minutes from the initial altitude.
We are doing so because scientist has further descended i.e. gone below the water.
Initial altitude is also in negative sign because of the fact that it is below sea level.
Therefore, the answer can be found as:
-102 - 41.6 = - 143.6
OR
143.6 below sea level is the answer.
Please help..............
Answers
Answer:
a- 3 1/3
Step-by-step explanation:
Billy bought 2 sweatshirts and 3 t-shirts. His friend Jordan bout 3 sweatshirts and 3 t-shirts. Billy's bill was $35 and Jordan's bill was $45. What is the price of one t-shirt and what is the price of one sweatshirt?
Answers
for billy: 2x+3y=35$
for jordan:3x+3y=45$
We need to get rid of one of the unknowns inorder to solve, therefore we will subtract the two equations from each other. This will get rid of the y variable(3y-3y=0)
2x+3y=35$
-
3x+3y=45$
=
-1x=-10$
we get rid of the negative, which leaves us with x=10$. Knowing this info, we can now easily calculate y:
2x+3y=35$
2(10)+3y=35$
20+3y=35$
3y=15
y=15/3
y=5
Hope this helps!
heeeeeeeeeeeeeeeeeeeeeellllllllllllllllllllllllp
Answers
write in word form 329.080 in word formwrite in word form 329.080 in word form
Answers
Answer:
Three Hundred Twenty-nine and Eighty Thousandths.
The area of a rectangular field is 5695 m².
If the width of the field is 67 m, what is its length?
Answers
Answer:
85 m
Step-by-step explanation:
5696/67=85
The rational number -21/28 in standard form is
a) -3/4
b) 3/4
c) 3/7
d)-3/7
Answers
-3/4
Explanation:
-21 and 28 are both multiples of 7. Divide the numerator and denominator by 7 to simplify it.
-21/28
= -3/4
I hope this helps!
3. Consider the following diagram.
Find the values of m and n that prove the two triangles are congruent by the
HL Theorem.
Answers
Answer:
m = 3, n = 6
Step-by-step explanation:
The hypotenuse leg (HL) theorem states that two triangles are said to be similar if one leg and the hypotenuse of the triangles are congruent.
From the diagram, comparing the hypotenuse of the triangles;
4m + 1 = 13
4m = 13 - 1
= 12
m = [tex]\frac{12}{4}[/tex]
= 3
m = 3
Also, comparing the sides;
2m + n = 8m - 2n
substitute the value of m to have,
6 + n = 24 - 2n
collect like terms,
n + 2n = 24 - 6
3n = 18
n = [tex]\frac{18}{3}[/tex]
= 6
n = 6
m = 3, n = 6
To solve the problem we must know about HL theorem.
What is the HL theorem?According to the HL theorem, If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore, the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
The value of m and n are 3 and 6, respectively.
Given to us
The hypotenuse of the first triangle = 13One leg of the first triangle = 2m+nThe hypotenuse of the second triangle = 4m+1One leg of the second triangle = 8m - 2nAccording to the HL theoremIf the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore,
the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
Hypotenuse Congruent[tex]4m + 1 =13\\\\4m=13-1\\\\m=\dfrac{12}{4}\\\\m=3[/tex]
Corresponding Congruent sides[tex]2m+n = 8m-2n\\[/tex]
Substitute the value of m,
[tex]2(3)+n = 8(3)-2n\\\\6+n = 24-2n\\\\6-24 = -2n-n\\\\-18 = -3n\\\\n=\dfrac{-18}{-3}\\\\n = 6[/tex]
Hence, the value of m and n are 3 and 6, respectively.
Learn more about HL theorem:
https://brainly.com/question/11804042
which missing piece of information would allow the triangle in the figure to be proven congruent by asa
Answers
Answer:
Step-by-step explanation:
if the angles c and l were marked with the angle curve like angles j and a
ASAP PLS Joselyn expects her new software company to increase its sales next year 2 3/4 the present value. Write this increase as a percent.
Answers
Answer:
175% i think
Step-by-step explanation:
Which equation is true for this triangle?
Answers
Answer:
c
Step-by-step explanation:
makes most sense
Answer:
c
Step-by-step explanation:
its a guess sorryyyjsjsjsssksk
Sid has £5 to buy apples and bananas.
He uses his money like this:
He buys 18 apples.
Then he buys as many bananas as possible.
With his change he buys more apples.
How many apples and bananas does he buy?
(Apples=6p Each)
(Bananas= 40p Each)
Answers
Bananas = 9 and Apples = 22
Explanation below -
Step-by-step explanation:
cost of 18 apples= 18x6p= 108p
£5-108p= x (will let it be x since i do not know the conversion)
maximum number of banana he can buy= x divide by 40p (rounded down to smallest whole number)= b
The change he have= x-(40×b) = y
apples bought with change= y divide by 6p= a
do the working above to find value for a and b, add a to the 18 apples bought initially and b is number of banana
please help me please will give brainliest to anyone who is good
show your work
Answers
Answer:
D
Step-by-step explanation:
$4665.60/(12x24)
= 4665.60/288
= 16.2 = $16.20
A woman has a ladder that is 10 feet long. If she sets the base of the ladder on level ground 8 feet from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the house?
1. 2
2. 5
3. 8
4. 6
Answers
Answer:
2 feet extra
Step-by-step explanation:
so if you do common subtraction 8-10is 2 so here is 2 feet over her house
THIS IS EASY!!! (PLEASE HELP... ILL GIVE BRAINLIST)
Answers
Answer:
-7(9) < -56
Step-by-step explanation:
-7(9) is -63 which is less than -56 so anything above that is less than 56-
Answer:
x=8
Step-by-step explanation:
Hope,it helps it wasn’t that easy (:
PLEASE HELP 30 POINTS
Solve the equation.
60% of 45 =
25% of 80 =
16% of 40 =
Answers
Answer:
60% of 45 = 0.6 × 45 = 27
25% of 80 = 0.25 × 80 = 20
16% of 40 = 0.16 × 40 = 6.4
2.20
3.6.4
hajahahahhah pls
Honestly I’ve cheated through all of geo, so someone help me out! (:
Answers
Answer:
x = 16
k = 145 degrees
Step-by-step explanation:
We can see that the polygon is 7 sided
The sum of the internal angles will
be:
(n-2)180: (7-2) * 180 = 900
By adding all internal angles, we get 900
5x + 10x + 9x + 1 + 9x - 14 + 9x + 1 + 10x + 5x = 900
57x -12 = 900
57x = 912
x = 912/57
x = 16
The side marked k
is 9x + 1
= 9(16) + 1 = 145 degrees
You start at (9, 9). You move left 8 units and right 4 units. Where do you end?
Answers
A married couple makes a combined $100,000 a year. This means their income will be taxed about 25%. How much money will they be left with after taxes are taken out of their paychecks?
Group of answer choices
$25,000
$50,000
$75,000
Answers
Answer:
$75,000
Step-by-step explanation:
$100,000 x 0.25 = $25,000
$100,000 - $25,000 = $75,000
How would I do this assignment I want to learn how to do it well explained with example?
Answers
Answer:
The value of t is 22
Step-by-step explanation:
Let us solve the question
In any triangle
∵ The sum of the measures of the interior angles of a triangle is 180°
∵ The angle of triangles are ∠1, ∠2, and ∠3
∴ m∠1 + m∠2 + m∠3 = 180°
∵ The three angles of the triangle are 2t, 3t, and 70°
∴ m∠1 = 2t
∴ m∠2 = 3t
∴ m∠3 = 70°
→ Substitute them in the rule above
∴ 2t + 3t + 70° = 180°
→ Add the like terms
∵ (2t + 3t) + 70 = 180
∴ 5t + 70 = 180
→ Subtract 70 from both sides
∵ 5t + 70 - 70 = 180 - 70
∴ 5t = 110
→ Divide both sides by 5
∴ t = 22
∴ The value of t is 22