Dilate the the triangle, scale factor = 3 (positive 3, ignore the
negative in the image below) with a center of dilation about
the origin.
A(-7,-6)
B(-5,-2)
C(-1,-5)
Answers
Answer:
The rule of dilation is [tex]P'(x,y) = 3\cdot P(x,y)[/tex].
The vertices of the dilated triangle are [tex]A'(x,y) = (-21, -18)[/tex], [tex]B'(x,y) = (-15,-10)[/tex] and [tex]C'(x,y) = (-3,-15)[/tex], respectively.
Step-by-step explanation:
From Linear Algebra, we define the dilation by the following definition:
[tex]P'(x,y) = O(x,y) + k\cdot[P(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Center of dilation, dimensionless.
[tex]k[/tex] - Scale factor, dimensionless.
[tex]P(x,y)[/tex] - Original point, dimensionless.
[tex]P'(x,y)[/tex] - Dilated point, dimensionless.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]k = 3[/tex], [tex]A(x,y) = (-7,-6)[/tex], [tex]B(x,y) = (-5,-2)[/tex] and [tex]C(x,y) =(-1,-5)[/tex], then dilated points of triangle ABC are, respectively:
[tex]A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)][/tex] (2)
[tex]A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)][/tex]
[tex]A'(x,y) = (-21, -18)[/tex]
[tex]B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)][/tex] (3)
[tex]B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)][/tex]
[tex]B'(x,y) = (-15,-10)[/tex]
[tex]C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)][/tex] (4)
[tex]C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)][/tex]
[tex]C'(x,y) = (-3,-15)[/tex]
The rule of dilation is:
[tex]P'(x,y) = 3\cdot P(x,y)[/tex] (5)
The vertices of the dilated triangle are [tex]A'(x,y) = (-21, -18)[/tex], [tex]B'(x,y) = (-15,-10)[/tex] and [tex]C'(x,y) = (-3,-15)[/tex], respectively.
Related Questions
What is the length of PR?
A: 13.5 inches
B: 7.5 inches
C: 10.5 inches
D: 9.5 inches
Answers
Answer:
The correct option is;
C: 10.5 inches
Step-by-step explanation:
In triangle ΔPQR the given parameters are;
The length of [tex]\overline {QP}[/tex] = 19.5 in.
The length of [tex]\overline {QR}[/tex] = 7.5 in.
In triangle ΔVWX, the given parameters are;
The length of [tex]\overline {WV}[/tex] = 13 in.
The length of [tex]\overline {WX}[/tex] = 5 in.
The length of [tex]\overline {VX}[/tex] = 7 in.
Given that we have;
[tex]\dfrac{\overline {QP}}{\overline {WV}} = \dfrac{19.5}{13} = 1.5 , \ \dfrac{\overline {QR}}{\overline {WX}} = \dfrac{7.5}{5} = 1.5[/tex]
The ratio of the corresponding sides of triangle ΔPQR and triangle ΔVWX are equal, therefore ΔPQR is similar to ΔVWX, from which we have for the corresponding sides, [tex]\overline {PR}[/tex] and [tex]\overline {VX}[/tex];
[tex]\dfrac{\overline {PR}}{\overline {WV}} = \dfrac{\overline {PR}}{\overline {7}} = 1.5[/tex]
∴ [tex]\overline {PR}[/tex] = 7 × 1.5 = 10.5
The length of [tex]\overline {PR}[/tex] = 10.5 inches
helpplsplsplsplsplsplsigiveiraliset
Answers
Which relation is not a function?
(-4, 6). (0, 6). (7, 6), (4, 6), (-7, 6)
(1, 3), (3, 5). (5, 7). (7, 9). (9,1)
(4, 1). (8, 2). (12, 3). (16, 4), (20, 4)
(7,3), (7, 6), (7, 9), (7, 12) (7, 15)
Answers
Answer: D ( 7,3 7,6 7,9 7,12 7,15)
Step-by-step explanation:
A- (-4, 0, 7, 3, -7) There are no repeating domains, therefore, this is a function
B- (1, 3, 5, 7, 9) The domain does not repeat, therefore this is a function
C- (4, 8, 12, 16, 20) The domain does not repeat, therefore this is a function
D- (7, 7, 7, 7, 7) The entire domain repeats, therefore this cannot be a function
Correct answer is D ( 7,3 7,6 7,9 7,12 7,15)
Jimmys garden has a length of 2b
+ 4 and a width of 7b + 2. What is
the perimeter of the garden?
Answers
Answer: 18b + 2
Step-by-step explanation:
Length: 2b + 4
Width: 7b + 2
I assumed the garden is a rectangle shape since the length and width are different.
Perimeter = 2( L + w)
Then we just plug the values in.
2 (2b + 4 + 7b + 2)
2 (9b + 6) = 18b + 12
So, the equation for the perimeter of Jimmy's garden will be 18b + 2.
PLEASE HELP Consider these functions f(x)=x+1
Answers
Answer:
fo(g(X)= 2/X +1.
Option C
Step-by-step explanation:
Hey there!
Given;
f(X) = x+1
g(x) = 2/X
Now, To find: (f o g(x))
[tex]fo(g(x)) = f(g(x))[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = f( \frac{2}{x} )[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2}{x} + 1[/tex]
Therefore, fo(g(X)= 2/X +1.
Hope it helps...
Select each pair of expressions that are equivalent. 3x + 14 – x + 112 and 4x + 134 2 + 6x and 2(3x + 1) 3(x + 1) – (1 – x) and 2x + 3 3x and 4(x + 1) – x – 4 5.5 + 2.2x + 3.8x – 4.1 and 1.4 + 6x
Answers
Answer:
Options (2), (4) and (5)
Step-by-step explanation:
Option 1
(3x + 14 - x + 112) and (4x + 134)
Since, (3x + 14 - x + 112) = (3x - x) + (12 + 112)
= 2x + 124
Therefore, (3x + 14 - x + 112) ≠ (4x + 134) [Not equivalent]
Option 2
(2 + 6x) and 2(3x + 1)
2(3x + 1) = (6x + 2)
Therefore, (2 + 6x) = (6x + 2) [Equivalent]
Option 3
3(x + 1) - (1 - x) and (2x + 3)
Since, 3(x + 1) - (1 - x) = 3x + 3 + x - 1
= (3x + x) + (3 - 1)
= 4x + 2
Therefore, (2x + 3) ≠ (4x + 2) [Not equivalent]
Option 4
3x and 4(x + 1) - x - 4
Since, [4(x + 1) - x - 4] = 4x + 4 - x - 4
= (4x - x) + (4 - 4)
= 3x
Therefore, 3x = [4(x + 1) - x - 4] [Equivalent]
Option 5
(5.5 + 2.2x + 3.8x - 4.1) and (1.4 + 6x)
Since, (5.5 + 2.2x + 3.8x - 4.1) = (2.2x + 3.8x) + (5.5 - 4.1)
= (6x + 1.4)
Therefore, (1.4 + 6x) = (6x + 1.4) [Equivalent]
Approximate the percent of values on the box and whisker plot that lie below 68?
50
75
25
49
Answers
One diet uses a ratio of 9:5:4 for carbohydrates, protein, and fat. A nutritionist is developing a diet that provides 450 calories from protein per day. Find the number of calories that should come from carbohydrates
Answers
Answer:
There are 810 calories from carbohydrates
Step-by-step explanation:
carbohydrates: protein: fat
9 :5 :4
We want 450 calories from protein
450 /5 =90
Multiply each term by 90
carbohydrates: protein: fat
9*90 :5*90 :4*90
810 450 360
There are 810 calories from carbohydrates
Answer:
810 calories are carbohydrates
Step-by-step explanation:
We know that the ratio 9:5:4 tells us that 18 equal amounts' of calories make up a meal. Now we know that 450 calories equals 5 of this parts (since protein is made out of 5 of this parts. Now we have to find out the amoung of calories in one of this 18 parts and multiply it by 9. So we do......
450 / 5 = 90
90 x 9 = 810
ANSWER ASAPPPP MARKING BRAINLIEST HELP
Answers
Answer:
A. 30800
B.39600
C. 17600
Step-by-step explanation: 0.12*$35000= 4200 35000-4200 = $30800
$45000*0.12=$5400 $45000-$5400= $39600
$20000*0.12=$2400 $20000-$2400= $17600
formula for an for the arithmetic sequence.
ah = -1, d = -7
Answers
Answer:
The formula for the arithmetic sequence will be:
[tex]a_n=-7n+6[/tex]Step-by-step explanation:
Given
a₁ = -1d = -7We know that we can get the next term of the Arithmetic sequence by taking the current term and adding the common difference.so
a₂ = a₁ + d
= -1 + (-7) ∵ a₁ = -1
= -1 - 7
= -8
similarly,
a₃ = a₂ + d
= -8 + (-7)
= -8 - 7
= -15
and so on
Thus, the Arithmetic sequence becomes
a₁, a₂, a₃, ...
-1, -8, -15, ...
as
a₁ = -1d = -7Therefore, An arithmetic sequence has a constant difference d and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting a₁ = -1 and d = -7
[tex]a_n=-7\left(n-1\right)-1[/tex]
[tex]a_n=-7n+6[/tex]
Hence, the formula for the arithmetic sequence will be:
[tex]a_n=-7n+6[/tex]Lola gets two 20-minute breaks at work each day. She works 5 days a week. How much time does she spend on break each week?
Group of answer choices
Answers
Answer:
200 minutes / 3 hours & 20 minutes.
Step-by-step explanation:
This is quite simple.
First, since we know that Lola takes two 20 minute breaks at work each day, let's multiply 20 and 2.
20 × 2 = 40
This means she is on break for a total of 40 minutes each day.
Finally, let's take that 40 and multiply it by 5.
40 × 5 = 200
This means she spend 200 minutes (3 hours & 20 mins) on break each week.
6(3x/2-4) =30
Side note: 3x/2 is a fraction
Answers
Answer:
x = 6
Step-by-step explanation:
Given
6( [tex]\frac{3x}{2}[/tex] - 4 ) = 30 ( divide both sides by 6 )
[tex]\frac{3x}{2}[/tex] - 4 = 5 ( add 4 to both sides )
[tex]\frac{3x}{2}[/tex] = 9 ( multiply both sides by 2 to clear the fraction )
3x = 18 ( divide both sides by 3 )
x = 6
Answer:
x = 6
Step-by-step explanation:
[tex]6( \frac{3x}{2} - 4) = 30[/tex]
Dividing both the sides by 6 ,
[tex] = > \frac{6( \frac{3x}{2} - 4) }{6} = \frac{30}{6} [/tex]
[tex] = > \frac{3x}{2} - 4 = 5[/tex]
Adding 4 on both the sides ,
[tex] = > \frac{3x}{2} - 4 + 4 = 5 + 4[/tex]
[tex] = > \frac{3x}{2} = 9[/tex]
Multiplying both the sides by 2 ,
[tex] = > \frac{3x}{2} \times 2 = 9 \times 2[/tex]
[tex] = > 3x = 18[/tex]
Dividing both the sides by 3,
[tex] = > \frac{3x}{3} = \frac{18}{3} [/tex]
[tex] = > x = 6[/tex]
Can I get help with this I been stuck for days
Answers
Answer:
y = f(x + 2)
Step-by-step explanation:
URGENT NEED HELP ILL GIVE YOU BRAINLEST
Answers
Answer:
y = -1/3x +2
Step-by-step explanation:
subtract -1/3x to the side of 2
The triangles below are congruent and their corresponding parts are marked.
Answers
Answer:
I think it's a but I'm not 100 percent sure but I'd say a
Sylvie and Bono hiked to the 6,288-ft summit of Mount Washington, then hiked to Carter Notch Hut for the night. Carter Notch Hut is located at an elevation of 3,288 ft. A number line going from negative 4000 to positive 4000 in increments of 1000. Which point represents the change of elevation in feet on the hike from the summit to Carter Notch Hut? –4000 –3000 3000 4000
Answers
Answer: the answer is -3000 i meant
Step-by-step explanation:
$18 if it has 9 attendees. If there are 26 attendees, how much will the corporate team-building event cost? Solve using unit rates.
Answers
Answer:$52
Step-by-step explanation: I would first set up an equation. 9a=18 (a means attendees). Then, I would divide both sides by 9 to isolate the a. I would get a=2. So now I know that 1 attendee costs 2 dollars. If I want to find the cost for 26 attendees, all I would have to do is multiply both sides of the equation a=2 by 26. I would get 26a=52. So, 26 attendees cost $52. I hope this helps you out!
Describe what makes 2 lines parallel. Give me a real-world example of a paralell lines.
Answers
Answer:
Step-by-step explanation:
If to lines are parallel then they could go on forever without touching at any given point.
Simplify
-d+C-3+7d-8c
given d=2
C= -4
Answers
Answer:
40
Step-by-step explanation:
for what value of “x” is the figure the given special parallelogram?
Answers
Answer:
x = 6
Step-by-step explanation:
(In reference to my diagram.... my diagram is similar to the diagram in the question)
We know that diagonals of a square bisect each other at right angles.
In ΔBOC ,
•OB = OC (Diagonals of square bisect each other)
=> ∠OBC = ∠OCB = (7x + 3)° (∵ OB = OC)
• ∠BOC = 90° (Diagonals intersect at right angles)
Using angle sum property of triangle ,
∠OBC + ∠OCB + ∠BOC = 90°
[tex] = > 7x + 3 + 7x + 3 + 90 = 180[/tex]
[tex] = > 14x + 6 = 180 - 90 = 90[/tex]
[tex] = > 14x = 90 - 6 = 84[/tex]
[tex] = > x = \frac{84}{14} = 6[/tex]
A plant is already 8.75 meters tall, and it will grow 25 centimeters every month. the plants height, H (in meters), after x months is given by the following function H(x)=0.25x+8.75 What is the plants height after 40 months?
Answers
Answer:
18.75 meters
Step-by-step explanation:
8.75 + 0.25(40) = 18.75
50 POINTS. Select the correct answer from each drop-down menu.
15
In AABC, m B = 90°, COS(I) = 17, and AB = 16 units.
V
V
units.
Based on this information, mzA= v ,mzc=
o, and AC =
Note that the angle measures are rounded to the nearest degree.
Answers
Answer:
m∠C=28°, m∠A=62°, AC=34.1 units
Step-by-step explanation:
Given In ΔABC, m∠B = 90°, , and AB = 16 units. we have to find m∠A, m∠C, and AC.
As,
⇒
By angle sum property of triangle,
m∠A+m∠B+m∠C=180°
⇒ m∠A+90°+28°=180°
⇒ m∠A=62°
Now, we have to find the length of AC
⇒
The length of AC is 34.1 units
Ralph’s current annual income is $32,000. Using the graph shown below, Ralph has calculated that he will have to pay a total of $9,280 in federal taxes this year. Which of the following statements is true?
A circle graph titled Simpson's Annual Expenses. Federal taxes, 24 percent; State/local taxes, 10 percent; Housing and household, 23 percent; Food, 6 percent; Medical care, 8 percent; Transportation, 11 percent; Recreation, 3 percent; Clothing, 5 percent; Other, 10 percent.
a.
Ralph’s calculation is too high, he has only calculated state taxes.
b.
Ralph’s calculation is too high, his calculation includes state taxes.
c.
Ralph’s calculation is correct, he will have to pay $9,280 in federal taxes this year.
d.
Ralph’s calculation is too low, he did not include medical care in his calculation.What is gross pay
Answers
c.
Step-by-step explanation:
Ralph’s calculation is correct, he will have to pay $9,280 in federal taxes this year.
Ralph ’s calculation is too high, as his calculation includes state taxes.
CalculusGiven that Ralph's current annual income is $32,000, and he has calculated that he will have to pay a total of $9,280 in federal taxes this year, knowing that he has to pay 24% in federal taxes, to determine if his calculation is correct you must perform the following calculation:
32000 x 0.24 = X7680=XTherefore, Ralph ’s calculation is too high, as his calculation includes state taxes.
Learn more about calculus in https://brainly.com/question/13204916
PLEEAAASE IIIIIIIIIII NNNNNNNNNEEEEEEEEEEEEDDDDDDDD HEEEEEEEEEEEEEEEELLLLLLLLLLLPPPPPPPPPPPP
Answers
Answer:
9
Step-by-step explanation:
In order for this problem to have more than one solution, one will have to make it such that the two sides are equal. Call the unknown quantity "x", and solve this equation like a literal equation;
5u + 3(4u - 6) = -3u - 27 + 20u + x
Simplify, (distribute and combine like terms);
5u + 12u - 18 = 17u - 27 + x
17u - 18 = 17u - 27 + x
Inverse operations;
17u - 18 = 17u - 27 + x
-17u - 17u
-18 = -27 + x
+27 + 27
9 = x
Answer: 9
Step-by-step explanation:
What is y equal to ?
Answers
Answer:
y= 42
Step-by-step explanation:
angles in a triangle add up to 180
48+90=138
180-138= 42
(if you need the value of x)
180-48=132
132/2=66
x=66
(value of z)
90+66=156
180-156=24
z=24
Mega Movies hosted a film premiere on Friday night. They charged $7 for adults and $4 for children. One hundred nine adults and children attended, and $703 was made in ticket sales. How many children and how many adults went to the film premiere?
A.
20 children; 89 adults
B.
17 children; 92 adults
C.
24 children; 85 adults
D.
14 children; 95 adults
Answers
Hope this helps
Have a great day/night
(7,-4) and (-11,4) finding slope
Answers
Answer:
-4/9
Step-by-step explanation:
HELP ME ASAP PLEASE!!!!
Answers
Answer:
D good luck
Step-by-step explanation:
please help me I have until Monday to do 82 questions
Answers
Answer and Step-by-step explanation:
We are solving for x.
A)
Multiply each side by 5 to get x by itself.
x = 15
B)
Multiply each side by 2 to get x by itself.
x = 17
#teamtrees #WAP (Water And Plant)
Approximate the percent of values on the box and whisker plot that lie below 68?
50
75
25
49
Answers
Answer:
50
Step-by-step explanation: