Graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin.
Answers
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Explanation:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2 means we multiply each coordinate of each point by the value 2
A = (0,0) becomes A' = (0,0). No change happens. This point is fixed
B = (2,-4) becomes B' = (4,-8). This point does move
C = (-4,-4) becomes C' = (-8,-8). This moves as well
So all you need to do from here is draw triangle A'B'C'.
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Side note: the lengths of triangle A'B'C' are twice as long as their counterparts on triangle ABC. Consequently, this means the perimeter of A'B'C' is twice as long as the perimeter of ABC. Also, triangle A'B'C's area is four times larger than the area of triangle ABC.
Triangle with the three corner points at
A' = (0,0). B' = (4,-8). C' = (-8,-8). what is Dilation?Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the objects. The result of this transformation is an image with the same shape as the original.
Given:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2
A = (0,0) --> A' = (0,0).
B = (2,-4) --> B' = (4,-8).
C = (-4,-4) --> C' = (-8,-8).
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Related Questions
Jessica saved money to buy holiday gifts for her family. She started her holiday
shopping by spending 2/7 of the money on flowers for her mother. Then she spent of 3/5
the remaining money on chocolates for her father. Jessica used the rest of the money
to buy a bracelet for her sister.
B) What fractional part of the money did Jessica spend on her father's gift?
C) If Jessica spent $12 on her sister's bracelet, how much money had she saved
altogether to buy holiday gifts for her family?
Answers
Answer:
B) 3/7
C) $42
Step-by-step explanation:
B) 1-2/7=5/7 remaining.
5/7x3/5=15/35=3/7
C) She spent 2/7 on her mother and 3/7 on her father. That leaves 2/7 for her sister. $12 is 2/7 of $42 (12 divided by 2/7)
FIRST GETS BRAINLLEST HURRYYYY Jon spins the spinner below 200 times. Predict how many times the spinner landed on blue.
Answers
Answer:
1/2
Step-by-step explanation:
There are four spots in total in the circle. Two of them are blue. Therefore, the probability of it lading on blue is 2/4, which simplifies to 1/2. Hope this helped.
Find the area of the shaded regions (the green). I'll give brainliest for the correct answer!
Answers
Answer:
[tex]Area \ of \ Sector = 56.5 \ cm^2[/tex]
Step-by-step explanation:
[tex]Area \ of \ Sector = \frac{1}{2} \ r^2 \theta[/tex]
Where r = 9 cm, θ = 80 degrees
=> Firstly 80 degrees in radians
80° = 1.4 radians
=> Now, The solution:
[tex]Area \ of \ Sector = \frac{1}{2} \ r^2 \theta[/tex]
[tex]Area \ of \ Sector = \frac{1}{2} (9)^2(1.4)\\Area \ of \ Sector = \frac{1}{2} (81)(1.4)\\Area \ of \ Sector = \frac{113.1 }{2}\\[/tex]
[tex]Area \ of \ Sector = 56.5 \ cm^2[/tex]
Answer:
[tex]\boxed{18\pi \: \mathrm{cm^2}}[/tex]
Step-by-step explanation:
Apply formula for area of a sector.
[tex]\pi r^2 \times \frac{\theta }{360}[/tex]
[tex]\theta =80\° \\r=9[/tex]
Plug in the values.
[tex]\pi \times 9^2 \times \frac{80}{360}[/tex]
[tex]\pi \times 81 \times \frac{80}{360}[/tex]
[tex]\pi \times 81 \times \frac{2}{9}[/tex]
[tex]\pi \times 18[/tex]
[tex]18\pi[/tex]
The area of the sector is [tex]18\pi \: \mathrm{cm^2}[/tex].
Question 16 of 25
What are the coordinates of the vertex of the parabola described by the
equation below?
y=-7(x-4)^2-5
A. (-4,5)
B. (5,4)
C. (4,-5)
D. (-5, -4)
Answers
Answer:
To get the vertex of the parabola we proceed as follows;
y=-7(x-4)^2-5
The above can be written as:
y=-7x^2+56x-117
The values of a,b and c are:
a=-7, b=56 and c=-117
x=-b/(2a)
x=-56/(-7*2)=4
but;
y=-7x^2+56x-117
y=-7(4)^2+56(4)-117
y=-5
Thus;
x=4 and y=-5
The vertex will be at point (4,-5)
Hope it helped... Plz mark as BRAINLIEST... And follow me..
Thanks
The coordinates of the vertex of the parabola is given by V ( 4 , -5 )
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the equation of the parabola be represented as f ( x )
Now , f ( x ) = -7 ( x - 4 )² - 5
And , equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
Comparing the given equation to the vertex form, we can see that the vertex is at (4, -5), and the coefficient a = -7.
Hence , the coordinates of the vertex are (h, k) = (4, -5)
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PLEASE HELLLLLLP MEEE
Answers
Answer:
None of the above
Step-by-step explanation:
In my opinion, I believe the answer is none of the above because
answer A says it has a peak from 10 to 15 km but the graph goes higher than 15 km
answer B says it has a gap from 25 to 30 km but the graph doesn't go that high.
Hope did helps:)
Can someone please help with this question below!! i’ll put question 18 in another post right now
Answers
Answer: B
Step-by-step explanation:
In an equilateral triangle, altitudes are also medians. Thus, the bisect their vertex angles.
Hope it helps <3
What is (7 / 14) * (b - 6) when b is 7?
Answers
Answer:
1/2
Step-by-step explanation:
Well if b is 7 we plug it into the following equation,
(7 / 14) * (b - 6)
So if b is 7, we do 7-6 which is 1.
Then 7 / 14 which is 1/2.
So 1/2 * 1 is 1/2.
Answer:
1/2 or 0.5 (same thing)
Step-by-step explanation:
If you simplify 7/14, you get 1/2, or 0.5.
Plug in 7 for b. 7-6 is 1, so 1/2 * 1 is 1/2.
PLEASE HELP THE QUESTION IS BELOW!!
Answers
Answer:
The answer is option D.
Their angles measures cannot be equal.
Answer:
D
Step-by-step explanation:
Hello,
What the question requires of us is just the property of complimentary angles and which is
The sum of their angles must be equal to 90°.
When two angles combine together to form angle 90°, it is said to be complimentary and they're referred to as a right angled triangle.
From the option, none of the angles can be up to a right angle triangle (90°)
The sum of their angles can be an acute triangle I.e 45°
45° + 45° = 90°
Knowing the fact that the angles can both be an acute angle (45°), it would be wrong to say both angles cannot be equal.
Hence option D is is wrong and it's the right answer in this case
How many gallons each of 15% alcohol and 5% alcohol should be mixed to obtain 10 gal of 14% alcohol?
How many gallons of 15% alcohol should be in the mixture? _____ gal
Answers
Answer:
Step-by-step explanation:
Refer https://brainly.com/question/17122506
find the height of trapazium in which parallel side are 26 cm and 60 cm
Answers
Answer:
no solution
Step-by-step explanation:
It does not work because you need the area as well as the parrallel sides to find the height.
Simplify the expression 4(2x - 3)
Answers
Answer:
8x - 12
Step-by-step explanation:
4(2x - 3) (use distributive property, see attached)
= (2x)(4) - 3(4)
= 8x - 12
what is the average rate of change of f over the interval [-3,9]
Answers
Answer:
According to the graph, f(−3)=3 and f(9)=-7
-7-3/9-(-3)= −10/12
Therefore the answer is -5/6
From Khan
The average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.
What is Polynomial? What are exponents? What is the general equation of a straight line? A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.An exponent is a number that is placed as a superscript over a number. In other words, it indicates that the base is raised to a certain power. Tis expression means that -[tex]b^x = \underbrace{b \times \dots \times b}_{x \text{ times}}[/tex]
The general equation of a straight line is : y = mx + cwhere : [m] → is slope of line and [c] → is the y - intercept
We have the following function -
f(x) = x³ - 9
The average rate of change would be -
r = {720 - (- 36)}/{9 - (- 3)}
r = 756/12
r = 63
Therefore, the average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.
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[ Complete question -
what is the average rate of change of f(x) = x³ - 9 over the interval [-3,9] ]
explain the importance to count change
Answers
When the power goes out, they can handle it. You don’t want to have to close down the shop just because counting change back manually is too hard for your team!
It’s more accurate. Clerks can use it to double check.
Employees can fix mistakes. Say a purchase was $2.36. If the customer gives the clerk a fifty but the clerk enters $5 into the cash register by accident, she can figure out the change due on her own.
How to Count Change
Counting change back to a customer is actually pretty easy when you understand what you’re doing.
There are a couple of ways you can count change. First, you can read the number on the cash register and count that amount to the customer. This ensures you grabbed said amount. Second, you can count up from the sale total. This ensures the customer actually gets the right change back.
The number on the cash register:
If you count the the number on the cash register, all you’re really doing is ensuring that you got that amount from the register. But what if you entered the amount incorrectly to begin with? Then your cash register’s displayed amount will be wrong and so will the amount you hand to the customer.
Counting up from the amount tendered:
There is no way you can go wrong with this method. Let’s say the total is $7.38. The customer hands the clerk a twenty. She doesn’t have to know what the change is going to be – she doesn’t have to do any subtraction. All she needs to do is count up from $7.38.
Steps to Count Change
1. Start with the pennies to reach a multiple of 5 or 10.
2. Next use a nickle or a dime as you get to a multiple of 25.
3. Use quarters until you reach a dollar.
4. Use one dollar bills until you reach a multiple of 5 or 10.
5. Use five dollar bills until you reach 10 or ten dollar bills until you reach 20.
A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the points (3, 1) and (4, 3).
On a coordinate plane, a line goes through (0, 3) and (2, 5).
What is the solution to the system of equations?
Answers
Answer:
(8, 11)
Step-by-step explanation:
The 2-point form of the equation of a line is useful for the one where only points are given.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (3 -1)/(4 -3)(x -3) +1
y = 2(x -3) +1
We can equate this to the expression for y in the given equation.
x +3 = 2(x -3) +1
x +3 = 2x -5 . . . . . . eliminate parentheses
8 = x . . . . . . . . . . . . add 5-x
Using the given equation, we can find y:
y = x +3 = 8 +3
y = 11
The solution to the system is (x, y) = (8, 11).
Answer:
8,11
Step-by-step explanation:
I NEED THIS ASAP, PLEASE HELP!!!
What is the lower quartile of the data set shown? {20,22,23,24,26,26,28,29,30}
What is the interquartile range of this data set?
{62,63,64,65,67,68,68,68,69,74}
What is the upper quartile of the data set shown?
{7,8,8,9,10,12,13,15,16}
Answers
Answer: 22.5 ; 5 ; 14
Step-by-step explanation:
Given the dataset:
{20,22,23,24,26,26,28,29,30}
The lower quartile (Q1) = 1/4(n + 1)th term
Where n = number of observations, n = 9
Q1 = 1/4 (9 + 1)th term
Q1 = 1/4(10) = 2.5
We average the 2nd and 3rd term:
(22 + 23) / 2
45 / 2 = 22.5
B) The interquartile range(IQR) of the dataset :
{62,63,64,65,67,68,68,68,69,74}
IQR = Q3 - Q1
The lower quartile (Q1) = 1/4(n + 1)th term
Where n = number of observations, n = 10
Q1 = 1/4 (10 + 1)th term
Q1 = 1/4(11) = 2.75 term
We take the average of the 2nd and 3rd term:
(63 + 64) / 2
45 / 2 = 63.5
The upper quartile (Q3) = 3/4(n + 1)th term
Where n = number of observations, n = 10
Q3 = 3/4 (10 + 1)th term
Q3 = 3/4(11) = 8.25 term
We take the average of the 8th and 9th term:
(68 + 69) / 2
137 / 2 = 68.5
IQR = Q3 - Q1
IQR = 68.5 - 63.5
IQR = 5
C) give the dataset :
{7,8,8,9,10,12,13,15,16}
The upper quartile (Q3) = 3/4(n + 1)th term
Where n = number of observations, n = 9
Q3 = 3/4 (9 + 1)th term
Q3 = 3/4(10) = 7.5 term
We take the average of the 7th and 8th term:
(13 + 15) / 2
28 / 2 = 14
In the circle below, O is the center and mĞ= 150°. What is the measure of angle HIG?
Answers
Answer:
15°
Step-by-step explanation:
∠GOI=150°
∠HOG=30°
∠HIG=30°/2=15°(Circle angle)
On a piece of paper, graph yz -2x - 2. Then determine which answer choice
matches the graph you drew.
Answers
Answer:
B
Step-by-step explanation:
y≥-2x-2
put x=0,y=0
0≥-2
which is true.
so (0,0) lies on it.
graph is a solid line.
so B satisfies it.
Can someone explain the answer? I really need help!
Answers
Answer:
6. b.
7. b.
8. c.
Step-by-step explanation:
6. The 3 expands the graph vertically by factor 3; -3 reflects across the y-axis and - 1 moves the graph 1 down.
7. The 1/2 expands it horizontally by a factor 2, the -1 moves it 1 right and the + 5 moves it 5 up.
8. The + 3 translates the graph 3 units up.
I made a square frame for my favorite bird picture from four wooden pieces. Each piece is a rectangle with a perimeter of 24 inches. What is the area and perimeter of the picture and frame, together?
I don't mind an undetailed explanation c:
Answers
Answer:
The perimeter of the picture frame is 38.4 in.
The area of the picture frame is 92.6 in.².
Step-by-step explanation:
The given information are;
Perimeter of side piece of picture frame = 24 inches
Length of side piece = L
Width of side piece = W
Perimeter of side piece = 2 × (L + W) = 24
∴ L + W = 24/2 = 12 inches
Dimension of picture frame = Square frame with side length s
Number of side piece in picture frame = 4
Given that the length L > the width W, we have
Side length of wooden frame = L
Also, where the side piece are placed side by side, we have;
Side length of wooden frame = 4 × W
Therefore;
4 × W = L
Which gives
L + W = 12 inches
4 × W + W = 12 inches
W×(4 + 1) = 5·W = 12 inches
W = 12/5 = 2.4 inches
L = 4 × W = 4 × 12/5
L = 48/5 = 9.6 inches Side length of wooden frame, s
The perimeter of the picture frame = 4 × s = 4 × 9.6 = 38.4 in.
The area of the picture frame = s × s = 9.6 × 9.6 = 92.6 in.².
Use the parabola tool to graph the quadratic function. f(x)=2x^2+4x−16 Brainlest and 35pts plz help me!!!
Answers
Answer:
you would place the y-intercept at (0,-16). and then the coordinates would be (-4,0) and (2,0). and the graph would be facing up or positive .
Step-by-step explanation:
If f (x) = x+13, then f (4) =
O 16
8
04
2.
Answers
Answer:
17
Step-by-step explanation:
f (x) = x+13
Let x = 4
f(4) = 4+13
= 17
Answer:
[tex]17[/tex]
Step-by-step explanation:
[tex]f(x)=x+13[/tex]
[tex]\mathrm{Plug \: x \: as \: 4 \: and \: evaluate.}[/tex]
[tex]f(4)=4+13[/tex]
[tex]f(4)=17[/tex]
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, -6), B(5, -6), C(5, -2) and D(2, -2). What is the perimeter of rectangle ABCD?
Answers
Answer:
Step-by-step explanation:
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \\\\[/tex]
A(2, -6), B(5, -6),
[tex]AB =\sqrt{(5-2)^{2}+(-6-[-6])^{2}}\\\\=\sqrt{(5-2)^{2}+(-6+6)^{2}}\\\\=\sqrt{3^{2}+0}\\\\=\sqrt{3^{2}}\\\\=3 units\\[/tex]
B(5,-6) ; C(5,-2)
[tex]BC = \sqrt{(5-5)^{2}+(-2-[-6])^{2}}\\\\ = \sqrt{0+(-2+6)^{2}}\\\\ = \sqrt{4^{2}}\\\\[/tex]
BC = 4 units
C(5, -2) ; D (2,-2)
[tex]CD = \sqrt{(2-5)^{2}+(-2-[-2])^{2}}\\\\ = \sqrt{(-3)^{2}+(-2+2)^{2}}\\\\ = \sqrt{(-3)^{2}}[/tex]
CD = 3 units
A(2,-6) ; D(2,-2)
[tex]AD = \sqrt{(2-2)^{2}+(-2+6)^{2}}\\\\ = \sqrt{0 +(4)^{2}}\\\\ = \sqrt{(4)^{2}}\\[/tex]
= 4 units
Perimeter = AB + BC + CD + AD
= 3 + 4 + 3 + 4
= 14 units
What is the quotient?
x-1/7x2-3x-9
Answers
=2x-10
How can you tell the difference between systems with no solution and infinite solutions?
Answers
Answer:
The given system of equations has "No solution” means that the constants are the numbers without variables. If the coefficients are the equal on both sides then their constants will not equal,they did not satisfy the given equations and therefore it said to have no solution
The given system of equations has "infinitely many solutions" if the given linear system of equations has both the equations represents to the same line.
Step-by-step explanation:
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.
What is the mean average deviation (MAD) of the data set shown below? Round your answer to the nearest tenth when necessary.
Answers
Answer:
18
Step-by-step explanation:
to find the MAD you add all of the numbers first 22+19+30+13+17+21+8+15+12+23= 180
then you divide it by how many numbers there are for instance there are 10 because there are 10 pairs of numbers then you divide it by 180 and you get 18
hope it helped :)
____________ are events whose outcomes are not affected by the outcomes of the other event(s). a) Complementary events b)Primary events c)Independent events big d) Dependent events'
Answers
Answer:
independent events
Step-by-step explanation:
they dont depend on other events anyhow
Answer:
Independent events.
Step-by-step explanation:
use the rules of exponents to evaluate or simplify. wright without negative exponents. 5 • 7^0 = ___ ^a0
Answers
Answer:
5 x 7^0 = 35
or
5 x 7 = 35
Step-by-step explanation:
Plz mark brainliest
Is the sequence arithmetic or geometric? 1, 2, 4, 8, 16, ...
Answers
Answer:
The answer is geometric
Step-by-step explanation:
To solve this problem you will need to know the difference between an arithmetic and a geometric.
An arithmetic is a sequence where a person is adding the same number over and over again so lets say you start with 1 and the common difference (the number being added each time) is 2, the sequence will look something like this 1, 3, 5, 7, 9 and so on.
A geometric sequence is when the same number is being multiplied over and over again. So lets say that the number we start with is 2 and you are multiplying by three every single time, so you would get a sequence looking like this 2, 6, 18, 54 and so on.
We can see in the sequence that the number that is being multiplied over and over again is 2 so the answer is a geometric sequence.
Estimate to the nearest hundredth: √48 A. 6.93 B. 7.12 C. 24.00 D. 6.55
Answers
Answer:
The answer is option A.
√48 = 6.93 to the nearest hundredth
Hope this helps you
Answer:
A
Step-by-step explanation:
From the set {6, 16, 24}, use substitution to determine which value of x makes the inequality true. 4 + x < 20 A. 16 B. 6 C. none of these D. 24
Answers
================================================
Explanation:
In math, the term "substitution" basically means "replace". Keep in mind that x is a placeholder for a number. Think of it as a box we place a number inside.
We have the items {6, 16, 24} to use as replacements for x. We only do one number at a time
Let's try x = 6
4 + x < 20
4 + 6 < 20 ... replace x with 6
10 < 20 ... this is a true statement as 10 is less than 20
So x = 6 is a solution
Let's try x = 16
4+x < 20
4+16 < 20
20 < 20 ... this is false because we can't have a number smaller than itself
Lastly, let's try x = 24
4+x < 20
4+24 < 20
28 < 20 ... also false; 28 is not smaller than 20
We've shown that x = 16 and x = 24 are not solutions. Only x = 6 is a solution from the set {6,16,24}. This is why the answer is choice B.
-----------------
Alternative method:
4+x is the same as x+4. We can add two numbers in any order we want.
x+4 < 20 solves to x < 16 after subtracting 4 from both sides. So the set of solutions is anything smaller than 16. Looking at {6,16,24} we see that the only allowed answer is x = 6.
x = 16 is not a solution because x < 16 would turn into 16 < 16, but again we can't have a number smaller than itself.