PLEASE HELP ME!
Two similar triangles are shown on the following coordinate grid:
Which set of transformations has been preformed on triangle EFG to form triangle E’F’G’?
Answers
Answer:
Reflection across y-axis followed by dilation with scale factor 4 and center (0,0).
Step-by-step explanation:
From the given figure it is noticed that the vertices of preimage are E(-2,1), F(-2,0) and G(-3,0). The vertices of image are E'(8,4), F'(8,0) and G'(12,0).
The triangle E'F'G' is enlargement of mirror image of EFG. Therefore reflect the triangle EFG across y-axis. If a point reflects across y-axis, then
[tex](x,y)\rightarrow (-x,y)[/tex]
The new vertices of the triangle are E(2,1), F(2,0) and G(3,0).
Length of FG is 1 unit and length of F'G' is 4 units. The scale factor is
[tex]\frac{F'G'}{FG}=\frac{4}{1}=4[/tex]
Length of OF is 2 unit and length of OF' is 8 units.
[tex]\frac{OF'}{OF}=\frac{8}{2}=4[/tex]
Rule of dilation with scale factor k and origin as center of dilation is defined as
[tex](x,y)\rightarrow (kx,ky)[/tex]
The vertices of image are E'(8,4), F'(8,0) and G'(12,0).
Since the distance ratio of image and preimage from the origin is same as the scale factor, therefore the center of dilation is origin.
Thus, the triangle EFG can form the triangle E’F’G’ using reflection across y-axis followed by dilation with scale factor 4 and center (0,0).
Notes: In this case dilation with scale factor 4 and center (0,0) followed by reflection across y-axis will give the same results.
Answer:
Dilation by a scale factor of 4 followed by reflection about the y-axis
Step-by-step explanation:
Hope this helps
Related Questions
hope everyone can help me I'll really need your help
Answers
Answer:
See below. The solutions are x=-1/3 and y=-4/3
Step-by-step explanation:
[tex]\frac{1}{2}\log_2 y-\log_4 x = 1\\\frac{1}{2}\log_2 y = \log_4 x+1=\log_4x+\log_4 4=\log_4 4x\\\frac{1}{2}\log_2y = log_44x\\\frac{1}{2}\frac{\log_4y}{\log_4 2}=\log_4 4x\\\log_4y=\log_44x\\4^{\log_4y}=4^{\log_44x}\\y = 4x\\\\x-y = 1\\4x -y = 0\\\rightarrow\\3x=-1\implies x = -\frac{1}{3}, y=-\frac{4}{3}[/tex]
if k(x) = 2x-3x then k(9) is. A.315 B.307 C.159 Or D.153 show work plzz thanks
Answers
Answer:
none of the solutions
Step-by-step explanation:
if k(x) = 2x-3x
We can substitute x=9 to find k(9)
k(9) = 2(9) -3(9)
= 18 -27
= -9
k(9)= 2•9-3•9
k(9)= 18-27
k(9)= -9
answer: none of the above
398.574986215 to the nearest ten-thousandth.
Answers
Answer: [tex]398.5750[/tex]
Step-by-step explanation:
It is important to remember that the fourth digit after the decimal point is in the ten-thousandth place.
Then, given the following number:
[tex]398.574986215[/tex]
You can follow these steps in order ti round it to the nearest ten-thousandth:
1. You can identify that the digit in the ten-thousandth place is:
[tex]9[/tex]
2. Identify the digit to the right of [tex]9[/tex]. This is:
[tex]8[/tex]
3. Since:
[tex]8>5[/tex]
You must round up. Increase the digit [tex]9[/tex] by 1. (Notice that [tex]9+1=10[/tex], then the digit to the left of [tex]9[/tex] increases by 1 too). Then:
[tex]398.5750[/tex]
You Start At (1,9) You Move Left 1 Unit And Up 1 Unit.Where Do You End?
Answers
Answer:
(0, 10)
Step-by-step explanation:
x=1 y=9
Up 1 means add 1 to the y coordinate
Left 1 means subtract 1 from the x coordinate
(1-1, 9+1)
(0, 10)
You and your friends play a game of miniature golf. On the first hole, the scores of your group are 6, 2, 3, 2, 4, and 1. What is the range of the scores?
Answers
Answer: Hello mate!
our set of numbers is 6, 2, 3, 2, 4, and 1.
the two extremes of the set are the lower and bigger numbers, so in this case are 1 and 6, so the range of the values in the set is {1,6} and the distance between these points is 6 - 1 = 5.
this means that all the numbers in our set are in the range between 1 and 6.
Write a rule of sequence for 25.7, 24.1, 20.9, 19.3
Answers
Answer:
It deducts 1.6 each time so the next one would be 22.5
Which equation could generate the curve in the graph below?
y = 9x2 + 6x + 4
y = 6x2 – 12x – 6
y = 3x2 + 7x + 5
y = 2x2 + 8x + 8
Answers
Answer:
y = 2x^2 + 8x + 8
Step-by-step explanation:
The graph touches the x axis at only one point.
so there is only one real solution.
If there is only one real solution then determinant =0
Now we find out the equation that has determinant 0
Determinant is [tex]b^2 - 4ac[/tex]
Let find b^2 - 4ac for each equation
(a) [tex]y = 9x^2 + 6x + 4[/tex]
a= 9 , b = 6 and c=4
[tex]b^2-4ac= 6^2 - 4(9)(4) = -108[/tex]
determinant not equal to 0
(b) [tex]y = 6x^2 – 12x – 6[/tex]
a= 6 , b = -12 and c=-6
[tex]b^2-4ac= (-12)^2 - 4(6)(-6) = 288[/tex]
determinant not equal to 0
(c) [tex]y = 3x^2 + 7x + 5[/tex]
a= 3 , b = 7 and c=5
[tex]b^2-4ac= (7)^2 - 4(3)(5) = -11[/tex]
determinant not equal to 0
(d) [tex]y = 2x^2 + 8x + 8[/tex]
a= 2 , b = 8 and c=8
[tex]b^2-4ac= (8)^2 - 4(2)(8) = 0[/tex]
determinant equal to 0. So there is only one real solution.
Answer:
It's D. on EtDtGtE
Step-by-step explanation:
the eauation of the line has the points (0,-1) and (2,5) is:
Answers
Answer:
y = 3x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 5)
m = [tex]\frac{5+1}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3
the line crosses the y-axis at (0, - 1) ⇒ c = - 1
y = 3x - 1 ← equation of the line
What is the surface area of the cylinder? 14ft length 9ft height
A.) 126πft²
B.) 273πft²
C.) 224πft²
D.) 175πft²
Answers
Answer:
C
Step-by-step explanation:
I am assuming the top and bottom are closed.
Surface are = area of the curved side + 2 * area of the top
= 9* 14 * π + 2 * π * 7^2
= 126π + 98π
= 224π ft^2
Answer:
224
Step-by-step explanation:
A 60 by 80-foot rectangular walk in a park surrounds a flower bed. If the walk is of uniform width and its area is equal to the area of the flower bed, how wide is the walk?
Answers
Answer: 17.14 ft
Step-by-step explanation:
The area of the flower bed is 60 ft x 80 ft = 4800 ft²
The perimeter of the sidewalk that surrounds the flower bed is:
2(60 ft) + 2(80 ft) = 120 ft + 160 ft = 280 ftThe area of the sidewalk is:
perimeter x width= 280warea of sidewalk = area of flower bed
280w = 4800
[tex]\text{w}=\dfrac{4800}{280}[/tex]
[tex]=\dfrac{120}{7}[/tex]
≈ 17.14
Emma,brandy,and Damian will cut a rope that is 29.8 feet long into 3 jump ropes. Each of the 3 ropes will be the same length.Write a division sentence using compatible numbers to estimate the length of each rope
Answers
To estimate the length of each rope, the division sentence 30 ÷ 3 = 10 can be used, suggesting that each jump rope would be approximately 10 feet long using compatible numbers.
Explanation:The student's question involves dividing a rope into equal lengths to create jump ropes.
To estimate the length of each jump rope using compatible numbers for the division sentence, we can round 29.8 feet to a number that is easier to divide by 3, such as 30 feet.
Therefore, the division sentence would be 30 ÷ 3 = 10. So, each jump rope would be approximately 10 feet long.
This is an estimate that allows us to perform calculations quickly in our head or on paper, and it is very close to the exact answer.
Final answer:
To estimate the length of each rope from a total length of 29.8 feet when the rope is divided into 3 parts, compatible numbers are used, rounding 29.8 to 30, and the division sentence is 30 ÷ 3, resulting in each estimated rope being about 10 feet long.
Explanation:
To estimate the length of each rope when a 29.8-foot long rope is cut into 3 equal parts, we could use compatible numbers for easier division in our head. Compatible numbers are numbers that are close to the actual numbers and make it easy to do mental arithmetic. We could round 29.8 feet to 30 feet because 30 is divisible by 3. Here's the division sentence using compatible numbers:
30 feet ÷ 3 = 10 feet
Thus, each rope would be approximately 10 feet long. This process is similar to converting units where the scale factor may be omitted at the end when it is 1, as in converting 3.55 m to 355 cm.
Jason is selling video games. To earn his monthly bonus, he must sell a minimum of 5 games. He has 30 he can sell. The video games cost $20 each. The function f(x) = 20x can be used to represent this situation. What is the practical range of the function? Question 16 options:
1. All whole numbers from 5 to 30, inclusive.
2. All whole numbers from 100 to 600, inclusive.
3. All real numbers.
4. All multiples of 20 between 100 and 600, inclusive.
Answers
Answer:
Correct choice is B
Step-by-step explanation:
The function [tex]f(x)=20x[/tex] represents the situation, where x is the number of sold video games and f(x) is the total cost of sold games.
Jason must sell a minimum of 5 games, this means that [tex]x\ge 5.[/tex] He has 30 video games he can sell, then [tex]x\le 30.[/tex]. Thus, the domain of the function is [tex]5\le x\le 30.[/tex]
The range of the function f(x) is
[tex]20\cdot 5\le f(x)\le 20\cdot 30,\\ \\100\le f(x)\le 600.[/tex]
pls help me on this word proplem?
Answers
Equation: 300+35x=1700; where x represents the amount of teams participating in the tournament
Answer: 40 teams competed in the lacrosse tournament
How to solve-
300+35x=1700
300-300+35x=1700-300
35x=1400
35/35x=1400/35
x=40
How many complex zeros does the polynomial function have?
F(x)=2x^4 +5x^3 - x^2 +6x-1
Answers
Answer:
Two complex roots.
Step-by-step explanation:
F(x)=2x^4 +5x^3 - x^2 +6x-1
is a polynomial in x of degree 4.
Hence F(x) has 4 roots. There can be 0 or 2 or 4 complex roots to this polynomial since complex roots occur in conjugate pairs.
Use remainder theorem to find the roots of the polynomial.
F(0) = -1 and F(1) = 2+5-1+6-1 = 11>0
There is a change of sign in F from 0 to 1
Thus there is a real root between 0 and 1.
Similarly by trial and error let us find other real root.
F(-3) = -1 and F(-4) = 94
SInce there is a change of sign, from -4 to -3 there exists a real root between -3 and -4.
Other two roots are complex roots since no other place F changes its sign
Final answer:
The polynomial function has 4 complex zeros.
Explanation:
A polynomial function is a function of the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_1, a_0 are constants and n is a non-negative integer. The number of complex zeros of a polynomial function is equal to its degree.
The given polynomial function is f(x) = 2x^4 + 5x^3 - x^2 + 6x - 1. The highest power of x in the function is 4, so the degree of the function is 4. Therefore, the function has 4 complex zeros.
if the company has set a goal of producing 20 radios for the cost of $3,000 which statement is true
Answers
if that's what you asked
Answer:
60,000 i believe :)
your company manufactures dolls each doll requires
2 feet of ribbon for bows how many yards of ribbons will be required to make 600 dolls
Answers
Answer:
400 yd
Step-by-step explanation:
There are 2 ft of ribbon for 1 doll.
For 600 dolls,
Ribbon = 600 × 2/1
Ribbon = 1200 ft
=====
Convert feet to yards
1 yd = 3 ft
Ribbon = 1200 × 1/3
Ribbon = 400 yd
Someone help me find x and y?
Answers
The values of x and y for the Isosceles triangle are 90° and 43° respect.
By observation, the triangle ∆ABC is an Isosceles triangle with the markings on both legs of the triangle so the base angles are equal,
angle C = angle B = 47°.
Since the line AD bisects the angle A, then line AD is perpendicular to the base BC and so angle x is a right angle
x = 90°
Considering the right triangle ∆ADB can evaluate for y as follows;
x + y + angle B = 180° {sum of interior angles of a triangle}
y + 90 + 47 = 180
y + 137 = 180
y = 180 - 137
y = 43°.
Therefore, the values of the x is equal to 90° and that of y is 43° for the Isosceles triangle ∆ABC.
5b2-10b-15 factor this
Answers
Answer:
5(b - 3)(b + 1)
Step-by-step explanation:
take out a common factor of 5
= 5(b² - 2b - 3)
to factor the quadratic consider the factors of - 3 which sum to - 2
These are - 3 and + 1, thus
= 5(b - 3)(b + 1)
Which values of P and Q result in an equation with exactly one solution? 2x+Q=Px−31 Choose all answers that apply: Choose all answers that apply: A -Q=−31 and P=−2 B- Q=31 andP=2 C - Q=−31 and P=2 D - Q=-2Q=−2 and P=2
Answers
Answer:
Option A is correct
Values of P = -2 and Q = -31
Step-by-step explanation:
Given the equation: [tex]2x+Q= Px-31[/tex]
Now, we put the given values
A.
Q = -31 and P = -2
2x + (-31) = -2x - 31
2x - 31 = -2x -31
4x = -31 + 31
4x = 0
x = 0 [one solution]
B.
Q = 31 and P = 2
2x + Q = Px -31
2x + 31 = 2x -31
Subtract 2x from both sides we get
31 = -31 False.
C.
Q = -31 and P = 2
2x + (-31) = 2x - 31
2x - 31 = 2x - 31 [More than one solutions, for any x]
D.
Q = -2 and P = 2
2x + Q = Px -31
2x + (-2) = 2x -31
2x -2 = 2x -31
2x - 2x = -31 + 2
Combine like term;
0 = -29 False.
Therefore, the values of P and Q results in an equation with exactly one solution is; P = -2 and Q = -31
A house on the market was valued at 34,000 . After several years, the value decreased by 16%. By how much did the house's value decrease in dollars? What is the current value of the house?
Answers
plug in the number of years for where x is
34,000(.84)ˣ
and then do
.84ˣ
and then when you get that answer, multiply by 34,000
need help asap!!!thanks
Answers
Answer:
Step-by-step explanation: Thew figures are similar becasue 5/15 equals 3/9. They bothe equal one third. This shows that they are bhoth orportionate to eachoither. The ratios of the lengths of their corresponding sides are equal.
Which portion would you use to solve this problem?
Nine is 4% of what number?
A. 9/x = 40/100
B. 9/x = 4/100
C. 4/9 = x/100
D. X/9 = 4/100
Answers
[tex]p\%=\dfrac{p}{100}\\\\4\%=\dfrac{4}{100}\\\\\dfrac{9}{x}=\dfrac{4}{100}\to\boxed{B.}[/tex]
sal is making bracalets for a fundraser he uses 6 inches of yarn per bracalet how many bracalets can sal make with 5 ft of yarn
Answers
Answer:
10 bracelets
Step-by-step explanation:
we need to convert 5 ft to inches
1 ft = 12 inches
multiply by 5
5 ft = 60 inches
60 inches of yarn, 6 inches per bracelet
60/6 = 10
10 bracelets
Use the Polygon tool to draw the image of the given quadrilateral under a dilation with a scale factor of 3/4 and center of dilation (0, 0) .
If you could tell me the point that the new quad will be at that would be great!
Answers
Answer:
Given : scale factor(k) = [tex]\frac{3}{4}[/tex]
Labelled the given diagram as A, B , C and D
Also, From the given quadrilateral figure:
The coordinates are;
A=(-8, 4).
B=(-4, -4),
C=(0, -8) and
D=(4, -4)
The rule of dilation with scale factor k and centered at origin is given by;
[tex](x, y) \rightarrow (kx, ky)[/tex]
or
[tex](x, y) \rightarrow (\frac{3}{4}x, \frac{3}{4}y)[/tex]
Then, the coordinates of the dilated given figures are;
[tex]A(-8, 4) \rightarrow (\frac{3}{4}(-8), \frac{3}{4}(4)) = A'(-6, 3)[/tex]
[tex]B(-4, -4) \rightarrow (\frac{3}{4}(-4), \frac{3}{4}(-4)) = B'(-3, -3)[/tex]
[tex]C(0, -8) \rightarrow (\frac{3}{4}(0), \frac{3}{4}(-8))=C' (0 , -6)[/tex]
[tex]D(4, -4) \rightarrow (\frac{3}{4}(4), \frac{3}{4}(-4)) = D'(3, -3)[/tex]
You can see the graph given below in the attachment
Explain why each relation below is or is not a function
Answers
Answer:
No
Yes
Yes
No
Step-by-step explanation:
X's repeat
X's don't repeat
X's don't repeat
X Values repeat
yes, x's do not repeat
yes, it passes the vertical line test
no, it does not pass the vertical line test.
A house valued at $100000 gains 6%in value. Which expression shows the current value of the house in dollars
Answers
Answer:
Current value of house is $106000
Step-by-step explanation:
We are given
A house valued at $100000
gains 6%in value
so,
current value = past house value + gain(%) * (past house value)
past house value =100000
gain(%)=6%
so, we can plug value
Current value is
[tex]=100000+\frac{6}{100}\times 100000[/tex]
[tex]=106000[/tex]
how to graph 2x+4y=28
Answers
Step-by-step explanation:
First, set the x value to be 0:
2(0) + 4y = 28
4y = 28
y = 28/4 = 7
So when x = 0, y = 28/4
Now set the y value as 0:
2x + 4(0) = 28
2x = 28
x = 14
So when x = 14, y = 0
Simply plot these two values:
(0, 7) and (14 , 0)
And join them up, an attatched image shows this graph.
Hope this helps!
Answer:
y = -1/2 + 7
Step-by-step explanation:
You have to isolate y so...
2x + 4y = 28 is the original problem. Then subtract 2x on both sides. After you subtract 2x, you have to divide 4 to both sides. Then after you divide 4 to both sides, it'll be y = -2/4 + 7. After that, simplify -2/4, and you'll get y = -1/2 + 7 as your answer.
Mr. Smith has a maximum of $50 to spend at a museum. A ticket costs $7. he can spend x dollars to buy other things at the museum. Write an inequality to find the possible values for x.
Answers
Answer:
The correct answer is D.
Step-by-step explanation:
p + 7 = ≤ 50
because I did it for the ECA 3 Exam. :>
The inequality which helps to find the possible values for x will be x + 7 ≤ 50.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
Total budget = $50
Ticket cost = $7
Total spent ≤ total budget
x + 7 ≤ 50
x ≤ 43
Hence "The inequality which helps to find the possible values for x will be x + 7 ≤ 50".
For more about inequality,
brainly.com/question/20383699
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College algebra ! Help ASAP !!!
Answers
Answer:
{1}
Step-by-step explanation:
We find determinant for the given matrix and set it equal to -1
To find determinant we apply formula
[tex]|A| = a_{11}(a_{22}a_{33} − a_{32}a_{23}) - a_{12}(a_{21}a_{33} − a_{31}a_{23})+a_{13}(a_{21}a_{32} - a_{31}a_{22})[/tex]
[tex]|A| = x(1x - 2) - 0(7-7) + 0(14-7x) [/tex]
|A| = x^2 - 2x
Now we set the determinant = -1
[tex]x^2 - 2x=-1[/tex]
Add 1 on both sides
[tex]x^2 - 2x + 1=0[/tex]
Now factor it
(x-1)(x-1) = 0
Set each factor =0 and solve for x
x- 1=0 so x=1
The equation below represents Function A and the graph represents Function B: Function A f(x) = 6x - 1 Function B graph of line going through ordered pairs 1, 4 and negative 1, negative 2 and negative 2, negative 5 Which equation best compares the slopes of the two functions?
Answers
Answer:
Slope of function A is 6 and slope of function B is 3. Slope of A is twice of slope of function B. The relationship between slopes is
[tex]\text{Slope of Function A}=2\times \text{Slope of Function B}[/tex]
Step-by-step explanation:
The function A is,
[tex]f(x)=6x-1[/tex]
It can be written as,
[tex]y=6x-1[/tex]
It is the slope intercept form like [tex]y=mx+c[/tex], where m is the slope. On comparing the function A with the slope intercept form, we get the value of slope of function A is 6.
[tex]m_{A}=6[/tex]
The graph of function B passing through the point (1,4), (-1,-2) and (-2,-5).
If a line passing through the points and , then the slope of line is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choose any two points of function B. Let the function B is passing through the points (1,4) and (-1,-2).
[tex]m_{B}=\frac{-2-4}{-1-1}[/tex]
[tex]m_{B}=\frac{-6}{-2}[/tex]
[tex]m_{B}=3[/tex]
The slope of function B is 3.
Since slope of function A is 6 and the slope of function B is 3, so we can say that the slope of function A is twice of slope of function B.
[tex]\text{Slope of Function A}=2\times \text{Slope of Function B}[/tex]
The slope of Function A is 6 and the slope of Function B is 3. Therefore, the slopes of the two functions are not equal.
The equation representing Function A is f(x) = 6x - 1.
The graph representing Function B is a line passing through the ordered pairs (1, 4), (-1, -2), and (-2, -5).
To compare the slopes of the two functions, we can calculate the slope of each function and see if they are equal.
The slope of Function A is 6, and the slope of Function B can be found using the formula (y2 - y1)/(x2 - x1) by choosing any two pairs of ordered points.
For example, using (1, 4) and (-1, -2).
The slope of Function B is (4 - (-2))/(1 - (-1)) = 6/2 = 3.
Since the slope of Function A is 6 and the slope of Function B is 3, we can conclude that the slopes of the two functions are not equal.
Learn more about Slope of functions here:
https://brainly.com/question/12904030
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