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!
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
fred buys a video game disk for $8 after a 20% discount. what is the original price?
if the company has set a goal of producing 20 radios for the cost of $3,000 which statement is true
Answer:
60,000 i believe :)
What is the surface area of the cylinder? 14ft length 9ft height
A.) 126πft²
B.) 273πft²
C.) 224πft²
D.) 175πft²
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:
how to graph 2x+4y=28
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.
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.
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
#SPJ2
Someone help me find x and y?
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.
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.
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]
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
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
398.574986215 to the nearest ten-thousandth.
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]
how do u graph x>-6 on a line graph?
<, > - opened circle
≤, ≥ - closed circle
<, ≤ - draw line to left
>, ≥ - draw line to right
Answer in the attachment.
<,> - dotted line
≤, ≥ - solid line
<, ≤ - shadow to left
>, ≥ - shadow to right
x = -6 - its a vertical line
hope everyone can help me I'll really need your help
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
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
pls help me on this word proplem?
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
A ball is thrown vertically upward from the top of a
building 96 feet tall with an initial velocity of 80 feet
per second. The distance, s (in feet), of the ball from
the ground after t seconds is given by the function:
() = 96 + 80 − 16
2
a. How long does it take for the ball to reach its
highest point?
b. What is the maximum height the ball reaches?
Answer:
It takes 2.5 seconds for the ball to reach its highest point
Maximum height is 196 feet
Step-by-step explanation:
h(t) = -16t^2+80t +96
a=-16, b= 80, c=96
To find the maximum height , we need to find vertex
Let find x coordinate of vertex
[tex]t=\frac{-b}{2a}[/tex]
Plug in the values
[tex]t=\frac{-80}{2(-16)}= 2.5[/tex]
It takes 2.5 seconds for the ball to reach its highest point
Now plug in 2.5 for t to find maximum height
[tex]h(t) = -16t^2+80t +96[/tex]
[tex]h(2.5) = -16(2.5)^2+80(2.5) +96=196[/tex]
Maximum height is 196 feet
victor is building a square patio in his backyard. the area of the patio is 150 square feet. What is the length of each side rounded to the neareth tenth?
Answer:
The length of each side is 12.2 ft
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?
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.
Explain why each relation below is or is not a function
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
5b2-10b-15 factor this
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)
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?
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
Find the average rate of change for f(x)=x^2-3x-10 from x=-5 to x=-10
Answer:
-18
Step-by-step explanation:
f(x) = x² - 3x -10
f(-10) = (-10)² – 3(-10) – 10
f(-10) = 100 + 30 - 10
f(-10) = 120
f(-5) = (-5)² – 3(-5) – 10
f(-5) = 25 + 15 - 10
f(-5) = 30
=====
The average rate of change is the slope m of the straight line joining the two points.
m = (y₂ - y₁)/(x₂ - x₁)
m = (30 - 120)/(-5 – (-10))
m = -90/(-5+10)
m = -90/5
m = -18
solve for 3x+4=9x+3
A. 1/3
B. 1/6
C. -1/3
D. None of the above.
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
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.
4^x+2=1/2 solve for x (log equation)
[tex]\log_ab=c\iff a^c=b\\\\4^{x+2}=\dfrac{1}{2}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^2)^{x+2}=2^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+2)}=2^{-1}\iff2(x+2)=-1\qquad\text{use distributive property}\\\\(2)(x)+(2)(2)=-1\\\\2x+4=-1\qquad\text{subtract 4 from both sides}\\\\2x=-3\qquad\text{divide both sides by 2}\\\\\boxed{x=-1.5}[/tex]
Write a rule of sequence for 25.7, 24.1, 20.9, 19.3
Answer:
It deducts 1.6 each time so the next one would be 22.5
a triangular prism has a volume of 240 cubic meters which of the measurements below are not possible dimensions for the area of the base and the height of the prism
Answer:
I) B = 20 m², h = 4 m are NOT possible dimensions for the area of the base and the height of the prism.
Step-by-step explanation:
Given that the triangular prism has a volume = 240 m³, we can use the formula for the volume of a triangular prism to check the given answers for possible dimensions. V = Bh, where B = the area of the base and h = height of the prism. In this case, we simply need to multiply each of the given dimensions together to see if they equal 240 m³:
F) B = 48 m², h = 5 m: v = 48 x 5 = 240 m³ (possible)
G) B = 24 m², h = 10 m; v = 24 x 10 = 240 m³ (possible)
H) B = 12 m², h = 20 m: v = 12 x 24 = 240 m³ (possible)
I) B = 20 m², h = 4 m: v = 20 x 4 = 80 m³ (NOT possible)
College algebra ! Help ASAP !!!
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
You Start At (1,9) You Move Left 1 Unit And Up 1 Unit.Where Do You End?
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)
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
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:
need help asap!!!thanks
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.