The scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.
What is the dilation of the figure?Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.
Point c is the center of dilation. Line segment BA is dilated to create line segment b prime, a prime. The image of the given problem is attached below. The length of CA is 4.
[tex]CA=4[/tex]
The length of a prime is 16.
[tex]AA'=16[/tex]
The new dimension will be,
[tex]CA'=CA+AA'\\CA'=4+16\\CA'=20[/tex]
Now, the scale factor is the ratio of the new dimension to the original dimension. Thus, the scale factor of the dilation is,
[tex]r=\dfrac{20}{4}\\r=5[/tex]
This will be the same for the line segment BA. Thus, the scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.
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Answer:
the answer is 5
Step-by-step explanation:
D
Find the length of side a.
A. 4
B. 2
C. 34
D. 16
Answer:
Side A is 4
Step-by-step explanation:
Answer:
A.4
Step-by-step explanation:
a = √(c² - b²)
a= √(5² -3b²)=4
Find the common factor of all the terms of the polynomial 16x2 - 14x. O A. 2x² O B. 44² O c. 2x O D. 4x
Answer:
c. 2x.
Step-by-step explanation:
16x2 - 14x
Common factor of 16 and 14 = 2'
for x2 and x it is x,
Answer: 2x.
perform the translation (x, y) - (x-2, y+3)
Answer:
The coordinate of the image of a point is (2, +3) under the translation (x , y) → (x - 2),( y + 3). Find the coordinate of the preimage.
We are just looking for x and y and we know (2, +3) → (x - 2, y + 3)
2 = x - 2
x = 4
-3 = y + 3
y = -6
(x , y) = (4, -6)
How to find a
Marvin is saving $5.25 a week to buy a new video game that costs 69.15. How many
weeks will he have to save to buy the game?
Answer: 10.62 irrational
Step-by-step explanation: You can divide 69.15 by 5.25 which equals 74.4 then divide by 7 which equals 10.62
$20,000 is borrowed at an interest rate of 15% p.a. (per annum) to be paid back over 10
years, calculate the amount of interest, the total repayment and the monthly repayment.
Answer:
30000 simple interest ,50000 total repayment.
Step-by-step explanation:
sorry iam terrible at explaining,
Find the average squared distance between the points of r{(x,y): 0x, 0y} and the point (,)
The average squared distance between the points is their variance
The average squared distance is 8/3
How to determine the average squared distance?The given parameters are:
R={(x,y): 0<=x<=2, 0<=y<=2}
The point = (2,2).
f(x,y) = (x-2)² + (y-2)²
The squared distance is calculated as:
D² = f(x,y) = (x-2)² + (y-2)²
Where the area (A) is:
A = xy
Substitute the maximum values of x and y in A = xy
A = 2 * 2
A = 4
The minimum values of x and y are 0.
So, the limits for the integrals are 0 to 2
The integral becomes
[tex]D\² = \int \int (x-2)\² + (y-2)\² dx dy[/tex]
Expand
[tex]D\² = \int \int x\² -4x + 4 + (y-2)\² dx dy[/tex]
Evaluate the inner integral with respect to x from 0 to 2
[tex]D\² = \int \frac 13x^3 -2x^2 + 4x + x(y-2)\² |\limits^2_0 dy[/tex]
Expand
[tex]D\² = \int [\frac 13(2)^3 -2(2)^2 + 4(2) + (2)(y-2)\²] dy[/tex]
Simplify
[tex]D\² = \int \frac 83 + (2)(y-2)\² dy[/tex]
Expand
[tex]D\² = \int \frac 83 + 2y^2-8y + 8 \ dy[/tex]
Evaluate the integral with respect to y from 0 to 2
[tex]D\² = [\frac 83y + \frac 23y^3- 4y^2 + 8y ]|\limits^2_0[/tex]
Expand
[tex]D\² = \frac 83*2 + \frac 23*2^3- 4*2^2 + 8*2[/tex]
D² = 32/3
The average squared distance (AD²) is calculated as:
AD² = D²/A
So, we have:
AD² = 32/3 [tex]\div[/tex] 4
Evaluate the quotient
AD² = 32/12
Simplify
AD² = 8/3
Hence, the average squared distance is 8/3
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The average squared distance between the points of R = {(x,y): 0<=x<= h, 0<=y<=k } is 8/3.
How do determine the average squared distance?
From the given parameters R = {(x,y): 0<=x<= h, 0<=y<=k }
The squared distance from point (h, k) is calculated as
D² = f(x,y) = (x-2)² + (y-2)²
Where the area (A) will be
A = xy
Substitute the maximum values of x and y
A = 2 × 2 = 4
The minimum values of x and y are 0.
So, The integral becomes
[tex]D^{2} = \int \int(x-2)^2 +(y-2)^2 dx dy\\\\D^{2} = \int \int\limits^2_0 (x)^2 -4x + 4+(y-2)^2 dx dy\\\\D^{2} = \int1/3(x)^3-2x^{2} +4x + 4+x(y-2)^2 dy\\\\D^{2} = \int8/3+2y^{2} -8y +8 dy[/tex]
[tex]D^2 = {8/3y +2/3y^2 -4y^2+8y[/tex]
By expanding we get,
D^2 = 32/3
The average squared distance (AD²) is calculated as:
AD² = D²/A
AD² = 32/3 4
AD² = 32/12
AD² = 8/3
Hence, the average squared distance is 8/3
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Solve this linear system using determinants:
2x + 3y = 6
- 8x - 3y = 12
A=
Az =
[Ayl =
2×+3y=6
-8×-3y=12
-6×=18
×=18/-6
×=-3
——————
2×+3y=6
2(3)+3y=6
6+3y=6
3y=6-6
3y=0
Y=0/3
Y=0
——————
×=3
Y=0
————
2×+3y=6
2(3)+3(0)=6
6=6
xLasersx✨44 friends evenly divided up an nnn-slice pizza. One of the friends, Harris, ate 111 fewer slice than he received.
How many slices of pizza did Harris eat
Answer:
(n/4)-1
Step-by-step explanation:
can someone please help!!
I need the answer and explanation pls
Step-by-step explanation:
percentage of green marbles=
(total green marbles÷ total marbles )×100
Right equation of the line that is perpendicular to the line Y equals negative 3X +8 and passes through the point -2, 3. Right equation in point slope form
=======================================================
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, flop it over, and change its sign.
In this case, we take [tex]\boxed{-3}[/tex], change its sign:
[tex]\boxed{3}[/tex]
3 can also be written as
[tex]\boxed{\frac{3}{1} }[/tex]
Now the numerator & denominator switch places:
[tex]\boxed{\frac{1}{3}}[/tex]
So that's the slope of the new line.
Now, let's write the equation in point-slope form:-
[tex]\bigstar{\underline{\boxed{\pmb{y-y_1=m(x-1)}}}[/tex]
Where
y₁ is the y-coordinate of the point (in this case, y₁ = 3)
m = slope (1/3)
x₁= the x-coordinate of the point (in this case, it's -2)
Plug in the values:-
[tex]\bigstar{\boxed{\pmb{y-3=\frac{1}{3}(x-(-2)}}[/tex]
[tex]\bigstar{\boxed{\pmb{y-3=\frac{1}{3}(x+2)} }\longleftarrow\sf{Point-Slope~Formula:)}}[/tex]
===============================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
In circle C with m \angle BCD= 46m∠BCD=46 and BC=3BC=3 units, find the length of arc BD. Round to the nearest hundredth.
The length of arc of the given circle, to the nearest hundreth, is: 2.41 units.
What is the Length of an Arc?Length of arc = ∅/360 × 2πr, where the radius of the circle is r, and the reference angle is ∅.
We are given the following:
Radius (r) = 3 units
Reference angle (∅) = 46°
Plug in the values into the length of arc formula:
Length of arc = 46/360 × 2π(3)
Length of arc = 2.41 units.
Therefore, the length of arc of the given circle, to the nearest hundreth, is: 2.41 units.
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Solve this QUICKLY and explain, please
Answer:
Step-by-step explanation:
c
so you have to combine like terms so subtract 8 - 4 and the 4 disappears so it be like this
8 - 2x = 4 + x
-4 -2x = -4 + x
4 - 2x = x
next combine the like terms of the 2x so
4 - 2x = x
4 + 2x = +2x
4 = 2x
now you divide 4 by 2 so like this
4 = 2x
2 2
and your answer is x = 2 try to solve the other one if you need help ask me
f the last 18 trains to pull into Castroville Station, 12 were full. Considering this data, how many of the next 12 trains would you expect to be full?
Answer:
8
Step-by-step explanation:
first multiple 12 by 12 then divide by 18 then you'll get 2 times 4 and that's how you get 8.
Can someone please help me with this? It's urgent! I need to turn it in tomorrow, please
Answer:
Step-by-step explanation:
Anything going from lower left to upper right is a positive slope.
The lines are not easily seen. My best estimate is that one point is (2,5)
Use the two points you are sure of.
(0,-1) and (1,2)
Givens
x1 = 0x2 = 1y1 = - 1y2 = 2Formula
m = (y2 - y1)/(x2 - x1)
Solution
m = (2 - - 1) / (1 - 0)
m = 3/1
m = 3
Please help me answer this question on congruent triangles. 30 points
Answer:
h = 24 cm
Step-by-step explanation:
Let [tex]x[/tex] = height of ΔCBD
Let [tex]h[/tex] = height of ΔABE
As ΔABE ~ ΔCBD then AE : CD = [tex]h[/tex] : [tex]x[/tex]
Given:
AE = 20 cmCD = 10 cm[tex]\implies 20 : 10 = h : x[/tex]
[tex]\implies \dfrac{20}{10}=\dfrac{h}{x}[/tex]
Cross multiply:
[tex]\implies 20x=10h[/tex]
Simplify:
[tex]\implies 2x=h[/tex]
As we are told that [tex]x+h=36 \ \sf cm[/tex]
[tex]\implies h=36-x[/tex]
Equate the two equations for [tex]h[/tex] and solve for [tex]x[/tex]:
[tex]\implies 2x=36-x[/tex]
[tex]\implies 3x=36[/tex]
[tex]\implies x=12[/tex]
Since [tex]h=2x[/tex] then
[tex]\implies h=2 \cdot 12[/tex]
[tex]\implies h=24 \ \sf cm[/tex]
A boy sees a bird sitting on a tree at an angle of elevation of 20°. If a boy is standing 10 miles away from the tree, at what height bird is sitting?
Let that be x
[tex]\\ \rm\rightarrowtail tan\theta=\dfrac{Perpendicular}{Base}[/tex]
[tex]\\ \rm\rightarrowtail tan20=\dfrac{x}{10}[/tex]
[tex]\\ \rm\rightarrowtail 0.364=\dfrac{x}{10}[/tex]
[tex]\\ \rm\rightarrowtail x=10(0.364)[/tex]
[tex]\\ \rm\rightarrowtail x=3.64mi[/tex]
Answer:
[tex]\displaystyle 4\:mi.[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{10}{h} = cot\:20 \hookrightarrow 10 = hcot\:20 \hookrightarrow \frac{10}{cot\:20} = h; 3,6397023427... \\ \\ \boxed{4 \approx h}[/tex]
OR
[tex]\displaystyle \frac{h}{10} = tan\:20 \hookrightarrow 10tan\:20 = h; 3,6397023427... \\ \\ \boxed{4 \approx h}[/tex]
I am joyous to assist you at any time.
What is the coefficient for the 5th term of (2x-y)^8
Answer:
256x^8
Step-by-step explanation:
Hope this helped
Maybe mark brainiest?
please help me out with this I will give brainliest if the answer is right
Answer:
60 cm
Step-by-step explanation:
The perimeter of a polygon means adding up all the side lengths.
In this case, we need to add up 13, 12, 8, 8, and 19
Adding all of these gets us 60
Joey has 23 cards in his baseball card collection. Monica has 24 cards in her collection. How many times more cards does Monica have than Joe?
Answer:
Monica has 1 more card than Joey
Step-by-step explanation:
its simple math
The volume of the triangular block is 4 cubic inches. A triangular prism has a volume of 4 cubic inches. The right triangle bases have side lengths of x and a hypotenuse length of y. THe height of the prism is x. What is the approximate length of y? Round to the nearest tenth of an inch. 1. 4 in. 2. 0 in. 2. 8 in. 3. 5 in.
The value of the hypotenuse y will be equal to y = 2.8 inches.
What is volume of prism?The volume of the prism is equal to the product of the area of its base and the height of the prism.
[tex]\rm V=Area \ of\ triangular \ base\times Height \ of \ prism[/tex]
The volume oif the prism is =4 cubic inches
Height of the prism = x inches
Base of the right angle isosceles triangle will be =x inches
The hypotenuse is given = y
Now
[tex]\rm V=\dfrac{1}{2}\times Base\times Height \times height \ of \ prism[/tex]
[tex]V=\dfrac{1}{2} \times x \times x \times x[/tex]
[tex]x^3=8[/tex]
[tex]x=2[/tex]
Now by pythagorus theorem
[tex]y^2=h^2+b^2[/tex]
[tex]y^2=x^2+x^2[/tex]
[tex]y^2=2x^2=2\times 2^2[/tex]
[tex]y=2\sqrt{2}=2.82[/tex]
Thus the value of the hypotenuse y will be equal to y = 2.8 inches.
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Answer:
2.8 INCHES
Step-by-step explanation:
Find the area of the quadrilateral
Answer:
58.58
Step-by-step explanation:
[tex] \frac{1}{2} \times 10 \times 3 \\ 5 \times 3 = 15.....(1)[/tex]
[tex] \frac{1}{2} \times 10 \times 10 \\ 5 \times 10 = 50...(2)[/tex]
Add one and two :- 15+ 50 = 65
Pls help!!
Question:
The polynomial f (x) = ax2 + bx + c has zeros 4 and 5, and f (−1) = 60. Evaluate a, b and c.
a = 2, b = -18, c = 40
Step-by-step explanation:[tex]Given:\ Polynomial\ f(x)=ax^2+bx+c\ has\ zoroes\ 4\ aud\ 5[/tex]
[tex]and\ f(-1)=60[/tex]
[tex]Tofind:\ a,\ b,\ c[/tex]
[tex]Solution:\ As\ 4\ and\ 5\ are\ zeroes\ so\ f(4)=f(5)=0[/tex]
[tex]f(4)=a(4)^2+b(4)+c=0\Rightarrow16a+4b+c=0-(1)[/tex]
[tex]f(5)=a(5)^2+b(5)+c=0\Rightarrow25a+5b+c=0[/tex]
[tex]f(-1)=a(-1)^2+b(-1)+c=60\Rightarrowa-b+c=60-(3)[/tex]
[tex]subtracting\ (1)\ from\ (2)[/tex]
[tex]25a+5b+c-(16a+4b+c)=0\Rightarrow9a+b=0\Rightarrowb=-9a[/tex]
[tex]subtracting\ (3)\ from(2):[/tex]
[tex]25a+5b+c-(a-b+c)=0-60\Rightarrow24a+6b=-60[/tex]
[tex]putting\ b=-9a[/tex]
[tex]24a+6(-9a)=-60\Rightarrow24a-54a=-60\Rightarrow-30a=-60[/tex]
[tex]a=\frac{-60}{-30}=2[/tex] [tex]\Rightarrow[/tex] [tex]a=2[/tex]
[tex]b=-9a=-9\times2=-18[/tex]
[tex]c=-a+b\neq60=-2-18+60=-20+60=40[/tex]
I hope this helps you
:)
Point K is shown on the number line below .
Which number sentence BEST describes the value represented by point K?
Answer: B. K < 13. K is 12.5, 12.5 is less than 13
1. Its not D because at the ending points of the number line; 10-20, which is less than 30.
2 It is not C because K is not on 15
3 It is not A because 12.5 is less than 13.
Hope it helps!!
travis measured 5 different-colored pencils to the nearest inch, 1/2 inch, and 1/4 inch. He records the measurements in the chart below. He draws a star next to the measurements that are exact.
Answer:
5x/1/2 = 1x
answer 1.12 <3
hope it helps
use brainly<3
Step-by-step explanation:
can someone please help me
Answer:
y = x - 5
Step-by-step explanation:
Line A
It has 1/2 the slope of Line BIts y-intercept is 2 x 2.5 spaces belowEquation
Line A ⇒ y = 1/2(2x) + 2(-2.5)Line A ⇒ y = x - 5: A group of 28 people bought tickets to a museum. The total cost for the tickets was $315. What was the cost of each ticket?
Answer:
he correct answer is D. 12 adult tickets, 4 child ticket
Step-by-step explanation:
Omg please help! NO LINKS NO FILES PLEASE!
Answer: Square is a 17*17. Ok so its 121-25=96
Step-by-step explanation:
96
The graph of g(x) is shown. Determine the transformations from the parent function f(x)=x2 to the new function g(x)=15x2+5
Answer:
The graph of g is translated down 5 units from the graph of f and stretched horizontally
Step-by-step explanation:
was correct on test :)
pls brainliest XD
.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.
Last one i promise but i need help
Answer:
a
Step-by-step explanation:
If the area of a circle is 64 pie square centimeters, then what is its radius
Answer:
8
Step-by-step explanation:
A=πr^2
64π=πr^2
since answer is in terms of pi, ignore the pi.
sqrt(64)=8