The original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m
How does dilation affect length, area, and volume of an object?Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.
So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:
L = k × M
where 'k' will be called as scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.
So area of first figure = k² × area of second figure
Similarly,
Volume of first figure = k³ × volume of second figure.
It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.
For this case, we're given that;
Surface area of pre-image = 35 m²Surface area of dilated image = 315 m²Height of pre-image = 5.8 mHeight of dilated image.Let the scale fator of dilation be k.
Then:
So area of pre-image = k² × area of dilated image
Thus, we get:
[tex]35 = k^2 \times 315\\\\k = \sqrt{\dfrac{35}{315}} = 1/3[/tex]
(took positive root as scaling is done by non-negative factors as only magnitude matters mostly)
Thus, we get:
Height of pre-image = (1/3) × Height of dilated image (say h)
[tex]5.8 = (1/3) \times h\\h = 3 \times 5.8 = 17.4 \rm \: m[/tex]
Thus, the original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m
Learn more about dilation here:
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Given KL←→− is tangent to ⊙F at point J, select all the statements that must be true
Given that the tangent KL to the circle at point J and the interior triangles ∆JGL, and ∆JFL, we have;
C. mHJL = mJGH
D. mGHJ = mKJG
How can the true statements be found?From the tangent secant interior angles measure theorem, we have;
mHJL = 0.5•mJFH
mJGH = 0.5•mJFH
Therefore;
mHJL = mJGHSimilarly
mGHJ = mKJGLearn more about the tangent and secant of a circle here:
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The table represents some points on the graph of a linear function
x y
-7 -2
-3 4
5 16
15 31
What is the rate of change of y with respect to for this function?
A. 2/3
B 3/2
C - 2/3
D - 3/2
Answer:
D
Step-by-step explanation:
C666666666666666666666
HELP PLEASE I WILL GIVE BRAINLIEST
Answer:
y= -1/2x
Step-by-step explanation:
Option B passes through the origin, by -1/2x
Can someone please help?
Simplify, 81^1/4
Answer:
3
Step-by-step explanation:
81^(¼) can also be witten as the fourth root of 81, which happens to be 3.
Answer:
3
Step-by-step explanation:
(3*(to the fourth power))1/4
Zoe has a circular shaped rug on her bedroom floor. The diameter of the rug is 8 feet. What is the circumference of the rug?
Answer:
It is 25.13 (simplified)
Step-by-step explanation:
3.14(pi) x 8 is 25.14
A scale model of a ramp is a right triangular prism as given in this figure. in the actual ramp, the triangular base has a height of 0.5 yards. what is the surface area of the actual ramp, including the underside? enter your answer as a decimal in the box.
The surface area of the actual ramp including the underside is 16.8 ft²
The height of the actual ramp = 1.2 feet
The height of the model = 6 cm
What is the surface area of a right triangular prism?A right triangular prism is a 3-dimensional triangle with two congruent triangular faces and 3 rectangular faces that connect the triangular.
The surface area of a right triangular prism
= (Perimeter of the base × Length of the prism) + (2 × Base Area)
Scale factor = 1.2 feet / 6 cm = 0.2 ft/cm
Actual base = 16 cm × 0.2 ft/cm = 3.2 ft
convert the units
9 cm = 9 cm × 0.2 ft/cm = 1.8 ft
10 cm = 10 cm × 0.2 ft/cm = 2 ft
The surface area of a right triangular prism
= (Perimeter of the base × Length of the prism) + (2 × Base Area)
Surface area of actual ramp = 2(0.5 × 3.2 ft × 1.2 ft) + 2(2 ft × 1.8 ft) + (1.8 ft × 3.2 ft)
= 16.8 ft²
Hence, the surface area of the actual ramp including the underside is 16.8 ft²
Learn more about the area here:
brainly.com/question/25292087
Answer:
7.2 yd² for K12
what are factors of the expression [tex]x^{2}[/tex]+x 20?
Answer:
Step-by-step explanation:
answer: (x-4)(x+5)
x^2 + x - 20
x^2 + 5x -4x -20
x^2 + 5x - 4x - 20
x(x+5) -4 (x+5)
x(x+5)-4(x+5)
(x-4)(x+5)
A stained glass window has the dimensions shown. What is the perimeter of the hole that should be cut in the wall in order for the window to be installed?
Answer: She observed older fossils that contained many of the same minerals as the newer ones
Step-by-step explanation:
Answer:
chaupapi
\\
Step-by-step explanation:
I really need help!!!!!!!!!!!!!!
Answer:
Step-by-step explanation: After purchasing 21 DVDs the membership is worth the money with a total spending of 104 dollars compared to 105 dollars without the membership.
Membership: -20, -24, -28, -32, -36, -40, -44, -48, -52, -56, -60, -64, -68, -72, -76, -80, -84, -88, -92, -96, -100, -104
No Membership: 0, -5, -10, -15, -20, -25, -30, -35, -40, -45, -50, -55, -60, -65, -70, -75, -80, -85, -90, -95, -100, -105
How many ice cream desserts consisting of four scoops, of either vanilla or hazelnut flavor, are possible
2 flavors and 4 scoops
total different possibilities = 2^4 = 16
answer: 16
please help need this now
Answer:
hope this helps
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
Its A
Step-by-step explanation
just trust me
Which parabola will have one real solution with the line y = x – 5? y = x2 x – 4 y = x2 2x – 1 y = x2 6x 9 y = x2 7x 4
System of equations y = x² + 7x + 4 has one real root with the line y = x -5.
What is the discriminant in the quadratic equation?A quadratic equation is the polynomial equation of two degrees in one variable. The general form of a quadratic equation is ax² + bx + c = 0.
The quadratic equation formula for the solution of roots.
[tex]\rm (\alpha ,\beta ) = [ -b[/tex]±[tex]\rm \sqrt{b^{2} - 4ac} /2ac[/tex]]
The discriminant is the [tex]\rm \sqrt{b^{2} - 4ac}[/tex] part of the quadratic equation
If D is greater than zero then the roots are real and distinct.
If D is equal to zero then the roots are real and equal.
If D is less than zero then the roots are imaginary and unequal.
y = x² + 7x + 4
From First option, System of equations
y = x² + x – 4
y = x – 5
So, x - 5 = x² + x – 4
x² + x – 4 - x + 5 = 0
x² + 1 = 0
discriminant = b²- 4×a×c
= 0²- 4×1×1
-4 < 0, therefore the equation has no real roots.
From Second option, System of equations
y = x² + 2x – 1
y = x – 5
So, x - 5 = x² + 2x – 1
x² + 2x - 1 - x + 5 = 0
x² + x + 4 = 0
discriminant = b²- 4×a×c
= 1²-4×1×4
-15 < 0 therefore, the equation has no real roots.
From Third option, System of equations
y = x² + 6x + 9
y = x – 5
So, x - 5 = x² + 6x + 9
x² + 6x + 9 - x + 5 = 0
x² + 5x + 4 = 0
discriminant = b²- 4×a×c
= 5²-4×1×4
9 > 0 therefore, the equation has two different real roots.
From Fourth option, System of equations
y = x² + 7x + 4
y = x – 5
So. x - 5 = x² + 7x + 4
x² + 7x + 4 - x + 5 = 0
x² + 6x + 9 = 0
discriminant = b²- 4×a×c
= 6²-4×1×9 = 0
0 therefore, the equation has one real root.
Since, System of equations y = x² + 7x + 4 has one real root with the line y = x -5.
Learn more about quadratic equations;
https://brainly.com/question/2263981
Answer:
D on edge
Step-by-step explanation:
Mr. Jacobsen is an electrical engineer. He earns 150,000 (GROSS) a year. He pays 20% income tax. How much income tax does he pay?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 15000}}{\left( \cfrac{20}{100} \right)15000}\implies 30000[/tex]
Please answer I am stuck on this problem
Answer:
20+2C
Step-by-step explanation:
sum means addition
if Craig's age is c than twice his age is 2xC, also expressed as 2C
20+2C
If square root 6 is the geometric mean between 4 and another number, then the number is?
Answer:
The answer is 1.5
pls give brainliest ily<3
3 students are in a race. How many ways can they finish in 1st, 2nd, and 3rd place?
6. Find the mean and the median for these data,
Mean
Median
The points scored by a basketball team in its last 6 games
are shown. Use these data for 7 and 8.
Points Scored
73
77
85
84
37
115
7. Find the mean score and the media
Answer:
73+77+85+84+34+115 and the basket ball team got from the game
I Don’t get this, someone help!!
Step-by-step explanation:
4)For answer of no 4
the third side can be gotten by pythagoras theorem;
It says,
hyp^2=opp^2 + adj^2
hyp= ?
opp=30
adj=40
so,
hyp^2=30^2 + 40^2
hyp^2=900+1600
hyp^2=2500
square rooting both sides,
hyp=50ft
Therefore the missing side is 50ft
5) for number 5
opp is missing
remember,
hyp^2=opp^2+adj^2
opp^2= hyp^2-adj^2
opp^2=41^2-40^2
opp^2=1681-1600
opp^2=81
square rooting both sides,
0pp=9Inches
Cover the entire area except for today's date and year April, 1st, Monday
Answer:
It's friday for me so here u go
Step-by-step explanation:
A train track through a mountain is 1600 feet long and makes an angle of 1.6 with the horizontal. What is the change in elevation from one end of the tunnel to the other.
Step-by-step explanation:
law of sine :
a/sinA = b/sinB = c/sinC
with the sides and correlating angles being always opposite to each other.
we are dealing with a right-angled triangle here.
the train track is the Hypotenuse (the side opposite of the 90° angle) : 1600 ft.
the horizontal level "connection" from beginning to the end of the track is one leg, and the elevation difference at the end of the track is the second leg.
the 2 legs enclose a 90° angle, as the elevation goes straight up from the horizontal level.
so, we have
1600/sin(90) = elevation difference / sin(1.6)
sin(90) = 1
1600 = elevation difference / sin(1.6)
elevation difference = 1600 × sin(1.6) =
= 1600 × 0.027921639... =
= 44.67462196... ft
≈ 44.7 ft
What quadrilateral always has 4 congruent angles and opposite sides that are congruent and parallel? Please answer it correctly.
Answer:
Square
Step-by-step explanation:
Requirements that make a square, a square;
Four sidesCongruent angles (all 90°)Opposite sides are congruent/the same.Opposite sides are also parallel because the lines of a square do not intersect.Answer:
Square
Explanation:
A square has four congruent angles as each angle measure is 90°. A square can never have an angle other than 90°. A square also has all four equal sides, and its opposite side lengths are parallel because all angles of a square must be 90°.
Please look at attached image for reference.
-3/10x (-0.1) can you please help ASAP
[tex] \frac{ - 3}{10} \times ( - 0.1)[/tex]
[tex] \frac{ - 3}{10} \times \frac{ - 1}{10} [/tex]
–3 × –4
10
[tex] \frac{12}{10} [/tex]
[tex] \frac{6}{5} answer[/tex]
HOPE THIS HELPS :)How much material is needed to make the popcorn container?
look at the screenshot
Answer:
x = 5
y = 2
Step-by-step explanation:
multiply by -2 the second equation and add the first equation to eliminate "x"
[tex]4x+5y=30\\-4x-10y=-40[/tex]
_______________
[tex]-5y=-10\\y=\frac{-10}{-5} =2[/tex]
To find "x", substitute the value of "y" in any equation. I do it in the first
[tex]4x+5(2)=30[/tex]
[tex]4x+10=30[/tex]
[tex]4x=30-10\\x=20/4=5[/tex]
Hope this helps
Answer:
i got you
Step-by-step explanation:
first you will make the easiest equation into y=mx+b
2x=5y=20
subtract 2x from it self and 20, you will eliminate the 5 but keep the y then you will get y=2x+20
then you will substitute it into the y in the other equation 4x+5(2x+20)=30
after doin that you will multiply 5 by both the number in the parenthesis
4x+15x+100=30 add like terms 4x+15x =
19x+100=30 subtract 100 fromm itself and 30 you will get -70
-70 divided by 19x then you will get your answer
ba^4 * (2ba^4)^-3
Please help
Answer:
1/(8b^2a^8)
Step-by-step explanation:
The given expression can be simplified using the rules of exponents.
[tex]ba^4\times(2ba^4)^{-3}=\dfrac{ba^4}{(2ba^4)^3}=\dfrac{ba^4}{8(ba^4)^3}=\dfrac{1}{8(ba^4)^2}=\boxed{\dfrac{1}{8b^2a^8}}[/tex]
__
The applicable rules of exponents are ...
a^-b = 1/a^b
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
__
Additional comment
It can be useful to think of an exponent as indicating repeated multiplication: 2^3 = 2×2×2, for example. Of course, the repeated multiplication can be nested: (4^2)^3 = (4^2)×(4^2)×(4^2) = (4×4)×(4×4)×(4×4) = 4^6
Numerator and denominator factors cancel in the usual way.
Item 3
Solve for b.
16=a2+b2
b=16−a2
b=4−a
b=±16+a2−−−−−−√
b=±16−a2−−−−−−√
Answer:
I'm taking the test right now so i'll tell you the right answer after I submit my test but for now I think it's C.
help me out i will give brainlist
Answer:
no
Step-by-step explanation:
0.06 = [tex]\frac{6}{100}[/tex] ← that is 6 books out of 100
she requires to have 60 out of 100 , that is
[tex]\frac{60}{100}[/tex] = 0.6
Find the perimeter.
Write your answer as a fraction or as a whole or mixed number.
3
mm
4
M
3
mm
|*
mm
3
mm
Last one for today thank youu
Answer:
3mm
Step-by-step explanation:
4 (3/4)
4x3/4
=3
brainiest please
Answer:
3 mm⠀
Step-by-step explanation:
⠀
We know,
[tex]{\longrightarrow \qquad \boldsymbol{\pmb{Perimeter_{(square)} \it=4a }}}[/tex]
⠀
Where,
a is the side length of the square. Here, a = [tex] \sf \: \dfrac{3}{4} [/tex] mm⠀
Now, Substituting the values in the formula :
⠀
[tex]{\longrightarrow \qquad {\rm{Perimeter_{(square)} = \it4 \times \it \dfrac{3}{4} }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm{Perimeter_{(square)} = \it \cancel4 \times \it \dfrac{3}{ \cancel4} }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\boldsymbol {\pmb{Perimeter_{(square)} = 3 }}}}[/tex]
⠀
Therefore,
The perimeter of the square is 3 mmA triangle has angles of 124°, 28°, and 28°. Will these angles create a triangle?
Answer:
yes it will
Step-by-step explanation:
28+28=56
124+56=180
a triangle consists of angles that add up to 180 degrees