Answer:
Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4
Part B:
P''(-1, 0)
Q''(0, -1)
R''(2, -1)
Part C:
The two Triangles PQR and P''Q''R'' are not congruent
Step-by-step explanation:
The coordinates of triangle PQR are;
P(4, 0)
Q(0, 4)
R(-8, -4)
The coordinates of triangle P'Q'R' are;
P'(1, 0)
Q'(0, -1)
R'(-2, -1)
Part A:
The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' can be found from the ratio of the respective coordinates as follows;
The ratio of the x, and y coordinates of the points are;
P'/P = x'/x = 1/4, y'/y =0/0
R'/R = x'/x = -2/-8 = 1/4, y'/y =-1/-4 = 1/4
Therefore, the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' = 1/4
Part B: For reflection across the y-axis, we have;
Pre-image (x, y) becomes the image, (-x, y)
Therefore, we have;
Reflection of P'(1, 0) about the y-xis becomes P''(-1, 0)
Reflection of Q'(0, -1) about the y-xis becomes Q''(0, -1)
Reflection of R'(-2, -1) about the y-xis becomes R''(2, -1)
Part C:
The two Triangles PQR and P''Q''R'' are similar but they are not congruent as the dimensions of PQR are larger than the dimensions of the sides of triangle P''Q''R''.
(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4
(B) Coordinates of Δ P"Q"R"
P" (-1,0)
Q"(0,-1)
R"(2,-1)
(C) Triangles PQR and P"Q"R" are not congruent.
Given
ΔPQR is transformed into ΔP'Q'R'
Coordinates of P, Q, R are
P (4,0),
Q(0,-4)
R(-8,-4)
Coordinates of P'Q'R' are
P'(1,0)
Q'(0,-1)
R'(-2,-1)
(A) By Distance formula we can find the distance between P Q and P'Q'
Distance formula = [tex]D= \sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2 }[/tex]
Where D = Distance between two points [tex](X_1.Y_1) \; and\; (X_2.Y_2)[/tex]
from distance formula we can write that
[tex]PQ = \sqrt{(0-4)^2+ (-4-0)^2} }\\[/tex]
PQ = [tex]4\sqrt{2}[/tex]
Similarly
P'Q'= [tex]\sqrt{2}[/tex]
PQ /P'Q' = 4
hence the scale factor of dilation is 1/4 (Compression)
(B )The Coordinates of Reflection about y axis can be written for a point
[tex](x,y ) \; as \; (-x,y)[/tex]
So the Coordinated of Δ P"Q"R" can be written as
P" (-1,0)
Q"(0,-1)
R"(2,-1)
(C) ΔPQR and ΔP"Q"R" are similar triangles but they are not congruent because their sides are not equal in size.
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The area of a square of side X is 8. What's the area of a square of side 3x
Answer:
Step-by-step explanation:
We know, for square
[tex](side)^2=(Area)\\=>X^2=8\\[/tex]
∴[tex]X=2\sqrt{2}[/tex] unit
[tex]Now, Side=3X[/tex]
[tex]Then,Area=(3X)^2=(3*2\sqrt{2} )^2=(6\sqrt{2} )^2=72 sq. unit[/tex]
hope you have understood this...
pls mark my answer as the brainliest
The area of square of side 3X is 72 square unit.
What is square?The square is a 4 sided figure, each side of the square is equal and make a right angle.
The area of square having sided a unit can be given by a² square unit.
Given that,
Area of square having side X is 8.
Since, formula for area of square having side X is X².
Implies that,
X² = 8
X = 2√2
The area of square having side 3X
side =3 × 2√2
side = 6√2
The area of square = (6√2)²
= 36 x 2
= 72
The area of square is 72 square unit.
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please help me out I'll greattlyyy appreciate it!!!!!!!!! (no links)
Which of the following is a true proportion of the figure based on the triangle proportionality theorem?
Answer: Choice C
i/j = h/k
=============================================
Explanation:
The triangle proportionality theorem basically says that if we draw a parallel line somewhere inside the triangle like this, then we'll split the sides into smaller pieces that are proportional to one another (eg: the longer side is say 3 times longer than the shorter side for each piece of the original triangle).
One statement we can make is j/k = i/h. This then can be rearranged into i/j = h/k after doing a bit of algebra. Other equations are possible, so there are many combos we could try.
Please help ASAP. The question is down below.
Answer:
Question 1.
Option A: 2m
Question 2
Option D: (1, 1) minimum point
Step-by-step explanation:
Question 1.
Let the original length of the garden (before expansion) be = x
The new length of the garden will be x + 10m
Recall that the garden has a square geometry. That means that its area is obtained by squaring any of its sides.
This means that [tex](x +10)^2 = 144[/tex]
We can now solve for x
[tex](x +10)^2 = 144\\x^2 +20x +100 = 144\\x^2 + 20x =44\\x^2 + 20x - 44=0\\x = 2 or -22[/tex]
x cannot be a negative number, so the original length of a side of the garden is 2m. Option A
Question 2:
The coordinates of the vertex of the graph (turning point) are (x, y) [1,1]
To know whether it is a minimum or maximum point, we will have to check the coefficient of [tex]x^2[/tex] in the equation [tex]y = x^2-2x+2[/tex]
The coefficient of [tex]x^2[/tex] in the equation is 1. (If no number is present, just know that the coefficient is a one).
If the coefficient is positive, then the point is a minimum point. However, if it is negative, then the point is a maximum point.
Our coefficient is positive hence, the graph has a minimum point.
6a+2b-6c+4 if a=5,b=3,and c=-1
Answer:
46
Step-by-step explanation:
First, start off by substituting the values of a, b, and c, into the equation.
We know a = 5, b = 3, and c = -1, so now substitute.
6a + 2b - 6c + 4
6(5) + 2(3) - 6(-1) + 4
Now that we've substituted the values, we can solve the equation.
6(5) + 2(3) - 6(-1) + 4
30 + 6 + 6 + 4
= 46
So, the answer is 46.
I hope this helps! ôヮô
Answer:
46
Step-by-step explanation:
All you need to do is subsitute the variable with what it says the number is.
Let's first start out with 6a from the equation. We know that a= 5, so that means it wants you to multiply 6 by 5, which is 30.
Now let's do 2b. It says b= 3, so do 2 times 3. It equals 6.
So far we have 30+6-6c+4
Let's do -6c. We know that c= -1, so let's multiply -1 and -6. Negative and negative equals positive. And 6 times 1 is 6. So the outcome is positive 6.
We got 30+6+6+4
Solve.
30+6= 36
36+6= 42
And 42+4= 46. :)
Select the correct answer. The velocity of a train relative to the ground is represented by the distance from A to B in the diagram. The velocity of a ball thrown inside the train at an angle of 66° relative to the train is represented by the distance from B to C. What is the distance from A to C (the velocity of the ball relative to the ground), correct to two decimal places? Assume that all the points in the diagram lie in the same plane. A. 21.14 m/s B. 18.03 m/s C. 17.20 m/s D. 15.00 m/s
Answer:
Step-by-step explanation:
we use cosine formula
2×15×10×cos(180-66)=15²+10²-AC²
-300 cos 66=225+100-AC²
AC²=325+300 cos 66
[tex]AC=\sqrt{325+300 cos 66} \approx 21.14 ~m/s[/tex]
The distance from A to C is 21.14. The correct option is A.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.
Velocity is defined as the ratio of the distance moved by the object at a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.
Given that the velocity of a train relative to the ground is represented by the distance from A to B in the diagram. The velocity of a ball thrown inside the train at an angle of 66° relative to the train is represented by the distance from B to C.
The distance A to C will be calculated as,
2×15×10×cos(180-66)=15²+10²-AC²
-300 cos 66=225+100-AC²
AC=√(325+300 cos 66)
AC = 21.17 m/s
Therefore, the distance from A to C is 21.14. The correct option is A.
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Find the height of the triangle
Answer:
The height is 12 cm
Step-by-step explanation:
Hi there!
We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).
This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.
One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.
Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:
a=15
b=20
c=25
Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle
15²+20²=25²
225+400=625
625=625
So we can safely say that the triangle is a right triangle
This makes the problem way easier, as there are 2 ways to find the area of a right triangle:
The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2
The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2
First, we need to figure out which sides are the legs, and which side is the hypotenuse
By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs
So let's find the area of the triangle using the legs
A=[tex]\frac{15*20}{2}[/tex]=[tex]\frac{300}{2}[/tex]=150
So the area of the triangle is 150 cm²
However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2
Which means that the area is also:
A=[tex]\frac{25x}{2}[/tex] cm²
As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)
[tex]\frac{25x}{2}=150[/tex]
Multiply both sides by 2
25x=300
Divide both sides by 25
x=12 cm
So the height of the triangle is 12 cm
Hope this helps!
A book contains 27 pages with print, 8 pages with print and pictures, and 3 blank
pages. What is the theoretical probability of NOT opening the book to a printed
page only?
P(NOT printed page) =
Answer:
P(NOT printed page) = 3/38
Step-by-step explanation:
Total pages = 27+8+3=38
Types of pages that satisfy requirement(s)= 3
Therfore, P(NOT printed page) = 3/38
WILL GIVE BRAINLEST!Two machines are printing shirts. The first machine can produce 2.400 shirts in 150 minutes. The second machine can produce 2.400 shirts in 120minutes. If the two work together, how long will it take them to produce 6,480 shirts? If necessary, round your answer to the nearest whole number.
Step-by-step explanation:
see the answer in attached picture
pls mark me as brainliest pls
Answer:
If two machine works together it takes 180 minute to complete 6480 shirts
Step-by-step explanation:
2400 ÷ 150 = 6
So here,
1st machine produces 20 shirts per minutes
let, x=minutes for shirt's production
Now,
(16+20)x=6480
36x=6480
x=6480/36
Therefor, x=180 minutes
What is the area of a circle with a radius of 35 inches?
in 2
(Use 3.14 for Pi.)
Answer:
3846.5 in.
Step-by-step explanation:
πr² = (3.14)(35)² = 3846.5 in.
this geometric sequence?
What is the explicit formula for
8, 4, 2, 1, ...
Answer:
D
Step-by-step explanation:
the first term is 8, the ratio is 1/2 ( 8*1/2 = 4, 4*1/2 = 2, 2*1/2 = 1)
the formula for an explicit geometric formula is :
[tex]a_{n} = a_{1} * r^{(n-1)}[/tex]
plug in your numbers :
[tex]a_{n} = 8 * (\frac{1}{2}) ^{(n-1)}[/tex]
90 to the nearest tenth
Answer:
90
Step-by-step explanation:
Hey there!
Well 90.000 to the nearest tenth is just 90 because there is no decimal places to round.
Hope this helps :)
Answer:
90
Step-by-step explanation:
90 has 0 ones so 90 is just 90, but rounded...
Evaluate 0.6721 x 0.0261 and express your answer in standard form
Answer:
Step-by-step explanation:
0.6821 multiplied by 0.0261 is .01754181
putting that into standard from would be 1.754181 x 10^-2
Find the value of x. A. 53–√ m B. 241−−√ m C. 6 m D. 6+35–√ m
Answer:
x = 2√41 mStep-by-step explanation:
Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x
Using Pythagoras theorem we have
a² = b² + c²
where a is the hypotenuse
From the question x is the hypotenuse
So we have
[tex] {x}^{2} = {8}^{2} + {10}^{2} [/tex][tex] {x}^{2} = 64 + 100[/tex][tex] {x}^{2} = 164[/tex]Find the square root of both sides
We have the final answer as
x = 2√41 mHope this helps you
Answer:
2 sqrt(41) =c
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
8^2 + 10^2 = c^2
64+ 100 = c^2
164 = c^2
take the square root of each side
sqrt(164) = sqrt(c^2)
sqrt(4*41) = c
2 sqrt(41) =c
use the given information to find the new price
wholesale price: $35
markup: 95%
Answer:
i think the answer is either $68.25 or $110
i hope this helped
Which equation represents a proportional relationship between
x and y?
A: k/x = y
B: k - x = y
C: k + x = y
D: k * x = y
Answer:
D: k*x=y
Step-by-step explanation:
a proportional relationship is basically a linear equation (y=mx+b)
What is the surface area of the cylinder with height 5 ft and radius 2 ft? Round your
answer to the nearest thousandth.
Answer:
87.965
Step-by-step explanation:
surface area of a cylinder,
2πr²+2πrh (where r = radius, h = height)
given, h = 5, r = 2
so,
2πr²+2πrh
= 2π×2²+2π×2×5
= 8π+20π
= 28π
= 87.9645943..
= 87.965 (rounded to the nearest thousand)
hello could you please help me with this math problem with full explanation which I am unable to solve? Thanks.
Answer:
8 / sqrt(3)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan A = BC / AC
tan 30 = BC / 8
8 tan 30 = BC
8 * sqrt(3)/3 = BC
8/3 sqrt(3) = BC
On a separate piece of graph paper, graph y=-Ixl +3 then click on the graph until the correct one appears.
Answer:
That is the graph for y = -|x| + 3
Coherence
5. Simon's teacher asked him to e-mail her a copy of the outline for his essay on American
History: When drafting the e-mail, what level of diction should Simon use?
informal
formal
standard
foundational
Answer:
The correct option is;
Formal
Step-by-step explanation:
The common levels of diction are formal, informal, and popular, with formal diction being the most selective of the word choices
Formal diction is used when when communicating in a situation that is formal
Formal diction uses languages that is devoid of slang and grammatically correct
Formal language is precise, grammatically correct language that does not use slang used in communication for legal, professional, business and academic purposes.
Think about the proportion and the cross products for this problem: Shelley sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20. Because the cross products are equal, which statements are true? Select all that apply.
3×4·20 equals to 12.6 please thats youre awnser
Answer:
The ratios are equivalent.
The ratios are a proportion.
Step-by-step explanation:
What is the circumference of the circle whose equation is (x − 9)2 + (y − 3)2 = 64?
Answer:
C = 16pi or ≈50.24 units
Step-by-step explanation:
(x − 9)^2 + (y − 3)^2 = 64
This equation is in the form
(x-h)^2 + (y-k)^2 = r^2
The radius is 8
The circumference is given by
C = 2*pi*r
C = 2*pi*8
C = 16 pi
Using 3.14 as an approximation for pi
C = 16(3.14)
C ≈50.24
help me solve please
Answer:
B
Step-by-step explanation:
The side you have drawn in is 4√3 (calculate via pythagoras as √(8²-4²) = √48 = √16·3 = √4²·3 = 4√3)
So the area of the small triangle is 4*2√3 and the area of the small rectangle is 2*4√3. Together makes 4*2√3 + 2*4√3 = 16√3
Find the Perimeter of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
Answer:
Does the answer help you?
Find the distance between the points A(13, 2) and B(7, 10). The distance between the two points is
Answer:
The answer is 10 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question , the points are
A(13, 2) and B(7, 10)
The distance between them is
[tex] |AB| = \sqrt{( {13 - 7})^{2} + ({2 - 10})^{2} } \\ = \sqrt{ {6}^{2} + ( { - 8})^{2} } \\ = \sqrt{36 + 64} \\ = \sqrt{100} [/tex]We have the final answer as
10 unitsHope this helps you
Determine the intercepts of the line.
y - 4= 7(x – 6)
x-intercept:
y-intercept:
i hope this helppppsss
PLEASE ANSWER QUICKLY ASAP
READ THE QUESTIONS CAREFULLY
Answer:
I hope it helps.
The solutions in photo ^_^
Right or wrong ????
Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H', are shown on the coordinate plane below:
G
H
5
G
Н"
F
2
A
חד
A
2
7
B
B
-7-6-5-4-2-2=1
E
-2
E
D.
-5
D
C
С
If the center of dilation is at the origin, by what scale factor was octagon ABCDEFGH dilated? (4 points)
Answer:
c 1/2
Step-by-step explanation:
You are incorrect.
We are going from ABCDEFGH to A'B'C'D'E'F'G'H'. We are going from the large octagon to the small octagon. The scale factor of a dilation is the number you multiply the original lengths to get the lengths of the dilation.
[tex]scale~factor = \dfrac{length~of~dimension~in~dilated~image}{length~of~corresponding~dimension~in~original~figure}[/tex]
Look at point (6, 0) which becomes (3, 0) in the dilation.
The distance from the origin to (6, 0) is 6 units.
The distance from the origin to (3, 0) is 3 units.
scale factor = dilated/original = 3/6 = 1/2
The scale factor of the dilation is 1/2.
Also look at segment AB whose length is 4. The length of segment A'B' is 2.
scale factor = dilated/original = 2/4 = 1/2
Answer: 1/2
Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2ab-6a+5b+___
Answer:
-15
Step-by-step explanation:
We proceed as follows;
In this question, we want to fill in the blank so that we can have the resulting expression expressed as the product of two different linear expressions.
Now, what to do here is that, when we factor the first two expressions, we need the same kind of expression to be present in the second bracket.
Thus, we have;
2a(b-3) + 5b + _
Now, putting -15 will give us the same expression in the first bracket and this gives us the following;
2a(b-3) + 5b-15
2a(b-3) + 5(b-3)
So we can have ; (2a+5)(b-3)
Hence the constant used is -15
A retailer bought 1000 glass tumblers at rs 80 each.50 glass tumblers were broken and he sold the rest at Rs 96 each .find his profit or loss percent
Step-by-step explanation:
Soln
Given
Cp of 1 glass tumbler=80.1000
=Rs 80000
Number of broken glass tumbler=50
Number of remaining glass tumbler=1000-50
=950
Sp of one glass tumbler=96
Sp of 950 glass tumbler=96.950
=91200
Now
Sp > Cp so it is profit
Profit%=sp-cp/cp.100
=91200-80000/80000.100
=11200/80000.100
=14%
Answer:
14%profit
Step-by-step explanation:
Cost of 1000 tumblers=1000×80=80,000
50 of them were broken: 1000-50=950
: He sells 950 tumblers of rs.96 each= ( 950×96)
S.P=91200
We can clearly see he gains for rs.11200.
P%=gain/C.P×100
11200×80000×100
=14%
ANYONE PLEASE HEEEEEEELLLLLLLPPPPPP!!!!! WILL GIVE BRAINLIEST!!!
Question 4(Multiple Choice Worth 1 points) (06.04 LC) Choose the correct simplification of the expression −3x2(5x − 4x2 − 6). −7x4 + 2x3 − 9x2 12x4 − 15x3 + 18x2 12x4 + 15x3 + 18x2 −12x4 + 15x3 − 18x2
Answer:
12x⁴ - 15x³ + 18x²
Step-by-step explanation:
1. distribute -3x²
-3x² • 5x = -15x³
-3x² • -4x² = 12x⁴
-3x² • -6 = 18x²
2. combine terms and put in descending order (standard form)
12x⁴ - 15x³ + 18x²
Answer:
12x⁴ - 15x³ + 18x²
Step-by-step explanation:
1. distribute -3x²
-3x² • 5x = -15x³
-3x² • -4x² = 12x⁴
-3x² • -6 = 18x²
2. combine terms and put in descending order (standard form)
12x⁴ - 15x³ + 18x² correct answer would be this