Triangle ABC was dilated and translated to form similar triangle A'B'C'.
What is the scale factor of the dilation?
A. 1/5
B. 2/5
C. 5/2
D. 5/1
Answers
On this exercise is asked to find the scale factor by which the triangle ABC was
dilated to produce the triangle A'B'C'.
Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.
As can be see on the picture the dilation produce was an enlargement meaning that the image is larger that the preimage.
Of this form you can discard the choices A and B as possible solutions.
Lets try 5/2 as the possible scale factor:
(x,y)-- (kx, ky)
A(0,2)--(5/2(0),5/2(2))=A'(0,5)
B(2,2)--(5/2(2),5/2(2))=B'(5,5)
C(2,0)--(5/2(2),5/2(0))=C'(5,0)
Lets try 5/1 or 5 as the scale factor:
A(0,2)--(5(0),5(2))=A'(0,10)
B(2,2)--(5(2),5(2))=B'(10,10)
C(2,0)--(5(2),5(0))=C'(10,0)
As said at the beginning of the question the triangle was not only dilated.
After a dilation and a translation, the scale factor of the dilation is letter C or 5/2.
correct answer is 5/2
Related Questions
What is a possible value of sin(theta) when cos2(theta)=0.73?
a.0.37
b.0.63
c.0.26
d.0.74
Answers
sin^ 2 (theta) + cos^ 2 (theta) = 1
We substitute the values:
sin ^ 2 (theta) + 0.73 = 1
We cleared:
sin ^ 2 (theta) = 1-0.73
sin ^ 2 (theta) = 0.27
Answer:
a possible value of sin ^ 2 (theta) is:
c.0.26 (nearest option)
The correct answer is option a. 0.37.
Given that [tex]cos(2\theta) = 0.73[/tex], find a possible value of sin(theta).
It is known that:
[tex]cos(2\theta) = 1-2sin^2(\theta)[/tex].
Substituting the given value:
[tex]0.73 = 1-2sin^2(\theta)[/tex]
Rearrange to solve for sin²(theta):
[tex]2sin^2(\theta)=1-0.73[/tex]
[tex]2sin^2(\theta)=0.27[/tex]
[tex]sin^2(\theta)=0.135[/tex]
So, [tex]sin(\theta) = \sqrt{0.135}\ or\ sin(\theta) = -\sqrt{0.135}[/tex].
Since we are looking for a possible value, we take the positive root:
[tex]sin(\theta) \approx 0.367[/tex]
Considering the options given, the closest possible value is 0.37.
3. In the rhombus, what are m∠1, m∠2 and m∠3? The diagram is not drawn to scale.
Answers
Answer: m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.
Step-by-step explanation: We are given to find the measures of ∠1, ∠2 and ∠3 in the figure.
As shown in the attached figure, ABCD is a rhombus, where m∠A = 128°.
We know that, in a rhombus, all the sides are congruent, the opposite angles are congruent and the adjacent angles are supplementary.
So, from rhombus ABCD, we have
[tex]m\angle A=m\angle C~~~~~\textup{[opposite angles]}\\\\\Rightarrow m\angle 1=128^\circ.[/tex]
Also, in ΔBCD, we have
[tex]BC=CD~~\textup{[all the sides are congruent]}\\\\\Rightarrow m\angle 3=m\angle 2~~\textup{[angles opposite to congruent sides care congruent]}.[/tex]
Now, since the sum of three angles of a triangle is 180°, we have from ΔBCD that
[tex]m\angle 1+m\angle 2+m\angle 3=180^\circ\\\\\Rightarrow 128^\circ+m\angle 2+m\angle 2=180^\circ\\\\\Rightarrow 2\times m\angle 2=180^\circ-128^\circ\\\\\Rightarrow 2\times m\angle 2=52^\circ\\\\\Rightarrow m\angle 2=26^\circ.[/tex]
Therefore, m∠3 = 26°.
Thus, m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.
-4x ²-3x+2=0
can you help me solve this
Answers
Answer:
x = (-3 ±√41)/8
Step-by-step explanation:
When you match your equation to the form ...
... ax² +bx +c = 0
you can see that ...
a = -4b = -3c = 2These are the values you use in the quadratic formua to find the solutions for x.
... x = (-b ±√(b²-4ac))/(2a) . . . . . . the quadratic formula
... x = (-(-3) ±√((-3)² -4(-4)(2)))/(2(-4)) . . . . fill in a, b, c
... x = (3 ±√(9+32))/(-8) . . . . simplify a bit
... x = (-3 ±√41)/8 . . . . . . put the minus sign in the numerator
For each value of w, determine whether it is a solution to -56=7(w-3).
Answers
Two numbers are in the ratio of 5:6 if the sum of the numbers is 66 find the largest number
Answers
k = 6
30 : 36
Solution 2:
so 5x+6x=66
or 11x=66
or x=6
so the value of the larger number is 6*6=36
Alex was thinking of a number. Alex subtracts 14 from it and gets an answer of 29.6. What was the original number?
Answers
43.6 - 14 = 29.6
Hope this helped!
Can anyone answer this ???
Answers
The payment is 190,000*(.0725/12)/(1 -(1 +.0725/12)^(-12*20)) ≈ 1501.71
The total of all payments is 240*1501.71 = 360,410.40, so the interest cost is this amount less the principal, or $170410.40.
Total loan cost = $2800 + 1%*190,000 +170,410.40 = 175,110.40
Mortgage B:
The payment is 190,000*(.0525/12)/(1 -(1 +.0525/12)^-240) ≈ 1280.30
The total of all payments is 240*1280.30 = 307,272.00, so the total interest cost is $117,272.00.
Total loan cost = $2800 +5%*190,000 +117,272.00 = 129,572.00
Mortgage A has a larger total cost than Mortgage B by $45,538.40
A rectangular box contains 336 cubic inches. If it is 12 inches long and 7 inches wide, how deep is it?
Answers
Your answer is 4 inches deep :))
Hope this helps
Round each number to the nearest hundred and estimate the sum.
1,841 + 964
2,900
2,800
2,700
2,600
Answers
964 ≈ 1000 (nearest hundred}
1,841 + 964 ≈ 1800 + 1000 = 2800 (Answer B)
Answer:
The answer is 2,800 (B)
Good Luck :)
HELPPPPPPPPPPPPPPPPPPPPPPPP
Answers
.. d = b^2 -4*a*c
When the roots are imaginary, it is less than zero. You have a=4, so that means
.. b^2 -16c < 0
.. b^2 < 16c . . . . . . . . . . . . . . . . . coresponds to the 7th choice
The discriminate is sqrt(b^2 - 4ac)
a is given as 4.
That makes the discriminate = sqrt(b^2 - 16c)
To get imaginary roots, you have to be taking the square root of something < 0
The answer is
b^2 < 16c <<<< answer
The Rotation R maps all 60° about O the center of the regular hexagon. State the image of B for the following rotation.
R^6 =
B
E
O
Answers
Answer:
B will be at same place after all six rotations.
Step-by-step explanation:
If rotation maps to [tex]60^{\circ}[/tex]
Then [tex]R^6[tex] means six rotations .
The given B after one rotation will shift in place of A
After second rotation will shift in place of F
After third rotation will shift in place of E
After fourth rotation will shift in place of D
After fifth rotation will shift in place of C
After sixth rotation will shift in place of B itself.
Therefore, B will come back to same place after all the required rotations.
A charged particle is projected in the air such that its horizontal (x) and vertical (y) shifts are given by x(t) = 10t − t2 and y(t) = 6t, where x and y are in meters and time t is in seconds. What is the ratio of y to x at t = 4 seconds?
Answers
what is the factored form of the expression? w^2 + 12w + 36
Answers
Answer:
[tex](w+6)^2[/tex] is the factored form of the given expression.
Step-by-step explanation:
The given expression is:
[tex]w^2+12w+36[/tex]
Simplifying the above given expression, we get
[tex]w^2+6w+6w+36[/tex]
[tex]w(w+6)+6(w+6)[/tex]
[tex](w+6)(w+6)[/tex]
[tex](w+6)^2[/tex]
Which is the required factored form of the given expression.
at the school carnival tickets can be exchanged for prizes. Mason wants a comic book that cost a 176 tickets. He needs 8 times as many tickets as he has now. How many tickets does mason have now?
Answers
Which description best describes the graph?
A graph is shown. A straight line begins at the upper left side of the coordinate plane and moves down towards the right side. The line crosses the y-axis at y equals 3 and the x-axis at x equals 1.5
Linear increasing
Linear decreasing
Nonlinear increasing
Nonlinear decreasing
Answers
As the x-values increase, the y-values decrease; this means it is a decreasing graph.
The graph shows a straight line with a constant rate of change, so it is linear.
Answer:
B. Linear decreasing
Step-by-step explanation:
We are given that,
The graph of the function is passing through the points (0,3) and (1.5,0).
Then, the rate of change is [tex]m=\frac{0-3}{1.5-0}=\frac{-3}{1.5}=-2[/tex]
So, the function is represented by a straight line with constant rate of change -2.
Thus, the function is a linear function.Moreover, as the value of x is increasing, we see that the value of y is decreasing.
So, the function is a decreasing function.Hence, option B is correct.
Place the indicated product in the proper location on the grid.
(3a + 2c )(9a 2 - 6ac + 4c 2 )
Answers
27a^3+8c^3
Explanation.
In this question you are expected to expand (3a+2c)(9a^2-6ac+4c^2
(3a+2c)(9a^2-6ac+4c^2
=(3a×9a^2 )-(3a×6ac)+(3a×4c^2 )+(2c×9a^2 )-(2c×6ac)+(2c×4c^2 )
27a^3-18a^2 c+12ac^2+18a^2 c-12ac^2+8c^3
27a^3+8c^3
The expansion of the expression, (3a+2c)(9a^2-6ac+4c^2) is 27a^3+8. This is what the question requires.
Answer:
The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]
Step-by-step explanation:
Given: Polynomial [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]
We have to place the indicated product in the proper location o the grid.
Consider the given product [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]
Using distributive property, Multiply each term of first bracket with each term of last bracket, we have,
[tex]=3a\cdot \:9a^2+3a\left(-6ac\right)+3a\cdot \:4c^2+2c\cdot \:9a^2+2c\left(-6ac\right)+2c\cdot \:4c^2[/tex]
Apply plus-minus rule [tex]+\left(-a\right)=-a[/tex] , we have,
[tex]=3\cdot \:9a^2a-3\cdot \:6aac+3\cdot \:4ac^2+2\cdot \:9a^2c-2\cdot \:6acc+2\cdot \:4c^2c[/tex]
Simplify, we have,
[tex]=27a^3-18a^2c+12ac^2+18a^2c-12ac^2+8c^3[/tex]
Adding similar terms, we have,
[tex]=8c^3+27a^3[/tex]
Thus, The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]
Location on grid is as shown below
Which number is a solution of the inequality? Y>1.9 (1 point)
A. -9
B. -2
C. 2
D. 1.9
Please help!! I'm way behind!
Answers
The answer is 2
Choose the graph that matches the following system of equations: 2x + y = −1 3x + 2y = −6
Select one:
a. picture of coordinate plane with line y equals negative 2x plus 1 and line y equals 3 halves x minus 6. They intersect at 2, negative 3
b. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9
c. picture of coordinate plane with line y equals 2x minus 1 and line y equals negative 3x minus 3. They intersect at negative 0.4, negative 1.8
d. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals 3 halves x plus 6. They intersect at negative 2, 3
Answers
Firstly, we express both equations with y on the left hand side since all choices are in that form:
[tex]y=-2x-1[/tex]
[tex]y=- \frac{3}{2}x-3 [/tex]
Knowing these, we can immediately rule out options a, c, and d since they have the wrong equations. This will leave us with option b.
You can verify if the point of intersection provided in option b is true by plugging in the values of x and y to both equations (you will find that it is indeed true).
ANSWER: b. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9.
Answer:
B
Step-by-step explanation:
Got it right on the test
Hope this helps :)
Printer paper is sold in packages of 500 sheets. of a printing job uses 1 3/4 packages of paper how may sheets is that
Answers
[tex]1 \dfrac{3}{4} \text { package of papers = } 500 \times 1 \dfrac{3}{4} [/tex]
[tex]1 \dfrac{3}{4} \text { package of papers = } 500 \times \dfrac{7}{4} [/tex]
[tex]1 \dfrac{3}{4} \text { package of papers = } 875 \text { sheets}[/tex]
The printing job that uses 1 3/4 packages of printer paper requires 875 sheets.
To determine how many sheets of paper are used in a printing job that uses 1 3/4 packages of paper, follow these steps:
First, understand that 1 package contains 500 sheets of printer paper.Next, convert the mixed number 1 3/4 to an improper fraction. This is done by multiplying the whole number (1) by the denominator (4) and adding the numerator (3), giving us 7/4.Now, multiply the number of packages (7/4) by the number of sheets per package (500):7/4 * 500 sheets = (7 * 500) / 4 = 3500 / 4 = 875 sheets.
Therefore, the printing job uses 875 sheets of paper.
Which of the following is the graph of
btw A is wrong (the 2nd pic)
Answers
x+2=0→x+2-2=0-2→x=-2
Asymptote x=-2
Lim x→Infinite y =
Lim x→Infinite 1/(x+2)+1
1/(Infinite+2)+1
1/Infinite+1
0+1
1
Horizontal asymptote y=1
Answer: Third graph (left to right)
Find all solutions in the interval [0, 2π).
sec2x - 2 = tan2x
a) No solution
b) x = pi/3
c) x = pi/4
d) x = pi/6
Answers
sec²x - 2 = tan²x--------> equation 1
and we know
identity-----------> tan²x=sec²x-1------------> equation 2
I substitute 2 in 1
sec²x - 2 = sec²x-1----------> -2=-1---------> no solution
the answer is the option a) No solution
Explanation:
sec²x - 2 = tan²x
tan²x=sec²x-1
sec²x - 2 = sec²x-1
-2=-1
there is no solution
Twice the sum of two consecutive integers equals 42
Answers
Let's assume n the first integer
n+1 the greater
n+(n+1)=2n+1 is odd but 42 (universel answer in Robots IE) is even!!!!
Not answer!
Find the area of the shaded polygons:
Answers
now, notice, is really just a large triangle in red, with a base of 4 and a height of 3 units, and two smaller triangles below it, one has a base 1 and a height of 1, and the other has a base of 3 and a height of 1.
so just get the area of each, sum them up, and that's the shaded area.
The total area of the figure is 8 square units.
How to find the area?
Remember that the area of a triangle is equal to its height times its base over 2.
In the image we can see 3 triangles, the larger one has a height of 3 units and a base of 4 units, so its area is:
A = 3*4/2 = 6 square units.
The bottom left triangle has a base of 1 unit and a height of 1 unit, so its area is:
A' = 1*1/2 = 0.5 square units.
The bottom right triangle has a base of 3 units, and a height of 1 unit, so its area is:
A'' = 1*3/2 = 1.5 square units.
The total area is:
A + A' + A'' = (6 + 0.5 + 1.5) square units = 8 square units.
If you want to learn more about area, you can read:
https://brainly.com/question/24487155
John says the transformation rule (x, y) --> (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, –2). What was his error?
Answers
(x, y) -> (x + 4, y + 7)
The ordered pair to which the transformation is applied is:
(x, y) = (4, 5)
Therefore, applying the transformation we have:
(4, 5) -> (4 + 4, 5 + 7) -----> (8, 12)
The error for this case is that John made the following transformation:
(4, 5) -> (4 - 4, 5 - 7) -----> (0, -2)
That is, rest the numbers instead of adding.
Answer:
his error was subtract instead of adding.
The correct answer is:
(8, 12)
Answer:
The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.
Two buildings are 200 feet apart. the height of the taller building is 50 ft. the angle of depression from the top of the taller building to the top of the shorter building is 8°. what equation below will correctly determine the height (h) of the shorter building?
Answers
(50-h) ft
tan x=opposite/adjacent
thus
tan 8=(50-h)/200
200*tan 8=50-h
28.11=50-h
h=50-28.11
h=21.89
the height of the shorter building is h=21.89 ft
How many feet are in 100 meters if 1 meter is 1.09 yards? Will mark brainliest if you include clear steps. Thank you!
Answers
[tex]\bf 100~\underline{m}\cdot \cfrac{1.09~\underline{yd}}{\underline{m}}\cdot \cfrac{3~ft}{\underline{yd}}\implies \cfrac{100\cdot 1.09\cdot 3~ft}{1}\implies 327~ft[/tex]
notice, we use the ratio, and whichever unit you want cancelled, you simply flip the ratio to have it cancelled, if the "m" is atop and you need that cancel, use the ratio with the "m" at the bottom, m/m = 1, and so they cancel out, and so on.
Given sinx=0.9 , what is cosx ? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answers
It is given sinx=0.9 .We need to find cosx.
We use the identity :
[tex] sin^{2} x + cos^{2} x =1 [/tex]
Substituting sinx=0.9
[tex] (0.9)^{2} +cos^{2} x =1 [/tex]
[tex] 0.81+cos^{2} x=1 [/tex]
Substracting 0.81 both sides:
[tex] cos^{2} x =1-0.81 [/tex]
[tex] cos^{2} x=0.19 [/tex]
Taking root of both sides cosx=0.435
Rounding to nearest hundredth
cosx=0.44.
Somebody please help .. What is the exact volume of this right cone ?
Answers
Find the slope-intercept form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
(1, -5) and (5, -1)
Answers
Which expressions are polynomials?
Select each correct answer.
A.20x² + y
B.20x2+y12
C.20x2y
D.20x²
Answers
All the given answers are polynomials
A.20x² + y
B.20x*2+y*12
C.20x*2*y
D.20x²
Answer:
Step-by-step explanation:
Polynomial :
An expression that can have constants (like 4), variables (like x or y) and exponents (like the 2 in [tex]y^{2}[/tex]), that can be combined using addition, subtraction, multiplication and division, but:
no division by a variable.
a variable's exponents can only be 0,1,2,3,... etc.
it can't have an infinite number of terms.
Thus according to definition all are polynomials
A.20x² + y
B.20x2+y12
C.20x2y
D.20x²