Answers
By applying the equation of dilation, the coordinates of the vertices of the triangle ABC are A'(x, y) = (-12, 0), B'(x, y) = (0, -9) and C'(x, y) = (-12, -9).
How to find the image of a triangle
A dilation is a type of rigid transformation. Rigid transformations are transformations applied to geometric loci such that Euclidean distances are conserved.
There is a triangle and its image must be a triangle, the new triangle is found by transforming the three vertices of the prior one following this formula:
A'(x, y) = P(x, y) + k · [A(x, y) - P(x, y)] (1)
Where:
P(x, y) - Center of reflection.A(x, y) - Original vertexA'(x, y) - New vertexk - Dilation factorIf we know that P(x, y) = (0, 0), A(x, y) = (-4, 0), B(x, y) = (0, -3) and C(x, y) = (-4, -3), then the new vertices of the triangle are, respectively:
Point A
A'(x, y) = (0, 0) + 3 · [(-4, 0) - (0, 0)]
A'(x, y) = (-12, 0)
Point B
B'(x, y) = (0, 0) + 3 · [(0, -3) - (0, 0)]
B'(x, y) = (0, -9)
Point C
C'(x, y) = (0, 0) + 3 · [(-4, -3) - (0, 0)]
C'(x, y) = (-12, -9)
Lastly, we draw the two triangles, which are presented in the image attached below.
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Related Questions
Which expression gives the distance between the points
(-3, 4) and (6, -2)?
O A. (-3-4)²+(6+2)²
O B. (-3-6) +(4+2)²
O C. (-3-6)²+(4+2)²
O D. (-3-4)²+(6+2)²
Answers
The expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]
How to determine the expression?The points are given as:
(-3, 4) and (6, -2)
The distance between two points is calculated using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
This gives
[tex]d = \sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]
Hence, the expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]
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Factor 6x¹ − 5x² + 12x² − 10 by grouping. What is the resulting expression?
(6x + 5)(x²-2)
(6x - 5)(x²+2)
(6x² + 5)(x-2)
(6x²-5)(x+2)
Answers
Answer:
[tex](6x-5)(x^2+2)[/tex]
Step-by-step explanation:
[tex]~~~6x^3 -5x^2 +12x -10\\\\=6x^3-5x^2+12x-10\\\\=x^2(6x-5) +2(6x-5)\\\\=(6x-5)(x^2+2)[/tex]
One week, Genesis earned $367.40 at her job when she worked for 22 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $584.50?
Answers
Answer:
35 hrs
Step-by-step explanation:
Hope this helps! Have a great day!!
if a= 2x-3 and b= 2x+5
determine the product of a and b by using formulae. if x=2, ab= what?
help pleasee would appreciate a lot
Answers
Answer:
a= 2x-3 b= 2x+5
ab= (2x-3)(2x+5)
= 2x*2x+ 2x*5- 3*2x- 3*5
= 4x+ 10x- 6x- 15
= 14x- 6x- 15
= 8x -15
x= 2
= 8(2)- 15
= 16-15
= 1
A high school track coach wanted to test whether giving the students an energy drink could affect performance during the 100 meter race. The coach split the 18 boys into two equal sized groups, where Group 1 was given the energy drink and Group 2 was not. The 100 meter race times were recorded during practice and shown in the table below. What inference can be made about the results?
Answers
Based on the difference in the observed means given, we can infer that energy drink does indeed have an effect on performance.
Can the energy drink affect performance?First find the observed mean difference:
= 11.6 - 10.8
= 0.8 seconds
When the exercise is done only once, we see that on average, those who took the energy drink were faster and so finished earlier than those who didn't.
We can therefore infer that the energy drink has an effect on performance.
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A subtrahend is the number being subtracted in a subtraction problem. Robert
misread the digit l in the ones place of the subtrahend as 7 and the digit 7 in the tens place of the subtrahend as 1. The difference in the subtraction then became 222. What would be the actual difference if he had read the numbers correctly?
Answers
From the calculation below, the actual difference, if Robert had read the numbers correctly, is 168.
How to use subtrahend in the calculation?Let X represents the number from which subtrahend is subtracted.
Therefore, we can calculate X as follows:
X – 17 = 222
X = 222 + 17 = 239
If the subtrahend is read correctly as 71 and then subtracted from 239, we have:
Actual difference = 239 – 71
Actual difference = 168
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First two two terms of the given number sequence 3n + 1 are...
Answers
Answer:
the sequence begins as {4, 7, ... }
Step-by-step explanation:
a(n) = 3n + 1
The first term is a(1) = 3(1) + 1 = 4, and
the second term is a(s) = 3(2) + 1 = 7
So the sequence begins as {4, 7, ... }
Which of the following statements is true concerning ABC below?
B
11
11
A
OA. ZB is the smallest angle.
B. ZA is the largest angle.
OC. ZA is the smallest angle.
D. ZB is the largest angle.
14
C
Answers
Angle B is the largest angle. , Option D is the correct answer.
What is an Isosceles Triangle ?A triangle that has two sides equal is called an Isosceles Triangle.
It is given in the question a triangle ABC
With BA =BC
therefore angle A is equal to angle C
In a triangle the angle opposite to the longest side is the biggest angle
Therefore angle B is the largest angle.
Option D is the correct answer.
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In the past week, Joe has recorded the number of tickets that a movie theater has sold during each day from Monday to Saturday. This information was shown through the following Bar Graph.
How does the Bar Graph misrepresent the data?
A. The scale along the vertical axis is divided into unequal intervals.
B. The categories along the horizontal axis are missing one of the days.
C. The widths of the bars are not equal.
D. The heights of the bars representing Monday and Thursday are not same.
Answers
Based on the information shown through the bar graph, a misrepresentation of the data is that: B. the categories along the horizontal axis are missing one of the days.
What is a bar graph?A bar graph can be defined as a type of chart that is used for the graphical represent of data (information), especially through rectangular bars or vertical columns.
Based on the information shown through the bar graph in the image attached below, we can logically deduce that a misrepresentation of the data is that the categories along the horizontal axis are missing one of the days (Friday).
In conclusion, this bar graph misrepresented the data because Friday is missing from the categories along the horizontal axis.
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Please help!! So confused
Answers
Answer:
A.2x^2 + 12x
Step-by-step explanation:
Here,
f(x) = 1/2 x^2 + 3x
Now,
4.f(x) = 4(1/2 x^2 + 3x) = 4/2 x^2 + 12x = 2x^2 + 12x
i am BEGGING FOR HELP on this question please help IM GIVING 5 STAR AND BRAINLIEST PLEASE ANSWER QUICKLY PLEASE ⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️
Answers
Answer: COSINE
Step-by-step explanation:
I PROMISE
Answer:
See below
Step-by-step explanation:
For a right triangle, with the information given, tangent function is most appropo
tan 41 = 4/x re-arrange to
x = 4 / tan(41) then x = 4.60
Question 9 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answers
Answer:
B. ∠TRF and ∠NRLC. ∠LRE and ∠FRAStep-by-step explanation:
→ The lines TN and FL intersect each other
at the point R forming the opposite angles ∠TRF and ∠NRL
then
∠TRF and ∠NRL are verticals angles.
………………………………………………………………………
→ The lines LF and AE intersect each other
at the point R forming the opposite angles ∠LRE and ∠FRA
then
∠LRE and ∠FRA are verticals angles.
Question 5
The price of an apple is $1.25. If you get 20% discount, how much do you have to
pay?
Answers
Answer:
you will only pay one dollar I did this question before, and it was easy Please mark me brainiest please
Step-by-step explanation:
What is the perimeter of the following shape? (use an approximate value) pie = 3.14
Answers
===========================================================
Explanation:
A full circle of radius r = 14 cm has a circumference of...
C = 2pi*r
C = 2*3.14*14
C = 87.92
This is the approximate distance around the circle, aka the perimeter.
Half of this is 87.92/2 = 43.96 which is the curved distance of this semicircle.
The straight line portion is 14+14 = 28 cm long.
The total perimeter of the semicircle shown is 43.96+28 = 71.96 cm
Express the trig ratios as fractions in simplest terms.
(Image above)
Help please
Answers
The value of the angle P and Q are equal which is equal to 36.86°.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
From Δ it is obtained that;
[tex]\rm cos P = \frac{B}H} \\\\ \rm cos P = \frac{16}{20} \\\\ P=cos^{-1}\frac{16}{20} \\\\ P= 36.86 ^0[/tex]
[tex]\rm sin \ Q = \frac{12}{20} \\\\ Q= sin^{-1}(0.6) \\\\ Q= 36.86^0[/tex]
sin P= sin Q
Hence, the value of the angle P and Q are equal which is equal to 36.86°.
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Alex got 27 questions out of 30 correct. what present of the questions did he get correct?(use fish method)
Answers
if we take 30 to be the 100%, what is 27 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 30 & 100\\ 27& x \end{array} \implies \cfrac{30}{27}=\cfrac{100}{x} \\\\\\ \cfrac{10}{9}=\cfrac{100}{x}\implies 10x=900\implies x=\cfrac{900}{10}\implies x=90[/tex]
What is the length of segment R S?
Answers
Answer:
C
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{RS}{FG}[/tex] = [tex]\frac{ST}{GH}[/tex] ( substitute values )
[tex]\frac{RS}{21}[/tex] = [tex]\frac{4}{12}[/tex] ( cross- multiply )
12 RS = 84 ( divide both sides by 12 )
RS = 7 cm
A whole year level of 164 students is to be divided into 18 groups. By rounding
both numbers to the nearest 10, approximate the number of students in each
group.
Answers
Answer:
10
Step-by-step explanation:
no. of students in each group=164/18=9.111111...=10 (nearest 10)
Answer:
8
Step-by-step explanation:
When rounding to the nearest 10:
If the units are 0, 1, 2, 3 or 4 → round downIf the units are 5, 6, 7, 8 or 9 → round upTherefore:
164 rounded to the nearest 10 = 160
18 rounded to the nearest 10 = 20
To approximate the number of students in each year group, divide the rounded number of students by the rounded number of groups:
⇒ 160 ÷ 20 = 8
If ln=12x+16 what is the length is ln units
Answers
Move point C so that ∠BAC and ∠CAD form a pair of supplementary angles, or angles whose sum is 180°. Record each of the angle measurements for this case.
Answers
The recorded angle measurements of ∠BAC and ∠CAD could be 110° and 70°, vice versa.
What are supplementary angles?Supplementary angles are a pair of angles that always sum up to 180°. These angles can either;
adjacent non-adjacent. Adjacent supplementary anglesAdjacent supplementary are angles with a common vertex and arm.
Non-adjacent supplementary anglesNon- adjacent supplementary angles are angles without a common vertex or arm.
∠BAC and ∠CAD are adjacent supplementary angles because they have a common vertex, A, and a common arm AC.
They add up to 180°.
∠ BAC = 110° and ∠CAD = 70°
Hence, the angles could be 110° and 70°.
Note, this is an overview as the question is not complete.
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Answer: When the two angles are supplementary, m∠BAC = m∠CAD = 90° and m∠DAB = 180°.
Step-by-step explanation: Edmentum Answer
Function k is a transformation of the parent exponential function f. what are the domain and range of function k? k(x)= 2^x
Answers
Answer:
Domain: All real numbersRange: All real numbers greater than 0Help me please!!!!!!!!
Answers
Answer:
the third option
Step-by-step explanation:
because the numbers down there are the coefficients of the top equations
(x + 3) (x + 5) (x + 7) (x + 9) + 16
Answers
Find the length of the arc
Answers
Answer:
A
Step-by-step explanation:
the length of the arc is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{120}{360}[/tex]
= 2π × 8 × [tex]\frac{1}{3}[/tex]
= 16π × [tex]\frac{1}{3}[/tex] = [tex]\frac{16\pi }{3}[/tex] m
I need help finding both volume and surface area
Answers
Answer:
Volume
For the rectangle, h = 3cm, l = 8cm, w = 6cm
V = length x width x height
V = 8cm x 6cm x 3cm
V = 144cm^3
For the semi circle, we need to find the radius. The radius is width/2, so 6cm/2 = 3cm. r = 3cm, [tex]\pi[/tex] = 3.14
V = radius^2 x height x [tex]\pi[/tex]
V = 3cm^2 x 3cm x 3.14
V = 84.8 cm^3/2 (because the cylinder needs to be divided to form a semi-circle)
V= 42.4cm^3 (there are two cylinders though so we will multiply this by 2 in the total volume)
Total volume:
V = 144cm^3 + 42.4cm^3(2)
V = 186.4cm^3
Surface Area
Rectangular prism:
A = 2[w(l) + h(l) + h(w)]
A = 2[6cm(8cm) + 3cm(8cm) + 3cm(6cm)]
A = 180cm^2
But there are two sides that are covered by the semi-circular prisms, so we will have to calculate those sides and remove them.
A = l x w
A = 6cm x 3cm
A = 18cm^2(2) (2 being the two faces)
A = 36cm^2
A = 180cm^2 - 36cm^2
A = 144cm^2 (the area of the rectangle)
Semi-circular prism:
A = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex]r^2
Earlier, we found out that the radius of the circle is 3cm, so we will plug that in.
A = 2(3.14)(3cm)(3cm) + 2(3.14)(3cm)^2
A = 113.09cm^2
Total surface area:
A = 144cm^2 + 133.09cm^2
A = 277.09cm^2
Therefore the total volume of the prism is 186.4cm^3 and the total surface area is 277.09cm^2.
HELP ASAPPPP 10 POINTS
Answers
Does anyone know the answer to this question here ?
Answers
Answer:
True
Step-by-step explanation:
can someone please hepl me on tis
Answers
Answer:
Answer is in pictures
Step-by-step explanation:
36=6x6 90=9x10
256+7=263 104=98+6-2
678=678 81+9=90
13) Greenhouse gases are contributors to climate change as they absorb outgoing solar radiation and convert it to thermal energy. The main contributors to the
warming are carbon dioxide, methane, dinitrogen monoxide, and F-gases. The sources of these gases are shown in the pie chart here. What questions are relevan
these gases and their impacts on the climate change over the past 100 years? Select ALL that apply.
A) Does an increase in fossil fuel combustion create a local weather change?
B) Can a legislation that reduces the F-gases help prevent a global climate change?
C) Can reforestation of trees reduce the amount of carbon dioxide that is present in the atmosphere?
D) Can an increase in meat production occur without increasing methane and nitrogen from fertilizers?
E) Can a reduced reliance on fossil fuels decrease the atmospheric carbon dioxide and prevent rising global temperatures?
Answers
Answer:
e)as we know in this current century many modern country is polluting air pollution that may lead to impact our health
wright the follwing in decimlal form:3/11
Answers
Answer:
3/11 in decimal form is 0.272727272727....
Step-by-step explanation:
Yw ! :)