Write the coordinates of the vertices after a dilation with a scale factor of 1/5, centered at the origin.
Answers
Answer:
The coordinates of the vertices after the dilation by a scale factor 1/5 centered at the origin will be:
U'(-1, -2)V'(0, -2)W'(-1, 2)Step-by-step explanation:
We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.
If the scale factor > 1, the image is enlarged
If the scale factor is between 0 and 1, it gets shrunk
If the scale factor = 1, the object and the image are congruent
Rule to calculate the dilation by a scale factor 1/5 centered at the origin
P(x, y) → P'(1/5x, 1/5y)
Here, P'(1/5, 1/5y) is the image of P(x, y).
Given the vertices of the triangle UVW
U (-5, -10)
V (0, -10)
W (-5, 10)
so
Rule to calculate the dilation by a scale factor 1/5 centered at the origin
P(x, y) → P'(1/5x, 1/5y)
U (-5, -10) → U'(1/5(-5), 1/5(-10)) → U'(-1, -2)
V (0, -10) → V'(1/5(0), 1/5(-10)) → V'(0, -2)
W (-5, 10) → W'(1/5(-5), 1/5(10)) → W'(-1, 2)
Therefore, the coordinates of the vertices after the dilation by a scale factor 1/5 centered at the origin will be:
U'(-1, -2)V'(0, -2)W'(-1, 2)Related Questions
A biology test is worth 100 points and has 36 questions.
a. Multiple-choice questions are worth 2 points each and essay questions are worth 6 points each. How many questions of each type are on the test?
b. Your friend says that it is possible for the multiple-choice questions to be worth 4 points each. Is your friend correct? Explain.
Answers
Answer:
(a) 7 essays and 29 multiple questions
(b) Your friend is incorrect
Step-by-step explanation:
Represent multiple choice with M and essay with E.
So:
[tex]M + E= 36[/tex] --- Number of questions
[tex]2M + 6E = 100[/tex] --- Points
Solving (a): Number of question of each type.
Make E the subject of formula in [tex]M + E= 36[/tex]
[tex]E = 36 - M[/tex]
Substitute 36 - M for E in [tex]2M + 6E = 100[/tex]
[tex]2M + 6(36 - M) = 100[/tex]
[tex]2M + 216 - 6M = 100[/tex]
Collect Like Terms
[tex]2M - 6M = 100 - 216[/tex]
[tex]-4M = - 116[/tex]
Divide both sides by -4
[tex]M = \frac{-116}{-4}[/tex]
[tex]M = 29[/tex]
Substitute 29 for M in [tex]E = 36 - M[/tex]
[tex]E = 36 - 29[/tex]
[tex]E = 7[/tex]
Solving (b): Can the multiple questions worth 4 points each?
It is not possible.
See explanation.
If multiple question worth 4 points each, then
[tex]2M + 6E = 100[/tex] would be:
[tex]4M + xE = 100[/tex]
Where x represents the number of points for essay questions.
Substitute 7 for E and 29 for M.
[tex]4 * 29 + x * 7 = 100[/tex]
[tex]116 + 7x = 100[/tex]
Subtract 116 from both sides
[tex]116-116 + 7x = 100 -116[/tex]
[tex]7x = 100-116[/tex]
[tex]7x = -16[/tex]
Make x the subject
[tex]x = -\frac{16}{7}[/tex]
Since the essay question can not have worth negative points.
Then, it is impossible to have the multiple questions worth 4 points
Your friend is incorrect.
The test contained 29 multiple choice questions and 7 essay questions.
Let x represent the number of multiple questions and y represent the number of essay questions.
Given that there are a total of 36 questions, hence:
x + y = 36 (1)
Also, the test is worth a total of 100 points, hence:
2x + 6y = 100 (2)
Solving equation 1 and 2 simultaneously gives:
x = 29, y = 7
Therefore the test contained 29 multiple choice questions and 7 essay questions.
Find out more at: https://brainly.com/question/16763389
Which similarity statement is true?
ASRQ - ATRS
ASRQ - ARTQ
ASRQ - ARTS
ASRQ-AQRT
Answers
Answer:
It would be B (The 2nd option)
Step-by-step explanation:
The two triangles that can be considered similar are RTQ and SRQ. These two have one right angle and share angle Q, make them similar by AAA.
Both the 2nd option and the 4th option mention these triangles, but the triangles are not named correctly in the 4th option.
The similarity statement that is true is
ΔSRQ - ΔRTQ
The correct option is B.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
The two triangles that are similar are RTQ and SRQ. According to the AAA (Angle-Angle-Angle) similarity criterion, since they share two congruent angles, ∠RTS and ∠STQ, they must be similar. Therefore, we can write:
ΔRTQ ~ ΔSRQ
This similarity statement means that triangle RTQ is similar to triangle SRQ. So, we can use the corresponding parts of similar triangles to write:
SR / RT = SQ / TQ = RQ / RQ
where SR, RT, SQ, TQ, and RQ are the corresponding side lengths of the two triangles.
Since RQ / RQ = 1, we can simplify the above equation to:
SR / RT = SQ / TQ
This means that the ratios of the corresponding side lengths of the two triangles are equal. We can use this to find the true similarity statement:
ΔSRQ ~ ΔRTQ
So, the correct similarity statement is:
ΔSRQ - ΔRTQ.
To learn more about the congruent;
https://brainly.com/question/12413243
#SPJ7
Identify the like terms in the expression.
10x+5+3x-1+x2
Answers
Answer:
x2 +13x+4
Step-by-step explanation:
1+2+3= 4 quick maths
How do I solve [tex]cot(x) = -\sqrt{3}[/tex] ? I have to be able to solve it without a calculator :/
Answers
Answer:
No solution
Step-by-step explanation:
Since cos(x) e [-1,1],the equation has no solution in the Set of real numbers.
Answer:
7=7
Step-by-step explanation:
Please help. I need to refresh my mind of this problem and a few more if you don't mind
Answers
Answer: c
Step-by-step explanation:
look at the equation and insert the value of X from the table into the equation and figure out which one will give you the same sum for the values. for example f(x) = 3(-2)-1
this answer gives you f(x)= -6 -1 which will give u a sum of -7
another one : f(x)= 3(0)-1
3 multiplied by 0 gives you 0 therefore you are left with -1
by doing this you prove that this equation works with ur x values and gives you the same sum you have for f(x)
Please help
when two triangles have two pairs of congruent sides, how are the third pair of sides and the pair of angles opposite the third pair of sides related
Answers
Answer:
b77fe jegd isf edre h7rwyr e7e7eoetr 38 eyg dbuyr e HFUGRG duetyr fgisyvbfvdyirrrg7h
Step-by-step explanation:
In the fraction 1/2, the number 1 is:?
Answers
Answer:
the numerator
Step-by-step explanation:
A piece of machinery depreciates $6000 the first year,
$5700 the second year, and $5400 the third year. If the
rate of depreciation is constant, what is the amount of
depreciation of the piece of machinery in the sixth year?
Answers
Answer:
$4500
Step-by-step explanation:
it decreases $300 per yeae
Based on the rate of depreciation each year, the amount of depreciation of the machinery in the sixth year will be $300.
What is the annual depreciation amount?The depreciation in the second year is:
= 6,000 - 5,700
= $300
The depreciation in the third year is:
= 5,700 - 5,400
= $300
If this amount remains constant till the sixth year therefore, then it means that the sixth year depreciation amount is also $300.
Find out more on annual depreciation at https://brainly.com/question/1287985.
#SPJ2
Writing Assignment: Your friend in another school has just sent you a
screenshot of a math problem and needs your help. IN WORDS, you must
describe how to solve the problem and you must include your solution.
Remember to use COMPLETE sentences. Include math vocabulary (coefficent,
variable, functions, etc) in your verbal description. Here is the problem:
Evaluate if x = 4.
f(x) = = - 3x + 8
Answers
Given that,
f(x) = -3x + 8
To find,
The value of f(x) at x = 4.
Solution,
We have,
f(x) = -3x + 8
We need to find the value of f(x) at x = 4
Pu x = 4 in f(x).
f(4) = -3(4) + 8
= -12 +8
= -4
So, f(4) is equal to -4.
Barbara's gross earnings for the week ending on December 21 amount to \$1,100 . Her cumulative gross earnings for the year up through her tast pay date amount to 55,000. Using the table below, calculate the FICA tax deduction for the current pay period . FICA Tax ( 1496 10%
Answers
Answer:
b) $44Step-by-step explanation:
Barbara's cumulative gross earnings for the year up through her last pay date amount to 55000.
As per attached table this amount falls in 4% region ($50001 - $70000).
Her tax per current pay period is:
$1100*0.04 = $44Correct choice is b)
Two linear functions are shown. Which function has the greater initial value
Answers
function b ..............
Harry purchased a table with Rs. 7000 and sold it at an amount of Rs. 7900. Find his gain percent.
Answers
Answer:
12%
Step-by-step explanation:
Answer:
12.89%
Step-by-step explanation:
[tex] \frac{900}{7000} \times 100 = 12.85714286[/tex]
#4.. are the triangles congruent using SSS Congruence Theorem. Explain
Answers
Four of you enter in the race. You are told that only one will complete the course. What is the probability if you complete the Course. What is probability that you will not complete the course.
Answers
Answer:
25% probability that you complete the course
75% probability that you do not complete the course
Step-by-step explanation:
If there are a total of 4 individuals entering the race and only one is able to complete the course then the probability that you will complete the course would be
1/4 = 0.25 or 25%
This is because you only represent 1 out of the 4 total participants. The opposite would be the case to calculate the probability that you will not complete the course since there are three other candidates with that could have completed it, therefore...
3/4 = 0.75 or 75%
Solve for x: 5x + 13 = 1/3(9x – 6) + 7x
Answers
Step-by-step explanation:
5x + 13 = 1/3(9x – 6) + 7x
5x + 13 = 3x-2+7x
5x-3x= -2-13
2x= -15
x= -7.5
in the diagram below, the expression in each circle is the result of the sun of the two rectangles connected to it. complete the diagram, writing the expressions in their simplified form
Answers
Answer:
this is the answer for the empty circle and rectangle
1. Charlene makes $10 per hour babysitting and $5 per hour gardening. This week, she wants to make at least $80.
Let b represent the hours she babysits and a represent the hours she gardens.
a. Create an inequality to represent the number of hours she should babysit or garden to make at least
$80.
b.How much would she have to garden if she did not babysit at all?
C.How much would she have to babysit if she did not garden at all
Answers
Answer:
Step-by-step explanation:
Well is she wanted to make $80 “b” she would have to garden for 16 hours to make a maximum of $80
“C” if she wanted to make it out of babysitting she would have to work the same for 8 hours if she babysit
Workout : b part = 10+10+10+10+10+10+10+10 Key:10=2
:c part = 20+20+20+20. Key:20=2
Sorry I didn’t do a but just add all the things above and u get your answer
y = 2x + 1
x - y = -3
Is (2, 5) a solution of the system?
Yes
No
Answers
Answer:
No
Step-by-step explanation:
If you substitute the numbers into either of the two functions when you solve you don't get the right numbers
Hi I rly need some help plz answer;)
Answers
Answer:
Step-by-step explanation:
1.8kg into grams
1.8kg = 1800 grams
Total toys = 6
Weight of one toy = 1800 ÷ 6 = 300 grams
Weight of 4 toys = 300 x 4 = 1200 grams = 1.2kg
Answer:
Step-by-step explanation:
a) 1 Kg = 1000 grams
1.8 Kg = 1.8 * 1000 = 1800.0 = 1800 grams
b) Weight of one toy = Weight of all the 6 toys ÷ 6
= 1800 ÷ 6
= 300 grams
c) Weight of 4 toys = 4 * 300
= 1200 grams
= 1200 ÷ 1000
= 1.2 Kg
30 divided
3 diveded
[tex]30 \: diveded[/tex]
Answers
Answer:
30÷3=10
Step-by-step explanation:
thank you for the pints I hope you have a good day :)
Answer:
30 divided by 3 is 10
Step-by-step explanation:
I don't know why you put the extra divided
What is the measure of angle 7?
Explain?
Answers
65 degrees. alternate exterior angles of two parallel lines intersected by a transversal are equal
Answer:
60 or 65 degrees.
Step-by-step explanation:
A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is
an hourly wage of $22. Option B is a commission rate of 4% on weekly sales. How much does he
need to sell this week to earn the same amount with the two options?
thank you so much!
Answers
His salary for 40 hours per week with an hourly rate is hours x the rate:
40 hours x $22 per hour = $880 per week.
If he is paid commission, to make the same , he needs to make $880 iin commissions.
The commission rate is 4%, to find how much sales is needed divide the amount he needs to make ( $880) by the rate:
880/ 4% = 880/ 0.04 = $22,000
He needs to sell $22,000
A triangle in which all of the angles are smaller than 90° is called an ____ ____.
Answers
Answer:
acute triangle
Step-by-step explanation:
Find the Area of a rectangle whose width is 16 inches and diagonal is 20 inches?
What are the dimensions of the rectangle? Show your work and explain how you got your answer in complete sentences.
Answers
b=12
Area is 12x16=192
HELP PLEASE HURRY WILL MARK BRAINLIEST!!!!!!
Answers
Answer:
c . 63
Step-by-step explanation:
what's the value of x??
Answers
Answer:
ABCDEFGHIJKLMNOPQR*X*
Step-by-step explanation:
ikaw ex na
Answer:
x = 30°
Step-by-step explanation:
As we can see it is right angled triangle so
2x + x + 90° = 180° (Sum of angels of triangle )
3x + 90° = 180°
3x = 180° - 90°
3x = 90°
x = 90° / 3
x = 30°
Hope it will help :)❤
help it is impossible
Answers
Answer:
6,0
Step-by-step explanation:
Isolate x to get x=3/2y+6
6 is the x intercept.
In (x,y) form it is (6,0)
a cyclist rode 3.75 miles in 0.3 hours how fast was she going in miles per hour?
Answers
Answer:
12.5 miles per hour
Step-by-step explanation:
Math
Answer:
12.5 MPH
Step-by-step explanation:
Miles per hour can also be written as miles/hour
therefore 3.75 miles in .3 hours can also be written as 3.75 miles/.3 hours
3.75 / .3 = 12.5
Therefore the cyclist was going 12.5 miles per hour
Will give Brainlyest PLEASE HELP!!
Answers
Answer:
6.98 feet that the anwers
For f (x) = 3x + 1 and g(x) = x^2 -6, find (f-g) (x)
Answers
Answer:
D
Step-by-step explanation:
(f - g)(x) = f(x) - g(x), so
f(x) - g(x)
= 3x + 1 - (x² - 6) ← distribute by - 1
= 3x + 1 - x² + 6 ← collect like terms
= - x² + 3x + 7 → D