Answer:
The answer is below
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.
The distance between two points on the coordinate plane is given as:
[tex]Distance=\sqrt{(x_2-x_1}^2+(y_2-y_1)^2 \\\\Therefore\ in\ triangle\ PQR:\\\\|QR|=\sqrt{(-2-(-2))^2+(4-0)^2}=4\\\\|PQ|=\sqrt{(-2-4)^2+(0-4)^2}=\sqrt{52}=2\sqrt{13} \\\\|PR|=\sqrt{(-2-4)^2+(4-4)^2}=6[/tex]
In triangle STU:
[tex]|ST|=\sqrt{(-1-2)^2+(-2-(-4))^2}=\sqrt{13}\\\\|SU|=\sqrt{(-1-2)^2+(-4-(-4))^2} =3\\\\|TU|=\sqrt{(-1-(-1))^2+(-4-(-2))^2}=2[/tex]
|QR| / |TU| = 4/2 = 2
|PR| / |SU| = 6/3 = 2
|PQ| / |ST| = 2√13 / √13 = 2
Hence:
|QR| / |TU| = |PR| / |SU| = |PQ| / |ST|
Therefore, △PQR and △STU are similar triangles since the ratio of their sides are in the same proportion.
Similar triangles may or may not be congruent
Triangles PQR and STU are similar by SSS theorem.
The vertices of triangle PQR are given as:
[tex]P= (4, 4)[/tex]
[tex]Q= (-2, 0)[/tex]
[tex]R = (-2, 4)[/tex]
The vertices of triangle STU are given as:
[tex]S = (2, -4)[/tex]
[tex]T = (-1, -2)[/tex]
[tex]U =(-1, -4)[/tex]
Start by calculating the side lengths of the two triangles, using the following distance formula
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
For triangle PQR, we have:
[tex]PQ = \sqrt{(4 --2)^2 + (4 -0)^2} = \sqrt{52}[/tex]
[tex]PR = \sqrt{(4 --2)^2 + (4 -4)^2} = 6[/tex]
[tex]QR = \sqrt{(-2 --2)^2 + (0 -4)^2} = 4[/tex]
For triangle STU, we have:
[tex]ST= \sqrt{(2 --1)^2 + (-4 --2)^2} = \sqrt{13}[/tex]
[tex]SU= \sqrt{(2 --1)^2 + (-4 --4)^2} = 3[/tex]
[tex]TU= \sqrt{(-1 --1)^2 + (-2 --4)^2} = 2[/tex]
Check if the side lengths of both triangles are similar, by dividing corresponding sides
[tex]k = \frac{PQ}{ST} = \frac{\sqrt{52}}{\sqrt{13}} = 2[/tex]
[tex]k = \frac{PR}{SU} = \frac{6}{3} = 2[/tex]
[tex]k = \frac{QR}{TU} = \frac{4}{2} = 2[/tex]
Because the scale factors of the side lengths are the same, then both triangles are similar by SSS theorem.
Read more about similar triangles at:
https://brainly.com/question/8691470
If 8 boxes of crayons cost $20 , what would 6 boxes cost ?
Answer:
$15
Step-by-step explanation:
To figure thsi out, you do 20 divided by 8, which gives you 2.5 ($2.50.)
Next you do 2.50 x 6 which gives you 15 ($15.)
The answer is $15.
(The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest. If my answer was wrong and you got marked wrong for it, I deeply apologize and hope you will forgive me, since everyone makes mistakes sometimes. If you need me to elaborate on my answer or give further explanation on it, please ask and I will do so. If you need to explain your reasoning on your work feel free to use my words- word for word- without crediting me, the answer was made for you anyways! Hope yall learn from my answer and it helps you in the future with assignments, quizzes, test’s, and more!
- •Trix•
( Yes I know my - •Trix• thingy is not my user but it’s what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)
Please help due in 15 min
whats 1+1+8-3+5-8+4-8+3-5+8-7-7+5+4+3+9+8+2+14+78+
Answer:
115
Step-by-step explanation:
Hope this helps! Brainliest is appreciated!! Happy Holidays!!!
Answer:
The answer of this question is 123
what does x equal in 3.8x = -19
Answer:
x=5
Step-by-step explanation:
3.8x5=19 so 19 divided by 5 = 3.8
Jane buys a pack of 6 towels for 15.60 .
Find the unit price in dollars per towel.
If necessary, round your answer to the nearest cent.
Answer:
2.6
Step-by-step explanation:
EASY 7TH GRADE MATH QUESTION FIRST PERSON MARKED BRAINLIEST!
Answer:
30.
Step-by-step explanation:
its due today and please give a step by step answer
Answer:
x=3.333 or 10/3
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*x-(2*(-6*x+18)+14)=0
Pull out like factors :
-6x + 18 = -6 • (x - 3)
to make 3x - (-12 • (x - 3) + 14) = 0
Pull out like factors :
15x - 50 = 5 • (3x - 10) to get
5 • (3x - 10) = 0
Solve : 3x-10 = 0
Add 10 to both sides of the equation :
3x = 10
Divide both sides of the equation by 3:
x = 10/3 = 3.333
Answer:
f
Step-by-step explanation:
substitue the y
3x=2(-6x+18)+14
distrubute
3x=-12x+36+14
combine like terms
3x=-12x+50
add -12x on both sides
15x=50
divide 15 on both sides
x=50/15
simplify
x=10/3
Find the area. Simplify your answer.
3x
7
Answer:
21x?
Step-by-step explanation:
I think so
Plz, Help me with this question.
Please help im bad at this pls dont just steal my points =(
Answer:
the slope is a positive and the point is (-1,-2) the equation is 3=(×1,2)
Step-by-step explanation:
if im wrong im so sorry
Maddie bought 3 2/3 yards of satin ribbon at the craft store. She wanted to make hair bows for the cheer squad. Each bow requires 2/3 of a yard of ribbon. How many complete bows can she make?
Answer:
4
Step-by-step explanation:
Given that:
Total yards of satin bought by Maddie = [tex]3\frac{2}{3}[/tex] yards
Number of yards required make one ribbon = [tex]\frac{2}{3}[/tex] yards
To find:
Number of complete bows that can be made ?
Solution:
First of all, let us learn about converting the mixed fraction to fractional form.
Formula:
[tex]a\dfrac{b}{c} = \dfrac{a\times c+b}{c}[/tex]
Therefore, total yards of satin bought by Maddie can be written in fractional form as:
[tex]3\dfrac{2}{3} = \dfrac{3\times 3+2}{3} = \dfrac{11}{3}[/tex]
One hair bow requires [tex]\frac{2}{3}[/tex] yards of ribbon.
Number of hair bows that can be made, can be found by dividing the total ribbon length by ribbon required for making one hair bow.
Answer is:
[tex]\dfrac{\frac{11}{3}}{\frac{2}{3}}\\\Rightarrow \dfrac{11\times 3}{2\times 3}\\\approx 4[/tex]
4 hair bows can be made.
33% of what number Is 1.45?
ANSWER : Approximately 4.39
WHY? : You must round up the answer "x=4.3939". If thought of like .33X=1.45, then you divide 1.45 by .33
Every day, the Clinton Pet Store uses 3 bags of dog food to feed the dogs. How many days will 3/4 of a bag of dog food last?
3/4 of a bag of dog food will last for 2.25 days.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
If 3 bags of dog food are used every day, then in one day, 1 bag of dog food will last:
1 day = 1/3 bag of dog food
To find how many days 3/4 of a bag of dog food will last, we can divide 3/4 by 1/3:
(3/4) ÷ (1/3)
= (3/4) × (3/1)
= 9/4
= 2.25
Therefore,
3/4 of a bag of dog food will last for 2.25 days.
Learn more about expressions here:
https://brainly.com/question/3118662
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Minnie is making tea. She knows that her tea tastes best if she lets her tea bag sit in the hot water for exactly fifteen minutes. However, depending how hot the water is, she may have to leave her tea bag in the water for 2 minutes more or less than usual. Write and solve an absolute value equation to describe this situation
Answer:
|x - 2| = 15 ; |x + 2| = 15
Step-by-step explanation:
Given that:
Wait time = 15 minutes
Variation in wait time depending on level of hotness = 2 minutes
X ± 2 = 15
x + 2 = 15 or x - 2 = 15
x = 15 - 2 = 13 or x = 15 + 2 = 17
Hence, to express the above as an absolute value equation :
|x - variation| = mean time
|x - 2| = 15 ; |x + 2| = 15
Select the correct locations on the graph
select the lines that represent functions
Step-by-step explanation:
Using the vertical line test, we can see which lines are functions, and which are not. If a vertical line were to hypothetically appear, would it touch more than one part of the line? If so, it is not a function.
The lines outlined in a black box are the correct answers.
Answer:the other person is right
Step-by-step explanation:
(a) 4x - 3y = 6,
7x + 3y = 27.
(d)
12x + 19y= 22,
18x + 23y = 44.
(g) 53x +41y = 147,
41x + 53y =135.
g
PLEASEEEEE HELPPPP!
Answer:
it is not 3.
l think correct answer is 2 .
Step-by-step explanation:
(y-b+a):m
A juggler tosses a ball into the air. The balls height, h, and the t seconds can be represented by the equation h(t)=16t^2+40t+4. Suppose the juggler missed and the ball hit the ground. Find the maximum height of the ball and the time it took the ball to reach the ground. Round all answers to the nearest hundredth
Answer:
h= -20
t = -0.104 and -2.39s
Step-by-step explanation:
A juggler tosses a ball into the air. The balls height, h, and the t seconds can be represented by the equation h(t)=16t^2+40t+4. Suppose the juggler missed and the ball hit the ground. Find the maximum height of the ball and the time it took the ball to reach the ground. Round all answers to the nearest hundredth
The velocity of the body at its maximum height is zero
V= dh/dt
dh/dt = 32t + 40
0 = 32t+40
-32t = 40
t = 40/-32
t = -1.25s
Substitute t = -1.25 into the expression
h(t)=16t^2+40t+4.
h(-1.25)=16(-1.25)^2+40(-1.25)t+4.
h = 16(1.5625)-50+5
h = 25-45
h =-20
Hence the maximums height is -20m
The ball will reach the ground at h = 0
Substitute
h(t)=16t^2+40t+4.
0 = 16t^2+40t+4
Divide through by 4
0 = 4t²+10t+1
Factorize
-10±√10²-4(4)/2(4)
t = -10±√100-16/8
t = -10±√84/8
t =-10+9.17/8
t = -0.83/8 and -19.17/8
t = -0.104 and -2.39s
Find three consecutive even integers such that the sum of the second and third is 3 times the first integer.
Answer:
[tex]6[/tex], [tex]8[/tex] and [tex]10[/tex]
Step-by-step explanation:
Let [tex]x =[/tex] smallest consecutive even integer.
Since the second and third consecutive even integers can be expressed by our smallest even consecutive integer, we can express them as:
Second consecutive even integer = [tex]x+2[/tex]
Third consecutive even integer = [tex]x+4[/tex]
From "the sum of the second and third is 3 times the first integer", we can write:
[tex]x+2+x+4 = 3x[/tex]
[tex]2x+6 = 3x[/tex] (collect like-terms)
[tex]x=6[/tex]
∴ The first consecutive even integer is 6
Now, we can use substitution to find the values of the second and third consecutive even integers:
Second consecutive integer = [tex]x+2[/tex]
[tex]=6+2[/tex]
[tex]=8[/tex]
Third consecutive integer = [tex]x+4[/tex]
[tex]=6+4[/tex]
[tex]=10[/tex]
∴ The three consecutive even integers are [tex]6[/tex], [tex]8[/tex] and [tex]10[/tex].
Hope this helps :)
Can someone please solve number 9 and ten please
Answer:
In question number 9 I think is: 3. In question number 10 is: 3. If is not corect well...Im sorry I tried my best :) Hope it helps!
Step-by-step explanation:
What is the product of (4i) and (4+i)
Answer:
-4 + 16 i
Step-by-step explanation:
You are dealing with imaginary numbers so i dont remember y but i know that it is that answer
Answer:
- 4 + 16i.
Step-by-step explanation:
4i(4 + i)
= 16i + 4i^2 Now i^2 = -1 so we have:
16i - 4 (answer)
which expression is equivalent to
2(3g-4)-(8g+3)?
-2g-1
-2g-5
-2g-7
-2g-11
Answer:
-2g - 11
Step-by-step explanation:
Expand the brackets, multiply 2 over 3g and -4. One plus and one minus make a minus.
2(3g-4) - (8g+3) = 6g - 8 - 8g - 3
Evaluate like terms.
6g - 8 - 8g - 3 = -2g - 11
Tom and his friend both purchased some CD’s from an online store. The CD’s were all the same price. Tom purchased 5 CD’s for $80.00 and his friend purchased 3 CD’s for $52.00. Let x represent the number of CDs purchased, and y represent the total cost of the CDs. Write the equation in slope intercept form (y=mx+b). Show your work? NEED ASAP!
9514 1404 393
Answer:
y = 14x + 10
Step-by-step explanation:
We are given two points, (x, y) = {(5, 80), (3, 52)}. The 2-point form of the equation for a line can be used to find the equation.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (52 -80)/(3 -5)(x -5) +80 . . . . . fill in the given values
y = (-28/-2)(x -5) +80 . . . . . simplify a bit
y = 14x -70 +80 . . . . . eliminate parentheses; next, collect terms
y = 14x +10
can someone tell ne the equation of this word problem.
will give brainliest
Answer:
Dude. The word problem is non-existent.
Answer:
????
Step-by-step explanation:
there ain't nothing 2 solve
what is the slope of the line
PLSSS HELPPP
8.75x-2 i need help please
Answer:
-17.5
Step-by-step explanation:
there we go I can finally anwser here ya go have a good night keep working good :)
Where is the circumcenter of this triangle located?
O at a vertex of the triangle
O outside the triangle
Thing
O on a side of the triangle
O inside the triangle
Answer:
I don't see a picture but the circumcenter is usually inside the triangle.
Can somebody plz answer both these questions correctly thanks!! (Word problem)
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DDD
Answer:
a. 40%
b. 7.5%
Step-by-step explanation:
a. 60/ 150 x 100
b. 4.5/ 60 x 100
What information is needed to determine that the two triangles are congruent be ASA?
Answer:
ASA: If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. SAS: If any two angles and the included side are the same in both triangles, then the triangles are congruent.
9514 1404 393
Answer:
see below
Step-by-step explanation:
ASA requires two angles and the side that lies between them. The list below is a list of such. (The ends of the segments are the vertices of the angles.)
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
6x – 15y = 135
Answer:
Step-by-step explanation:
Slope-intercept form means the equation of a line should be in this form:
[tex]y=mx+b[/tex]
So we re-write our equation into this form like this:
[tex]6x-15y=135\\-15y=-6x+135\\y=\frac{-6x+135}{-15} \\\\y=\frac{-6x}{-15}+\frac{135}{-15} \\\\y=\frac{2}{5}x-9 \\[/tex]