Answer:
Yes
ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down
Step-by-step explanation:
The coordinates of the vertices of the triangles are;
F(1, 0), D(1, 3), and E(5, 0), and Q(-1, -2), R(-1, -5), and P(-5, -2),
Length of FD = √((3 - 0)² + (1 - 1)²) = 3
Length of DE = √((5 - 1)² + (0 - 3)²) = 5
Length of FE = √((5 - 1)² + (0 - 0)²) = 4
For triangle QRP, we have;
Length of QR = √((-5 - (-2))² + (-1 - (-1))²) = 3
Length of RP = √((-5 - (-1))² + (-2 - (-4))²) = 5
Length of PQ = √((-5 - (-1))² + (-2 - (-2))²) = 4
For a reflection across the x-axis, we have;
For a rotation of 180° about the origin, we have;
For a coordinate of the preimage before reflection of (x, y), the coordinates of the image after reflection is (-x, -y)
When followed by a translation 2 units down, we have the coordinates of the image will be (-x, -y-2)
Therefore;
For the points F(1, 0), D(1, 3), and E(5, 0) on triangle FDE, we have;
Rotation 180° about the origin gives;
F(1, 0) → Rotation by 180° → F'(-1, 0)
D(1, 3) → Rotation by 180° → D'(-1, -3)
E(5, 0) → Rotation by 180° → E'(-5, 0)
For a translation 2 unites of the coordinates of the vertices of the above triangle ΔF'D'E',
F'(-1, 0) → Translation 2 units down → F''(-1, -2)
D'(-1, -3) → Translation 2 units down → D''(-1, -5)
E'(-5, 0) → Translation 2 units down → E''(-5, -2)
The coordinates of the vertices of triangle ΔF''D''E'' are equivalent to the coordinates of the ΔQRP
Therefore, ΔDEF, and ΔRPQ are congruent, because ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down.
Answer:
Yes
ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down
Step-by-step explanation:
The information is in the picture
Answer:
B is correct option that helps
LOOK AT THE PICTURE
Which statement best explains if the graph correctly represents the proportional relationship y = 3.5x?
It does, the points shown on the line would be part of y = 3.5x.
It does not, proportions cannot be represented on a graph.
It does not, the points shown on the line would not be part of y = 3.5x.
It does, all proportions can be shown on the graph of this line.
Answer:
I don't think any of the answers here are right. They aren't a proportional relationship since they don't pass through the origin. So I would believe the answer would be C. Sorry if I'm wrong!!
Step-by-step explanation:
I learned about this stuff :D
Answer:
C, because you would need two numbers to find the slope of the graph.
Step-by-step explanation:
I had to take a minute to understand this question.
what are the slope and the y-intercept of the linear function that is represented by the table?
the slope is -2/5, and the y-intercept is -1/3.
the slope is -1/3, and the y-intercept is -2/5.
the slope is 1/3, and the y-intercept is -2/5.
the slope is 2/5, and the y-intercept is -1/3.
Answer:
la respuesta correcta es la letra B es decir la pendiente es -1/3 y la intersección con el eje y es -2/5 segun mis calculos
Step-by-step explanation:
The 2 triangles are congruent
JKL=PQR
Answer:
w = 3
The rest doesn't have enough information to complete, (Sorry for previous answer)
Find the values of x and y that satisfy the equation –21 + 5yi = 7x – 10i.
Answer:
The values of x and y are x = -3 and y = -2
Step-by-step explanation:
In the complex numbers if a + bi = c + di, then the real parts are equal and the imaginary parts are equal
a = cb = dLet us use this rule to solve the question
∵ -21 + 5yi = 7x - 10i
∴ The real parts are -21 and 7x
∴ The imaginary parts are 5y and -10
∵ The real parts are equal
∴ 7x = -21
→ Divide both sides by 7
∴ [tex]\frac{7x}{7}[/tex] = [tex]\frac{-21}{7}[/tex]
∴ x = -3
∵ The imaginary parts are equal
∴ 5y = -10
→ Divide both sides by 5
∴ [tex]\frac{5y}{5}[/tex] = [tex]\frac{-10}{5}[/tex]
∴ y = -2
∴ The values of x and y are x = -3 and y = -2
It is known that x1 and x2 are roots of the equation 3x^2+2x+k=0, where 2x1=−3x2. Find k.
Answer:
k = 8
Step-by-step explanation:
Since the roots of the equation 3x² + 2x + k are x₁ and x₂ and 2x₁ = 3x₂.
By the roots of an equation, ax² + bx + c , where its roots are x₁ and x₂. It follows that sum of roots are x₁ + x₂ = -b/a and product of roots are x₁x₂ = c/a.
Comparing both equations, a = 3 b = 2 and c = k.
So, x₁ + x₂ = -b/a = -2/3 and x₁x₂ = c/a = k/3
x₁ + x₂ = -2/3 and x₁x₂ = k/3
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
Since 2x₁ = -3x₂, and -2x₁ = 3x₂substituting this into equations (1) and (2) above, we have
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
3x₁ + (-2x₁) = -2 and x₁(3x₂) = k
3x₁ - 2x₁ = -2 and x₁(3x₂) = k
x₁ = -2 and x₁(-2x₁) = k
x₁ = -2 and -2x₁² = k
Substituting x₁ = -2 into -2x₁² = k, we have
-2x₁² = k
-2(-2)² = k
2(4) = k
8 = k
So, k = 8
The required value of k is -18
Given the quadratic equation [tex]3x^2+2x+k=0[/tex]
Let the roots of the equation be [tex]x_1 \ and \ x_2[/tex]
From the quadratic equatin:
a = 3, b = 3 and c = k
Sum of root = -b/a
x1 + x2 = -3/3
x1 + x2 = -1 ....................... 1
product of roots = c/a
x1x2 = k/3 ....................... 2
Recall that 2x1=−3x2
x1 = -3x2/2 ........... 3
Substitute equation 3 into 1:
x1 + x2 = -1 ....................... 1
-3x2/2 + x2 = -1
-3x2 + 2x2 = -2
-x2 = -2
x2 = 2
From equation 2:
x1x2 = k/3
2x1 = k/3
-3x2 = k/3
-3(2) = k/3
-6 = k/3
k = -18
Hence the required value of k is -18
Learn more on quadratic function here: https://brainly.com/question/11631534
Given the number 47,135,280, what is the place value of the number 3
Answer:
ten thousand
Step-by-step explanation:
Answer:
3 would be ten thousand
Step-by-step explanation:
in words it would be thirty five thousand and two hundred eighty.
the number 3 would be in the tenth thousand because its the 2nd one in the thousands. It’s the 10th thousands thats why.
In circle J with mZHLK = 18, find the mZHJK.
Answer:
The measure of angle HJK is 36°
Step-by-step explanation:
In a circle, the measure of the inscribed angle equal half the measure of the central angle subtended by the same arc
In circle J
∵ J is the center of the circle
∵ H and K lie on the circle
∴ ∠HJK is a central angle subtended by arc HK
∵ L lies on the circle
∴ ∠HLK is an inscribed angle subtended by arc HK
→ By using the rule above
∵ ∠HJK and ∠HLK are the central angle and inscribed angle
subtended by the same arc HK
∴ m∠HLK = [tex]\frac{1}{2}[/tex] m∠HJK
∵ m∠HLK = 18°
∴ 18 = [tex]\frac{1}{2}[/tex] m∠HJK
→ Multiply both sides by 2
∴ 36 = m∠HJK
∴ The measure of angle HJK is 36°
okay i have two 'true or false' questions from algebra 1:
1.) "A dotted line is ordered pairs that make the equation/inequality true. True or false?"
2.) "When you have a solid line, any point in the shaded region or on the line will make the inequality true. True or false?"
You mix 2 pints of blue paint for every 5 pints of red paint to make purple paint. You use 18 pints of red paint. How much purple paint do you make?
moya picked 3 dozen apples she wents to share her apes in equal groups. show how many different way can she do this
10 + 10 - 10 x 10 / 10
Answer:
10
Step-by-step explanation:
Thanks for the Points! Have a great day!
:)
Answer:
10 zzz
Step-by-step explanation:
Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice cream shop for $8 per hour, Leah cannot
work more than 20 hours per month
How did you determine the pair(s) (x,y) that Leah could work to meet the given conditions in item 157
Answer:
Sorry if I am wrong
Step-by-step explanation:
If you do 5x10 then you would get 50 right then if you also do 8x10 then you would get 80 add those together you get 130. that means if Leah worked 10 hours at Ice cream and 10 hours at babysitting she would not only meet her goal she would have 10 extra dollars.
What is the value x ?
Answer:
x= 62
Step-by-step explanation:
The value of a triangle is 180 degrees.
68.5+49.5= 118
180-118= 62 degrees
Please let me know wwhich is the answer! Will mark brainliest!
Answer:
A
Step-by-step explanation:
what is the sale price for a object that cost $75 but is on sale for 20% .
Answer:
$60
Step-by-step explanation:
$60
Step-by-step explanation:
20% = 0.2
75× 0.2 = 15
75-15=60
9.45 x 10^-5 In standard form
4879 divided by 200 as a mixed number
Answer:
Step-by-step explanation:
4879/200
is already in the simplest form. It can be written as 24.395 in decimal form.
then : 24 + 0.395
0.395 * 1000 79
_____ ____ = __
1 1000 200
then : 24 + 79 / 200
answer: 79
24--------
200
A movie theater sends out a coupon for 15% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. The equation is y what (Use integers or decimals for any numbers in the expression).
Answer:
y = 0.85x
Step-by-step explanation:
Given that:
Coupon (c) = 15% off
x = original price of ticket
y = price of ticket with coupon
Price of ticket with coupon = (100 - c)% * original price)
y = (100 - 15)% * x
y = 85% * x
y = 0.85x
Which of the following is a term of -5.92?
1.45 x
2 1/4
-7.78 x with an exponent of 2
3/5
Answer:
2 1/4
Explanation
I took the test it was right.
What is the equation of the line that passes through the point (-6, 1) and has a slope of -3/2?
Answer:
y=-3/2x-8
Step-by-step explanation:
Which scatterplot suggests a linear relationship between x and y?
what is the sum of the interior angles of a heptagon ?
Let n be rhe number of vertices in the polygon, then the sum of all interior angle is (n - 2) × 180°.
Number of sides in a heptagon = 7
So, n = 7
So,
the sum of the interior angles of a heptagon
= (7 - 2) × 180°
= 5 × 180°
= 900°
Answer:
900
Step-by-step explanation:
Which expression is equivalent to 5 – 6
A. -5+ (-6)
B. 5 -(-6)
C. 6 - 5
D. - 6+5
Rahima goes jogging on a course that is 2.75kilometers long. If she completes the full course every morning, how many kilometers does she jog in
one week? Explain how you got your answer.
Answer:
19.25kmStep-by-step explanation:
Step one:
given data
we are told that the distance that Rahima covers on a daily is 2.75km long
we also know that a week has 7 days that is Mon-Sunday
Required
the total distance for a week
Step two:
Hence the total distance covered for 7 days is
=2.75*7
=19.25km
Simply multiply the distance covered in a day by 7 to get the distance covered in a week
Answer:
why would i go jogging on a course that is 2.75kilometers long. XD
Step-by-step explanation:
If it takes 3 1/3 minutes to fill 3/8 of a water tank, how long will it take to fill it completely?
Answer:
[tex]8 \frac{8}{9}[/tex] minutes
Step-by-step explanation:
plz mark brainlyest
If V= 1/3Bh, then what is the value of B?
Pls answer I need help with this question
Answer:
Well B is the base of the shape
If thats what you mean
Step-by-step explanation:
HELP ASAP!!! PLEASE!!! MARKING BRAINLIEST! MATH!!!
Answer:
9x50=450
Step-by-step explanation:
hope this helps
ZA and ZB are supplementary angles. If mZA = (5x
ZB (2x + 10), then find the measure of ZB.
19) and m
Answer:
i need this question too
Step-by-step explanation:
What is 25% of 167??????
Answer:
41.75
Step-by-step explanation:
Hope this helps and have a nice day :)