After applying a translation of (x, y) → (x + 1, y - 2) and a dilation with a scale factor of 3 centered at the origin, the original coordinates of R (1, 5) transform to the new coordinates (6, 9).
Let's consider the given quadrilateral RUST with vertex R at coordinates (1, 5). We need to apply a translation followed by a dilation to find the new coordinates of R.
The translation is given by the transformation (x, y) → (x + 1, y - 2), which means that we will shift the figure 1 unit to the right along the x-axis and 2 units downward along the y-axis.
To find the new coordinates after the translation, we can apply the translation to the original coordinates of R:
x' = x + 1
y' = y - 2
Substituting the original coordinates of R into these equations:
x' = 1 + 1 = 2
y' = 5 - 2 = 3
After the translation, the new coordinates of R are (2, 3).
A dilation involves resizing a figure by a certain scale factor. In this case, the scale factor is 3, and the center of dilation is the origin (0, 0).
To perform the dilation, we multiply the coordinates of the translated point R by the scale factor. Let's denote the new coordinates after dilation as (x'', y'').
x'' = scale factor * x'
y'' = scale factor * y'
Substituting the translated coordinates of R into these equations and using the scale factor of 3:
x'' = 3 * 2 = 6
y'' = 3 * 3 = 9
After the dilation, the new coordinates of R are (6, 9).
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Complete Question:
Quadrilateral RUST has a vertex at R (1,5)What are the coordinates of R after the translation (x, y) (x+ 1, y - 2),followed by a dilation by a scale factor of 3, centered at the origin?
model aeroplane is made to a scale of 1 by two of the size of the real plane the area of the wings of the real plane are 40 m square find the area of the wings of the model in centimetre square
The area of the wings of the model is 100000 square centimeters
How to determine the model area of the wings?The given parameters are:
Scale factor, k = 1/2
Actual area of wings, A = 40 square meters
The model area is calculated as
Model area = Actual area * k^2
This gives
Model area = 40 * (1/2)^2
Evaluate
Model area = 10 square meters
Convert square meters to square centimeters
Model area = 10 * 10000 square centimeters
Evaluate
Model area = 100000 square centimeters
Hence, the area of the wings of the model is 100000 square centimeters
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The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. For the
next few hours, the temperature drops 2 degrees every hour.
Which equation represents the temperature, t, at hour h?
OA. t= 2h+32
B. t= -2h+ 32
C. t = 32h-₂
OD. t= -32h+2
You would multiply the change per hour by number of hours to get -2h
That would be added to the starting temperature.
Answer: B, t = -2h + 32
Answer: The answer is B
Step-by-step explanation:
The question says it drops ( which means subtraction) by 2 degrees every hour, so -2h
the price of an all access take it to the fair is $42.99 before tax roland bought the all access ticket for 40% off then he pay 7% sales tax on the discounted price part a how much did roland paid in sale tax? part b what is the total amount that roland paid for the ticket ?
The total amount that roland paid for the ticket is $27.60
Given that the price of an all-access ticket to the fair is $42.99 before tax. Roland bought the all-access ticket for 40% off.
We need to calculate the total amount paid by the roland
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100
The price after 40% off -
= 42.99*60% = $25.794
Sales tax on 25.794
= 25.794*7% = $1.80558
Total amount Paid for the ticket
= 1.80558 + 25.794 = $27.59958
= $27.60
Hence the total amount paid by roland is $27.60
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A triangle on a coordinate plane has three vertices A(2 , 3), B(5, 4), and C(3, 6). Use this description to do the following transformations (if needed, draw this triangle on a sheet of paper):
a. Dilation 1: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the origin? How did you determine these points?
b. Dilation 2: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the point (6, 8)? How did you determine these points?
c. What series of transformations would carry dilation 1 onto dilation 2? Compare Dilation 1 to Dilation 2. Explain what conclusions you can draw about the scale factor, difference in area, and center of dilation.
d. What is the proportion of the side lengths from Dilation 1 to Dilation 2? What is the proportion of their angle measures? Explain your answer.
The dilation by a scale factor of 2 of the points A(2, 3), B(5, 4), C(3, 6) gives;
a. A'(4, 6), B'(10, 8), C'(6, 12)
b. A'(-2, -2), B'(4, 0), C'(0, 4)
c. The transformation that would carry dilation 1 onto dilation 2 is T(-6, -8)
The area of dilation 1 and 2 are the sameThe center of dilation does not change the aread. The proportion of the side length of Dilation 1 and Dilation 2 is 1:1
The angle measures are the sameHow can the new coordinates be found?The general formula for finding the coordinates of the image of a point following a dilation is presented as follows;
[tex]D _{(a , \: b)k}(x, \: y) = (a + k \times (x - a) , \: b+ k \times (y - b))[/tex]
Where;
(a, b) = The center of dilation
k = The scale factor of dilation
(x, y) = The coordinate of the pre-image
The given points are;
A(2, 3), B(5, 4), C(3, 6)
a. The scale factor of dilation = 2
The center of dilation = The origin (0, 0)
Therefore;
[tex]D _{(0 , \: 0)2}(2, \: 3) = (0 + 2 \times (2 - 0) , \: 0+ 2 \times (3 - 0)) = (4, \:6)[/tex]
Therefore dilation about the origin, with a scale factor of 2 gives;
A(2, 3) → A'(4, 6)Similarly
B(5, 4) → B'(10, 8)C(3, 6) → C'(6, 12)b. With the center of dilation at (6, 8), we have;
[tex]D _{(6 , \: 8)2}(2, \: 3) = (6 + 2 \times (2 - 6) , \: 8+ 2 \times (3 - 8)) = (-2, \:-2)[/tex]
A(2, 3) → A'(-2, -2)[tex]D _{(6 , \: 8)2}(5, \: 4) = (6 + 2 \times (5 - 6) , \: 8+ 2 \times (4 - 8)) = (4, \:0)[/tex]
B(5, 4) → B'(4, 0)[tex]D _{(6 , \: 8)2}(3, \: 6) = \mathbf{(6 + 2 \times (3 - 6) , \: 8+ 2 \times (6 - 8))} = (0, \:4)[/tex]
C(3, 6) → C'(0, 4)c. The difference between the coordinates of the points on dilation 1 and 2 is a shift left 6 places and a shift downwards 8 places
Using notation, we have;
Dilation 1 T(-6, -8) → Dilation 2The area of the images of dilation 1 and 2 are equal given that the scale factor is the same.
The location of the center of dilation does not change the area of the imaged. From the above calculation, given that the difference between pre-image point and the center is multiplied by the scale factor followed by the addition of the x and y-values, the lengths of the sides of dilation 1 and 2 are the same, such that we have;
The proportion of the side lengths is 1Given that the side lengths are the same, by AAA congruency postulate, we have;
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Answer:
The angle measures are the same.
Step-by-step explanation:
The volume of a cube is 36 cm3. What is the surface area of the cube, rounded to the nearest tenth of a cm2
Answer:
65.4 cm²
Step-by-step explanation:
The volume of a cuboid is calculated by multiplying the length, base, and height together. Since a cube has equal sides, the formula for the volume of a cuboid can be simplified as shown below.
Volume of cube
= side ×side ×side
= side³
Given that the volume is 36 cm³, let's find the length of each side.
side³= 36
Cube root both sides:
side=[tex]\sqrt[3]{36}[/tex]
Total surface area of a cube is the sum of the surface areas of its 6 identical square faces.
Area of a square
= side ×side
= side²
Surface area of 1 face= [tex](\sqrt[3]{36})^2[/tex]
Total surface area
= [tex]6(\sqrt[3]{36} )^2[/tex]
= 65.416 (5 s.f.)
= 65.4 cm² (nearest tenth)
Additional:
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There can be 18, 12, 9, 6, 4 , 3 or 2 students on each team depending on the number of teams selected.
How to know the number of students on each team?Considering there are at least 2 teams but no more than 19 teams, let's calculate the number of students in each case:
2 teams: 18 students per team (36/2 = 18)3 teams: 12 students per team (36/3 =12)4 teams: 9 students per team (36/4 = 9)6 teams: 6 students per team (36/6 = 6)9 teams: 4 students per team (36/9 = 4)12 teams: 3 students per team (36/12= 3)18 teams: 2 students per team (36/18 = 2)Learn more about teams in: https://brainly.com/question/10750297
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what is 1/2y+3.2=20? Does it have no solution?
Answer:
y = 33.6
Step-by-step explanation:
1/2 y + 3.2 = 20 subtract 3.2 from both sides of the equation
1/2y = 16.8 multiply both sides by 2
y = 33.6
Compute a value for t that satisfies the equation below. "-2/3" t - 2 = - 3
Answer:
t = 3/2
Step-by-step explanation:
Instead of randomly guessing values of "t" that will satisfy the equation, you can easily find the correct value by solving the equation in terms of "t". In other words, you can set the equation equal to "t" to find the final answer.
(-2/3)t - 2 = -3 <----- Original equation
(-2/3)t = -1 <----- Add 2 to both sides
t = 3/2 <----- Divide both sides by -2/3
You can check this value by plugging it into "t" and determining whether both sides of the equations will be equal.
(-2/3)t - 2 = -3 <----- Original equation
(-2/3)(3/2) - 2 = -3 <----- Plug 3/2 into "t"
-6/6 - 2 = -3 <----- Multiply -2/3 and 3/2
-1 - 2 = -3 <----- Simplify -6/6
-3 = -3 <----- Subtract
A recipe for fruit punch calls for 333 liters of orange juice and 222 liters of pineapple juice. Jo creates a drink by mixing 444 liters of orange juice with 333 liters of pineapple juice. Which recipe will have the stronger pineapple taste
The jo's drink have stronger pineapple taste.
Given that fruit punch calls for 333 liters of orange juice and 222 liters of pineapple juice and Jo creates a drink by mixing 444 liters of orange juice with 333 liters of pineapple juice.
In the Recipe for fruit punch calls
The Number of liters of orange juice = 333.
The Number of liters of pineapple juice = 222.
Thus, Total number of liters of juice = 222+333= 555 liters
Now, % of pineapple juice in fruit punch is
P₁=(222/555)×100
P₁=0.4×100
P₁=40%
Further, % of orange juice in fruit punch is
O₁=(333/555)×100
O₁=0.6×100
O₁=60%
In Jo's drink
The Number of liters of orange juice = 444.
The Number of liters of pineapple juice = 333.
Thus, Total number of liters of juice = 444+333= 777 liters
Now, % of pineapple juice in jo's drink is
P₂=(333/777)×100
P₂=0.43×100
P₂=43%
Further, % of orange juice in jo's drink is
O₂=(444/777)×100
O₂=0.57×100
O₂=57%
Hence, the taste of both drinks was not the same, jo's drink will have a stronger pineapple taste and jo's drink will have a lesser orange taste.
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Need Help with this question
Answer:
23/35
Step-by-step explanation:
there's 12 red cards and 23 black cards
total = 35 cards
probability to pick a black card = 23/35
Answer: 23/35
Step-by-step explanation:
Probability is the measure of the likelihood of an event occurring. It is measured by the number of favorable outcomes over the total number of possible outcomes.
Here, the event is a black card being drawn. Since there are 12 + 23 = 35 cards in the deck, there are 35 possible outcomes of what card is picked. Out of those 35 cards, 23 are black, making 23 of the 35 options be the option we want.
23 black cards out of 35 total cards can also be written as [tex]\frac{23}{35}[/tex], which is the probability that a black card is chosen.
Solve the equation: -8(2a-1)=36
-8.(2a - 1) = 36
-16a + 8 = 36
-16a = 36 - 8 = 28
a = 28/(-16) = -7/4
The correct answer is -7/4 = -1.75
The solution to the given equation is [tex]\frac{-7}{4}[/tex].
What is an expression?Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.
We have,
Expression -8(2a - 1) = 36
So,
Now,
To get the solution to this expression,
i.e.
-8(2a - 1) = 36
Rewrite it as,
i.e.
Opening Brackets,
We get,
-16a + 8 = 36
Now,
Taking variable terms on one side and other terms on another side,
We get,
-16a = 36 - 8
On solving we get,
-16a = 28
i.e.
a = [tex]\frac{-28}{16} = \frac{-7}{4}[/tex]
So,
The solution to the given equation is [tex]\frac{-7}{4}[/tex].
Hence, we can say that the solution to the given equation is [tex]\frac{-7}{4}[/tex].
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Which term best describes the figure shown below?? WILL MARK BRAINLIEST!!!
Answer:
Line LM
Step-by-step explanation:
Answer:
A line is a straight path on a plane that extends forever in both directions with no endpoints.
The answer will be lineLM
Drag each expression to the correct location on the table. Simplify each exponential expression using the properties of exponents and match it to the correct answer. 3². (33) ².3-8 3 (32) (2-3)-3 2-3 (2-¹)(3- (3-5 1-2) -2)* 3 1 25-35.6-5 (23) (2-3)-¹ 22 113
3 2 1
The expression has been dragged the correct location on the table.
What is an exponential expression?It should be noted that an exponential expression simply means a way to write Lowe's in short form.
In this case, the expression has been dragged the correct location on the table.
This is attached below.
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Which of the following is the graph of the quadratic function y = x² - 6x-16?
++
10
-10
10-
-20-
-10
-10-
4
10
-10
O A. Graph A
OB. Graph D
C. Graph B
O D. Graph C
10
-10-
B.
10
10
D.
10
Answer:
C
Step-by-step explanation:
Graph C is the only one that has a y-intercept of (0, -16): note that when x = 0, y = 0^2 - 6(0) - 16, or y = -16 when x = 0.
Multiplica: (5 ft 6 in) x 4.
Answer: 22 ft
Step-by-step explanation:
Gavin made a patio area out of square blocks that are by . The area of his patio is and the length is . a) Determine the width of his patio. b) Determine the number of blocks Gavin used to make his patio.
The width of his patio is 19.5 feet based on the information about the area given.
How to calculate the width?Area = Length × Width
175.5 = 19.5 × w
Width = 175.5/19.5
Width = 9 feet
The width of his patio is 19.5 feet.
The number of blocks that were used will be:
= 175.5/(1.5 × 1.5)
= 175.5/2.25
= 78 blocks
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Complete question
Gavin made the patio area out of square block that are 1.5 by 1.5 feet. The area of the patio is 175.5 ft² and the length is 19.5ft.
a. Determine the width of his patio.
b. Determine the number of blocks Gavin used to make his patio.
y = x + 3 what is the the graph lines for this ?
Answer:
screenshot attached of graph
Step-by-step explanation:
Are the triangles similar? If so, state the similarity and postulate or theorem that justifies your answer
Answer:
Yes
Step-by-step explanation: The answer is Side Angle Side (SAS)
Use the diagram to complete the following tasks.
Given: S is the midpoint of QT.
Finish the following statement: AQRS = A_
Identify the congruent Zs.
Justify your answer.
The given statements:
1) ΔQRS ≅ ΔSTU (according to the ASA axiom)
2) The congruent ∠S: ∠RSQ ≅ ∠UST (Vertical angles)
What does the ASA axiom state?The ASA axiom states that "two triangles are said to be congruent if two pairs of corresponding angles and the sides between these angles are equal".
Finding the given tasks:It is given that,
S is the midpoint of QT.
So, SQ ≅ ST <S>
Since ∠S is at the intersection of two transversal lines, ∠RSQ ≅ ∠UST <A>. This is beacuse they are vertically opposite.
And QT is the transverse line for the parallel lines, QR║UT. So, the alternate angles(interior) are congruent. I.e., ∠SQR ≅ ∠UTS <A>.
From this, the given triangles have two equal corresponding angles and congruent sides in between them.
So, ΔQRS ≅ ΔSTU according to ASA axiom.
Therefore, ΔQRS ≅ ΔSTU and ∠RSQ ≅ ∠UST.
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Find the midpoints of A(-3,-9) and B (-8,-2) graphically
The midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)
Midpoint of coordinatesCoordinate points are written in the form (x, y). The midpoint of two points (x1, y1) and (x2, y2) is expressed as:
M(x, y) ={(x1+x2)/2, (y1+y2)/2}
Given the following coordinates A(-3,-9) and B (-8,-2)
M(x, y) = {(-3+(-8))/2, (-9-(-2))/2}
M(x, y) = {(-3-8)/2, (-9+2)/2}
M(x, y) = (-11/2, -7/2)
M(x, y) = (-5.5, -3.5)
Hence the midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)
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-2(x-0.5+1) i have this question and i really really really need help in solving it so...yeah!
Answer:
Step-by-step explanation:
Find the service area of a cylinder with a base diameter of 6ft and height of 4ft
The service area of the cylinder is 42[tex]\pi[/tex] square fts.
What is cylinder?Two parallel bases joined by a curving surface make up the three-dimensional solid known as a cylinder.
Typically, the bases are shaped like circles. The height "h" of the cylinder stands for the perpendicular distance between the bases, while "r" stands for the cylinder's radius.
The uses of cylinder are-
A popular piece of scientific equipment used to determine the volume of a liquid is a graduated cylinder, sometimes referred to as a measuring cylinder or mixing cylinder. Its form is slender and cylindrical. The measured amount of liquid is shown by each marked line on the graduated cylinder.Total surface area of the cylinder formula:
It is the sum of the base surface area and the lateral surface area;
Total area = base area + lateral area , or
Total area = 2 π r² + (2 π r) h , or
Total area = 2 π r (r + h)
Calculation for the total area of the cylinder;
Base diameter is 6 ft
Radius is 6/2 = 3 ft
Height is 4 ft
Total area = 2[tex]\pi[/tex]3(3 + 4)
= 6[tex]\pi[/tex]×7
= 42[tex]\pi[/tex]
Therefore, the total surface area of the cylinder is 42[tex]\pi[/tex] square fts.
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1. A circle has a radius of 12 in. Find:
The diameter of the circle.
The circumference of the circle.
The area of the circle.
2. A circle has a radius of 4.4 cm. Find:
The diameter of the circle.
The circumference of the circle.
The area of the circle.
3. A circle has a diameter of 60 m. Find:
The radius of the circle.
The circumference of the circle.
The area of the circle.
4. A circle has a diameter of 1.8 km. Find:
The radius of the circle.
The circumference of the circle.
The area of the circle.
Answer:
1.
a.) 24in
b.)75.36in
c.)452.16in
Step-by-step explanation:
1a. The radius is half of the diameter, so all you have to do is add 12 + 12 which is 24.
1b. the circumfrence of a circle is C (Circumfrence)=[tex]2\pi r[/tex] so replace radius for 12 and then do 3.14(pi) x 2 which will get you 6.28 times 6.28 by 12 and you will get 75.36.
1c. Area=[tex]\pi r^{2}[/tex] so first do the radius by the second power, or [tex]r * r[/tex], susitute r for 12 and you will get 144, times 144 by pi and you will get 452.16in
Sorry I could not answer every question but hope this helps!
Helen needs a replacement ball bearing for this part. The surface area of each spherical ball bearing is approximately 452.16 square millimeters. What is the radius of the bearing that Helen needs to buy? Round your answer to a whole number.
Helen needs a replacement ball bearing whose radius is 5.99mm
A sphere is a perfectly round geometrical 3-dimensional object. It can be characterized as the set of all points located distance r (radius) away from a given point (center). It is perfectly symmetrical, and has no edges or vertices.
The formula of surface area of the sphere is [tex]4\pi r^{2}[/tex] where r represents radius
Given: Surface area of ball = 452.16[tex]mm^{2}[/tex]
Using formula we get,
[tex]4\pi r^{2}[/tex] = 452.16[tex]mm^{2}[/tex]
r^2 = 452.16/4[tex]\pi[/tex]
r = 5.99 mm
Thus Helen needs a replacement ball bearing whose radius is 5.99mm
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Go to a clothing store with
your parent/guardian and
pick out one item that you
would like to purchase. How
much of a discount would
you have if the item had
25% off sale? What would
a
the sale price be?
Answer:
original price $75
discount $18.75
sale price $56.25
Step-by-step explanation:
I found a pair of dress pants for $75.
Since the discount is 25%, then the discount is
25% of $75 = 0.25 × $75 = $18.75
The sale price is the original price, $75, minus the discount, $18.75.
$75 - $18.75 = $56.25
Write an equation of a line that goes through (-18,13) and is perpendicular to 6x+4y=-16
Here,
y=mx+c
the slope of the line 6x+4y= -16 is -20.
if the two lines are perpendicular, the slope of 1st line * slope of second line=-1
the slope of the 2nd line is -1/2
y-y1=m(x-x1)
y-13=-1/2(x- -18)
when you solve, you get the equation of the line as 2y+x=50
In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.
If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.
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A system of linear equations is given by the tables. one of the tables is represented by the equation . x y 0 5 3 6 6 7 9 8 x y -6 9 -3 8 0 7 3 6 the equation that represents the other equation is y = x . the solution of the system is ( , )
The solution of the system would be (3,6).
Lets solve the problem,
Other equation: y = 1/3x+5
Slope-Intercept Form: y = mx + b
Slope Formula:
y2-y1/x2-x1 = m
Have to find equation now:
m = (6 - 5)/(3 - 0)
m = 1/3
y = 1/3x + b
5 = 1/3(0) + b
b=5
y = 1/3x + 5
Lets put the substituition method here,
1/3x + 5 = -1/3x + 7
2/3x + 5 = 7
2/3x = 2
x = 3
y = 1/3(3) + 5
y = 1 + 5
y = 6
Therefore the coordinates are (3,6)
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can anyone solve this 100+3-4(4-5) divided by 6+5+5+5+300
If you place a 39-foot ladder against the top of a building and the bottom of the
ladder is 33 feet from the bottom of the building, how tall is the building? Round to
the nearest tenth of a foot.
Answer:
20.8
Step-by-step explanation:
Just use the The Pythagorean Theorem
which is a^2+b^2=c^2
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A spinner has two equal sections, one green and one orange. The spinner is spun three times, resulting in the sample space S
The graph that is used to represent this probability distribution is the graph of b.
What is probability?In mathematics and the field of statistics, the probability is used tp denote likelihood of an event occurring.
The sample space is given as
S = {GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO}.
X=0, the Probability of having Orange(O), in GGG is given to be 1/8
X=1, we have to get the probability, in G G O , GOG,and O G G, this gives a total of 3 = 3/8
X=2, Probability of Orange O, in GOO , OGO, oog = 3/8
X=3, Probability of Orange O in all is also given as 1. Hence the probability is = 1/8
Complete questionA spinner has two equal sections, one green and one orange. The spinner is spun three times, resulting in the sample space S = {GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO}. If the random variable X represents the number of times orange, O, is spun, which graph represents the probability distribution?
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