Final answer:
To find the perimeter of the dilated rectangle A'B'C'D', we need to know the dimensions of the original rectangle ABCD and the scale factor of the dilation. The perimeter of A'B'C'D' is equal to the sum of the lengths of all the sides in the dilated rectangle. Since AB = A'B' and BD = B'D', the perimeter can be simplified to AB + BC + CD + BD.
Explanation:
To find the perimeter of the dilated rectangle A'B'C'D', we need to know the dimensions of the original rectangle ABCD and the scale factor of the dilation.
If the scale factor is 3, it means that each side of the original rectangle will be multiplied by 3 to get the corresponding side of the dilated rectangle.
Since the rectangle ABCD is dilated with a center of dilation at vertex D, the length of side AB remains the same in the dilated rectangle A'B'.
To find the perimeter of A'B'C'D', we need to compute the lengths of all the sides in the dilated rectangle and sum them up.
Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A'
Since AB = A'B' and BD = B'D', the perimeter can be simplified to:
Perimeter of A'B'C'D' = AB + BC + CD + BD
The perimeter of rectangle A'B'C'D', which is a dilation of rectangle ABCD by a scale factor of 3 with center D, is three times larger than the original perimeter of ABCD.
Explanation:If rectangle ABCD is dilated by a scale factor of 3 with a center of dilation at vertex D, to find the perimeter of A'B'C'D', we must first understand that a dilation scales all dimensions by the given factor. If the original lengths of the sides of rectangle ABCD are 'a' and 'b', with CD and AD being adjacent to vertex D, then after the dilation, the lengths of the corresponding sides would be '3a' and '3b'.
Since the perimeter of a rectangle is calculated by adding together the lengths of all its sides, the formula for the perimeter 'P' before dilation is P = 2a + 2b. After dilation, the new perimeter 'P' of A'B'C'D' will be P = 2(3a) + 2(3b) = 6a + 6b, which is simply three times the original perimeter. Therefore, the perimeter of rectangle A'B'C'D' after dilation is three times larger than the perimeter of the original rectangle ABCD.
Mags wants to know what the hottest hairstyle Trend in is in our town what is the best group to survey of to find this information
Answer:
You should choose the last option because it is the most random at choosing salons to ask and so will give the least biased answer.
Step-by-step explanation:
ask the hair salon and they will tell you what hairstyle is hottest
PLEASE HELP ME!!!
Kevin is responsible for delivering sacks of grains to a grocery shop on the tenth floor of a departmental store. Each sack weighs 364 pounds and Kevin weighs 150 pounds. The capacity of the elevator is 2,000 pounds. If six sacks are to be taken at a time, what should be the weight of each sack? Question 6 options: at the most 308 pounds at least 308 pounds exactly 308 pounds at the most 803 pounds
At the most 308 pounds / exactly 308 ((2000-150)/6=308) hope it helps
Answer:
At most 308 pounds
Step-by-step explanation:
Let x pounds be the new weight of the sacks,
⇒ The weight of 6 sacks = 6x,
Now, the weight of Kevin = 150 pounds,
Thus, the total weight Kevin and 6 sacks = 150 + 6x,
Given,
The capacity of the elevator is 2,000 pounds,
⇒ 150 + 6x ≤ 2000
⇒ 6x ≤ 2000 - 150 ( Subtraction property of inequality )
⇒ 6x ≤ 1850
⇒ x ≤ 308.33 ≈ 308
Hence, the weight of each sack is approximately atmost 308 pounds.
someone please help me answer this i have about 20 min left to this quiz and this is the last question.
The regression line modeling the number of push-ups Juan does each day is y = 0.631x + 0.0357.
Which one doesn't explain the graph correctly?
1. There is a negative correlation between time (in days) and the number of push-ups Juan does.
2. Juan increases the number of push-ups he does by about 0.631 each day.
3. The response variable is the number of push-ups
4. The explanatory variable is time (days)
Answer:
The correct Answer is C: The response variable is the number of push-ups. Good luck kid!
Step-by-step explanation:
If the length of each edge of the cube is doubled, the surface area will increase 2 times.True or false
Answer:
False. The surface area of the cube will increase to four times its initial value.
Step-by-step explanation:
Consider a cube with edge of lengths [tex]a[/tex]. What will be its surface area?
Each face of a cube is a square. The lengths of sides of the square are also [tex]a[/tex].
The area of each square will be the square of its sides: [tex]a \cdot a = a^{2}[/tex].
It takes six such squares to make a cube. The sum of the area of the sube [tex]6a^{2}[/tex] will also be the surface area of the cube.
In case the length of each side of the cube is doubled to [tex]2a[/tex].
The area of each face will become [tex](2a)^{2} = 4a^{2}[/tex].The sum of the area of the six sides will become [tex]6 \times 4a^{2} = 24a^{2} = 4 \times 6a^{2}[/tex], which is four times the initial surface area of [tex]6a^{2}[/tex].Find the vertex, focus, directrix, and focal width of the parabola.
-1/16x^2 = y
a. Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16
b. Vertex: (0, 0); Focus: (-8, 0); Directrix: x = 4; Focal width: 64
c. Vertex: (0, 0); Focus: (0, 4); Directrix: y = -4; Focal width: 4
d. Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 64
Answer:
Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16 ⇒ answer (a)
Step-by-step explanation:
* Lets revise some facts about the parabola
- Standard form equation for a parabola of vertex at (0 , 0)
- If the equation is in the form x² = 4py, then
- The axis of symmetry is the y-axis, x = 0
- 4p equal to the coefficient of y in the given equation to
solve for p
- If p > 0, the parabola opens up.
- If p < 0, the parabola opens down.
- Use p to find the coordinates of the focus, (0 , p)
- Use p to find equation of the directri , y= − p
- Use p to find the endpoints of the focal diameter, (±2p , p)
* Now lets solve the problem
- The vertex of the parabola is (0 , 0)
∵ -1/16x² = y ⇒ multiply each side by -16
∴ x² = -16y
∴ 4p = -16 ⇒ ÷ 4 tbe both sides
∴ p = -4
∵ The focus is (0 , p)
∴ The focus is (0 , -4)
∵ The directrix is y = -p
∴ The directrix is y = -(-4) = 4 ⇒ y = 4
∵ The endpoints of the focal diameter, (±2p , p)
∴ The focal width = 2p - (-2p) = 4p
∴ The focal width = 4 × I-4I = 16
* Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16
Answer:
A
Step-by-step explanation:
i just took the edg quiz
The price of a gallon of milk was $2.65. The price rose y dollars after the last hurricane. Then the price dropped $0.15 and later rose again by $0.05. Which expression represents the current price of milk? A) 2.40 + y B) 2.45 + y C) 2.50 + y D) 2.55 + y
Answer:
D
Step-by-step explanation:
So you start with $2.65 and a variable y. What we will do is work without the dollar and keep it for the end as it quite disturbs and work our way while keeping the y. So first we have 2.65. Now it rose by y so. The price = 2.65 + y. Then it dropped by 0.15. So 2.65 + y - 0.15. Here you see we have like terms so we reduce and get 2.50 + y. Now it rose by 0.05. So 2.50 + y + 0.05. Again, like terms, reduce. 2.55 + y. There you go with the answer.
Final answer:
The current price of milk, after it first increased by an unknown amount y, then decreased by $0.15, and finally increased by $0.05, is represented by the expression $2.55 + y, which is Option D.
Explanation:
The question asks us to calculate the current price of a gallon of milk after a series of price changes. The original price was $2.65. After a hurricane, the price increased by y dollars. Subsequently, the price dropped by $0.15, and then again rose by $0.05.
To find the new price, we start with the original price and apply the changes step by step:
Original price: $2.65
Price after hurricane increase: $2.65 + y
Price after $0.15 drop: ($2.65 + y) - $0.15 = $2.50 + y
Price after $0.05 rise: ($2.50 + y) + $0.05 = $2.55 + y
Hence, the correct answer representing the current price of milk after these changes is Option D) $2.55 + y.
When you purchase an item in a store, you may be charged __________. Income tax capital gains tax sales tax property tax
Sales tax
At least 20 characters blahhhhh
Answer:
The answer is sales tax.
Step-by-step explanation:
When you purchase an item in a store, you may be charged sales tax.
A sales tax is imposed on the buyer, when he purchases something. This tax is imposed by the government on the sale of goods and services.
A typical sales tax is applied at the point of sale and collected by the retailer or seller and then passed on to the government.
Please help me please
Answer:
60°
Step-by-step explanation:
The radius of the circle is given as 7 ( centre of circle to point C )
The other radius is also 7 ( from centre to point D)
CD = 7
The triangle is therefore equilateral ( all 3 sides = 7 )
The angles of an equilateral triangle are equal and measure 60°
Hence mCD = 60°
Find the derivative of f(x) = -2x2 + 11x at x = 9.
a) -25
b) -243
c) 63
d) 19
[tex]\bf f(x)=-2x^2+11x\implies \left. \cfrac{df}{dx}=-4x+11 \right|_{x=9}\implies -4(9)+11\implies -25[/tex]
Answer:
a) -25
Step-by-step explanation:
First you have to find the derivative of F(x):
[tex]f(x)=2x^{2} +11x\\Derivative=2(2x)+1(11)\\Derivative=4x+11[/tex]
Now you just have to calculate the vale of f(x) when x=9
[tex]-4x+11=\\-4(9)+11=\\-36+11=-25[/tex]
So when x=9, the derivative of [tex]f(x)=2x^{2} +11x[/tex] is equal to -25
A bacteria culture begins with 13 bacteria which triple in amount at the end of every hour. How many bacteria are grown during the 10th hour?
Answer:
255,879
Geometric Sequence Formula
[tex]a_n = a1r^{(n-1)}\\\\a_1 :13\\\\r:3\\\\n:10\\[/tex]
Steps:
[tex]a_1_0=13 (3)^{(10-1)}\\\\a_1_0=13(3)^{(9)}\\\\a_1_0=(13)19683\\\\a_1_0=255,879[/tex]
A medical company tested a new drug on 100 people for possible side effects. This table shows the results. Compare the probability that an adult has side effects with t he probability that a child has side effects. Draw a conclusion based on your results.
Answer:p(side effects| child)=0.42
P(side effects|adults)=0.12
Step-by-step explanation:
Children are twice as likely as adults to experience side effects from the new drug.
The probability that an adult has side effects is 0.12,
while the probability that a child has side effects is 0.42.
This means that children are more likely to experience side effects from the new drug than adults.
We can calculate the probability of side effects for each group by dividing the number of people who experienced side effects by the total number of people in the group:
Probability of side effects in adults = [tex]\frac{6}{50}[/tex] = 0.12
Probability of side effects in children = [tex]\frac{21}{50}[/tex]= 0.42
We can also see this difference in the table provided. Children are more likely to experience side effects from the new drug than adults.
Children are more likely to experience side effects from the new drug than adults
For similar question on side effects
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Please help :)........
Answer:
SSS
Step-by-step explanation:
Ratio of the corresponding sides of both triangles are equal, so triangles are similar by SSS.
[tex]\frac{6}{9} =\frac{2}{3} \\\frac{14}{21}=\frac{2}{3}\\\frac{16}{24}=\frac{2}{3}[/tex]
Find the value of csc theta ; if cos theta= -1/4 ; 180° < theta < 270°.
can y'all explain your answer for me lol
A.) 4/-15
B.) 4/√15
C.) -4
D.) -4/√15
Answer:
D
Step-by-step explanation:
Using the trigonometric identities
• cscx = [tex]\frac{1}{sinx}[/tex]
• sin²x + cos²x = 1
Given
cosΘ = - [tex]\frac{1}{4}[/tex] , 180 < Θ < 270
then Θ is in the third quadrant where sinΘ < 0
sinx = - [tex]\sqrt{1-cos^2x}[/tex]
sinΘ = - [tex]\sqrt{1-(-1/4)^2}[/tex] = - [tex]\sqrt{\frac{15}{16} }[/tex] = -[tex]\frac{\sqrt{15} }{4}[/tex]
Hence
cscΘ = [tex]\frac{1}{-\frac{\sqrt{15} }{4} }[/tex] = - [tex]\frac{4}{\sqrt{15} }[/tex]
please help me out
The equation 9(w + 7) = 27 solved in several steps below.
For each step, choose the reason that best justifies it.
The options are the same for each one.
For this case we have the following equation:
[tex]9 (w + 7) = 27[/tex]
To solve we follow the steps below:
We apply Distributive Property to the terms of parentheses:
[tex]9w + 63 = 27[/tex]
We apply Subtraction Property of equality by subtracting 63 from both sides of the equation:
[tex]9w + 63-63 = 27-63\\9w = -36[/tex]
We apply Division Property of equality by dividing by 9 on both sides of the equation:
[tex]\frac {9w} {9} = \frac {-36} {9}[/tex]
simplifiying
w = -4
Answer:
[tex]w = -4[/tex]
A local radio station surveyed people going into a grocery store about whether or not they liked country and if they listed to that station. The results are shown in the table.
Is listening to the radio station independent of liking country music? Explain.
A) No, the probability of not liking country is the same as the probability of not liking country given that they listen to the station.
B) Yes, the probability of not liking country is the same as the probability of not liking country given that they listen to the station.
C) No, the probability of not liking country is different from the probability of not liking country given that they listen to the station.
D) Yes, the probability of not liking country is different from the probability of not liking country given that they listen to the station.
Answer:
B
Step-by-step explanation:
51 /22= 2.3
19/8=2.3
The correct option is D) Yes, the probability of not liking country is different from the probability of not liking country given that they listen to the station.
What is the probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
Given that, a local radio station surveyed people going into a grocery store about whether or not they liked country and if they listed to that station,
We need to determine that if listening to the radio station independent of liking country music,
So, here the answer will be yes, because both the events are not connected to each other.
The probability of not liking or liking the country music is nowhere related to whether a person is listening to the radio station or not.
Hence, the correct answer is D
Learn more about probability click;
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Please explain how to do unit conversion, for example a rectangle has a width of 12cm and a length of 5cm and you're solving for the area obviously, it would be 60cm but in the answer key for this question, it has it as 60mm squared. please explain! i'd also like to know when you square and cubed! :)
6 CM would make it 60mm because you would do length timeth width
" The area of the rectangle is 60 cm², which is equivalent to 6000 mm².
To calculate the area of a rectangle, one multiplies the length by the width. In this case, the rectangle has a width of 12 cm and a length of 5 cm. Therefore, the area (A) is calculated as follows:
[tex]\[ A = \text{length} \times \text{width} \][/tex]
[tex]\[ A = 5 \, \text{cm} \times 12 \, \text{cm} \][/tex]
[tex]\[ A = 60 \, \text{cm}^2 \][/tex]
The area is obtained in square centimeters (cm²) because we multiplied two lengths measured in centimeters.
Now, to convert the area from square centimeters to square millimeters, we need to remember that there are 10 millimeters in a centimeter. Therefore, when converting from cm² to mm², we must square the conversion factor because we are dealing with a two-dimensional measurement:
[tex]\[ 1 \, \text{cm}^2 = (1 \, \text{cm})^2 = (10 \, \text{mm})^2 = 100 \, \text{mm}^2 \][/tex]
Now, we can convert the area from cm² to mm²:
[tex]\[ 60 \, \text{cm}^2 = 60 \times 100 \, \text{mm}^2 \][/tex]
[tex]\[ 60 \, \text{cm}^2 = 6000 \, \text{mm}^2 \][/tex]
Say I have an 81 in a class and my final assignment is 30%of my grade, If i fail how much will that bring my grade down?
Answer:
A lot. probably down to a 60
Determine the equation of the graph:
Answer:
Choice A
Step-by-step explanation:
In order to determine the equation of the graph, we can simply graph the four equations using an online graphing utility like desmos graphing tool and then run a comparison to identify the appropriate equation of the given graph.
Below are the graphs of the 4 given equations. The graphs were obtained using the desmos online graphing utility;
From the graphs below, the graph that matches the given graph is the one obtained from;
y = x cosx
This is the equation of the given graph
Help me on my geometry homework
Answer: hell na
Step-by-step explanation:
Answer:12
Step-by-step explanation:
(15x-26)+26=180
15x=180
X=12
A right cone has a radius of 13 cm and an altitude of 52 cm. Find its surface area.
A. 2,668.7 cm2
B. 865.8 cm2
C. 849.5 cm2
D. 2,720.0 cm2
Answer:
Option B. [tex]865.8\pi\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the cone is equal to
[tex]SA=\pi r^{2} +\pi rl[/tex]
we have
[tex]r=13\ cm[/tex]
[tex]h=52\ cm[/tex]
Find the slant height l
Applying Pythagoras \theorem
[tex]l^{2}=r^{2} +h^{2}[/tex]
substitute the values
[tex]l^{2}=13^{2} +52^{2}[/tex]
[tex]l^{2}=2,873[/tex]
[tex]l=53.6\ cm[/tex]
Find the surface area
[tex]SA=\pi(13)^{2} +\pi(13)(53.6)=865.8\pi\ cm^{2}[/tex]
You usually buy a 5.4 ounce bottle of lotion. There is a new bottle that says it gives you 20% more free.
Use the drop-down menus to build an equation that could be used to find the size of the larger bottle, .
Answer: If you want to find out how much 20 percent of 5.4 is, you have to multiply, the equation would be
5.4 x .2 = 1.08, so it will give you 1.08 more
Step-by-step explanation:
You're given two side lengths of 3 centimeters and 5 centimeters. Which measurement can you use for the length of the third side to construct a valid triangle? A. 8 centimeters B. 6 centimeters C. 4 centimeters D. 10 centimeters E. 2 centimeters Select all answersCorrect answers plezz
Answer: To find the third side of a triangle (there are two answers you could get), you need to use the Pythagorean formula: a^2+b^2=c^2. First answer, 3^2+5^2=c^2. Solve for c. c=5.83. The second answer, 3^2+b^2=5^2. Solve for b. b=4.
\
Which function has a range of (- π/2, π/2) ?
The function with a range of (-π/2, π/2) is the arc sine function, denoted as y = sin-1(x) or y = arcsin(x).
Explanation:The range of a function is the set of all possible output values it can produce. When referring to a function with a range of (-π/2, π/2), we are usually considering trigonometric functions, particularly the inverse trigonometric functions. The function that has a range between -π/2 and π/2 is the arc sine function, denoted as y = sin-1(x) or y = arcsin(x). This is because the arc sine function is the inverse of the sine function, which oscillates between -1 and 1, and thus its inverse must have a range where the angle could be between -π/2 and π/2 to accommodate this domain.
The sine function itself, which a student might initially think of due to its oscillation, has a domain of all real numbers and a range of [-1,1], so it does not fit the criteria given by the range (-π/2, π/2). It is important to recognize that, while a sine function oscillates between +1 and -1, its inverse function, arc sine, is the one with the specified range as mentioned in the question.
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What is the function rule represented by the following mapping diagram?
y = -5x + 1
y = x + 1
y = -3x - 1
y = -4x
Answer:
i feel like the answer is y=-3x - 1 but at the same time i think its wrong.
Step-by-step explanation:
Answer:y=-3x - 1
Step-by-step explanation:
You buy a new home in Metropolis (CONGRATULATIONS!) for $374,848. Prices of homes in your area are continuously increasing by 5% per year. How much should your new home be worth in 13 years?
Answer:
618499.2
answer step by step
5%×13=65
65%×374848=243651.2
243651.2+374848=618499.2
Fifteen points for an answer! Brainliest for a step-by-step/explanation!
What is the factored form of this expression?
3x-9
Answer:
3(x-3)
Step-by-step explanation:
First, we can see that both 3 and 9 are divisible by 3. So we know that 3/3=1 and 9/3=3.
When factoring equations, there have to be parenthesis so it's more organized. So we can put 3 outside of parenthesis:
3(x-3)
The reason we put the 3 outside of parenthesis is because when we multiply 3 by everything in the parenthesis, we will get the equation we originally started with, which is 3x-9.
So the answer is 3(x-3)
Hope I helped!
~Mschmindy
The base of a regular pyramid is a hexagon.
What is the area of the base of the pyramid?
Enter your answer in the box. Express your answer in radical form.
cm²
ANSWER
[tex] 96 \sqrt{3} {cm}^{2} [/tex]
EXPLANATION
The area of a regular polygon is
[tex]Area= \frac{1}{2} ap[/tex]
where 'a' is the apothem of the polygon and 'p' is the perimeter of the polygon.
From the diagram,
[tex] \sin(60) = \frac{a}{8} [/tex]
a=8sin(60)
[tex]a = 4 \sqrt{3} [/tex]
[tex] \cos(60) = \frac{l}{8} [/tex]
[tex]l = 8 \cos(60) [/tex]
[tex]l = 4[/tex]
The length of one side of the hexagon is 2×4=8.
The perimeter of the hexagon is
p=6×8=48
The area of the hexagon is
[tex] = \frac{1}{2} \times 4 \sqrt{3} \times 48[/tex]
[tex] = 96 \sqrt{3} {cm}^{2} [/tex]
a 4 sided cube, numbered 1-4, is rolled twice. Determine the sample space. how many possible outcomes are there?
Answer:
16
Step-by-step explanation:
1 1
1 2
1 3
1 4
2 1
2 2
2 3
2 4
Three and four are done exactly the same way. the total is 16 ways.
Write the equation in standard form for the circle x2+y2–36=0.
Answer:
x^2 + y^2 = 36
Step-by-step explanation:
Just add 36 to both sides. This is a circle with the center at the origin and radius 6.
Final answer:
The equation in standard form for the circle x² + y² – 36 = 0 is x² + y² - 9x - 12y + 36 = 0.
Explanation:
The equation in standard form for the circle x² + y² – 36 = 0 is:
x² + y² - 9x - 12y + 36 = 0
This equation can be obtained by completing the square. Rewrite the equation as: (x² - 9x) + (y² - 12y) = 36. Complete the square for both the x and y terms by adding the square of half the coefficient of each term.
To complete the square for the x terms, add (9/2)² = 81/4, and for the y terms, add (12/2)² = 36 to both sides of the equation.
Simplify the equation to: x² - 9x + (81/4) + y² - 12y + 36 = 36 + (81/4) + 36.
Combine like terms and simplify further to obtain the standard form of the equation: x² + y² - 9x - 12y + 36 = 0.
Please help me out.....
Answer:
a = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Since the triangle is right use the tangent ratio to find a, that is
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{a}{12}[/tex]
Multiply both sides by 12
12 × tan30° = a
12 × [tex]\frac{1}{\sqrt{3} }[/tex] = a
Rationalise the denominator on the left side by multiplying the numerator/ denominator by [tex]\sqrt{3}[/tex]
12 × [tex]\frac{\sqrt{3} }{3}[/tex] = a ( cancel the 12 and 3 )
a = 4[tex]\sqrt{3}[/tex]