The correct coordinates of the center of dilation are (2.8, 3.8).
What is dilation?
In geometry, dilation is a transformation that changes the size of an object. When a figure is dilated, each point of the original figure is moved away from or toward the center of dilation.
Dylan's claim is incorrect because the center of dilation is not necessarily located on the line segment PP'.
To find the center of dilation, we need to locate the image point of a known point after dilation.
Let's consider a point Q on the same line as PP', but on the other side of P', such that PQ = 1 unit. After dilation with a scale factor of 4, the image of Q will be on the line passing through P and P'. Let's denote this image point by Q'.
Since PQ : P'Q' = 1 : 4, the distance from P to Q' is 4 units. Similarly, since PP' : PQ' = 1 : 5, the distance from P to Q' is 5 times the distance from P to P'. Thus, the distance from P to P' is 1 unit and the distance from P to Q' is 5 units.
Therefore, the center of dilation is located on the line passing through P and Q', and is 4 units away from P and 1 unit away from Q'.
Using the midpoint formula, we can find the coordinates of the center of dilation:
[tex]x &= \frac{1}{2}(4.8 + 0.8)[/tex]
[tex]&= 2.8[/tex]
[tex]y &= \frac{1}{2}(3.2 + 4.4)[/tex]
[tex]&= 3.8[/tex]
Thus, the correct coordinates of the center of dilation are (2.8, 3.8).
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Help Please! (And FAST) THANK YOU
Answer:
(6,3)
(-6,3)
Step-by-step explanation:
14. (Find LCM of) : ax² - (a² + ab)x+ a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x+ c²a
Answer:
Step-by-step explanation:
To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.
ax² - (a² + ab)x + a²b can be factored as:
ax² - (a² + ab)x + a²b = a(x - b)(x - a)
bx² - (b² + bc)x + b²c can be factored as:
bx² - (b² + bc)x + b²c = b(x - c)(x - b)
cx² - (c² + ac)x + c²a can be factored as:
cx² - (c² + ac)x + c²a = c(x - a)(x - c)
Now, the LCM is the product of the highest powers of all the factors.
The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:
LCM = a²b²c²(x - a)(x - b)(x - c)
Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).
Find the surface area of the composite figure shown below that
consists of a right cone sitting atop a right cylinder. Use 3.14 form and
give the answer in square meters.
1-20 m
r 13 m
h=13m
Using the right cone formula we know that the surface area is 1281.77638m³ respectively.
An axis that is perpendicular to the base plane defines a right circular cone. By rotating a right triangle around one of its legs, we may create a right cone.
The right circular cone in the illustration has an axis that is perpendicular to the base and a circular base with a radius r.
So, the formula for the surface area of the right cone is as follows:
πr(r+√h²+r²)
We have the values: r = 13m and h = 13m
Now, insert values as follows:
= πr(r+√h²+r²)
= π13(r+√13²+13²)
= 1281.77638
Therefore, using the right cone formula we know that the surface area is 1281.77638m³ respectively.
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Relationships and Equations Homework
For #1–3, evaluate to find the value of y. Show your work.
y=4x-7
If x=8, what is y?
If x=3, what is y?
y=2x2
If x=3, what is y?
If x=5, what is y?
y=(2+x)2
If x=1, what is y?
If x=3.5, what is y?
For #8–15, write < , > , or = to make each statement true.
2.4 2.8
53 1.666….
1.43 .296
92 4.500
5.62 5.602
0.32 0.032
314 318
3437 3435
Answer:
Step-by-step explanation:
If x=8, y = 4(8) - 7 = 25
If x=3, y = 4(3) - 7 = 5
If x=3, y = 2(3^2) = 18
If x=5, y = 2(5^2) = 50
If x=1, y = (2+1)^2 = 9
If x=3.5, y = (2+3.5)^2 = 30.25
2.4 < 2.8
53 > 1.666…
1.43 > .296
92 > 4.500
5.62 > 5.602
0.32 > 0.032
314 < 318
3437 > 3435
The Harris Family Entertainment Club deposited R3 600 in an investment account a year ago, with the intention of purchasing new equipment in four years’ time. Today, it is adding a further R5 000 to this account. Plans are to make a final deposit of R7 500 in the account next year. How much will be available when the family is ready to buy the equipment, assuming the investment earns a 7% rate of return?
Answer:
Step-by-step explanation:
To calculate this, we need to use the formula for future value of an annuity:
FV = PMT x ((1+i)^n - 1)/i
Where:
PMT = the periodic payment (or deposit)
i = the interest rate per period
n = the number of periods
In this case, there are three deposits:
- R3,600 deposited one year ago
- R5,000 deposited today
- R7,500 to be deposited next year
We can calculate the future value of each of these deposits separately, and then add them together to get the total future value:
Future value of R3,600 deposited one year ago:
n = 4 (4 years until the equipment purchase)
i = 7% per year
PMT = R3,600
FV = R3,600 x ((1+0.07)^4 - 1)/0.07 = R4,661.07
Future value of R5,000 deposited today:
n = 3 (3 years until the equipment purchase)
i = 7% per year
PMT = R5,000
FV = R5,000 x ((1+0.07)^3 - 1)/0.07 = R6,885.02
Future value of R7,500 to be deposited next year:
n = 2 (2 years until the equipment purchase)
i = 7% per year
PMT = R7,500
FV = R7,500 x ((1+0.07)^2 - 1)/0.07 = R8,733.63
Total future value = R4,661.07 + R6,885.02 + R8,733.63 = R20,279.72
Therefore, there will be R20,279.72 available when the family is ready to buy the equipment, assuming a 7% rate of return on the investment.
Note: For questions 13–21, remember to show all of the steps that you use to solve the problem. You can use the comments field to explain our work. Your teacher will review each step of your responses to ensure your receive proper credit for your answers.
Note: Your teacher will grade your response to this question to ensure you receive proper credit for your answer.
Complete the proof.
Given: AB · BE = CB · BD
Prove: ΔABC ~ ΔDBE
PLEASE HELP! LAST ONE! ILL GIVE BRAINLIST AGAIN IF I CAN!
We have shown that ΔABC ~ ΔDBE because the corresponding angles are congruent and the corresponding sides are proportional.
Does a ratio imply equality?The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well.
We must demonstrate that the respective angles of the two triangles are congruent and the corresponding sides are proportionate in order to demonstrate that ABC DBE.
To begin with, we can relate the sides of the two triangles using the following equation AB BE = CB BD. Let x, y, and z all be equal to AB. Next, we have:
x · BE = y · z (substituting the given values)
y/x = BE/BD (dividing both sides by BD and then by x)
Now, we can utilise the knowledge that a triangle's angles sum to 180 degrees to get the length of ABC:
ACB - 180° = ABC (from the given triangle ABC)
ABC = 180 degrees - BDE (corresponding angles)
The measure of BDE can then be determined using the connection between the sides that we discovered earlier:
y/x = BE/BD (from above)
BE/DE = y/(x+z) (substituting z = BD)
BDE is equal to tan(y/(x+z)) Inverse tangent is used.
Now, we can use the fact that a triangle's angles sum to 180 degrees to determine the size of the DBE:
DBE = 180°, BDE, and BED
DBE is equal to 180 - tan(y/(x+z)) - ∠BED (substituting the angle measure we just found) (substituting the angle measure we just found)
DBE is equal to 180° - tan(y/(x+z)) - tan(y/z) (using inverse tangent again)
tan(z(y+x)/(xz-yz)) = DBE (using the tangent of the sum formula)
In order to demonstrate that the sides of the two triangles are proportional, we can once more use the relationship between the sides:
BE/BD = AB/CB (from the given equation and simplification)
Y/x = AB/CB (from the relationship between the sides)
As a result, we have demonstrated that ABC DBE since the associated angles and sides are congruent and proportionate, respectively.
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can someone please solve????!! thanks
Answer:
(a) Figure 3
(b) 66.2 meters per second
Step-by-step explanation:
You want to know the figure that shows the best fit of a curve to the data, and you want to know the value of the curve when x = 8 seconds.
Best fitThe fit is best when the difference between the data points and the curve is minimized. Often the sum of the squared differences is the metric that is minimized when the fit is best.
The gaps between the data points and the curve shown are greatest in Figures 1 and 2, so Figure 3 has the best fit.
Estimated valueThe speed is estimated by the equation of the curve of best fit as ...
y = 0.6x² +2.1x +11
A slight rearrangement can make this easier to evaluate:
y = (0.6x +2.1)x +11
For x=8, the value of y is ...
y = (0.6·8 +2.1)·8 +11 = 6.9·8 +11 = 66.2
The predicted speed at 8 seconds is 66.2 meters per second.
help plsssss… i don’t understand & or know how to do it
Answer: sorry I can't see it.
Step-by-step explanation:
Simplificacion de 18/25
Answer:
Step-by-step explanation:
Ici, nous allons réduire la fraction 18/25 aux termes les plus bas et la convertir en un nombre fractionnaire, si nécessaire.
Dans la fraction 18/25, 18 est le numérateur et 25 est le dénominateur.
On commence par trouver le plus grand diviseur commun de 18 et 25, qui est 1. Ensuite, on divise 18 et 25 par le plus grand diviseur commun pour obtenir la plus petite expression, écrite comme suit :
(18 ÷ 1) / (25 ÷ 1)
= 18/25
Wally Martin purchased an office chair for $167.87. He received a $19.95 rebate from the manufacturer and a $8.95 rebate from the store. What is the final price?
What is the area of circle C rounded to the nearest tenth?
Use 3.14 for π .
138.2 cm 2
276.3 cm2
1314.8 cm 2
1519.8 cm2
Answer:
D. 1519.8
Step-by-step explanation:
Demi went for a run in the park. The graph shows her speed during the run
The answer of the given question based on the graph and the function the answer are,
a) Demi's speed is decreasing over time.
b) Demi's speed decreases from approximately 8.5 miles per hour to 5 miles per hour and Demi's speed decreases from approximately 6 miles per hour to 3 miles per hour.
What is Speed?Speed is measure of how fast object is moving, or rate at which it covers certain distance over time. Mathematically, speed is calculated as distance traveled divided by time it takes to travel that distance.
a. When the function is decreasing, Demi's speed is decreasing over time. This means that she is running more slowly as time goes on. On the graph, this will be shown as a downward slope or a negative slope. The steeper the slope, the faster her speed is decreasing.
b. From the graph, we can see that the function is decreasing in two intervals. The first interval is from 0 to 5 minutes, where Demi's speed decreases from approximately 8.5 miles per hour to 5 miles per hour. The second interval is from 10 to 15 minutes, where Demi's speed decreases from approximately 6 miles per hour to 3 miles per hour.
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Incomplete question ,the full question is ,Demi went for a run in the park. The graph shows her speed during the run.
a. Describe the graph when the function is decreasing.
b. In how many intervals is the function decreasing?
*PLEASE HELP ME!*
Explore
Here is a number pyramid puzzle. Fill in the blanks so that each number is the product of the two numbers directly beneath it.
The blanks of the number pyramid puzzle can be filled with numbers calculated below.
How fill in the blanks of the number pyramid puzzle?
A number pyramid puzzle is a type of mathematical puzzle where a pyramid-shaped grid of numbers is given, with some of the numbers missing.
Check the attached image for labeling. Since each number is the product of the two numbers directly beneath it. We can say:
m = -4 * 0.5 = -2
k = 0.5 * 1/8 = 1/16
x * (-1/8) = 8
x = 8/(-1/8)
x = -64
y = x * 1/8
y = -64 * 1/8
y = -8
j = m * k
j = -2 * 1/16 = -1/8
p = -48 * m
p = -48 * (-2) = 96
n = y * 8
n = -8 * 8 = -64
t = p * j
t = 96 * (-1/8) = -12
w = -1/2 * n
w = -1/2 * (-64) = 32
c = t * 1/16
c = -12 * 1/16 = -3/4
u = 1/16 * w
u = 1/16 * 32 = 2
d = c * u
d = -3/4 * 2 = -3/2
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Find the mean of the data set. 3, 22, 0, 15, 9, 23
Answer:
12
Step-by-step explanation:
Mean = 3+22+0+15+9+23=72
72÷6 =12
prove this question in the image please
The parallelogram ABCD's congruency can be proven using Side-Angle-Side (SAS) congruence theorem.
How to prove congruency?Prove that ΔABC ≅ ΔDCB using the Side-Angle-Side (SAS) congruence theorem.
Given that ABCD is a parallelogram, AB || CD and BC || AD. Therefore, ∠ABC ≅ ∠DCB and ∠ACB ≅ ∠DCA because they are corresponding angles.
AB ≅ CD and BC ≅ AD because opposite sides of a parallelogram are congruent.
Lastly, AC ≅ AC because it is a shared side between the two triangles.
Therefore, the following congruent parts:
∠ABC ≅ ∠DCB (by corresponding angles)
AB ≅ CD (by opposite sides)
BC ≅ AD (by opposite sides)
AC ≅ AC (shared side)
The SAS congruence theorem concludes that ΔABC ≅ ΔDCB.
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Image transcribed:
Prove ΔABC ≅ ΔDCB
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $200.
If they offer a 2 year extended warranty for $22, what is the company's expected value of each warranty sold?
$
Therefore , the solution of the given problem of percentage comes out to be the firm expects that each warranty it sells will be worth $1.41.
What is percentage?In statistics, "a%" is used to refer to a figure or number that is expressed as a percentage of 100. Additionally rare are the forms that "pct," "pct," or "pc". It is typically represented by the symbol "%," though. Additionally, there are not any indicators and the proportion of each item to the overall amount is flat. Since percentages typically add up to 100, they are essentially integers. Either the expression "fraction" or the symbol for percentage (%) .
Here,
The price to substitute each item is $200. The anticipated price for each component is thus:
Expected cost per product equals Replacement cost x Failure Probability
=> Cost per product anticipated = 0.008 x $200
=> Expected price per item is $1.60.
So, the following is the anticipated value of each warranty sold:
Expected worth of the warranty = Failure rate x (Replacement cost - Cost of warranty)
=> Expected guarantee value = 0.008 * ($200 - $22 - $1.60).
=> Expected guarantee value = 0.008 * $176.40
=> Expected warranty worth is $1.41
As a result, the firm expects that each warranty it sells will be worth $1.41.
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PLEASE HELP! Find missing side lengths of B and C. Explain
Answer:
b=7 & c=7√2
Step-by-step explanation:
b=7 as it is an isosceles triangle
now using Pythagoras theorem,
(c)^2= (7)^2+(7)^2
⇒(c)^2= 49+49
⇒(c)^2= 98
⇒c= √98
⇒c=7√2
Answer:
b = 7c = 7√2Step-by-step explanation:
You want the missing side lengths in an isosceles right triangle with one side given as 7.
Isosceles right triangleThe two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:
b = 7
The hypotenuse of an isosceles right triangle is √2 times the side length:
c = 7√2
__
Additional comment
You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.
c² = 7² + b²
c² = 7² +7² = 2·7²
c = √(2·7²) = 7√2
The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.
The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.
The radius of a circle is 11 meters. What is the circle's circumference?
Use 3.14 for л.
r=11 m
Answer:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of r=11 m and using π = 3.14, we get:
C = 2πr
C = 2 x 3.14 x 11 m
C = 69.08 m
Therefore, the circumference of the circle is 69.08 meters
Is ∆PQR a right triangle? Explain
Answer:
Yes, ∆PQR is a right triangle.
Step-by-step explanation:
A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.
Mr. Valdez has $95 in his budget to buy paint brushes and
boxes of colored pencils. He will buy an equal number of
each art supply. The cost of each item is shown in the table.
The inequality 3n+ 5n at least 95 can be used to find the
number of each item that he can buy. How much money will
Mr. Valdez have left in the budget after buying the greatest
number of paint brushes and colored pencils?
Answer:
3n + 5n = 8n = 95
n = 11
$95 - $88 = $7
(11 paint brushes, 11 boxes of colored pencils)
21 students in the class like chocolate ice cream. this is 75% of the class. how many students are in the class?
Answer:
28 people
Step-by-step explanation:
21 / 3 = 25
7 = 25%
25 x 4 = 100%
so
7 x 4 = 28
28 people are in the class
70% of 140 is what value? 20 70 84 98
Answer:
Step-by-step explanation:
70% of 140 is equal to 0.7 x 140 = 98. Therefore, the answer is 98.
Answer:
98
Step-by-step explanation:
70% can also be written as 0.7, therefore, we can multiply 140 by 0.7.
140 x 0.7 = 98.
Write a quadratic function for the area of the figure. Then, find the area for the given value of x. x = 20 A quadratic function for the area of the figure is A(x) = (Simplify your answer.) ... X
answer: x= 20x
Step-by-step explanation: 2+2 is 4, 4+4 is 8, quick maths
What is the image of the point (7, 0) when the translation rule (x, y)→(x+1, y−2) is used?
(1, −2)
(8, −2)
(6, 2)
(5, 1)
Answer:
To find the image of the point (7, 0) under the given translation, we apply the translation rule:
(x, y) → (x + 1, y - 2)
Substituting (7, 0) for (x, y), we get:
(7, 0) → (7 + 1, 0 - 2)
= (8, -2)
Therefore, the image of the point (7, 0) under the given translation is (8, -2).
So, the correct answer is (8, −2).
Step-by-step explanation:
hope its help <:
Just number 9 with work
The answer of the given question based on rational parent function , to identify a correct transformation of the function, The correct answer choice is (c) Left 5.
What is Function?A function is mathematical relationship that assigns unique output value for each input value. It describes relationship between two variables, where output value is dependent on input value. A function can be represented by equation, a graph, or table. In its simplest form, function takes input value, performs a specified operation on that value, and produces corresponding output value.
Functions are used to model real-world phenomena, to solve problems, and to analyze and understand complex systems. They are fundamental concept in mathematics and are used in wide variety of fields, like science, engineering, economics, and finance.
The given equation is y = 12/(x + 5), which represents the rational parent function. To identify a correct transformation of the function, we can consider the effect of each transformation on the parent function.
a) Vertical reflection: This transformation would change the sign of the function, resulting in y = -12/(x + 5). This is not the given equation, so it is not a correct transformation.
b) Vertical stretch by 12: This transformation would multiply the function by 12, resulting in y = 12(12/(x + 5)) = 144/(x + 5). This is not the given equation, so it is not a correct transformation.
c) Left 5: This transformation would shift the function to the left by 5 units, resulting in y = 12/(x + 10). This is a correct transformation of the function, as it represents a horizontal shift of 5 units to the left.
d) Down 5: This transformation would shift the function down by 5 units, resulting in y = 12/(x + 5) - 5. This is not the given equation, so it is not a correct transformation.
Therefore, the correct transformation of the rational parent function as described by the given equation is a horizontal shift of 5 units to the left. The answer choice is (c) Left 5.
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The correct transformation of the function on rational parent function as described by the given equation. The correct answer choice is (c) Left 5.
What is Function?A function is mathematical relationship that assigns unique output value for each input value. It describes relationship between two variables, where output value is dependent on input value. A function can be represented by equation, a graph, or table. In its simplest form, function takes input value, performs a specified operation on that value, and produces corresponding output value.
The given equation is y = 12/(x + 5), which represents the rational parent function. To identify a correct transformation of the function, we can consider the effect of each transformation on the parent function.
a) Vertical reflection: This transformation would change the sign of the function, resulting in y = -12/(x + 5). This is not the given equation, so it is not a correct transformation.
b) Vertical stretch by 12: This transformation would multiply the function by 12, resulting in y = 12(12/(x + 5)) = 144/(x + 5). This is not the given equation, so it is not a correct transformation.
c) Left 5: This transformation would shift the function to the left by 5 units, resulting in y = 12/(x + 10). This is a correct transformation of the function, as it represents a horizontal shift of 5 units to the left.
d) Down 5: This transformation would shift the function down by 5 units, resulting in y = 12/(x + 5) - 5. This is not the given equation, so it is not a correct transformation.
Therefore, the correct transformation of the rational parent function as described by the given equation is a horizontal shift of 5 units to the left. The answer choice is (c) Left 5.
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please help, thank you!
Answer:
To find all values of x for which f(x) = 26, we can set up the equation:
8x + 15/x = 26
Multiplying both sides by x, we get:
8x^2 + 15 = 26x
Bringing all the terms to one side, we get:
8x^2 - 26x + 15 = 0
We can factor this quadratic equation using the factoring method or by using the quadratic formula. Here, we will use the factoring method:
8x^2 - 26x + 15 = 0
(4x - 3)(2x - 5) = 0
Setting each factor equal to zero and solving for x, we get:
4x - 3 = 0 OR 2x - 5 = 0
4x = 3 OR 2x = 5
x = 3/4 OR x = 5/2
Therefore, the values of x for which f(x) = 26 are x = 3/4 or x = 5/2.
A shipping container is in the form of a right rectangular prism, with dimensions of
30 ft by 8 ft by 8 ft 9 inches. How many cubic feet of shipped goods would it hold
when it is full? Round your answer to the nearest tenth if necessary.
Answer:2,160ft
Step-by-step explanation: Volume=length * width * height
30x8x9=2160
can someone please solve?
Answer:
Vertex: (0,0)
Step-by-step explanation:
Two points on the left: (-10,25), (-20,100)
Two points on the right: (10,25), (20,100)
All I need to know is the answer to this problem so I can compare mine.
Answer:
we will do TanA = perpendicular / Base
A = 35°
Tan 35° = 217 / W
value of Tan 35° is approx = 0.7
0.7 = 217/ W
W = 217 / 0.7
W = 310
is AP stats easy???????
not to sure about that try researching that
depends on ur teacher for me its really hard but the material wouldnt be too bad if you have a good teacher. it contains a lot of logistics and specific wording but memorization is key