A Dilation factor of 3 means that all dimensions of the figure are three times larger than those of the original figure. This applies to every dimension of the figure including height, width, and depth (if applicable). An example is a rectangle with original measurements 2 cm by 4 cm becoming 6 cm by 12 cm after dilation.
When a figure undergoes a dilation, all its dimensions are altered by the dilation factor.
In this case, the dilation factor is 3, which means that each dimension of the figure is three times larger than before.
It is important to note that this applies to all dimensions: height, width, and depth (if applicable).
For instance, suppose you have a rectangle with a height of 2 cm and width of 4 cm.
If the rectangle is dilated by a factor of 3, the new dimensions would be 6 cm (2 cm * 3) for height and 12 cm (4 cm * 3) for width.
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The question probable may be:
Explain the concept of dilation and provide an example illustrating how the dimensions of a figure change when subjected to a dilation factor. In particular, discuss the scenario where a rectangle with a height of 2 cm and width of 4 cm undergoes a dilation by a factor of 3. What are the new dimensions, and how does this align with the general principle of dilation?
Which of the following pairs of numbers contain like fractions?
6/7 and 1 5/7
3/2 and 2/3
5/6 and 10/12
3 1/2 and 4 3/4
Answer:
6/7 and 1 5/7
Step-by-step explanation:
Answer:
6/7 and 1 5/7
5/6 and 10/12= 5/6
If you invested $500 at 5% simple interest for 2 years, how much interest do you earn? Show work and answer in complete sentences to earn full credit.
If you invest $500 at 3% compounded monthly for 2 years, how much interest you do earn? Show work and answer in complete sentences to earn full credit.
Which would you rather do?
Answer:
i) $500 at 5% simple interest for two years.
Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years.
Interest = 530.88 - 500 = $30.88
I would take the first option i)$500 at 5% simple interest for two years.
Step-by-step explanation:
i) $500 at 5% simple interest for two years.
Initial amount, P = $ 500
Rate of interest, r = 0.05
Time in years, t = 2
Therefore Final amount A = P(1 + rt) = 500(1 + (0.05 2) ) = $550
Therefore Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years
Initial or Principal Amount, P = $500
Rate of interest, r =0.03
number of conversions, m = 12
Time in years, t = 3
Therefore final amount, = $530.88
Therefore Interest = 530.88 - 500 = $30.88
I would take the first option i) $500 at 5% simple interest for two years.
Albert rode to the park at 12 mph and then back home at 20 mph. If the round trip took 4 hours and it is 30 miles each way, how long did the ride to the park take?
Answer:
It took Albert 2 1/2 hours to ride to the park
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Speed of Albert to the park = 12 mph
Speed of Albert back home = 20 mph
Total time of the round trip = 4 hours
Distance each way = 30 miles
2. How long did the ride to the park take?
Let's recall that the formula of speed is:
Speed = Distance/Time, therefore Time = Distance/Speed
Time it took Albert to ride to the park = 30/12
Time it took Albert to ride to the park = 5/2 = 2 1/2 hours
Time it took Albert to ride back home = 30/20
Time it took Albert to ride back home = 3/2 = 1 1/2 hours
It took Albert 2 1/2 hours to ride to the park
What is the value of y if formula is 4/5
Step-by-step explanation:
The complete question:
What is the value of y in the formula shown when x = [tex]\dfrac{4}{5}[/tex] ?
[tex]y=\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex]
We have,
[tex]\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex] ...... (1)
To find, the value of y = ?
Put x = [tex]\dfrac{4}{5}[/tex] in equation (1), we get
[tex]y=\dfrac{4}{\dfrac{4}{5}}+\sqrt{\dfrac{4}{5}+0.2}-5(\dfrac{4}{5})[/tex]
[tex]=5+\sqrt{0.8+0.2}-4[/tex]
[tex]=1+\sqrt{1}[/tex]
= 1 + 1
= 2
Thus, the value of y is equal to 2.
Mariela bought 15 pounds of birdseed for $10.00. Mark bought 12 pounds of birdseed for $8.00. Daryl bought 18 pounds of birdseed for $12.00. If the cost per pound remains the same, what should be the cost of one pound of birdseed?
Answer:
The cost for one pound of birdseed is $0.67
Step-by-step explanation:
Use Mariela's example first
To find the cost per pound, get the pounds to 1.
15 pounds = $10.00 Divide both sides by 15 to get 1 pound
1 pound = $0.67
Use Mark's example to see if it is the same rate
12 pounds = $8.00 Divide both sides by 12 pounds to get one pound
1 pound = $0.67
Use Daryl's example to prove the other answers
18 pounds = $12.00 Divide both sides by 8 pounds to get one pound
1 pound = $0.67
The area of a right triangle is 315 square meters. The height of the right triangle is 15 meters. What is the length of the hypotenuse of the right triangle rounded to the nearest meter? No points given without showing your work.
Answer:
45 metres
Step-by-step explanation:
You have to get the base to answer the question.
Do this by dividing 315 by 15 then timesing by 2
You get 42.
Do 42^2 = 1764
Do 15 ^2 = 225
Because you want the hypotenuse you add them
1764 + 225 =1989
Do the square root of 1989 which is 45 to the nearest metre
Answer:
25.80
Step-by-step explanation:
Area = 315 [tex]m^{2}[/tex]
Area = l*b
315 = 15 *b
b= 315/15
b = 21
From Right angled Triangle ,
Hypotenuse square = side square + side square
[tex]x^{2}[/tex] = [tex]21^{2}[/tex] + [tex]15^{2}[/tex]
[tex]x^{2}[/tex] = 441 + 225
[tex]x^{2}[/tex] = 666
apply sq root on both sides, the we get
[tex]\sqrt{x^{2}} = \sqrt{666}[/tex]
x= 25.80
Mofor’s school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 6 student tickets for a total of $96. The school took in $202 on the second day by selling 8 senior citizen tickets and 13 student tickets. Find the price of a senior citizen ticket and the price of a student ticket.
Answer:
Senior citizen tickets = 9
Student tickets = 10
Step-by-step explanation:
We begin by converting the question into simultaneous linear equations;
Senior citizen tickets = a
Student tickets = b
4a + 6b = 96
8a + 13b = 202
to find a,
if 4a +6b = 96
a = 96/4 - 6b/4
a = 24 - 1.5b
We now substitute this into the second equation
8(24 - 1.5b) + 13b = 202
192 - 12b + 13b = 202
b = 202 - 192
b = 10
We now put the value of b in either equation
4a + 6b = 96
4a + 6(10) = 96
4a + 60 = 96
4a = 96 - 60
4a = 36
a = 9
Is y=15/x a linear function
Answer:
NO
Step-by-step explanation:
The equation y = 15/x is not a linear function. A linear process follows the form y = a + bx and graph as a straight line. The given equation doesn't track that form or behavior; hence, it is not linear.
Explanation:No, the equation y = 15/x is not a linear function. In Mathematics, a linear function is defined by the equation y = a + bx, where a is the y-intercept, b is the slope, x is the independent variable, and y is the dependent variable. In this equation, the relationship between x and y is direct, meaning if x increases or decreases, y will also increase or decrease at a constant rate.
However, in the equation y = 15/x, the relationship between x and y is inverse. If x increases, y decreases, and vice versa. Furthermore, the form of the equation doesn't follow the standard form of a linear equation (y = a + bx) because the x variable is in the denominator. Therefore, it is not linear because it will not graph as a straight line.
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What is the equation of a line through the points (0, 9) and (3, 0)?
because m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9 because m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 3 because m = StartFraction 3 minus 0 Over 0 minus 9 EndFraction; y = negative one-third x + 9
because m = StartFraction 3 minus 0 Over 0 minus 9 EndFraction; y = negative one-third x + 3 Mark
Answer:
m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9
Step-by-step explanation:
The given points are the y-intercept and the x-intercept, so they can be used directly in the intercept form of the equation of a line.
x/(x-intercept) +y/(y-intercept) = 1
x/3 +y/9 = 1
Multiplying by 9 gives ...
3x +y = 9
This can be rearranged to the slope-intercept form ...
y = -3x +9
_____
The answer selection shown above is the only one that matches the slope and y-intercept of the line through the given points.
Answer:
because m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9
Step-by-step explanation:
160 dogs,there are 17 trucks each truck can hold 9 dogs.how much trucks you will need to hold 9 dogs in each truck?
Answer:
160-153=7 dogs
you will need 1 more truck to hold 160 dogs
Step-by-step explanation:
1 truck=9 dogs
9x17=153 dogs
160-153=7 dogs
you will need 1 more truck to hold 160 dogs
Sabra joins a cooking club for $8.50 and pays $6.25 each month. She also joins a movie club for $12 and pays $3.75 each month. Write an expression that represents the total amount of money Sabra spends on both clubs after m months. Then enter the simplified expression in the boxes.
+
m
Simplified expression for total amount spent is 10(2.05 + m)
Step-by-step explanation:
Step 1: Write expression for expense on joining cooking club for m months.Expense = 8.50 + 6.25 × m
Step 2: Write expression for expense on joining movie club for m months.Expense = 12 + 3.75 × m
Step 3: Calculate the total amount spent on both clubsTotal Amount = 8.50 + 6.25m + 12 + 3.75m = 20.5 + 10m = 10(2.05 + m)
Sabra spends a total amount represented by the simplified expression 20.50 + 10m after m months on both the cooking and movie clubs.
To find the total amount of money Sabra spends on both clubs after m months, we need to consider the costs of joining each club and the ongoing monthly fees.
Sabra's cooking club costs $8.50 to join and $6.25 per month. This can be represented by the expression:
8.50 + 6.25mSabra's movie club costs $12 to join and $3.75 per month. This can be represented by the expression:
12 + 3.75mTo find the total amount spent on both clubs, we sum these expressions:
(8.50 + 6.25m) + (12 + 3.75m)Simplifying this expression, we get:20.50 + 10mSo, the total amount of money Sabra spends on both clubs after m months can be expressed as 20.50 + 10m
What is the answer to 5(1 + 5n)
Answer: 5 + 25n
Explanation: Let's simplify this problem using the distributive property.
In this problem, the 5 "distributes" through the parentheses which means that it multiplies by each of the terms inside.
So we have 5(1) + 5(5n) which simplifies to 5 + 25n.
1. What is the solution to the equation -5(s - 30) = -10?
Answer:
s = 32
Step-by-step explanation:
-5(s - 30) = -10
-5s + 150 = -10
-5s = -10 - 150
-5s = -160
s = -160/-5
s = 32
The equation 3y=5x represents a proportional relationship. what is the constant of proportionality for this relationship
The constant of proportionality for this relationship is [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Proportional relationship is the relation between two variables that vary directly with each other
If x and y are proportion, then y = k x, where k is the constant of proportionalityIf x and y are proportion, then [tex]\frac{y}{x}=k[/tex], where k is the constant of proportionality∵ The equation is 3 y = 5 x
∵ x and y are proportional
- That means y = k x, where k is the constant of proportionality
∴ Put the equation in the form y = k x
- Divide both side by the coefficient of y
∵ The coefficient of y is 3
∴ Divide both sides of the equation by 3
∴ y = [tex]\frac{5}{3}[/tex] x
- The value [tex]\frac{5}{3}[/tex] is constant
∴ k = [tex]\frac{5}{3}[/tex]
∵ k represents the constant of proportionality
∴ The constant of proportionality = [tex]\frac{5}{3}[/tex]
The constant of proportionality for this relationship is [tex]\frac{5}{3}[/tex]
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what is the area of the composite figure? Use 3.14 for π
Answer:
80.52
Step-by-step explanation:
For triangle it is
100-36=64 Root 64=8
24cmsquared
for the half cirlce it is
18pie=56.52
A teacher wrote the equation 3y + 12 = 6x on the board. For what value of b would the additional equation 2y = 4x +
b form a system of linear equations with infinitely many solutions?
b= -8
b=-4
b = 2
b= 6
Answer:
The answer A) b=-8
Step-by-step explanation:
Answer:
b = -8
Step-by-step explanation:
What is the measurement of Complement of 33°
Answer:
The complement of 33 is the angle that when added to 33 forms a right angle
Step-by-step explanation:
it is un needed for a explanation
8 1/9-6 7/9
Show how you got the answer
Answer:
7 10/9 - 6 7/9
1 4/9
Step-by-step explanation:
the denominator stays the same
Change the FIRST fraction to an improper mixed fraction
then keep the denominators the same and subtract the numerators
subtract the whole numbers
If the circumference of each tire on a vehicle is approximately 88 in., how many miles will the vehicle travel when the tires make
23
23,000 revolutions?
Answer:
31.94 miles
Step-by-step explanation:
we know that
The circumference of a tire represents the distance traveled by the vehicle in one revolution
so
by proportion
Find out the distance traveled by the vehicle in 23,000 revolutions
[tex]\frac{88}{1}\ \frac{in}{rev}=\frac{x}{23,000}\ \frac{in}{rev}\\\\x=88(23,000)\\\\x=2,024,000\ in[/tex]
Convert inches to miles
Remember that
[tex]1\ mile=63,360\ inches[/tex]
To convert inches to miles divided by 63,360
therefore
[tex]2,024,000\ in=2,024,000/63,360=31.94\ miles[/tex]
Find the area of the figure.
triangle with base 27.5 m and height 4.8 m
Answer:66
Step-by-step explanation:
27.5x4.8/2
Answer:
66 meters squared
Step-by-step explanation:
You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.
What is an written expression for 20+5×9
Answer:
Five times nine plus twenty
Step-by-step explanation:
Just remember the order of operations... multiplication and division are done first before adding and subtracting.
Each of the four sides of a swimming pool measures 12 meters the pool is 6 meters deep how much water will be needed to fill it completely
It will need 864 meters³ of water to fill it completely
Step-by-step explanation:
The formula of the volume of a prism is V = B h, where
B is the area of its baseh is the length of its heightThe swimming pool is shaped a prism
∵ The length of each side of the four sides is 12 meters
- That means its base is shaped a square with side length 12 meters
∵ Area of a square = (side)²
∴ The area of the base of the swimming pool = (12)² = 144 meters²
∴ B = 144
∵ The pool is 6 meters deep
- That means its height is 6 meters
∴ h = 6
The volume of the water in the swimming pool is equal to the volume of the swimming pool because it will be needed to fill completely
∴ The volume of the water = B h
∴ The volume of the water = 144(6)
∴ The volume of the water = 864 meters³
It will need 864 meters³ of water to fill it completely
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From a group of 5 candidates, an environmental committee of 3 people is selected. How many different committees are possible?
Therefore possible committees are [tex]^5C_3[/tex] =10
Step-by-step explanation:
Given , from a group of 5 candidates , an environmental committee of 3 people is selected.
Therefore possible committees are [tex]^5C_3[/tex] =10
Due to a slump in the economy a mutual fund has dropped by 30% from last year to this year. If the fund is now worth $13,902, how much was the fund last year?
Answer: The Fund last year was 19,860
Step-by-step explanation:
Just set up a ratio using 70 over 13902 and set it equal to 100 over x and cross multiply to get x = 19,860
Please help me on this I’m super stuck
Answer:
BC = 3.1666
Step-by-step explanation:
To solve this you need to know that cosine∅ = adjacent/hypotenuse. We already know that hypotenuse = 5 and that ∅ = 70*. By substituting these in you will get cosine 70* = adjacent/5. Evaluate cosine 70* on the calculator and get 0.633... Multiply both sides by 5 and get adjacent is about equal to 3.1666. Because BC is the adjacent side of the triangle, this is the length of BC.
How many places do you need to move the decimal to the right to write the
number below in scientific notation?
0.00000092
A.8 B.7 C.2 D.6
Answer:
Step-by-step explanation:
For a number to be written in standard form, it must be in a format
A×10^n
Now, n can be positive or negative, i.e n is an integer
Also, A must be between 0 and 10. It must not be outside those number
i.e 0<A<10
Therefore, to answer the question
0.00000092
The point will start to move for the negative and it will stop after the first number
If it is moving rightward, n is negative.
if it is moving leftward, n is positive
So,
9.2×10^-7 is the answer.
Then the answer is B
n=7 it moves 7 time to get to 9.2
Answer:
B.7
Step-by-step explanation:
The range of scientific notation is
0.9999999 to 9.999999999
a recycling plant processes an average of 1/3 ton of glass each minute.At approximately what rate does the recycling plant process glass,in tons per day?
Answer:
480 tons
Step-by-step explanation: You have to figure out how many minutes are in 24 hours. (1440 min) Then, you multiply 1440 x 1/3.
Answer:
the answer is 480
Step-by-step explanation:
it is common sense but in your case it is uncommon sense
The stock of Company A gained 4% today to $47.84. What was the opening price of the stock in the beginning of the day?
Answer:
46
Step-by-step explanation:
47.84 / 1.04, which is 46
The opening price of Company A's stock before the 4% increase to the closing price of $47.84 was $46.00.
To calculate the opening price of Company A's stock at the beginning of the day, before the 4% gain, we need to work backwards from the closing price. Since the stock closed at $47.84 after gaining 4%, we can represent the closing price as 104% of the opening price. Thus, the equation to find the opening price (OP) is:
OP x1.04 = $47.84
Now we solve for OP:
OP = $47.84 / 1.04
OP = $46.00
The opening price of Company A's stock at the beginning of the day was $46.00.
8
Factor x2 + 12x + 35.
x2 + 12x + 35 =
Answer:
(x + 7) (x + 5)
Step-by-step explanation:
Factor the following:
x^2 + 12 x + 35
The factors of 35 that sum to 12 are 7 and 5. So, x^2 + 12 x + 35 = (x + 7) (x + 5):
Answer: (x + 7) (x + 5)
Reflecting the graph of y = sinx across the y-axis is the same as reflecting it across
the x-axis.
Answer:
The statement is true.
Step-by-step explanation:
Given : Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis.
To find : Is this statement true or false?
Solution:
Rules of reflection :
Along across y-axis if we have a point
So, y=sinx
The reflection across y-axis→ .......[1]
Along across x-axis if we have a point
so, y=sinx
The reflection across x-axis → .....[2]
Hence, [1] and [2] both of them are equal
Therefore, the statement is true.
Answer:
The answer is true for A P E X
Step-by-step explanation: