Answer:
Only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.
Step-by-step explanation:
When we transform a certain shape, we normally associate the original shape as 'object', while the transformed shape is associated as "image',
If any shape like triangle, parallelogram or any other certain quadrilateral is rotated, reflected or translated, it wold preserve the same size. Hence, the resulting transformed image would be similar and also called 'congruent' to the original object.
But, if any shape like triangle, parallelogram or any other certain quadrilateral is enlarged or resized, it would certainly change in size. Therefore, the resulting transformed image would still be considered as similar, but it would no longer congruent to the original object.
Hence, when two transformation are performed on a figure in the coordinates plane. The first transformation is a translation 8 units to the left. A dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.
In all other cases, like a clockwise rotation of 90 degrees about the center, A clockwise rotation of 180 degrees about the center and a dilation by a scale factor of 1 with the origin as the center of a dilation would not not alter the size of the shape, and the resulting transformed image would be similar as well as called 'congruent' to the original object.
Hence, only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.
Therefore, only option D is correct.
Keywords: dilation, transformation
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The Sedona transformation that will result in an image that is similar to, but not congruent to the original figure is D. A dilation by a scale factor of 1/2 with the origin as the center of dilation.
How to get an image that is similar but not congruent to the original figure?To get an image that is similar but not congruent to the original figure, we shall perform a transformation that changes the size of the figure while keeping the same shape.
This is because when a figure is translated 8 units to the left, its position changes, but its size and shape remain the same.
A dilation by a scale factor of 1/2 with the origin as the center of dilation means the image would be reduced to half of its original size while maintaining the same shape.
This transformation results in a figure that is similar but not congruent to the original figure, as it has the same shape but a different size.
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The height of a tree is a function of its age example
Answer & Explanation:
To determine the age of a tree, first find its diameter by measuring the circumference of the trunk in inches and then dividing that number by pi. Once you have the tree's diameter, look up the growth factor for the type of tree you're measuring, which is how much width it gains annually.
The height and diameter of a tree is a function of its age.
What is meant by growth rate ?Growth rate of a system is defined as the rate at which the system grows by length, breadth, height, etc.
Here,
The growth rate of a tree represents the age of the tree. The measurement of the height and diameter of the tree is used to calculate the age of the tree. These measurements of height and radius of the tree can be considered as a function of its age.
The method of calculating the age of the tree is,
The circumference at a height above 4.5 feet from the ground is measured(breast height).
Dividing the circumference at breast height with pi(3.14), thus we get the diameter at breast height.
Multiplying the diameter with growth factor will give the age of the tree in years.
Hence,
The height and diameter of a tree is a function of its age.
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a bottle of shampoo has a capacity of 0.43 L. how many milliliiters of shampoo does the bottle contain?
Answer:
0.43 liters = 430 milliliters
Step-by-step explanation:
There are 1000 milliliters in each liter so all you have to do is multiply 0.43 by 1000. :)
Answer:
0.43 liters = 430 milliliters
0.43 liters = 430 milliliters
Step-by-step explanation:
There are 1000 milliliters in each liter so all you have to do is multiply 0.43 by 1000. :)
Is this true or false 4/3 = 8/9
Someone please help me with this
Answer:
see explanation
Step-by-step explanation:
(a)
f(0)
Since x = 0 < 5, then
f(0) = x + 4 = 0 + 4 = 4
(b)
f(6)
Since x = 6 meets the condition 5 ≤ x < 7, then
f(6) = 8
Simplify -7(-5 + 8x) +11x
Answer:
35 - 45x
Step-by-step explanation:
-7(-5) + -7(8x) + 11x => 35 - 56x + 11x => 35 - 45x
Lui deposited $3,500 into a savings account. The simple interest is 4%. How much interest will the account earn in 2 years?
Answer:
$280
Step-by-step explanation:
Principal = $3,500
Time = 2 Years
Interest Rate = 4%
Interest = Principal x Time x Interest Rate
Interest = $3,500 x 2 x 0.04
Interest = $280
Which of the following are solutions to the following equation?
2x^2–98=0
Check all that apply.
Answer:
x=-7
x=7
Step-by-step explanation:
we have
[tex]2x^{2}-98=0[/tex]
Solve for x
Adds 98 both sides
[tex]2x^{2}-98+98=0+98[/tex]
[tex]2x^{2}=98[/tex]
Divide by 2 both sides
[tex]2x^{2}/2=98/2[/tex]
[tex]x^{2}=49[/tex]
take square root both sides
[tex]x=\pm7[/tex]
therefore
The solutions are
x=-7
x=7
What is the value of y in terms of x in the equation 3x+y/2x=15/2 ?
Answer:
y=15x-6x^2
Step-by-step explanation:
3x+y/2x=15/2
y/2x=15/2-3x
y=2x(15/2-3x)
y=15x-6x^2
A hat store sells 900 hats in its first year. If the number of hats it sells in the next year is 50% higher, how many hats will it sell in its second year?
Answer: 1,350 hats
Step-by-step explanation: First, it's important to understand that 50% is equivalent to the fraction 1/2.
So, the next year that hat store will sell 1/2 more hats.
First, we need to divide 900 by 2 which gives us 450.
Now, we simply add 450 to to the number of hats the store sold the first year.
450 + 900 = 1,350
This means that the hat store will sell 1,350 hats the next year.
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
2x + y = 8
y = -x+ 5
O A. (4,1)
O B. (3, 2)
O C. (5,0)
O D. (2,3)
B clearly because u would substitute the x and y with the ordered pairs
help me again?- please.
Answer:
Step-by-step explanation:
y - 6 = b
y = b + 6
Answer:
6+b=y
Step-by-step explanation:
If you plug in real values (y=8 and b=2) you can see that at first, you had y-6=b. Basically, 8-6=2. In order to find eight, you would need to reverse the equation to 6+2. The answer is 6+b=y.
What is the radian measure of the central angle of a circle of radius 1.5 meter that intercepts an arc of length 600 centimeters
Radian measure of the central angle is 4 radian
Solution:
Given that,
A circle of radius 1.5 meter that intercepts an arc of length 600 centimeters
To find: Radian measure of the central angle
Let us find the circumference of circle
The circumference of circle is given as:
[tex]\text{ circumference of circle } = 2 \pi r[/tex]
Where "r" is the radius of circle
[tex]\text{ circumference of circle } = 2 \times \pi \times 1.5 = 3 \pi[/tex]
Therefore circumference of circle = [tex]3 \pi[/tex] meters , which subtends central angle of [tex]2 \pi[/tex] radian
Given that arc of length 600 centimeters. Let us convert 600 centimeter to meter
We know that, to convert centimeter to meter divide the length value by 100
[tex]\text{ 600 centimeter } = \frac{600}{100} \text{ meter } = 6 \text{ meter}[/tex]
Therefore arc of 6 meter will subtend a central angle of:
[tex]\rightarrow \frac{6}{3 \pi} \times 2 \pi = 4[/tex]
Therefore radian measure of the central angle is 4 radian
Find the area of a square if its sides measure 2 2/3m
Answer:
[tex]7\dfrac{1}{9}\ m^2[/tex]
Step-by-step explanation:
If the length of the square side is a units, then the area of the square is
[tex]A=a^2\ un^2.[/tex]
In your case, the side length is
[tex]a=2\dfrac{2}{3}\ m,[/tex]
then the area is
[tex]A=2\dfrac{2}{3}\cdot 2\dfrac{2}{3}\\ \\ \\A=\dfrac{2\cdot 3+2}{3}\cdot \dfrac{2\cdot 3+2}{3}\\ \\ \\A=\dfrac{8}{3}\cdot \dfrac{8}{3}\\ \\ \\A=\dfrac{64}{9}\\ \\ \\A=7\dfrac{1}{9}\ m^2[/tex]
What is 16% of 43 minutes? Round answer to tenths place.
Answer: [tex]6.9\ minutes[/tex]
Step-by-step explanation:
Let "x" represents the 16% of 43 minutes.
Once you analize the information given in the exercise, you can identify that 43 minutes is the 100%.
Then, with this data, you can set up the following proportion:
[tex]\frac{100}{43}=\frac{16}{x}[/tex]
Now you must solve for "x". The steps are:
- Multiply both sides of the equation by "x"
[tex](x)(\frac{100}{43})=(\frac{16}{x})(x)\\\\\frac{100x}{43}=16[/tex]
- Multiply both sides by 43:
[tex](43)(\frac{100x}{43})=(16)(43)\\\\100x=688[/tex]
- Divide both sides by 100:
[tex]\frac{100x}{100}=\frac{688}{100}\\\\x=6.88[/tex]
- Rounding to the tenths place:
[tex]x\approx6.9[/tex]
You are gathering data in the cafeteria, recording which condiments are most popular on students' hamburgers. The data you gather is
A. quantitative.
B. categorical.
C. discrete.
D. bivariate.
In a 3-digit number, the hundreds digit is four more than the units digit, and the tens digit is twice the hundreds digit. If the sum of the digits is 12, find the three digits. Find the number.
Final answer:
The units digit is 0, the hundreds digit is 4, and the tens digit is 8, making the 3-digit number 480.
Explanation:
The question involves finding a 3-digit number where the hundreds digit is four more than the units digit, the tens digit is twice the hundreds digit, and the sum of the digits is 12. To solve this, we can use algebra.
Let's designate the units digit as 'u'. According to the problem, the hundreds digit will then be 'u + 4'. The tens digit is twice the hundreds digit, which gives us '2(u + 4) = 2u + 8'. Now we can use the information that the sum of the digits equals 12 to create the equation: u + (u + 4) + (2u + 8) = 12.
Simplifying this equation, we get: 4u + 12 = 12, which further reduces to 4u = 0. This indicates that u, the units digit, is 0. Thus, the hundreds digit is 0 + 4 = 4 and the tens digit is 2×4 = 8.
The 3-digit number we are looking for is therefore 480.
Find f(-5) if f(x) = Ix+1I
Answer:
x = 4
Step-by-step explanation:
f(x) = I x+1 I
when x = -5
f(-5) = I (-5) +1 I
= I -5+1 I
= |-4|
= 4
Answer:
substitute x for -5
f(-5)=|-5+1|
f(-5)=|-4|
however, absolute value is the distance from 0 and so is always positive since you cannot have negative distance.
so f(-5)=4
Helppppp please i need it
Greta and Marge are collecting money for a local charity by taking donations outside of busy
local businesses. Hoping to collect the most money today, Greta gets to her collection spot and
begins collections at 8am. Marge wanted to sleep in so she didn't start collections at her spot
until 11am, by which time Greta had already collected $45.00. If Greta continues to collect
money at a rate of $15 per hour, Marge collects money at a rate of $20 per hour and they each
take a 1 hour break at 2pm, at what time will Greta and Marge have collected the same amount
of money?
Answer:
At 9pm Greta and Marge have collected the same amount of money.
Step-by-step explanation:
Consider the provided information.
Let x represents the number of hours Greta and Marge are both collecting.
It is given that Greta had already collected $45.00 till 11 am.
Greta = 45 + 15x
Marge collects money at a rate of $20 per hour.
Marge = 20x
Greta and Marge have collected the same amount of money.
Thus,
45 + 15x = 20x
45 = 5x
9 = x
Hence, once Marge starts collecting, it would take 9 hours to collect same amount of money.
9 hours after 11am is 8pm. It is given that there is a break time of 1 hour
Hence, at 9pm Greta and Marge have collected the same amount of money.
Find the following angle measures.
MZEAD =
mZCAB =
Answer:
m∠EAD = 29°
m∠CAB = 119°
Step-by-step explanation:
m∠EAD = 180 - 61 - 90 = 29°
m∠CAB = 180 - 61 = 119°
if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? Why or why not?
Answer:
All the right triangles will be similar.
Step-by-step explanation:
See the attached diagram.
Let us assume any two right triangles are drawn on the line OP, and AB and A'B' as the hypotenuse on the same line OP.
Since the slope of the line OP is constant and assume that it makes x° with the positive x-axis.
Hence, [tex]\tan x = \frac{AC}{BC} = \frac{A'C'}{B'C'}[/tex]
⇒ [tex]\frac{AC}{A'C'} = \frac{BC}{B'C'}[/tex]
Therefore, the sides of the two right triangles are in the same ratio and hence, Δ ABC and Δ A'B'C' are similar.
Hence, all the right triangles will be similar. (Answer)
what solution is
y=9x+35
y=-8/9x+4/5
Answer:
x=-1539/445, y=1724/445. (-1539/445, 1724/445).
Step-by-step explanation:
y=9x+35
y=-8/9x+4/5
-------------------
9x+35=-8/9x+4/5
9x-(-8/9x)=4/5-35
9x+8/9x=4/5-175/5
81/9x+8/9x=-171/5
89/9x=-171/5
x=(-171/5)/(89/9)
x=(-171/5)(9/89)
x=-1539/445
y=9(-1539/445)+35
y=1724/445
Is x=4 and y=5 perpendicular
Answer:
The statement is true
The lines are perpendicular
Step-by-step explanation:
we have
[tex]x=4[/tex] ----> equation A
The equation A represent a vertical line (is parallel to the y-axis)
The slope is undefined
[tex]y=5[/tex] ----> equation B
The equation B represent a horizontal line (is parallel to the x-axis)
The slope is equal to zero
Remember that
The y-axis and the x-axis are perpendicular lines
so
Line A and line B are perpendicular lines too
therefore
The statement is true
Find the slope of 3,6 and 6,9
Hey there!
To find the slope of the two points that you were given, use the slope formula:
[tex]\frac{y2-y1}{x2-x1}[/tex]
y2 is the y value of the second point pair, y1 is the y value of the first point pair, x2 is the x value of the second point pair, and x1 is the x value of the first point pair.
Now, plug in your values:
y2= 9
y1= 6
x2= 6
x1= 3
[tex]\frac{9-6}{6-3}[/tex] = [tex]\frac{3}{3}[/tex] = 1
Therefore, the slope of the two points is 1.
Lizzie buys 8 books and pays with a $50 dallor bill.
Alex buys 3 books and pays with a $20 dallor bill.
Lizzie and Alex both get the same amount of change. How much dose one book cost?
The cost of one book is $6.
Step-by-step explanation:
Given,
Lizzie paid for 8 books = $50 bill
Alex paid for 3 books = $20 bill
As the both received same change.
Let,
x represent cost of one book.
y represent the change received.
According to given statement;
50-8x=y Eqn 1
20-3x=y Eqn 2
Putting value of y from Eqn 1 in Eqn 2
[tex]20-3x=50-8x\\-3x+8x=50-20\\5x=30[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{30}{5}\\x=6[/tex]
The cost of one book is $6.
Keywords: linear equation, substitution method
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-7/8 is less than or greater than -3/4?
Answer:
-3/4
Step-by-step explanation:
The least common denominator is 8.
So you make -3/4 into -6/8 by multiplying 2 in the numerator and denominator.
Now just compare them -6/8 compared to -7/8
-6/8 is bigger since it is closer to 0 (since we are dealing with negative numbers.)
Have a great day!
the points (3,-2) and (7,r) lie on a line with the slope 3/4. Find the missing coordinate r.
Answer:
the answer is 1
Step-by-step explanation:
X1=3 X2=7
Y1=-2 Y=r
M=y2-Y1/X2-X1
3/4=r-(-2)/7-3
3/4=r+2/4
Cross multiply
4(r+2)=4*3
4r+8=12
collect like terms
4r=12-8
4r=4
divide the by the co efficient of x
r=1
To find the missing coordinate “r” given two points on a line and the slope, we can use the slope formula. Using the given slope and the coordinates of the points, we can set up an equation to solve for the missing value of “r”. By solving the equation, we find “r” is equal to 1.
Explanation:To find the missing coordinate r, we can use the slope formula. The slope m is given as 3/4, and the coordinates of the two points are (3, -2) and (7, r).
We can use the formula: m = (y2 - y1) / (x2 - x1) to find the missing value of r. Substituting the values, we have:
3/4 = (r - (-2)) / (7 - 3)
Solving for r:
3/4 = (r + 2) / 4
Multiplying both sides by 4:
3 = r + 2
Subtracting 2 from both sides:
r = 1
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What is the distance in units from (-15, 20) to (-15, - 3) on the coordinate place
O. 17
!. 23
R. 30
V. 35
Answer:
!. [tex]\displaystyle 23[/tex]
Step-by-step explanation:
Use the Distance Formula:
[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[15 - 15]^2 + [-20 - 3]^2} = \sqrt{0^2 + [-23]^2} = \sqrt{0 + 529} = \sqrt{529} = 23[/tex]
Since we are talking about distance, we ONLY want the NON-NEGATIVE root.
I am joyous to assist you anytime.
quaker oatmeal is a very popular breakfast cereal .If susan wrapped the entire container with out any overlapping paper what is the minimum amount of wrapping paper that she will need
the cylinders hight is 11
and the dimater is 6
Answer:
263.76
Step-by-step explanation:
To answer this question, we need to know the equation for surface area of a cylinder which can be given as Surface Area=2*pi*[tex]R^{2}[/tex]+2*pi*R*H, where R is the radius of the cylinder (also can be calculated as Diameter/2=6/2=3) and H is the height of the cylinder which is given as 11. Considering pi=3.14, the surface area of the cylinder can now be calculated as 2*3.14*[tex]3^{2}[/tex]+2*3.14*3*11=263.76.
what is the slope of the line that passes through (1,4) and (-3, -3)
Answer: m = 7/4
Step-by-step explanation: Use the slope formula to find the slope m.
Hope this helps you out! ☺
Answer:
7/4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-3-4)/(-3-1)
m=-7/-4
m=7/4