Triangle DEF is the image of triangle ABC after a sequence of transformations. After you reflect ABC in the y-axis, what must you do? Describe a sequence of transformations that proves the triangles congruent.
Answers
Answer:
Step-by-step explanation:
After reflection about y-axis, A'B'C' must be translated down 6 units to create image DEF.
ABC and DEF are congruent due to the following common properties of reflections and translations.
1. does not change the nature of geometric elements, i.e. maps a line to a line, a segment to a segment, etc.
2. preserve lenths of segments.
3. preserves angles
By the congruent theorem of SSS, the two triangles are congruent.
The sequence of transformations that proves the triangles congruent is explained in the solution below.
What is transformation?The geometric transformation is a bijection of a set that has a geometric structure by itself or another set. If a shape is transformed, its appearance is changed.
After reflection about y-axis, A'B'C' must be translated down 6 units to create image DEF.
ABC and DEF are congruent due to the following common properties of reflections and translations.
It does not change the nature of geometric elements, i.e. maps a line to a line, a segment to a segment, etc., preserve lengths of segments, and preserves angles.
By the congruent theorem of SSS, the two triangles are congruent.
Learn more about transformation, click;
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Related Questions
In a survey men in a certain country (ages 20-29), the mean height was 62.8 inches with a standard deviation of 2.8 inches, what height represents the 99th percentile?
Answers
Answer:
the height that represents the 99th percentile is 69.324 inches
Step-by-step explanation:
Given that :
the mean height = 62.8 inches
standard deviation = 2.8 inches
For 99th percentile;
Let X be the random variable;
SO, P(Z≤ z) = 0.99
From the standard normal z tables
P(Z )= 2.33
The standard z score formula is :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]2.33 = \dfrac{X- 62.8}{2.8}[/tex]
2.33 × 2.8 = X - 62.8
6.524 = X - 62.8
6.524 +62.8 = X
69.324 = X
X = 69.324
Therefore; the height that represents the 99th percentile is 69.324 inches
Please can someone help me
Answers
Answer:
706.86 cm
Step-by-step explanation:
=4pi(r^2)
=12.56(r^2)
=12.56(7.5^2)
=12.56(56.25)
=706.86
The library has 6 new books it would like to display near the checkout desk. The librarian plans the six books between a set of bookends. How many different ways can the books be placed between the bookends if order is important?
Answers
Answer:
The answer is 6 factorial or 6!
6! = 6 * 5 * 4 * 3 * 2 * 1
which equals 720
Step-by-step explanation:
Answer:
720
Step-by-step explanation:
right here press the picture
Answers
Answer:
1133.54 in.^2
Step-by-step explanation:
The answer is the area of the circle which is in white inside the square. We are not looking for the shaded area.
A = (pi)r^2
r = d/2 = 38 in./2 = 19 in.
A = (3.14)(19 in.)^2
A = (3.14)(19 in.)(19 in.)
A = 1133.54 in.^2
Answer:
1133.54 [tex] {in}^{2} [/tex]Step-by-step explanation:
Given,
Diameter ( d ) = 38
Radius ( r ) = 38/2 = 19
π = 3.14
Now, let's find the area :
[tex]\pi \: {r}^{2} [/tex]
Plug the values
[tex]3.14 \times {(19)}^{2} [/tex]
Evaluate the power
[tex]3.14 \times 361[/tex]
Calculate the product
[tex]1133.54 \: {in}^{2} [/tex]
Hope this helps..
Best regards!!
if paul and Steve are the same height and they are both correct write and equationto represent this relationship put puals expresiion on the left side of the equal sign and steves expression on the right
Answers
Answer:
Paul=Steve
Step-by-step explanation:
Answer:
The expression that represents Paul’s height in inches is 3/4t - 16. The expression that represents Steve’s height in inches is 4/3t - 6. Paul and Steve are the same height, so the equation that represents this relationship is
3/2t - 16 = 4/3t - 6
( PLATO/EDMENTUM ANSWER)
Janie was asked to bring water for her daughter's soccer team. The coach told her he wants each player to drink 1 8 gallon of water after a game. There are 9 players on the team. How much water should Janie bring?
Answers
Answer:
1 gallon and 1 pint
Step-by-step explanation:
I guess that the actual amount of water needed per player is 1/8 of gallon and not 18 gallons.
You will need to bring 9 x 1/8 = 9/8 = 1 ¹/₈ gallons or 1 gallon and 1 pint
1 gallon = 4 quarts = 8 pints = 16 cups = 128 ounces
or
1 gallon = 3.785 liters
The US is one of the few countries (along with Liberia, and Myanmar) that still uses the imperial system to measure things, e.g. inches, feet, yards, pounds, miles, pints, gallons, etc. The rest of the world uses the metric system, e.g. meters, liters, kilograms, etc.
Answer:
1 1/8
Step-by-step explanation:
i did it on edge
I really need help with this! PLEASE HELP ME...
Answers
Answer:
The last graph.
Step-by-step explanation:
According to the question, she will spend just 36 hours on those activities combined, so the shading will be anything less than the diagonal line with a slope of -1.
She spends at least 12 hours running, so the shaded area will be anything above the horizontal line at 12.
She spends at least 12 hours bicycling, so the shaded area will be anything to the right of the vertical line at 12.
The only graph that fits all the conditions is the last graph, with a shaded triangle.
Hope this helps!
John is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 5 miles per hour and returns along the same route at an average speed of 7 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
(A) 5.5
(B) 5.8
(C) 6.0
(D) 6.3
(E) 6.5
Answers
Answer:
Average speed
= 5 5/6 mph , or
= 5.83 mph (to 2 decimals)
Step-by-step explanation:
Average speed is total distance divided by the total time it takes to cover the given distance.
Since uphill = 5 mph, and downhill = 7 mph, we know the average speed is between 5 and 7 mph.
Let
x = distance uphill, and also distance downhill.
Total distance = 2x miles
Total time = x/5 + x/7 hours = 12x/35 hours
Average speed
= total distance/total time
= 2x / (12x/35) mph
= 70x / 12x
= 5 5/6 mph
= 5.83 mph (to 2 decimals)
What you first want to do to find the average speed is add 5 miles and 7 miles together. You don’t need to convert the time because they both are in mph. Then you divide it by 2, getting the average of the trip up and down the mountain. If you need to find the average of something, use the mean formula.
Construct a 99% confidthence interval for the population mean .Assume the population has a normal distribution. A group of 19 randomly selected employees has a mean age of 22.4 years with a standard deviation of 3.8 years. Round to the nearest tenth.
A) Determine the critical value ta/2 with n-the 1 degrees of freedom
B) Determine the lower and upper bound of the confidence interval
C) Interpret the confidence interval.
Answers
Confidence interval for mean, when population standard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean
n= sample size
s= sample standard deviation
[tex]t_{\alpha/2}[/tex] = Critical t-value for n-1 degrees of freedom
We assume the population has a normal distribution.
Given, n= 19 , s= 3.8 , [tex]\overline{x}=22.4[/tex]
[tex]\alpha=1-0.99=0.01[/tex]
A) Critical t value for [tex]\alpha/2=0.005[/tex] and degree of 18 freedom
[tex]t_{\alpha/2}[/tex] = 2.8784
B) Required confidence interval:
[tex]22.4\pm ( 2.8744)\dfrac{3.8}{\sqrt{19}}\\\\=22.4\pm2.5058\\\\=(22.4-2.5058,\ 22.4+2.5058)=(19.8942,\ 24.9058)\approx(19.9,\ 24.9)[/tex]
Lower bound = 19.9 years
Uppen bound = 24.9 years
C) Interpretation: We are 99% confident that the true population mean of lies in (19.9, 24.9) .
(1.6x+1.8)÷2.4−0.8=4.2
Answers
Answer:
x = 6.375
Step-by-step explanation:
Step 1:
4.2+0.8 = 5
(1.6x+1.8)÷2.4 = 5
Step 2:
5 · 2.4 = 12
1.6x + 1.8 = 12
Step 3:
12 - 1.8 = 10.2
1.6x = 10.2
Step 4:
10.2 ÷ 1.6 = 6.375
x = 6.375
What pattern exists in the three places in each period?
356,039
I don't understand this
also
Use number names and numerals to write 900,000+60,000+3,000+100+4
Answers
Answer:
the pattern is (hundreds, tens, ones)963 thousand 104Step-by-step explanation:
a) Each place in our decimal place-value number system has a name. In the number 356,039, the left-most digit 3 is in the hundred-thousands place, so it is read (by itself) as "three hundred thousand." Together, the digits 356 of that number signify three hundred fifty-six thousand. They are said to be in the "thousands period." Each period of three digits will be grouped like that to specify the number of hundreds, tens, and ones in the period.
__
b) The given expanded form adds up to give ...
963,104
Based on the above discussion, the name of this number is ...
"nine hundred sixty-three thousand one hundred four"
Using digits to help write this, it would be 963 thousand 104.
You are enlarging a photograph to make a poster. The posterwill be similar to the original photograph. The photograph is6 inches tall and 4 inches wide. The poster will be 2.5 feet wide.How tall will the poster be? Find the poster’s perimeter.
Answers
Answer:
Poster’s perimeter = 150 in
Step-by-step explanation:
Given:
Width of poster = 2.5 ft = 2.5 × 12 = 30 in
Find:
Poster’s perimeter.
Computation:
Height of poster = [30×6]/4
Height of poster = 45 in
Poster’s perimeter = 2 [Width of poster + Height of poster]
Poster’s perimeter = 2 [30+45]
Poster’s perimeter = 2 [75]
Poster’s perimeter = 150 in
Which set of ordered pairs represents a function?
{(7,-2),(-8, -1),(-6,1), (-6, – 7)}
{(-4,1), (6,1),(7,-6), (7,0)}
{(2,-6), (1, -3), (-5,7),(1,0)}
{(-9,3), (-5,1), (7,-5), (4,3)}
Answers
The correct is:
[tex][(-9,3),\:(-5,1),\:(7,-5),\:(4,3)][/tex]
The definition of a function is that for every value of [tex]x[/tex] we get one from [tex]y[/tex].
In the first appears [tex](-6,1)[/tex] y [tex](-6,-7)[/tex], it is not a function, since it does not meet the definition given above, there can only be one value for x, if there are [tex]2[/tex] or more, called relation.
In 2 repeat: [tex](7,-6)[/tex] and [tex](7,0)[/tex]
In 3 repeat: [tex](1,-3)[/tex] and [tex](1,0)[/tex]
The quadratic function f(x) = -x2 - 6x - 8 is graphed.
What are the solutions of the quadratic equation 0 =-
x2 - 6x-8?
2
O 2 and 4
-2 and 4
0-2 and -4
O2 and 4
2
X
-654-3
Next
Submit
Save and Exit
Mark this and return
Answers
Answer:
The roots of the quadratic function [tex]f(x) = -x^{2}-6\cdot x -8[/tex] are [tex]x_{1} = -4[/tex] and [tex]x_{2} = -2[/tex].
Step-by-step explanation:
Let be [tex]f(x) = -x^{2}-6\cdot x -8[/tex], the function is now graphed by using a graphing tool and whose outcome is added below as attachment. After looking the image, the roots of the polynomial are [tex]x_{1} = -4[/tex] and [tex]x_{2} = -2[/tex], respectively. It can be also proved by algebraic means:
1) [tex]-x^{2}-6\cdot x -8=0[/tex] Given
2) [tex]-(x^{2}+6\cdot x+8 )= 0[/tex] Distributive property/ [tex]-(x) = -x[/tex]
3) [tex]-(x^{2} +4\cdot x +2\cdot x +8)= 0[/tex] Addition
4) [tex]-[x\cdot (x+4)+2\cdot (x+4)] = 0[/tex] Distributive property/Associative property
5) [tex]-(x+2)\cdot (x+4) = 0[/tex] Distributive property/Result
Which supports the graphic findings.
The roots of the quadratic function [tex]f(x) = -x^{2}-6\cdot x -8[/tex] are [tex]x_{1} = -4[/tex] and [tex]x_{2} = -2[/tex].
Which expression is equivalent to 4 square root 6 divided by 3 root 2?
Answers
Answer:
[tex]\sqrt[12]{55296}[/tex]/2
Step-by-step explanation:
[tex]\sqrt[4]{6}[/tex]/[tex]\sqrt[3]{2}[/tex]=1.2422
[tex]\sqrt[12]{27}[/tex]/2=0.66 <-- not matching with the top expression.
[tex]\sqrt[4]{24}[/tex]/2=1.11<--not matching with the top expression.
[tex]\sqrt[12]{55296}[/tex]/2=1.2422<-- matches!!
[tex]\sqrt[12]{177147}[/tex]/3=0.91<-- not matching with the top expression.
Answer:
It is C) ^12 square root 55296/2
Step-by-step explanation: I checked with my calculator.
What is the volume in cubic inches of the solid figure, rounded to the nearest cubic inch? Do not use units or commas in your answer.
Answers
Answer:
1131 cubic inches.
Step-by-step explanation:
The front side of the figure contains a rectangle and a semicircle.
Area of rectangle is
[tex]A_1=length\times breadth[/tex]
[tex]A_1=11\times 12[/tex]
[tex]A_1=132\text{ in}^2[/tex]
Radius of semicircle is
[tex]r=17-11=6\text{ in}[/tex]
Area of semicircle is
[tex]A_2=\dfrac{1}{2}\pi r^2[/tex]
[tex]A_2=\dfrac{1}{2}\pi (6)^2[/tex]
[tex]A_2\approx 56.55[/tex]
Area of front side is
[tex]A=A_1+A_2=132+56.55=188.55\text{ in}^2[/tex]
Let front side is the base of prism and height is 6 in. So, volume of given figure is
[tex]V=\text{Base area}\times height[/tex]
[tex]V=188.55\times 6[/tex]
[tex]V=1131.3[/tex]
[tex]V\approx 1131\text{ in}^3[/tex]
Therefore, the required volume is 1131 cubic inches.
4. A number m is such that when it is divided by 30, 36, and 45 the remainder is always 7,
find the smallest possible value of m
Answers
Answer:
187
Step-by-step explanation:
A number m is such that when it is divided by 30, 36 and 45 the remainder is always 7.
We should first find the LCM of 30, 36 and 45
We get that the LCM of the three numbers is 280 (working attached).
So now;
[tex]\frac{180}{30}[/tex] = 6
[tex]\frac{180}{36}[/tex] = 5
[tex]\frac{180}{45}[/tex] = 4
But we need a number that leaves a remainder of 7 so we add 7 to 180 to get; 180 + 7 = 187.
What is the equation of the line that passes through the point (-6, 6) and has a
slope of
1/3?
Answers
Answer:
Using point-slope form we get:
y - 6 = 1/3(x + 6)
y - 6 = 1/3x + 2
y = 1/3x + 8
100 points timed Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles? 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side 5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answers
Answer: A
Step-by-step explanation:
The answer is A. It accurately describes the equation shown. Negative values are represented by negative tiles and positive values are represented by positive tiles.
Hope it helps <3
18a - 24ay + 48b - 64by
Answers
Answer:
Step-by-step explanation:
6a(3-4y)+16b(3-4y)
(6a-16b)(3-4y)
2(3a-8)(3-4y)
The 2 equations only pls
Payday context:
It’s the end of the month which means it is time to pay your coffee shop employees. Make sure each employee gets paid the correct amount
(write an equation for each situation and solve) identify variables when applicable
Answers
Answer:
she works 50 hours for that week
Step-by-step explanation:
She is paid $18 per hour and received a bonus of $125 per bonus for the first week . she claims her compensation for the first week should be $1025 . The number of hour she worked base on her claim can be calculated below.
Let
the number of hours she worked = a. Therefore,
18a + 125 = 1025
18a = 1025 - 125
18a = 900
divide both sides by 18
a = 900/18
a = 50
she works 50 hours for that week
What the answer to this question
Answers
Answer:
44
Step-by-step explanation:
There are 18cans on a shelf a customer bought 7 cans then jake pu 6cans on the shelf how many cans are on the shelf
Answers
Answer:
17 cans
Step-by-step explanation:
18 cans
7 are taken away
18-7 =11
Then we put 6 back on
11+6 = 17
There are now 17 cans
A farmer uses 3/5 of his land to grow cassava, 1/3 of the remainder for yam and the rest for maize. Find the part of the land used for maize
Answers
Answer:
Step-by-step explanation:
Cassava = 1/3 of his land
Remaining after planting Cassava = 1 - 1/3 = 2/3 of his land
Maize = 2/5 x 2/3 = 4/15 of his land
Vegetables = 2/3 - 4/15 = 2/5 of his land
If vegetables = 10 acres
2/5 of his land = 10 acres
1/5 of his land = 10 ÷ 2 = 5 acres
5/5 of his land = 5 x 5 = 25 acres
If f(x) = 3x + 2, what is f(5)?
Answers
3(5)+2= 17.
Answer:
17
Step-by-step explanation:
f(5) = (5*3)+2
f(5) = 17
10 of 100 objects are defective you take 6 what's the probability that 2 are defective?
Answers
Answer:
to be honest I'm not sure how to do this question plz
Find the value.
6x+3 when x=-1/2
PLEASE HELP!!!
Answers
Answer:
0
Step-by-step explanation:
6(-0.5) + 3 = -3 + 3 = 0
Answer:
0
Step-by-step explanation:
x= - 1/2 [given]
Now,
> 6x + 3
>6 × - 1/2 + 3
> -6/2 +3
> -3/1 + 3
> -3 + 3
> 0
what is the distance formula
Answers
Answer:
14.42 units
Step-by-step explanation:
Assuming that this is a right triangle (i.e ∠ACB = 90°), we can use the Pythagorean formula to solve this:
AB² = AC² + BC²
AB² = 12² + 8²
AB = √(12² + 8²)
AB = 14.42 units
On the day after my birthday this year, I can truthfully say: "The day after tomorrow is a Monday". On which day is my birthday?
Answers
Answer: Friday
Step-by-step explanation:
Answer:you got this
Step-by-step explanation:
Can somebody plz help me 15-[7+(-6)+1]^3
Answers
Answer:
7.
Step-by-step explanation:
15 - [7 + (-6)+ 1]^3
Using PEMDAS:
= 15 - [ 7-6+1]^3
Next work out what is in the parentheses:
= 15 - 2*3
Now the exponential:
= 15 - 8
= 7.
Step-by-step explanation:
Hi,
I hope you are searching this, right.
=15[7+(-6)+1]^3
=15[7-6+1]^3
=15[2]^3
=15-8
=7...is answer.
Hope it helps..