Plot point F so that △ABC ≅ △FGH. Identify a sequence of rigid motions that maps △ABC onto △FGH and use a theorem to complete the explanation of why the triangles are congruent.
Answers
Answer:
Step-by-step explanation:
Point F is plotted at (5, 4)
Translate ΔABC so that point B maps to point G.
B(1, -1) → G(0, 3)
Rule for the translation,
(x, y) → [x - 1, y + 4]
By this rule,
Point C will map the point,
C(-1, -2) → C'[(-1 - 1), (-2 + 4)]
→ C'(-2, 2)
A(-4, 0) → A'[(-4 - 1), (0 + 4)]
→ A'(-5, 4)
Now reflect these points across y-axis.
Rule for the reflection across y-axis,
(x, y) → (-x, y)
Points after reflection will be,
A'(-5, 4) → F(5, 4)
B'(0, 3) → G(0, 3)
C'(-2, 2) → H(2, 2)
Distance formula,
d = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
AB = [tex]\sqrt{(1+4)^2+(-1-0)^2}[/tex] = [tex]\sqrt{26}[/tex]
BC = [tex]\sqrt{(-2+1)^2+(-1-1)^2}[/tex] = [tex]\sqrt{5}[/tex]
CA = [tex]\sqrt{(-4+1)^2+(-2-0)^2}[/tex] = [tex]\sqrt{13}[/tex]
FG = [tex]\sqrt{(5-0)^2+(4-3)^2} =\sqrt{26}[/tex]
GH = [tex]\sqrt{(2-0)^2+(2-3)^2}=\sqrt{5}[/tex]
HF = [tex]\sqrt{(4-2)^2+(5-2)^2}=\sqrt{13}[/tex]
AB ≅ FG, BC ≅ GH, CA ≅ HF
By the SSS property Triangle congruence theorem, ΔABC ≅ ΔFGH
Related Questions
5 of 10
Which of the following are one-dimensional figures?
Check all that apply.
O A. Segment
B. Ray
O C. Angle
O D. Line
D E. Plane
F. Cube
Its (Ray , Segment, line, )
Answers
Segment, ray and line are one-dimensional figures.
We need to check from the given options which are one-dimensional figures.
What are one-dimensional figures?One-dimensional: Only a single measurement is possible for a one-dimensional figure. A line segment drawn on a surface is a one-dimensional object, as it has only length and no width.
Here, the segment is a one-dimensional figure.
Ray is a one-dimensional figure.
Angle is a two-dimensional figure.
A line is a one-dimensional figure.
The plane is a two-dimensional figure.
A cube is a three-dimensional figure.
Therefore, segment, ray and line are one-dimensional figures.
To learn more about one-dimensional figures visit:
https://brainly.com/question/17967616.
#SPJ2
Multiply. Express your answer in simplest form. 9 1/6 × 1 1/11. A. 10 B. 9 1/66 C. 10 1/17 D. 10 5/6
Answers
Answer:
9 1/66
Step-by-step explanation:
9 x 1 is 9 so its that but to add more proof the problem is 9 1/6, 1 1/11 multiply 6 and 11 it is 66 so the answer is 9 1/66
Will give brainliest if your answer is correct, please help me with this question it is past due (I have more questions like this that are also pat due, check my profile and go to questions to see them once I post the questions)
Answers
Answer:
Right Angles, Alternate Interior Angles, Supplementary Angles, Equal Angles.
Step-by-step explanation:
Since S and R are both parallel lines, and line T is perpendicular to line S and R, we know that angles 16 and 17 form all right angles. Since all parts are right angles, we know that they are equal. Since two 90 degree angles form a supplementary angle, we know that angle 16 plus angle 17 is supplementary. We also know that these angles are alternate interior angles, as they are in the interior of each separate perpendicular part.
Question 4 (1 point)
SPIRAL REVIEW QUESTION: In the equation y = 6x + 3, the SLOPE is:
a
6
be
6x
3
d
у
Answers
Answer:
6
Step-by-step explanation:
slope is m in the y=mx+b
A line passes through the point (-9,8) and has a slope of
-4/3
Write an equation in slope-intercept form for this line.
Answers
Answer:
y = -4/3x - 4
Step-by-step explanation:
Given
(x1,y1) = (-9,8)
slope, m = -4/3
Required
Determine the line equation
The equation is of the form
y - y1 = m(x - x1)
Substitute values for y1, x1 and m
y - 8 = -4/3(x - (-9))
y - 8 = -4/3(x + 9)
y - 8 = -4/3x - 12
y = -4/3x - 12 + 8
y = -4/3x - 4
-2/3 - (-1 1/3)
A. -1 2/3
B. -2/3
C. -1/3
D. 2/3
Answers
Answer is 2/3
Hope this helps
A projectile is launched straight up from the ground with an initial velocity of 120 ft/s. If acceleration due to gravity is –16 ft/s2, after about how many seconds will the object reach a height of 200 ft?
Answers
Answer:
The projectile will reach a height of 200 ft after 1.910 seconds and 13.090 seconds of being launched.
Step-by-step explanation:
This projectile is experimenting a free fall, that is, an uniform accelerated motion of the projectile due to gravity and in which effects of air friction and Earth's rotation are neglected. Given that initial and final heights, initial velocity and gravitational acceleration are known, we need to calculate time by solving the appropriate equation of motion described below:
[tex]y = y_{o} +v_{o}\cdot t +\frac{1}{2}\cdot g \cdot t^{2}[/tex] (Eq. 1)
Where:
[tex]y_{o}[/tex] - Initial height of projectile, measured in feet.
[tex]y[/tex] - Final height of projectile, measured in feet.
[tex]v_{o}[/tex] - Initial velocity of projectile, measured in feet per second.
[tex]g[/tex] - Gravitational acceleration, measured in feet per square second.
As we must remember, quadratic functions have two roots and if we get that [tex]y_{o} = 0\,ft[/tex], [tex]y = 200\,ft[/tex], [tex]v_{o} = 120\,\frac{ft}{s}[/tex] and [tex]g = -16\,\frac{ft}{s^{2}}[/tex], then, the quadratic function is:
[tex]-8\cdot t^{2}+120\cdot t -200 = 0[/tex]
Roots are found by the Quadratic Formula:
[tex]t_{1,2} = \frac{-120\pm \sqrt{120^{2}-4\cdot (-8)\cdot (-200)}}{2\cdot (-8)}[/tex]
Whose solutions are:
[tex]t_{1} \approx 13.090\,s[/tex] and [tex]t_{2} \approx 1.910\,s[/tex].
Both roots are physically reasonable, first root represents the instant when the projectile reaches 200 feet when it is moving downwards, whereas second root represents the projectile moving upwards. Therefore, the projectile will reach a height of 200 ft after 1.910 seconds and 13.090 seconds of being launched.
Answer:
It will take 2.5 s to reach a height of 200ft.
Step-by-step explanation:
On day 3 of a canned food drive, the students had collected 80 cans and were 40% of the way to their goal. What was their goal for the total number of cans they hoped to collect?
Answers
Answer:
200 cans
Step-by-step explanation:
use rate method
80 40
x 100
40x=8000
x=8000/40
x=200
What is the answer for number 7
Answers
What is
f(x) = x3 – 4x2 – 7x + 10 in factored form given that 5 is a zero of the function?
Answers
Answer:
(x-2)(x+1)(x-5)
Step-by-step explanation:
Given m|n, find the value of x.
t
xo
>m
53°
Answers
Answer:
32 degrees goto the x vaule
which expression is equivalent to the expression shown f(5^4)^2
Answers
PLEASEE HELLPPPPP im dumb
Answers
Answer:
Im dumbmbbn slalsodl soak w uelwoelcome
Step-by-step explanation:
Answer:
1. A
2. it might be impetigo??
Step-by-step explanation:
Not sure but I believe this is correct.
The entry fee is $11, and the entrants make the recipes at home and vote for their favorite, which cannot be their own recipe. The top 2 finishers win money. First place wins $58, and second place wins $48. You give yourself an X chance of finishing in the top 2, and if you finish top 2, then you have an equal chance of finishing first or second.
Required:
What is x such that entering this tournament is a fair gamble for you as an expected value maximizer?
Answers
Answer:
The value is [tex]X = 0.1719 [/tex]
Step-by-step explanation:
From the question we are told that
The entry fee is [tex]a = \$ 11[/tex]
The outcome for first place is [tex]b = \$ 58[/tex]
The outcome for second place is [tex]c = \$ 48[/tex]
The outcome for losing is [tex] d = - \$ 11[/tex]
The chance of finishing in the top two is X
Given that there are equal chance of finishing first or second, then the chance of finishing first is [tex]\frac{X}{2}[/tex]
and the chance of finishing second is [tex]\frac{X}{2}[/tex]
Then the chance of losing(i.e not finishing in the first two) is [tex]1 - X[/tex]
given that the game is a fair gamble for the player as an expected maximizer then it mean is that the expected value of entering the tournament E(X) = 0
So
[tex]E(X) = b * \frac{X}{2} + c * \frac{X}{2} * d * ( 1 - X)[/tex]
=> [tex]0 = 58 * \frac{X}{2} + 48 * \frac{X}{2} * -11 * ( 1 - X)[/tex]
=> [tex]0 = \frac{58X}{2} + \frac{48X}{2} * -11 + 11X)[/tex]
=> [tex]X = \frac{64}{11}[/tex]
=> [tex]X = 0.1719 [/tex]
how can you plot,compare,and order rational numbers using a number line?
Answers
light travels 3 x 10^5 kilometers in one second. how far does it travel in 7.6 seconds?
Answers
Answer:
1800000 kilometers
Step-by-step explanation:
i think im not 100% sure
Consider versus A random sample of 16 observations taken from this population produced a sample mean of 75.8. The population is normally distributed with a. Calculate the p-value. Round your answer to four decimal places.
Answers
Answer:
The p-value is 0.0012.
Step-by-step explanation:
The hypothesis is:
H₀: µ = 72 vs. Hₐ: µ > 72
The information provided is:
[tex]n =16\\\bar x=75.8\\\sigma=5[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{75.8-72}{5/\sqrt{16}}\\\\=3.04[/tex]
Compute the p-value as follows:
[tex]p-value=P(Z>3.04)\\\\=1-P(Z<3.04)\\\\=1-0.99882\\\\=0.00118\\\\\approx 0.0012[/tex]
*Use a z-table.
Thus, the p-value is 0.0012.
Problem 7.43 A chemical plant superintendent orders a process readjustment (namely shutdown and setting change) whenever the pH of the final product falls below 6.92 or above 7.08. The sample pH is normally distributed with unknown mu and standard deviation 0.08. Determine the probability: (a) of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is operating as intended and mu
Answers
Complete Question
Problem 7.43
A chemical plant superintendent orders a process readjustment (namely shutdown and setting change) whenever the pH of the final product falls below 6.92 or above 7.08. The sample pH is normally distributed with unknown mu and standard deviation 0.08. Determine the probability:
(a)
of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is operating as intended and [tex]\mu[/tex] = 7.0 probability
(b)
of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is slightly off target, namely the mean pH is [tex]\mu[/tex] = 7.02
Answer:
a
The value is [tex]P(X < 6.92 or X > 7.08 ) = 0.26431 [/tex]
b
The value is [tex]P(X < 6.92 or X > 7.08 ) = 0.29344 [/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 7.0[/tex]
The standard deviation is [tex]\sigma = 0.08[/tex]
Considering question a
Generally the probability of readjusting when the process is operating as intended and mu 7.0 is mathematically represented as
[tex]P(X < 6.92 or X > 7.08 ) = P(X < 6.92 ) + P(X > 7.08)[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(\frac{X - \mu }{\sigma} < \frac{6.9 - 7}{0.08} ) + P(\frac{X - \mu}{\sigma} > \frac{7.08 - 7}{0.08} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma} = Z(The \ standardized \ value \ of \ X)[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < \frac{6.9 - 7}{0.08} ) + P(Z > \frac{7.08 - 7}{0.08} )[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < -1.25) + P(Z > 1 )[/tex]
From the z table the probability of (Z < -1.25) and (Z > 1 ) is
[tex]P(Z < -1.25) = 0.10565[/tex]
and
[tex]P(Z > 1 ) = 0.15866[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.10565 + 0.15866 [/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.26431 [/tex]
Considering question b
Generally the probability of readjusting when the process is operating as intended and mu 7.02 is mathematically represented as
[tex]P(X < 6.92 or X > 7.08 ) = P(X < 6.92 ) + P(X > 7.08)[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(\frac{X - \mu }{\sigma} < \frac{6.9 - 7.02}{0.08} ) + P(\frac{X - \mu}{\sigma} > \frac{7.08 - 7.02}{0.08} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma} = Z(The \ standardized \ value \ of \ X)[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < \frac{6.9 - 7.02}{0.08} ) + P(Z > \frac{7.08 - 7.02}{0.08} )[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < -1.5) + P(Z > 0.75 )[/tex]
From the z table the probability of (Z < -1.5) and (Z > 0.75 ) is
[tex]P(Z < -1.5) = 0.066807[/tex]
and
[tex]P(Z > 0.75 ) = 0.22663[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.066807 + 0.22663 [/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.29344 [/tex]
The auxiliary equation for the given differential equation has complex roots. Find a general solution. y''-10y' 29y=0
Answers
Answer:
[tex]y = Acos5x - Bsin5x[/tex]
Step-by-step explanation:
Given the differential equation y''-10y'+29y=0
First, we need to rewrite it as an auxiliary equation as shown:
Let y'' = m²y and y' = my
Substitute the values into the general equation
m²y-10my+29y = 0
Factor out y:
(m²-10m+29)y = 0 [The auxiliary equation]
Solve the auxiliary equation and find the roots of the equation
m²-10m+29 = 0
m = -b±√(b²-4ac)/2a
a = 1, b = -10, c = 29
m = -10±√(10²-4(1)(29))/2(1)
m = -10±√(100-116)/2
m = -10±√-16/2
m = (-10±4i)/2
m = -10/2 + 4i/2
m = -5+2i
Comparing the complex number with a+bi, a = -5 and b = 2
The general solution for complex solution is expressed as:
[tex]y = Acosax + Bsinax[/tex]
Substitute the value of a in the equation
[tex]y = Acos(-5)x + Bsin(-5)x\\y = Acos5x-Bsin5x[/tex]
Hence the general solution to the differential equation is [tex]y = Acos5x - Bsin5x[/tex]
A sample of size 100 is selected from a population with p = .40.
a. What is the expected value of p(bar)?
b. What is the standard error of p(bar)?
c. Show the sampling distribution of p(bar)?
d. What does the sampling distribution of p show?
Answers
Answer:
(a) 0.40
(b) 0.049
(c) [tex]\bar p\sim N(0.40,0.049^{2})[/tex]
(d) Explained below
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]E(\bar p)=p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]SE(\bar p)=\sqrt{\frac{p(1-p)}{n}}[/tex]
Given:
n = 100
p = 0.40
As n = 100 > 30 the Central limit theorem is applicable.
(a)
Compute the expected value of [tex]\bar p[/tex] as follows:
[tex]E(\bar p)=p=0.40[/tex]
The expected value of [tex]\bar p[/tex] is 0.40.
(b)
Compute the standard error of [tex]\bar p[/tex] as follows:
[tex]SE(\bar p)=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.40(1-0.40)}{100}}=0.049[/tex]
The standard error of [tex]\bar p[/tex] is 0.049.
(c)
The sampling distribution of [tex]\bar p[/tex] is:
[tex]\bar p\sim N(0.40,0.049^{2})[/tex]
(d)
The sampling distribution of p show that as the sample size is increasing the distribution is approximated by the normal distribution.
your job requires that you work at least 40 hours a week you have already worked 15 and there are 4 more days left in the week how many hours do you have to work each day to get at least 40 hours: inequality and solution
Answers
Answer:
6.25 hours
Step-by-step explanation:
this is rather simple really,
first, you have to work 40 hours a week
you have already worked 15 so now you can subtract that
40-15= 25hrs
if you have 4 more days of the week you divide the remaining hours by the days left
25/4= 6.25hrs
that would be the bare minimum of hours for you to work a 40 hour week.
Andy was at Level –1 and took the elevator to Level 21. How many levels did the elevator move upward?
Answers
Answer: 22 Levels
Step-by-step explanation: He would need to go one level higher just to get to level one, and another 21 to get to the level that he wants to, so the total would be 22 levels.
Answer:
The elevator moved up 21 levels
Hector wants to tile his rectangular shed floor with rubber tiles. He found a company that will cut custom square tiles up to 60 inches by 60 inches. The length of his shed floor is 240 inches, and the width is 144 inches.
a. What is the side length of the largest square tile Hector can use to tile his shed floor so that there are no gaps or overlaps and the entire floor is covered? Use paper to show your work. Enter your answer in the box.
The side length of the largest square tile Hector can use to tile his shed floor is
inches.
b. How many floor tiles will Hector need to cover his shed floor?
Answers
Answer:
60 inches and he will need 4 tiles
a baseball field is being constructed. the builders noticed that the batters would have the sun in their eyes when batting from point a. the builders decided to rotate the model 90 counterclockwise about the origin where is the new location of the batter?
A) E
B)F
C)G
D)H
Answers
Answer:
b
Step-by-step explanation:
Answer:
G
Step-by-step explanation:
4. Tell whether the equation is a linear equation.
4x-3y = 2
Answers
Answer:
What Is X and Y
Step-by-step explanation:
Answer:
It is a linear equation.
Step-by-step explanation:
It has no squares in the equation, meaning the line is straight, therefore meaning the equation is linear.
Which of the following is equal to −|−43|
-43
0
43
-(-43)
Answers
Answer:
i think ur answer is -43.i hope u get it
Answer:
the answer is i guess -43
Step-by-step explanation:
|-43| = 43
so -|-43| = -43
2
Divide: 4:- =
5
HELP FAST!!!!!!!!!
Answers
10/4 if its right also have a good my dude
Solve the following equation for x using inverse operations 7x-15=1
Answers
Answer:
x = [tex]\dfrac{16}{7}[/tex]Step-by-step explanation:
Equation
7x - 15 = 1 → Move the -15, reversing the sign:
7x = 1 + 15 → Solve the sum:
7x = 16 → We have a fraction:
x = [tex]\dfrac{16}{7}[/tex]
x = 2.28571428571
To keep it simple, the answer could be just [tex]\dfrac{16}{7}[/tex].
Hope this helps!
Good studies! ☺
The solution of the equation for x is;
⇒ x = 16/7
What is an expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
The expression is given as;
7x - 15 = 1
Now, Solve the expression for x by using inverse operations as;
7x - 15 = 1
Since 15 is subtract and inverse of subtraction is addition.
Hence,
Add 15 both side we get;
7x - 15 + 15 = 1 + 15
7x = 16
7 is multiply by x, and inverse of multiplication is divide;
So, Divide by 7 both side;
x = 16/7
Thus, The solution of the equation for x is;
⇒ x = 16/7
Learn more about the inverse operations visit:
https://brainly.com/question/17136818
#SPJ5
what is the place value of 4 and 3 in 4532160
Answers
Answer:
The 4 is in the 1,000,000´s place and 3 is in the 10,000 place
Step-by-step explanation:
3: ten thousandths place
3^2 *3^x =81. Find the value of x.
Answers
Answer:
The answer is 16
Mark me as brainliest if it was helpful
