Answers
Answer:
A dilation by a factor of three about Point T followed by a translation of two units downwards.
Step-by-step explanation:
When transforming functions, we will reflect/dilate the figure first and then translate it. This is directly from the order of operations.
Since we are trying to determine the transformation that was performed, we can try to map ΔS'T'U' onto ΔSTU. We can start by translating the figure and then determining any reflections/dilations.
First, we can translate ΔS'T'U' up two units to map T' onto T. This is represented by the black triangle in the image below. Let the black triangle be ΔS''T''U''. (T'' and T are the same point.)
Next, notice that from Point T'' to U'', we move nine units right and six units up.
From Point T to Point U, we move three units right and two units up.
Likewise, from Point T'' to S'', we move six units left and nine units up.
From Point T to Point S, we move two units left and three units up.
Therefore, to map ΔS''T''U'' onto ΔSTU, we dilate ΔS''T''U'' about Point T by a factor of 1/3.
Hence, by reversing the transformations, to acquire ΔS'T'U', we can see that we will dilate ΔSTU by a factor of three about Point T and then a perform a translation of two units downwards.
Related Questions
The slope of a line is -, and the y-intercept is 10/3. What is the equation of the line written in general form?
Answers
As slope is y=mx+b so substitute your slope for the coefficient of x and then add your y intercept to the end.
How do you find the amplitude, period, and shift for f(x)=−4cos(3x−π)+1?
Answers
Answer:
(a) Amplitude = 4
(b) [tex]T = \frac{2\pi}{3}[/tex] --- Period
(c)
[tex]C = \frac{\pi}{3}[/tex] --- phase shift
[tex]D =1[/tex] --- vertical shift
Step-by-step explanation:
Given
[tex]f(x) = -4\cos(3x - \pi) + 1[/tex]
Rewrite the function as:
[tex]f(x) = -4\cos(3(x - \frac{\pi}{3}) + 1[/tex]
Solving (a): The amplitude
A cosine function is represented as:
[tex]f(x) = A\cos[B(x - C)] + D[/tex]
Where:
[tex]|A| \to Amplitude[/tex]
So, in this equation (by comparison):
[tex]|A| = |-4|[/tex]
[tex]|A| = 4[/tex]
The amplitude is 4
Solving (b): The period (T)
This is calculated as:
[tex]T = \frac{2\pi}{B}[/tex]
By comparison:
[tex]B =3[/tex]
So:
[tex]T = \frac{2\pi}{3}[/tex]
Solving (c): The shift
The phase shift is C
The vertical shift is D
By comparison:
[tex]C = \frac{\pi}{3}[/tex] --- phase shift
[tex]D =1[/tex] --- vertical shift
Which system of equations is represented by the matrix below?
54 5-167
7 -4 23
O A. x+ 5y = -16
x - 4y = 23
OB. 4x + 5y = -16
7x - 4y = 23
C. 4x + 5y = -16
7x + 4y = 23
Answers
9514 1404 393
Answer:
B
Step-by-step explanation:
In order for the matrix to represent the equations, the coefficients in the equations need to match the terms in the matrix. That is only the case for choice B.
__
Details are important in math.
9. Use the Distributive Property to simplify (-5 - c)(-1).
a 5 - C
b C
c-5 + c
d 5 + C
Answers
Answer:
D. 5 + c
Step-by-step explanation:
( - 5 - c ) ( - 1 )
use distributive property ; to multiply -5 and - c by -1.
= -1 × - 5 - ( +1 ) × - c= 5 + cA gardener wants to plant 875 roses in the garden. Can he plant them in rows having 7 plants each without any plants left? Justify your answer. *
Answers
Answer:
Yes
Step-by-step explanation:
875 roses / 7 plants per row
875 / 7 = 125 rows, which is a whole number, meaning nothing is left over
plzzzzzzzzzzzzzzzzz help meeeeeeeeeeeeeeeeeee
i do anything just help
1.) Create a table of x and y values that represents a proportional relationship.
a) Explain how you know the relationship is proportional.
b) What equation models the values in the table?
2) Create a table of x and y values that represents a linear, non-proportional relationship.
a) Explain how you know the relationship is non-proportional.
b) What equation models the values in the table?
Answers
Answer:
Table could be first x = 2, y = 4, then x = 4, y = 8. It is proportional because both (x,y) values equal 1/2. The equation is x = 1/2y. Last, the table could be the same, or you could do first, x = 6, y = 12, then x = 12, y = 24, because they still equal 1/2.
Step-by-step explanation:
which elements in the following set are integers -8,3/4,-0.18,0,0.16,5,-2/7,6
Answers
Answer:
345
Step-by-step explanation:
How many numbers lie between the squares of 39 and 40
Answers
Answer:
i guess its 1...
Step-by-step explanation:
Answer:
79 numbers
Step-by-step explanation:
39 x 39 = 1521 ( Find the square of 39)
40 x 40 = 1600 (Find the square of 40)
1600 - 1521 = 79 ( Finding the difference of the two squares)
What is the HFC of the following: 4 (x2-x+1) and 28 (x3+1)?
Answers
Your Answer is in the above image.
Use the distributive property to write the next step in simplifying th
numerical expression
7(2 + 7)
A. 7• 2+7•7
B. 7• 2+7
C. (7+2) • (7 + 7)
D. 7+2 • 7+ 7
Answers
Answer:
A)
Step-by-step explanation:
Which statement proves the given triangles are similar?
Answers
Answer:
it's the second one
Step-by-step explanation:
a binomial distribution
has 30% rate of SUCCESS.
there are 6 triats. what
is probability that there
will be exactly 2 Successes
Answers
Answer:
0.324
Step-by-step explanation:
Given that :
Success rate = 30%
p = 30% = 0.3
q = 1 - p = 1 - 0.3 = 0.7
Number of trials, n = 6
Probability of having exactly 2 successes ; x = 2
P(x = 2)
Usibgbtge binomial probability relation :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 2) = 6C2 * 0.3^2 * 0.7^4
P(x = 2) = 15 * 0.3^2 * 0.7^4
P(x = 2). = 0.324135
P(x = 2) = 0.324
Find the value of each shape so that they will add up to give you the specified sums in each row and each column.
How does this solving problem relate to system of equations?
Answers
Answer:
Step-by-step explanation:
Which of the following phrases would represent this expression?
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3
Answers
Answer:
the quotient of x and 3
Step-by-step explanation:
x divided by 3
division answers are called quotients
Answer:
Step-by-step explanation:
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3 is correct. We are dividing x into 3, not 3 into x.
Nine subtracted from four times a number is -21 what is the number?
Answers
Answer:
-3
Step-by-step explanation:
My knowledge ;D
Consider random samples of size 86 drawn from population A with proportion 0.43 and random samples of size 60 drawn from population B with proportion 0.15
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
(b) Are the sample sizes large enough for the Central Limit Theorem toa
Yes or No?
Answers
Answer:
a) The standard error is s = 0.071.
b) Yes, as both sample sizes are above 30.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Samples of size 86 drawn from population A with proportion 0.43
This means that [tex]n = 86, p = 0.43[/tex]. So:
[tex]s_A = \sqrt{\frac{0.43*0.57}{86}} = 0.0534[/tex]
Samples of size 60 drawn from population B with proportion 0.15:
This means that [tex]n = 60, p = 0.15[/tex]. So:
[tex]s_B = \sqrt{\frac{0.15*0.85}{60}} = 0.0461[/tex]
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
This is:
[tex]s = \sqrt{s_A^2 + s_B^2}[/tex]
[tex]s = \sqrt{(0.0534)^2 + (0.0461)^2}[/tex]
[tex]s = 0.071[/tex]
The standard error is s = 0.071.
(b) Are the sample sizes large enough for the Central Limit Theorem. Yes or No?
Yes, as both sample sizes are above 30.
Question attached below
Answers
Answer:
s(8) = 1162
Step-by-step explanation:
We are told that the acceleration is;
a(t) = 18t + 16
Now, acceleration is the first derivative of velocity. Thus, we will integrate the acceleration function to get the velocity function.
v(t) = ∫a(t) = ∫(18t + 16)
v(t) = 9t² + 16t + c
We are told that at t = 0, v(0) = 16
Thus;
9(0)² + 16(0) + c = 16
c = 16
Thus;
v(t) = 9t² + 16t + 16
Also, the velocity is the first derivative of distance. Thus;
S = ∫v(t) = ∫9t² + 16t + 16
S = 3t³ + 8t² + 16t + c
At t = 0, s(t) = 10. Thus;
10 = 3(0³) + 8(0²) + 16(0) + c
c = 10
Thus;
s(t) = 3t³ + 8t² + 16t + 10
At t = 8;
s(8) = 3(8³) + 8(8²) + 16(8) + 10
s(8) = 1162
ASAP PLEASE!!The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed. Find the probability P(T=1). write your answer as a fraction.
Answers
Answer:
[tex]P(T = 1) = \frac{3}{8}[/tex]
Step-by-step explanation:
The table, along with the relative frequency chart, state that the probabilities are:
[tex]P(T = 0) = \frac{1}{8}[/tex]
[tex]P(T = 1) = \frac{3}{8}[/tex]
[tex]P(T = 2) = \frac{3}{8}[/tex]
[tex]P(T = 3) = \frac{1}{8}[/tex]
Find the probability P(T=1)
As given by the table, and by the relative frequency chart, [tex]P(T = 1) = \frac{3}{8}[/tex]
Quick !
The perimeter of the rectangle below is 118 units. Find the length of side AD.
Answers
Answer:
24
Step-by-step explanation:
the perimeter is all sides added up
therefore to solve for "z"
3z + 3z + 4z + 3 + 4z + 3 = 118
simplify
14z + 6 = 118
isolate z by first subtracting 6 from both sides and then dividing by 14 for both sides
z=8
plug z into side CB as AD and CB are congruent
3(8)
=24
The area of a triangular sign is 6x² + 24x What is the measure of the base? (View attachment)
Answers
Answer:
[tex]2x + 8[/tex]
Step-by-step explanation:
Area of triangle equal
[tex] \frac{b \times h}{2} = a[/tex]
where b is the base and h is the height.
Plug in what we know.
[tex] \frac{b \times 6x}{2} = 6 {x}^{2} + 24x[/tex]
Multiply 2 by both sides.
[tex]b \times 6x = 2(6 {x}^{2} + 24x)[/tex]
Divide 6x by both sides.
[tex]b = \frac{12 {x}^{2} + 48x }{6x} = 2x + 8[/tex]
Find all derivatives of y^n of the function y=√x+5
Answers
Hello,
As somebody has distroyed my question, (may be he have not understood ?)
i will reply to y=(√x)+5
[tex]\displaystyle \boxed{\dfrac{d^n y}{dx^n} =(-1)^n*n!! *\dfrac{1}{2^n} *x^{-\frac{2n+1}{2} }\\}\\y'=\dfrac{1}{2} *x^{-\frac{1}{2}} \\\\y''=-\dfrac{1}{4} *x^{-\frac{3}{2}} \\...\\[/tex]
eople
Find the perimeter and area of the figure pictured below.
odules
fice 365
3.7 m
om
11.4 m
ades
2.3 m
9.2 m
Q
Perimeter
m
Area -
m2
Answers
Answer:
Perimeter: 41.2 m
Area: 54.83 m^2
Step-by-step explanation:
REFER TO THE IMAGE ATTACHED AS A
GUIDE.
PERIMETER:
(ADD UP ALL THE LENGTHS OF EACH SIDE)
Must be all 6 sides (see image, I solved for the two missing lengths)
3.7 + 9.1 + 11.4 + 9.2 + 2.3 + 5.5 = 41.2
perimeter is 41.2 m
AREA:
(See image again)
Shape is divided into two rectangles:
Top rectangle area: 11.4 x 3.7 = 42.18 m^2
Bottom triangle area: 5.5 x 2.3 = 12.65 m^2
ADD:
42.18 m^2 + 12.65 m^2 = 54.83 m^2
The area of the whole figure is 54.83 m^2
HOPE THIS HELPS
emma can read 4 pages of a book in 8 minutes how many pages can she read per minute if she still had it 24 pages how many pages are there in the book
Answers
Answer:
Emma can read 30 pages per minute
Number of book pages 28
Step-by-step explanation:
PLEASE HELP ME
WITH STEPS
Answers
Answer:
,(i) answer is 203,918
(ii)answer is227,306.36
Which expression is equivalent to -6(-⅔+2x)?
O-4-12x
O-4+ 2x
O 4-12x
O 4+ 12x
Answers
Answer:
4-12x
Step-by-step explanation:
opening the brackets;
(-6×-2/3)- 12x
-2×-2 -12x
4-12x
Answer:
4 - 12x
Step-by-step explanation:
We can find an equivalent expression by distributing
-6(-⅔+2x)
Distribute by multiplying -6 times what's inside of the parenthesis ( -2/3 and 2x )
-6 * -⅔ = 4
-6 * 2x = -12x
We would be left with 4 - 12x
Identify the domain of the function shown in the graph. Need heal ASAP
Answers
Answer:
D
Step-by-step explanation:
the domain of the function is the boundaries in the X condition. using the graph we see X starts at 2 and ends at 7 so the domain is
[tex]2 \leqslant x \leqslant 7[/tex]
Can someone please please please help me? I need this to be correct or else I’m gonna be grounded for the rest of the summer…
The difference between two numbers is 28. The first number is three times the other number. What are the numbers?
A. 14 and 42
B. 26 and 42
C. 14 and 14
D. 15 and 43
No links or fake answers please
Answers
Answer:
A
Step-by-step explanation:
42-14=28
Answer:
A. 42 and 14
Step-by-step explanation:
first number = x
second number = y
x - y = 28
3x - x = 28
(y is now x because it says the second number is whatever x was, but three times less)
x = 14
3(14) - (14) = the original number, 28
Which of the following phrases are expressions?
Answers
Answer:
C ,D , E just follow it . thank me later if its right
Answer:
E
Step-by-step explanation:
(10+7)(50+1)
=17×51
=867
help me please if you can't don't touch it
Answers
Answer:
option B : 31.4 cm
Step-by-step explanation:
Given radius , r = 5cm
Circumference = [tex]2 \pi r[/tex]
= 2 x 3.14 x 5
=10 x 3.14
= 31.4 cm
Answer:
b. 31.4
Step-by-step explanation:
The radius of the circle can be plugged into C=(pi)2r. So 5x2= 10 and 10x(pi)= 31.4
PLEASE HELP
If the absolute value represents the distance from zero, can we have a negative distance?
Answers
Answer:
No, you cannot have a negative distance.
Step-by-step explanation:
No, you cannot have a negative distance.
Let's say you were asked for the absolute value of -4. How many units is -4 away from 0? The answer would be 4. There is no negative distance from 0.
Hope this helps, please mark brainliest! :)