The transformed function becomes; f'(x) = (1/2)[(-x - 77)² - 5] after its shifting and compression.
What is the procedure for obtaining a new function from a parent function?Let us suppose we have such a parent function y=f (x). By simply introducing a constant c, a new function y=g(x) can be generated from the parent function.The following are the function transformation / translation principles: f (x) + b multiplies the function by b.f (x) + b shifts a function b units upward.f (x) − b shifts a function b units downward.f (x + b) shifts a function b units to the left.f (x − b) shifts a function b units to the right.−f (x) reflects a function in x-axis (that is, upside-down)For the given question;
The parent function is given as; f(x) = x².The function is shifted 5 units down, then y coordinates will get reduced by 5 units as; f(x) = x² - 5.Now, there is a shift of 77 to the right, then x coordinates will get reduced by 77 units; f(x) = (x - 77)² - 5.There is a reflection of function about y-axis, then value of x coordinates will change to its negative; f(x) = (-x - 77)² - 5.At last, there is a vertical compress by a factor 2, reduced the function to its half; f'(x) = (1/2)[(-x - 77)² - 5].Thus, the transformed function becomes; f'(x) = (1/2)[(-x - 77)² - 5].
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suppose you walk at the of 210 ft/min. you need to walm 10,000 ft. how many more minutes will it take you to finish if you have already walked 550 ft.
It will take you 45 more minutes to finish walking the remaining distance.
If you have already walked 550 ft, subtracting it to the total distance you need to walk, then the remaining distance will be:
10,000 ft - 550 ft = 9450 ft
Rate is the relationship between two quantities of different units. Rate of speed is the amount of distance over total time.
If you walk at the rate of 210 ft/min, then the time it will take you to finish the remaining distance will be:
rate = distance/time
time = distance/rate
time = 9450 ft/(210 ft/min)
time = 45 mins
Hence, it will take you 45 more minutes to finish the walk.
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raise the difference of h and 4 to the 10th power
Answer:
h-4^10
Step-by-step explanation:
The difference of h and 4 is h-4
to the 10th power, is putting 10 as the exponent.
Find the y-intercept of the line 15x+y=-4
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.
u vu h,j h j h jcuvugogjjvjccjcjcvk
FISRT RIGHT THEN EQUATION IN THE GENERAL FORM y=mx+c
y=-4-15x
In the y intercept the x coordinate in the axis is 0.
therefore we can plug in the value 0 in the place of x and solve for y
[tex]y = - 4 - 15(0) \\ y = - 4[/tex]
The y intercept is -4.
PLEASE HELP I AM GROUNDED FOR MY GRADES
Answer:
a=41
Step-by-step explanation:
Answer:
a = 49
Step-by-step explanation:
41 + a + 90 = 180
solve for a
hope this helped
have a good day ^^
PLS HELP ASAP WILL GIVE BRAINLIEST
The statements that are true if the given pairs of triangles are congruent are:
1. ∠A ≅ ∠T; AC ≅ QT; ∠C ≅ ∠Q; ∠ABC ≅ ∠QRT
2. ∠ATF ≅ ∠LYZ; FT ≅ YL
3. B
4. ∠TAW ≅ ∠ERS; AW ≅ ER; WT ≅ SE
5. ∠GER ≅ ∠WAC; GE ≅ AC; AW ≅ ER; RE ≅ WA
What are Congruent Triangles?If two triangles are congruent to each other, every part of the triangles that corresponds to each other will have congruent or equal measures.
1. Triangle ABC and TRQ are congruent to each other, therefore, the statements that are true are:
∠A ≅ ∠TAC ≅ QT∠C ≅ ∠Q∠ABC ≅ ∠QRT2. Triangle FAT and LZY are congruent to each other, therefore, the statements that are true are:
∠ATF ≅ ∠LYZFT ≅ YL3. Two triangles are congruent if and only if their corresponding parts are congruent, therefore, the answer is: B.
4. Triangle WAT and ERS are congruent to each other, therefore, the statements that are true are:
∠TAW ≅ ∠ERSAW ≅ ERWT ≅ SE5. Triangle GRE and CWA are congruent to each other, therefore, the statements that are true are:
∠GER ≅ ∠WACGE ≅ ACAW ≅ ERRE ≅ WALearn more about congruent triangles on:
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find the f(x)=3x-2 domain on a graph
The domain of the f(x)=3x-2 form a graph is -∞ < x<∞. See the attached graph. The interval notation is given as (-∞, ∞)
What is a domain?It is to be noted that the domain of a function is the set of input or argument values for which the function is real and defined. Note from the graph that the function has no undefined points nor domain constraints. Hence, the domina is expressed as the notation:
-∞ < x < ∞.
If one were to solve for x,
Then
y = 3x -2
=
3x -2 = y [Flipping the eqation]
3x -2 + 2 = y + 2 {Added two to both sides]
Hence,
3x = y +2
Divide both sides by 3 to get:
3x/3 = (y+2)/3
x = [1/3y] + [2/3]
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help PLEASE❗️❗️❗️❗️❗️❗️❗️
Answer:
lol its 2x your afh
Step-by-step explanation:
The quotient of a number y and 3, less 2 is between –7 and 4.
A statement is 2 less than the quotient of a number y and 3. The algebraic expression is (y/3)-2.
Given that,
A statement is 2 less than the quotient of a number y and 3.
According to question,
An algebraic expression can be written by use of 2 less than the quotient of a number y and 3.
To evaluate an algebraic expression is to determine its value when a certain number is used in lieu of the variable. In order to evaluate an expression, we first replace the variable with the supplied number, then we streamline the expression using the order of operations.
Here, expression is (y÷3)-2=(y/3)-2.
If we substitute the values 0,1,2,3,4...
We get the values between -7 and 4.
Therefore, the algebraic expression for the statement 2 less than the quotient of a number y and 3 is written as (y/3)-2.
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p²-q² = 7 and p-q=2. Find the value of p + q.
Write the second ligament definition above as a biconditional. Use "if" and "only if".
2. A ligament is a bond of tissue connecting bones or holding organs in place.
Using "if" and "only if" for the second definition of ligament gives:
A ligament is a bond of tissue if and only if, it connects bones or hold organs in place.
What is a biconditional statement?This is a term used to refer to a type o statement that brings two conditional statement together, Most of the times biconditional statements use if and only if to combine the two conditions.
In the given statement, the two conditions are
A ligament is a bond of tissue ligaments connects bones or hold organs in place.Biconditional statements ensures that the two statements are maintained for the statement to be valid.
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Got the answer to a already just need b
a) Number of points the team has is 18
b) Number of games lost by the team is 9
a) How many point does the team have?
Number of wins the team has = W= 5
Number of draws the team has = D= 3
Number of points of the team = P
The equation is given by,
P = 3W +D
P= 3*5 + 3
P = 15+3
P = 18
Number of points the team has 18 points
b) How many games has this team lost?
Number of points of the team =P = 50
Number of draws the team has = D= 14
Number of wins the team has = W
Number of matches played by the team =T= 35
The equation is given by,
P = 3W +D
50 = 3W+ 14
3W = 50- 14
3W = 36
W = 12
Rewriting as equation,
Lost matches = Total matches - (Win matches+ Draw matches)
= T - (W+ D)
= 35 - (12+ 14)
=35 - 26
= 9
Number of games lost by the team = 9
What is an equation?
An equation declares that two things are equal. It will include an equals sign ' =' similar to this. The terms left-hand side and right-hand side refer to the expressions on each side of the equals sign. It's very common to presume that an equation's right side is zero. The generality can be realized by deducting the right-hand side from both sides, assuming that this does not reduce it.To learn more about equations, refer:
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You harvest 50 cherry tomatoes from your garden. you randomly inspect 15 tomatoes and find that 3 have bad spots on them. what is the experimental probability that a tomato has a bad spot?
Answer: 1 out of 5
Step-by-step explanation: 15 divided by 3 is 5. Which also means out of the 50 cherry tomatoes, 10 of them have bad spots.
Marta went to the local discount store to stock up on school supplies. She bought four spiral notebooks at $1.50 each, a package of pens for $3.95, three felt tip markers at $.99 each, and a three-ring binder for $5.00. The sales tax is 6.5%. What was the total price Marta paid at the checkout counter?
Answer: 18.7598
Step-by-step explanation:
4 x 1.50= 6
6+ 3.95=9.95
3x 0.99= 2.97
2.97 + 9.95= 12.92
12.92+ 5= 17.92
6.5% of 12.92= 0.8398
6.5% of 12.92 + 17.92= 18.7598.
The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.
The rational numbers are represented by P, Q, R, and S is mathematically given as
R= -4/3S= -5/3P= 7/3Q = 8/3This is further explained below.
What are the rational numbers?We make use of the idea of a number line, which displays the actual numbers in ascending order from left to right and from left to right to left.
One unit represents the distance between point U and point T.
It is separated into three sections that are all the same size.
Generally, the equation for TR is mathematically given as
TR = RS = SU
Therefore
TR = RS = SU = 1/3
[tex]R = -1 - (1/3)\\ R= -4/3\\\\S = -1 - (2/3) \\S= -5/3[/tex]
Considering the value of P
[tex]P = 2 + 1/3 = 6/3 + 1/3[/tex]
P= 7/3
Considering the value of Q
[tex]Q = 2 + 2/3 = 6/3 + 2/3[/tex]
Q = 8/3
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Determine whether y varies directly with x. If so, find the constant of variation and write the equation. x=-2,-4,-16 y= -4, -8, -32
For given data y varies directly with x and the constant of variation is 2.
And the equation is y = 2x
In this question, we have been given some values of x and y.
we need to determine whether y varies directly with x.
If so, find the constant of variation and write the equation.
x = -2, -4, -16
y = -4, -8, -32
Consider the ratio y/x
-4/-2 = 2
-8/-4 = 2
-32 / -16 = 2
As y/x ratio is constant, y varies directly with x.
and the constant of variation is 2.
Also, the equation from given x, y values would be,
y = 2x
Therefore, for given data y varies directly with x and the constant of variation is 2.
And the equation is y = 2x
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Question 1 : given the replacement set {0,1, 2, 3, 4} . solve 5x - 6 = 9
Question 2: Given the replacement set {2, 3, 4, 5} . Solve 8x + 4 = 5x - 6
The solution to the equations are x = 3 and no solution in the set, respectively
How to solve the equations using the replacement sets?Question 1
The equation is given as:
5x - 6 = 9
The replacement set is given as
{0,1, 2, 3, 4}
So, we replace the variables using the elements in the replacement set
When x = 0, we have
5(0) - 6 = 9
- 6 = 9 -- false
When x = 1, we have
5(1) - 6 = 9
- 1 = 9 -- false
When x = 2, we have
5(2) - 6 = 9
4 = 9 -- false
When x = 3, we have
5(3) - 6 = 9
9 = 9 -- true
Hence, the value of the equation is x = 3
Question 1
The equation is given as:
8x + 4 = 5x - 6
The replacement set is given as
{2, 3, 4, 5}
So, we replace the variables using the elements in the replacement set
When x = 2, we have
8(2) + 4 = 5(2) - 6
20 = 4 -- false
When x = 3, we have
8(3) + 4 = 5(3) - 6
28 = 9 -- false
When x = 4, we have
8(3) + 4 = 5(4) - 6
28 = 14 -- false
When x = 5, we have
8(5) + 4 = 5(5) - 6
44 = 19 -- false
Hence, the value of the equation is not in the solution set
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A triangle has vertices at A (-2, -2), B (-1, 1), and C (3, 2). Which of the following transformations produces an image with vertices A' (2, -2), B' (1, 1), and C' (-3, 2)?
O (x, y) -> (x, - y)
O (x, y) -› (-y, x)
O(x,y) → (-x,y)
O (x, y) -> (y, -x)
Answer:
[tex](x, y) \rightarrow (-x, y)[/tex]
(Option 3)
Step-by-step explanation:
Let's take into account ΔABC.
A(-2, -2) B(-1, 1) C(3, 2)
This process is entirely trial and error. Try out the different transformations and see which one results the image from the preimage.
In this case, our transformation is (-x, y). Let's put this into trial and error:
[tex]A(-2, -2) \rightarrow A'(2, -2)\\B(-1, 1) \rightarrow B'(1, 1)\\C(3, 2) \rightarrow C'(-3, 2)[/tex]
Simply, the values we got for the image is the same as provided in the question. So we know that option 3 is the right answer.
Answer:
Mackenzie the answer is the 3rd option:)
Step-by-step explanation:
ABCDE is a rectangular-based pyramid with a height of 14 cm.
13 cm
E
Submit Answer
1
0
D
Find the angle between the line DE and the plane ABCD.
Give your answer correct to 1 decimal place.
C
10 cm.
Answer:
59.6°
Step-by-step explanation:
Please help TwT math is hard
Answer:
b
Step-by-step explanation:
The graph was horizontally stretched by a factor of 2.
A cash discount of 8% is allowed on an item which costs £45. How much money is saved if a customer decides to pay in cash? How much more can he save if the discount is 9%?
well, if she decides to pay in cash, the savings is 8%!!!! yeah!!!, well hell how much is that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 45}}{\left( \cfrac{8}{100} \right)45}\implies \text{\LARGE \pounds 3.6}[/tex]
what if 9%? well, how much is 9%?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{9\% of 45}}{\left( \cfrac{9}{100} \right)45}\implies 4.05~\hfill \underset{\textit{more in savings}}{\stackrel{4.05~~ - ~~3.6}{\text{\LARGE \pounds 0.45}}}[/tex]
21. If x: y = 3: 4, find (3x + 4y): (5x + 6y).
please fast answer I will mark you brain list answer
Answer: Correct option is B)
Put x=3y=4
(3x+4y):(5x+6y)=(3×3+4×4):(5×3+6×4)
=(9+16):(15+24)
=25:39
Step-by-step explanation:
solve it if u can i bet u
The value of x³(x³ - 18) if x(x - 3) = -1 is -1.
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
We have been given that
x(x - 3) = -1 ....... eq(1)
Find out the value of
x³(x³ - 18) ........eq(2)
We first simplify the value of x in equation (1)
x(x−3)=−1
Divide by x on both side
x(x−3)/x = −1/x
(x−3)=−1 /x
Rewrite as
x + 1/x = 3
Taking cube on both sides
(x + 1/x)³ = 3³
x³ + (1/x)³ = 27 - 3×3
x³ + (1/x)³ = 27 - 9
x³ + (1/x)³ = 18
Multiply by x³
x^6 + 1 = 18x³
x^6 - 18x³ = -1
x³(x³ - 18) = -1
Hence, the value of equation x³(x³ - 18) is also -1.
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Which of the following statements is true when comparing numbers using a number line?
The number closest to zero is always the least.
The number farthest from zero is always the greatest.
The number farthest right is always the least.
The number left is always the least.
From the given statements, the statement which is true when comparing numbers using a number line is :
The number left is always the least.
The definition of a number line is a straight line that shows numbers arranged at equal distances.
A number line is often shown horizontally and can be extended indefinitely in any direction.
Moving right causes the numbers to increase (or become greatest), while moving left causes the numbers to decrease ( or becomes least).
Larger numerals on the number line are always to the left of smaller numbers. Positive numbers have a negative opposite, and negative numbers have a positive opposite. Because it is defined as the distance from zero (the origin) on a number line, the absolute value of any real number is always positive.
Hence the right statement is that the number left is always the least.
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D. The number left is always the least
4x12=6 x n guys please help me on this im in 4th grade and dont know it
Answer:
4x12=6x
48=6x
x=48/6
x=8
12y3 ― 4y3 = _____ help plez
Exponents and power - [tex]12y^3 - 4y^3 = 8y^3[/tex]
What are exponents and power?
Exponents and powers are two techniques for simplification of extremely big or extremely small numbers. For instance, we can write 3 x 3 x 3 x 3 as [tex]3^{4}[/tex], where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner. There is a claim of power throughout the entire sentence [tex]3^{4}[/tex].
How do you perform exponentiation operations?
Rule 1: All operations enclosed in parenthesis must be simplified.
Rule 2 states that all exponents should be simplified, starting from the left.
Rule 3: When multiplying and dividing, always go from left to right.
Rule 4: Always add and subtract by moving from left to right.
[tex]8y^{3}[/tex] is the correct answer to the given equation.
[tex]12y^{3} - 4z^{3}\\ = (12-4)y^{3}\\= (8)y^{3}\\ =8y^{3}[/tex]
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evaluate the product $$ (\sqrt{5} \sqrt{6} \sqrt{7}) (\sqrt{5} \sqrt{6} - \sqrt{7}) (\sqrt{5} - \sqrt{6} \sqrt{7}) (-\sqrt{5} \sqrt{6} \sqrt{7}) $$
By applying algebra, radical and power properties, we find that the simplified form of (√5 + √6) · (√7 - √5) is equal to √35 + √42 - 5 - √30.
How to simplify a product of two binomials with radical numbers
Herein we need to apply algebra and radical and power properties to simplify the expression described in the statement, whose procedure is shown below:
(√5 + √6) · (√7 - √5) Given
(√5 + √6) · √7 + (√5 + √6) · (- √5) Distributive property
√7 · √5 + √6 · √7 + √5 · (- √5) + √6 · (- √5) Distributive property
√35 + √42 - 5 - √30 (- a) · b = - a · b/ √a · √b = √a · b/Result
By applying algebra, radical and power properties, we find that the simplified form of (√5 + √6) · (√7 - √5) is equal to √35 + √42 - 5 - √30.
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QUESTION: William started with 40 pieces of candy and gave away x pieces. Hannah had 70 pieces of candy and gave away three times as many pieces as William did.
How many pieces of candy did William give away if they had the same number of pieces of candy left?
A. 30
B. 18
C. 15
D. 8
The pieces of candies that William gave away is 15.
How many pieces of candy did William give away?The linear expression that can be used to determine the number of candies left is:
Pieces of candies left = initial pieces of candies - number of candies given out
Pieces of candies left when William gave out candies : 40 - x
Pieces of candies left when Hannah gave out candies : 70 - 3x
If they have the same pieces of candies left, the two above expressions would be equal.
40 - x = 70 - 3x
3x - x = 70 - 40
2x = 30
x = 15
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if your heart beats 700 times in 10 minutes how many times in 2 minutes
Answer:
your heart beats 140 times in two mintutes or 70 times per minute
Step-by-step explanation:
to find how many beats per minute :
700/10= 70
and then to find for two minutes :
70x2= 140
Hope this helped
Write the following number in standard decimal form. four and eight hundredths
Answer:
4.08.
Step-by-step explanation:
8/100
= 0.08
Five CD’s cost 80. If each CD cost the same, how much does one cost
Answer:
16
Step-by-step explanation:
Divide to find this answer.
If you're allowed to use a calculator, divide 80÷5 or
80/5 This will give you the answer 16.
If you are not permitted to use a calculator, see attached image for an example of a long division