Answers
in function notation, we get that the transformed function is:
g(x) = -2*f(x - 10) + 800
How to identify the transformation?
Here the parent function is:
f(x) = x^2
And the transformed function is the one graphed in the lower right side of the given image.
Notice that the y-intercept of the transformed function is y = 600.
The x-intercepts are x = -10 and x = 30
Then the polynomial is something like:
y = a*(x + 10)*(x - 30)
Using the fact that the y-intercept is y = 600, then:
600 = a*(0 + 10)*(0 - 30) = a*-300
600/-300 = a = -2
The transformed function is:
g(x) = -2*(x + 10)*(x - 30)
Expanding that:
g(x) = -2( x^2 + 10x - 30x - 300)
Completing squares we get:
g(x) = -2*( x^2 - 20x - 300)
= -2*(x^2 - 2*10*x - 300)
Now we can add and subtract 100, so we get:
-2*(x^2 - 2*10*x - 300 + 100 - 100)
-2*( (x - 10)^2 - 400)
Finally, expanding that:
g(x) = -2*(x - 10)^2 + 800
Writing it in function notation, we get that the transformed function is:
g(x) = -2*f(x - 10) + 800
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Related Questions
82 78 80 72 85 80 calculate the mean and standard deviation of service speed using the formula for each. Show work.
Answers
The mean is 79.5.
The standard deviation is 3.99
What is the mean and standard deviation?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
(82 + 78 + 80 + 72 + 85 + 80) / 6 = 477 / 6 = 79.5
Standard deviation is used to determine how the values in a group differs from the mean of the values in the group.
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation:79.50
Determine the difference between each value and the mean and then square the result: (82 - 79.5)² + (78 - 79.5)² + (80- 79.5)² + (72- 79.5) ²+ (85- 79.5)² + (80- 79.5)² = 6.25 + 2.25 + 0.25 + 56.25 + 30.25 + 0.25 = 95.5
Determine the mean of the sum of the squared differences and then find the square root of the mean:
√95.5 / 6 = 3.99
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Scarlett left her house at time zero and drove to the store, which is 3 blocks away, at a speed of 1 block per minute. Then she stopped and went into the store for 4 minutes. From there, she drove in the same direction at a speed of 5 blocks per minute until she got to the bank, which is 15 blocks away from the store. She stopped at the bank for 3 minutes. Then she drove home at a speed of 3 blocks every minute. Make a graph of showing the number of blocks away from home that Scarlett is xx minutes after she leaves her house, until she gets back home.
Click twice to plot a segment.
Click a segment to delete it.
0
Time Elapsed (Minutes)
Distance (Blocks from Home)
x
y
Answers
The required block diagram that shows how much distance Scarlett is away from the home is shown in the image attached.
As given in the question Scarlett left her house at time zero and drove to the store, which is 3 blocks away, at a speed of 1 block per minute.
Then she stopped and went into the store for 4 minutes.
she drove in the identical at a rate of 5 blocks per minute until she got to the bank, which is 15 blocks away from the store.
Here,
1 Approach, Scarlett moves with the speed of a block per minute
Total distance travel = 3 block
Approach 2 Scarlett moves with the speed of 5 blocks per minute for 3 minutes
Total distance travel = 15 block
Approach 3 Scarlett moves with the speed of 3 blocks per minute for 1 minute
Total block traveled = 3 + 15 = 18
Now, Approach 3 is to retrace the path at the rate of 3 blocks per minute,
All these calculations is been shown in the block diagram.
Thus, the required block diagram that shows how much distance Scarlett is away from the home is shown in the image attached.
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can you guys solve it please i will give bonus if so
Answers
x + (x + 2) + (x + 4) = 18
3x + 6 = 18
3x = 12
x = 4
The dimension of the triangle whose perimeter is 18 feet will be 4 feet, 6 feet, and 10 feet.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
Let 'x' be the first side of the triangle. Then the second and third sides of the triangle will be (x + 2) and (2 + x + 2). Then the equation is given as,
x + (x + 2) + (x + 2 + 2) = 18
3x + 6 = 18
3x = 12
x = 4
Then the dimension of the triangle will be given as,
x = 4
x + 2 = 4 + 2 = 6
x + 2 + 2 = 4 + 6 = 10
The dimension of the triangle whose perimeter is 18 feet will be 4 feet, 6 feet, and 10 feet.
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If a train is going 3 miles in a hour how much will it go into 2 3/4 a hour
Answers
Answer: 8.25 miles in 2 3/4 hours
Step-by-step explanation:
8.25 miles!!!!!!!!!!!!!!!’nnnn
At the beginning of the day the stock market goes down 50 1/2 points and stays at this level for most of the day. At the end of the day the stock market goes up 120 3/4 points from the low at the beginning of the day. What is the total change in the stock market from the beginning
Answers
The total change in the stock market from the beginning based on the information will be 171 1/4 points.
How to illustrate the information?It should be noted at the beginning of the day the stock market goes down 50 1/2 points and stays at this level for most of the day and at the end of the day the stock market goes up 120 3/4 points from the low at the beginning of the day.
Therefore, the total change in the stock market from the beginning will be the difference between the fractions that are given. This will be:
= 120 3/4 - (- 50 1/2)
= 120 3/4 + 50 1/2
= 171 1/4
Therefore, the total change in the stock market from the beginning based on the information will be 171 1/4 points.
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3-2y=9 so (3-2y)2
Please tell me what it equals
Answers
Answer:
81
Step-by-step explanation:
the model represents a polynomial of the form ax2 bx c. an algebra tile configuration. 4 tiles are in the factor 1 spot: 3 x , 1 negative. 2 tiles are in the factor 2 spot: 1 x, negative. 8 tiles are in the product spot in 4 columns with 2 rows. first row: 3 x squared, 1 negative x. second row: 3 negative x, 1 . which equation is represented by the model? 3x2 – 4x – 1
Answers
The Quadratic equation modeled is [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex].
Quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are numbers and a cannot be 0.
the given equation Much easier to understand with the symbol [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex]
[tex]3x^{2} -4x+1= 9x^{2} -6x+1\\6x^{2} -2x=0[/tex]
That is how I interpreted the "tile" set up.
Now count up the factors:
These are (4 -x) and ( x +1) factor of Quadratic equation.
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HELP? PLEASE?
solve for v. V + 1/9 = 7
ik its easy but im exhausted n my brain wont work
Answers
Answer:
If I know how to do math rn, your answer would be v= [tex]\frac{69} {9}[/tex]
-----------------------------------
Hope this helps!
Have a great day and God bless! :)
Answer:
Exact Form:
V = 62/9
Decimal Form:
V = 6.88888 (never-ending 8's)
Mixed Number Form:
V = 6 8/9
Hope this helps <33
I need help and I’m not sure how to solve this. we’re supposed to copy the answers from our workbooks but I haven’t got mine :(
Answers
Step-by-step explanation:
here you go i don't know if this will be helpful or not
what is the value of (x+y)^2 when x=2 and y= -4?
Answers
Answer: 20
Step-by-step explanation:
Everything within the parenthesis gets an exponent of two, so you should have (x^2+y^2).
After this, you plug in the 'x' and 'y' given, so the next part should look like (2^2+(-4)^2)
After step 2, do 2*2 and -4*-4 (exponents ask you to multiply numbers by a specific amount. In this case, both numbers are multiplied by themselves 2 times).
A negative times a negative is a positive, so -4^2 or -4*-4 is 16. 2^2 or 2*2 is simply 4.
Add 4 and 16 together to get your final answer of 20.
Hope this helps!
6.
(11x-47)
(6x-2)
m
1
Solve for missing variable l and m are parallel
Answers
The solved polynomial is 66x² -304x+94.
We are given a problem related to the polynomial function, where Polynomial functions are expressions that will contain factors of changing degrees, coefficients, positive types, and constants.
Since the given equation (11x-47)(6x-2), both the term are in the form of multiplication, so here we use the distribute rule,
we multiply the 6x-2 individually with the 11x and 47
11x(6x-2) -47(6x-2 )= 66x² -22x -282x + 94
Now, we have two common variables of coefficients -22 and -282, after adding both of them, the final outcome we get is
= 66x²-304x +94
The solved function for the given equations is 66x2 -304x+94,
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A cab company charges a $6.00 fee to pick up a fare plus $0.20 per mile. If you pay the cab driver $9.40, how many miles did you go?
Answers
Answer is 6.00+0.20-9.40
3.2
or
6.00-0.20-9.40
3.2
Answer:3.2
Step-by-step explanation:
10^-2 in expanded form
Answers
10⁻² in expanded form is [tex]\frac{1}{100}[/tex] in fractional form or 0.01 is decimal form.
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It is also known as standard form in the UK and scientific form, standard index form, and standard form.The number 10⁻² is written in scientific notation.
Mathematically 10⁻²= [tex]\frac{1}{10^2}[/tex]=1/100 =0.01
Hence the expanded form of 10⁻² is 0.01 .
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Determine whether the equation 32 +15= 3(x+5) has one solution, no solution, or infinitely many solutions.
one solution
infinitely many solutions.
O no solution
1
2
POSSIBLE PO
3 4
U
Answers
the volume of the atlantic ocean is about 3.1 \cdot 10^{17}3.1⋅10 17 3, point, 1, dot, 10, start superscript, 17, end superscript cubic meters. the mississippi river has an annual flow of 6.3 \cdot 10^{11}6.3⋅10 11 6, point, 3, dot, 10, start superscript, 11, end superscript cubic meters. how many times would the annual flow of the mississippi river fit in the atlantic ocean?
Answers
4.92*10^5 times the annual flow of the Mississippi River fit in the Atlantic Ocean
Given that,
Volume of the Atlantic Ocean = 3.1*10^17cubicmetres
Annual flow of the Mississippi River = 6.3*10^11cubicmeters
Now, we have to find how many times the annual flow of the Mississippi River fit in the Atlantic Ocean
So,
= Volume of the Atlantic Ocean / Annual flow of the Mississippi River
= 3.1*10^17 / 6.3*10^11
= 0.4921*10^6 (Approximately)
=4.92*10^5
Therefore,
It takes 4.92*10^5 times for the Mississippi River to fit into the Atlantic Ocean.
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Find the equation of the line that passes through the points (1,2) and 3, 10).
Answers
Answer:
y=4x-2
Step-by-step explanation:
m=[tex]\frac{8}{2}[/tex]=4
2=4(1)+b 2=4+b -2=b
two sides of a triangle have the same length. the third side measures 6 m less than twice the common length. the perimeter of the triangle is 10 m. what are the lengths of the three sides?
Answers
As for the answer, the length of the three sides was x=4.
Let [tex]x[/tex] be the length of the two sides that are the same.
Then the third side would be 2x-3
The perimeter of the triangle will come from adding all of the sides together and setting it equal to the value given, 13.
That is,
x + x + (2x-3)=13
4x-3=13
4x=13+3
4x=16
x=4
The length of each of the common sides is 4, making the third side 5, to get a total perimeter of 13.
What are two sides of a triangle?The hypotenuse of a right-angled triangle is its longest side, the base is its lower side, and the perpendicular, which stands next to the right angle, is its standing line.
You may determine the sides of a right-angled triangle using a number of techniques, such as the Pythagoras theorem or the triangle's perimeter.
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Ramon has $4896 in his bank account. he has been depositing the same amount of money monthly for 2 years. how much money did ramon deposit monthly?
Answers
Answer:
Ramon deposited $204 monthly
Step-by-step explanation:
Step 1: Firstly convert 2 years to month
1 year = 12 month
∴ 2 years = 24 month
Step 2: Divide $4896 by 24
➟ 4896 ÷ 24
➟ 204
is i get one point each 5 minutes how long until i get 50 points?
Answers
Answer:
250 minutes.
Step-by-step explanation:
1/5=50/x
cross product
5*50=1*x
250=x
find an equation for a line:
a. with slope 6 passing through (-1, 4)
b. that passes through (-5, 0) and (5, 6)
Answers
Answer:
y=6x-1
y=3/5x+5
Step-by-step explanation:
6-0= 6= 3/5
5+5 =10
Malcolm answered 12 questions correctly on his social studies assignment and scored 75%. how many questions were on the assignment
Answers
If Malcolm answered 12 questions correctly on his social studies assignment and scored 75%, then the total number of questions on the assignment were 16.
The number of questions on the assignment can be determined by converting the given percentage.
A percentage is a numeral expressed as a fraction of 100
75% = 75 / 100 = 0.75
The equation can be formed as,
75 % of x = 12
Here x is equal to the total number of questions on the assignment
As 75% = 75 / 100 = 0.75
0.75 x = 12
x = 12 ÷ 0.75
x = 16
As x represented the total number of questions, hence the total number of questions on the assignment were calculated to be 16.
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a high school graduating class is made up of 410 students. there are 66 more girls than boys. how many boys are in the class?
Answers
Total number of boys in class are 172
A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
We have total number of students in class = 410
We assume that the number of boys in class = X
Number of girls in class is 66 more then boys we assume total number of girls = X+66
If we add number of girls and boys then we found total strength of classX+X+66=4102X+66=4102x=344X=172
Number of boys = 172
Number of girls =238
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7x - 2y = 1
3x + 4y = 15
Substitution method Linear Equations
Answers
The value of 'x' and 'y' is '1' and '3' , respectively.
Substitution method :The substitution method is the algebraic method to solve simultaneous linear equations.
The first step in the substitution method is to find the value of any one of the variables from one equation in terms of the other variable.
Lets solve the given linear equations:
7x − 2y = 1 ... eq. (1)
3x + 4y = 15 ... eq. (2)
By equation 1 we got,
x = (1 + 2y)/7
Now, we will put x = (1 + 2y)/7 in equation 2,
3x + 4y = 15
3 [(1 + 2y)/7] + 4y = 15
3/7 × (1 + 2y) = 15 - 4y
3(1 + 2y) = 7(15 - 4y)
3 + 6y = 105 - 28y
6y + 28y = 105 - 3
34y = 102
y = 102/34
y = 3
Now, put the value y =3 in equation 1,
7x - 2y = 1
7x - (2×3) = 1
7x - 6 = 1
7x = 1 + 6 = 7
7x = 7/7
x = 1
Hence, the value of x is 1 and y is 3.
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6.) The quotient of Jorge's age and 3 minus 2 is 30. How old is Jorge?
Answers
Answer:
96 years
Step-by-step explanation:
let Jorge's age be x
then the quotient of his age and 3 is x divided by 3 , so
[tex]\frac{x}{3}[/tex] - 2 = 30 ( add 2 to both sides )
[tex]\frac{x}{3}[/tex] = 32 ( multiply both sides by 3 to clear the fraction )
x = 3 × 32 =96
Jorge is 96 years old
In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a length of $18.$ What is the length of the hypotenuse of the triangle?
Answers
The length of the hypotenuse of the triangle is; AB = 2√106 ≈ 20.591
How to use the Pythagorean theorem?The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs. Thus;
For median AM, we have;
AM² = CM² +AC² = (BC/2)² +AC²
For median BN, we have;
BN² = CN² +BC² = (AC/2)² +BC²
The sum of these two equations gives us;
AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)
AM² +BN² = (5/4)(AB²)
Thus, we conclude that the length of the hypotenuse of triangle ABC is;
AB = √(4/5(AM² +BN²))
AB = 2√((19² +13²)/5)
AB = 2√106 ≈ 20.591
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Consider the polynomials:
A(x) = (3-x)2² - (x-3) (7x+4)-18+2x²
B(x) = (3x + 2)² - (x - 1)²
1) Develop and reduce A (x).
2) Factorize A (x) and B (x).
3) Solve the equation A (x)= B(x)
4) Prove that B (X) -3 = 2x(4x+7) , then solve the equation B(x) =3
Answers
Answer:
1) -5x² + 13x + 6
2) B(x) =(4x + 1 )(2x + 3)
A(x) = (5x +2)(3-x)
Step-by-step explanation:
1) Expand the equation by using distributive property. Then simplify by combining the like terms.
A(x) = (3 -x)2² - (x -3)(7x+ 4) - 18 + 2x²
= (3 - x)4 - [x*7x + x*4 - 3*7x - 3*4] - 18 + 2x²
= 3*4 - x*4 - [7x² + 4x - 21x - 12] - 18 + 2x²
= 12 - 4x - 7x² - 4x + 21x + 12 - 18 + 2x²
= 2x² - 7x² -4x - 4x + 21x + 12 + 12 - 18
= -5x² + 13x + 6
B(x) = (3x + 2)² - (x - 1)²
Identities:
(a + b)² = a² + 2ab + b² ; Here a =3x & b = 2
(m -n)² = m² - 2mn + n² ; Here m = x & n = 1
2) B(x) = (3x)² + 2*3x*2 + 2² - [x² - 2*x*1 + 1]
= 9x² + 12x + 4 - [x² - 2x + 1]
= 9x² + 12x + 4 - x²+ 2x - 1
= 9x² - x² + 12x + 2x + 4 - 1
= 8x² + 14x +3
Product = 8*3 = 24
Sum = 14
Factors = 2 , 12 {2*12 = 24 & 2 +12= 14}
= 8x² + 2x + 12x + 3 {Rewrite the middle term}
= 2x(4x + 1) + 3(4x + 1)
= (4x + 1 )(2x + 3)
A(x) = - 5x² + 13x + 6
= -5x² + 15x -2x + 6
= 5x(-x +3) +2 (-x + 3)
= (5x +2)(3-x)
4) B(x) - 3 = 8x² + 14x + 3 - 3
= 8x² + 14x
= 2x *4x + 2x *7
=2x(4x + 7)
Hence proved.
B(x) = 3
8x² + 14x + 3 = 3
8x² + 14x + 3 - 3 = 0
8x² + 14x = 0
2x(4x + 7) = 0
2x = 0 or 4x + 7 = 0
x = 0 or 4x = -7
[tex]\sf x = \dfrac{-7}{4}[/tex]
x = 0 or [tex]\sf \dfrac{-7}{4}[/tex]
evaluate 7x2x7x5 using property of numbers name the property in each step
7x2x7x5:
7x7x2x5
(7x7)x(2x5)
49x10= 410
Answers
By the commutative property, the value of the expression 7 x 2 x 7 x 5 is 490
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression using mathematical properties?The expression is given as
7 x 2 x 7 x 5
The above expressions are grouped by the product sign
This means that the factors of the expressions can be rearranged by the commutative property
So, we have
7 x 7 x 2 x 5
Group the factors
So, we have
(7 x 7) x (2 x 5)
Evaluate the products
So, we have
49 x 10
Evaluate the products
So, we have
490
Hence, the value of the expression 7 x 2 x 7 x 5 is 490
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i need help with this please
Answers
Answer:
x = 67.5
Step-by-step explanation:
90 + x + 3x = 360
90 + 4x = 360
4x = 360 - 90
4x = 270
x = 270 / 4
x = 67.5
Hope it helps!!!
Solve the following integers
Answers
Step-by-step explanation:
here is the answer of each question respectively
(-3) + (+1) = -2
(-2) . (-7) = 14
(+3) . (-1) = -3
(-4) . (-7) = 28
(-18) + (-6) = -24
(+8) .(+3) = 24
(-4) - (-1) = -3
(+6) - (-2) = 8
(-1) . (+5) = -5
(+9) + (-3) = 6
(+6) + (-5) = 1
What’s the answer to question B???????
Answers
Answer:
71.
Step-by-step explanation:
The "machine" is subtracting 6 from whatever number she puts in. Ergo, 77 - 6 = 71.