Answers
The function according to the rigid transformation g(k + 3) = - 4 · f(k + 3), where f(x) = x² - x - 1, is equal to the quadratic equation g(k + 3) = - 4 · k² - 20 · k - 44.
How to evaluate a quadratic equation
In this problem we find the definition of a quadratic equation and besides we are asked to find the result of horizontal translation, a reflection about the x-axis and a dilation, all of them rigid transformations. In other words, we must look for the resulting expression according to this definition:
g(k + 3) = - 4 · f(k + 3)
g(k + 3) = - 4 · [(k + 3)² - (k + 3) - 1]
g(k + 3) = - 4 · [(k² + 6 · k + 9) - (k + 3) - 1]
g(k + 3) = - 4 · (k² + 5 · k + 11)
g(k + 3) = - 4 · k² - 20 · k - 44
To learn more on rigid transformations: https://brainly.com/question/10285343
#SPJ1
Related Questions
Savita is dividing 3 1/4 kg of sweets equally among her seven friends. How much does each
friend receive?
Answers
Answer:
13/28 kg
Step-by-step explanation:
Convert to 28 in the denominator.
[tex]\frac17 \cdot (3+\frac14) = \frac37+ \frac{1}{28} = \frac{3\cdot4}{7\cdot4}+ \frac{1}{28} = \frac{12}{28}+ \frac{1}{28} = \frac{13}{28}[/tex]
Convert 66 miles per hour into feet per second show all your work
Answers
Answer:
96.8 fps
Step-by-step explanation:
the formula is
x * 1.46666667
66 * 1.46666667
≈96.8
Read each question. Then write the letter of the correct answer on your paper.Find all the roots of 2 x⁴+x³-8 x²-4 x=0 .
(A) x=-2, x=-0.5, x=0, x=2 (B) x=-2, x=-0.5, x=2 (C) x=-2, x=0.5, x=0, x=2 (D) x=-2, x=0.5, x=2
Answers
All the roots of the polynomial 2x⁴+ x³-8x²- 4x = 0 are x = -2, x = -0.5, x = 0, x = 2 ( Option A ).
Given polynomial :
2x⁴+ x³-8x²- 4x = 0
The highest power of the polynomial is 4. This implies that this polynomial will have 4 roots or 4 zeroes.
There are numerous ways of finding roots or zeroes of a polynomial of any degree.
A root or zero of a polynomial is a solution or value of the variable which gives the value of the polynomial equal to 0.
Since this is a multiple choice based question, the easiest approach to this question is by eliminating options and finding the correct answer.
Option B and C get eliminated instantly because they have only three roots, however this is a polynomial of degree 4 and should have 4 roots.
For option A and C, we put x= -2, x = -0.5, x = 0, x = 2, and x = 0.5 in the given polynomial to check if the answer is equal to zero.
For x = -2, we get 2x⁴+ x³-8x²- 4x = 0
For x = 2, we get 2x⁴+ x³-8x²- 4x = 0
For x = 0, we get 2x⁴+ x³-8x²- 4x = 0
For x = -0.5, we get 2x⁴+ x³-8x²- 4x = 0
For x = 0.5, we get 2x⁴+ x³-8x²- 4x = -3.75
From this result, option C gets ruled out and all the values in option A check out as a root of the given polynomial.
Therefore, we get all the roots of the polynomial 2x⁴+ x³-8x²- 4x = 0 as x = -2, x = -0.5, x = 0, x = 2
Learn more about Polynomials here:
https://brainly.com/question/11536910?referrer=searchResults
#SPJ9
Use the gcf of 48 and 30 to write the sum of the two numbers as the product of their gcf and another sum
Answers
Answer:
The resultant expression is 48 + 30 = 6 (8 + 5) = 6 (13) = 78.
Step-by-step explanation:
It is given that the GCF of 48 and 30 to write the sum of the two numbers as the product of their GCF and another sum.
Now,
The largest number that can divide two numbers is known as the GCF. The formula for 48 plus 30 is as follows;
=> 48 + 30
=> 6 (8 + 5)
=> 6 (13)
=> 78
Here, the numbers are given as 48 and 30 so, the expression is;
=> 48 + 30
And their GCF is 6 so, we get;
=> 48 + 30 = 6 × 8 + 6 × 5
=> 48 + 30 = 6 (8 + 5)
=> 48 + 30 = 6 (13)
=> 48 + 30 = 78
Therefore, the resultant expression is 48 + 30 = 6 (8 + 5) = 6 (13) = 78.
To know more about this topic, click here:
https://brainly.com/question/13198516
#SPJ9
Given the linear function f(x) = −4x 8, what is the value of x if f(x) = 24? x = 104 x = −4 x = −8 x = −88
Answers
The value of x = -4
The given linear function is f(x) = -4x+8
We have to find the x corresponding to f(x) = 24
For our convenience, let f(x) = y
Then y = -4x + 8
This equation implies y in terms of x.
Isolating x to one side of the equation, we get,
x = (y - 8)/-4 = (8-y)/4
This equation gives x in terms of y.
So when f(x) = y = 24,
x = (8-24)/4
⇒ x = -4
Learn more about linear functions at https://brainly.com/question/15602982
#SPJ4
The average temperature in the mountains is 65° in April. The average temperature in that same spot is −5° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.\
65 + |−5| = 70°, 65° is the farthest from 0°
65 − |−5| = 60°, 65° is the farthest from 0°
65 + |−5| = 70°, −5° is the farthest from 0°
65 − |−5| = 60°, −5° is the farthest from 0°
Answers
Option A, 65 + |−5| = 70°, 65° is the farthest from 0°
Here, we are given that.
The average temperature in the mountains is 65° in April.
The average temperature in that same spot is −5° in December.
Thus, the difference in the temperature will be-
65 - (-5)
= 65 + 5
= 70°
Therefore, this location is 70° warmer in April than in December.
Now, their distance from 0 will be-
|65 - 0| = 65
as distance cannot be negative, we look at only the absolute difference.
Similarly |-5 -0| = 5
Thus, we see that 65° is the farthest from 0°.
Hence, option A, 65 + |−5| = 70°, 65° is the farthest from 0°, is the correct answer.
Learn more about the absolute value function here-
https://brainly.com/question/4106049
#SPJ9
PLEASE HELP I AM DESPERATE I WILL GIVE BRAINLIEST!!!!
Answers
There will be more than a percentage of 33 % of households that have an interfaith marriage from 2017 onwards.
How to analyze and interpret linear equations
In this problem we find a linear equation that models the percentage of households with an interfaith marriage in time. The expression indicates that the percentage increases uniformly in time. Herein we must look up for the year, from which the percentage is at least 33 % greater. Then:
I = (1 / 4) · x + 23
(1 + 33 / 100) · 23 = (1 / 4) · x + 23
30.59 = (1 / 4) · x + 23
(1 / 4) · x = 7.59
x = 30.36
To learn more on linear equations: https://brainly.com/question/13738061
#SPJ1
A model rocket is launched with an initial upward velocity of 57m/s. The rocket's height h (in meters) after t seconds is given by the following.
h=57t-5t^2
Find all values of for which the rocket's height is 29 meters.
Answers
The values of for which the rocket's height is 29 meters are 0.75 and -0.67.
What is a velocity?Velocity can be described as a vector quantity having both direction and magnitude which is the distance traveled per time.
We were given the rocket's height h as [tex]h=57t-5t^2[/tex] which is an equation, and we were been given the height which is the value that can be input into the equation as is 29 meters , then we can proceed to simplify the equation as
[tex]h=57t-5t^2[/tex]
29=57t-5t^2
then we will have [tex]57t-5t^2-29=0[/tex]
with the use of quadratic formula the values of t are : 0.75 and -0.67
Then we can chose 0.75 seconds
Therefore, after the calculation with the use of the quadratic equation, we can come into conclusion that the values that are required in the question are 0.75 and -0.67.
Learn more about velocity at:
https://brainly.com/question/4535155
#SPJ1
NOTE: This is a complete question, there were no given options, even on the internet.
Determine whether each function is an example of exponential growth or decay. Then find the y -intercept.
y=100(0.25) x
Answers
The function y = 100 ( 0.25 ) ˣ is an exponential decay function.
An exponential function is defined as y = a ˣ where x is a variable, and a is a constant called the base of the function.
We are given a function:
y = 100 ( 0.25 ) ˣ
We need to tell whether is is a exponential growth or decay function.
We can see that the value of a ˣ = (0.25) ˣ
So, the value of a = 0.25.
Since, it is a decimal and not an integer, its value will decrease with the increase in exponent x.
So, it will be a exponential decay function.
Therefore, we get that, the function y = 100 ( 0.25 ) ˣ is an exponential decay function.
Learn more about exponential decay function here:
https://brainly.com/question/2046253
#SPJ4
What time is on the clock face?
Answers
Answer: I think it's 9: 48
Step-by-step explanation: hope this helps!
Answer:
8:45
because the small hand (hour hand) is a little passed 8
and the long hand (minute had) is at 45 minutes
Step-by-step explanation:
with slope = 5/6, through (22, 12) with slope intercept form
Answers
The point-slope equation of something like the line, with slope equal to 5/6 but instead passing through the point at(22 , 12), is:
(y - 12) = 5/6(x - 22).
The equation of a line describe as:A line's equation can be stated in three different ways:
standard formslope-intercept formpoint-slope form.The typical form of a line equation is ax + by = c, where a but rather b are the coefficients of variables x and y, respectively, as well as c is a constant if all possible values must be integers. In the meantime, the slope-intercept form is given by the formula y = mx + b, where m is the line's slope as well as b is the y-intercept. Given the slope m and a point on the line (x, y), we can formulate the equation using point-slope form, (y - y1) = m. (x - x1).
According to the given data:To build up the equation, use the point slope form and enter in the values.
(y - y1) = m(x - x1)
where;
m = 5/6
(x1 , y1) = (22 , 12)
(y - 12) = 5/6(x - 22)
In slope-intercept form, the equation of the line is:
(y - 12) = 5/6(x - 22)
y - 12 = 5/6 x - 110/6
y = 5/6 x - 19/3
In standard form, the equation of the line is:
y = 5/6 x - 19/3
5/6 x - y = 19/3
Multiplying both sides by 6,
5x - 6y = 38.
The point-slope equation of something like the line, with slope equal to 5/6 but instead passing through the point at(22 , 12), is:
(y - 12) = 5/6(x - 22).
To know more about equation of the line visit:
https://brainly.com/question/21511618
#SPJ9
10.
(8y + 17)°
(6x - 7)°
(3x-29)
Find x and y
Answers
[tex] \large \bf \implies{x = 24 \degree \: and \: y = 15 \degree}[/tex]
Step-by-step explanation:[tex] \bf \longrightarrow(6x - 7 ) \degree+ (3x - 29) \degree = 180 \degree \\\bf \longrightarrow (9x - 36) \degree = 180 \degree \\\bf \longrightarrow 9x = 180 \degree + 36 \degree \\\bf \longrightarrow 9x = 216 \degree \\\bf \longrightarrow x = \frac{ \cancel{216} \degree}{ \cancel{9} } \\\bf \longrightarrow \boxed{ \bold{ x = 24 \degree}}[/tex]
[tex] \red{ \rule{7cm}{0cm}}[/tex]
[tex]\bf \longrightarrow(8y + 17) \degree = (6x - 7) \degree[Vertical \: angles] \\\bf \longrightarrow 8y = 6 \times 24 - 7 - 17 \\ \bf \longrightarrow8y = 144 - 24 \\\bf \longrightarrow 8y = 120 \\\bf \longrightarrow y = \frac{ \cancel{120}}{ \cancel{8} } \\\bf \longrightarrow \boxed{ \bold{y = 15 \degree}}[/tex]
Can someone help me with this?
Answers
Answer:
x = 9
A(lol,brainly wont let me post this)F = 19
Step-by-step explanation:
see image. Since F is the midpoint, both halves of the segment must have the same measure.
If AhalfF is 2x+1, then the other half of AD must also be 2x+1.
We were given the length of the whole thing as well, so we can set up an equation to solve. See image.
Evaluate each expression for x=-2,0 , and 2 .
10x⁺¹
Answers
The value of given expression for x=0 is 0, x=-2 is -20 and x=2 is 20.
Given the expression is (10x)⁺¹.
Firstly, we will simplify the given expression (10x)⁺¹ for x=0.
Substitute the value x=0 in given expression, we get
(10x)⁺¹=(10×0)⁺¹
As we know that something multiply to zero is 0.
So, we get
(10x)⁺¹=0
Now, we will simplify the given expression (10x)⁺¹ for x=-2.
Substitute the value x=2 in given expression, we get
(10x)⁺¹=(10×2)⁺¹
Now, we will know that if we multiply any number with 2 we get twice of it, we get
(10x)⁺¹=(20)⁺¹
(10x)⁺¹=20
Furthermore, we will simplify the given expression for x=-2.
Substitute the value x=-2 in given expression, we get
(10x)⁺¹=(10×(-2))⁺¹
Now, we will know that if we multiply any number with 2 we get twice of it, we get
(10x)⁺¹=(-20)⁺¹
(10x)⁺¹=-20
Hence, the value of expression (10x)⁺¹ for x=0, 2 and -2 is 0, 20 and -20.
Learn more about the expression from here brainly.com/question/945593
#SPJ4
simplify x(2x+1)-(4x-5)
Answers
WAIT I THINK X = 3±i√31/4
Answer:
2x*-3x-5
* = squared
Step-by-step explanation:
step 1: distribute “x” to “2x+1”
-you now have the equation: 2x*+1x-4x-5
step 2: combine like terms (combine “1x” and “-4x”. that gets you “-3x”.)
-you now have the equation: 2x*-3x-5
step 3: you have no more like terms, your equation is solved.
final equation: 2x*-3x-5
Need to know the answer
Answers
What is the mean absolute deviation of the following set?
(23, 24, 29, 30, 38, 48}
Need help
Answers
Answer:
7 and 1/3
O___O
17. priti wants to wish her 5 subject teachers by giving them a self-made greeting card on teacher's day. she has chosen a green colored square sheet of paper.a side of that paper measures 20.5 cm. what is the area of each card? ii) find the edge of each card correct to two decimal places
Answers
The area of each card is 80.05cm^2, and the edge of each card is 8.95cm.
Priti chose a green coloured square paper of 20.5cm, since its a square the length and breadth of the card are equal
l = b
Recall the area of a square is
A = l^2
A = (20.5)^2
A= 20.5 × 20.5
A= 400.25cm^2
Since the paper is to be used for 5 cards, therefore the is divided in 5 equal cards. The are area of each card will be
A = A/5
A = 400.25/5
A = 80.05cm^2
The edge of each card is the side of the each card which can either be the length or the breadth since all the sides are equal for a square.
Recall that
A = l^2
Since the Area of each card is 80.05cm^2. Therefore,
80.05 = l^2
Finding the square root of both sides
(80.05)^1/2 = (l^2)^1/2
l = 8.947cm
Approximate l to 2 decimal place
l = 8.95cm
Therefore, the edge of each card is 8.95cm
To learn more about area of square. Click, https://brainly.com/question/27776258
#SPJ4
Simplify each expression. x²/₃ y⁻¹/₄ / x¹/₂ y⁻¹/₂
Answers
This is an expression testing the knowledge on indices. Solve the like terms and apply the index rule: a^m÷ a^n = a^m-n.
x²/₃ y⁻¹/₄ / x¹/₂ y⁻¹/₂
x²/₃ y⁻¹/₄ ÷ (x¹/₂ y⁻¹/₂)
x²/₃÷ (x¹/₂) . y⁻¹/₄ ÷ (y⁻¹/₂)
x^(2/3-1/2)y^(-1/4--1/2)
x^1/6.y^1/4
Find out more on indices at: brainly.com/question/28595104
#SPJ4
The measures of two sides of a triangle are 8x+8 and 2x+7. If the perimeter
measures 15x+22, what is the measure of the third side, in terms of x?
Answers
Answer:
5x + 7
Step-by-step explanation:
8x + 8 + 2x + 7 = 10x + 15
15x + 22 - (10x + 15) = 5x + 7
Simplify each expression. x¹/₂ y⁻¹/₃ / x³/₄ y¹/₂
Answers
The expression can be simplified through division of the exponential (power).
In the given expression, if the powers have the same base, we can actually divide the power. In order to carry out the division of the exponential (power), we can subtract their exponential.
In the general form, a-m=1/am
As there are two different base terms x and y in the numerator and denominator, we will subtract the powers of x terms and powers of y terms.
Let us simplify the x terms,
x¹/₂÷x³/₄=x(1/2)-(3/4)
Solving the powers,(½)–(¾)=(2/4)–(¾)=(2-3)/4=-1/4
x¹/₂÷ x³/₄=x(1/2)-(3/4)= x-1/4
Let us simplify the y terms,
y⁻¹/₃÷y¹/₂= y(⁻¹/₃)-(¹/₂)
Solving the powers, (-1/3)-(1/2)=(-2/6)-(3/6)=-5/6
y⁻¹/₃÷y¹/₂= y(⁻¹/₃)-(¹/₂)=y-5/6
Putting the terms together gives us,
x-1/4 *y-5/6
It can be expressed as a fraction as a-m=1/am
x-1/4 *y-5/6=1/x1/4y5/6
Hence, x¹/₂ y⁻¹/₃ / x³/₄ y¹/₂= x-1/4 *y-5/6=1/x1/4y5/6
Learn more about division of exponential:
https://brainly.com/question/28354101
#SPJ4
In the diagram below, m/AGF = 62° and m/DGB = 32°. Find m/CGE.
Step
1
2
try
Angle
m/AGF = 62°
m/DGB = 32°
m/
B
D.
O
Select a Reason
32°
G
62°
Reason
Given
Given
A
Answers
Step-by-step explanation:
per the laws of intersecting lines the angles on one side of any of the lines must be the same as the angles on the other side of that line - just left-right mirrored.
for that reason, CGE = DGF.
also to remember : the sum of all angles around a point on one side of a line is always 180° (because they represent a half-circle with that point being the center). in other words, these angles are supplementary (together 180°).
therefore,
180 = 62 + 32 + DGF
DGF = CGE = 180 - 62 - 32 = 86°
x + 4y = 9 solve for x
Answers
Answer:
x=−4y+9
Step-by-step explanation:
Let's solve for x.
x+4y=9
Step 1: Add -4y to both sides.
x+4y+−4y=9+−4y
x=−4y+9
Answer:
x = 9 - 4y
Step-by-step explanation:
please do this fraction thanks
Answers
Answer:
1 3/10
Step-by-step explanation:
A florist buys a dozen roses for $12.96 what is the cost of one rose
Answers
cheese.io
jeffrey opened a savings account where his funds will acccrue 1.2% intrest. if he originally investeed $4,500.00 into his account, how much intreat will he accrue in 10 years
Answers
Jeffery will obtain $54 as interest on $4,500.00
What do we mean by interest?In finance and economics, interest is the payment of an amount above the repayment of the principal sum (that is, the amount borrowed) by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by borrower or deposit-taking financial institution. It differs from a fee that the borrower may pay to the lender or a third party. It is also distinct from a dividend, which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a fixed rate, but rather on a pro-rata basis as a share of the reward gained by risk-taking entrepreneurs when revenue exceeds total costs.If Jeffery originally invested $4,500.00.
Then, 1.2% interest on 4,500.00 will be:
= 4,500.00/100 × 1.2= 45 × 1.2= $54Therefore, Jeffery will obtain $54 as interest on $4,500.00.
Know more about interest here:
https://brainly.com/question/25793394
#SPJ1
Feng went shopping for a new pair of pants because of a sale. The store was offering a 40% discount. If the price on the tag was $33, what would be the price after the discount but before tax, to the nearest dollar and cent?
Answers
We need to know about percentage to solve the problem. The price of the pair of pants after discount but before tax is $19.8
Percentage of a number gives us a certain part of the quantity, suppose we say that 20% of 100 then we have 20. It can be defined as a given part in every hundred. In this question we know that the store Feng goes to buy a pair of pants offers 40% discount, which means that Feng can save 40% of the price of the pants. The original price on tag is given as $33, we have to find what 40% of $33 is and then subtract that amount from $33 to get the price of the pair of pants after discount but before tax.
Discount=[tex]\frac{40}{100}[/tex]x33=132/10=13.2
The price of the pants after discount =$(33-13.2)=$19.8
Therefore we found that the price of the pair of pants after discount but before tax is $19.8
Learn more about percentage from here:
https://brainly.com/question/28220735
#SPJ9
An auto transport carrier takes trucks and cars to dealerships around the country. The total weight of the load, in tons, can be found using the expression 3t+2c , where t is the number of trucks being transported and c is the number of cars being transported. What is the meaning of the 2 in the expression?
Answers
The meaning of the 2 in the expression 3t + 2c is the weight of each car
What are expressions?
Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine what is the meaning of the 2 in the expression?The expression is given as
3t + 2c
From the question we have the following parameters:
t is the number of trucks being transportedc is the number of cars being transportedThis means that the weight of each car is 2
Hence, the meaning of the 2 in the expression 3t + 2c is the weight of each car
Read more about expressions at
https://brainly.com/question/723406
#SPJ1
can 8/15 be simplified? If so by what?
You don't need to do the math just yes or no and by what
Answers
Answer: No
Step-by-step explanation:
It is already in its simplest form, but the decimal for it would be 0.53.
Answer: 8/15 can`t be simplified
Step-by-step explanation:
[tex]\displaystyle\\\frac{8}{15} =\\\\\frac{2*4}{3*5} \\\\Hence,\\\\ 8/15\ can`t\ be\ simplified[/tex]
5x-17=2x+50
Find x, pls show work
Answers
Answer:
x = 22 1/3
Step-by-step explanation:
5x - 17 = 2x + 50
~Add 17 to both sides
5x = 2x + 67
~Subtract 2x to both sides
3x = 67
~Divide 3 to both sides
x = 22 1/3
Best of Luck!