Answers
Using the absolute value function, we have that:
1) The table is:
x = 0, |x| = 0.x = 1, |x| = 1.x = 2, |x| = 2.x = 3, |x| = 3.x = -1, |x| = 1.x = -2, |x| = 2.x = -3, |x| = 3.2) The graph is given at the end of the answer.
3) The rule is: g(x) = |x - 3|.
4) The rule is: D(x) = |x| - 5.
5) The rule is: K(x) = |x - 3| - 5.
What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin.
Hence, applying the rule, the table is completed as follows:
x = 0, |x| = 0.x = 1, |x| = 1.x = 2, |x| = 2.x = 3, |x| = 3.x = -1, |x| = 1.x = -2, |x| = 2.x = -3, |x| = 3.The function is graphed at the end of the answer.
A translation right of 3 units is given by:
f(x - 3).
Hence:
g(x) = |x - 3|.
A translation down 5 units is given by:
f(x) - 5.
Hence:
D(x) = |x| - 5.
For item 5, the function was shifted 5 units down and 3 right, hence it is given by:
K(x) = |x - 3| - 5.
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Related Questions
Write an absolute value equation that has the given solution.
X= 4 and X= -10
Answers
An absolute value equation that has the given solution is mathematically given as
I3 + xI - 7 = 0 where the solutions (or roots) are in X= 4 and X= -10
This is further explained below.
What is the absolute value equation?Generally, in this case, we want an absolute value equation that has the solutions x = 4 and x= -10.
A cheap way to do this is to look for a number N that:
N + 4 = -(N - 10)
then, isolating N we get:
2N = 6 + 10 = 6
N = 6/2 = 3
then
=N +4
= 3 + 4
= -8
and
=N - 10
= 3 - 10
= -7
In conclusion, we know that I-7I = I7I = 7
now we can write our equation as:
I3 + xI - 7 = 0
where the solutions (or roots) are in X= 4 and X= -10
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Last nights game at the arena in cleverland was 251 seats short of being filled to capacity. How many people attended the game?
Answers
A line that includes the point (0, -3) and has a slope of 6. What is its equation in slope-intercept form?
Answers
Answer:
y=6x-3
Step-by-step explanation:
6 is the slope bur (0,-3) is the y-intercept. Therefore, you just need to plug in the y-intercept and slope into y=mx+b which will give you y=6x-3.
Write each equation in exponential form.
log₇16,807=5
Answers
The given equation in logarithmic form is 7^5 =16807
As given to us, the function is log₇16807=5
Let us write this function in exponential form using the definition of logarithm
logₐx=b
a^b=x
here the logarithm is log₇16807=5
thus 7^5=16807
hence the given equation in logarithmic form is 7^5 =16807
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which angles of the transformation figures have the same measure as
Answers
Answer:
34
Step-by-step explanation:
I really don't know I just wanted to answer for points
30 points
Answers
MARKING BRAINLEIST IF RIGHT
Answers
Answer:
x = 15 , ∠ B = 108°
Step-by-step explanation:
∠ A and ∠ Bare alternate exterior angles and are congruent
∠ A = ∠ B , that is
6x + 18 = x + 93 ( subtract x from both sides )
5x + 18 = 93 ( subtract 18 from both sides )
5x = 75 ( divide both sides by 5 )
x = 15
Then
∠ B = x + 93 = 15 + 93 = 108°
I NEED HELP PLS ITS TOO HARD AND I CANT FIGURE IT OUT!
Answers
The equation to find the nth term of the sequence is aₙ = 4n - 17
How to find the equation of a sequence?The equation of the sequence can be represented as follows;
a₃ = - 5, a₄ = - 1, a₅ = 3, a₆ = 7, a₇ = 11
Therefore, let's find the equation of the nth term.
Using arithmetic formula,
aₙ = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore,
d = 11 - 7 = 4
Hence, let's find the first term using 7th term
11 = a + 6(d)
11 = a + 6(4)
11 - 24 = a
a = - 13
Therefore, the equation to find the nth term of the sequence is as follows:
aₙ = -13 + (n - 1)4
aₙ = - 13 + 4n - 4
aₙ = - 13 - 4 + 4n
aₙ = 4n - 17
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Can you guys help me ?
Answers
Answer:
The solution to this equation is (9t)^(12) / (4a)^(6).
Step-by-step explanation:
It is given that [(4a³t²)/(9at^6)]^-3 which is to be simplified and solved to get the final answer.
Now,
let us have a look at the equation and observe the powers given;
=> [(4a³t²)/(9at^6)]^-3
So, let us convert the powers using the rules;
=> [(4a²)/(9t^4)]^-3
Further, we will apply the rule known as product of powers and we get an equation that is;
=> (4a)^(-6) / (9t)^(-12)
Now, after reciprocating both the powers as per the rules we get;
=> (9t)^(12) / (4a)^(6)
Therefore, the solution to this equation is (9t)^(12) / (4a)^(6).
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Solve each equation. 2 ln x=4
Answers
The Solution for equation 2 ln x=4 is 7.4088.
What is an equation ?2 ln x=4
( [tex]x^{2}[/tex]) = [tex]e^{4}[/tex]
[tex]x^{2}[/tex] = 54.598
x = √54.598
x = 7.4088
A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.
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HELPPP ASAPPP!!!!In 5-7 complete sentences, write a real world situation that can be modeled by the equation. 19.25x =17.25x +26.77
Answers
A real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?
What is a equation?It should be noted that an equation is used to show the relationship between the variables that are illustrated.
In this case, a real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?
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[tex]5xx^{2} -9x-10[/tex]
Answers
Answer:
The values of x for the equation 5x² - 9x - 10 is x = 9 ± √(281) / 10.
Step-by-step explanation:
In this question we need to solve the given equation that is 5x² - 9x - 10 to obtain the value of x using the complex solution method.
Now, the given equation is 5x² - 9x - 10 in which we need to apply the quadratic formula to find the solution;
So, the quadratic formula is => -b ± √(b² - 4ac) / 2a
Now, on comparing the equation 5x² - 9x - 10 we get the values;
a = 5
b = -9
c = -10
Further, on substituting the values given above in the quadratic formula to obtain the value of x.
=> -(-9) ± √((-9)² - 4(5×(-10)) / 2×5
=> 9 ± √(81 +200) / 10
=> 9 ± √(281) / 10
After simplifying the above equation we obtained the value of x that is;
=> x = 9 ± √(281) / 10
Now, the final values of x from the above condition are;
=> x = 9 + √(281) / 10
and
=> x = 9 - √(281) / 10
It can be further represented in the decimal form;
=> x = 2.57630546...
and
=> x = −0.77630546...
Thus, the values of x for the equation 5x² - 9x - 10 is x = 9 ± √(281) / 10.
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I am F years old and my brother is B years older. What is the sum of our ages? What will be the sum of our ages in 3 years? What was the difference of our ages 3 years ago?
Answers
F+b
The sum in 3 years is:
(F+3)+(B+3)
Lastly the difference 3 years ago would be:
(F-3)-(B+3)
The odds in favor of a randomly selected person in a certain classroom is left handed are 3:22. What is the PROBABILITY that a randomly selected person from the room is left handed (as a percent!)
P(left)=
Answers
Answer:
12%
Step-by-step explanation:
Odds in favor means number of favorable outcomes : number of unfavorable outcomes
Here favorable outcome is selecting a left-handed person
So odds of 3:22 means that the ratio of selecting left-handed person to right-handed person is [tex]\frac{3}{22}[/tex]
P(left) = [tex]\frac{3}{3+22} = \frac{3}{25}[/tex]
P(left) as percent = [tex]\frac{3}{25}\cdot100[/tex] = 12%
Our family has a small pool for relaxing in the summer that holds 1500 gallons of water. I
decided to fill the pool for the summer. When I had 5 gallons of water in the pool, I decided
that I didn't want to stand outside and watch the pool fill, so I wanted to figure out how
long it would take so that I could leave, but come back to turn off the water at the right
time. I checked the flow on the hose and found that it was filling the pool at a rate of 2
gallons every 5 minutes. How many gallons of water will be in the pool after 50 minutes?
How many minutes will it take to fill the pool? Justify your answer with a mathematical
model of the problem situation.
Answers
1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes
2) the amount of water in the pool after 50 minutes = 105 gallons
3) and the amount of time required to fill the pool = 12 hours 46 minutes
In this question,
a small pool hold 1500 gallons of water.
When there's is 5 gallons of water in the pool, the person decided
that not to stand outside and watch the pool fill.
This means, from the time he had decided, the amount of water in the pool = 5 gallons.
the water was filling the pool at a rate of 2.
Let t be the time in minutes.
So, the amount of water in the pool after 't' minutes would be,
f(t) = 2t + 5
We get an mathematical model for given situation,
f(t) = 2t + 5, where t is the time in minutes
We need to find the amount of water in the pool after 50 minutes
For t = 50 minutes
f(50) = 2(50) + 5
f(50) = 100 + 5
f(50) = 105 gallons
Also, we need to find the amount of time required to fill the pool.
1500 = 2t + 5
1495 = 2t
t = 747.5 minutes
t = 12 hours 46 minutes
Therefore, 1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes
2) the amount of water in the pool after 50 minutes = 105 gallons
3) and the amount of time required to fill the pool = 12 hours 46 minutes
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a number was multiplied by 12 the result was doubled and the final answer was 144
What is the number
Answers
Answer: 1
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let the number =x
So, x*12*2=144
=12x=144/2
=12x=72
=x=72/12
=x=6
So the answer is 6 because 6*12=72 and doubling 72 gives us 144.
Have a great day!!!
Express y^-9 using a positive exponent
Answers
Answer:
[tex]\frac{1}{y^9}[/tex]
Step-by-step explanation:
Exponent rule → [tex]a^{-b}=\frac{1}{a^b}[/tex]
Using exponent rule → [tex]y^{-9}=\frac{1}{y^9}[/tex]
Final result → [tex]=\frac{1}{y^9}[/tex]
A basil plant grows about half an inch per week. When Finnegan buys the plant, it is 7
inches tall.
a. How tall is the basil plant after 1 week?
Answers
Answer:7 and a half
Step-by-step explanation:
Simple enough, if it seven inches and grows half an inch a week than after a week it grows half an inch, so its just 7 + a half, your awnser is 7 and a half
PLEASE HELP!! THIS IS BEYONDDDD MEEEEE. I will mark brainliest
Answers
X=2
X=168
X=21
X=pie
If this shape was rotated 270 degrees counter-clockwise around , what would the new point for D be?
A parallelogram with point C at negative 4 comma 6, point D at negative 7 comma 2, point E at 6 comma 6, and point F at 3 comma 2.
Answers
After rotating a parallelogram 270° counterclockwise points of D will be (2,7).
What are the types of translation?There are 4 types of translation they are, translation, rotation, and dilation.
We know when we rotate a shape 270° counter-clockwise the coordinates (x,y) becomes (y, -x) that is we switch x and y and make x negative.
Given a parallelogram with points C(-4,6), D(-7,2), E(6,6) and F(3,2).
Assuming point D when rotated 270° becomes D'.
∴ The points of D will switch which is (2,-7) and then we will make x negative.
So, D' becomes (2,7).
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-7(4x) + 4 ≥ −18 + 7x
Answers
Answer:
x ≤ 22/35=====================
Given inequality:
-7(4x) + 4 ≥ −18 + 7xSimplify and collect like terms:
- 28x + 4 ≥ −18 + 7x7x + 28x ≤ 4 + 1835x ≤ 22x ≤ 22/35What are the solutions of each equation? Check your answers.
(b) ln (3 x+5)²=4
Answers
The solution for equation ln (3 x+5)²=4 is 0.796.
What is an equation ?
ln (3 x+5)²=4
2 ln (3x + 5)= 4
3x + 5 = [tex]e^{2}[/tex]
3x = 7.389-5
x = 0.796
A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.
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the area of the compound shape below is 75cm squared. find the value of x
Answers
Answer:since the bottom is 10cm and both tops are the same length that means its 5cm
Step-by-step explanation:YOU can divide 10 by 2
Joaquin wants to make his famous chocolate chip cookies to bring to his friend's birthday party. The original recipe serves 5 people and requires one quarter of a cup of butter, but he needs it to serve 28 people. How many cups of butter will he need?
a. 2 and one fourth cups
b. 1 and one fifth cups
c.1 and two fifths cups
d.1 and one fourth cups
Answers
Help
Pls thx math work
Answers
The value of 6300 kg in grams written in standard form will be 6.3 × 10^6.
How to calculate the values?It should be noted that the value of 6300 kg in grams will be:
1000 grams = 1 kilogram
= 6300 × 1000
= 6300000
= 6.3 × 10^6
Therefore, the value of 6300 kg in grams written in standard form will be 6.3 × 10^6.
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Classify each number as rational or irrational:
Answers
Classification of each of the listed as rational or irrational are done below
√5 * √5 rational2√9 * √4 rational√3 * √16 irrational7√3 * √3 rationalWhat is a rational numbers?
This is a term used in mathematics to refer to some set of numbers that are fractions where the numerator and the denominator are non zero digits. Rational numbers can be expressed as fractions.
What is a Irrational numbers?Irrational numbers refers to numbers that cannot form a fraction
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1,29,27,28,30,27 what’s the mean
Answers
Answer:
mean is the sum of all the values divided by the total values.
Step-by-step explanation:
so total values are 6, and the sum of all the values is: 1+29+27+28+30+27
= 142
so now the mean is 142÷6= 23.67
Number 12 please help was Answer
Answers
Find the inverse of each function. Is the inverse a function?
y=4-3 x
Answers
The inverse function returns the original value for which the output of a function was given.
The inverse of this function is [tex]f^{-1[/tex](x) = -(x - 4/3)
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
A function's inverse is not always a function! To ensure that the inverse function is also a function, the original function must be a one-to-one function. A one-to-one function is one in which each second element corresponds to exactly one first element. (Each x and y value is only used once).
The inverse of a function is thought to be a reflection of the original function along the line y = x. Simply put; the inverse function is obtained by swapping the original function's (x, y) values.
Let the function be y = 4 - 3x
f(x) = 4 - 3x
y = 4 - 3x
simplifying the value of x, we get
x = 4 - 3y
x - 4 = -3y
x - 4/-3 = y
[tex]f^{-1[/tex]= - (x - 4/3)
The inverse of this function is [tex]f^{-1[/tex](x) = -(x - 4/3).
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Problem (PLEASE HELP AND EXPLAIN)
Jamar wants to hire a plumber to fix his shower. The plumber informs him that 1 shower job requires 3 hours of work. The plumber charges $25 per hour, but he will only accept British Pounds as payment. Every British Pound is worth $1.62. How many British Pounds will Jamar need to pay the plumber for the shower job?
Which two units canceled?
Why is it important to cancel units when solving problems with multiple units? Use at least 2 complete sentences.
Answers
Answer:
[tex] \sf \fbox{46.296 British Pounds}[/tex]
Step-by-step explanation:
1 shower job requires 3 hours of work,
plumber will fix only 1 shower that means he will work for 3 hours,
Charges of 1 hour = 25$
Charges of 3 hour = 25× 3 = 75$
The currency that plumber accept is British pound (£),
1 British pound (£) = 1.62 dollar ($)
x British pound = 75 dollar
[tex] \frac{1}{x} = \frac{1.62}{75} [/tex]
taking reciprocal both the side,
[tex] \frac{x \cancel £}{1\cancel£} = \frac{75 \: \cancel\$ }{1.62 \:\cancel \$} [/tex]
[tex]x = 46.296[/tex]
Jamar need to pay 46.296 British Pounds to plumber for the shower job.
The two units that were cancelled was Dollar & Pound.
It is required to cancel units because, mathematical operation does not work for different units. For e.g. If I have given two measurement one is volume(cm³) & another is length(cm) so I cannot add them.
[tex] \sf Volume + Length = Not \: possible [/tex]
Same thing happens with division Operation of two different units, the magnitude gets cancelled but unit still remains there.
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