The equation of the new function g(x) is g(x) = 2 - |x+2|
Transformation of functionTransformation is. way of changing the position of an object on an xy-plane.
Given the parent function f(x) = |x+3|.
If the function is translated 2 units down and 1 unit right, then the resulting function will be |x+3 - 1| - 2 which is equivalent to |x+2| - 2
The reflection of the resulting function across the x-axis is given as:
g(x) = -(|x+2|-2)
g(x) = 2 - |x+2|
Hence the new function g(x) if the parent function undergo the transformation is g(x) = 2 - |x+2|
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given : AD is perpendicular to DC, <1 and <2 are complementary Proven: <1 is congruent to <3
When two straight lines or rays intersect at a single endpoint, an angle exists formed. If 2 and 3 exists complements, and m2= 55°, then m3 = 90 - 55 = 35 degrees.
What is meant by angle?When two straight lines or rays intersect at a single endpoint, an angle exists formed. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Complements sum to 90 degrees.
If 1 and 2 are complements and m1 = 35°, then
m2 = 90 - 35 = 55 degrees.
Now if 2 and 3 are complements, and m2= 55°,
then m3 = 90 - 55 = 35 degrees.
The complete question is:
Given: 1 and 2 are complements, 2 and 3 are complements, and m1 = 35°. Prove: m3 = 35° Complete the missing parts of the paragraph proof. By then, we know that angle 1 is congruent to angle 3. The measure of angle 1 equals the measure of angle 3 by the definition of angles. Then, using the property, the measure of angle 3 is the degree.
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Elyse uses 42 gallons of water for a 10-minute
shower. Write and solve a prediction problem that uses this information.
Water used in three minutes in the shower is 12.6 gallons.
What is unit rate?An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Given Data
Elyse uses 42 gallons of water for a 10-minute shower,
Let
the time in minutes at position x
y=the quantity of water in gallons
The fact that
[tex]\frac{y}{x}[/tex] = [tex]\frac{42}{10}[/tex] = 4.2x
The unit price equals
The slope of the linear equation is equal to the unit rate.
then
y=4.2x
Problem
How much water will Elyse use in her shower for three minutes?
x = 3 minutes
substituting in the previous equation
y = 4.2x
y = 4.2(3)
y = 12.6
Water used in three minutes in the shower is 12.6 gallons.
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The length of a rectangular sign is 12 ft less than twice its width. Its perimeter is 144 ft. Find the length and the width of the sign.
The rectangular sign is 30 feet in length and 42 feet in width.
The perimeter of the rectangular sign = 144 ft
Let the width of the rectangular sign be x, and the length of the sign will be x-12
The formula for the perimeter of the rectangle:
P = 2(l+w)
where P = perimeter of the rectangle
l = length of the rectangle
w = width of the rectangle
Substituting the values in the formula we get:
144 = 2(x-12+x)
144 = 2(2x-12)
144 = 4x -24
168=4x
x= 42
So, the length is 30ft and the width is 42ft
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The cat rescue is selling cat beds as a fundraiser. If its goal is to raise $1300, how many cat beds must be sold at $15.00 each to meet the goal?
The cat rescue must sell 87 beds to meet the goal
How calculate the number of beds that must be sold ?The car rescue is selling cat beds as a fundraiser
The goal is to raise $1300
Each cat bed is sold at $15
The number that must be sold to reach the goal can be calculated as follows
= 1300/15
= 86.6
= ≅ 87
Hence 87 cat beds must be sold to reach the goal
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twice the diffrence of a number and 2 equals 8
Answer:
2(x - 2) = 8
x = 6
Step-by-step explanation:
2(x - 2) = 8
2(x - 2) = 8
2x - 4 = 8
+4 +4
-----------------
2x = 12
÷2 ÷2
----------
x = 6
I hope this helps!
Please list the number below least to greatest.PLEASE
27/4 , -3.2, -∛60 ,√48, 7.05 when arranged in ascending order we get:
-3.2 , -∛60 , 27/4 , √48, 7.05
How to order numbers from least to greatest?Determine the number of digits in each number.The number with the fewest digits is the smallest, so write it first.The number with the most digits is the largest, so it is placed last.
Given list of numbers,
27/4 , -3.2 , -∛60 , √48 , 7.05.
simplifying each numbers ,
=> 27 / 4 = 6.75
=> -∛60 = - ∛(2 × 2 × 3 × 5)
= -3.9149.
=> √48 = √(2 × 2 × 2 × 2 × 2)
= 4√3
= 6.928
So the list after simplification is ,
6.75 , -3.2 , -3.9149 , 6.928 , 7.05
Now arrange the numbers from least to greatest,
-3.2 , -3.91 , 6.75 , 6.928 , 7.05
= -3.2 , -∛60 , 27/4 , √48, 7.05.
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Fill in the blank to make a perfect square trigeminal x^+18x+
The number that fills in the blank to make a perfect square trigeminal of the given expression is 81.
Given expression:
[tex]x^2+18x +[/tex] _
We have to find the number that will fill the blank.
A perfect square trigeminal is an algebraic expression that is of the form ax 2 + bx + c, which has three terms. It is obtained by the multiplication of a binomial with itself.
Let the number that fills the blank be a.
Hence, the expression becomes:-
[tex]x^2+18x +a[/tex]
To make it a perfect square geminal, the expression must be a perfect square of a binomial.
We know that,
[tex](x+y)^2=x^2+2xy+y^2[/tex]
Comparing it with given expression, we get
2xy = 18x and,
[tex]y^2=a[/tex]
Hence,
y = 9
a = [tex]9^2[/tex] = 81
Hence, the number that fills the blank is 81.
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The assets and liabilities of a credit union banker are listed below.
What is the total net worth is the banker pays off the student loans?
A. $219,869
B. $247,517
C. $233,693
D. $252,304
Given the credit union banker's assets and liabilities, their total net worth is C. $233,693.
What is the net worth?The net worth of an individual is the difference between their assets (long-term and short-term) and their liabilities (long-term and short-term).
The net worth is equivalent to the equity of a business, which refers to the net assets owned by the stockholders after paying off all debts.
Assets:Car Value = $29,850
Savings Accounts = $12,409
Treasury Bonds = $10,000
Checking Account Balance = $19,419
Home Value = $194,450
Total assets = $266,128
Liabilities:Car loan = $10,560
Student Loans = $13,824
Credit Card Balance = $8,051
Total liabilities = $32,435
Net worth = $233,693 ($266,128 - $32,435)
Thus, the banker's net worth is not $219,869, $247,517, or $252,304 but Option C.
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Answer:
$247,517
Step-by-step explanation:
ITS RIGHT ON THE TEST GUYS ! :)
Please answer ASAP and thank you
Answer:
The last answer is correct.
Step-by-step explanation:
The plant start at 4 inches (0,4) and then grows 1 inch each week.
(1,5), (2,6).(3,7) and so on.
You and a friend are going to the movies. Tickets cost $5 each and you both buy popcorn and soda. Each costs a different amount. Write an algebra expression to represent the cost of your friends and your trip to the movies.
Answer:
2(5)+2x+2y
Step-by-step explanation:
since you both have the tickets the amount of the prize is going to double. You both also bought popcorn and soda if we take 1 popcorn as "x" it is also going to multiple 2 times same with the soda except different variable.
what is 2/3 times 1/16
Answer:
1/24
Step-by-step explanation:
Answer:
1/24
Step-by-step explanation:
so first you cross out the 2 and 16 because 2*8=16
then you multiply the numerator and the denominator.
then bam! your answer!
1/24
help me please help huhu
Answer:
(1) p(x) = 7x³ + 4x² + 6 - 9x⁴
Standard Form: - 9x⁴ + 7x³ + 4x² + 6Degree: 4Leading Coefficient: -9Leading Term: -9x⁴(2) p(x) = 1 + 3x - 9x⁵
Standard Form: -9x⁵ +3x + 1Degree: 5Leading Coefficient: -9Leading Term: - -9x⁵(3) y = 9x² - x³ + x⁹
Standard Form: x⁹ - x³ + 9x²Degree: 9Leading Coefficient: 1 (x⁹ = 1x⁹)Leading Term: x⁹(4) f(x) = (x +3)(x-2)(x+5)
Standard Form: x³ + 6x² - x - 30Degree: 3Leading Coefficient: 1Leading Term: x³Step-by-step explanation:
Standard form has terms arranged from the highest to the lowest power
Degree is the highest power
Leading coefficient is the coefficient of the highest term
Leading term is the term containing the highest power
(x + 3) (x - 2)(x + 5)
(x + 3) (x - 2) = x² + x - 6 using the FOIL method
(x² + x - 6)(x +5) = x³ + 6x² -x - 30
Step-by-step explanation:
come on, we explained this already in previous questions. if you understood the explanations there, you should have been able to some that here without any problems.
again, standard form is the sorted polynomial from highest variable exponent to the lowest (as the potential constant at the end represents the x⁰ term).
the leading term is the first term on the left (with the highest exponent).
the leading coefficient is the factor in this leading term.
degree is the highest exponent used in the polynomial (again, given by the leading term).
so, what is still the problem ?
i have a slight problem with your handwriting. it is unclear, if there is 7x³ or 17x³. or 13x or 3x.
1.
p(x) = 17x³ + 4x² + 6 - 9x⁴
now, just sort this from the highest to the lowest exponent.
p(x) = -9x⁴ + 17x³ + 4x² + 6
if it should be 7x³ instead of 17x³, please use 7x³ in the polynomial.
degree = 4
leading coefficient = -9
leading term = -9x⁴
2.
p(x) = 1 + 13x - 9x⁵
again sort from highest to lowest exponent
p(x) = -9x⁵ + 13x + 1
again, if it should be 3x instead of 13x, please use 3x in the polynomial.
degree = 5
leading coefficient = -9
leading term = -9x⁵
3.
y = 9x² - x⁵ + x⁹
remember, y = f(x)
that is the same thing, means the same thing. it just gives the result variable a specific name.
again sort by exponent.
y = f(x) or p(x) or ... = x⁹ - x⁵ + 9x²
degree = 9
leading coefficient = 1
leading term = x⁹
4.
f(x) = (x+3)(x-2)(x+5)
this is really like the other question I just answered.
so, we always multiply 2 terms. that result we multiply by the third term. and if they're are more, then that result with the fourth term, and that with the 5th term,...
I usually start at the left :
(x+3)(x-2) = x² - 2x + 3x - 6 = x² + x - 6
now
(x² + x - 6)((x+5) = x³ + 5x² + x² + 5x - 6x - 30 =
= x³ + 6x² - x - 30
so,
f(x) = x³ + 6x² - x - 30
degree = 3
leading coefficient = 1
leading term = x³
Find the area of square plot of land whose each side measures 17/2
The area of the land is 289/4 square units
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the area of the shape?The given parameters are
Shape = Square
Side length = 17/2
The area of a square shape is
Area = Side length^2
So, we have
Area = (17/2)^2
Evaluate the exponent
Area = 289/4
Hence, the area of square plot of land whose each side measures 17/2 is 289/4 square units
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given that f(x) =3x+7 and g(x) x2/2 what is the value of f(g(4))
Given the following functions:
[tex]\begin{gathered} f(x)=3x+7 \\ g(x)=\frac{x^2}{2} \end{gathered}[/tex]to find f(g(4)), we can start by finding g(4) first:
[tex]\begin{gathered} x=4 \\ \Rightarrow g(4)=\frac{(4)^2}{2}=\frac{16}{2}=8 \\ g(4)=8 \end{gathered}[/tex]now that we know that g(4) = 8, we can calculate the composition f(g(4)):
[tex]undefined[/tex]Answer:
f(g(4) ) = 31
Step-by-step explanation:
evaluate g(4) then substitute the value obtained into f(x)
g(4) = [tex]\frac{4^2}{2}[/tex] = [tex]\frac{16}{2}[/tex] = 8 , then
f(8) = 3(8) + 7 = 24 + 7 = 31
In a given country, the average price of a gallon of unleaded gasoline in 1995 was $2.54. In 2010, the average price was $3.18. Find and interpretThe average rate of change in the price of a gallon of gasoline per year. The average rate of change is $ ___ per year.(Type an integer or a decimal. Round to the nearest cent as needed.)
The rate of change is found using the slope formula
m = ( y2-y1)/(x2-x1)
We have two points
( 1995, 2.54) ( 2010, 3.18)
m = (3.18-2.54) / (2010-1995)
=.64/15
$.042666666 per year
Rounding to the nearest cent
$.04 per year
We know that the price went up from 1995 to 2010 so the price increased
It increased an average of $.04 each year
A. The price of a gallon of gasoline increased by an average of $_.04__ per year from 1995 to 2010
write 14/3 as a decimal.if necessary,use a bar to include which digit pr group of digits repeats.
To convert a fraction to a decimal, we simply divide.
Shown below:
This is never ending decimal with the "6" repeating.
Thus, we can put a bar over "6".
So,
[tex]\frac{14}{3}=4.\bar{6}[/tex]Mr. Mole left his burrow and started digging his way down. A represents Mr. Mole's altitude relative to the ground (in meters) after t minutes.
Based on the model that shows the altitude of Mr. Mole relative to the ground, the rate at which Mr. Mole was digging was 2.3 meters down per minute.
How to find the rate?When given a linear function, the rate that the model progresses is given by the slope. The slope in a linear function can be found as:
y = mx + b
m = slope
b = y-intercept
In the model given for Mr. Mole's digging, which is -2.3t - 7, the slope is -2.3.
This means that Mr. Mole is digging downwards at 2.3 meters per minute.
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nathan eats 2 pounds of lunch meat every 8 days how much meat does he eat per day
Sandy is buying t shirts for her school. The company she called charges $5.75 per shirt plus a $35 set up fee. Write an expression that represents the total cost for x number of shirts?
The expression that represents the given condition is given by
5.75x + 35.
In mathematics, an expression that was created using integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
However, since they are not produced from integer constants and algebraic operations, transcendental numbers such as such and e are not algebraic. The production of is often done as a geometric expression, but the definition of e requires an infinite number of algebraic operations. An expression is considered rational if it can be reduced to a rational fraction using the properties of arithmetic operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).If x shirts are bought, cost of x shirts at $5.75 = 5.75x
Set up fee $ 35
Total cost of x shirts = 35 + 5.75x
Therefore the required expression = 35 + 5.75 x
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The table shows information about the masses of some dogs. a) Work out the minimum number of dogs that could have a mass of more than 27 kg. b) Work out the maximum number of dogs that could have a mass of more than 27 kg. Mass, x (kg) 0≤x≤10 10≤x≤20 20≤x≤30 30≤x≤40 Frequency 3 9 13 4
Information regarding various dogs' masses is displayed in the table.
(a) 4 bare minimum number of dogs that could weigh more than 27 kg.
(b) 17 dogs, in total, may weigh more than 27 kg.
Given that,
Information regarding various dogs' masses is displayed in the table.
(a)Calculate the bare minimum number of dogs that could weigh more than 27 kg.
(b)Calculate how many dogs, in total, may weigh more than 27 kg.
(a) 4 bare minimum of dogs that could weigh more than 27 kg.
Because the minimum number so lets assume that all dogs in 20≤x<30 are less then 27.
Therefore, 4 bare minimum of dogs that could weigh more than 27 kg.
(b) 17 dogs, in total, may weigh more than 27 kg.
Because the maximum number so lets assume that all dogs in 20≤x<30 are more then 27.
4+13=17
Therefore,17 dogs, in total, may weigh more than 27 kg.
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Answer:
Step-by-step explanation:
15/14 multiplied by 4/3
State all integer values of x in the interval 3 ≤ x ≤ 9 that satisfy the following
inequality:
-4x+10> -7
The integer values of x in the interval 3 ≤ x ≤ 9 that will satisfy the inequality include 3, 4, 5, 6, 7, 8, and 9.
How to illustrate the information?It should be noted that an integer is simply used to represent a given number which can be positive.
From the information, we are given the information 3 ≤ x ≤ 9. This means that 3 is less than or equal to x and x is less than or equal to 9.
Therefore, the number that fits are from 3 to 9.
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253 x 67 using the turtle method
The value of the expression 253×67 using the turtle method is given by 16951.
The turtle method of multiplication was designed in order to make the multiplication of larger numbers easier. The larger numbers can be multiplied imagining them as the form of a turtle's head and neck. It involves mainly three steps of multiplication. The first step includes the multiplication of the numbers lying on the neck of a turtle. The next step includes making the collar of the turtle, taking care of the carryovers, and laying the egg of the turtle. The last step involves the multiplication of the other numbers. In the question, we are given the expression 253×67. We multiply this expression in the turtle method as attached in the figure.
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Marking for BRAINLIEST!!!
A maximum number of 4 points are available for this question. Part A is worth 1 point. Part B is worth 1 point. Part C is worth 2 points.
Greg is shopping at a bicycle store. The store is having a sale and discounting all bicycles by 20% of the marked price. He decides to buy a bicycle with a marked price of $199.75.
Part A: Set up a proportion that can be used to find the dollar amount of the discount (d).
Part B: Given that the sales tax in Greg's state is 7%, what is the final cost of the bicycle he buys?
Part C: Greg's brother, Max, lives in a different state with a 5.5% sales tax rate. Max found the same bicycle discounted 25% from a regular price of $215.99. If Max buys the bicycle, who pays the lower total cost? Justify your answer.
evaluate log49 base 1/7
Answer:
Step-by-step explanation:
Exact Form:
1/2
Decimal Form:
-0.5
Answer:
- 2
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{\frac{1}{7} }[/tex] 49 = n , then
49 = [tex](\frac{1}{7}) ^{n}[/tex]
49 = [tex](7^-1)^{n}[/tex] , that is
7² = [tex]7^{-n}[/tex]
since bases on both sides are equal then equate exponents
- n = 2 ( multiply both sides by - 1 )
n = - 2
squared root 50 x squared root 8
surds
Answer:
20
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{50}[/tex] × [tex]\sqrt{8}[/tex]
= [tex]\sqrt{50(8)}[/tex]
= [tex]\sqrt{400}[/tex]
= 20
Which transformation
does not always preserve distance?
1 (x,y) → (x + 2, y)
2 (x,y) → (-y, -x)
3 (x,y) → (2x, y - 1)
4 (x,y) → (3-x, 2-y)
From Option 1,2,3 and 4.
Option 3 transformation is A dilation does not always preserve distance.
Give that,
We have to find which transformation does not always preserve distance.
1 (x,y) → (x + 2, y)
2 (x,y) → (-y, -x)
3 (x,y) → (2x, y - 1)
4 (x,y) → (3-x, 2-y)
Option 3 is A dilation does not always preserve distance.
Dilation means a modification of this kind that alters the size of the image is called a dilatation. How much larger or smaller the image is is determined by the scale factor, often known as the scalar factor. A picture of each type of dilatation is shown below (one that gets larger and one that gest smaller).
Therefore, Option 3 transformation is A dilation does not always preserve distance.
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Create an Equivalent expression for 18^-7*18^5
the volume of a cube shaped crate i 27 cubic feet. what is the length of one edge of the crate?
Answer: The length of the edge of the crate is 3 feet.
Step-by-step explanation:
The formula of the volume of a cube is the cube of edge length.
The volume of the cube (V) = (edge)³ ...................................(1)
In the given question volume is 27 cubic feet.
So, V = 27 cubic feet
Now we replace the Volume with the edge using equation (1)
i.e. (edge)³ = 27
or we can say that the cube root of the edge is equal to 27
i.e. edge = ∛27
which is equal to 3
hence, edge = 3 feet
To calculate the cube root write prime factors of 27 and group them in groups of three
i.e. ∛27 = ∛(3×3×3) = ∛ (3)³ = 3
Help, this is Math.
Dividing fractions
Step-by-step explanation:
don't panic. just breathe and then use common sense.
1.
1 math question in 1/200 second
2 minutes have 2×60 seconds = 120 seconds.
each of the seconds has 200 1/200 seconds.
so, in 2 minutes we have
120 × 200 time units to finish math questions.
in each time unit 1 math question can be answered.
120×200 = 24,000
the computer can answer 24,000 math questions in 2 minutes.
2.
it can run for 15 minutes.
15 minutes have
15×60 = 900 seconds (as every minute has 60 seconds)
it can vacuum 1/2 ft² in 1 seconds.
in 900 seconds it can then vacuum 900×1/2 = 450 ft².
so, yes, it can clean 400 ft² without recharging.