The transformed function is:
g(x) = 2*|x + 1| - 6
How to write the transformed function?
We start with the original function f(x), and we define the transformed function as g(x).
First, we have a translation of 1 unit to the right, so we have:
g(x) = f(x - 1)
Then, we have a vertical stretch by a factor of 2.
g(x) = 2*f(x - 1)
A translation of 4 units down:
g(x) = 2*f(x - 1) - 4
And we know that f(x) = |x + 2| - 1
Replacing that, we get:
g(x) = 2*( |x -1 + 2| - 1) - 4
g(x) = 2*|x + 1| - 2 - 4
g(x) = 2*|x + 1| - 6
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suppose the reading rate of 6th grade students is uniformly distributed (this phrase tells you to use the uniform distribution!) between 100 and 180 words per minute. calculate probability that a selected student has a reading rate less than 115 words per minute.
Answer:
0.84 or 0.48 I cant remember
Step-by-step explanation:
my picture of good luck
Which statement best defines an angle?
A.
two lines that share a common line segment called the vertex
B.
two rays that share a common endpoint called the vertex
C.
two line segments that intersect at a point called the vertex
D.
two lines that intersect at a point called the vertex
The correct statement for the best definition of an angle is,
''two rays that share a common endpoint called the vertex''.
Option B is true.
What is mean by angle?
A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Given that;
Define an angle with the help of definition.
Now,
Since, We know that;
A figure which is formed by two rays that shares a common endpoint vertex is called an angle.
Thus, the best definition of an angle is,
''two rays that share a common endpoint called the vertex''.
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PLEASE HELP ME I NEED HELP
Convert 5 hours to minutes. O A. 300 minutes O B. 500 minutes O C. 50 minutes D. 150 minutes
300
1) Converting 5 hours
1 hour----------60 minutes
5 -------------- x
x = 300, since 5 times 60 is equal to 300 minutes.
So A, 300 minutes.
At school, the maximum number of students that can be in a classroom is 27. If there are 18 students signed up for the art class, how many more students can join the class?
I am trying to get the inequality as a problem
Step-by-step explanation:
x is the number of students than can still join.
x <= 27 - 18
so,
x <= 9
max. 9 more students can join.
A laptop is selling at Digital Direct. The store has an anniversary sale, and everything is 25% off. We have to pay 13% HST on all items purchased from the store. What is the original price of the laptop if you have to pay a total of $677.15 at the cash register?
The original price of the laptop is $479.40.
Given:
Discount on the laptop = 25%
HST paid on the laptop = 13%
Total price of the laptop = $677.15
Let the original price of the laptop be $x.
Price of the laptop after 25% off = x + 25% of x
= $ (125x/100)
Total Price of the laptop after paying 13% HST
= (125x/100) + 13% of (125x/100)
= (125x/100) + (65x/400)
= $ (565x/400)
Now, it is given that the total price paid is $677.15 at the cash register.
565x/400 = 677.15
x = (677.15 × 400)/565
x = $479.40
Therefore, the original price of the laptop is $479.40.
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Which table does not represent a proportional relationship?
Answer:
Table 3
Step-by-step explanation:
The ratio of x and y is not constant.
three tanks a b and c are used to store oil
tank a contains n litres of oil tank b contains (n+150) litres of oil
tank c is empty
oil is pumped from tank a and from tank b into tank c so that all three tanks contain the same amount of oil
500 litres of oil are pumped from tank a into tank c
work out the value of n
The value of n is 1650 after oil is transferred from Tank A and Tank B to Tank C.
How to solve basic algebra word problems?It is given that initially,
Oil in tank A = n
Oil in tank B = n + 150
Oil in tank C = 0
Amount of oil transferred to tank C by tank A = 500 liters
Let us say 'x' amount of oil was transferred to tank C from tank B.
The amount of oil left in tank A after transferring 500 liters to tank C = n-500
Amount of oil left in tank B after transferring 'x' litres to tank C
= n + 150 - x
Amount of oil in tank C now = 500 + x
Since it is given that all three tanks contain the same amount of oil now. i.e. the new amount of oil in tank A = new amount of oil in tank B
n - 500 = n + 150 - x
x = 650
The new amount of oil in tank B = new amount of oil in tank C
n + 150 - x = 500 + x
n = 350 + 2x
Since x = 500
n = 350 + 2*650
n = 1650
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Identify the mistake and explain why the graph of the aggregate expenditures line does not correctly illustrate the economy's equilibrium.
Given that the 45° line is appropriately positioned in the graph, we may conclude that the aggregate expenditure line does not accurately depict the economy's equilibrium. [See attached Image]
What is the explanation for the above answer?The economy reaches equilibrium when the 45° line intersects the Aggregate Expenditure line. It is worth noting that this occurs at a real domestic output of 280, rather than 340, as indicated by the dashed lines in the graph.
It is to be noted that Aggregate spending is a measure of national income in economics. The present value of all finished products and services in the economy is described as aggregate spending. Thus, aggregate spending is the total of all expenditures made in the economy by the factors over a certain time period.
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Evaluate. Write your answer as a fraction in simplest form. 4/3 to the power of 3
Answer:
[tex]2 \frac{10}{27}[/tex]
Step-by-step explanation:
4/3 to the power of 3 = to 4/3 x 4/3 x 4/3
which in the end equals to 64/27
there's no common factor between them to simplify, but we can turn them into a mixed number, which is 2 10/27 by dividing 64 and 27
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $61. A season ski pass costs $350. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
7 days would the skier have to go skiing in order to make the season pass less expensive than the daily passes.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. Every mathematical equation begins with L.H.S = R.H.S.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Let s be the cost of skiing per day.
So, the season pass plus ski rentals equates to daily skiing plus ski rentals
450 + 20s = 64s + 20s
450 = 64s
7.03 ≈ s
Hence, 7 days would the skier have to go skiing in order to make the season pass less expensive than the daily passes.
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If log (m + n) = log m+log n, show that m =n/n-1
log (m + n) = log m+ log n and proved it m =n/n-1
Given;
If log (m + n) = log m+ log n
To show that the m =n/n-1
Now, According to the question:
We know that,
Log (m + n) = log m + log n
Log (m + n ) = log (mn). [log a + log b = log ab ]
Cancelling the log on both sides.
then,
m + n = mn
=> n = mn - m
=> n = m (n - 1)
=> m = n / n - 1
Hence Proved
log (m + n) = log m+ log n and proved it m =n/n-1
What is Logarithm?
A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2.
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Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5
The equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe is D. y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe.
The equation will be:
y = 5.5 + x
where y = total wheat
The option that correctly reflects this is D.
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Answer:
The answer is D
Step-by-step explanation:
A business has $11,080 to spend on new laptops and tablet computers for its salespeople. The laptops cost $515 each. The tablets cost $285 each. The business wants each salesperson to have either a laptop or a tablet. There are 30 salespeople. Create a system of equations that models how many of each type of computer the business should buy.
a. 515x + 285y = 11,080
x + y = 30
b. 515x + 285y = 30
x + y = 11,080
c. 515x + y = 30
x + 285y = 11,080
d. x + 285y = 30
515x + y = 11,080
Jill converted the equation of the line 15x-4y=-2 into slope-intercept form and found the slope and y-intercept of
the line as follows.
15x-4y=-2
15x-4y-15x--2-15x
-4y=-2-15x
-4y -2-15x
-4
22
-4
y-2--16x
y-1-15x
y=-15x+12/2
15
4
slope =
Answer: She got the sign of the slope wrong
Step-by-step explanation:
She did -4y -2 - 15x
-4 = -4
and turned that into ,
-2 - -15x
-4 (minus) -4
which is wrong, because she did the negative twice. Therefore, she mixed up the sign of the slope.
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Subtracting Exponents examples
Answer:
Step-by-step explanation:
Exponents are powers or indices. An exponential expression consists of two parts, namely the base, denoted as b and the exponent, denoted as n. The general form of an exponential expression is b n.
How to Subtract Exponents?
The operation of subtracting exponents is quite easy if you have a good understanding of exponents. In this article, you will learn the rules and how to apply them when you need to subtract with exponents.
But before we can embark on subtracting with exponents, let us remind ourselves some of the basic terms about exponents.What is an exponent?
Well, an exponent or power denotes the number of times a number is repeatedly multiplied by itself. For example, when we encounter a number written as, 53, it simply implies that 5 is multiplied by itself three times. In other words, 53 = 5 x 5 x 5 = 125The same format of writing exponents applies with variables. Variables are represented by letters and symbols. For instance, when x is multiplied repeated by itself 3 times, then we write this as; x3. Variables are usually accompanied by coefficients. A coefficient is therefore an integer that is multiplied by variable.
For instance, in 2x3, the coefficient is the number 2 and x is the variable. When a variable has no number before it, the coefficient is always 1. This is also true when a number has no exponent. The coefficient of 1 is normally negligible, and therefore cannot be written with a variable.
Subtraction of exponents really does not involve any a rule. If a number is raised to a power. You simply compute the result and then perform the normal subtraction. If both the exponents and the bases are the same, you can subtract them like any other like terms in algebra. For example, 3y – 2xy = x y.
Subtracting exponents with the same base
Let’s explain this concept with the help of a few examples.
Example 1
23– 22 = 8 – 4 = 4
53 – 52 = 75 – 25 = 50
Subtract x 3 y 3 from 10 x 3 y 3
In this case the coefficients of exponents are 10 and 1
The variables are like terms and hence can be subtracted
Subtract the coefficients = 10 – 1
= 9
Thus, 10x 3y 3– x 3y 3 = 9 (xy)3
You can notice that, the subtraction of exponents with like terms is done by finding the difference of their coefficients.
Subtract 8x2 – 4x2
In this case, the variables 4x2 and 8x2 are like terms and their coefficients are 4 and 8 respectively.
= 8x2 – 4x2
= (8-4) x2.
= 4 x2
Work out (-7x) – (-3x)
Here, -7x and -3x are like terms
= -7x – (-3x)
= -7x + 3x,
= -4x.
15x – 4x – 12y – 3y
Subtract like terms
15x – 4x = 11x
12y – 3y = 9y
Thus, the answer is 11x – 9y.
Subtract (4x + 3y + z) – (2x + 3y – z).
These variables are like terms
(2x + 3y – z) – (4x + 3y + z)
Open the parenthesis;
= 2x + 3y – z – 4x – 3y – z,
Rearrange the like terms, and perform the subtraction
= 2x – 4x + 3y – 3y – z – z
= -2x + 0 – 2z,
= -2x – 2z
Subtracting exponents with different base
Exponents with different bases are computed separated and the results subtracted. On the other hand, variable with unlike bases can not be subtracted at all. For, example subtraction of a and b can not be performed and the result is just a -b.
To subtract a positive exponents m and negative exponents n, we just connect both the terms by changing the subtraction sign to a positive sign and write the result in the form of m + n.
Therefore, subtraction of a positive and a negative unlike exponents m and -n = m + n.
Example 2
42 – 32 = 16 – 9 =7
Subtract: 11x – 7y -2x – 3x.
= 11x – 2x – 3x – 7y.
= 6x – 7y
Evaluate 3x2 – 7y2
In this case, the two exponents 3x 2 and 7y2 are unlike terms and so it will remain as it is.
Here 3x and 7y both are unlike terms so it will remain as it is.
Therefore, the answer is 3x2 – 7y2
Evaluate 15x – 12y – 11x
= 15x5 – 11x5 – 12y5
= 4x5 – 12y5
Martha paid $6.35 for five pounds of chicken last week .What is the chicken's price per pound.
Answer:
$1.27
Step-by-step explanation:
Name one pair of parallel planes. All lines and planes that appear to be parallel are parallel.
The parallel plane is the plane that has the same in-between distance at all points on the plane so plane ABF is parallel with plane DCG so option (C) is correct.
What is the plane?The plane is a two dimension(2D) surface that has a surface area.
We can draw lines on a plane and two or more planes can intersect or parallel.
If two planes are parallel then the perpendicular distance between both planes must be the same.
The angle of inclination of two parallel planes with a single reference plane is also the same.
In the given cuboid the plane ABF is parallel with plane DCG.
So, ABF || DCG.
Hence "The parallel plane is the plane that has the same in-between distance at all points on the plane so plane ABF is parallel with plane DCG".
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A box is used to hold bolts for an assembly line. When there are 40 bolts in the box, the total mass is 280 g. When there are 65 bolts in the box, the total mass is 405 g. Find the mass of the box and the mass of each bolt.
The box contains 40 bolts, each weighing 280 g. The package weighs 405 g when there are 65 bolts inside. The bolt's mass is thus 5g, while the box's mass is 80g.
What makes linear equations significant?In many practical applications in daily life, linear equations are a crucial tool in science.
They let scientists, among other things, make predictions, compute rates, and characterize connections between two variables in the physical world. In order to see trends, linear equations are often graphed.
What exactly is the idea behind solving equations?A condition on a variable is an equation when it ensures that two expressions in the variable have the same value.
The variable’s value for which the equation holds true is referred to as the equation’s solution.
Bolts are kept in a box for an assembly line. The package weighs 280 g when there are 40 bolts inside.
In the event that there are 65 bolts in the box, the total mass is 405 g. Find the mass of the bolt and box.Let ‘x’ be the mass of each bolt and ‘y’ be the mass of the box, then we have:
40x + y = 280(1)
65x + y = 405(2)
If we subtract these 2 equations that are for (2) – (1) we get:
25x = 125
X = 5
Using (1) we get
Y = 280-40x
Y = 280-40*5
Y = 80.
Hence the mass of the bolt is 5g and the mass of the box is 80g.
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Write the equation in point slope form using either point
I NEED HELP ASAPPPPPPPPP
Answer:
y + 2 = 3/4 (x - 1)
Step-by-step explanation:
You would pick one of the points in this case I picked (1, -2), for point-slope form your equation is y - y1 = m(x-x1).
Finding the slope (m) is easy you just do rise (up/down) OVER run (left/right).
So in this case your slope (m) is 3/4.
then you just plug everything in but because two negatives equal a positive you equasion should look like this y + 2 = 3/4(x - 1)
p(x) = -3x - 1
graph the linear function
Answer:
Step-by-step explanation:
1) First find the y-intercept point
You can find it easily by finding the number without the variable. In this case, it is -1. With this draw a point on the y-axis line down to -1.
2) Find the slope.
Next, you can find a point by substituting a number for x. So in this example, I will be subbing x for 1.
y = -3(1) - 1
y= -3 - 1
y= -4
So there will be a point at (1,-4).
3) Graphing.
After you find that you can easily draw a straight line through both points.
A sailboat costs $26,232. You pay 10% down and amortize the rest with equal monthly payments over a 8-year period. If you must pay 7.5% compounded monthly.what is your monthly payment? How much interest will you pay?Monthly payments: $(Round to two decimal places.)Interest: $(Round to two decimal places.)
Step 1- Write out the Present Value of Annuity formula:
[tex]PV=P\times\frac{1-(1+\frac{r}{n})^{-t\times n}}{\frac{r}{n}}[/tex]Where
[tex]\begin{gathered} PV=\text{ the present value} \\ P=\text{ the periodic payment} \\ n=\text{ the number of payments in a year} \\ r=\text{ annual interest rate} \end{gathered}[/tex]Step 2- Write out the given values and substitute them into the formula:
[tex]\begin{gathered} PV=\$26232(1-0.1)=\$26232\times0.9=\$23608.80 \\ n=12 \\ r=0.075 \end{gathered}[/tex]Substituting the values into the formula, we have:
[tex]23608.80=P\times\frac{1-(1+\frac{0.075}{12})^{-8\times12}}{\frac{0.075}{12}}[/tex]Therefore,
[tex]23608.80=72.0260P[/tex]Dividing both sides by 72.0260, we have:
[tex]P=\$327.78[/tex]Hence, the monthly payment is $327.78.
The total amount T paid is given by:
[tex]T=\$327.78\times8\times12=\$31466.88[/tex]Hence, the interest I is given by:
[tex]I=31466.88-23608.80=\$7858.08[/tex]Therefore, the monthly payment is $327.78 and the interest paid is $7858.08
What could be the time of a place at 90-degree West longitude if the Greenwich Time is 12pm
The time would be 6 AM at the place at 90-degree West longitude.
This is a problem with coordination and time. We can solve this problem by using a few steps.
We should recall that each degree west is equivalent to 4 minutes before.
The given place is at 90-degree West longitude. Therefore, the total time difference is (90 × 4) = 360 minutes.
360 minutes is equal to 360/60 = 6 hours.
We have to deduct the time from GST, (12 - 6) = 6 AM
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Nolan drank 2/3 of a glass of water in the morning and 1/2 of a glass in the afternoon. How much water did Nolan drink in all?\
Answer: 7/6
Step-by-step explanation:
4/6 + 3/6
4+3+6
=7/6
Is the following a function??
The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. Alternatively, we may say that the graph of f is the graph of the equation y.
Explain about the function?A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Up until function composition, that is essentially all there is to "operations on functions." Don't be alarmed by the topic's notation; it simply means what it says: add, subtract, multiply, or divide; then, when necessary, simplify and evaluate.
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You have 200 feet of fencing to enclose a rectangular plot that borders on a river (a long side borders the river). If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
The maximum Area that can be enclosed will be 5000 square feet.
In the given question, it is stated that 200 feet of fencing will be done to enclose a rectangular plot with borders on a river. It has a long side on the border of a river which does not needs fencing. We need to find out the Length and Width of the plot that will maximize the area and also find out the Maximum area that can be enclosed.
It is given that the total length of the fence is 200 feet.
Let the length of the plot be l
let the width of the plot be w
=> Total Perimeter will be = l + 2w because the longer side or 1 side of length does not need fencing. Putting the perimeter as 200 we get
=> l + 2w = 200 => Equation (1)
Now, we know the Area of the plot will be l*w,
By equation (1) we get l = 200 - 2w, Putting the values in the Area:
=> Area = (200-2w) * w
=> A = 200w - 2w²
For maximum Area, the derivative of A with respect to w will be 0
=> [tex]\frac{dA}{dW} = 200 - 4w[/tex]
=> [tex]0 = 200 - 4w[/tex]
=> w = 50
Putting w = 50 in Equation (1) we get
=> l = 100
We got our Length l = 100 feet, and Width w = 50 feet. Now we will Calculate the maximum Area to enclose.
=> Area = l*w
=> A = 100*50
=> A = 5000
Hence, the Maximum area to enclose will be 5000 square feet.
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Write the phrase "Four times the difference of six and y equals five less than y" as a variable expression:
Write the phrase "six more than nine times n is twenty" as an equation:
Answer: 4(6-y)
Step-by-step explanation: Since you are multiplying 4 by the difference of 6 and y, you put 6 and y in parenthesis with the 4 on the outside. Then 6-y goes inside the parenthesis.
Also the second one would be (6+9)n=20
HELP MEEEE PLEASEEEE
A pound of peppers costs $0.62. The total cost varies directly with the pounds of peppers purchased. Write an equation that relates the total cost, c, and the number of pounds of peppers purchased, p.
If a pound of peppers costs $0.62, then multiply the cost by how many pounds you're getting.
An 8 1/2 sheet of paper is being cut into 1 9/16 inch strips to make a paper chain. How many strips can be made from one sheet of paper?
Answer:27/5
Step-by-step explanation: divid 8 1/2 by 1 9/16 and get 5.4 then you put that in fraction form and if I’m correct you get 27/5
Which graph represents the solution to the inequality 2(b + 2) > 24?
Answer:
number line with open point at 10 with arrow pointing left
Step-by-step explanation:
Answer:a
Step-by-step explanation: