Using translation concepts, it is found that the equation of the transformed function is:
y = |x + 3| - 2.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The absolute value function is given by y = |x|, and has vertex at (0,0). After the transformations, the function has vertex (-3, -2), which means that:
It was shifted 3 units to the left, hence x -> x + 3.It was shifted 2 units down, hence y -> y - 2.Thus, the equation of the function is now given by:
y = |x + 3| - 2.
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Answer:y = |x + 3| - 2.
Step-by-step explanation: B on edge
Solve the linear differential equation 2xy' + y = 2√x
Answer:
Step-by-step explanation:
General form of the linear differential equation can be written as:
[tex]\frac{dy}{dx}+P(x)y=Q(x)[/tex]
For this case, we can rewrite the equation as:
[tex]\frac{dy}{dx}+\frac{1}{2x}y=\frac{\sqrt{x}}{x}[/tex]
Here [tex]P(x) =\frac{1}{2x}; Q(x)=\frac{\sqrt{x}}{x}[/tex]
To find the solution (y(x)), we can use the integration factor method:
[tex]Fy(x)=\int Q(x)Fdx+C \rightarrow F=e^{\int P(x)dx[/tex]
Then [tex]F=e^{\int \frac{1}{2x}dx}=e^{\frac{1}{2}\ln|x|\right}=\sqrt{|x|}[/tex]
So, we can find:
[tex]y\sqrt{|x|}=\int \frac{\sqrt{x}\sqrt{|x|}}{x}dx+C[/tex]
Suppose that [tex]x\in \double R[/tex], then [tex]\sqrt{|x|}=\sqrt{x}[/tex] , and we find:
[tex]y\sqrt{x}=x+C \rightarrow y(x)=\sqrt{x}+\frac{C\sqrt{x}}{x}[/tex]
To check our solution is right or not, put your y(x) back to the ODE:
[tex]y' = \frac{1}{2\sqrt{x}}-\frac{C}{2\sqrt{x^{3}}}[/tex]
[tex]2xy'=\frac{x-C}{\sqrt{x}}[/tex]
[tex]2xy'+y=\frac{x-C}{\sqrt{x}}+\sqrt{x}+\frac{C\sqrt{x}}{x}=2\sqrt{x}[/tex]
(it means your solution is right)
If you deposit $300 in an account and it grows by 6% each year, how much money will be in your account after 1 year?
Answer:
318
Step-by-step explanation:
300 + (300 * 6%) = Answer
300 + (300 * 0.06) = 318
A game app costs a base fee of $5.
You can download additional booster packs for $1.50 per pack.
If you spend a total of $23 on the game, which equation correctly models the situation, where n is the number of booster packs purchased?
Answer:
Step-by-step explanation:
So you have a constant value of 5 dollars and a variable value of 1.50 dollars. some equation of these numbers equals 23 dollars. That equation is
23=5+(1.50n) where n is the number of booster packs.
Answer:
$23 = $5 + 1.5x
Step-by-step explanation:
We can make a format to find the equation.
Total = base fee + $ per pack
Let x = the number of packs
Therefore, the equation will be like this:
$23 = $5 + 1.5x
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find the sum of the first 10 terms 125,50,20
Answer:
208.3
Step-by-step explanation:
Since the numbers are decreasing as multiples, its a geometric progression.
[tex]S_{n}=\frac{a(1-r^{n} )}{1-r} ; r\neq 1 \ and\ r \ is\ less\ than\ 1\\common\ ratio=\frac{20}{50}=\frac{2}{5}\\ S_{10}=\frac{125(1-(2/5)^{10} )}{1-(2/5)} \\=208.3[/tex]
. Question 3 Terrance made a list of his expenses. He is creating a check off matrix to organize when his bills are due. A check off matrix is a table without dollar amounts. You can use a matrix to indicate what time of the year an expense will occur Help Terrance complete his check off matrix by placing an X in the correct cells of the table according to his list of expenses, mortgage payment monthly • Utilities, monthly • Insurance quarterly • Internet monthly cell phone monthly . car loan: semiannually lawn care: monthly, April-September • food: monthly day care every other month beginning with February gym membership: annually. July . в тухх, m. AL 10pt Oct Dec Nov Feb Mar Sep Jul Jun Aug May Jan x Expense mortgage payment X X X x x X x insurance y internet cellphone car loan 1 x Iawn care X x X x food X day Care rym membership
=====================================================
Explanation:
The first two rows are already done. They have X's for every month to indicate a monthly payment regularly throughout the year without any extra conditions/requirements.
The third row will have exactly 4 copies of X in it. Two of them are already placed for January and April. The other two payments are in July and October. Notice the months are spaced 3 apart and how 12/4 = 3.
The fourth row will have X's across every cell in the same way the first row does since the internet bill is monthly. The same applies to the cell phone bill and food rows.
Something like the car loan will only have 2 copies of X in that row. Semiannual means twice a year, aka every 6 months. One copy of X is already placed for us in this row. This is in January (month 1). Six months later in month 1+6 = 7 (July) is when the next car loan payment occurs.
Lawn care will have X's only for the months of April through September; any other month won't have an X.
Day care will have X's for February, April, June, August, October, December. We start with February and alternate each month to fill out the rest of the year. This is due to the phrasing "every other month".
The gym membership will have one X for July only, since it's an annual payment.
Bus A travels according to the function y = 125/2x where y is distance traveled in miles and x is time in hours. Bus B travels according to the graph below, where the distance y is a function of time x. Which bus travels faster. we Include all necessary calculations in your final answer.
Answer:
Bus B
Step-by-step explanation:
For both buses, the slope is the speed.
Bus A: y = 125/2 x
m = 125/2 = 62.5
Bus A travels at 62.5 mph
For Bus B, wee look at the graph.
When x = 3, y = 200.
m = 200/3 = 66.666...
Bus B travels at 66.7 mph
Answer: Bus B
1. Select the three rational numbers.
A. 5/1
B. 7/0
C. -0.02
D. 4.17(the 7 repeats)
E. 3.14 (pi)
F. 3.14 (pi squared)
Answer:
A. 5/1
C. -0.02
D. 4.177777....
Step-by-step explanation:
Rational numbers can be written as a ratio of numbers, such as 5/1. As decimals, the numbers either
*** "terminate" the decimal has a certain number of digits and then stops, such -0.02, this can be written as a ratio -2/100 which is -1/50
OR
*** "repeats" , such as 4.17777... which can also be written as a ratio, 4.1777... = 188/45
7/0 is undefined and the pi numbers are irrational, the digits of the decimal do not repeat and do not ever end, therefore NOT rational.
find the number that must be added to 40% of 225 to give 200
Answer:
x = 110
Step-by-step explanation:
find the number : x
that must be added : +
to :
40/100 * 225 + x = 200
2/5 * 225 + x = 200
90 + x = 200
x = 200 - 90
x = 110
IM STUCK CAN SOMEBODY SOLVE THE EQUATION
Answer:
m = 4
(0, 1)
y = 4x + 1
Step-by-step explanation:
Slope using first two points (-2, 7) & (-1, -3):
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{-3+7}{-1+2} =\frac{4}{1}[/tex]
m = 4
Y-intercept, b: (0, 1)
Equation:
y = mx + b
y = 4x + 1
Solve the equation.
x^2 − 6 + 34 = 0
Answer:
[tex]x=6-\sqrt{ -100}/2=3-5i=3.0000-5.0000i\\x=6+\sqrt{-100} )/2=3+5i=3.0000+5.0000i[/tex]
Step-by-step explanation:
Step 1: Trying to factor by splitting the middle term
The first term is, x² its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +34
Step-1 : Multiply the coefficient of the first term by the constant 1 • 34 = 34
Step-2 : Find two factors of 34 whose sum equals the coefficient of the middle term, which is -6 .
-34 + -1 = -35
-17 + -2 = -19
-2 + -17 = -19
-1 + -34 = -35
1 + 34 = 35
2 + 17 = 19
17 + 2 = 19
34 + 1 = 35
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1:
x² - 6x + 34 = 0
Parabola, Finding the Vertex:
Find the Vertex of y = x^2-6x+34
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.0000
Plugging into the parabola formula 3.0000 for x we can calculate the y -coordinate :
y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 34.0
or y = 25.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-6x+34
Axis of Symmetry (dashed) {x}={ 3.00}
Vertex at {x,y} = { 3.00,25.00}
Function has no real roots
Solve Quadratic Equation by Completing The Square
Solving x2-6x+34 = 0 by Completing The Square .
Subtract 34 from both side of the equation :
x2-6x = -34
Now the clever bit: Take the coefficient of x , which is 6 , divide by two, giving 3 , and finally square it giving 9
Add 9 to both sides of the equation :
On the right hand side we have :
-34 + 9 or, (-34/1)+(9/1)
The common denominator of the two fractions is 1 Adding (-34/1)+(9/1) gives -25/1
So adding to both sides we finally get :
x2-6x+9 = -25
Adding 9 has completed the left hand side into a perfect square :
x2-6x+9 =
(x-3) • (x-3) =
(x-3)2
Things which are equal to the same thing are also equal to one another. Since
x2-6x+9 = -25 and
x2-6x+9 = (x-3)2
then, according to the law of transitivity,
(x-3)2 = -25
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-3)2 is
(x-3)2/2 =
(x-3)1 =
x-3
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-3 = √ -25
Add 3 to both sides to obtain:
x = 3 + √ -25
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Since a square root has two values, one positive and the other negative
x2 - 6x + 34 = 0
has two solutions:
x = 3 + √ 25 • i
or
x = 3 - √ 25 • i
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-6x+34 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -6
C = 34
Accordingly, B2 - 4AC =
36 - 136 =
-100
Applying the quadratic formula :
x = 6 ± √ -100/2
In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written (a+b*i)
Both i and -i are the square roots of minus 1
Accordingly,√ -100 =
√ 100 • (-1) =
√ 100 • √ -1 =
± √ 100 • i
Can √ 100 be simplified ?
Yes! The prime factorization of 100 is
2•2•5•5
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 100 = √ 2•2•5•5 =2•5•√ 1 =
± 10 • √ 1 =
± 10
So now we are looking at:
x = ( 6 ± 10i ) / 2
Two imaginary solutions :
x =(6+√-100)/2=3+5i= 3.0000+5.0000i
or:
x =(6-√-100)/2=3-5i= 3.0000-5.0000i
Two solutions were found :
x =(6-√-100)/2=3-5i= 3.0000-5.0000i
x =(6+√-100)/2=3+5i= 3.0000+5.0000i
I’m not good at these I need help
Answer:
f(3) = 9
Step-by-step explanation:
From the table, when can see that when x is 3, f(x) is 9.
Therefore, f(3) = 9
Answer:
[tex]f(3)[/tex]=9
Step-by-step explanation:
[tex]f(x)[/tex] is x times a function.
so if you look at the table on the 'x' side and go down the table until you reach '3' and see what number on the 'f(x)' side corresponds with it, you will see '9'
so [tex]f(3) = 9[/tex]
and that means your answer is D
jack had m math problems to complete during his vacation. he solved the same number of problems every day and finished them all in 5 days. Suppose Jack was solving 15 problems per day. Use this information and the answer to part (a) to build an equation. (the answer too part a was m/5)
Answer:
m/5=15
Step-by-step explanation:
Since Jack was solving m/5 problems per day, the equation to solve this would be the one given above.
The equation that represents the situation is m = 75x.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
If Jack solved m math problems in 5 days by solving the same number of problems every day, then he solved m/5 problems per day.
Now suppose Jack was solving 15 problems per day.
We want to find out how many problems he had to solve in total, so we can set up an equation using these two pieces of information:
15x = m/5
Here, x represents the number of days Jack took to solve all the problems.
We can solve for m by multiplying both sides of the equation by 5:
75x = m
So the equation we get is:
m = 75x
Therefore, this equation relates the total number of math problems Jack had to solve (m) to the number of days he took to solve them (x), given that he solved 15 problems per day.
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Group b.. pls help me
Answer:
Step-by-step explanation:
m∠ABC + m∠BAC + m∠ACB = 180°
a + 2a + 6a = 180°
9a = 180°
a = 20°
m∠ABC = 20°
m∠BAC = 2 × 20° = 40°
m∠ACB = 6 × 20° = 120°
A
seventy-eight and nineteen hundredths
B
seven hundred eighty and nineteen hundredths
C
seventy-eight point zero one nine
D
seventy-eight and nineteen thousandths
Find the axis of symmetry and the vertex of the graph of y = 6x2 − 24x + 11.
A. x = 2; (2, −13)
B. x = 4; (4, 11)
C. x = −2; (−2, 83)
D .x = −4; (−4, −11)
Answer:
I believe its b
Step-by-step explanation:
Tim bought all of the 2 3/4 lb packages for a party. How many pound of meat did tim buy?
Four adults and three childern go to the teater for 74, whereas two adults and five childern are chraged 58. find the price of an adult's ticket and a child's ticket.
Answer:
the price of the adult's ticket is 14 and the price of the child's ticket is 6
Step-by-step explanation:
[tex]let \: x \: = adult \\ y = child \\ 4x + 3y = 74 - - - - 1\\ 2x + 5y = 58 - - - - - 2 \\ multiplying \: - - 2 \: by \: two \\ 4x + 10y = 116 - - - - 3 \\ eqn3 - eqn1 \\ 4x - 4x + 10y - 3y = 116 - 74 \\ 7y = 42 \\ y = \frac{42}{7} \\ y = 6 \\ putting \: the \: value \: of \: y \: into \: eqn2 \\ 2x + 5(6) = 58 \\ 2x = 28 \\ x = \frac{28}{2} \\ x = 14[/tex]
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what digit is in the ten thousand place in 796,142 what is the answer
Answer:
9
Step-by-step explanation:
2 is in the ones place
4 is in the tens
1 is in the hundreds
6 is in the thousands
9 is in the ten thousands
Answer:
The number that is in the ten thousands is 9, whose value is 90,000.
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I hope help you :)
Kind regards, Antonio.
Which statement is a TRUE statement about rectangles?
The sides in a rectangle are not parallel.
The angles in a rectangle are all different.
The opposite sides in a rectangle are equal.
All the sides in a rectangle are equal.
Answer:
The opposite sides in a rectangle are equal.
Step-by-step explanation:
If all sides were equal, you would have a square.
If the opposite sides were not parallel, you would not have 4 sides that meet at 90 degrees.
All angles in a rectangle are 90 degrees.
Answer:
The opposite sides in a rectangle are equal.
Step-by-step explanation:
hope this helps hope you get it correct
3.2 In the diagram below, ABCD is a parallelogram with Đ=9x-30° and B = 4x+20° 9.-30 B a 420 - 3.2.1 Calculate with reasons the value of x.
Answer:
D=9×30 and B=4x+20°=9.-30 B a 420
please help me on this thanks
[tex]\cos \angle H =\dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{IH}{GH}=\dfrac{28}{53}[/tex]
What causes a heart attack?
A. When the arteries increase
B. When LDL metabolizes cholesterol
C. When the heart is starved of oxygen
D. When HDL returns cholesterol to the heart
Answer:
C.When the heart is starved of oxygen
Please somebody help me. I’m begging.
Answer:
d=1
Step-by-step explanation:
d=2*r
r=(1/2)
d=2*(1/2)=1
Use the following statement to answer parts a) and b). One hundred raffle tickets are sold for $3 each. One prize of $500 is to be awarded. Winners do not have their ticket costs of $3 refunded to them. Raul purchases one ticket.
a) Determine his expected value.
b) Determine the fair price of a ticket.
Using the expected value of a discrete distribution, it is found that:
a) His expected value is of -$2.5.
b) The fair price of a ticket is of $0.5.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, the distribution for the net value of the ticket is:
P(X = 497) = 1/1000.P(X = -3) = 999/1000.Item a:
The expected value is given by:
[tex]E(X) = 497\frac{1}{1000} - 3\frac{999}{1000} = -2.5[/tex]
His expected value is of -$2.5.
Item b:
With an unknown ticket price, the distribution is:
P(X = 500 - x) = 1/1000.P(X = -x) = 999/1000.The game is fair if E(X) = 0, hence:
[tex]\frac{500 - x}{1000} - \frac{999x}{1000} = 0[/tex]
0.5 - x = 0
x = 0.
The fair price of a ticket is of $0.5.
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find the area of the polygon
Answer:
D. 984
Step-by-step explanation:
The are of the trapozoid is 1/2(B1+B2)+h
Russell needs to fertilize the grass in his
back yard, shown below. In order to know
how much fertilizer to buy, he must know
the square footage of his yard.
If the entire yard is covered with grass,
how many square feet of grass does he
have?
< 60 feet->
36 feet
60 feet
36 feet
30 feet
Answer:
60 feet?
Step-by-step explanation:
The area covered with grass, in square feeet, is the area of the shape of the yard.
What is the Area of a Yard?The area of a yard can be calculated by determining the shape of the yard, and using the appropriate area formula of the shape to find the area of the yard.
Image of the yard is missing. However, assuming the yard is a rectangular shape with a dimension of 10 ft by 6 ft, therefore:
The square feet of grass Russell has = area of rectangle = (10)(6) = 60 ft²
In summary, the area covered with grass, in square feeet, is the area of the shape of the yard.
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What type of association is shown by the scatterplot?
Answer:
Positive
Step-by-step explanation:
The graph goes up (puff puff positive)
The perimeter of the rectangle is 104 ft.
2x+4
X
What is the length and width
Answer:
x=16ft 2x+4=36
Step-by-step explanation:
perimeter o rectangle=2(l+b)
2(2x+4+x)=104
4x+8+2x=104
x=16ft,2x+4=36ft
triangle ABC is circumscribed about circle touching the circle at P,Q,R . if AP=4 cm, BP=6cm, AC=12cm, then find the radius of the circle.
Oliver earns five dollars for each lawn he mowed.If he he’d six lawns to move but forgot to mow three of them how much money did he actually earn
$15
Explanation:
For each lawn he mows = $5
He should mow 6 lawns but did only 3 lawns as other 3 he forgot to mow.
earned:
mows lawn-d * $53 * $5$15