Answers
========================================================
Explanation:
The vertex of f(x) is (-3,4)
The vertex of -f(x) is (-3,-4). Note the y coordinate flips in sign. This is effectively because y = f(x).
Shifting the vertex down 2 units will get us to g(x) = -f(x)-2
So that's how we end up with (-3, -6)
Related Questions
A rectangle has sides measuring (2x + 7) units and (5x + 9) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for polynomials?
Answers
Part A
Use the FOIL rule to expand out the expression below
(2x+7)(5x+9)
2x*5x + 2x*9 + 7*5x + 7*9
10x^2 + 18x + 35x + 63
10x^2 + 53x + 63 is the final answer for part A
==========================================================
Part B
The degree is 2. This is a quadratic trinomial.
The degree is simply the largest exponent after expanding everything out. The degree directly determines the type of polynomial. Since the degree is 2, we have a quadratic. The polynomial is a trinomial because it has 3 terms.
==========================================================
Part C
Imagine we had a machine in which we deposit 2 coins into it. One would happen on either side. After the coins are deposited, a third coin pops out. The 2 coins going in and the third coin coming out are the same currency. This represents an example of closure.
In mathematics, the idea of closure is taking any two objects of the same type, applying an operation on them, and getting the same type of object as the input.
For example, we could take two whole numbers and multiply them together. The result is always a whole number. The set of whole numbers is closed under multiplication because you can't leave the set (hence the gate is closed not letting anything out).
Similarly, taking any two polynomials and multiplying them together will always lead to some other polynomial. Part A shows this in action because (2x+7), (5x+9) and 10x^2 + 53x + 63 are all polynomials.
[tex]\rm 10x^{2} + 53x + 63[/tex] is the expression that represents the area of the rectangle. This is a trinomial expression.
What is a quadratic equation?A quadratic equation is the polynomial of second degree in one variable only. The standard form of a quadratic equation is [tex]\rm ax^{2} +bx+c=0[/tex]
Where, x is the variable and a,b, and c are real numbers.
Part A
Let length of a rectangle = (2x+7)
Let width of a rectangle = (5x+9)
The area of the rectangle = length × width
= (2x+7)(5x+9)
= 2x × 5x + 2x × 9 + 7 × 5x + 7 × 9
= [tex]\rm 10x^{2} + 18x + 35x + 63[/tex]
Therefore, [tex]\rm 10x^{2} + 53x + 63[/tex] is the expression that represents the area of the rectangle.
Part B
The degree is 2 in the expression. This is a trinomial expression.
The degree is simply the largest exponent. The degree directly represents the type of polynomial. Since the degree is 2. The polynomial is a trinomial because it has 3 terms.
Part C
Applying multiplication operations such that taking any two polynomials and multiplying them together will always lead to some other polynomial. Part A shows this multiplication because (2x+7), (5x+9) and [tex]\rm 10x^{2} + 53x + 63[/tex] are all polynomials.
Learn more about quadratic equations;
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HELP PLEASE I WILL MARK BRAINLIEST
Answers
Answer:
A
Step-by-step explanation:
I just took This test
Out of 50 people surveyed, 42 respond ‘yes’ to the survey question. What is the probability of a ‘yes’ response? Write your answer as a decimal.
Answers
Answer:
0.84Step-by-step explanation:
Given
Total no. of observation = 50
Given, No. of observations that told yes = 42
Therefore,
Probability of getting response as yes
[tex] = \frac{42}{50} [/tex]
[tex] = \frac{21}{25} [/tex]
In decimal form ,
= 0.84 (Ans)
A rectangle has an area of 48 square feet and a perimeter of 32 feet. Which of the following could be its dimensions?
12 ft and 4 ft
6 ft and 8 ft
2 ft and 24 ft
3 ft and 16 ft
Answers
Answer:
12 feet and 4 feet
Step-by-step explanation:
12 times 4 is 48
and the perimeter is 12 times 2 and 4 times 2 which is 32
hope this helped :D
A florist sold 16 flower bouquets yesterday, including 8 lily bouquets. Based on past data, how many of the next 10 bouquets sold should you expect to be lily bouquets?
Answers
Answer:
The answer is 5
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
The number of 10 bouquets sold should you expect to be lily bouquets will be 5.
What are ratios and proportions?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other.
Given that a florist sold 16 flower bouquets yesterday, including 8 lily bouquets. Based on past data. The number of bouquets sold is 10.
The number of the Lily bouquets will be calculated as:-
Number = ( 8 / 16 ) x 10
Number = ( 1 / 2) x 10
Number = 5
To know more about ratios and proportions follow
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what's the answer
show full explanation
wrong ones are gonna get reported
Answers
Answer:
Step-by-step explanation:
Hope this helps u!!
Answer:
Hope u got it :)
Step-by-step explanation:
[tex]9x^2 - 30xy + 25y^2 = (3x)^2 - 2 (15xy) + (5y)^2[/tex]
[tex]= (3x)^2 - 2(3x \times 5y) + (5y)^2\\\\[/tex]
[tex]This \ is \ of \ the \ form \ a^2 - 2ab + b^2 , \ that \ is \ (a-b)^2\\\\a = 3x, \ b = 5y[/tex]
[tex]9x^2 - 30xy + 25y^2 = (3x - 5y)^2[/tex]
Ashley deposits $200 into an account that pays simple interest at a rate of 3% per year. how much money will she make in 3 years.
Answers
Alan purchased 16 shares of company stock for $390.40. A month later, the total value of his shares fell to $291.20. What is the current price per share if each share costs the same?
Answers
Answer:
$18.00
Step-by-step explanation:
390.40/16 = 24.40
291.20 - 390.40 = 99.20
99.20/16 = 6.20
24.20 - 6.20 = $18.00
If you apply the changes below to the absolute value parent function, fx) = |xl, what is the equation of the new function?
• Shift 2 units to the right.
• Shift 3 units down.
A. g(x) = lx- 2l - 3
B. g(x) = lx+ 2l - 3
C. g(x) = lx+3l -2
D. g(x) = lx - 3l- 2
Answers
Answer:
it's A
Step-by-step explanation:
just took the test
g(x) = lx- 2l - 3 is the equation of the new function when the parent function f(x) = |xl shift 2 units to the right and Shift 3 units down.
The given parent function is fx) = |xl.
We need to shift the parent function 2 units to the right and 3 units down.
To shift the absolute value function 2 units to the right.
We need to replace x with x - 2 inside the absolute value, as follows:
g(x) = |x - 2|
To shift the function 3 units down
We need to subtract 3 from the entire function, as follows:
g(x) = |x - 2| - 3
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Si alicia se gasta 2 pesos, le quedaría el doble de dinero que si se gastara 4 pesos ¿cuantos tiene alicia?
Answers
Answer:
La cantidad de dinero que tiene Alicia es 6 pesos.
Step-by-step explanation:
Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones lineales, en el cual se relacionan dos o más incógnitas.
Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema. Es decir, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en las ecuaciones.
Siendo:
x= cantidad de dinero que tiene Alicia.y= dinero que le quedaría a Alicia si gasta 4 pesos.Entonces el sistema de ecuaciones a resolver es:
[tex]\left \{ {{x-2=2*y} \atop {x-4=y}} \right.[/tex]
Sustituyendo la ecuación 2 en la primer ecuación:
x-2= 2*(x -4)
Resolviendo:
x -2= 2*x -2*4
x -2= 2*x -8
-2 + 8= 2*x -x
6= x
Entonces, la cantidad de dinero que tiene Alicia es 6 pesos.
please can someone help asap ? thank you ! :)
Answers
Answer:
[tex] \frac{x + 2}{3x - 1} [/tex]
Step-by-step explanation:
Things you should before solving this question :-
a²- b² = (a + b)(a - b)where a and b are any two variables.
SIMPLIFYING THE EXPRESSION
[tex] \frac{ {x}^{2} - 9 }{3 {x}^{2} + 8x - 3} \div \frac{x - 3}{x + 2} \\ [/tex]
using the identity discussed above
[tex] \frac{ (x + 3)(x - 3) }{3 {x}^{2} + 8x - 3} \div \frac{x - 3}{x + 2} [/tex]
simplifying 3x² + 8x - 3
[tex] \frac{ {x}^{2} - 9 }{3 {x}^{2} + 9x -x - 3} \div \frac{x - 3}{x + 2} [/tex]
as 8x can be written as 9x - x
[tex] \frac{ (x - 3)(x + 3) }{3 {x}(x + 3) - 1(x + 3)} \div \frac{x - 3}{x + 2} \\ \frac{ (x - 3)(x + 3) }{(3 {x} - 1)(x + 3) } \div \frac{x - 3}{x + 2} [/tex]
flipping the fraction that follows division sign and inserting multiply in place of divide
[tex] \frac{ (x - 3)(x + 3) }{(3 {x} - 1)(x + 3) } \times \frac{x + 2}{x - 3} [/tex]
canceling (x - 3) and (x + 3) as they're common in both denominator and numerator
[tex] \frac{x + 2}{3x - 1} [/tex]
8) Round 2.3428 to the nearest hundredth.
Answers
hope this helped !!!!!!!
Which numbers have 23 as their absolute value?
I need help like fast- pls
Answers
Answer:
- 23 and 23
Step-by-step explanation:
Absolute value is the distance from a number to zero on a number line. Absolute value is always positive.
- 23 is 23 space away from 0, and so is 23.
Explain how to find the percent for a fraction that does not have a denominator which is a factor of 100
Answers
Answer: Use division to convert the fraction to a decimal: 1/4 = 1 ÷ 4 = 0.25.
Multiply by 100 to get percent value: 0.25 × 100 = 25%
Step-by-step explanation:
Need help on this one! 10 points
Answers
sin^2x + cos^2x = 1
sin^2x + (7/11)^2 = 1
sin^2x + 49/121 = 1
sin^2x = 72/121
sinx = square root of 72/121
sinx = (6 root 2) / 11
sin2x = 2sinxcosx
sin2x = 2[(6 root 2)/11] (7/11)
sin2x = (2*6*7*root 2) / (11*11)
sin2x = 84 root 2 / 121 :)
Which function has the same domain as y=2square root x? O y=square root of 2x O y=2 cube root of x O y square root of x-2 O y=cube root of x-2
Answers
Answer:
A
Step-by-step explanation:
Domaine of y=2 square root x is x>=0 same for y=square root 2x
Answer: First option or A on your test
Step-by-step explanation: y= root of 2x
The Bawden family is shopping for a new television. They are making their decision based on brand and size. The family has 20 possible outcomes for choosing a television. Which is a possible number of brands and sizes that the family has to choose from? 10 brands and 10 sizes O 5 brands and 4 sizes 4 brands and 16 sizes 2 brands and 20 sizes Save and Exit Mark this and return.
Answers
Answer:
the naswer is 5
Step-by-step explanation:
Answer:
The Answer is B.
Step-by-step explanation:
B: 5 Brands and 4 Sizes
Please anwser one question!!
Answers
Answer:
I think d is 9°.......
Step-by-step explanation:
(6d+8)°+(3d+1)°=90°
d =9°
Find the area of the sector. Use 3.14 for it.
PLEASE HURRY
Answers
Answer:
the answer is a
Step-by-step explanation:
formula= (angle / 360) x π x (diameter / 2)^2
i this case we have the radius already so
= (240/360)*(pi)*(11)^2
=2/3(3.14)*(121)
= around 253.29
= which leads me to believe a is correct
Answer:
Solution given;
angle =240°
radius [r]=11cm
we have
length of arc =240°/360°×π*r²
=240°/360°×2×3.14*11²=253.29cm²
length of the arc is 253.29cm².
-\frac{1}{10}-x^3+x^4+3x
−
10
1
−x
3
+x
4
+3x
Answers
Answer:
Its really simple
Step-by-step explanation:
first you take the 10 then turn it into joe then mama
Answer:
-1/10 - 1x^3 + x^4 + 3x
Step-by-step explanation:
negative one tenth minus 1x exponet 3 plus x exponent 4 plus 3x
Write an equation in slope intercept form of the line that passes through the points (1,−6) and (5,−6).
Answers
slope intercept form = y=mx+b
m= slope
b= y-intercept
the slope is rise over run, so if the points are (1, -6) and (5, -6), the slope is 0
the y intercept is -6
y = 0x-6
or
y = -6
The sum of two numbers is 8. Their difference is 24. What are the two numbers ? Write a system of linear equations and solve using the elimination method.
Answers
Answer:
x=16
Step-by-step explanation:
let:
> x be one number
> y be the other number
system of Equations:
> x+y=8
> x-y=24
Using elimination method the y's cancel each other out, and we are left with
2x = 32
divide by 2 on both sides to get x by itself
AND
x=16
Find the values of x and y. Write your
answer in simplest form
Answers
Answer:
ok so the angles are
60
90
30
so we can just use the formulas
y=15
x=25.981 or 26
Hope This Helps!!!
On a school trip to a theme park, 4 busses each carry 70 students.
35% of the students are bringing their own lunch.
1
7
of the students are buying lunch when they get to the theme park.
The teachers are worried that some students have not made plans for lunch.
Find how many students have not made plans for lunch.
Answers
Answer:
165 Students Have No Made Plans For Lunch.
Step-by-step explanation:
According To the Question,
Given,On a school trip to a theme park, 4 busses each carry 70 students Then Total Number Of Students on a trip is 70×4=280 Students.And,35% of the students are bringing their own lunch. Thus,35% Of 280 Students is 98 Students. Then Remaining 182 Students not bring their own lunch.Now, 17 of the students are buying lunch when they get to the theme park. Thus students Who have not made plans for lunch is 182-17⇒165Students
a. List all the factors of 42.
b. What is the greatest common factor of 42 and 15?
C. What is the greatest common factor of 42 and 50?
Ahhhh please help!!!
Answers
oh and alsoo can someone plzzzzz add an explanation
Answers
Answer:
Brian sold 35 tickets
Step-by-step explanation:
42/6 = 7
7 x 5 = 35
35/42 = 5/6
Brian sold 35 tickets
(I know this isn't part of the question, but Brain didn't sell 7 tickets)
Math geometry help please show work thanks
Answers
Part (a)
Refer to the diagram below to see the two triangles separated.
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Part (b)
If the 3 meter portion is perpendicular to the horizontal portion, then the triangles are similar. We can prove this using the AA similarity theorem. One pair of angles would be the shared overlapping 25 degree angles. The other pair of congruent angles would be the two 90 degree angles. We only need two pairs of congruent angles to use AA. You could use three pairs (and the aptly named AAA theorem) but that's overkill in my book.
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Part (c)
There are a few ways to approach this, but one way is shown below
y/3 = (8.4+6.6)/(6.6)
y/3 = 15/(6.6)
6.6y = 3*15 .......... cross multiply
6.6y = 45
y = 45/(6.6)
y = 6.81818 approximately
When rounding to one decimal place, we get y = 6.8
If 9 exercise books cost
$540.00. how much will
14 of such cost?
Answers
Answer:
$840 dollars
Step-by-step explanation:
Divide 540 by 9 to get the cost of 1 book then multiply it by 14
Answer:
$840
Step-by-step explanation:
[tex]\frac{14}{9}: \frac{y}{540}[/tex]
y × 9 = 540 × 14
9y = 7560
9y ÷ 9 = 7560 ÷ 9
y = 840
does else anybody worry about the future?.
like i still dont know what i wanna do after highschool and i haven't cared where i end up but somehow i just get anxious thinking about it
Answers
Answer:
i worry ab mine all the time bc like im the type of person thats called an over thinker i over think alot and it just gives me alot of anxidy so ur not the only one lol
Step-by-step explanation:
Harry buys 6 yards of rope to make a swing. Lenny spends $16 on rope.
How much do the two boys spend in all?