Answer:
(a) The coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.
(b) The y-intercept has a value of 6
(c) The coordinates of the x-intercepts have a value of x=3 and x=-1
Step-by-step explanation:
You know y= -2*(x-1)² + 8
(a) Every quadratic function can be expressed by the canonical form:
f(x)=y= a*( x- h)² + k
where a is the principal coefficient and the ordered pair (h; k) are the coordinates of the vertex of the parabola.
The quadratic function will have a maximum or minimum value at the vertex. If a> 0, the parabola is concave, that is, it will have its branches upwards, therefore the vertex will indicate the minimum of the function. But if a <0 the parabola is convex and the vertex will indicate the maximum of the function.
Comparing the given equation with the canonical form of a quadratic function you can see that:
a=-2h=1k=8Then, the coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.
(b) The y-intercept arises from evaluating the function at x = 0. So, in this case:
y= -2*(0-1)² + 8
Solving:
y= -2*(-1)² + 8
y= -2*1 + 8
y= -2+8
y= 6
The y-intercept has a value of 6
(c) The roots or coordinates of the x-intercepts arise from evaluating the function at y = 0. So, in this case:
0= -2*(x-1)² + 8
Solving:
-8= -2*(x-1)²
[tex]\frac{-8}{-2} =(x-1)^{2}[/tex]
4= (x-1)²
√4= |x-1|
⇒ 2=x-1 → 2+1=x → 3=x
⇒ -2=x-1 → -2+1=x → -1=x
The coordinates of the x-intercepts have a value of x=3 and x=-1
Write the equation of the line in slope intercept form that passes through the two points: (1,-6) and (-3,2)
Please explain so I can understand this
Answer:
y = -2x - 4
Step-by-step explanation:
Formula is y = mx + b where m is the slope and b is the y-intercept
(1, -6) (-3, 2)
[tex]\frac{-6-2}{1-(-3)}=\frac{-8}{4} =-2[/tex]
The slope is -2
y = -2x + b
So let's find b, insert 2 for y and -3 for x to find b
2 = -2(-3) + b
2 = 6 + b
Subtract 6 from both sides to get b alone
-4 = b
We found what b equals (the y-intercept), which is -4
So, the equation is y = -2x - 4
Hope this helps and pls do mark me brainliest:)
Each week mrs endo bikes 0.86 mile to the garden. Then she bikes 2.3 miles along the river back home. About how many miles will mrs endo bike in a year?
Answer: 164.32 miles
Step-by-step explanation:
Given that:
Weekly coverage :
Miles biked to the river = 0.86 miles
Miles biked along the river back home =. 2.3 miles
Total miles biked weekly:
(0.86 + 2.3) miles = 3.16 miles weekly
Number of weeks per year = 52
Miles biked yearly : (number of weeks per year * miles biked weekly)
= 52 * 3.16 miles
= 164.32 miles
Mrs endo will bike about 164.32 miles in a year.
What is the total cost of a pair of jeans that are priced $50.00 if there is 7 1/2% sales tax?
$57.50
$53.75
$55.50
Answer:
See below.
Step-by-step explanation:
Divide the percentage to find the decimal form.
[tex]\frac{7.5}{100} =0.075[/tex]
Multiply the total by the percentage.
[tex]50*0.075=3.75[/tex]
Add that to the total.
[tex]50 +3.75=53.75[/tex]
Answer: [tex]53.75[/tex]
:)
Plz I need help, I’m confused and lost :(
4. Tres albañiles trabajaron en una construcción. Francisco trabajó el doble de horas que Eduardo y Eduardo trabajó el cuádruple de horas de las que trabajó Hugo. Entre los tres hermanos trabajaron 104 horas ¿Cuántas horas trabajó cada uno? Planteamiento algebraico: Procedimiento:
Answer:
La cantidad de horas que trabajó Hugo son 8, mientras que Eduardo trabajó 32 horas y Francisco 64 horas.
Step-by-step explanation:
En primer lugar, para determinar la ecuación que debes resolver, es conveniente establecer la variable a la que debes encontrar una solución en la ecuación. Entonces, llamas x a la cantidad de horas que trabajó Hugo.
Luego, sabes que Eduardo trabajó el cuádruple de horas de las que trabajó Hugo, esto es, cuatro veces más de las horas trabajadas por Hugo. Esto se expresa matemáticamente como 4*x.
Finalmente, Francisco trabajó el doble de horas que Eduardo, que se calcula multiplicando a las horas trabajadas por Eduardo por 2: 2*4*x= 8*x
Entre los tres hermanos trabajaron 104 horas. Esto indica que la suma de las horas trabajadas por Francisco, Eduardo y Hugo debe ser 104 horas. Esto se expresa matemáticamente como:
x + 4*x+ 8*x= 104 (Planteamiento algebraico)
Resolviendo (Procedimiento):
13*x=104
[tex]x=\frac{104}{13}[/tex]
x=8
Esto significa que la cantidad de horas que trabajó Hugo son 8.
Eduardo trabajó 4*x, esto es 4*8, que da como resultado 32 horas. Entonces Eduardo trabajó 32 horas.
Por último, Francisco trabajó 8*x. Siendo x=8, entonces 8*8=64. Entonces Francisco trabajó 64 horas.
Hugo trabajó 8 horas, Eduardo trabajó 32 horas y Francisco trabajó 64 horas.
Dado que tres albañiles trabajaron en una construcción, y Francisco trabajó el doble de horas que Eduardo y Eduardo trabajó el cuádruple de horas de las que trabajó Hugo, y entre los tres hermanos trabajaron 104 horas, para determinar cuántas horas trabajó cada uno se debe realizar el siguiente cálculo:
E + F + H = 104F = 2EE = 4HF = 8HH + 4H + 8H = 10413H = 104H = 104 / 13H = 8Así, Hugo trabajó 8 horas, Eduardo trabajó 32 horas y Francisco trabajó 64 horas.
Aprende más en https://brainly.com/question/22195033
Gerald deposits $50 every week into a savings account. At week 16, the account balance is $1650. Write an equation that models the balance, y, and the number of weeks, x.
Line M is represented by the following equation: x − y = 8
Which equation completes the system that is satisfied by the solution (18, 10)? (4 points)
a
2x − y = 26
b
x + y = 18
c
2x − 2y = 36
d
x − y = −28
Answer:Let's plug in (18,10) into each answer choice until we find the one that has it as a solution.
A) 2x - y = 26
2(18) - 10 = 26
36 - 10 = 26
26 = 26
Your answer is A.
I'll just do the rest to show that you the they are incorrect.
B) x + y = 18
18 + 10 = 18
28 ≠ 18
C) 2x - 2y = 36
2(18) - 2(10) = 36
36 - 20 = 36
16 ≠ 36
D) x - y = -28
18 - 10 = -28
8 ≠ -28
Your answer is A) 2x - y = 26.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
2(18) - (10) = 26
36 - 10 = 26
HELP ME PLEASE: I WILL GIVE BRAINLIEST AND IT IS 20 POINTS
Answer:
0
Step-by-step explanation:
any log with a base of one and it becomes logv5 (1) after logv5(logV3 (3) because log3(3) equal one so then logv5 (1) is 0
HELLLLLLLLLLLPPPPPPPPP
Answer:
there is no quick way around this. U need to plug in -4,2,8 into x value into the function, and see what y returns to
Step-by-step explanation:
what is 5,250 ÷ 6 = to? i have been having trouble
Answer:
875
Step-by-step explanation:
Answer:
Simply line it up and divide it.
Then you get the answer:
875
Help me ASAP Please!!!!
that's a lot of damage
What is the value of the expression 2x2 + 5x – 6 when x = 2?
Answer:
2×2^2 +5×2 -6
= 2×4 +10 -6
= 8+10-6
= 18-6
= 12
Using bangle side relationship theorem use the angle measures to list the side lengths of the triangle in order from longest to shortest
Answer:
AC= longest side
BC=middle side
AB=shortest side
Step-by-step explanation:
there is 180 degrees in a triangle, therefore
95+50=145
180-145=35
so we have angles 95, 50, 30
and we know that the side opposites with the angle corresponds to how big the side will be compared to the other sides
Therefore,
AC= longest side
BC=middle side
AB=shortest side
what is 4/7 in the lowest terms
Answer:
4/7 is already in lowest terms
If the domain is {0, 2,-6}, what is the range of y = -2x + 3?
Answer:
Step-by-step explanation:
y = f(x) = - 2x + 3
f(0) = 3
f(2) = - 2(2) + 3 = - 1
f(- 6) = - 2(- 6) + 3 = 15
Range is {3, -1, 15}
Alright y'all here is a easy one!!!!
Answer: Its C
Step-by-step explanation: 24 only pops up and the bottom of the equation and all of the other answers are being used in the problem.
Mason breaks on average 1.5 pencils each day. How many pencils will he break in a school week?
Answer:
how long is the school week??
Answer:
He will break 7.5 pencils during a 5-day school week!
Can someone please explain how functions work? With graphs?
Answer:
no, yes, no, no, yes, no
there you go!
Step-by-step explanation:
PLEASE HELP! Will mark brainliest,
The sum of three consecutive numbers is 84. What is the largest of these numbers?
26
27
28
29
Answer:
29
Step-by-step explanation:
27 + 28 + 29 = 84
Answer:
D
Step-by-step explanation:
Let the first number be n.
Then the consecutive number will be (n+1).
And the second consecutive number will be (n+2).
We know that it totals 84. So, we can write the following equation:
[tex]n+(n+1)+(n+2)=84[/tex]
Let’s now solve for n. Combine like terms:
[tex]3n+3=84[/tex]
Subtract 3 from both sides:
[tex]3n=81[/tex]
Divide both sides by 3:
[tex]n=27[/tex]
So, our n or first term is 27.
This means that our sequence is: 27, 28, and 29.
So, our largest number is 29.
Hence, our answer is D.
WILL GIVE BRAINLY!!!! HELP!!!!
Answer:
A is correct, the one you selected
Step-by-step explanation:
Answer:
A is the correct option
Step-by-step explanation:
sorry im a bit late lol
:)
Doug did this work to solve an equation. Did he make an error? 7x-8=-x-(12)
HURRY PLZ!!!
Answer: What error is there, the answer to the equation is x= -1/2
Answer:
Step-by-step explanation:
Answer this math problem if you love to mama
Answer:
Answer is 50°.
The interior angles are supplementary.
Answer:
LET THE UNKNOWN ANGLES BE X THEN,
X+130°=180°
REASON=BEING SUM OF COINTERIOR ANGLES IS EQUAL TO 180°)
X=180°-130°
X=50°answer...
Can somebody help me? Will mark brainliest!
Answer:
I believe it would be 3 reflection followed by translation.
Step-by-step explanation:
Please help me I don’t understand
Answer:
the first and fifth one
Step-by-step explanation:
Answer:
the first and second one
Step-by-step explanation:
Can someone help me out with this picture listed above??
Answer:
Step-by-step explanation:
This is an exponential decay, because the base is fraction < 1
A man invested 1000 rupees,split onto two schemes,at annual rates of interest 8% and 9%.After one year he got 875 rupees as interests from both. How much did he invest in each?
Given :
Total amount, T = 10000 . ( It should not 1000 )
Annual rates of interest in both scheme is 8% and 9% .
After one year he got 875 rupees as interests from both.
To Find :
How much did he invest in each.
Solution :
Let, amount invested in 8% annual interest scheme is x.
So, amount in other scheme is 10000-x .
Now, sum of interest is equal to 875.
[tex]\dfrac{x\times r_1 \times 1}{100}+\dfrac{(10000-x)\times r_2\times 1}{100}=875\\\\8x + 9(10000-x)=87500\\\\x = 90000-87500\\\\x = 2500[/tex]
Therefore, amount invested in 8% and 9% annual interest scheme is 2500 and 7500 rupees respectively.
Hence, this is the required solution.
What is the binary number for 17
Answer:
♡ hi there! madeline here. ♡
- your answer is 10001
also, since I answered first, can I get the brainliest?
thank you, have a great day sandra!
✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧
Step-by-step explanation:
If the US released 5.877 billion metric tons of carbon dioxide and 1 trillion pounds=0.4536 billion metric tons, how many trillions of pounds of carbon dioxide did the US release?
Answer: 12.96 trillion pounds
Step-by-step explanation:
From the question, we are informed that:
1 trillion pounds = 0.4536 billion metric tons
Therefore, if the US released 5.877 billion metric tons of carbon dioxide, the trillions of pounds of carbon dioxide that the US release will be:
= 5.877 / 0.4536
= 12.96 trillion pounds
Plz help
What is the length of side X if two similar rectangles have the following measurements?
Rectangle 1:6 ft by 10 ft
Rectangle 2: 3 ft by X ft
pls help what is Increase 5.4 by 1 1/27.
PLS HELP
T-T
Answer:
5/4
Step-by-step explanation:
1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.2p