Select the correct answer. What is the value of a in the function’s equation?
Answers
Answer:
[tex]a = -2[/tex]
Step-by-step explanation:
Given
The attached function (graph)
Required
Find a
The given function is quadratic and will be solved using:
[tex]y = ax^2 + bx + c[/tex]
From the attachment:
[tex](x,y) = (-3,4)[/tex]
[tex](x,y) = (-2,2)[/tex]
[tex](x,y) = (-4,2)[/tex]
Substitute these values in [tex]y = ax^2 + bx + c[/tex]
For: [tex](x,y) = (-3,4)[/tex]
[tex]4 = a(-3)^2 + b(-3) + c[/tex]
[tex]4 = 9a -3b + c[/tex]
For: [tex](x,y) = (-2,2)[/tex]
[tex]2 = a(-2)^2 + b(-2) + c[/tex]
[tex]2 = 4a -2b + c[/tex]
For: [tex](x,y) = (-4,2)[/tex]
[tex]2 = a(-4)^2 + b(-4) + c[/tex]
[tex]2 = 16a -4b + c[/tex]
So, we have:
[tex]4 = 9a -3b + c[/tex] --- (1)
[tex]2 = 4a -2b + c[/tex] ---- (2)
[tex]2 = 16a -4b + c[/tex] --- (3)
Make c the subject in (1)
[tex]c = 4 - 9a + 3b[/tex]
Substitute [tex]c = 4 - 9a + 3b[/tex] in (2) and (3)
[tex]2 = 4a -2b + c[/tex]
[tex]2 = 4a -2b + 4 - 9a + 3b[/tex]
Collect Like Terms
[tex]-4 + 2 = 4a - 9a-2b + 3b[/tex]
[tex]-2 = - 5a+b[/tex] --- (4)
[tex]2 = 16a -4b + c[/tex]
[tex]2 = 16a - 4b + 4 - 9a + 3b[/tex]
Collect Like Terms
[tex]2 -4 = 16a - 9a + 3b- 4b[/tex]
[tex]-2 = 7a -b[/tex] --- (5)
Add 4 and 5
[tex]-2 = - 5a+b[/tex]
[tex]-2 = 7a -b[/tex]
--------------------------
[tex]-2 - 2 = -5a + 7a +b - b[/tex]
[tex]-4 = 2a[/tex]
Divide through by 2
[tex]-2 = a[/tex]
[tex]a = -2[/tex]
Related Questions
el peso de una moneda de 5 es 7.07 geamos si tienes 1000 monedas de $5, ¿cuantos pasaran en total?
Answers
Answer:
Please translate this to English so I can help you?! :)
Step-by-step explanation:
Rule: multiply by 2 Pattern: 3,6,12,24,48 Observation: Observation = something similar about the numbers
Answers
Step-by-step explanation:
This numerical sequence corresponds to a geometric progression, which occurs when there is a multiplication of the sequence numbers for a common reason whose result will always be the successor number of the numerical sequence.
Like for example:
3,6,12,24,48
The common reason for the geometric progression is the number 2, so the first term of the sequence multiplied by 2 will be equal to the second term of the sequence and so on:
3x2 = 6
6x2 = 12
12x2 = 24
24x2 = 48
It is necessary to emphasize that the ratio of a geometric progression will always be constant and will always be a number other than zero.
PLZ HELP WITH MATYHSN
Answers
Answer:
26mm because w=6mm and the perimeter of the smaller triangle is 48mm
How much will
11. The markup on a restaurant meal is 250%. A meal costs $7.30 to produce.
the customer be charged before tax and tip?
hsdhjdjs
Answers
Answer:
2.5t 7.3=18.25
Step-by-step explanation:
250/100,please mark as brilliant
A local little league has a total of 60 players, of whom 40% are left-handed. How many left - handed players are there?
Answers
Answer:
24 players
Step-by-step explanation:
Answer:
24. 60 X 4/10 is 24
Step-by-step explanation:
3 Each expression below shows the length and width of
a rectangle in yards. Write each expression in the
correct box according to the area it represents.
Answers
Answer:
less than 1yd²:
2/3x3/5= 2/5
1/4x5/3= 5/12
1/2x9/10= 9/20
equal to 1yd²
1/4x4/1= 1
4/3x6/8= 1
more than 1yd²
2/3x5/3= 1.1
Step-by-step explanation:
2/3x3/5= 2/5
1/4x4/1= 1
2/3x5/3= 1.1
1/4x5/3= 5/12
1/2x9/10= 9/20
4/3x6/8= 1
Answer:
2..........3
--- x ---
3............5
Step-by-step explanation:
goes to area less than 1square yard
what is the percent of change from 85 to 64
Answers
Answer:
-24.71%
Step-by-step explanation:
Rectangle A has a length of 6 and width of 4. Rectangle A prime has a length of 9 and width of 6. Find the scale factor of the dilation shown. 1/2 3/2 2 2/3
Answers
Answer: The scale factor of the dilation [tex]=\dfrac32[/tex]
Step-by-step explanation:
[tex]\text{Scale factor}=\dfrac{\text{Side in image}}{\text{Corresponding side in preimage}}[/tex]
Given: Rectangle A has a length of 6 and width of 4.
Rectangle A prime has a length of 9 and width of 6.
Scale factor = [tex]\dfrac{9}{6}\ \ \ or \ \ \dfrac{6}{4}[/tex]
[tex]=\dfrac32[/tex]
Hence, the scale factor of the dilation [tex]=\dfrac32[/tex]
Answer:
3/2
Step-by-step explanation:
Write each fraction as an expression using a negative exponent other than -1. 3. 1 ___________ 4 24. 1 ___________ 100
Answers
Answer:
[tex]\frac{1}{4} = 2^{-2}[/tex]
[tex]\frac{1}{100} = 10^{-2}[/tex]
Step-by-step explanation:
The question is poorly formatted. However, I am able to get:
1. 1/4 and 2. 1/100
Required
Write as an expression of negative expression
1. 1/4.
Express 4 as 2^2
[tex]\frac{1}{4} = \frac{1}{2^2}[/tex]
Apply
law of indices [tex](\frac{1}{a^b} = a^{-b})[/tex]
[tex]\frac{1}{4} = 2^{-2}[/tex]
2. 1/100.
Express 100 as 4^2
[tex]\frac{1}{100} = \frac{1}{10^2}[/tex]
Apply law of indices [tex](\frac{1}{a^b} = a^{-b})[/tex]
[tex]\frac{1}{100} = 10^{-2}[/tex]
1. The fare of 12 kg of luggage for a distance of 36km is 24 rupees
How much fare will be charged for a luggage of 18kg for a distance
of 12km?
Answers
Answer:
16 rs maybe not sure sry if wrong
Paula salió de su casa rumbo al trabajo avanzo 8km al este y 13km al norte. Si hubiera un camino recto desde su casa a su trabajo ¿Que distancia recorrería por ese camino?
Answers
Answer:
15.26km
Step-by-step explanation:
Con la informacion de la pregunta e hecho un diagrama de la situacion. Podemos ver en el diagrama que el recorido forma un triángulo rectángulo. Entonces para saber la distancia que recorreria por el camino recto desde su casa a su trabajo tendriamos que calcular el valor de x, que se puede calcular usando el teorema de pitagoras que es el siguiente.
[tex]a^{2} + b^{2} = c^{2}[/tex]
donde a y b son el ancho y el alto del triangulo y el c seria x
[tex]8^{2} + 13^{2} = x^{2}[/tex]
[tex]64 + 169 = x^{2}[/tex]
[tex]233 = x^{2}[/tex]
[tex]15.26 = x[/tex]
Finalmente, podemos ver que la distancia seria 15.26km
Someone help please
Answers
Last year there were 80 members in chess club this year membership decreased by 20% how many members are there? Sorry
Answers
Answer:64 people
Step-by-step explanation: total no. of members=80
%decrease=20
20/100 x 80=16(people that left)
people rem.=80-16
Finding a percentage of o total amount without a calculator...
An item is regularly priced at $35. It is on sale for 40% off the regular price. How much (In dollars) Is discounted from the regular price?
Amount discounted: si
х
5
?
Help
Answers
35 - 0.80*35 = x
35 - 28 = x
7 = x
x = 7
He paid $7
radius:
diameter:32 meters
circumference:
area:
Answers
Given diameter is 32, radius would be 16 bc radius is always half of diameter, and circumference would be 2(pi)*radius, which would be 100.5309649.... and area is (pi)*radius^2 which would be 804.2477193........
Name three collinear points and non collinear points
I want all the answers please
Answers
two sides of a second triangle, then the triangles are congruent if the angle
between the congruent sides is equal.
The temperature in Minneapolis changed from -7 °F at 6 A.M. to 7°F at noon. How much did the temperature increase?
Answers
Answer:
14 degrees F
Step-by-step explanation:
Answer:
Step-by-step explanation:
from -7 degrees F to 0 are 7 degrees change
from 0 to 7 are also 7 degrees,
in total are 14 degrees in change
IVIIxed N
Douglas was planting grape vines. He completed 2-
rows of
grapes
each hour he worked. After completing 140 rows of grapes, how many
hours had he worked?
0000
48 hours
50 hours
52 hours
60 hours
Answers
Answer: He completes 2 4/5 rows per hour
if he completed 140 rows, how many hours did it take?
We should divide the work completed by the amount of work done per hour.
So, 140/(2 4/5) =
2 4/5 is equivalent to 2.8
so 140/2.8 = 50 hours
Step-by-step explanation:
When graphing a system of equations with INFINITE SOLUTIONS,
the SLOPES of the two lines will be__________.
Answers
Answer:
Step-by-step explanation:
Hgbuf7g
Un escalador sube 225m de altura. El asenso lo hizo en 3 etapas. En la primera subio un quinto en la, en la tercera un cuarto. ¿cuanto hizo en la segunda?
Answers
Answer:
Segunda etapa= 123.75 metros
Step-by-step explanation:
Altura total= 225 metros
En la primera estapa subió el 20% (un quinto):
Primera etapa= 225*0.2= 45 metros
En la tercera etapa subió 25% (un cuarto):
Tercera etapa= 225*0.250 56.25 metros
Ahora debemos determinar cuánto subió en la segunda etapa:
Segunda etapa= altura total - total subido
Segunda etapa= 225 - (45 + 56.25)
Segunda etapa= 123.75 metros
A farmer sells 6.7 kilograms of pears and apples at the farmer's market. 3/5 Of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
Answers
Answer: She sold 2.68kg of apples in the market
Step-by-step explanation:
Weight of pears and apples= 6.7 kg
weight of pears = 3/5 x 6.7 kg= 4.02 kg
Weight of apples = Total weight of the fruits - weight of pears
= 6.70kg- 4.02kg =2.68 kg
17
How long will it take for $1,000 to increase to $3,000 if placed into an account earning 3.2% compound
quarterly? (round to the nearest year)
5
Answers
Find the slope/
please help me
х
y
Rise =
6
-3
Run =
0
1
0 -3
3
3
m =
-6
5
Answers
Use this to answer
Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run
(5x-8)
+
(2x+19)
Find the value of x.
OA.5
B.7
C.9
D.11
Answers
Answer:
x=9 option C
Step-by-step explanation:
explanation above
Please mark me as brainlist
HELP ME IT WOULD MEAN A LOT
Answers
Answer:
123
Step-by-step explanation:
72+51=123
123 - 72 = 51
Answer:
72+51=123
123 - 72 = 51
Step-by-step explanation:
Martha spent $12.35 at the local farmer's market. She bought 3 bundles of collards and paid $4.30 for some fruit. How much did each bundle of collards cost?
Answers
Answer:
12.35-4.30=8.05
8.05÷3= 2.68333333333333....
≈2.68
What is the value of x?
Answers
Answer:
x = 22
Step-by-step explanation:
hope I helped!!
1 and 1/3 - 5/6
(ill mark when 2 answers)
(have a good day )
(HELP MEH PLZZ)
Answers
Answer:
1 1/3 - 5/6 = 1/2
Step-by-step explanation:
First we will need to make a common denominator on both sides, so since we have the second side divided in six, we can do the same to the first side as shown;
1/3 = 2/6
now this will help us a lot, now all we have to do is take what we can out of the fraction (2/6) out of the first side so it is equal to 0, NOTE this is not a professional way to do it but it helps me a lot;
5/6 - 2/6 = 3/6
this makes it easy all of a sudden, cause now its in a simpler form, we can tell this because we know that 3/6 is equal to 1/2, so now all we have to do is take 1/2 from our 1 that we are left over with, and VWOLA;
1 - 1/2 = 1/2
GRAND TOTAL;
1 1/3 - 5/6 = 1/2
(note: the space between the 1 and the 1/3 indicates that they are two separate numbers, so you dont have to put the 'and' there)
What is the sum of i° + k°?
Answers
Answer
1 + 32 + 243 + 1024 + .. + n5
Step-by-step explanation:
um sapato é vendido a r$ 180,00. se a compra for a vista a loja oferece um desconto de 10%. qual o valordo sapato na compra a vista?
Answers
Preço de um sapato = $ 180,00
Desconto concedido se o sapato for comprado em dinheiro = 10%
Custo do calçado quando comprado à vista :
[tex] =\tt 180 - 10\% \: \: de \: \: 180[/tex]
[tex] = \tt180 - \frac{10}{100} \times 180[/tex]
[tex] =\tt180 - \frac{10 \times 180}{100} [/tex]
[tex] = \tt180 - \frac{1800}{100} [/tex]
[tex] =\tt 180 - 18[/tex]
[tex]\color{plum} =\tt\$162.00[/tex]
▪︎Assim, preço do sapato quando comprado em dinheiro = $ 162,00