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
please help!
In right triangle ABC, angle C is a right angle, AB = 13, and BC = 5.
What is the length of AC?
Answers
Answer:
Step-by-step explanation:
AC=[tex]\sqrt{13^{2} -5^{2} }[/tex]
=12
21-8x-4+9x please step by step
Answers
Answer:
=x+17
Step-by-step explanation:
happy to help ya :)
-8x+9x=1x
21--4=21+4
21+4=25
Answer-->25
The price have changed from $120 to $75. By how many
percent did it change?
Plz show how you did it
Answers
Answer:
35.7%
Step-by-step explanation:
The change is 45 dollars. (120-75)
The percent of change is the dollars divided by the original price.
45/120=0.357
Or 35.7%
Answer:
35.7
Step-by-step explanation:
The sale price of an item is Rs 176. If a discount of 20% is allowed on its Marked price, what is the marked price of the item
Answers
Answer: $140.80
Step-by-step explanation:
Original price = Rs. 176.
Marked price has discount that is 20% lower than the above.
= 20% * 176
= $35.20
Marked price = Sales price - discount
= 176 - 35.20
= $140.80
Si para introducirun producto al país se pagan $225 por concepto de impuestos y dicho producto cuesta $1,200
Answers
Complete question :
si para introducir un producto al país se pagan $225 por concepto de impuestos y dicho producto cuesta $1,200 ¿que porcentaje se cobra por impuesto?
Responder:
18,75%
Explicación paso a paso:
Dado que:
Monto cobrado por impuestos = $ 225
Costo del producto sujeto a impuestos = $ 1200
El porcentaje del precio de costo del producto que se grava:
Sea porcentaje = x%
x% * precio de coste = importe de impuestos
0.01x * $ 1200 = $ 225
12x = 225
x = 225/12
x = 18,75
Por tanto, porcentaje de impuesto = 18,75%
Solve for the volume of the 3D shape.
27 m3
27
180 m3
180m
360 m3
360 m
Answers
Answer:
360 m3
Step-by-step explanation: just multiply 18m times 5m times 4 m then you get your answer :)
hope this helps :D
Answer:
360 m3
Step-by-step explanation:
Make the other guy brainlist cuz he helped me. :p
If 12 blueberries weigh 7.2 grams, find the weight of 32 blueberries.
Answers
Answer:
The weight of 32 blueberries is 19.2
Step-by-step explanation:
We need to find what one blueberry weigh:
7.2 divided by 12 = 0.6
0.6 x 32 = 19.2
PLSSS HELPPP !!!At least how many square feet of canvas are needed to make one cover? (Use
A 44 ft.2
B 22 ft.2
C 770 ft. 2
D 154 ft.2
Answers
Answer:
154ft.2 witch is d
Step-by-step explanation:
i just know
Please answer ASAP
The perimeter of a rectangle is 176 m. The length is equal to 3 times the width decreased by 4. Find the dimensions of the rectangle.
Answers
Answer:
L=65m
W=23m
Step-by-step explanation:
[tex]3W-4=L\\2L+2W=176\\\\2L+2W=176\\-2L+6W=8\\8W=184\\W=23m\\L=23*3-4=65m[/tex]
The length and width of the rectangle are 63m and 25m.
What is a rectangle?A rectangle is a quadrilateral, a 2d shape that has four sides and four vertices.
We have,
The perimeter of a rectangle = 176 m
Length of the rectangle = L = 3 x (W- 4 )
Width of the rectangle = W
The perimeter of a rectangle is given by:
176 = 2 ( L + W )
176 = 2 ( 3 ( W - 4 ) + W )
176 = 2 ( 3W - 12 + W )
176 = 2 ( 4W - 12 )
176 = 8W - 24
176 + 24 = 8W
200 = 8W
W = 200 / 8
W = 25 m
Now,
Put W = 25 in L = 3 x ( W - 4 )
L = 3 x ( 25 - 4 )
L = 3 x 21
L = 63 m
We can cross-check:
Perimeter = 2 ( 63 + 25 ) = 2 ( 88 ) = 176 m
Thus the length and width of the rectangle are 63m and 25m.
Learn more about rectangles here:
https://brainly.com/question/14207995
#SPJ2
What is the distance between the points (2, 3) and (5, -4)?
PLEASE HELP ASAP!!
Answers
Answer:
7 point 6
Step-by-step explanation:
what expression is equivalent to -19x+8y-2+7-40y+43
Answers
Answer:
[tex] - 19 \times - 32y + 48[/tex]
this from usatestprep
Answers
Answer:
either b or a
Step-by-step explanation:
Answer:
A I believe
Step-by-step explanation:
I am not very good at math, and my daughter finished her math assignment and wasn't sure if she did everything correctly. Can someone make sure this is correct?
Answers
Answer:
I think its correct I don't know tho
Step-by-step explanation:
if the line y=5x was graphed, what would the x coordinate be when y=14?
Answers
Answer:
X=2.8 when y =14
Step-by-step explanation:
[tex]5x = 14 \\ x = \frac{14}{5} \\ x = 2.8 [/tex]
aiudaaa
1. Encierra en un circulo los monomios semejantes.
a. –3x2 + 2yz – 3x² + yx - 6
b. 0.7abc-3ab + 8c - ab + 7abc
C x+1 - 2x" + 6x"-2 8x" + 3x"-2 4x
d. mn – 2m?n + 5m³n* -mn³ + 0.5m2n – 3
e. -8ab - 6a²b² + V3ab + 0.5a?b? + 5ab
2. Reduce los términos semejantes en cada polinomio.
a. 3a-8a + 60-70
b. *y + 6x?y – 0.5x?y
C. ab – 7ab +ab
d. x2n – 2x2n + 6x2n
e. 7xy+6xy3 – xy3
3. Determine el perímetro de las siguientes figuras. 4. Halle el área de la parte sombreada de cada fig
Answers
Answer:
Traduzca el resto en inglés
Step-by-step explanation:
Simplificando
6x + -2 + 2x = -2 + 4x + 8
Reordenar los términos:
-2 + 6x + 2x = -2 + 4x + 8
Combinar términos semejantes: 6x + 2x = 8x
-2 + 8x = -2 + 4x + 8
Reordenar los términos:
-2 + 8x = -2 + 8 + 4x
Combinar términos semejantes: -2 + 8 = 6
-2 + 8x = 6 + 4x
Solving
-2 + 8x = 6 + 4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4x' to each side of the equation.
-2 + 8x + -4x = 6 + 4x + -4x
Combine like terms: 8x + -4x = 4x
-2 + 4x = 6 + 4x + -4x
Combine like terms: 4x + -4x = 0
-2 + 4x = 6 + 0
-2 + 4x = 6
Add '2' to each side of the equation.
-2 + 2 + 4x = 6 + 2
Combine like terms: -2 + 2 = 0
0 + 4x = 6 + 2
4x = 6 + 2
Combine like terms: 6 + 2 = 8
4x = 8
Divide each side by '4'.
x = 2
Simplifying
x = 2
WILL MARK BRAINLEST, 15 POINTS
HURRY FAST
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 80 miles per hour. The westbound train travels at 90 miles per hour. How long will it take for the two trains to be 204 miles apart?
Do not do any rounding.
Answers
Answer:
one hour and 12 minutes
Answer:
1 hour and 12 minutes
Step-by-step explanation:
Let's say x = time it takes for the trains to be 204 miles apart.
Speed = Distance/Time,
Time = Distance/Speed,
x = 204/ (80 + 90) = 204/170 = 1 and 1/5 hours or 1 hour and 12 minutes
A cone has a volume of 47.1 cm³ and a radius of 3 cm what is its height?
Answers
Radius of cone ( r ) = 3 cm,
Curved surface area of a cone= 47.1 cm²
Curved surface area of a cone= πrl
47.1 = πrl
47.1 = 3.14 × 3 × l
l = 47.1 / (3.14 × 3)
l = 15.7 / 3.14= 1570/314= 5 cm
slant height (l) = 5 cm
Height of a cone (h) = √(l²) - (r²)
h = √ 5² -3²
h = √ 25 - 9 = √ 16 = 4 cm
h = 4 cm
Volume of cone= ⅓(πr²h)
= ⅓(3.14 × 3 × 3 × 4)
= 3.14 × 12= 37.68 cm³
Hence, the volume of a cone is 37.68 cm³.
Determine the equation that this graph represent
Answers
and slope = rise/run
I hope that’s right.
The graph below is the graph of a function.
True or False??
Answers
Answer:
mmmmmmmm I wanna say it's false. like almost positive
Explanation: what makes a graph function is a set of points in the plane is the graph of a function if and only if no vertical line intersects the graph in more than one point
Solve the equation graphically :-
4x-3y = 0
2x + 3y -18 = 0
Answers
Sunning itself on a cliff 5.8 feet above sea level. The iguana dove into the water from the cliff. When the iguana reached the deepest part of its dive, its total change in elevation was 8.3 feet. What was the iguana's position relative to sea level at the deepest part of its dive?
Answers
Answer:
deepest part of dive is 2.5 feets below sea level ;
-2.5 feets
Step-by-step explanation:
Given :
Initial Position = 5.8 feets above sea level = +5.8
Deepest part of dive = x
Change in elevation between initial position and deepest part of dive = 8.3 feets
Position relative to sea level at deepest part of dive :
x = change in elevation - Initial position
x = 8.3 feets - 5.8 feets
x = 2.5 feets
Hence, deepest part of dive is 2.5 feets below sea level
Vinay bought a flat for ₹ 4,50,000. He spent ₹ 10,000 on its paintings and repair. Then he sold it for ₹ 4,25,500. Find his gain or loss and also its percent.
Answers
Step-by-step explanation:
hence you got the answer
Was it helpful?
comment down
If there is any kind of suspicious mistake
then sorry
What’s the answer plz help!
Answers
Answer:
40 and 60
Step-by-step explanation:
can someone please help me I only have a few minutes
Answers
Answer:
(x + 8)(y - 3)
Step-by-step explanation:
Since you have a few minutes left, I will make this quick.
Focus on one letter within the trapezoid ABCD. Pick a certain letter that can correlate to trapezoid A'B'C'D'.
If we move B to B', we would notice it takes 8 skips,therefore (x + 8). If we do the same for y, we would notice it takes 3 skips down. Therefore (y - 3)
hi please help i will mark brain list giving all my points
Answers
Answer:
B
Step-by-step explanation:
It looks like addition to me.
Answer:
Its B. Addition Property of Equality
Step-by-step explanation:
The perimeter of a rectangle is (10x+2). If it’s width is (2x-1) whit h expression reprehensible length ?
Answers
Answer 3002 I'm not sure I'm just answering tons of things coins
Step-by-step explanation:
Please I need help with this?
Answers
9514 1404 393
Answer:
(a) positive and increasing
Step-by-step explanation:
Point c is on the x-axis, and point d is above it. The curve between points c and d is positive and increasing.
find the measure of the angle
PLEASE HELP!!!
I-ready!
Answers
Answer:
35,.......,..............
plsss help if u can 6th grade math
Answers
Answer:
The minimum: 3
The lower Q: 7
The median: 7
The upper Q: 6
Maximum: 11
Step-by-step explanation:
The height of 5 boys is 5.4 ft, 6.12 ft., 7.02 ft. 4.9 ft, and 6.25 ft. What is the average
height of these 5 boys?
What are the operation to solve the problem?
pls answer
Answers
Wll not just this question, but whenever you need to find average, you have to:
Wait, for example let's take ur question:
1st step we will add up all the values aka heights:
5.4+6.12+7.02+4.9+6.25=29.69
And then how many values did you take???
Its, 5 values
1st value= 5.4
2nd value=6.12
aaand so on....
However, then we will have to divide the sum by no.of values
29.69÷5=5.938
Aaand this is your FINAL ANSWER
Done!!!!
Hope I helped you!!!
Step-by-step explanation:
For the average height of fhe boys:
[tex] \frac{5.4ft + 6.12ft + 7.02ft + 4.9ft + 6.25ft}{5} \\ = 5.938 \: ft[/tex]
In solving for the average height, we used addition and division operations.
