The system of equations is:
-2 = a + b + c
7 = 4a - 2b +c
-2 = 25a + 5b + c
The polynomial is:
y = (1/3)*x^2 - 6x - 1/3
How to write and solve the system of equations?The general polynomial of degree 2 can be written as:
y = a*x^2 + b*x +c
If we use the fact that it passes through the 3 given points, then we can write the 3 equations:
-2 = a*1^2+ b*1 + c
7 = a*(-2)^2 + b*-2 + c
-2 = a*5^2 + b*5 + c
We can simplify these to get the system of equations:
-2 = a + b + c
7 = 4a - 2b +c
-2 = 25a + 5b + c
First, isolate c on the first equation to get:
c = -2 - a- b
Replace it on the other two:
7 = 4a - 2b + (-2 - a - b)
-2 = 25a + 5b + (-2 - a - b)
9 = 3a - 3b
0 = 24a + 4b
Using the second equation we can rewrite:
-24a = 4b
-24a/4 = b
-6a = b
Ande replace that in the other equation:
9 = 3a - 3*(-6a)
9 = 3a + 18a
9/21 = a
1/3 = a
And the value of b is:
-6*(1/3) = b
-2 = b
And the value of c is:
c = -2 - (-2) - 1/3
c = -1/3
The polynomial is:
y = (1/3)*x^2 - 6x - 1/3
Learn more about polynomials at:
https://brainly.com/question/4142886
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Sam owns a chain of fast food restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does the restaurant operate in 2007?
Answer:
370 stores
Step-by-step explanation:
Given data
initial number of stores P= 200
r= 8%
t= 1999-2007= 8 years
Let us apply the compound interest expression to find the final amount of stores
A= P(1+r)^t
A= 200(1+0.08)^8
A= 200(1.08)^8
A= 200*1.85
A=370
Hence the number of stores in 2007 is 370 stores
EXERCISE 6.1
1. What will be the unit digit of the squares of the following numbers?
(i)81 -
(ii) 272 -
(iii) 799 -
(iv) 3853 -
(v) 1234 -
(vi) 26387-
(vii) 52698
(vii) 99880
(ix) 12796
(x) 55555-
retail price= $120
markup percent= 40%
what is the original cost
Is one-half of a square smaller than one-quarter of the same square? How do you know?
Answer:
No
Step-by-step explanation:
one-half is bigger than one-quarter of the same square
Calculate the area of a kite that has diagonals that measure 6 centimeters and 8 centimeters.
9514 1404 393
Answer:
24 cm²
Step-by-step explanation:
When the diagonals of a quadrilateral cross at right angles, the area of it is half their product.
A = (1/2)(d1)(d2)
A = (1/2)(6 cm)(8 cm) = 24 cm²
The area of the kite is 24 square centimeters.
Pls help me with this my sister’s going to take my phone in 10 minutes and I will give brainleast
Answer:
What are the closer two numbers together the then you find the slope
Step-by-step explanation:
Answer:
1x-6
Step-by-step explanation:
Slope Form: Mx+b
Slope Formula: y2-y1/x2-x1
(4,-2) (5,-1)
-1-(-2)= 1
5-4=1
1/1=1
Y-intercept: -6
Hope this helps!
its a screen shot do do do doooo
Depends on what pi is.
It could be
50.24 yards (pi is rounded)
OR
16π yards
Need help with math question 8th grade math
Answer:
Step-by-step explanation:
I am also in 8th grade, anyways
x reprsents = 30 nickles
y represents = $1.02.
I am very sorry i do not know EQ1 and EQ2, but hopefully this is helpful!
Answer:
Step-by-step explanation:
x reprsents = 30 nickles
y represents = $1.02.
Cheryl signs up for a savings account that guarantees an increase in her savings at a fixed rate of $15 per month. She plans to withdraw the money when it is more than twice the original amount of $200. Find the least number of complete months that Cheryl has to keep the money in the account for.
Answer: 14 months.
Step-by-step explanation:
Given: Original amount = $ 200
Fixed rate of growth = $15 per month
Let x be the number of months that Cheryl has to keep the money in the account for.
Then, [tex]200+15x=2(200)[/tex]
[tex]\Rightarrow\ 200+15x>400\\\\\Rightarrow\ 15x >400-200\\\\\Rightarrow\ 15x>200\\\\\Rightarrow x>\dfrac{200}{15}\\\\\Rightarrow x>13.333333\\\\\Rightarrow\ x=14[/tex]
Hence, it will take 14 months .
Factorise x²+8x+12plz give answer
Answer:
(x+6)(x+2)
Step-by-step explanation:
we have
ax²+bx+c
To factor parabolas we need to find a number that adds to b (or 8) and mulitplies to a*c (or 12)
The numbers 6 and 2 fit this criteria which means we have
(x+6)(x+2)
Answer:
i.d.k the answer so sorry
Step-by-step explanation:
knkn
just answer please hurry
Answer:
2.7 pages and 1.7 pounds of rice
Step-by-step explanation:
2.7 pages in one minute because 27/10=2.7
and 1.7 pounds of rice can be purchased for a dollar because 15/9 is about 1.7
Eight less than 7 times a number is -29.
Answer:
7x-8=-20
Step-by-step explanation:
4 Mr. Von's 5th-grade class is going on a field trip. Each
student is given a name card to wear that is 1/4 foot wide 1/3 foot long
1/4foot x 1/3 foot = square foot
Answer:
the answer is 1/12 square foot
Step-by-step explanation:
.
7 + 9 divided by 2
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Pewdie-pie coco-melon dis-track cause yt banned. You can find it on StilBS chan.nel
Find the value of x and y.
Answer:
This is a triangle with 2 equal angles and equal to 60
=> this is an equilateral triangle
=> y = 60
4x.3 = 54
=> y = 60
x = 54/12 = 4.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
if two angles are 60 degrees, the third one is also 60 degrees
that means all the sides are equal
if one side is 4x
4x+4x+4x=54
12x=54
x=4.5
Andre has 5 notebooks. Each notebook contains 60 sheets of paper. How many total sheets of paper does Andre have in his notebooks?
Answer:
5 x 60 = 300 pages
Step-by-step explanation:
Answer:
5x60=300
Step-by-step explanation:
If he has 5 note books with 60 pages each he has 300 pieces of paper
Rhea earned P9,876.88 a month while Jane earned P10,675.50. How much more did Jane earn month than Rhea?
1. What is asked in the problem?
2. What are the given facts?
3. What is the operation to be used?
4. What is the number sentence?
5. What is the correct answer
Help me please and thank you
True for one value: -1
True for no values: 0
True for all values: 5
In triangle ABC, point D is the centroid, and BD = 6. Find BE.
Given:
In triangle ABC, point D is the centroid, and BD = 6.
To find:
The measure of side BE.
Solution:
We know that the centroid divides each median in 2:1.
In the given figure BE is a median and point D is the centroid. It means point D divides the segment BE in 2:1.
Let BD and DE are 2x and x respectively.
We have, BD = 6 units.
[tex]2x=6[/tex]
[tex]x=\dfrac{6}{2}[/tex]
[tex]x=3[/tex]
Now,
[tex]BE=BD+DE[/tex]
[tex]BE=6+x[/tex]
[tex]BE=6+3[/tex]
[tex]BE=9[/tex]
Therefore, the measure of side BE is 9 units.
3 1183 long division
Please I need help.
Find the measure of the angle DCB in the rhombus ABCD.
Answer:
53
Step-by-step explanation:
its the same to DAB because it is in the opposite side to the DAB
Answer:
Step-by-step explanation:
In Rhombus, diagonals are angle bisectors.
So, ∠DAC = ∠CAB
∠A = ∠DAC+∠CAB
= 53 + 53
∠A = 106
In Rhombus, opposite angles are equal.
∠DCB = ∠A
∠DCB = 106°
Calculate the slope of the line that contains the points (-3, -2) and (7, 2)
Answer:
the slope= 2/5
What is the average rate of change of g over the interval [-2,4]
Answer:
3Average = sum of all the observations
Total number of observations
Average = 2+4
2
Average = - 6
2
3
(Grade 7 math) What is the area of the triangle when b=3.5 and h=3? B is the base and h is the height
Answer:
The area of the triangle
A = 5.25 square units
Step-by-step explanation:
Explanation:-
Given that the base of the triangle(b) = 3.5
The height of the triangle(h) = 3
The area of the triangle
[tex]A = \frac{1}{2} base X height[/tex]
[tex]A = \frac{1}{2} (3.5) (3)[/tex]
A = 5.25 square units
[tex] {n}^{6} \times \frac{4}{25} {n}^{2} \times \frac{5}{4} {n}^{3} \times n[/tex]
Step-by-step explanation:
reduce the numbers by solving and add the powers
E
C
5
4
9
B
D
C
Solve for x
Que se debe hacer es una pregunta???
What is the line of reflection for the trapezoids?
On a coordinate plane, trapezoid A B C D has points (5, 4), (6, 4), (8, 3) and (5, 3). Trapezoid A prime B prime C prime D prime has points (1, 4), (0, 4), (negative 2, 3), (1, 3).
Answer:I believe it’s A(x=3)
Step-by-step explanation:
There was an activity planned outdoors, but it started to rain. They took a vote and 45 people of the 60 people wanted to stay inside. The other 15 people voted to go outside in the rain. What percent of the class wants to go outside? Round to the nearest percent if needed.
Answer:
15/60×100=25%
Step-by-step explanation:
the number of students wanted to go outside/the whole number of students×100
15/60×100=25%
possible number of learners in the
in a village, the bell rings every 30 minutes at the Junior School and every 40
minutes at the High School Both schools start lessons at 8:00 am
At what times between 8.00 am and 2.30p.m do the bells both rring
Find multiples of 30 and 40:
30: 30, 60, 90, 120, 150
40: 40, 80, 120, 160
The least common multiple is 120, so every 120 minutes they willl both ring.
1 hour = 60 minutes:
120/60 = 2 hours.
The bells ring together every 2 hours.
8 + 2 = 10 am
10 + = 12pm
12 + 2 = 2 pm
The bells will ring together at am, 12 pm and 2 pm.
Answer:
Solution :-At first common multiple of 30 an 40
[tex] \sf \to \: 30 = 30,60,90,120[/tex]
[tex] \sf \to \: 40 = 40,80,120[/tex]
Common Multiple = 120
Time taken = 120/60 = 2 hrs
Now,
8.00 + 2 = 10.00 am
10.00 + 2 = 12.00 noon
12.00 + 2 = 2.00 pm
[tex] \\ [/tex]
A car travels at an average speed of 68 miles per hour. How many miles does it travel in 5 hours and 45 minutes?
Answer:
391.
Step-by-step explanation:
There is 60 minutes every hour, so you divide by 60. 68 / 60 = 1.1333333333.
Now, we have to find out how many minutes there are in 5 hours and 45 minutes. Since there is 60 minutes every hour, 6 x 5 + 45 = 300 + 45 = 345. 1.1333333333 x 345 = 390.9999999885, rounded = 391.