Answer:
f(x) = - 4x² - 20x + 56Step-by-step explanation:
f(x) = a(x - x₁)(x - x₂) - factored form of the equation of the parabola with zeros x₁ and x₂
x-intercepts at (2,0) and (-7,0) means zeros: x₁=2 and x₂=-7
So:
f(x) = a(x - 2)(x + 7) - factored form of the equation of the parabola with x-intercepts at (2,0) and (-7,0)
The parabola passing through point (1, 32) means if x=1 then f(x)=32
Then:
32 = a(1 - 2)(1 + 7)
32 = a(-1)(8)
32 = - 8a
a = - 4
Therefore the equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32):
f(x) = -4(x - 2)(x + 7)
Expanding to standard form:
f(x) = -4(x - 2)(x + 7)
f(x) = -4(x² + 7x - 2x - 14)
f(x) = -4x² - 20x + 56
The equation of the parabola with x-intercepts at (2,0) and (-7,0) and passes through the point (1,32) is
f(x) = -4 ( x - 2 ) ( x + 7 )
Its standard form is
f(x) = -4x² - 20x + 56.
What is a parabola?It is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
We have,
To find the equation of a parabola we use the factored form of a quadratic equation.
f(x) = a ( x - m ) ( x - n)
Where a is the leading coefficient and m and n are the zeros of the quadratic.
The equation has x-intercepts at (2, 0) and (-7, 0) so we can say that,
m = 2
n = -7
Now the equation passes through (1, 32) = (1, 32) so we have,
32 = a ( 1 - 2 ) ( 1 - (-7) )
32 = a ( -1 ) ( 1 + 7 )
32 = a ( -1 )8
32 = -8a
a = -32 / 8
a = -4
We have,
m = 2
n = -7
a = -4
The equation of the parabola is:
f(x) = a ( x - m ) ( x - n)
f(x) = -4 ( x - 2 ) ( x + 7 )
We can expand to its standard form as:
f(x) = ( -4x + 8 ) ( x + 7 )
f(x) = -4x² - 28x + 8x + 56
f(x) = -4x² - 20x + 56
Thus the equation of the parabola with x-intercepts at (2,0) and (-7,0) and passes through the point (1,32) is f(x) = -4 ( x - 2 ) ( x + 7 ) and its standard form is f(x) = -4x² - 20x + 56.
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Find a number that is a solution of the inequality x < –8.
–5
0
–10
Answer:
-10
Step-by-step explanation:
hope this can help :)
Answer:
-10
Step-by-step explanation:
because 0 is greater than all the other numbers and -5 is closer to 0 than -10.
solve for the indicated information solve for n
Answer:
n = 81
Step-by-step explanation:
The left angle in the upper triangle and 44° are Alternate angles and congruent.
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
n is an exterior angle of the upper triangle, thus
n = 44 + 37 = 81
Given the expression below, write an equivalent expression that does not contain parentheses.
Answer:
-2x - 12 - 2
Step-by-step explanation:
Apply the distributed property: -2x - 12 - 2I hope this helps!
Find the A distance B between and .
Step-by-step explanation:
26 should be the answer
1) What would be another way to name plane M?
(picture attached)
A. plane KJH
B. plane J
C.plane HJG
D.plane GJN
Answer:
C. plane HJG
Step-by-step explanation:
hope this helped :-)
Nate bought a new pair of shoes that were on sale for 25% off. If the shoes were $5 originally, what is the sale price of the shoes?
its proportions btw
Answer:
The sale price would be $3.75
Step-by-step explanation:
5*25%=1.25
5-1.25=3.75
the sale price of the shoes would be $3.75 because 5÷4=1.25 and 5-1.25=3.75, unless you are including tax. hope you get a good grade!
Thirty-five cents is what fraction, in simplest form, of a dollar?
Answer:
.35/100
Step-by-step explanation:
35 cents over 1.00
Answer:
7/20 is the simplest form
Step-by-step explanation:
What does R mean in this
Answer:
Step-by-step explanation:
its 0 i think
In a survey of 500 people, 31% percent said they were afraid of flying what decimal represents the number of people who said they were afraid of flying?
Answer:
0.31
Step-by-step explanation:
Given that :
Total number surveyed = 500
Percentage who are afraid of flying = 31%
Decimal which represents number of people who are afraid of flying :
Converting 31% into decimal form:
31 / 100
= 0.31
Hence 0.31 of the people surveyed were afraid of flying
how to rewrite 11/12 in two different ways
Answer:
1) 33/36 = 11/12
2) 22/24 = 11/12
Step-by-step explanation:
Hope it helps you! Please give me Brainlest!
Step-by-step explanation:
As a decimal you divide 11 by 12 which is 0,916 (6 repeating)
now as a percent you multiply this decimal by 100 which is 91.6 (6 repeating)%
latisha has 7 boxes with 21 shells in each box. she has 6 bags with 17 shells in each bag. she uses 18 shells to make a design. which of these expressions can latisha use to find how many shells are left
Answer:
231
Step-by-step explanation:
7x21=147
6x17=102
147+102=249
249-18=231
Answer: Letter D 7x21+6x17-18
Bye yw!
Please Help Me, Answer The Questions and I give you 100 Brainly Points
Answer:
Whats the question??? and then i can help you>>
Step-by-step explanation:
What is the area of this triangle?
5cm
4cm
3cm
Answer:
3cm
Step-by-step explanation:
It because every triangle has three edges so that is why it 3cm
(x + 10) cm
(x - 3) cm
The area of the rectangle is 48 cm².
Show that x satisfies the equation x2+ 7x - 78=0
Answer:
area a=lxb
48=(x+10)x(x-3)
48=x2-3x+10x-30
0=x2+7x-30-48
0=x2+7x-78
hence it is proved
The requried, we have shown that x satisfies the equation x² + 7x - 78 = 0.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
The area of the rectangle is given by the formula:
Area = length x width
Substituting the given expressions for length and width, we have:
Area = (x + 10)(x - 3)
We are also told that the area of the rectangle is 48 cm², so we can set up the equation:
(x + 10)(x - 3) = 48
Expanding the left side using the FOIL method:
x² - 3x + 10x - 30 = 48
Simplifying:
x² + 7x - 78 = 0
Therefore, we have shown that x satisfies the equation x² + 7x - 78 = 0.
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The price of a television was reduced $250 to $200. By the percentage was the price of the television reduced?
A. 20%
B. 25%
C. 80%
D. 50%
please help I'm not good at math!!
Answer:
B. 25%Step-by-step explanation:
The price decreased by 50, and that is 25% of 200.
Answer:
The answer is 20%
Step-by-step explanation:
I'm not amazing at percentages so this is what I did. Search up 20 percent of 250. Then it says 50. 250 minus 200 is 50, so the answer is 20%
I hope this helped and if it did I would appreciate it if you marked me brainliest.
thank you and have a nice day!
help please :)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Answer:
c
Step-by-step explanation:
you do 520 divided by two hours
Answer:
208
Step-by-step explanation:
Since it made 520 dives in 5 hours you divide 520/5 which is 104
For two hours you multiply 104*2 = 208
Please help me, This is the only question I don’t understand pleas help me I would really appreciate it thank you!
Answer:
C
Step-by-step explanation:
A proportional equation is in the form:
[tex]\displaystyle y=kx[/tex]
Where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.
An important aspect of a proportional equation is that it passes through the origin. That is, it has no y-intercept (or a constant value).
From our choices, the only choices that don’t have y-intercepts are C and D.
However, D is not a linear function.
Therefore, our answer is C.
And our constant of proportionality is 1/2.
A circle has a diameter of 3 meters. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determined.
The numerical value of the circumference and area are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
Answer:
Step-by-step explanation:
A circle has a diameter of 3 meters. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determined.
The numerical value of the circumference and area are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
Using the area and the circumference of the circle, it is found that the correct statement is given by:
The numerical value of the circumference is greater than the numerical value of the area.
What is the area of a circle?The area of a circle of diameter d is given by:
[tex]A = \frac{\pi}{4}d^2[/tex]
What is the circumference of a circle?The circumference of a circle of diameter d is given by:
[tex]C = \pi d[/tex]
In this problem, we have that d = 3, hence:
[tex]A = \frac{\pi}{4} \times 3^2 = \frac{9\pi}{4} = 2.25\pi[/tex]
[tex]C = \pi \times 3 = 3\pi[/tex]
Hence the correct option is given by:
The numerical value of the circumference is greater than the numerical value of the area.
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Can someone please help me
Answer:
Step-by-step explanation:
difference of 10 and u = 10 - u
seven times the sum of twice a number m and 16 is 9 -
7 ( 2m + 16 ) = 9
5x + 6x - sum of 5 times a number and 6 times a number
8 ( x - 7 ) = -35 - 8 times the difference of a number x and 7 is -35
Hope this helps
plz mark as brainliest!!!!!
It costs $26 to join Gym X, plus an additional $33 per month. It
costs $59 to join Gym Y, plus an additional $30 per month.
After how many months of membership would it cost the
same to belong to either gym?
PLEASEE HELP !
8 months
Step-by-step explanation:
PLEASE HELP
Write equations of the horizontal and vertical lines that pass through the given
point.
12. (-3,-4)
Horizontal line:
Vertical line:
Answer:
horizontal line: y=-4
vertical line: x=-3
Step-by-step explanation:
This one is simple. all you need to do is look at the x and y in the ordered pair.
Horizontal goes left and right so it's for y
Vertical goes up and down so it's for x
let me know if you need more explaining :)
A grid model with 100 squares. 20 squares are shaded.
Which fraction is equivalent to 20%?
StartFraction 1 Over 20 EndFraction
StartFraction 2 Over 20 EndFraction
StartFraction 4 Over 20 EndFraction
StartFraction 5 Over 20 EndFraction
Will give brainliest for answer!!
Answer:
4 over 20
Step-by-step explanation:
did on edg 2020
Answer:
c
Step-by-step explanation:
What type of angles
eve these?
Linear pair
Acute
Complementary
Other:
I need help ASAP!!!!!
Write the equation of the line in slope intercept form that has the given slope and the y-intercept
4). m=2;y-intercept is -6
5). m= -1; y-intercept is 3
6). m= -1/3; y-intercept is -1
Answer:
4). y= 2x - 6
5). y= -1x + 3
6). y= -1/3x - 1
Which statement best describes the graphed function?
A.
The function has a relative maximum at (-2,4) and a relative minimum at (2,-4).
B.
The function has a relative minimum at (-2,4) and a relative maximum at (2,-4).
C.
The function has an absolute maximum at (-2,4) and an absolute minimum at (2,-4).
D.
The function has an absolute minimum at (-2,4) and an absolute maximum at (2,-4).
Answer:
The function has a relative maximum at (-2,4) and a relative minimum at (2,-4).
Step-by-step explanation:
The graph's highest point is at (-2,4) which would be considered the relative maximum of the graph. The graph's lowest point is at (2,-4) which is the relative minimum. Therefore the relative maximum is at (-2,4) and the relative minimum is at (2,-4)
Answer:
The function has a relative maximum at (-2,4) and a relative minimum at (2,-4).
Step-by-step explanation:
Plato/Edmentum
Pocahontas opens a savings account with $640 dollars that earns 3.9% interest per year not compounded. How much money to the nearest penny will Pocahontas have in 8 years
Given:
Principal value = $640
Rate of interest = 3.9% not compounded
Number of years = 8
To find:
The amount after 8 years.
Solution:
It is given that the interest is not compounded. It means, we need to find simple interest.
Formula for simple interest:
[tex]I=P\times r\times t[/tex]
where, P is principal, r is rate of interest and t is time in years.
Put P=640, r=0.039 and t=8.
[tex]I=640\times 0.039\times 8[/tex]
[tex]I=199.68[/tex]
So, the interest is $199.68.
Now, amount after 8 years is
[tex]A=P+I[/tex]
where, P is principal and I is interest.
[tex]A=640+199.68[/tex]
[tex]A=839.68[/tex]
Therefore, the amount after 8 years is $839.68.
Please mark brainliest !!!!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!
Answer:
um. its 70
Step-by-step explanation:
180-110.. parallel angels
Answer: 70°
Step-by-step explanation:
180-110 parallel angels
A man has $456.99 in his bank account. The man then writes a check for $45.99. How much money is in his account now?
Answer:
$411.00
Step-by-step explanation:
456.99-45.99
hiii, this geometry please help
Drag the tiles to the correct locations. Each tile can be used more than once, but not all tiles will be used. One or more locations will
remain empty.
Nitrosyl fluoride has the chemical formula NOF. Nitrogen has five valence electrons, oxygen has six, and fluorine has seven. Complete the
Lewis structure for this covalent compound.
Answer:
.. .. ..
o = N - F :
.. ..
Under the N just leave empty
Step-by-step explanation:
The complete lewis structure for NOF covalent compound is rewritten as: O=N-F
What type of bond is in NOF (Nitrosyl fluoride)?In a molecule of NOF, Oxygen is double bonded with Nitrogen. Nitrogen molecule of NOF is single bonded with flourine.
Rest of the valence electrons are not bonded.
Nitrogen's atomic number: 7, valence electron's count = 5Oxygen's atomic number: 8, valence electron's count = 6Florine's atomic number: 9, valence electron's count = 7Thus, with the above said description we will get:
.. .. ..
O = N - F :
.. ..
(double bond uses 2-2 electron of each atom).
Thus, the complete lewis structure for NOF covalent compound is rewritten as: O=N-F
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