Answer:
1) f(x) = 0.5*(x + 3)*(x - 4)
2) f(x) = -2*x^2 - 2*x + 12
Step-by-step explanation:
Wen we have a quadratic function like:
f(x) = a*x^2 + b*x + c*x
And it has roots at x1 and x2, we can write the function in the factored form as:
f(x) = a*(x - x1)*(x - x2)
then:
1) we have x-intercepts at: (-3, 0) and (4, 0) (then the roots of this function are x = -3 and x =4) and we know that f(1) = -6
we have:
x1 = -3
x2 = 4
then we can write f(x) as:
f(x) = a*(x - (-3))*(x - 4)
f(x) = a*(x + 3)*(x - 4)
Where a is a real number.
and now we can use the fact that f(1) = -6
then:
f(1) = a*(1 + 3)*(1 - 4) = -6
a*4*(-3) = -6
a*-12 = -6
a = -6/-12 = 1/2 = 0.5
Then the function is:
f(x) = 0.5*(x + 3)*(x - 4)
2) Now we have roots x = 2 and x = .3
Then:
x1 = 2
x2 = -3
Then this function is something like:
f(x) = a*(x - 2)*(x - (-3))
f(x) = a*(x - 2)*(x + 3)
Now we know that f(0) = 12.
then:
f(0) = a*(0 - 2)*(0 + 3) = 12
a*(-2)*3 = 12
a*(-6) = 12
a = 12/-6 = -2
f(x) = -2*(x - 2)*(x + 3)
And we do not want this one written in factored form, so we can just distribute the multiplications to et:
f(x) = -2*(x - 2)*(x + 3) = (-2*x + 4)*(x + 3) = -2*x^2 + 4*x - 6*x + 12
f(x) = -2*x^2 - 2*x + 12
What is 9867 rounded to the nearest 1000
Answer:
10,000Hope it helps
Have a good day
Please teach me how to do this thank youuu.
Answer:
-10.2
Step-by-step explanation:
To find the equation you have to pick to random points, find the slope, and the y-intercept.
(1,-2) (2,2)
Slope = 2 - - 2 / 2 - 1
Slope = 4 / 1
Slope = 4
an estimate of the y-intercept is -2.2 meaning the function is f(x) = 4x - 2.2
when x is replaced by -2 like the question is requesting f(-2) = 4(-2) - 2.2
f(-2) = -10.2
* i really hope this made sense
A right triangle has side lengths 5, 12, and 13 as shown below.
Use these lengths to find cos B, tan B, and sin B.
COS
B
13
5
5
tan
A
12
с
Sin
Answer:
c
Step-by-step explanation:
a. 3in, 4in, 5 in
5^2 ? 3^2 + 4^
25 ? 9 + 16
25 = 25
Because the two sides are equal, this is a right triangle.
b. 5in, 6in, 7in
7^2 ? 5^2 + 6^2
49 ? 25 + 36
49 < 61
Because 49 < 61, this is an acute triangle.
c. 8in, 9in, 12in
12^2 ? 8^2 + 9^2
144 ? 64 + 81
144 < 145
Because 144< 145, this is an acute triangle.
what is the value of x
10= 3x - 6
X=
Answer:
[tex]x= \frac{16}{3}[/tex]
Step-by-step explanation: Can i get brain plz!
Six added to the quotient of 84 and seven
Answer:
84 divided by 7 is 12 + 6 = 18
-2/9 +1/5 help me please
Answer:
-1/45
Step-by-step explanation:
I did the equation okay hope this help!! <3
Answer:
1/40
Step-by-step explanation:
-2/9+ 1/5=0.2r
0.2r convert to fraction=1/40
hope that helps
plz mark as brainliest
A 34-foot pole is casting a shadow that is 17 feet long. How far is the top of the flag pole from the end of the shadow?
Answer:
108
Step-by-step explanation:
GEOMETRY STUFF PLEASE ANDWER DUE IN 20 MINUTES
Answer:
Statement 2: m∠ ELD = (2x)°
Reason 4: Sum of angles on a straight line is equal to 180°
Statement 6: 2x = 56
Step-by-step explanation:
Since the first step talks about we being given m∠ ELG = 124°, the next thing we are given in the question is that; m∠ ELD = (2x)°
In statement 4,it is written that;
m∠ ELD + m∠ ELG = 180°
The reason behind this is that;
Sum of angles on a straight line is equal to 180°.
For reason 6, we are told it is a subtraction property.
Now the preceding statement gave us;
2x + 124 = 180
Which means that for subtraction property here, we will have;
2x = 180 - 124
2x = 56
The system of equations has .
the options are
1. one solution
2. no solution
3. infinitely many solutions
Answer: 3. Infinitely many solutions
Step-by-step explanation:
If you simplify the first equation you get the same equation of y=-2 which is infinitely many solutions
please, I need your help!! I will mark correct answer as brainliest.
Answer:
3, -3, 0
Step-by-step explanation:
The exlcusions of x are where the denominator =0
So we can write the following equations
x²-9=0
and
5x=0
Let's solve the first one
x²-9=0
x²=9
x= ±3
and
5x=0
x=0
Therefore x cannot equal 3, -3, 0
Answer: 3, -3, 0
So, yea. The answer ontop is also correct
hhhhheeeeeellllllppppp pppppllllllzzzzz!!!!!!!!
Answer:
c
Step-by-step explanation:
Answer:
HMMMMMM
Step-by-step explanation:
i think its b or c
Simplify a^5/a^3 and c^4/c^3
Answer:
a²
c¹
Step-by-step explanation:
a^5/a^3 = a^(5-3) = a²
c^4/c^3 = c^(4-3) = c¹
-4(y-2)=12
what does y equal
Answer:
y = -1
Step-by-step explanation:
-4 (y - 2) = 12
1. Multiply: -4y + 8 = 12
2. Subtract: -4y = 4
3. Divide: y = -1
What is the slope (-5,5) and (5,1)
Answer:
m= - 2/5
Step-by-step explanation:
Sports team is building a new stadium on a rectangular lot of land. It's a lot measures 10 X by five eggs and the sports field will be 6X by 2X, how much of the lot will be left over to build bleachers on
Answer:
4 X 2
8 unit²
Step-by-step explanation:
Given that:
Lot size = 10 X 5
Sport field = 6 X 2
Dimension of lot left :
(10 - 6) X (5 - 2)
4 X 2
Area left :
Length x width
4 * 2
= 8 units²
Write a linear equation in slope Intercept form of a line with a slope of -3 and y Intercept of 0
Answer:
y=-3x
Step-by-step explanation:
THe equation formula is y=mx+b, with m being the slope and b being the y-intercept. Because the y intercept is 0, you don't need to include it.
if a circle has an area of 100 cm squared, what would be the area of a section of 45 degrees?
Answer:
45 degrees/360 degrees=1/8
So the area would be 1/8 *100=100/8=25/2
Step-by-step explanation:
If a Canada savings Bond is worth $6225 after 7 years, and was originally bought for $5000, what was the annual simple interest rate? Answer as a percentage.
[Formulas are,
[I = P, R, T]
[A = P + I]
[A = P(1 + R times T)
Answer:
3.5%
Step-by-step explanation:
Given data
A=$6225
P=$5000
T= 7years
R=???
Simple interest
A=P(1+rt)
substitute
6225=5000(1+7r)
6225=5000+35000r
collect like terms
6225-5000=35000r
1225=35000r
r= 1225/35000
r=0.035
Hence the rate is 0.035*100= 3.5%
help with rounding off please !:(
Answer:
(a) 3800
(b) 7000
(c) Does unit mean ones place? 31
(d) 82.8
(e) 1000
(f) 0.48
Step-by-step explanation:
Find the length of the
missing side of the triangle
to the nearest tenth.
Trey is currently in debt and the balance of his account is -$24. If his
sister Catherine is in three times as much debt as he is, what is the balance
of Catherine's account?
PLZ HELP 2/3*2
THXXX
Answer:
4/3 or 1 1/3
Step-by-step explanation:
2/3 x 2/1 gets you 4/3
That's an improper fraction, so you can simplify it to 1 1/3 if necessary.
What is a solution to the inequality m<25
Answer:
I think the answer is m= -91
TS is the height of a building. PQR is a pole in front of the building. QT is a horizontal cable that supports the pole to the building. Find the height of the pole?
Answer:
The answer is 65.75
Step-by-step explanation:
Since tq is perpendicular to PR then qtsr becomes square
Then
[tex]qr = 30 \: \: \: \: \: and \: qt = 30 \\ [/tex]
Since the triangle pqt is right angled
Then
[tex]pq = qt \tan(50) = 30 \times \tan(50 ) = 35.75[/tex]
Then the height of the pole is equal to
[tex]pq + qr = 35.75 + 30 = 65.75[/tex]
HELP PLEASE IM GOING TO FAIL WILL GIVE BRAINLESS
Answer:
x= 20
AD= 23
DC= 23
AC= 46
Step-by-step explanation:
because it's a median that means that x+3=2x-17 solve for x and get x=20 which (I think) means that AD, DC= 23 and that AC= 46
F(x) = 24/x^2. When x=8
Answer:
3/8
Step-by-step explanation:
F(8)=24/8^2=24/(8*8)=24/64=3/8
4x³ + 9 + 16x² +4 + 12x³ + 17
combine like terms and order
Answer:
16x^3+16x^2+30
Step-by-step explanation:
what is $78 discounted 12%
Answer:
$78 discount off 12% you would get $68.64. That is $9.36 off
Find the side indicated by the variable. Round to the nearest tenth.
Answer:
b ≈ 25.6
Step-by-step explanation:
From the figure attached,
By applying tangent rule in the given triangle,
tan(32°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(32°) = [tex]\frac{16}{b}[/tex]
b = [tex]\frac{16}{\text{tan}(32)}[/tex]
b = [tex]\frac{16}{0.62487}[/tex]
b = 25.605
b ≈ 25.6
simplify the expression
3x +4 +yxy +7y -10x + 6
Answer:
- 7x + 10 + y² + 7 y
Step-by-step explanation:
Hope this will help