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
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:
simplify the expression
3x +4 +yxy +7y -10x + 6
Answer:
- 7x + 10 + y² + 7 y
Step-by-step explanation:
Hope this will help
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.
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
4x³ + 9 + 16x² +4 + 12x³ + 17
combine like terms and order
Answer:
16x^3+16x^2+30
Step-by-step explanation:
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!
hhhhheeeeeellllllppppp pppppllllllzzzzz!!!!!!!!
Answer:
c
Step-by-step explanation:
Answer:
HMMMMMM
Step-by-step explanation:
i think its b or c
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%
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.
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
What is 9867 rounded to the nearest 1000
Answer:
10,000Hope it helps
Have a good day
What is the slope (-5,5) and (5,1)
Answer:
m= - 2/5
Step-by-step explanation:
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]
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?
Find the length of the
missing side of the triangle
to the nearest tenth.
what is $78 discounted 12%
Answer:
$78 discount off 12% you would get $68.64. That is $9.36 off
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
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
-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
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:
Six added to the quotient of 84 and seven
Answer:
84 divided by 7 is 12 + 6 = 18
-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
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
What is a solution to the inequality m<25
Answer:
I think the answer is m= -91
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:
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
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.
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
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