Answer:
[tex]f(x)=x^2+3x+2[/tex]
Step-by-step explanation:
We want to write the equation of a quadratic whose graph passes through (-3, 2), (-1, 0), and (1, 6).
Remember that the standard quadratic function is given by:
[tex]f(x)=ax^2+bx+c[/tex]
Since it passes through the point (-3, 2). This means that when [tex]x=-3[/tex], [tex]f(x)=f(-3)=2[/tex]. Hence:
[tex]f(-3)=2=a(-3)^2+b(-3)+c[/tex]
Simplify:
[tex]2=9a-3b+c[/tex]
Perform the same computations for the coordinates (-1, 0) and (1, 6). Therefore:
[tex]0=a(-1)^2+b(-1)+c \\ \\0=a-b+c[/tex]
And for (1, 6):
[tex]6=a(1)^2+b(1)+c\\\\ 6=a+b+c[/tex]
So, we have a triple system of equations:
[tex]\left\{ \begin{array}{ll} 2=9a-3b+c &\\ 0=a-b+c \\6=a+b+c \end{array} \right.[/tex]
We can solve this using elimination.
Notice that the b term in Equation 2 and 3 are opposites. Hence, let's add them together. This yields:
[tex](0+6)=(a+a)+(-b+b)+(c+c)[/tex]
Compute:
[tex]6=2a+2c[/tex]
Let's divide both sides by 2:
[tex]3=a+c[/tex]
Now, let's eliminate b again but we will use Equation 1 and 2.
Notice that if we multiply Equation 2 by -3, then the b terms will be opposites. So:
[tex]-3(0)=-3(a-b+c)[/tex]
Multiply:
[tex]0=-3a+3b-3c[/tex]
Add this to Equation 1:
[tex](0+2)=(9a-3a)+(-3b+3b)+(c-3c)[/tex]
Compute:
[tex]2=6a-2c[/tex]
Again, we can divide both sides by 2:
[tex]1=3a-c[/tex]
So, we know have two equations with only two variables:
[tex]3=a+c\text{ and } 1=3a-c[/tex]
We can solve for a using elimination since the c term are opposites of each other. Add the two equations together:
[tex](3+1)=(a+3a)+(c-c)[/tex]
Compute:
[tex]4=4a[/tex]
Solve for a:
[tex]a=1[/tex]
So, the value of a is 1.
Using either of the two equations, we can now find c. Let's use the first one. Hence:
[tex]3=a+c[/tex]
Substitute 1 for a and solve for c:
[tex]\begin{aligned} c+(1)&=3 \\c&=2 \end{aligned}[/tex]
So, the value of c is 2.
Finally, using any of the three original equations, solve for b:
We can use Equation 3. Hence:
[tex]6=a+b+c[/tex]
Substitute in known values and solve for b:
[tex]6=(1)+b+(2)\\\\6=3+b\\\\b=3[/tex]
Therefore, a=1, b=3, and c=2.
Hence, our quadratic function is:
[tex]f(x)=x^2+3x+2[/tex]
Triangles ABC and DEF are similar. Find e.
A.) 11
B.) 12
C.) 10
D.) 9
Answer:
C) 10
Step-by-step explanation:
The triangle on the right shows that the side AB is 4 and the triangle on the left shows that the side DE is 8. Based on these two numbers I can conclude that the triangle DEF is double the size of triangle ABC. With this information, I can find e by doing 5*2=e and get 10 as my answer.
Hope this helps you :)
If you have 382 blocks that cost 44$ how much would it cost for 1 block
Answer:
Im pretty sure the answer in $8.70
Step-by-step explanation:
All you have to do is 382 divided by 44
Answer:
about 0.12 cents dollars or 12 cents.
Step-by-step explanation:
I divided 44 and 382. Hope this helps!
How do you factor f(x) = x^3 – 3x^2 – 10x + 24 ?
Answer:
f(x) = x³ – 3x² – 10x + 24 = (x + 3)(x – 2)(x – 4)Step-by-step explanation:
I would use the Horner method.
f(x) = x³ – 3x² – 10x + 24
f(2) = 2³ - 3·2² - 10·2 +24 = 0 ⇒ x=2 is the root of function
So:
| 1 | -3 | -10 | 24 |
2 | 1 | -1 | -12 | 0 |
therefore:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x² – x – 12)
For x² – x – 12:
[tex]x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot1\cdot(-12)}}{2\cdot1}=\dfrac{1\pm\sqrt{1+48}}{2}=\dfrac{1\pm7}{2}\\\\x_1=\dfrac{1+7}{2}=4\ ,\qquad x_2=\dfrac{1-7}{2}=-3[/tex]
It means:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x – 4)(x + 3)
if f(x) = 3x-2 and g(x) =2x+1 find (f+g)(x)
A. 5x-1
B. 5x-3
C. x-1
D. x-3
In class of 30 students there are 16 girls what is the ratio of boys to girls in the class
Answer:
No. of boys in class = 30-16=14
so,ratio=14:16
=7:8
plz help
What is the intersection of a plane and a solid figure called?
three-dimensional figure
cross section
two-dimensional figure
base
Answer:
B
Step-by-step explanation:
The intersection of both a solid figure and a plane is called a cross section
Answer:
cross section
Step-by-step explanation:
i had this same question on ossadayware
Find the component form of the vector that represents the velocity of an airplane at the instant its wheels leave the ground, if the plane is going 75 miles per hour and the body of the plane makes an9° angle with the horizontal.
Answer:
The component form of the vector that represents the velocity of the airplane is [tex](74.1 i , \ 11.73j)\ mph[/tex]
Step-by-step explanation:
Given;
velocity of the airplane, v = 75 mph
direction of the plane, θ = 9°
The vertical component of the velocity is given by;
[tex]V_y = vsin\theta\\\\V_y = (75)(sin \ 9^0)\\\\V_y = 11.73 \ mph[/tex]
The horizontal component of the velocity is given by;
[tex]V_x = vcos \theta\\\\V_x = (75)(cos9^0)\\\\V_x = 74.1 \ mph[/tex]
Therefore, the component form of the vector that represents the velocity of the airplane is given as;
[tex](V_x , \ V_y) = (74.1 , \ 11.73)\ mph[/tex]
Question
_______ is a solution to the equation 2(x - 5) = 9 - 3x + 6 + 8 + 3x + 7.
A.- x = 20
B.- x = 10
C.- x = 80
Answer:
C
Step-by-step explanation:
Answer:
C.- x = 80
Step-by-step explanation:
1) (-8,-8), (8,4)
Find the slope of the line through each pair of points
Answer: 3/4
Step-by-step explanation:
me need help. xjjd j dsj
Answer:
$4.67
Step-by-step explanation:
John + 2 friends = 3
Total cost = $14
$14/3 = $4.6666
$4.6666 ---> $4.67
Consider Brainliest! Hope I helped!
CAN SOMEONE GIVE ME THE STEPS I HAVE THE ANSWERS I JUST NEED THE STEPS
Problem 1:
1) 3/5x-1 x 3/4=9/10
3x/5-1 x 3/4=9/10
2) 3x/5-1 x 3/4=9/10
3x/5-3/4=9/10
3) 3x/5-3/4=9/10
+3/4 +3/4
4) 3x/5=33/20
5) 5 x 3x/5= 5 x (33/20)
6) 3x=33/4
7) 3x=33/4
/3 /3
8) x=11/4
Problem 2:
1) 6/7+2/5x=-4/5
6/7+2x/5=-4/5
2) 6/7+2x/5=-4/5
-6/7 -6/7
3) 2x/5= --58/35
4) 5 x 2x/5= 5 x (--58/35)
5) 2x= --58/7
6) 2x= --58/7
/2 /2
x= --29/7
If AC = 37 BC = 5x + 6, and AB = 2x + 3 Find BC
AC=37
BC=5X+6
AB=2X + 3
2x + 3 + 5x + 6 = 37
7x + 9 = 37
7x = 28
x = 4
BC = 5(4) + 6
BC = 26
Answer = BC = 26
3. The sum of the two numbers is5/9
If one of the numbers is
1/3 find the other
Step-by-step explanation:
let the one number be X.
and
second one 1/3
then
1/3 +X = 5/9
X = 5/9-1/3
X =( 5-3) /9
X = 2/9 Ans
Answer:
The other number will be 2/9.
Step-by-step explanation:
Let the second fraction be x :
[tex] \frac{1}{3} + x = \frac{5}{9} [/tex]
[tex]x = \frac{5}{9} - \frac{1}{3} [/tex]
[tex]x = \frac{5}{9} - \frac{3}{9} [/tex]
[tex]x = \frac{2}{9} [/tex]
The diagram below shows the side view of a ramp used to help load and unload a moving van.
Ramp
3 ft
9 ft
Which measurement is closest to the length of the ramp in feet?
9.5 ft
13.5 ft
8.5 ft
10.5 ft
If u get it right I will mark Brainliest!!
Answer: 9.5
Step-by-step explanation: I got it right in my test :)
Answer:
9.5 ft would be the closest to the length of the ramp in feet.
Step-by-step explanation:
I had the exact same question on my test, I got it correct :)
this is about angle pairs
Megan bought 2 1/4 pounds of bananas for $0.80 per pound and 1 1/2 pounds of strawberries for $1.10 per pound. How much more did Megan spend on bananas than on strawberries?
Answer:
$0.15
Step-by-step explanation:
Cost of each pounds of banana = $0.80
Number of pounds of banana = 2 1/4 pounds
Total cost of banana = $0.80 × 2 1/4 pounds
= 0.80 × 9/4
= 0.80 × 2.25
= 1.8
Total cost of banana = $1.8
Cost of each pounds of strawberry = $1.10
Number of pounds of strawberry = 1 1/2 pounds
Total cost of strawberry = $1.10 × 1 1/2 pounds
= 1.10 × 3/2
= 1.10 × 1.5
= 1.65
Total cost of strawberry = $1.65
How much more did Megan spend on bananas than on strawberries?
Total cost of banana - Total cost of strawberry
= $1.8 - $1.65
= $0.15
Answer:
$0.15
Step-by-step explanation:
Cost of each pounds of banana = $0.80
Number of pounds of banana = 2 1/4 pounds
Total cost of banana = $0.80 × 2 1/4 pounds
= 0.80 × 9/4
= 0.80 × 2.25
= 1.8
Total cost of banana = $1.8
Cost of each pounds of strawberry = $1.10
Number of pounds of strawberry = 1 1/2 pounds
Total cost of strawberry = $1.10 × 1 1/2 pounds
= 1.10 × 3/2
= 1.10 × 1.5
= 1.65
Total cost of strawberry = $1.65
How much more did Megan spend on bananas than on strawberries?
Total cost of banana - Total cost of strawberry
= $1.8 - $1.65
= $0.15
i dont understand how to do absolute values someone please help, and fast
Which of the following would be the best strategy?
Answer:
I think the answer is D
Step-by-step explanation:
I hope it was correct...
Five more than the product of a number and three is negative twenty-five.
Which ordered pair is a solution of the equation -4x + 7 = 2y - 3
Answer:
(0,5) (1,3) (2,1)
Step-by-step explanation:
a cone has a volume of 33 cubic inches. of a cylinder has the same height and radius as the cone, what is the volume of the cylinder
Answer: 40 cubic inch
Step-by-step explanation:
Simplify completely:
Answer:
(3)¼×¾
Step-by-step explanation:
3⁴/⁴
hope its write
Answer:
[tex]\frac{13}{4}[/tex] · [tex]\frac{15}{4}[/tex]
Step-by-step explanation:
Focusing on the first fraction, in order to simplify it, you have to multiply the denominator by the whole number; 4 x 3 is 12. You add the product to the numerator, so 12 + 1 would be 13. Therefore, the first fraction simplified would be [tex]\frac{13}{4}[/tex].
We can apply the same procedure to the next fraction, so 3 x 4 is 12, and 12 + 3 is 15. [tex]\frac{15}{4}[/tex] would be your answer.
Hope this helps! :)
Uh help please f(6)=1x+2
Please help me asap.......
Answer:
I'm pretty sure its A.
Step-by-step explanation:
There would be mirrors reflecting off of each other to get the light to reflect him in a different place
Please help.
Math - geometric
Answer:
FIRST option
Step-by-step explanation:
mark me brainlist btw help my sum plsss
Lisa's school requires each student to earn 75 hours of community service each year. Lisa has
already earned 27 hours. She plans to earn the remainder of her hours by volunteering at a
nursing home. If Lisa spends 2 hours at the nursing home per visit, which equation represents the
number of visits, v, that Lisa will need to make to fulfill her community service requirement?
Answer:
v=24
Step-by-step explanation:
-4x-y=24 missing value
Answer:
For solving x x= -24+y/4 For solving Y y=−24−4x
Step-by-step explanation:
This is solving for x
Add y to both sides.
−4x=24+y
Divide both sides by -4
and the answer is
x= -24+y/4
THis is solving Y
Add 4x to both sides
−y=24+4x
Multiply both sides by -1
and the answer is
y=−24−4x
Simplify (6g4h5)2
What is the answer
Answer:
12g8h10
Multiply each variable quantity by 2 and combine.
Donny joined a club that costs $40 per month. Is the cost over time a proportional or non-proportional relationship?
Answer:
The cost over time is a proportional relationship
Step-by-step explanation:
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality"
An electrician charges $45 per hour plus a fixed charge of $30. Which of these equations could be used to determine C , the cost an electrician charges for h hours worked?