Answer:
When x takes the value of 4, the expression takes the value of 9.
Step-by-step explanation:
We are given that the expression:
[tex]\displaystyle ax^2 + bx + c[/tex]
Evaluates to 0, 1, and 4 when x = 1, 2, and 3, respectively.
And we want to determine the value of the expression when x = 4.
The expression evaluates to 0 when x = 1. In other words:
[tex]\displaystyle a(1)^2 + b(1) +c = a + b + c = 0[/tex]
We can complete the same for the other two:
[tex]\displaystyle a(2)^2 + b(2) + c = 4a + 2b + c = 1\text{ and } \\ \\ a(3)^2 + b(3) + c = 9a + 3b + c = 4[/tex]
This yields a triple system of equations:
[tex]\displaystyle \left\{ \begin{array}{l} a + b + c = 0 \\ 4a + 2b + c = 1 \\ 9a + 3b + c = 4 \end{array}[/tex]
Solve. We can cancel out the c by multiplying the first equation by negative one and adding it to both the second and the third:
[tex]\displaystyle \begin{aligned} (4a + 2b + c) + (-a - b -c ) &= (-0) + (1) \\ \\ 3a +b &= 1\end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned} (9a + 3b + c) + (-a - b -c) &= (-0) + (4) \\ \\ 8a + 2b &= 4\end{aligned}[/tex]
Solve for the two resulting equations. We can multiply the first by negative two and add it to the second:
[tex]\displaystyle \begin{aligned}(8a + 2b) + (-6a -2b) &= (4) + (-2) \\ \\ 2a &= 2 \end{aligned}[/tex]
Hence:
[tex]a = 1[/tex]
Solve for b:
[tex]\displaystyle \begin{aligned} 3a + b &= 1 \\ b&= 1 - 3a \\ b&= 1 - 3(1) \\ b &= -2\end{aligned}[/tex]
And finally, solve for c:
[tex]\displaystyle \begin{aligned} a + b + c &= 0 \\ (1) + (-2) + c &= 0 \\ c &= 1\end{aligned}[/tex]
Hence, our expression is:
[tex]\displaystyle x^2 -2x + 1[/tex]
Then when x = 4:
[tex]\displaystyle (4)^2 - 2(4) + 1= 9[/tex]
In conclusion, when x = 4, the resulting value is 9.
simplify (a+1/a)^2-(a-1/a)^2
mike sold half of his comic books and then bought 9 more. he now has 14. how many did he begin with?
1200p x 1920p width of 12 inches
Answer:
nice TV
Step-by-step explanation:
Consider the function f(x) = tan 1/3 (x + pi/1) - 1
Help With All PleAsE
Answer:
8. ☐ A Up
☑ B Down 1
☑ C Left [tex]\displaystyle \frac{\pi}{2}[/tex]
☐ D Right
7. [tex]\displaystyle 3\pi[/tex]
6. ☑ A x = −2π
☐ B x = −π
☐ C x = [tex]\displaystyle \frac{\pi}{2}[/tex]
☑ D x = π
5. [tex]\displaystyle y = -1[/tex]
Explanation:
[tex]\displaystyle y = Atan(Bx - C) + D \\ \\ \boxed{y = tan\:(\frac{1}{3}x + \frac{\pi}{6}) - 1} \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{2}} \hookrightarrow \frac{-\frac{\pi}{6}}{\frac{1}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{\pi}{\frac{1}{3}} \\ Amplitude \hookrightarrow N/A[/tex]
Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Second, to find the period in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, on a universal scale of [tex]\displaystyle \frac{\pi}{4}[/tex] with a range of [tex]\displaystyle -2\pi\:to\:2\pi,[/tex] the vertical asymptotes are [tex]\displaystyle -2\pi = x\:and\:\pi = x.[/tex] From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you [tex]\displaystyle \boxed{3\pi} = \pi + 2\pi.[/tex] So, the period of this function is [tex]\displaystyle 3\pi.[/tex] Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of your graph, also known as the vertical shift, which in this case is at [tex]\displaystyle y = -1.[/tex]
Well, that just about wraps it up. Now that everything has been explained, you should understand it better. If you still have questions, do not hesitate to comment any you have.
I am delighted to assist you at any time.
The difference of x and 4
Answer:
x — 4
Step-by-step explanation:
Difference means subtraction, so x — 4 is the expression for your question.
The equations below has been solved. What properties were used to justify how this equation
was solved? Fill in the appropriate property of equality on the line provided. Addition(APE),
Subtraction(SPE), Multiplication(MPE), and Division(DPE)
Answer:
Step-by-step explanation:
APE - adding 8 on both sides (first line)
DPE - dividing by 7 on both sides (second line)
The scale from the drawing to the actual ramp is 2cm to 12in. What is the area of the actual side of the ramp?
The scale is 2 cm to 12 in so the actual length of the shorter side is 12 in, and the actual side of the longer side is (8/2)×12=48 in. So, the actual area of the ramp is (1/2)×12×48=288 Sq. in.
Scale used to convert the dimensions from drawing to actual is,
2 cm : 12 in
Height of the ramp in a skateboard park = 2 cm
Therefore, actual height 'x' of the ramp will be,
[tex]\frac{2}{12}=\frac{2}{x}[/tex]
x = 12 inches
Since, measure of the base of the ramp = 8 cm
Length of the base 'y' of the actual ramp will be,
[tex]\frac{2}{12}=\frac{8}{y}[/tex]
y = [tex]\frac{8\times 12}{2}[/tex]
y = 48 inches
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(48)(2)[/tex]
= 48 square inches
Learn more,
https://brainly.com/question/410946
50 points + geometry
No one is helping me :(
BC bisects LABD.
Step-by-step explanation:
a. 4x = 3x+3
4x-3x=3
x = 3
b. L ABC = 3x+3= 3(3)+3= 12°
c. L CBD = 4x = 4(3) = 12°
d. L ABD = 12+12 = 24°
If you were a member of water supply OR flood emergency department and you had foreseen a situation where a river near your city would cause flooding in the monsoon season. What would be your plan of action to save the city from flooding?
plz guys answer this
Answer:
I would first tell people to evacuate
Currently, you have made
78, 83, and an 80 on your tests in math. What do you need to make on the next test in order to get an average of an 82?
Answer:
87
Step-by-step explanation:
Mean(or average) = 82
let 'x' be the last test marks
Sum of marks of tests/Number of tests = Mean
(78 + 83 + 80 + x)/4 = 82
241 + x = 82 × 4
241 + x = 328
x = 328 - 241
x = 87
A number of students are evenly spaced around the circle. The fourth student is directly opposite the tenth student. How many students are there altogether?
Answer:
12 studentsStep-by-step explanation:
Between the fourth and tenth there are:
9 - 4 = 5 studentsThe total number is:
2 + 5*2 = 12 studentssimplify (-3)(-3)(-3)
Answer:
-27
Step-by-step explanation:
-3 x -3=9
9 x -3= -27
Answer:
-27
Step-by-step explanation:
Each polygon is divided into a number of triangles. Find the number of triangles if the number of sides in a polygon is: (a) 6
Answer:
4 triangles
Step-by-step explanation:
the number of triangles in a polygon is (the number of sides in the polygon - 2)
The number of triangles inside a polygon with six sides are 4.
What is a polygon? What is a mathematical function, equation and expression? polygon : A polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the number of sides in a polygon is 6.
If the polygon has {n} sides, then the number of triangle in a polygon is → (n – 2).For n = 6, the number of triangles would be - (6 - 2) = 4Therefore, the number of triangles inside a polygon with six sides are 4.
To solve more questions on polygons, visit the link below -
https://brainly.com/question/8789072
#SPJ5
-1/6(2x + 12) = 1/3x + 12
Indicate the answer choice that best completes the statem
Write each equa ton in standard form. Identify A, B, and c
y=3/8x+5
Answer:
y = 3 suh slid este ob cine este a, b și g au nevoie de acel kinfo pentru a termina
Step-by-step explanation:
solve for x
4xy+3x+2=12
show all the steps
HELPPGPPGPFPPDPSPPSS MEEEEK
Answer:
jsjwbsihdn3oiansjsos
MATH this is integers please help.
I'm giving brainly to CORRECT ANSWERS
Find the surface area of this cube in cm²? 25 mm
Someone help me with ASAP plz f(x) = x2 - 4x
Answer:
whats the choices?
Step-by-step explanation:
14>6>2 true or false
Answer:
I think this is if it is right then help me plz this is false ..
In the pair of supplementary angles shown below, the measure of the smaller angle is 36°.
Complete the equation that could be used to represent this situation. Then, solve the equation to complete the sentences.
120
36
34
180
38
144
90
56
(4x - 8) + ? = ?
Answer the question mark
The value of x is ?
Answer the question mark
The measure of the larger angle is ?
Answer the question mark
Answer:
4x _ 8 + 90 = 144
Step-by-step explanation:
you do parentheses then the rest you follow that order and it will all work ot really easy
What is (f + g)(x)? f(x) = -5x + 3 g(x) = -3x? Write your answer as a polynomial or a rational function in simplest form.
Answer:
- 8x + 3
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= - 5x + 3 + (- 3x)
= - 5x + 3 - 3x ← collect like terms
= - 8x + 3
Which of the following expressions is equivalent to the one shown below?
(43)5
O
48
19
e
C. 42
o
D. 415
SUBMI
Answer:
The choose D. 4¹⁵
I hope I helped you^_^
50 POINTS HELP WILL MARK BRAINLIEST
find the value of x.
(picture attached)
complete the square to find the vertex of the parabola.
Answer:
Step-by-step explanation:
[tex]y^2+6y+8x+1=0\\\\y^2+2*3y+9+8x+1-9=0\\(y+3)^2+8x-8=0\\8x=-(y+3)^2+8\\\\x=-\dfrac{(y+3)^2}{8}+1 \\Vertex=(1,-3)[/tex]
The vertex is (1,-3).
To find the the vertex of the parabola.
What is parabola?A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side.,
Given that:
[tex]y^{2} +6y+8x+1=0\\\\y^{2} +2*3y+8x+1+9-9=0\\\\(y+3)^{2}+8x-8=0\\\\8x=-(y+3)^{2}+8\\\\x=-\frac{(y+3)^{2}}{8} +1\\\\vertex=(1,-3)\\[/tex]
So, the vertex is (1,-3).
Learn more about parabola here:
https://brainly.com/question/24390399
#SPJ2
Please help me with my homework!!!!!!
Answer:
Step-by-step explanation:
Given that x = 3 and y = 2 we can figure these out
3x = 3x3 = 9
5y = 5 x 2 = 10
9+10=19
X times y - 1
3x2-1=5
X*+y* =
3x3+2x2 = 13
2x3*-2 =
2x3x3 - 2 = 16
-5x3+9
= -6
2x2-3+5+3*-3x2 =
9
f(x)=ax+b,f(3)=3 and f(2)=1 find the value of a and b
Answer:
a=2, b=-3
Step-by-step explanation:
f(x) = ax+b
f(3)=3, 3a+b=3
f(2)=1, 2a+b=1
Solving these two equations, we get a=2, b=-3
What is the solution to the system of equations?
. A fraction becomes 4 if one is added to both numerator and the denominator If 5 is subtracted from 5
both the numerator and the denominator the fraction becomes 1⁄2, find the fraction.
Class 10 cbse maths
the answer is 7/9. ...........