Answers
Answer:
(i) a = 2
b = -1
c = -1
(ii) x= 1
Step-by-step explanation:
Step 1: Factorise
[tex]f(x) = 2(x^{2} -2x+\frac{1}{2})[/tex]
Step 2: Use the complete square method.
[tex]f(x)=2(x^{2} -2x+(\frac{-2}{2})^{2} + \frac{1}{2} - (\frac{-2}{2})^{2} )[/tex]
Step 3: Have it to [tex]a(x+b)^{2} +c[/tex]
[tex]f(x)=2((x-1)^{2} -\frac{1}{2} )\\ = 2(x-1)^{2} -1[/tex]
Line of symmetry:
To find line of symmetry, we use -b/2a formula.
Based from [tex]2x^{2} -4x+1[/tex]:
a=2, b=-4
-b/2a = -(-4)/2(2) = 1
Related Questions
Use the cross product property to determine witch of the following equalities are proportions:
6.6/1.1 = 0.3/0.05
Answers
Answer:
proportion
Step-by-step explanation:
6.6/1.1 = 0.3/0.05
Using cross products
6.6 * .05 = 1.1 * .3
.33 = .33
Since this is a true statement, the statement is a proportion
please help!! i have no idea!
Answers
Answer:
θ = 60.34
Step-by-step explanation:
[tex]\frac{\left(12.8\cdot \:sin\left(90\right)\right)}{sin\left(52.3\right)}[/tex] = 16.177
[tex]\frac{\left(16.177\cdot \:sin\left(90\right)\right)}{18.6}[/tex] = θ = .869
[tex]arcsin\left(.869\right)[/tex] = 60.34
Answer:
60.4°
Step-by-step explanation:
There are two right triangles.
One right triangle (on the left side) has an acute angle measuring 52.3°.
Its opposite leg measures 12.8 cm.
We can find the length of its hypotenuse, x.
sin 52.3° = opp/hyp
sin 52.3° = 12.8 cm/x
x * sin 52.3° = 12.8 cm
x = 12.8 cm/sin 52.3°
x = 16.2 cm
Now we use the hypotenuse of the left side triangle which is a leg of the right side triangle.
For the right side triangle, we are looking for angle Θ. We know the opposite leg, 16.2 cm and the hypotenuse, 18.6 cm.
sin Θ = opp/hyp
sin Θ = 16.2/18.6
sin Θ = 0.8698
Θ = sin^-1 0.8698
Θ = 60.4°
Find the equation of the line through the points (-5,11) and (2,-3)
y=
Answers
Answer:
y = -2x + 1
Step-by-step explanation:
y2 - y1 / x2 - x1
-3 - 11 / 2 - (-5)
-14/ 7
= -2
y = -2x + b
-3 = -2(2) + b
-3 = -4 + b
1 = b
What is Index Law 1?
please give a definition
Answers
Answer:
LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . ... Example: In this example, the powers were multiplied together to give the answer which is 3 to the power of 6.
What is the midpoint of AB?
A
F GHI
B
+
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
3 4 5 6 7
5 6 7 8 9
+
+
point F
point G
point H
O point
Answers
Answer:
the answer is point G
It is found that Point G is the midpoint of AB.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
We are Given two points A and B which are located at -6 and 8 on the number line. We need to find the midpoint of AB.
First we have to calculate the distance between AB which can be calculated as;
8-(-6)=14 units
Now, to find the midpoint we have to divide the total distance by 2.
Hence, the mid point of AB is 7 units apart from both points A and B then G.
Learn more about midpoint here;
https://brainly.com/question/5127660
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ahmed is sitting on a dock watching a float plane in a harbour. At a certain time, the plane is 350 m above the water and 470 m from Ahmed. Determine the angle of elevation of the plane measured from Ahmed, to the nearest degree
Answers
Answer:
The angle of elevation of the plane measured from Ahmed is approximately 36.67°
Step-by-step explanation:
The given parameters of the float plane are;
The height of the float plane above the water, y = 350 m
The horizontal distance of the float plane from Ahmed, x = 470 m
Given that Ahmed is sitting on the dock, by the water, by trigonometric ratios, we have;
The height of the float plane, the distance of the plane from Ahmed and the line of sight forming the angle of elevation of the plane measured from Ahmed, form a right triangle
[tex]tan\angle X = \dfrac{Opposite \ leg \ length}{Adjacent \ Leg\ length}[/tex]
Therefore
[tex]tan(\theta) = \dfrac{y}{x}[/tex]
Where;
θ = The angle of elevation of the plane measured from Ahmed
y = The leg of the right triangle opposite the reference angle
x = The leg of the right adjacent to reference angle
Therefore;
θ = arctan(y/x) which gives;
θ = arctan(350/470) ≈ 36.67°
The angle of elevation of the plane measured from Ahmed, θ ≈ 36.67°.
Question 2 of 10
What is the length of MN?
M
4x
x + 3
250"
50
N
A. 4
o
B. 1
C. 7
ОО
D. 8
Answers
Answer:
4
Step-by-step explanation:
Since the base angles are the same, the side have to be the same
ML = MN
4x = x+3
Subtract x from each side
4x-x = x+3-x
3x= 3
Divide by 3
3x/3 = 3/3
x = 1
We want the length of MN
MN = x+3 = 1+3 = 4
The measurement of MN side is 4
What are the properties of Triangle?The properties of the triangle are:
1. The sum of all the angles of a triangle (of all types) is equal to 180°.
2. The sum of the length of the two sides of a triangle is greater than the length of the third side.
3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
Since the base angles are the same, the side have to be the same
ML = MN
4x = x+3
Subtract x from each side
4x-x = x+3-x
3x= 3
Divide by 3
3x/3 = 3/3
x = 1
We want the length of MN
MN = x+3 = 1+3 = 4
Learn more about triangles here:
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If Q = 5+2i, E = i, and D = 5-2i, find Q.E.D
Answers
Answer:
Q.D.E=(5+2i).(5-2i).i = (25-4i²)i = 25i-4i³
Step-by-step explanation:
Which of the following is a statement? (a) The fishes are beautiful (b) Study mathematics. (c) x is a capital of country y. (d) Water is essential for health.
Answers
Answer:
its letter a
Step-by-step explanation:
I hope you help
What is the minimum perimeter of a rectangle with an area of 625 mm^2
Question 2 options:
100 mm
125 mm
156.25 mm
312.5 mm
Show your work:
Answers
Answer:
100 mm
Step-by-step explanation:
Square root the area to find the length of each side
[tex]\sqrt[]{625} =25[/tex]
Multiply 25 by 4 to get the sum of all four sides for the perimeter
25 x 4 = 100
Quanto falta para a fração 8/6 chegar a 2 inteiros? respondem rapido pfv
Answers
Answer:
4/6
Step-by-step explanation:
8/6 + 4/6 = 12/6
12/6 = 2.
ANSWER ASAP ILL MARK BRAINLIEST!!! if the vertex of a parabola is (-1,-9) what is the equation of the axis of symmetry?
Answers
Answer:
x = -1
Step-by-step explanation:
the equation of the axis of symetry =>
x = -1
We have to find,
The equation of the axis of symmetry.
The answer will be,
→ x = -1
Therefore, this is the equation.
What is the value of the expression below when 4x=4? 2
x
2
+
x
−
5
2x
2
+x−5
Plzzz help!!
Answers
Answer:
I dont understand the problem because of the way its written out but I believe that the value of x itself is 1.
x=1
Step-by-step explanation:
1 x 4 = 4
(hope it helps a bit)
(x^2 + 5x + 2) – (5x^2 – x – 2) =
Answers
Answer:
[tex]{ \tt{( {x}^{2} + 5x + 2) - (5 {x}^{2} - x - 2) }} \\ = { \tt{(1 - 5) {x}^{2} + (5 + 1)x + (2 + 2)}} \\ = { \tt{ - 4 {x}^{2} + 6x + 4 }} \\ = { \tt{ - 2(2 {x}^{2} - 3x - 2) }}[/tex]
What is the area of trapezoid DEFG with coordinates D (4, 3), E (4, 0), F (2, 1), and G (2, 3)?
10 square units
5 square units
3 square units
2 square units
Answers
The area of the trapezoid is 10 square units
How to find the area of a trapezoid?The formula for finding the area of the trapezoid is expressed as:
A = 0.5(a+b)h
where:
a and b are the sides
h is the height
Given the following
a = 3
b = 2
h = 4
Determine the requried volume of the trapezoidSubstitute
A = 0.5(3 + 2)*4
A = 0.5(20)
A = 10 square units
Hence the area of the trapezoid is 10 square units
Learn more on area of trapezoid here: https://brainly.com/question/1463152
Answer:
B) 5 Square Units
Step-by-step explanation:
Answered from another colleague :)
B1 = 2
B2 = 3
H = 2
A = 1/2 (B1 + B2) H
1/2 (2+3) 2
1/2 (5) 2
(2.5)2
5
Two-Fifths of a number is 48. What is 3/4 of the SAME number?
Need help urgently
Answers
Answer:
[see below]
Step-by-step explanation:
"Two-Fifths of a number is 48."
(2/5)n = 48
((2/5n)(5/2) = 48 *(5/2)
n = 120
------------------------------------
120 * (3/4) = 90
Hope this helps you.
Which expression is equivalent to
8x^7y^8? Assume x>0.
Answers
Answer:
2x^3y^3Sqrt2 is the expression
If a real estate agent receives 17 percent of the selling price of each house he sells, then what would the agent make if the house sells for $180,000?
Answers
Answer:
$30600
Step-by-step explanation:
The selling price is $180,000
The commission rate is 17% of this
(17/100) * 180000 = 30600
4. If 2 Cos A-1 = 0, then the value acute value A is
Answers
Answer:
[tex]A=60^{\circ}[/tex]
Step-by-step explanation:
Given [tex]2\cos A-1=0[/tex],
Add 1 to both sides:
[tex]2\cos A=1[/tex]
Divide both sides by 2:
[tex]\cos A=\frac{1}{2}[/tex]
Take the inverse cosine of each side (note that the question stipulates that A is acute):
[tex]\arccos(\cos A)=\arccos(\frac{1}{2})[/tex]
[tex]A=\arccos(\frac{1}{2}), A\in (0^{\circ}, 90^{\circ}),\\A=\boxed{60^{\circ}}[/tex]
YOU’RE WELCOME:))
using trig solve for the missing angle
Answers
Answer:
The answer is 26.4
10. A rectangle whose length is twice its width has a diagonal equal to one side of a given square. The ratio of the area of the rectangle to the area of the square is
Answers
Answer:
2/5
Step-by-step explanation:
First, we can draw the rectangle out, as shown. The length is twice the width, and the diagonal, y, cuts across the rectangle. This forms a right triangle, and using the Pythagorean Theorem, we can say that
y² = x² + (2x)²
y² = x² + 4x²
y² = 5x²
square root both sides
y=√(5x²)
The diagonal, or y, is equal to √(5x²). This is equal to one side of the square
The area for the rectangle, which we need to find for the ratio, is length * width = x * 2x = 2x²
The area for the square, which we also need to find for the ratio, is (side length)² = √(5x²) = 5x²
The ratio for the area of the rectangle to the area of the square is therefore 2x²/5x² = 2/5 (crossing out the x² in both the numerator and the denominator). We know to put the rectangle on top because of the specific wording of "the ratio of the area of the rectangle to..."
10 fracciones que generen decimales exactos 10 fracciones que generen decimales inexactos puros y 10 fraccionarios que generen decimales periódicos mixtos
Answers
Answer:
Un número decimal exacto es algo de la forma:
3.27
Para reescribir este número como una fracción, podemos ver que tiene dos dígitos luego del punto.
Entonces podemos multiplicar y dividir por 100 (misma cantidad de ceros que dígitos luego del punto decimal)
así obtenemos:
3.27*(100)/(100) = 327/100
Entonces la fracción 327/100 genera un decimal exacto.
Así, encontrar 10 fracciones es trivial, 10 ejemplos son:
7/10 = 0.7
314/100 = 3.14
27/10 = 2.7
27/100 = 0.27
2/10 = 0.2
25/100 = 0.25
31/10 = 3.1
12/10 = 6/5 = 1.2
131/10 = 13.1
142/100 = 1.42
Ahora, un decimal inexacto puro es algo de la forma:
3.33...
donde el 3 se repite infinitamente.
Tratemos de reescribir este número como una fracción:
primero debemos ver la cantidad de dígitos que se repiten, en este caso es uno solo, el 3, entonces multiplicamos por 10:
3.33*10 = 33.33...
Ahora, podemos restar el numero original:
33.333... - 3.333... = 30
Entonces tenemos que:
3.33*9 = 30
3.33 = 30/9
La fracción:
30/9 nos da in decimal inexacto puro.
Ahora que sabemos construirlas, 10 ejemplos pueden ser:
30/9 = 3.33....
1/3 = 0.33...
40/9 = 4.44...
50/9 = 5.55...
60/9 = 6.66...
70/9 = 7.77...
20/9 = 2.22...
55/9 = 6.11...
544/99 = 5.5959...
10/9 = 1.11...
Finalmente, un periódico mixto es algo de la forma:
1.2343434...
Es decir, el 34 se repite infinitamente, pero también tenemos un 2 luego del punto decimal, por lo que este número no es puramente periódico.
Para construirlos, podemos tomar una fracción exacta, como
1.1 y una periódica, como 1.11...
Si las sumamos, obtenemos:
1.1 + 1.11... = 2.211...
donde el uno se repetirá infinitamente.
Así, simplemente sumando las fracciones del primer caso con las del segundo, obtendremos decimales periódicos mixtos, por ejemplo:
7/10 + 55/9 = 613/90 = 0.7 + 6.11... = 6.8111....
7/10 + 10/9 = 163/90 = 0.7 + 1.11... = 1.811....
31/10 + 10/9 = 379/90 = 3.1 + 1.11... = 4.2111...
31/10 + 20/9 = 479/90 = 3.1 + 2.22... = 5.322...
31/10 + 30/9 = 579/90 = 3.1 + 3.33... = 6.4333...
27/10 + 20/9 = 443/90 = 2.7 + 2.22... = 4.922...
37/10 + 20/9 = 533/90 = 3.7 + 2.22... = 5.922...
4/10 + 10/9 = 136/90 = 0.4 + 1.11... = 1.511....
3/100 + 10/9 = 1027/900 = 0.03 + 1.11... = 1.14111...
4/10 + 20/9 = 236/90 = 0.4 + 2.22... = 2.622....
The second hand on a clock is
8 cm long.
What is the distance the tip of the second hand travels in 10 minutes?
Answers
Answer:
8.37 cm rounded
Step-by-step explanation:
C = 2π r
C = 2π (8)
C = 16 π
C = 50.24
1/6 ( 50.24)= 8.37
what is the area of the triangle formed from (-2,2), (1,2) and (0,-6)
Answers
Answer:
I think it's 12
Step-by-step explanation:
Hope it helps!
Analyze the diagram below and complete the instructions that follow.
Quadrilateral LMNO is a rectangle. Find MN.
A.
7
B.
10
C.
18
D.
27
Answers
Answer:
there is no diagram ......
Angles of triangle are in the ratio of 23:5. What is the Size of the smallest angle?
Answers
Answer:
ratio 2 : 3 : 5
size of smallest angle
[tex]180 \times \frac{2}{10} \\ = 36[/tex]
Answer:
The smallest angle of a triangle is 36°.
Step-by-step explanation:
Given, the ratio of angles of a triangle is 2 : 3 : 5
Let the angles of a triangle be ∠A, ∠B and ∠C.
∠A = 2x, ∠B = 3x, ∠C = 5x
∠A+∠B + ∠C= 180°
[sum of all the angles of a triangle is 180°]
2x + 3x + 5x = 180°
10x = 180°
x=180°/10 =18°
∠A=2x=2 x 18° = 36°
∠B = 3x = 3 x 18° = 54°
∠C = 5x = 5 x 18° = 90°
Hence, the smallest angle of a triangle is 36°.
HOPE IT HELPS!!!
(4 x 10 ^ 7) ÷ (8 x 10 ^ 4) in standard form PLZ ANSWER QUICK
Answers
Answer:
4.67×10
4
=4.67×10000=46700
[tex]4.67 \times {10}^{4} [/tex]
[tex] = \: 4.67 \times 1000[/tex]
[tex] = \: 46700[/tex]
The difference between the square of two numbers is 11. Twice the square of the first number increased by the square of the second number is 97 find the numbers
Answers
Answer:
Below in bold.
Step-by-step explanation:
x^2 - y^2 = 11
2x^2 + y^2 = 97
From the first equation:
y^2 = x^2 - 11
Substituting in the second equation:
2x^2 + x^2 - 11 = 97
3x^2 = 108
x^2 = 36
x = 6, -6.
Substituting for x in the first equation:
(6)^2 - y^2 = 11
y^2 = 36 - 11 = 25
y = 5, -5.
El periodo de un movimiento circular uniforme es de
8 segundos. ¿Cuál es su velocidad angular?
Answers
Answer: I dont understand what your saying im sorry, I'd really like to help but I cant :(
Find the general term of the ap whose 7th term is -1 and 16th term is 17? (pls Hurry up I will mark you Brainliest and don't reply in a silly way or I'll report you)
Answers
Answer:
The answer is -13.
Step-by-step explanation:
The formula of the nth term of an AP(arthimetic progression) is a+(n-1)d.
So the 7th term will be a+6d= -1 ---(1)
The 16th term will a+15d=17 ---(2)
Subtract (2) and (1)
a+15d-(a+6d)=17-(-1)
=a+15d-a-6d=17+1
9d=18
d=18/9
d=2.
Substitute d in eq (1)
a+6(2)= -1
a+12=-1
a= -1-12= -13
Thus the general term of the ap is -13
