f(x)=x^2-2x-10 transforming Q. F. Form general form to vertex form​

Answers

Answer 1

As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.[tex]f(x)=x^2-2x-10[/tex]  general form to vertex form is y=[[tex](x-1)^{2}[/tex]-9]

What is a vertex?

The intersection of two or more curves, lines, or edges is known as a vertex in geometry (plural: vertices or vertexes), which is frequently represented by the letters S, P, Q, or R. As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The point where two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is the vertex of an angle.

[tex]f(x)=x^2-2x-10[/tex]

      = [[tex](x-1)^{2}[/tex]-9]

Use the form, [tex]ax^{2} + bx+c[/tex]

a=1

b=2

c=-10

Consider a vertex form of parabola,

[tex]a(x+d)^{2} + e[/tex]

find the value of d, using the formula d=[tex]\frac{b}{2a}[/tex]

d=[tex]\frac{2}{2*(-1)}[/tex]

simplify the right side,

d= -1

find the value of e, using e= [tex]c-\frac{b^{2} }{4a}[/tex]

e= [tex]-10\frac{2^{2} }{4*(-1)}[/tex]

simplify the right side,

e= -9

substitute the value of a, d and e into vertex form.

y=  [[tex](x-1)^{2}[/tex]-9]

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Related Questions

what is the answer???????

Answers

Answer: Where P is.

Step-by-step explanation

1.50 x 10 ^5 / 5.0 x 10^1 in scientific notation

Answers

Answer:
3.45 x 10^5
Explanation
i just good at math :p

Select the correct answer.
What is the solution to |x - 6| ≥ 5?

A. 1 ≤ x ≤ 11
B. -11 ≤ x ≤ 1
C. x ≥ 11 or x ≤ 1
D. x ≥ 1 or x ≤ -11

Answers

Answer:

C. x ≥ 11 or x ≤ 1

Step-by-step explanation:

x - 6 + 6 ≥ 5 + 6

x ≥ 11

x - 6 ≤ -5

x - 6 + 6 ≤ -5 + 6

x ≤ 1

Hope this helps! :)

I'm stuck in this word problem pls help me ty​

Answers

Answer:

GREAT question i have no idea

Step-by-step explanation:

(1) 51.4 - 2.6*w = 9.6+1.2*w
(2) 51.4-9.6 = 1.2w+2.6w
So 41.8 = 3.8w
So w = 41.8/3.8 = 11
11 weeks until the same weight

30 points please help asap!!

Which statement describes a reflection?

A.
A reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.
B.
A reflection moves points a specified distance along a line perpendicular to a specified line.
C.
A reflection moves points a specified distance along a line parallel to a specified line.
D.
A reflection occurs when an object moves in a circular arc around a point.

Answers

Answer:

A. A reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.

Hope this helps! :)

Evaluate u + xy, if u = 18, x = 10, and y = 8​

Answers

The value of  u + xy, if u = 18, x = 10, and y = 8​ is 98

What are algebraic expressions?

Algebraic expressions are defined as mathematical expressions that are made up of constants, variables, coefficients, terms and factors.

These algebraic expressions are also composed of arithmetic operations, such as;

SubtractionAdditionDivisionMultiplicationParenthesesBracket, etc

Given the expression;

u + xy

Where;

u = 18x = 10y = 8

Now, substitute the values into the expression;

18 + 10(8)

expand the bracket

18 + 80

Add the values

98

Hence, the value is 98

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Help me: Brainliest +lots of points
The line segment joining points (2,6) and (6,2) forms a diagonal of a square. Which of the following could be the coordinates of another vertex of that square?

Answers

Answer:

(2,2) and (6,6) would be the other two points to the square.

Step-by-step explanation:

Answer:

(2,2) or (6,6)

Step-by-step explanation:

looking at the graph you can see the diagonal of a square and I just followed the points if that make sense please tell me if you need more

two members of the math competition team solve 13 problems in 1 hour. If all team members solve problems at the same rate how many tema members are needed to solve 39 problems in 1 hour

Answers

In a case whereby  two members of the math competition team solve at the rate  13 problems in 1 hour, the members that are needed to solve 39 problems in 1 hour is 6 member of the team.

How can the rate be calculated?

Since two members solve 13 problems in 1 hour, which implies that

2 members= 13 problem/ hr

Then if we want to calculate the number of the team that will be able to solve the problem at the rate of 39 problems in 1 hour, we can represent the number required as X.

Then X = 39 problems/hr.

2 members= 13 problem/ hr

Then in this case we can cross multiply as follows:

13 problem/ hr * X =  39 problems/hr * 2

Then we can make X the subject of the formular as X =( 78 /13)

= 6 member of the team.

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14.2 to 1 decimal place

Answers

The answer is 14.2

the position of a digit after the decimal point, each successive position to the right having a denominator of an increased power of ten.

The only number after the decimal is 2 so the answer is 14.2 it is already to one decimal place.
if the question was 14.25 to one decimal place for example it would be 14.3 as you’d have to round up.
Hope this helps

At which ordered pair will the function f(x) = Vx - 4 + 7

Answers

The ordered pair at which the function f(x) = √(x - 4) + 7 would begin on the coordinate plane is (4, 7).

What is a graph?

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

What is an ordered pair?

An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.

By critically observing the graph of this function (see attachment), the ordered pair would begin at (4, 7) on the cartesian coordinate.

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Complete Question:

At which ordered pair will the function f(x) = √(x - 4) + 7 begin on the

coordinate plane?

A comet is about 6.64 × 107 miles from Earth. Write this number in standard form.

Answers

Answer:710.48 miles

Step-by-step explanation:

look it up

15 times 3 plus 12 time 2 using a t chart

Answers

Answer:

69

Step-by-step explanation:

15*3=45

12*2=24

45+24= 69

Answer: 114

Step-by-step explanation:

15×3+12×2

15×3=45

45+12=57

57×2=114

tony uses 12 4 1 and 7 to make a new number

Answers

Answer:

ishbekshbrishdhtjekdhhfjeid

Help needed for trigonometry !!!

Answers

Answer:

k = 53.13°

Step-by-step explanation:

[tex]{ tan (k) = \dfrac{\text{side opposite k}}{\text{side adjacent k}}}[/tex]

[tex]= \dfrac{35}{JK}\\\\\textrm{Since JK is a right triangle, by the Pythagorean theorem }\\JK = \sqrt{IK^2 - IJ^2}}\\\\= \sqrt{35^2 - 28^2}\\\\\\ =\sqrt{1225 - 784}\\\\= \sqrt{441}\\\\= 21[/tex]

[tex]\tan(k) = \dfrac{28}{21} = 1.333\\\\k = \tan^{-1}(1.333)\\\\= 53.13^\circ[/tex]

Simplify to create an equivalent expression.
\qquad{5(10k+1)+2(2+8k)}5(10k+1)+2(2+8k)5, left parenthesis, 10, k, plus, 1, right parenthesis, plus, 2, left parenthesis, 2, plus, 8, k, right parenthesis
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
66k+966k+966, k, plus, 9

(Choice B)
B
64k+964k+964, k, plus, 9

(Choice C)
C
66k+5466k+5466, k, plus, 54

(Choice D)
D
64k-964k−964, k, minus, 9

Answers

The correct answer is a

phythegorean theorem ​

Answers

Answer: 6.782

Step-by-step explanation:

URGENT!!!!!
math assignment(not to be confused with assessment) that I need help with

Answers

Answer: DF

Step-by-step explanation:

What is the y-intercept of the online given by the equation below
y= -10x+14

Answers

Answer:

y - intercept = 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 10x + 14 ← is in slope- intercept form

with y- intercept c = 14

pls help will give brainliest

Answers

The given point were reflected about the line y = x and the coordinates the reflected point (-5 , 3)  is (3, - 5)

According to the question, given that

point reflected line y =x,

Reflected point coordinates of (-5, 3), then find the coordinates of the point after in the line of symmetry :

(-5, 3) →  (3, - 5)

A reflection is referred to as a twist in geometry. A reflection is the mirror image of shape . A line, called the line of reflection, will agree an image to reflect without change it. When all of the points in a figure are evenly spaced apart from one another, the two figures are said to reflect each other. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context. ABC and A'B'C are used to represent the pre-image and image, respectively.

A reflection point is similar to staring at a flipped mirror picture of yourself.

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why is the answer that tho

Answers

What is the question?

Answer:

question tho??

What is the answer???

Answers

Answer:

f = 90 + 32

= 122° (exterior angle)

the exterior angle (f) is 122°

What is the area of trapezoid ABCD? Enter your answer as a decimal or whole number in the box. Do not round at any steps.​

Answers

The area of the trapezoid is given as 100. See the explanation for the same below.

What is a Trapezoid?

A trapezoid is a quadrilateral with at least one set of parallel sides in American and Canadian English. A trapezoid is known as a trapezium in British and other varieties of English.

To find the length of each side of the trapezoid, you need to use the distance formula.

AB = (-1,5) and (3,2)

BC = (3,2) and (0,-2)

CD =  (0,-2) and (-13, -11)

AD or DA =  (-1,5) and(-13, -11)

Now, just use the distance formula for each line.

The Distance Formula is given as: d=√((x2 – x1)² + (y2 – y1)²).

Distance AB = √((3 – (-1))² + (2 – 5)²).
= √(4)² + (-3)²
= √(16+9)
= √25
AB = 5

lets us repeat this for the other section we will get:

Doing so gives us for all the points:

AB = 5

BC = 5

CD = 15.811388300842

DA or AD = 20

Note that:

The height is AD, the first base is AB and the second base is BC. We can plug the values for these sides into the trapezoid area formula, which is:

A = (base 1 + base 2) /  2 x height.

A = (5+5)/2 x 20

A = 5 x 20

A = 100.

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URGENT!!!!
answer options:
cannot be determined
closer to point A
closer to point B
the same distance from both point a and b

Answers

Point M has the same distance from point A and point B (option d).

Given,

Line segment CD is the  perpendicular bisector of line segment  AB

AB ⊥ CD

Assume the conjecture that the set of  points equidistant from A

and B is the  perpendicular bisector of AB is true

Here,  line segment CD intersect line segment AB at M

Then, M is the mid-point of line segment AB

So, the length of  line AM = the length of line MB

That is, Point M has the same distance from both point A and point B.

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A circle P is circumscribed about a regular hexagon ABCDEF

a. central

b. exterior

c. interior

d. inscribed

Answers

It is True to state that Arcs AB, BC, CD, DE, EF, FA in the circumscribed hexagon are all equal. See the explanation below.

What is a regular hexagon?

In geometry, a hexagon is a six-sided polygon. A regular hexagon is one in which the lengths of all the sides and the measurements of all the angles are identical. The sides of a regular hexagon are therefore equivalent.

Allow point P to be the hexagon's and circle's center.

The dimension of arc AB is the same as the measure of central angle APB, which are both 360/6 = 60 degrees. This also applies to the other arc measurements. The whole 360-degree circle is divided into six equal parts, each measuring 60 degrees.

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Full Question:

Although the question seems incomplete you may have been referring to this:


A circle P is circumscribed about a regular hexagon ABCDEF

Arcs AB, BC, CD, DE, EF, FA are all equal

Select one:

a. False

b. True

Solve for the value of x in the given rational inequalities.​

Answers

Answer:

see explanation

Step-by-step explanation:

1

1 + [tex]\frac{x-5}{2}[/tex] - [tex]\frac{x+3}{5}[/tex] ≤ 0

multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions

10 + 5(x - 5) - 2(x + 3) ≤ 0 ← distribute parenthesis on left side and simplify

10 + 5x - 25 - 2x - 6 ≤ 0

3x - 21 ≤ 0 ( add 21 to both sides )

3x ≤ 21 ( divide both sides by 3 )

x ≤ 7

2

[tex]\frac{6x}{5}[/tex] - [tex]\frac{2}{3}[/tex] ≥ 4

multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions

18x - 10 ≥ 60 ( add 10 to both sides )

18x ≥ 70 ( divide both sides by 18 )

x ≥ [tex]\frac{70}{18}[/tex] , that is

x ≥ [tex]\frac{35}{9}[/tex]

3

[tex]\frac{x}{10}[/tex] - [tex]\frac{2}{8}[/tex] ≥ 1

multiply through by 40 ( the LCM of 10 and 8 ) to clear the fractions

4x - 10 ≥ 40 ( add 10 to both sides )

4x ≥ 50 ( divide both sides by 4 )

x ≥ [tex]\frac{50}{4}[/tex] , that is

x ≥ [tex]\frac{25}{2}[/tex]

Answer:

[tex]\textsf{1.} \quad x \leq 7[/tex]

[tex]\textsf{2.} \quad x \geq \dfrac{35}{9}[/tex]

[tex]\textsf{3.} \quad x \geq \dfrac{25}{2}[/tex]

Step-by-step explanation:

Question 1

Given inequality:

[tex]1+\dfrac{x-5}{2}-\dfrac{x+3}{5} \leq 0[/tex]

[tex]\textsf{Add \; $\dfrac{x+3}{5}$ \; to both sides}:[/tex]

[tex]\implies 1+\dfrac{x-5}{2}-\dfrac{x+3}{5} +\dfrac{x+3}{5}\leq 0+\dfrac{x+3}{5}[/tex]

[tex]\implies 1+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]

[tex]\textsf{Rewrite $1$ as $\dfrac{2}{2}$}:[/tex]

[tex]\implies \dfrac{2}{2}+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{2+x-5}{2}\leq \dfrac{x+3}{5}[/tex]

[tex]\implies \dfrac{x-3}{2}\leq \dfrac{x+3}{5}[/tex]

Cross multiply:

[tex]\implies 5(x-3)\leq 2(x+3)[/tex]

[tex]\implies 5x-15\leq 2x+6[/tex]

Subtract 2x from both sides:

[tex]\implies 5x-15-2x\leq 2x+6-2x[/tex]

[tex]\implies 3x-15\leq 6[/tex]

Add 15 to both sides:

[tex]\implies 3x-15+15\leq 6+15[/tex]

[tex]\implies 3x\leq 21[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3}\leq \dfrac{21}{3}[/tex]

[tex]\implies x \leq 7[/tex]

---------------------------------------------------------------------------------------

Question 2

Given inequality:

[tex]\dfrac{6x}{5}-\dfrac{2}{3} \geq 4[/tex]

[tex]\textsf{Add \; $\dfrac{2}{3}$ \; to both sides}:[/tex]

[tex]\implies \dfrac{6x}{5}-\dfrac{2}{3} +\dfrac{2}{3}\geq 4+\dfrac{2}{3}[/tex]

[tex]\implies \dfrac{6x}{5}\geq \dfrac{12}{3}+\dfrac{2}{3}[/tex]

[tex]\implies \dfrac{6x}{5}\geq \dfrac{12+2}{3}[/tex]

[tex]\implies \dfrac{6x}{5}\geq \dfrac{14}{3}[/tex]

Cross multiply:

[tex]\implies 3(6x) \geq 14(5)[/tex]

[tex]\implies 18x \geq 70[/tex]

Divide both sides by 18:

[tex]\implies \dfrac{18x}{18} \geq \dfrac{70}{18}[/tex]

[tex]\implies x \geq \dfrac{70}{18}[/tex]

Reduce the fraction by dividing the numerator and the denominator by 2:

[tex]\implies x \geq \dfrac{70 \div 2}{18 \div 2}[/tex]

[tex]\implies x \geq \dfrac{35}{9}[/tex]

---------------------------------------------------------------------------------------

Question 3

Given inequality:

[tex]\dfrac{x}{10}-\dfrac{2}{8} \geq 1[/tex]

[tex]\textsf{Add \; $\dfrac{2}{8}$ \; to both sides}:[/tex]

[tex]\implies \dfrac{x}{10}-\dfrac{2}{8} +\dfrac{2}{8}\geq 1+\dfrac{2}{8}[/tex]

[tex]\implies \dfrac{x}{10}\geq \dfrac{8}{8}+\dfrac{2}{8}[/tex]

[tex]\implies \dfrac{x}{10}\geq \dfrac{8+2}{8}[/tex]

[tex]\implies \dfrac{x}{10}\geq \dfrac{10}{8}[/tex]

Cross multiply:

[tex]\implies 8(x) \geq 10(10)[/tex]

[tex]\implies 8x \geq 100[/tex]

Divide both sides by 8:

[tex]\implies \dfrac{8x}{8} \geq \dfrac{100}{8}[/tex]

[tex]\implies x \geq \dfrac{100}{8}[/tex]

Reduce the fraction by dividing the numerator and the denominator by 4:

[tex]\implies x \geq \dfrac{100 \div 4}{8 \div 4}[/tex]

[tex]\implies x \geq \dfrac{25}{2}[/tex]

A submarine to study changes in the sea level of the Pacific Ocean
descends 420 feet below sea level. 3 hours later, it makes an ascent
of 170 feet. What is the submarine's new position?

Answers

It should be 250 feet below sea level

Which of the following is equivalent to (2x² − y)²?

Answers

the answer to this problem is 4x^4 - 4x^2 y + y^2! I hope this helps. <3

What is 2x-8=34?
please answer quickly​

Answers

Answer: x=21

Step-by-step explanation:

2x-8=34 (change the -8 into a positive since it doesn't have a variable)

34+8=42 (divide 34 by 2)

42/2=21

Check your answer

2 x 21 = 42

42-8=34

x=21

2x - 8 = 34
+ 8 + 8
——————-
2x = 42
— —
2 2
——————-
x = 21

at the end of the season, a team’s ratio of wins to losses was 3:5. if there were no ties, what percentage of its games did the team win? (show work)

A.) 33 1/3%
B.) 37 1/2%
C.) 40%
D.) 62 1/2%
E.) 75%

Answers

As per given data of end of the season , ratio of teams win to losses is 3:5 and no ties, then percentage of game win by team is equal 37 1/2%.

As given in the question,

For the given dat of end of season,

Ratio of teams win to losses is equal to 3:5

Let x be the percentage of game

As per given ratio we have,

3x+ 5x =100%

⇒ 8x = 100

⇒x =100/ 8

⇒ x= 12.5

Percentage of winning the game by team = 3x

                                                                   = 3(12.5)

                                                                   = 37.5%

                                                                   = 37 1/2%

Therefore, for given data of end of the season , ratio of teams win to losses is 3:5 and no ties, then percentage of game win by team is equal 37 1/2%.

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Which of the following is
equivalent to the complex number
I27?

Answers

The equivalent to the complex number i²⁷ is -i.

what is complex numbers?

Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfying the equation

i² = 1.

Given that,

i²⁷ is a complex number

i²⁷ = i²⁴⁺³

i²⁷ = i²⁴ ₓ i³

i²⁷ = i⁴⁽⁶⁾ ₓ i²⁺¹

i²⁷ = (i⁴)⁶ . i².i

Here, we know that i² = -1

so, i⁴ = (i²)²

i⁴ = 1

Hence, 1⁶(-1)(i) = -i

Therefore, the equivalent to the complex number i²⁷ is -i.

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