MATHEMATICS HIGH SCHOOL

The graph of which function has an axis of symmetry at x =-1/4 ?f(x) = 2x2 + x – 1

f(x) = 2x2 – x + 1

f(x) = x2 + 2x – 1

f(x) = x2 – 2x + 1

Answers

Answer 1

Answer:

we know that

The equation of the vertical parabola in vertex form is equal to

$y=a(x-h)^(2)+k$

where

(h,k) is the vertex

The axis of symmetry is equal to the x-coordinate of the vertex

$x=h$ ------> axis of symmetry of a vertical parabola

we will determine in each case the axis of symmetry to determine the solution

case A) $f(x)=2x^(2)+x-1$

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+1=2x^(2)+x$

Factor the leading coefficient

$f(x)+1=2(x^(2)+0.5x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+1+0.125=2(x^(2)+0.5x+0.0625)$

$f(x)+1.125=2(x^(2)+0.5x+0.0625)$

Rewrite as perfect squares

$f(x)+1.125=2(x+0.25)^(2)$

$f(x)=2(x+0.25)^(2)-1.125$

the vertex is the point $(-0.25,-1.125)$

the axis of symmetry is

$x=-0.25=-(1)/(4)$

therefore

the function $f(x)=2x^(2)+x-1$ has an axis of symmetry at $x=-(1)/(4)$

case B) $f(x)=2x^(2)-x+1$

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-1=2x^(2)-x$

Factor the leading coefficient

$f(x)-1=2(x^(2)-0.5x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-1+0.125=2(x^(2)-0.5x+0.0625)$

$f(x)-0.875=2(x^(2)-0.5x+0.0625)$

Rewrite as perfect squares

$f(x)-0.875=2(x-0.25)^(2)$

$f(x)=2(x-0.25)^(2)+0.875$

the vertex is the point $(0.25,0.875)$

the axis of symmetry is

$x=0.25=(1)/(4)$

therefore

the function $f(x)=2x^(2)-x+1$ does not have a symmetry axis in $x=-(1)/(4)$

case C) $f(x)=x^(2)+2x-1$

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+1=x^(2)+2x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+1+1=x^(2)+2x+1$

$f(x)+2=x^(2)+2x+1$

Rewrite as perfect squares

$f(x)+2=(x+1)^(2)$

$f(x)=(x+1)^(2)-2$

the vertex is the point $(-1,-2)$

the axis of symmetry is

$x=-1$

therefore

the function $f(x)=x^(2)+2x-1$ does not have a symmetry axis in $x=-(1)/(4)$

case D) $f(x)=x^(2)-2x+1$

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-1=x^(2)-2x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-1+1=x^(2)-2x+1$

$f(x)=x^(2)-2x+1$

Rewrite as perfect squares

$f(x)=(x-1)^(2)$

the vertex is the point $(1,0)$

the axis of symmetry is

$x=1$

therefore

the function $f(x)=x^(2)-2x+1$ does not have a symmetry axis in $x=-(1)/(4)$

the answer is

$f(x)=2x^(2)+x-1$

Answer 2

Answer: axis of symmetry is the x value of the vertex

for
y=ax^2+bx+c
x value of vertex=-b/2a

first one
-1/2(2)=-1/4
wow, that is right

answer is first one
f(x)=2x^2+x-1

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You cannot bisect an angle using paper folding constructions True or False

Answers

Answer:

The given statement:

You cannot bisect an angle using paper folding constructions is a False Statement.

Step-by-step explanation:

The construction of a angle bisector with the help of paper folding is done by:

Draw a angle ACB on a piece of paper such that the ray CB lie on the base.

Fold the paper in such a way that ray AC falls along the ray CB.

draw the line along the crease that is formed on the paper starting from point C.

So, the ray so formed is the angle bisector of the angle ACB.

Lucy has a hemisphere shaped goldfish pond in her backyard. The pond has a circumference of 11.9 feet . The pond has a population density of 3.6 cubic feet of water for each goldfish. How many goldfish are in Lucy's pond ?

Answers

40.38 my answer is 40.38 or 40 goldfish

Around 40.38 - 40 goldfish is your answer.

Konrad has $500 in a savings account at the beginning of the summer. He wants to have more than $200 in the account by the end of the summer. He withdraws $25 each week for food, clothes, and movie tickets. How many weeks can Konrad withdraw money from his account?

Answers

Answer:

Step-by-step explanation:

He has $500 to start with, and he takes $25 out of the account each week. But he wants more than 200 in his account by the end of summer. 25 goes into 500 20 times. But if he wanted more than 200 left, like 300-400, he could spend 4 week's worth of money to have 400 left, or 8 weeks to have 300 left. This is the best-case scenario.

the measure of angle 1 is twice the measure of angle 2, and angle 1 and angle 2 are linear pair. Find the measure of angle 1.

Answers

Answer:

m<1=120

Step-by-step explanation:

A linear pair adds up to 180 degrees.

So <1+<2=180

Let <2=X, that would make <1=2X because <1 is 2 times more.

So substitute that into the equation.

2x+x=180.

Combine like terms and get 3x=180

Divide both sides by 3 and get x=60.

Substitute that into <1 and get <1=120

Final answer:

Given that angle 1 and angle 2 forms a linear pair and angle 1 is twice angle 2, we can calculate angle 1 to be 120 degrees.

Explanation:

The subject of this question is Mathematics, specifically geometry. A linear pair of angles means that the two angles add up to 180 degrees. If the measure of angle 1 is twice the measure of angle 2 as stated in the question, we can represent this in equation form as 2x (angle 1) + x (angle 2) = 180.

Combining like terms, we get 3x = 180. Now, solve for x by dividing both sides by 3. Therefore, x equals 60 degrees. But the question asks for the measure of angle 1, so we substitute x into the equation 2x = angle 1. Therefore, angle 1 is 120 degrees (2 * 60).

Learn more about angle measure here:

brainly.com/question/33833061

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HELP PLEZ!!!!!!!!!!!Which equations are true for the values of x, y, and z? Select three options.

X° + 65° = 180°
x° = z°
y° = 65°
x° = 65°
x° + y° + z° = 115°

Answers

Answer:

a, b, and c

Step-by-step explanation:

a. x°+65°=180°

b. x°=z°

c. y°=65°

d. x°=65°

e. x°+y°+x°=115°

x = 115°

y = 65°

z = 115°

The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?a. P(B|A) = y
b. P(A|B) = y
c. P(B|A) = x
d. P(A and B) = x + y

e. P(A and B) = x/y

P(A)

Answers

The right answer for the question that is being asked and shown above is that: "d. P(A and B) = x + y." The probability of event A is x, and the probability of event B is y. If the two events are independent, the condition must be true is this d. P(A and B) = x + y

If two events are independent, then

$Pr(A\cap B)=Pr(A)\cdot Pr(B)$ .