Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?
Answers
x^2 -4x + 5 = 0
The 'x' value of the axis of symmetry = 'x' value of the vertex.
To get this value, take the derivative of x^2 -4x + 5 = 0 which equals
2x -4 =0
x = 2 which equals the axis of symmetry
Step-by-step explanation:
Please find the attachment of graph representing the axis of symmetry.
We are asked to choose the graph from our given choices, which shows the axis of symmetry for the function:
[tex]f(x)=(x-2)^2+1[/tex]
We can see that our function represents a parabola.
Since we know that axis of symmetry is a vertical line that divides parabola into two congruent parts. The axis of symmetry intersects parabola at its vertex.
Let us find the vertex of our given parabola using formula: [tex]x=\frac{-b}{2a}[/tex], where,
a = Coefficient of [tex]x^{2}.[/tex]
b = Coefficient of x.
To apply this formula we will represent our parabola as a quadratic equation [tex](ax^2+bx+c)[/tex] as:
[tex]f(x)=x^2-4x+4+1[/tex]
[tex]f(x)=x^2-4x+5[/tex]
Upon substituting a= 1 and b= -4 in the formula we will get,
[tex]x=\frac{-(-4)}{2*1}[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
Therefore, the vertical line passing through point x = 2 will be the axis of symmetry for our given function and graph B is the correct choice.
Related Questions
212 tens divided by 10 =
Answers
212×10/10
2120/10
212
did u mean this?
hope this helps u...
3tan3x=3
solve please
Answers
[tex]3 tan(3x)=3[/tex] ⇒ divide both sides by 3
[tex]tan(3x)= \frac{3}{3} [/tex]
[tex]tan(3x)=1[/tex] ⇒ then take arctan of 1
[tex]3x= tan^{-1}(1) [/tex]
[tex]3x=45[/tex]°
From here we can read the solution on tan(x) graph between a certain interval.
Say the interval is 0°<x<360°, the graph of tan(x) is given below, there are two solutions between this interval
3x = 45° and 225° ⇒ dividing each answer by 3
x = 15°, 75° ⇒ these are the answer to the equation for the equation between 0° and 360°
A certain triangle has two 45 angles. What type of triangle is it?
A. Acute scalene
B. Right scalene
c. Right isosceles
D. Acute isosceles
Answers
Answer:
C. Right isosceles
Step-by-step explanation:
In Acute scalene triangle, all angles are acute ( less than 90 degrees ) and different,
In Right scalene triangle, two angles are acute and different, while, the third angle is of 90°.
In Right isosceles triangle, two angles are acute and equal, while, the third angle is of 90°.
In Acute isosceles, all angles are acute in which any two angles are equal.
Now, given,
The two angle of the triangles are 45° and 45°,
Let x be the third angle,
⇒ x + 45° + 45° = 180°
⇒ x + 90° = 180°
⇒ x = 90°
Hence, the angles of given triangle are 45°, 45° and 90°,
By the above definitions,
It is clear that, given triangle is right isosceles.
Option C is correct.
Find the critical value tc for the confidence level cequals 0.95 and sample size nequals 19.
Answers
The critical values are fixed values which can be obtained from the standard t crit tables. We can find the critical value tc when the degrees of freedom and confidence level are given. The degrees of freedom is simply:
Degrees of Freedom = Number of samples – 1
Degrees of Freedom = 19 – 1
Degrees of Freedom = 18
From the t critical tables, the tc corresponding to Degrees of Freedom equal to 18 and Confidence level equal to 95% is as follows:
tc = 2.101
Therefore this means that any t value beyond 2.101, we already reject the null hypothesis.
a mail distribution center processes as many as 150,000 pieces of mail each day. the mail is sent via ground and air. each land carrier takes 1800 pieces per load and each air carrier 1500 pieces per load. the loading equipment is able to handle as many as 150 loads per day. let X be the number of loads by air carriers and y the number of loads by air carriers. write a system of inequalities that represents this situation
Answers
Final answer:
The system of inequalities representing this situation is:
1500X + 1800Y ≤ 150,000.
X + Y ≤ 150.
X ≥ 0 and Y ≥ 0.
Explanation:
Let's define X as the number of air carrier loads and Y as the number of land carrier loads. Given that the mail distribution center processes up to 150,000 pieces of mail each day and the loading equipment can handle a maximum of 150 loads per day, we can write the following system of inequalities:
The total mail processed by both air and land carriers cannot exceed 150,000 pieces:
1500X + 1800Y ≤ 150,000.
The total number of loads carried by both air and land carriers cannot exceed 150 loads:
X + Y ≤ 150.
Furthermore, since there cannot be a negative number of loads, both X and Y have to be non-negative:
X ≥ 0 and Y ≥ 0.
These inequalities model the constraints for the mail distribution center's operations.
The graph shows the number of paintballs a machine launches, y, in x seconds::
A graph titled Rate of Launch is shown. The x axis label is Time in seconds, and the x axis values are from 0 to 20 in increments of 4 for each grid line. The y axis label is Number of Balls, and the y axis values from 0 to 80 in increments of 16 for each grid line. A line is shown connecting points on ordered pair 4, 16 and 8, 32 and 12, 48 and 16, 64.
Which expression can be used to calculate the rate per second at which the machine launches the balls?
fraction 64 over 4
fraction 4 over 64
fraction 16 over 4
fraction 4 over 16
Answers
a fraction should be number of balls over time per second
so it should be 16/4 which is 4 balls per second
Answer: fraction 16 over 4
Step-by-step explanation:
The given graph shows the number of paintballs a machine launches, y, in x seconds.
We know that the rate of change of a line is given by :-
[tex]k=\frac{y_2-y_1}{x_2-x_1}[/tex]
The ordered pairs on the line in graph are (4, 16) and (8, 32) and (12, 48) and (16, 64).
Thus, the rate per second at which the machine launches the balls is given by :-
[tex]k=\frac{32-16}{8-4}=\frac{16}{4}
A pet store has 7 tanks of fish. Each tank has k fish. Using k, write an expression for the total number of fish in the store.
Answers
The expression which represents the total number of fish in the store is 7k.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given,
Number of tank = 7
Number of fish in each tank = k
The total number of fish = number of tanks x number of fish in each tank
The total number of fish = 7 x k = 7k
Hence "The expression which represents the total number of fish in the store is 7k".
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Rewrite the equation 8x+6x^2-7=x^2
in standard form and identify a, b, and c.
Answers
5x^2 + 8x -7 = 0
To rewrite the equation 8x + 6x^2 - 7 = x^2 in standard form, subtract x^2 from both sides and combine like terms. The standard form of the equation is 5x^2 + 8x - 7 = 0. The values of a, b, and c are 5, 8, and -7 respectively.
Explanation:The given equation is 8x + 6x^2 - 7 = x^2.
To rewrite it in standard form, we need to collect like terms. Subtracting x^2 from both sides, we get: 6x^2 + 8x - x^2 - 7 = 0.
Combining like terms, the standard form of the equation is 5x^2 + 8x - 7 = 0.
Here, a = 5, b = 8, and c = -7.
solve the equation using any method: -2x^2-4x=6
Answers
[tex]x= \frac{4+/- \sqrt{16-4(-2)(-6)} }{-4} [/tex]
[tex]x= \frac{4+/- \sqrt{64} }{-4} [/tex]
[tex]x= \frac{4+/-8}{-4} [/tex]
[tex]x= \frac{4+8}{-4}=-3 [/tex] and
[tex]x= \frac{4-8}{-4} =1[/tex]
Can someone solve #4 and explain it? I really appreciate it on this problem! Thank you :)
Answers
graph the line with the slope 1/3 and y-intercept -2
Answers
The graph of the line y = (1/3)x - 2 can be plotted on a graph paper by choosing some arbitrary values of x.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The given line in terms of the slope-intercept method can be written as,
y = (1/3)x - 2.
Now to plot the graph on graph paper or any digital tool we have to choose some arbitrary values of x that corresponds to some values of y.
Like at x = 0 y = -2 So, the coordinates are (0, -2).
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Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth
Answers
9.678937... (never ending)...it is irrational because it cannot be made into a fraction because it is infinite.
the decimal approximation to the nearest hundredth is : 9.68
2x+3y=-2 4x+7y=-6 solve for the system of equations
Answers
multiply first equation by -2 and add to 2nd equation
-4x-6y=4
4x+7y=-6 +
0x+1y=-2
y=-2
sub back
2x+3y=-2
2x+3(-2)=-2
2x-6=-2
2x=4
x=2
(x,y)
(2,-2)
Enter the slope-intercept equation of the line shown below.
Answers
What is the approximate distance between the points (-5, 1) and (-2, 3) on a coordinate grid ?
Answers
[tex]d= \sqrt{(x_{2} -x_{1})^{2} + (y_{2}-y_{1})^{2}} [/tex]
Therefore the distance between (-5,1) and (-2, 3) is
[tex] \sqrt{(-2+5)^{2} + (3-1)^{2}} =3.6056[/tex]
Answer: 3.61 (nearest hundredth)
4m - 4 = 4m
Please solve and show work
Answers
4m-4=4m
-4m -4m
-4≠0
There is no solution because 0 does not equal -4.
Add 4 to both sides.
4m = 4m + 4
Subtract 4m from both sides.
4m - 4m = 4
Simplify.
0 = 4
Therefore, there are no solutions.
~Hope I helped!~
50 POINTS FOR ANSWER!!!!!!!!!!!!!!!!!!!!!!
A mover uses a ramp to pull a 1000-Newton cart up to the floor of his truck, which is .8 meters high. If it takes 125 newtons to pull the cart, what is the length of the ramp?
Answers
= 101.93 * 0.8
= 81.54 N
2) force for horizontal displacement
which can be found out by subtracting above value from total force applied
= 200-101.93
=98.07
Now finding horizontal displacement
98.07 = 101.93 * d
d= 0.96 m
Now since we found out hori. and vertical dist. apply Pythagoras theorem to find out length of ramp.
l^2= 0.96 ^2 + 0.8 ^2
= 0.9216 + 0.64
= 1.56
L = 1.25 m approx.
A jar has 4 balls lettered A, E, D, and G. One ball is drawn from the jar and it's letter is noted. A second ball is also drawn without replacing the first ball and it's letter is noted. List all the possible outcomes and find the probability that the letters on the 2 balls drawn consist of at least 1 vowel, no vowels, and the same letter.
Answers
EA DA GA DE GE GD
P( at least one vowel) = 10/12 = 5/6
P( no vowels) = 2/12 = 1/6
P(same letter) = 0
The table below shows the velocity y, in miles per minute, of a toy car at different times x, in minutes: Time (x) (minutes) 10 20 30 40 Velocity (y) (miles) 0.2 0.8 0.1 0.4 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and velocity of the toy car. (4 points) [Choose the value of correlation coefficient from −1, 1, −0.04, 0.99] Part B: What is the value of the slope of the graph of velocity versus time between 10 minutes and 20 minutes, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation?
Answers
B. The slope of the graph is equal to y2-y1/x2-x1, In this case, it would specifically be v2-v1/t2-t1
Slope = 0.8-0.2/20-10 = 0.06 miles/s^2
The slope represents the acceleration at time 10 to 20 minutes.
C. The table in the graph shows causation rather than correlation. The points in the data occur in a sequential manner.
The number of lines that can be drawn perpendicular to a given line at a given point on that line in a plane is
Answers
it has a long proof.
Answer:
I JUST HAD THIS QUESTION 1
Step-by-step explanation:
In a store 60 cans of soup are arranged to be this play into equal rows why does the fraction 10 over 60 not represent the situation explain
Answers
This is given by the fraction 60 over 10.
The fraction 10 over 60 is not used to represent this situation because the fraction 10 over 60 gives the number of rows which is needed for 1 can. That is number of rows per can. But there is nothing like a fraction of a row. Hence the fraction 10 over 60 cannot be used to represent the situation.
A 10-foot piece of string is cut into two pieces so that the longer piece is 1 footfoot longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
Answers
shorter piece = x
longer piece = 2x+1
3x+1 =10
3x=9
x = 9/3=3
short piece = 3 feet
long piece = 2*3+1 = 7 feet
Find the volume of the square pyramid with length 14.7 inches and height 18 inches.
Answers
V=1296.54in³
a base edge. 14.7 in
h height. 18in
Find the length of a to the nearest tenth.
Answers
A low bal will always cause a hangover
Answers
What is the circumference of a circular disc with a diameter of 10 centimeters? (Round your answer to the nearest tenth.)
Answers
C = Pi • d
C = (3.14)(10 cm)
C = 31.41 cm or 31.4 cm, rounded to the nearest tenth.
The circumference of the circle is 31.4 cm
What is Circumference of circle?The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.
Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.
Center: The center of the circle is a point that is at a fixed distance from any other point from the circumference.Diameter: The diameter is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center.Radius: The radius of a circle is the distance from the center of a circle to any point on the circumference of the circle.The formula for the circumference of a circle is expressed using the radius 'r' of the circle and the value of 'pi'. It is expressed as, Circumference of a circle formula = 2πr.
Given:
diameter= 10 cm
So,
Circumference of circle is = πd
=3.14* 10
=31.4 cm
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Sara is 33 years younger than Rolando. The Sum of their ages is 105. Select the system of equations if Sara's age is represented by S and Rolando's age is represented by R.
A. s+r=33
s=r-105
B. s+r=105
r=s-33
C. s+r=105
s=r-105
D. s+r=105
s=r-33
E. None of these
Answers
So that is answer D.
Sara is 33 years yonder than Rolando: i.e. S<R specifically S=R-33.
They are 105 years old together: i.e. S+R=105
The only answer that has both is D.
(Be careful here, B is almost right but says that Sara is OLDER by 33 years.)
(03.01) Is the following relation a function? y equals the sine of 3 x
Answers
Answer:
Yes. This is a function.
Step-by-step explanation:
Given is a function as
[tex]y = sin 3x[/tex]
We find that for every x in the domain of real numbers there is a unique image for every x as sin 3x.
Thus this relation given satisfies the requirements of a function.
Also we find that this function is periodic with amplitude 1 and period = 2pi/3
So vertical line test if done will find that there is only one intersection for every vertical line throughout the domain
Hence this relation is definitely a function
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.
3 to the 2 over 3 power inches squared
3 to the 8 over 3 power inches squared
9 inches squared
9 to the 2 over 3 power inches squared
Question 4(Multiple Choice Worth 2 points)
(MC)
Rewrite the rational exponent as a radical.
5 to the 3 over 4 power, to the 2 over 3 power
the cube root of 5 squared
the twelfth root of 5
the square root of 5
the cube root of 5 the fourth power
Question 5(Multiple Choice Worth 2 points)
(MC)
Rewrite the radical as a rational exponent.
the cube root of 2 to the seventh power
2 to the 3 over 7 power
2 to the 7 over 3 power
2 to the power of 21
2 to the power of 4
Answers
[tex]A= \sqrt[3]{81}*3^{ \frac{2}{3} }= \sqrt[3]{3^4}*3^{ \frac{2}{3} } = 3^{ \frac{4}{3} }*3^{ \frac{2}{3} }=3^{ \frac{4}{3} + \frac{2}{3} }=3^2=9[/tex]
9 inches squared
#2
[tex]\left( 5^{ \frac{3}{4} } \right)^{ \frac{2}{3} }=5^{ \frac{3}{4} *\frac{2}{3} }=5^{ \frac{1}{2} }= \sqrt{5} [/tex]
C. the square root of 5
#3
[tex] \sqrt[3]{2^7}=2^{ \frac{7}{3} } [/tex]
2 to the 7 over 3 power
Kaveri has a total rs 590 as currency notes is the denominations ofrs50 , rs 20 , and rs 10 . the ratio of the number of rs 50 note and rs 2o is 3:5. if she has a total of 25 notes , how many notes of each denomination she has?
Answers
x = number of rs 50
y = number of rs 20
z = number of rs 10
Because there are 25 total notes,
x + y + z = 25 (1)
The ratio of rs 50 to rs 20 is 3:5, therefore
x = 0.6y (2)
The total amount is rs 590, therefore
50x + 20y + 10z = 590
or
5x + 2y + z = 59 (3)
Subtract (1) from (3).
4x + y = 34 (4)
Substitute (2) into (4).
4*(0.6y) + y = 34
3.4y = 34
y = 10
From (2), obtain
x = 6
From (1), obtain
z = 25 - 6 - 10 = 9
Answer:
Kaveri has
6 rs 50 notes,
10 rs 20 notes,
9 rs 10 notes.