The definition of absolute value is the magnitude of a number without the sign.
Hope this helps!
Final answer:
The absolute value of a number indicates its distance from zero on the number line without regard to direction, resulting in a non-negative value. In vectors, the absolute value denotes the magnitude, which is also always positive, even when multiplied by a negative scalar.
Explanation:
Absolute Value Definition
The absolute value of a number is its distance from zero on the number line, regardless of direction. The absolute value of a number is always non-negative, and it is represented by two vertical bars on either side of the number. For instance, the absolute value of -4 is 4, and the absolute value of 4 is also 4. In mathematical notation, this is written as |−4| = 4 and |4| = 4.
In the context of vectors, the absolute value can refer to the magnitude of the vector. When we multiply a vector by a scalar c, the magnitude of the resulting vector becomes the absolute value of cA. If c is positive, the direction of the vector remains the same. If c is negative, the direction is reversed. The magnitude of a vector is always positive, and when calculating the magnitude, we are essentially taking the absolute value of its length.
Significance of the absolute value concept extends to other areas of science as well, such as physics, where it can denote the magnitude of displacement or frequency. For example, the beat frequency between two sounds is defined as the absolute value of the difference between their frequencies because a negative frequency would not make sense.
what is the vertex form of y=2x^2-8x+1
Answer:
[tex]2(x-2)^2-7[/tex]
Step-by-step explanation:
[tex]y=2x^2-8x+1[/tex]
When comparing to standard form of a parabola: [tex]ax^2+bx+c[/tex]
[tex]a=2[/tex][tex]b=-8[/tex][tex]c=1[/tex]Vertex form of a parabola is: [tex]a(x-h)^2+k[/tex], which is what we are trying to convert this quadratic equation into.
To do so, we can start by finding "h" in the original vertex form of a parabola. This can be found by using: [tex]\frac{-b}{2a}[/tex].
Substitute in -8 for b and 2 for a.
[tex]\frac{-(-8)}{2(2)}[/tex]
Simplify this fraction.
[tex]\frac{8}{4} \rightarrow2[/tex]
[tex]\boxed{h=2}[/tex]
The "h" value is 2. Now we can find the "k" value by substituting in 2 for x into the given quadratic equation.
[tex]y=2(2)^2-8(2)+1[/tex]
Simplify.
[tex]y=-7[/tex]
[tex]\boxed{k=-7}[/tex]
We have the values of h and k for the original vertex form, so now we can plug these into the original vertex form. We already know a from the beginning (it is 2).
[tex]a(x-h)^2+k\\ \\ 2(x-2)^2-7[/tex]
To find the vertex form of a quadratic equation \( y = ax^2 + bx + c \), we can complete the square to transform it into the vertex form, which is written as \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
The quadratic equation given is \( y = 2x^2 - 8x + 1 \).
Here, \( a = 2 \), \( b = -8 \), and \( c = 1 \).
First, find \( h \) using the formula \( h = -\frac{b}{2a} \):
\[
h = -\frac{-8}{2 \cdot 2} = \frac{8}{4} = 2
\]
Next, we will use the value of \( h \) to find \( k \). The value of \( k \) is the y-value of the vertex, which we find by plugging \( h \) into the original equation:
\[
k = 2h^2 - 8h + 1
\]
Now substituting \( h = 2 \) into this formula, we get:
\[
k = 2(2)^2 - 8(2) + 1 = 2 \cdot 4 - 16 + 1 = 8 - 16 + 1 = -7
\]
Therefore, the vertex \( (h, k) \) is \( (2, -7) \).
Now, we rewrite the original quadratic equation in vertex form using the values of \( h \) and \( k \):
\[
y = a(x - h)^2 + k
\]
Substitute \( a = 2 \), \( h = 2 \), and \( k = -7 \) into this equation:
\[
y = 2(x - 2)^2 - 7
\]
So, the vertex form of the equation \( y = 2x^2 - 8x + 1 \) is \( y = 2(x - 2)^2 - 7 \).
Help what polynomials are there??
Answer:
All of them are polynomials except c.
Step-by-step explanation:
Polynomials are in the form:
[tex]a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+\cdots +a_nx^n[/tex]
You can see here there are no extra symbols like square root, cube root, absolute value, and so on on the variable x...
We also don't have division by a variable. All the exponents are whole numbers.
a) While it has a square root, it is not on a variable so a is a polynomial. The exponents on the variables are whole numbers.
b) b is a polynomial also because all the exponents are whole numbers.
c) This is not a polynomial because there is a square root on a variable.
d) This is a polynomial. All the exponents are whole numbers.
In the diagram, the only figure that could be parallel to line
c is
line a.
line b.
line d.
plane Q.
Answer:
The correct option is line d.
Step-by-step explanation:
The correct option is line d.
Two parallel lines are always on the same plane and never touch each other. They are always same distance apart....
Answer:
the answer is line d . just took the test.
Step-by-step explanation:
Which of the following statements is correct about the data set 2,4,6,8,10,12,14,16?
A. The data set has a median that is not in the data set
B. The data set has a mode that is not in the data set
C. The data set has an interquartile range of 9
D. The data set has the same median and mode
Answer:
A. The data set has a median that is not in the data set
Step-by-step explanation:
The given data is:
2,4,6,8,10,12,14,16
The median for the data set is:
(8+10)/2 = 9
The data set has no mode as no number is repeated in the data set.
The IQR is:
= [(12+14)/2-(4+6)/2)]
=[26/2 - 10/2]
=13-5
=8
By looking at the options, we can see that the correct answer is:
A. The data set has a median that is not in the data set
as 9 is not a member of the data set ..
the box plot shows a set of test scores. which statement is correct?
A box plot displays the distribution of a set of data values. To determine the correct statement, analyze its components: minimum, first quartile, median, third quartile, and maximum.
Explanation:A box plot, also known as a box-and-whisker plot, is a type of graph that displays the distribution of a set of data values. It shows the minimum, first quartile, median, third quartile, and maximum values of the data set.
To interpret the box plot and determine which statement is correct, you need to analyze its components:
Minimum: The smallest value in the data set.First Quartile: The median of the lower half of the data.Median: The middle value of the data set.Third Quartile: The median of the upper half of the data.Maximum: The largest value in the data set.By analyzing the position and spread of these values in the box plot, you can determine which statement is correct.
Learn more about Box Plot here:https://brainly.com/question/31856042
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a small candle costs $2.25 an a large candle costs $4.75. jerome cannot spent more than $80. write an inequality that models the amount spent on small and large candles. then given that jerome needs to buy at least 15 candles for his school play write an inequality that models the number of small and large candles he can buy.
Answer:
(1) 2.25s + 4.75l ≤ 80
(2) s + l ≥ 15
Step-by-step explanation:
2.25s = cost of a small candle
4.75l = cost of a large candle
2.25s + 4.75l = total cost of candles
You have two conditions:
A. Amount spent on small and large candles
(1) 2.25s + 4.75l ≤ 80
B. Number of small and large candles
(2) s + l ≥ 15
Answer:
2.25x+4.75y < 80
An elevator started on the 14th floor. It went down 7 floors, up 4 floors, up 9 floors, and down 3 floors. On what floor did the elevator finally stop?
Answer:
17
Step-by-step explanation:
14 - 7 = 7
7 + 4 +9 =20
20 - 3 = 17
Evaluate the expression when a = 13. 89 + a
will mark brainliest for 1st person
Answer:
102
Step-by-step explanation:
89 + a
Let a=13
89+13
102
A circle has its center at (1, 4) and a radius of 2 units. What is the equation of the circle? (1 point) (x + 2)2 + (y + 4)2 = 2 (x − 1)2 + (y − 4)2 = 4 (x + 1)2 + (y − 4)2 = 4 (x − 1)2 + (y − 4)2 = 2
Answer:
3rd one. The general form of a circle is set equal to the radius squared. So right side is 4 then plug in values until true.
Answer:
The answer is the second option
[tex](x-1)^{2}+(y-4)^{2}= 4[/tex]
Step-by-step explanation:
The general equation of a circle is:
[tex](x-h)^{2}+(y-k)^{2}= r^{2}[/tex]
in this equation (h,k) is the center of the circle and r is the radius, so if the center is in (1,4) and the radius is 2, the values of the constants are:
h = 1
k = 4
r = 2
And the formula for this circle is:
[tex](x-1)^{2}+(y-4)^{2}= 2^{2}[/tex]
[tex](x-1)^{2}+(y-4)^{2}= 4[/tex]
Evaluate In 5.
a) 0.62
b) 0.70
c) 1.61
d) 1.95
Answer:
C
Step-by-step explanation:
The actual answer is 1.60943
When you round it to the hundredths place, the answer becomes 1.61
C
Answer:
The correct answer is C. 1.61.
Step-by-step explanation:
What is the volume of a cube with a length of 10 cm width of 5 cm and a height of 8 cm
Answer:
400cm^3
Step-by-step explanation:
Volume = length * height * width
Volume = 5 * 8 * 10 = 400 cm^3
If a cylinder has a diameter of 10 units what is the radius
Answer:
the radius is 5
Step-by-step explanation:
First, divide the diameter by 2 and plug the values for volume, pi, and radius into the formula for volume of a cylinder.
Paul can purchase 3 muffins for $1.35. At this rate what is the cost of 10 muffins? A. $3.75. B. $4.00. C. $4.25. D. $4.50.
Answer: D. $4.50.
Step-by-step explanation: You need to find the individual cost of 1 muffin. To do this, divide 1.35 by 3. 1.35/3=0.45. Each muffin costs $0.45. Multiply this by 10 to get $4.50 for 10 muffins.
Shishir bought 4000 orange at 70 paisa each. But 400 of them were rotten. He sold 2000 oranges at 90 paisa each.If he plans to make a profit of RS 200 , at what rate must he sell the rest of the oranges ?
Answer:
He needs to sell the rest of the oranges at 75 paisa each.
Step-by-step explanation:
Consider the given information that, Shishir bought 4000 orange at 70 paisa each.
Note: 1 rupees = 100 paisa
Thus, 70 paisa = 70/100 rupees = 0.70 rupees
Therefore, the cost price of 4000 oranges is:
4000×0.70 rupees = 2800 rupees
The selling price of 2000 oranges is:
2000×0.90 rupees = 1800 rupees
The number of oranges now Shishir have:
4000 - 2000 - 400 = 1600
He wants to make a profit of RS 200. Thus the selling price of 4000 oranges should be:
2800 rupees + 200 rupees = 3000 rupees
He earned 1800 rupees by selling 2000 oranges at 90 paisa. So, the remaining amount that he needs to make with 1600 oranges is:
3000 rupees - 1800 rupees = 1200 rupees
Therefore, the cost of one orange is:
1600 oranges = 1200 rupees
1 orange = 1200/1600 rupees
1 orange = 0.75 rupees
Hence, he needs to sell the rest of the oranges at 75 paisa each.
4. Cindy bought a car for $21.330. A few years later, she sold the car for $19,700. Find the percent of change in the value
(SHOW WORK)
Answer:
-7.64%
Step-by-step explanation:
1. Find out how much the car went down in value.
21,330 - 19,700 = 1,630
2. Calculate how much 1% of the original value ($21,330) was. One percent is 1/100, which is .01 when divided.
21,330 × .01 = 213.3
3. Since we now know 1% is equal to $213.30 we can divide $1,630 by $213.30. Doing this will show us how many 1%s are in 1,630.
1,630/213.30 = 7.64181903
4. There are 7.64181903 1%s in 1,630. Because the car's value went down by 1,630, this also means it went down by 7.64181903% We will round this to the nearest hundredth for simplicity's sake.
7.64181903 → 7.641 one is less than 6 so we will round down → 7.64
5. The car decreased by 7.64% in value. This will be written as -7.64% because a decrease is negative.
Answer:
-7.64%
Step-by-step explanation:
what is the simplest fprm of x^2+5x-6/x^2+9x+18
Answer:
x - 1\x + 3
Step-by-step explanation:
Factoring quadratic expressions with a Leading Coefficient of 1 → In the first equation, you have to find two numbers that when differed to 5, they also multiply to 6, and those numbers are 1 and 6. Now, the tough part for you might be figuring out which term gets which sign. Well, if you look at your MIDST term [5], you would know that the negative symbol goes to 1 [-1] and the positive symbol goes to 6, so your numerator is [x - 1][x + 6]. Now, for the second equation, it is applied the same way, but in this case, we need two numbers that when added to 9, they also multiply to 18, and those numbers are 3 and 6, and automatically receive positive symbols, so your denominator is [x + 3][x + 6]. Now that we have our denominator and numerator, we now set it up: [x - 1][x + 6]\[x + 6][x + 3]. What do you see that is... MAGIC--AL? That is correct! The factors x - 6 neutralize each other and are left with x - 1\x + 3.
To be honest, if you had posted quadratic expressions with Leading Coefficients greater than 1, that would be a little bit more tough for you, meaning taking extra steps further, but if you post one in the future, it will be there to assist you because as always...,
I am joyous to assist anyone at any time.
Divide and express 3.7/2 to the nearest tenth.
3.7 divided by 2 is 1.85, rounded to the nearest tenth is 1.9.
To divide 3.7 by 2 to the nearest tenth, you first perform the division:
[tex]\[ \frac{3.7}{2} = 1.85 \][/tex]
Now, to express this result to the nearest tenth, you look at the first decimal place after the decimal point. Here, it's 8, which is closer to 9 than to 0. So, you round up the digit in the tenths place.
Thus, 3.7 divided by 2, rounded to the nearest tenth, is [tex]\(1.9\).[/tex]
if f(x)=3 x and g(x)= 1/x , what is the domain of (g o f)(x)?
Answer:
The domain is (-∞ , 0)∪(0 , ∞) OR The domain is {x : x ≠ 0}
Step-by-step explanation:
* Lets revise the composite function
- A composite function is a function that depends on another function.
- A composite function is created when one function is substituted into
another function.
- Ex: f(g(x)) is the composite function that is formed when g(x) is
substituted for x in f(x).
- In the composition (f ο g)(x), the domain of f becomes g(x).
* Lets solve the problem
∵ f(x) = 3x and g(x) = 1/x
- In (g o f)(x) we will substitute x in g by f
∴ (g o f)(x) = 1/3x
- The domain of the function is all real values of x which make the
function defined
- In the rational function r(x) = p(x)/q(x) the domain is all real numbers
except the values of x which make q(x) =0
∵ (g o f)(x) = 1/3x
∵ 3x = 0 ⇒ divide both side by 3
∴ x = 0
∴ The domain of (g o f)(x) is all real numbers except x = 0
∴ The domain is (-∞ , 0)∪(0 , ∞) OR The domain is {x : x ≠ 0}
Simplify the expression
(2b/3)^4
A. 16b^4/81
B. 16b^4/3
C. 8b^4/12
D. 6b^4
Answer:
A.16b^4/81
step-by-step explanation:
(2b/3)^4
= (2b)^4/3^4
= (2^4×b^4)/3^4
=16b^4/81
(as 16 and 81 cant simplify each other)
Answer:
A. 16b^4/81
Step-by-step explanation:
(2b/3)^4
We know (a/b)^c = a^c / b^c
(2b)^4 / 3^4
We also know (ab)^c = a^c * b^c
2^4 * b^4 / 3^4
16 b^4/ 81
The volume of a rectangular prism is given by the function V = lwh. Which statement is true?
A The volume of the prism depends on the product of only the length and the width.
B The volume of the prism depends on the product of only the length and the height.
CThe volume of the prism depends on the product of the length, the width, and the height.
D The volume of the prism depends on the product of only the width and the height.
Answer:
CThe volume of the prism depends on the product of the length, the width, and the height.
Step-by-step explanation:
V = lwh
Volume is the product of l, which is length, w which is width and h which is height
Answer:
C.The volume of the prism depends on the product of the length, the width, and the height.
Step-by-step explanation:
If the volume of a rectangular prism is given by the function V = lwh, the volume of the prism depends on the product of the length, the width, and the height.
(2x^2+x+3)/(x-2)with remainder
Answer:
2x+5 r. 13
Step-by-step explanation:
So using long division, you can solve for the quotient and the remainder.
Please look at the attached for the solution.
Step 1: need to make sure that you right the terms in descending order. (If there are missing terms in between, you need to fill them out with a zero so you won't have a problem with spacing)
Step 2: Divide the highest term in the dividend, by the highest term in the divisor.
Step 3: Multiply your result with the divisor and and write it below the dividend, aligning it with its matched term.
Step 4: Subtract and bring down the next term.
Repeat the steps until you cannot divide any further. If you have left-overs that is your remained.
Given the system of equations presented here:
4x + y = 4
2x + 6y = 24
Which action creates an equivalent system that will eliminate one variable when they are combined?
A.Multiply the first equation by -4 to get -16x - 4y = -16.
B.Multiply the second equation by -4 to get - 8x - 24y = -96.
C.Multiply the first equation by -2 to get -8x - 2y = -8.
D.Multiply the second equation by -2 to get - 4x - 12y = -48.
Answer:
D.Multiply the second equation by -2to get - 4x - 12y = -48.Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}4x+y=4\\2x+6y=24&\text{multiply both sides by (-2)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}4x+y=4\\-4x-12y=-48\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad11y=-44\qquad\text{divide both sides by 11}\\.\qquad\qquad y=-4\\\\\text{put the value of y to the first equation:}\\\\4x+(-4)=4\\4x-4=4\qquad\text{add 4 to both sides}\\4x=8\qquad\text{divide both sides by 4}\\x=2[/tex]
Answer:
Multiply the second equation by -2 to get [tex]- 4x - 12y = -48[/tex]
Step-by-step explanation:
[tex]4x + y = 4[/tex]
[tex]2x + 6y = 24[/tex]
To eliminate one variable the coefficient of a variable should be same with opposite sign.
LEts check with each option
Multiply the first equation by -4 to get [tex]-16x - 4y = -16[/tex]
the coefficient of x or y are not same when we compare with second equation
Multiply the second equation by -4 to get [tex]- 8x - 24y = -96[/tex]
the coefficient of x or y are not same when we compare with first equation
Multiply the first equation by -2 to get [tex]-8x - 2y = -8[/tex]
the coefficient of x or y are not same when we compare with second equation
Multiply the second equation by -2 to get [tex]- 4x - 12y = -48[/tex]
The coefficient of x terms are same with different sign when compare with first equation
So when we add first and second equation , the x will get eliminated.
What does the number 2 represent in this function
Your answer is C) The ant is crawling at 2 feet per minute.
This is because in the function y = 2t + 5, the 2 represents the slope of the line, which means that for every 1 unit that you go across, you need to go 2 units up. Therefore, for every 1 minute, the ant gains 2 feet so it is crawling at 2 feet per minute.
I hope this helps! Let me know if you have any questions :)
The length of segment XY is 9cm which statements regarding XYX are correct check all that apply
Answer:
The 1st, 3rd, and 5th statements are correct.
Step-by-step explanation:
YZ has the same angle as XY, so the length is the same.
A^2+B^2=C^2 shows that XZ equals 9 sqrt 2 cm.
The hypotenuse is always the longest segment in the triangle.
Help?????????????????????
Answer:
B. Graph B
Step-by-step explanation:
A graph with no solutions is one where the lines never intersect.
In Graph A, you have a solution at about (-2, 2).
In Graph C, all real numbers are solutions.
Solve the system -10=-2y+x 6y=3x+11
Answer: No Solutions exist
Step-by-step explanation:
We have the following system of equations
[tex]-10=-2y+x[/tex]
[tex]6y=3x+11[/tex]
Rewriting the second equation we have:
[tex]-11=-6y+3x[/tex]
Now we multiply the first equation by -3 and add it to the second equation
[tex]30=6y-3x[/tex]
[tex]-11=-6y+3x[/tex]
---------------------------------
[tex]19=0[/tex]
Equality is not satisfied. Then the system has no solution
Number 28 ignore the bubbled in answer
Answer:
y = -7x+34
Step-by-step explanation:
We have 2 points, so we can find the slope
m = (y2-y1)/(x2-x1)
= (6--1)/(4-5)
= (6+1)/(4-5)
= 7/-1
= -7
We can use point slope form to make an equation
y-y1 = m(x-x1)
y--1 = -7(x-5)
y+1 = -7(x-5)
Distribute
y+1 = -7x+35
Subtract 1 from each side
y+1-1 = -7x+35-1
y = -7x+34
Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
The equation of the line that passes through (-2, 4) with a slope of 2/5 is y = (2/5)x + 24/5. This is found using the point-slope form of a line and then simplifying it into the slope-intercept form.
Explanation:To find an equation of a line that passes through a given point with a specific slope, you can use the point-slope form of the equation of a line, which, after simplifying, can be converted to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Given the point (-2, 4) and the slope 2/5, we first use the point-slope form:
y - y1 = m(x - x1)
Substituting the given point and slope, we have:
y - 4 = (2/5)(x + 2)
Expanding and simplifying gives us the equation:
y = (2/5)x + (2/5)(2) + 4
y = (2/5)x + 4/5 + 20/5
y = (2/5)x + 24/5
So, the slope-intercept form of the line that passes through (-2, 4) with a slope of 2/5 is y = (2/5)x + 24/5.
One day Mr. Pritz drove for 6 1/3 hours. The next day he drove 9 1/2 hours. For how many hours did he drive during the two days?
Answer:
Step-by-step explanation:
First convert them into improper fractions: [tex]6\frac{1}{3} =\frac{19}{3}[/tex] and [tex]9\frac{1}{2} =\frac{19}{2}[/tex]. Now we add: [tex]\frac{19}{2}+\frac{19}{3}=\frac{95}{6}[/tex] or [tex]15\frac{5}{6}[/tex].
Which method will NOT get you to the point (5,2.5)?
(5,2.5)
R
CHECK
Starting at the origin, go 5 spaces to the right and then 2.5
spaces up
Starting at the origin, go 2.5 spaces up and then 5 spaces
to the right
Starting at the origin, go 2.5 spaces to the right and then
5 spaces up
Put one finger on 5 on the x-axis, and put another finger
halfway between 2 and 3 on the y-axis. Move the first
finger up and the second finger to the right until they meet.
Answer:
Starting at the origin, go 2.5 spaces to the right and then 5 spaces up.
Step-by-step explanation:
This is the RIGHT answer. It only goes 2.5 spaces on the X axis and the X axis is at 5
Answer:
Startingat the origin, go 2.5 spaces to the right and then go 5 spaces up.
Step-by-step explanation:
I got it right on IM
Remember it was asking for the wrong answer in the problem! This is the way that you SHOULDN'T answer the problem!