flooring a value, simply means, dropping it to the closest integer, so for the floor function or ⌊x⌋, that means
⌊ 2.5 ⌋ = 2
⌊ 2.00000001 ⌋ = 2
⌊ 2.999999999999⌋ = 2
⌊ -2.0000000001⌋ = -3
⌊ -2.999999999999⌋ = -3
let's recall that on the negative side of the number line, the farther from 0, the smaller, so -1,000,000 is a tiny number compared to the much larger -1.
⌊ -5.2 ⌋ = -6.
The notation [[x]] is not standard in typical mathematics; however, it seems that you are looking for a function that represents the floor of x. The floor function, often denoted as ⌊x⌋, is defined as the greatest integer that is less than or equal to x.
To find the floor of -5.2:
1. Identify the integer part of -5.2 without rounding. The integer part is -5 since this is the whole number component of -5.2.
2. Determine if the decimal part (.2 in this case) would cause the number to round up or down. Since the floor function requires us to find the greatest integer less than or equal to the number, we ignore the positive decimal part because it doesn't change the floor for negative numbers.
3. For positive numbers, the floor is the same as stripping away the decimal part without rounding. However, for negative numbers, if the number is not already an integer, the floor is actually one less than the integer part.
4. In the case of -5.2, because the number is negative and not an integer (due to the decimal part), the floor value is -6.
So, f(-5.2) = ⌊-5.2⌋ = -6.
10=6^2+a^2 what is a
Answer:
[tex]a=\pm i\sqrt{26}}[/tex]
Step-by-step explanation:
[tex]6^2+a^2=10\\\\36+a^2=10\qquad\text{subtract 36 from both sides}\\\\a^2=-26<0\\\\\bold{NO\ REAL\ SOLUTIONS}\\\\\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\a^2=-26\to a=\pm\sqrt{-26}\\\\a=\pm\sqrt{(-1)(26)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\a=\pm\sqrt{-1}\cdot\sqrt{26}\\\\a=\pm i\sqrt{26}[/tex]
Alice is selling lemonade and fresh squeezed orange juice at a booth. she sells cups of lemonade for $1 each and cups of orange juice for $3 each. write an expression that represents the amount of money that Alice selling drinks
Answer:
$1x + $3y = c
Step-by-step explanation:
To write an expression you need to pick a variable to represent the cups of orange juice and lemonade.
x = cups of lemonade sold
y = cups of orange juice sold
Now you have the variables to represent the amount of cups sold, so now you need a variable to represent the total cost.
c = amount of money earned from selling drinks
Now you have all the variables, so you need to write how much is cost for that drink.
$1 for one cup of lemonade so $1x
$3 for one cup of orange juice so $3x
Now put the expression together:
$1x + $3y = c
The expression that represents the amount of money that Alice selling drinks is $ (a+ 3b)
What are Algebraic expressions?An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.
How to find the expression that represents the amount of money that Alice selling drinks ?According to the problem,
Alice sells cups of lemonade for $1 each.She also sells cups of orange juice for $3 each.Let the number of cups of lemonade sold are a and the cups of orange juice sold are b.
Cost of 1 cup of lemonade is $ 1
∴Cost of a cups of lemonade = $ a
Similarly we can say,
Cost of 1 cup of orange juice is $ 3
∴ Cost of b cups of orange juice is $ 3b
So the total cost is represented by the expression : $(a + 3b)
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Consider reflections of AJKL.
What line of reflection maps point K to point Kat (-5,2)?
What line of reflection maps point L to point L'at
(-2,3)?
its y-axis for the first answer and the other one its, y=-x
The line of reflection which maps the point K to K' and L to L' is Y axis.
What is Line of Reflection?Reflection is the transformation where the image is flipped.
Line of reflection is the line for which a figure has a mirror image over that line.
Given a triangle JKL.
Let the coordinate of the triangle be J(4, 5), K(5, 2) and L(2, 3).
When a coordinate (x, y) is reflected over the X axis, then the coordinates changes to (x, -y).
When a coordinate (x, y) is reflected over the Y axis, then the coordinates changes to (-x, y).
Here,
K(5, 2) changes to K'(-5, 2).
Here x coordinate changes sign.
So the line of reflection is Y axis.
Similarly, the line of reflection for the other transformation is also Y axis.
Hence the line of reflection is Y axis.
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A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x
and the number of seats in each row by the function g(x) = 5x-2
Which function represents the total number of seats?
65x + 26
65x – 26
65x2 + 26x
65x2 – 26x
Answer:
65x^2 – 26x
Step-by-step explanation:
To determine the total number of seats, take the number of rows and multiply by the number of seats per row
f(x) * g(x)
13x * (5x-2)
65x^2 -26x
Answer:d
Step-by-step explanation:A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x and the number of seats in each row by the function g(x) = 5x – 2.Which function represents the total number of seats?65x + 2665x – 2665x2 + 26x65x2 – 26x
Select the correct answer.
Which transformation will always map a parallelogram onto itself?
a 90° rotation about its center
A.
B.
a reflection across one of its diagonals
c.
a 180° rotation about its center
D.
a reflection across a line joining the midpoints of opposite
Answer:
The answer is c.
This is because when it rotates a 180 degrees around its center it maps a parallelogram on to itself.
If y= x^2+3x+5, evaluate y given x= 2+i .
The value of y from the given equation with x=2+i is y= 7(i+2).
The given equation is y= x²+3x+5.
We need to evaluate y from the given equation for x= 2+i.
What are complex numbers?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z). Also, ib is called an imaginary number.
The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers.
Now, put x= 2+i in y= x²+3x+5 and simplify.
That is, (2+i)²+3(2+i)+5
=4+i²+4i+6+3i+5
=15-1+7i
=7i+14
=7(i+2)
Therefore, the value of y from the given equation with x=2+i is y= 7(i+2).
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Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books. One-third of Jason's collection and Nathan's entire collection add up to 31 books.
There are 21 books Jason's have and 24 books Nathan's have.
Given
Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books.
One-third of Jason's collection and Nathan's entire collection add up to 31 books.
Let the number of collection of books Jason's be x.
And the number of collection of books Nathan's be y.
Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books.
[tex]\rm 6x+\dfrac{1}{3} y=134\\\\\dfrac{18x+y}{3} =134\\\\ 18x+y = 134\times 3\\\\18x+y=402[/tex]
One-third of Jason's collection and Nathan's entire collection add up to 31 books.
[tex]\rm \dfrac{1}{3}x+y=31\\\\\dfrac{x+3y}{3} =31\\\\x+3y=31\times 3\\\\x+3y=93[/tex]
On solving both the equations;
From equation 1;
[tex]\rm 18x+y=402\\\\y = 402-18x[/tex]
Substitute the value of y in equation 2
[tex]\rm x+3y=93\\\\x+ 3(402-18x)=93\\\\x+1206 -54x=93\\\\-53x = 93-1206\\\\-53x =-1113\\\\x = \dfrac{-1113}{-53}\\\\x=21[/tex]
Substitute the value of x in equation 2
[tex]\rm x+3y=93\\\\21+3y=93\\\\3y=93-21\\\\ 3y =72\\\\ y = \dfrac{72}{3} \\\\ y=24[/tex]
Hence, there are 21 books Jason's have and 24 books Nathan's have.
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Some polyhedrons are both prisms and pyramids.
True or False?
Answer:
Some polyhedrons are both prisms and pyramids.- False
The provided statement "Some polyhedrons are both prisms and pyramids" is false.
What is geometry?It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional and three-dimensional figures.
We have a statement:
Some polyhedrons are both prisms and pyramids.
As we know,
A polygon-based solid figure is known as a polyhedron, for instance, a soccer ball, a cuboid, etc.
A strong figure with two equal bases is a prism for instance: Cube. Cylinder, Cuboid, etc.
A polyhedron with a base and an top at the top is called a pyramid, cone, a pyramid with triangles as its base, etc.
Thus, the provided statement "Some polyhedrons are both prisms and pyramids" is false.
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evaluate expression for given value 7x=8 WHEN X=2
Final answer:
The expression 7x = 8 evaluated with x = 2 results in 14, not 8. There was a misunderstanding in the question as it was not asking for a solution to the equation but rather an evaluation of the expression with a given value of x.
Explanation:
The question asks us to evaluate the expression 7x = 8 when x = 2. However, there seems to be a misunderstanding in the way the question is framed. Normally, an expression such as 7x = 8 would be an equation we solve to find the value of x. But since we are given that x = 2, it appears the task is to substitute this value into the expression 7x and see if it equals 8. Let's clarify and solve accordingly.
First, substitute x = 2 into the expression 7x:
7 * 2 = 14
Therefore, when we substitute x = 2 into the expression 7x, we get 14, not 8. It seems there was confusion in the question regarding what was being asked. If the task was to solve 7x = 8, then x would not equal 2 since 7*2 = 14. However, the original instruction was misunderstood, and the correct task was to substitute x = 2 into the expression and evaluate it, which we did correctly.
Determine the number of x-intercepts that appear on a graph of each function. f(x)= (x-6)^2(x+2)^2
Answer:
Two x-intercepts x = -2 and x = 6Step-by-step explanation:
[tex]f(x)=(x-6)^2(x+2)^2\to y=(x-6)^2(x+2)^2[/tex]
x-intercepts are for y = 0.
Put y = 0 to the equation:
[tex](x-6)^2(x+2)^2=0\iff(x-6)^2=0\ \vee\ (x+2)^2=0\\\\(x-6)^2=0\iff x-6=0\qquad\text{add 6 to both sides}\\\\x=6\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\x=-2[/tex]
Answer:
the awnser is 2
Step-by-step explanation:
Identify the discontinuity and zero of the function f(x)= 4x/x^2-16
Answer:
Step-by-step explanation:
ANSWER
Point if discontinuity:
{x}= \pm3
Zero of the function is
x = 0
EXPLANATION
The given rational function is:
f(x) = \frac{3x}{ {x}^{2} - 9}
This function is not continous when
{x}^{2} - 9 = 0
{x}= \pm \sqrt{9}
{x}= \pm3
The function is zero when,
3x = 0
x = 0
Answer:
x = 0 is the zero of this function and at x = ±4 function is discontinuous.
Step-by-step explanation:
The given function is [tex]f(x) = \frac{4x}{x^{2}-16}[/tex]
For this function we have to find the discontinuity and zeros of this function.
For zeros of the function [tex]0 = \frac{4x}{x^{2}-16}[/tex]
so zero of the function is x = 0
For x² - 16 = 0 this function not defined therefore, x = ± 4 function will be discontinuous.
Finally, x = 0 is the zero of this function and at x = ±4 function is discontinuous.
which of the following statements best describes the graph of x + y equals 4
Answer:
Step-by-step explanation:
the graph of x + y = 4 is the line passes by the point A(2,2) and the slope -1
because 2+2 =4 and y = -x +4
the degree of the polynomial 3x^3+0x^4+8
(A) 4
(B) 1
(C) 3
(D) 2
Answer:
(C) 3
Step-by-step explanation:
Let us define the degree of polynomial first
"The degree of a polynomial is the highest power of the variable in the given expression"
Now,
Given expression is:
3x^3+0x^4+8
The highest degree from first observation seems to be 4 but the term with exponent 4 is being multiplied with zero so the degree is then 3 ..
Therefore the correct answer is C. 3 ..
The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth. 10.2 inches 24.0 inches 28.2 inches 30.0 inches
Answer:
10.2 inches
Step-by-step explanation:
Ok let's assume we don't know the larger (the c value).
So this means using [tex]a^2+b^2=c^2[/tex] we have:
[tex]12^2+15^2=c^2[/tex]
[tex]144+225=c^2[/tex]
[tex]369=c^2[/tex]
Square both sides:
[tex]c=\sqrt{369} \aprox 19.2[/tex
Now assume we know the larger is 15 (this means c=15 now), then we have
[tex]a^2+12^2=15^2[/tex]
[tex]a^2+144=225[/tex]
Subtract 144 on both sides:
[tex]a^2=225-144[/tex]
Simplify:
[tex]a^2=81[/tex]
Square root both sides:
[tex]a=9[/tex]
The difference between 19.2 and 9 is 19.2-9=10.2.
Answer:
Option 1 - 10.2 inches.
Step-by-step explanation:
Given : The lengths of two sides of a right triangle are 12 inches and 15 inches.
To find : What is the difference between the two possible lengths of the third side of the triangle?
Solution :
Since, It is a right angle triangle so we apply Pythagoras theorem,
[tex]C^2=A^2+B^2[/tex]
Where, C is the hypotenuse the longer side of the triangle
A is the perpendicular
B is the base
There will be two cases,
1) Assume that C=15 inches and B = 12 inches
Substitute the value in the formula,
[tex]15^2=A^2+12^2[/tex]
[tex]225=A^2+144[/tex]
[tex]A^2=225-144[/tex]
[tex]A^2=81[/tex]
[tex]A=\sqrt{81}[/tex]
[tex]A=9[/tex]
Assume that A=15 inches and B = 12 inches
Substitute the value in the formula,
[tex]C^2=15^2+12^2[/tex]
[tex]C^2=225+144[/tex]
[tex]C^2=369[/tex]
[tex]C=\sqrt{369}[/tex]
[tex]C=19.2[/tex]
Therefore, The possible length of the third side of the triangle is
[tex]L=C-A[/tex]
[tex]L=19.2-9[/tex]
[tex]L=10.2[/tex]
Therefore, The difference between the two possible lengths of the third side of the triangle is 10.2 inches.
So, Option 1 is correct.
what is 362 equal to 126 substracted from r?
Answer:
488 = r
Step-by-step explanation:
362 = -126 + r
126 +126
----------------
488 = r
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Which of the following data represents an actual probability?
A computer randomly generates 6 out of 100 numbers.
An observer notes the number of pepperoni, cheese, vegetarian pizzas are ordered out of 100 orders.
None of the above.
Answer:
(A.)A computer randomly generates 6 put of 100 numbers.
Step-by-step explanation:
This is an actual probability.
What is the sum of the geometric series?
–122
–2
40
54
The sum of the first six terms of the geometric series will be -364. Hence, option (B) will be correct.
What is geometric series?A geometric series is a series in which the division of any consecutive two terms will be the same.
For example 3, 6, 12, 24 here if you divide 6 by 3 then it gives you 2, and if you divide 12 by 6 then also it gives you 2, and so on.
here, we have,
Given up series is 2, – 6, 18, – 54
The common ratio of this GP is -3 by that
The remaining elements of this gp will be 162, -486
So the sum will be 2 - 6 + 18 - 54 + 162 - 486 = -364 so it will the summation of the given gp.
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Use the grouping method to factor 2x^3+6x^2-7x-21
Answer:
[x + 3][2x² - 7]
Step-by-step explanation:
Start out by doing this: [2x³ + 6x² ] - [7x - 21]
↑ ⤻ ↑
GCF: 2x² GCF: -7
Do as so: 2x²[x + 3] -7[x + 3]
You see, one factor is already found [x + 3]. You only use it ONCE. Now, the other factor comes from your two Greatest Common Factors from both groups [2x² - 7]. Together, you end up with the above answer. That arrow under the negative tells you that it is attached to the 3 [distribution of the negative].
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Which answer choice correctly describes the inequality?
Answer:
the Answer is: D
Step-by-step explanation:
so that means he makes 11 dollars an hour so at most he can make that because he can work really work however long which means he can't really have less than 11 dollars an hour therefore its D
Points A and B are on opposite sides of a lake. A point C is 105.6 meters from A. The measure of ∠BAC is 70.5°, and the measure of ∠ACB is determined to be 38.833°. Find the distance between points A and B (to the nearest meter).
Answer:
= 70 Meters
Step-by-step explanation:
We can use the sine rule as follows:
Angle ABC=180-(70.5+38.833)
=70.667°
Using the sine rule and sides AB, AC and angles ABC and ACB:
b/Sin B=c/Sin C
Replacing with the values above we get:
AC/Sin ABC= AB/Sin ACB
105.6/Sin 70.667=AB/Sin 38.833
AB=(105.6 Sin 38.833)/Sin 70.667
=70.17 meters
The distance between the two points to the nearest meter is 70 meters
Answer:
70 m
Step-by-step explanation:
I got it correct on founders edtell
What are the domain and range of the absolute value parent function?
Answer:
The domain is all real numbers and the range is non-negative real numbers
(y ≥ 0) ⇒ answer B
Step-by-step explanation:
* Lets revise the parent function of the absolute value
- The absolute value or modulus |x| of a real number x is the
non-negative value of x
- The absolute value of a number means the magnitude of the number
without regard to its sign
- The parent function of the absolute value is f(x) = IxI
∵ The domain of the function is all the values of x which make the
function defined
∵ In the function f(x) = IxI, x can be any number
∴ The domain of the f(x) is any real number
∴ The domain is (-∞ , ∞) or {x : x ∈ R}
∵ The range is the set of values of y that corresponding with the
domain
∵ f(x) = IxI is non-negative value
∴ f(x) ≥ 0
∵ f(x) = y
∴ y ≥ 0
∴ The range is the set of real numbers greater than or equal zero
∴ The range is [0 , ∞) or {y : y ≥ 0}
* The true statement is: The domain is all real numbers and the range is
non-negative real numbers (y ≥ 0)
4 bananas and 3 peaches cost $10. We can represent this information as 4x +3y = $10. The x represents the cost of bananas and the y represents the cost of peaches.
a) Find an equation for 1 banana and 2 peaches cost $5
b) With the two equations, use a matrix method on your calculator to determine the cost of a banana and the cost of a peach.
Answer:
a x+2y =5
b x=1 y=2
Step-by-step explanation:
4x+3y = 10
So the cost of 1 banana is x and the cost of 1 peach is y
a) we want the cost of 1 banana and 2 peaches
1x+2y
That is equal to 5 dollars
1x+2y =5
x+2y =5
b
The matrixes are
1 2 x 5
* =
4 3 y 10
Using my calculator, x=1 y=2
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Answer:
Symbol Words Open dot or closed dot
> greater than open dot
[tex] \ge [/tex] greater than closed dot
or equal to
< less than open dot
[tex] \le [/tex] less than closed dot
or equal to
f(x) = 2x^2 what is f(3)
Answer:
18 since f(3)=18
Step-by-step explanation:
f(x)=2x^2 is give as our function. To find f(3) we need to replace x with 3.
f(3)=2(3)^2 (Replaced x with 3.)
f(3)=2(9) (Did 3^2 which was 3*3=9)
f(3)=18 (Did 2(9) which was 18)
[tex]f(3)=2\cdot 3^2=18[/tex]
Which of the following systems of linear inequalities is represented by the
solution graphed below?
Answer:
Option D is correct.
Step-by-step explanation:
Option D is correct.
y < 2 and y >= x
Because the dotted line shows that y < 2 and y >=x is shown is represented by diagonal line.
Option: D is the correct answer.
D. y<2 and y≥x
Step-by-step explanation:The graph of the system of linear inequalities are two lines:
1)
The first is a solid line which passes through (0,0) , (1,1)
i.e. the equation of the line is: y=x
and the inequality will be a inequality with a equality sign ( since the line is solid ) and the shaded region is above the line .
Hence, the inequality is: y≥x
2)
The second line is a dotted line.
This means that the inequality is strict.
Also, the line is a horizontal line parallel to the x-axis and the line pass through (0,2) and the shaded region is below the line.
Hence, the inequality is given by:
y<2
5/-7x (-9y/8)
multiply and simplify
Answer:
[tex]\large\boxed{\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{45y}{56x}}[/tex]
Step-by-step explanation:
[tex]\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{(5)(-9y)}{(-7x)(8)}=\dfrac{-45y}{-56x}=\dfrac{45y}{56x}[/tex]
The slope of the line passing through the points (-1, 5) and (3,5) is
Answer:
the slope = 0Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-1, 5) and (3, 5). Substitute:
[tex]m=\dfrac{5-5}{3-(-1)}=\dfrac{0}{4}=0[/tex]
It's a horizontal line y = 5.
Find the value of C in a triangle where a = 6, b = 8, and c = 12.
Answer: 117°
Step-by-step explanation:
Use the Law of Cosines:
c² = a² + b² - 2ab · cos C
12² = 6² + 8² - 2(6)(8)(cos C)
144 = 36 + 64 - 96 cos C
144 = 100 - 96 cos C
44 = -96 cos C
[tex]-\dfrac{44}{96}=cosC\\\\\\cos^{-1}\bigg(-\dfrac{44}{96}\bigg)=C[/tex]
117° = C
Assume that 4.5% is an annual interest rate. Find the interest rate for an account that is compounded
quarterly and monthly.
Answer:
B.
Step-by-step explanation:
Quarterly interest rate is 4.5 / 4 = 1.125%.
Monthly rate is 4.5 / 12 = 0.375%.
Answer:
B 1.25%-0.375%
Step-by-step explanation:
Compounded quarterly means there are 4 interest periods in 1 year, so divide the annual interest rate by 4.
4.5% ÷ 4 = 1.125%
Compounded monthly means there are 12 interest periods in 1 year, so divide the annual interest rate by 12.
4.5% ÷ 12 = 0.375%
The lines graphed below are parallel. The slope of the red line is 2/5What is
the slope of the green line?
Answer:
D
Step-by-step explanation:
for the 2 lines to be parallel, they have to have the same slope