The expression that represents the height of the rectangular prism is 3x + (10 / (2x - 4)) found by dividing the given volume expression by the base area expression.
To find the expression that represents the height of the rectangular prism, we need to rearrange the formula for the volume of a prism, which is Volume = Base Area x Height. Given the volume of the rectangular prism as 6x^2
- 2x + 8 and the base area as 2x - 4, we divide the volume by the base area to find the height:
Height = Volume / Base Area
Height = (6x^2 - 2x + 8) / (2x - 4)
This simplifies to:
Height = 3x + (10 / (2x - 4))
Therefore, the expression that represents the height is 3x + (10 / (2x - 4)).
Use the elimination method to solve the systems of equations choose the correct ordered pair 3x+6y=36 3x-6y=0
Answer:
(6, 3)
Step-by-step explanation:
Given the 2 equations
3x + 6y = 36 → (1)
3x - 6y = 0 → (2)
Add the 2 equations term by term to eliminate the y- term
(3x + 3x) + (6y - 6y) = (36 + 0)
6x = 36 ( divide both sides by 6 )
x = 6
Substitute x = 6 into either of the 2 equations and solve for y
(1) : 18 + 6y = 36 ( subtract 18 from both sides )
6y = 18 ( divide both sides by 6 )
y = 3
Solution is (6, 3)
Answer:
the solution is (6, 3)
Step-by-step explanation:
Subtract the second equation from the first, as indicated:
3x+6y=36
-( 3x-6y=0)
-----------------
12y = 36. Then y = 36/12 = 3.
Subbing 3 for y in the second equation, we get 3x - 6(3) = 0, or 3x = 18, or x = 6.
Thus, the solution is (6, 3).
Identify the type of function represented by f(x)=2(1/2)^x
Answer:
B: Exponential decay
Step-by-step explanation:
Answer:
exponential decay
Step-by-step explanation:
[tex]f(x)= 2(\frac{1}{2})^x[/tex]
[tex]f(x)= ab^x[/tex] is an exponential function, where 'a' is the initial value and 'b' is the exponential factor
When the value of 'b' is between 0 and 1 then it is exponential decay
when the value of 'b' is greater than 1 then it is an exponential growth
In the given exponential function , the value of b is 1/2 that is 0.5
The value of 'b' is between 0 and 1 so it is an exponential decay
What is the distance between(-3,-8) and (-12,-11)
Step-by-step explanation:
Use the distance formula:
d² = (x₂ − x₁)² + (y₂ − y₁)²
d² = (-3 − -12)² + (-8 − -11)²
d² = 9² + 3²
d² = 90
d = 3√10
Which two types of people help generate revenue for an organization directly?\
A.
repeat customers
B.
online shoppers
C.
human resource staff
D.
sales executives
E.
security personnel
Answer:
Answer: The Answer Is B
Answer:
I think is D is the best answer
Multiply the following using the vertical method
Answer:
Option C is correct.
Step-by-step explanation:
We need to multiply the following terms using vertical multiplication method
3x^2-5x+1
x x^2+2x+4
The vertical multiplication is shown in the figure attached.
The result is: 3x^4+x^3+3x^2-18x+4
So, Option C is correct.
The vertical method of multiplication involves multiplying each digit of one number by each digit of another, one at a time, recording partial results and adding them together for the final result.
Explanation:To perform multiplication using a vertical method, first write the numbers vertically aligning them properly. We will be multiplying like this:
123 (number 1) x456 (number 2)
Start from the rightmost digit of the second number (bottom number) and multiply it with each digit of the first number (top number), advancing from right to left. Record each result underneath, shifted appropriately (similar to 'carry digits' in addition). After fully multiplying by one digit, proceed to the next digit in the second number, remembering to shift your results accordingly. Finally, add all the results together to get the final answer. This is the vertical method of multiplication.
Learn more about Vertical Method Multiplication here:https://brainly.com/question/16823788
#SPJ3
Solve for x. Round your answer to the nearest thousandth.
a. 7.08 c. 8.442
b. 23.869 d. 10.903
Please select the best answer from the choices provided A B C D
Answer:
7.08
Choice A
Step-by-step explanation:
From the right-angled triangle we have been given the following;
One angle - 33 degrees
The hypotenuse - 13 units
We are required to determine the length of the side, opposite the angle, marked x.
Using the Mnemonic; SOHCAHTOA
The sine of an angle is; (opposite side)/(hypotenuse)
Therefore;
sin 33 = x/13
x = 13 * sin 33
x = 7.080
Answer: A
Step-by-step explanation:
14. Which one of the following formulas correctly expresses this statement: The number x is equal to another number n plus the square root of 3. A. x = n + √3 B. x = 3n2 C. x = √n + 3 D. x = n + 32
Answer:
I believe it's A.
Step-by-step explanation:
Because look at the parts: The number x / is equal to / another number n / plus / the square root of 3.
Hope my answer has helped you!
For this case we must express in an algebraic way the following expression:
"The number x is equal to another number n plus the square root of 3"
So:
The same "x" number is represented as:
[tex]x =[/tex]
A number "n" plus the square root of three is represented as:
[tex]n + \sqrt {3}[/tex]
So, the complete expression is:
[tex]x = n + \sqrt {3}[/tex]
Answer:
Option A
The area of a rectangle is 16 square units. Use the grid to draw what the rectangle could look like.
Answer:
8 * 2
Step-by-step explanation:
When you draw the rectangle make it an 8 units by 2 units rectangle.
Hello to all, how is everything, I think every one is getting more from this website, and your views are fastidious in support of new viewers. Dfbdgdgdcbga
Answer: This website is the greatest thing ever wjsijrbejwisjfb
If the polynomials (2x^3+ax^2+3x-5)and (x^3+x^2-2x+a) leave the same remainder when divided by (x-2). Find the value of a. Also find the remainder in each case
The polynomial remainer theorem says that a polynomial [tex]p(x)[/tex] leaves a remainder of [tex]p(c)[/tex] when divided by [tex]x-c[/tex]. When [tex]x=2[/tex], we have
[tex]2x^3+ax^2+3x-5=4a+17[/tex]
[tex]x^3+x^2-2x+a=a+8[/tex]
Both operations leave the same remainder, which means
[tex]4a+17=a+8\implies3a=-9\implies\boxed{a=-3}[/tex]
Then the remainders are both 5.
NEED HELP WITH A MATH QUESTION
Answer:
5/75 in my opinion. 75 is total of hot drink
Step-by-step explanation:
Match each function with the corresponding function formula when h(x) = 2 – 2x and g(x) = –2 x + 2.
Answer:
1 -> f
2 -> a
3 -> d
4 -> b
5 -> e
6 -> c
Step-by-step explanation:
We are given:
h(x) = 2 - 2x and g(x) = -2^x+2
a) k(x)= (g-h)(x) = g(x) - h(x)
= -2^x+2 - (2 - 2x)
= -2^x+2 - 2 + 2x
= -2^x+2x or 2x-2^x
k(x) = 2x-2^x = (g-h)(x)
So, 2 matches with a
b) k(x)= (g+h)(x) = g(x) + h(x)
= -2^x+2 + (2 - 2x)
= -2^x+2 + 2 - 2x
= -2^x+4-2x or 4 - 2^x -2x
So, k(x) = 4 - 2^x -2x = (g+h)(x)
So, 4 matches with b
c) k(x)= (2h - 2g)(x) = 2h(x) - 2g(x)
= 2(2 - 2x)-2(-2^x+2)
= 4 - 4x+2.2^x-4
= -4x+2^x+1 or 2^x+1-4x
So, k(x) = 2^x+1-4x = (2h - 2g)(x)
So, 6 matches with c
d) k(x) = (h-2g)(x) = h(x) - 2g(x)
= (2 - 2x)-2(-2^x+2)
= 2 - 2x+2.2^x-4
= -2-2x+2^x+1
= 2^x+1-2x-2
So, k(x) = 2^x+1-2x-2 = (h-2g)(x)
So, 3 matches with d
e) k(x) = (h-g)(x) = h(x) - g(x)
= (2 - 2x)-(-2^x+2)
= 2 - 2x+2^x-2
= -2x+2^x or 2^x-2x
So, k(x) = 2^x-2x = (h-g)(x)
So, 5 matches with e
f) k(x) = (2g+h)(x) = 2g(x)+h(x)
= 2(-2^x+2) + (2 - 2x)
= -2.2^x+4 + 2 - 2x
= -2^x+1+6-2x or 6 - 2^x+1-2x
So, k(x) = 6 - 2^x+1-2x = (2g+h)(x)
So, 1 matches with f
Final answer:
The function formulas are h(x) = 2 - 2x and g(x) = -2x + 2.
Explanation:
h(x) = 2 - 2x
g(x) = -2x + 2
Even function times an even function produces an even function, Odd function times an odd function produces an even function.
Given the graph below state whether or not the relation is a function, and give the domain and
range.
Answer:
NOT a functiondomain: [-2, 2]range: [-4, 4]Step-by-step explanation:
A vertical line intersects the graph twice, so the relation is not a function. It is only allowed to intersect once if the relation is a function.
The domain is the horizontal extent, which is from -2 to +2.
The range is the vertical extent, which is -4 to +4.
The relation is indeed a function, and its domain is [-2, ∞), and its range is (-∞, ∞), as you assumed. The verification process aligns with your initial statements.
If the assumed domain is [-2, ∞) and the assumed range is (-∞, ∞), it suggests that you believe the relation is a function that is defined for all real numbers and can output any real number.
To determine whether the relation is indeed a function, we need to check whether each input (x-value) corresponds to a unique output (y-value) and ensure it satisfies the vertical line test. Let's proceed with the verification:
Function Test (Vertical Line Test):Trace a vertical line through the entire graph. If the vertical line intersects the graph at only one point for each x-value, then the relation is a function. If the vertical line intersects the graph at more than one point for any x-value, then the relation is not a function.
Based on the assumed domain and range, it appears that you are considering the relation to be a function defined for all real numbers. In such a case, the relation would be a function by definition, as it assigns a unique y-value to each x-value.
To learn more about function, click here.
https://brainly.com/question/35114770
#SPJ3
PLEASE HELP I WILL GIVE BRAINLIEST What is the last step in constructing this equilateral triangle?
Answer:
A. Draw line segment AB
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
B
Step-by-step explanation:
The Guy Above Got It Wrong On The Exam.
What is the domain of y=log_5x
[tex](0. \infty)[/tex]
Step-by-step explanation:Since this is a logarithmic function, the domain is [tex](0. \infty)[/tex]. But what is the domain of a function? The domain of a function is the set of inputs. This is so, because for any logarithmic function[tex]y=log_{a}(x)[/tex], x must be greater than 0. So this function is continuous and has an x-intercept at [tex](1,0)[/tex], and y increases as x increases. Finally, its graph is shown below.
What are the zeros of the function shown in the graph?
Answer:
the zeros are -3,-1, and 1
Step-by-step explanation:
zeros are nothing more that where the function crosses or touches the x-axis
Answer: Third Option
-3, -1, 1
Step-by-step explanation:
By definition, the zeros of a function f(x) are all the values x for which f(x) = 0.
In other words, the zeros of a function f(x) are the intersections of the graph of f(x) with the axis of x.
Therefore, to identify the zeros of the function shown, identify the values of x in which the graph intersects the horizontal axis.
You can see in the graph that these intersections occur in
[tex]x = -3\\x = -1\\x = 1[/tex]
Finally the zeros are: -3, -1, 1
Identify the reflection of the figure with vertices P(−11,−13), Q(−17,19), and R(23,−27) across the x-axis.
P (−11, 13), Q (−17, −19), R (23, 27)
P (11, 13), Q (17, −19), R (−23, 27)
P (11, −13), Q (17, 19), R (−23, −27)
P (−13, −11), Q (19, −17), R (−27, 23)
Answer:
P (−11, 13), Q (−17, −19), R (23, 27)
Step-by-step explanation:
we know that
The reflection of a figure across the x-axis has the following rule
(x,y) -----> (x,-y)
so
P(-11,-13) -----> P(-11,13)
Q(-17,19) -----> Q(-17,-19)
R(23,-27) ----> R(23,27)
Answer:
P (−11, 13), Q (−17, −19), R (23, 27)
Step-by-step explanation:
Got it right on my test :)
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
The answer to your problem is 13%
There are 4 male freshmen and 30 students total.
Divide the amount of male freshmen by the amount of students and turn it into a percentage.
4/30= 0.1333 = 13%
Reiko is going to use AAS to prove that VWX=YZX. PLZ HELP ASAP
Answer:
Option C.
Step-by-step explanation:
In the given triangles XWV and XYZ we have to prove both the triangles are congruent.
Since side VW ≅ side YZ (Given)
∠WVX ≅ ∠XYZ (Given)
And by AAS theorem, we should prove ∠VXW = ∠YXZ
Since AAS theorem says, if two adjacent or corresponding angles and one opposite side of these angles are equal then the given triangles will be congruent.
Therefore, Option C. will be the answer.
Answer:
Prove that VXW TO YXZ by vertical angles
Traffic on saturday, it took ms. torres 24 minutes to drive 20 miles from her home to her office. during friday's rush hour, it took 75 minutes to drive the same distance.
a. what was ms. torres's average speed in miles per hour on saturday?
b. what was her average speed in miles per hour on friday?
Answer:
a. 50 mph.
b. 16 mph.
Step-by-step explanation:
a.Convert minutes to hours using dimensional analysis:
[tex]\displaystyle \rm 24 \; minutes \times \frac{1\; hour}{60\; minutes} = \frac{2}{5}\; hours[/tex].
Average speed is distance traveled over time taken:
[tex]\displaystyle \text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Taken}} = \rm \frac{20\; miles}{\dfrac{2}{5}\; hours} = (20 \times \frac{5}{2})\; mph= 50\; mph[/tex].
b.Similarly,
[tex]\displaystyle \text{Time Taken} = \rm 75 \; minutes \times \frac{1\; hour}{60\; minutes} = \frac{5}{4}\; hours[/tex].
[tex]\displaystyle \text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Taken}} = \rm \frac{20\; miles}{\dfrac{5}{4}\; hours} = (20\times \frac{4}{5})\; mph= 16\; mph[/tex].
The probability of drawing an ace from a deck of cards is 1/13. If you drew one card at a time (and put the card back each time) for 400 tries, how many times total could you expect to draw an ace
Answer:
31 aces
Step-by-step explanation:
To find the number of aces you would expect, take the probability of an aces and multiply by the number of tries
1/13 * 400 =30.76923
Rounding up, approximately 31 aces
Answer:
30 times
Step-by-step explanation:
1/3 * 400
30.76923
31 times
Solve the equation.
15x^2 – 28x + 5 = 0
Answer:
Step 1: Factor left side of equation.
(5x−1)(3x−5)=0
Step 2: Set factors equal to 0.
5x−1=0 or 3x−5=0
x=
1 /5
or x=
5 /3
Answer:::::::::
x=5/3 or x=1/5
Mr Solidarios charged Randolf Php 320.00 for parts and Php 150.00 per hour for labor to repair his bicycle.If he spent 3 hours repairing his bicycle,how much does Randolf owe him?
Answer:
Php 770.00
Step-by-step explanation:
The cost of labor is ...
(hours) × (hourly rate)
= (3 h) × (Php 150.00/h) = Php 450.00
The total cost is ...
total cost = cost of labor + cost of parts
= (Php 450.00) + (Php 320.00) = Php 770.00
Randolf owes Mr. Solidarios Php 770.00 for the repair.
Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480.
Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation.(2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answer:
Here's what I get.
Step-by-step explanation:
Part A. Equation in standard form
The question is asking you to find the equation of a straight line that passes through two points
Let x = the number of days
and y = the cost
Then the coordinates of the two points are (2,225) and (5,480).
(i) Calculate the slope of the line
[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\& = & \dfrac{480 - 225}{5 - 2}\\\\& = & \dfrac{255}{3}\\\\& = & 85\\\end{array}[/tex]
In other words, the daily rental is $85/day.
(ii) Calculate the y-intercept
[tex]\begin{array}{rcl}y & = & mx + b\\480 & = & 85 \times 5 + b\\480 & = & 425 + b\\b & = & 55\\\end{array}[/tex]
(iii) Write the equation for the line
y = 85x + 55
That is, the cost is $55 plus $85/day
Part B. Equation in function notation
Replace y with ƒ(x)
ƒ(x) = 85x + 55
Part C. Graphing
Let's say you want to plot a graph of the rental cost for up to ten days.
(i) Calculate two points on the graph.
When x = 0, y = 85; when x = 10, y = 905.
(ii) Scale your axes
A good number of intervals is about ten.
Your x-axis should have tick marks at 1-day intervals.
Your largest y-value is 905. Ten intervals would make about $90/interval. However, you should round that up to $100/interval for easy interpolation.
Your y-axis will run from 0 to $1000 in $100 intervals.
Plot your two points and draw a straight line through them.
(iii) Axis labels
x represents the number of days, so the label on the x-axis could be "No. of days."
y represents the cost of renting the boat, so the label on the y-axis could be "Rental cost."
Your graph should resemble the one below.
a survey asked two age groups which summer sport they most preferred. the results are shown in the table below. which sport was most preferred by people by ages 20-29 and what is the relative frequency within this age group?
Answer: Hiking was most prefered between ages 20-29
Answer:
Step-by-step explanation:
Given that a survey asked two age groups which summer sport they most preferred. the results are shown in the table below.
We have to find which sport was most preferred by people by ages 20-29 and what is the relative frequency within this age group
From the table we find that age group 20-29 prefers s
ski 15 [tex]\frac{15}{268}[/tex]
Swim 88 [tex]\frac{88}{268}[/tex]
Kayak 42 [tex]\frac{42}{268}[/tex]
Hike 123 [tex]\frac{123}{268}[/tex]
Total 268 1
We find that hike liking are more in this age group
Relative frequency calculated as frequency/268 is shown above.
Answer one of them!
1.Write a function that is shifted down 2 units and then reflected over the x-axis. Parent function is y = -5x - 8
2.Write a function that is reflected over the x-axis. Parent function is y = 5x - 8
3.Let g(x) be a vertical shift of f(x)= -x up 3 units followed by a vertical stretch by a factor of 4. Write the rule for g(x) .
4.Which transformation from the graph of a function f(x) describes the graph of 1/3 f(x)?
5.Write a function that is reflected over the x-axis. Parent function is y = -5x - 8
6. Let g(x) be a vertical shift of f(x)= -x up 4 units followed by a vertical stretch by a factor of 3. Write the rule for g(x).
Answer:
1. y=-5x+10
Step-by-step explanation:
if it reflect over the x it changes the y if it reflects over y it changes the x
The function y = f(x), when shifted down by 2 units and then reflected over the x-axis will become g(x) = 5x + 10.
What is reflection of line? What is the general equation of a straight line? What is triangle? What are parallel lines?A reflection over line is a transformation in which each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the opposite side of the line The general equation of a straight line is : y = mx + cwhere : [m] → is slope of line and [c] → is the y - intercept
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically : ∠x + ∠y + ∠z = 180°. There are different types of triangles such as : equilateral triangle , scalene triangle , isosceles triangle etc.Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions. These lines have same slope.We have the some sub - questions given in question.
We will solve part [1].
We have -
y = - 5x - 8
Shifting down by 2 units, we get -
y = - 5x - 8 - 2
y = - 5x - 10
Reflection over the [x] axis, would be -
g(x) = - y
g(x) = - (- 5x - 10)
g(x) = 5x + 10
Therefore, the function y = f(x), when shifted down by 2 units and then reflected over the x-axis will become g(x) = 5x + 10.
To solve more questions on 2 -D figures, visit the link below-
brainly.com/question/25950519
#SPJ2
The area of the base of a cylinder is found by dividing the volume of the cylinder by its height. If the volume of the cylinder is represented by 5x2 + 15x + 2 and the height is 5x, which expression represents the area of the base?
Answer:
Area = x + 3 + [tex]\frac{2}{5x}[/tex]
Step-by-step explanation:
Volume = 5x² + 15x + 2
Height = 5x
Area = Volume ÷ Height
Area = 5x²/5x + 15x/5x + 2/5x
Area = x + 3 + 2/5x
Answer:
x+3+2/5x
Step-by-step explanation:
Evaluate (–1)8 + (–1)7 + –16 + –14 – (–1)2.
A. –23
B. –4
C. 5
D. –3
Answer:
Step-by-step explanation:
(–1)8 + (–1)7 + –16 + –14 – (–1)2 = -8 -7 -16 -14 +2 = -45+2 = - 43
7. Which of the following relations is a function?
A.{(2, 3), (-2, 3), (3, 2), (-3,-2)}
B.{(8,-4), (-4, 8), (-4, -8), (-8,4)}
C.{(9, -1), (-1, 9), (9, 2), (2, -1)}
D.{(5, -7), (4, 6), (-3, 8), (5,9)}
A function means that each x can only have one y-value
B, C, and D are NOT functions because they have x-values that have multiple y-values.
For example
B. has two values for -4:
(-4, 8) and (-4, -8)
C. has two values for 9:
(9, -1) and (9, 2)
D. has two values for 5:
(5, -7) and (5, 9)
This makes A. the only function
Hope this helped!
~Just a girl in love with Shawn Mendes
Mercedes can download new songs for $1.39 each. Write an equation to show how many songs she can download for $15.00.
15x = 1.39
15 + x = 1.39
1.39x = 15
1.39 + x = 15
Answer:
1.39x=15
Step-by-step explanation:
each song is worth 1.39 dollers
If there are x songs, the total value would be 1.39x
1.39x=15
Answer:
Mercedes can download new songs for $1.39 each. Write an equation to show how many songs she can download for $15.00.
15x = 1.39
15 + x = 1.39
1.39x = 15
1.39 + x = 15
Step-by-step explanation:
The equation is the following:
1.39x = 15
15 $ is what you have to download the songs, and each unit is 1.39 $, by clearing the X of the equation, it is 15 / 1.39, and the result is the number of songs that Mercedes can download.