How can you tell whether a rational expression is in simplest form? Include an example with your explanation.
Rational numbers are numbers that are written as a ratio of two integers.
Let a and b be integers, hence a rational expression can be expressed as a/bIn order to tell whether a rational expression is in its simplest form, we need to ensure no integer can go in both the numerator and the denominator.
For instance, given the rational number 10/15, the simplest form of the rational number will be expressed as (5*2)/(5*3) = 2/3
learn more here: https://brainly.com/question/18736992
An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base of diameter 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. The volume of the original chamber is cubic inches. This is cubic inches less than the volume of the new chamber. NextReset
Answer:
added pictures of all the questions on this test
Step-by-step explanation:
Angle C is an inscribed angle of circle P. Angle C measures (5x-7) degrees and arc AB measures (2x) degrees. Find x.
Helpppppppppp me!!!!!!!!!
A) w/9=6
w=9*6
w=54
B) 5q=15
q=15/5
q=3
C)2s-3s=20
-1s=20
s=20/-1 = -20
s=-20
D)4-a=-12
a= 4+12 = 16
a=16
Explain how you would use trig ratios to find the height of the tree if you know you are standing 30 feet from the base of the tree when you measure the 37-degree angle.
From use of trigonometric ratios, it is seen that the height of the tree is; 22.61 feet
How to work with trigonometric ratios?We are told that you are standing 30 ft from the base of a tree.
Now, the distance from where you are standing to the top of the tree will be the hypotenuse of the triangle formed by you and the tree.
Thus, if the height of the tree is h and the angle the hypotenuse makes with the 30 ft base is 37°, then we have;
h/30 = tan 37
h = = 30 * tan 37
h = 22.61 ft
Read more about Trigonometric Ratios at; https://brainly.com/question/13276558
#SPJ2
List all your possibility of outcomes (there are 36 outcomes) if you roll a dice containing numbers 1-6 two times. Determine the probability of each outcome.
Sandy can assemble a particular type of light fixture in 3/8 hour. it takes her 2/3 hour to hang the fixture and another 1/6 hour to wire the fixture once it is hung. how many fixtures could sandy install in 29 hours?
Sandy can install a maximum of 24 fixtures in 29 hours.
Explanation:To calculate the number of fixtures Sandy can install in 29 hours, we need to determine the amount of time it takes for Sandy to complete one installation process (excluding assembly time).
Sandy takes 2/3 hour to hang the fixture and another 1/6 hour to wire it, totaling
2/3 + 1/6 = 7/6 hour.
Therefore, Sandy takes 7/6 hour per fixture.
Next, we can calculate the number of fixtures by dividing the total time available (29 hours) by the time it takes for one installation process.
Number of fixtures = Total time available / Time per fixture
Number of fixtures = 29 / (7/6) = 29 * (6/7) = 174/7 = 24.86
Since we can't have a fraction of a fixture, Sandy can install a maximum of 24 fixtures in 29 hours.
Learn more about installing fixtures here:https://brainly.com/question/24337233
#SPJ2
What is the inverse of f(x)=70x^3/4 ?
The inverse of the function [tex]f(x) = 70x^{(3/4)[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)[/tex].
Explanation:The inverse of the function [tex]f(x) = 70x^{(3/4)}[/tex] can be found by interchanging the roles of x and y and solving for y. The goal is to isolate y on one side of the equation.
Step 1: Replace f(x) with y: [tex]y = 70x^{(3/4)}[/tex]
Step 2: Swap x and y: [tex]x = 70y^{(3/4)}[/tex]
Step 3: Solve for y: Divide both sides of the equation by 70 and raise both sides to the power of 4/3 to undo the exponent: [tex]y = (x/70)^{(4/3)}[/tex]
Therefore, the inverse of [tex]f(x) = 70x^{(3/4)}[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)}[/tex].
One side of triangle is half the longest side. the third side is 7 feet less than the longest side. the perimeter is 43. find all three sides.
At a certain university the student to teacher ratio is 16:1. If there are 2,000 students enrolled, how many teachers must be employed to maintain this ratio?
A. 28,000 B. 200 C. 215 D. 125
Mark for review (Will be highlighted on the review page)
Answer:
D. 125
Step-by-step explanation:
Ratio between students and teacher = 16:1 , 16/1 =2000 /x , x = 2000/16 = 125 teachers
The number of teachers in the school will be 125. The correct option is D.
What are ratios and proportions?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3.
Given that at a certain university the student-to-teacher ratio is 16:1. If there are 2,000 students enrolled.
The number of teachers will be calculated as,
16 / 1 = 2000 / t
t = 2000 / 16
t = 125 teachers
Therefore, the count of teachers in the school is 125.
To know more about ratios and proportions follow
https://brainly.com/question/2914376
#SPJ2
Directions: Describe the transformation. (x,y) -> (5x,5y)
The transformation (x, y) -> (5x, 5y) is a scaling transformation that dilates a point by a factor of 5 in both the x and y directions, making the entire figure five times larger while preserving its shape.
Explanation:The transformation described by (x, y) -> (5x, 5y) is a scaling transformation or dilation in both the x and y directions by a factor of 5. What this means is that any point on the plane, when subjected to this transformation, will move five times further away from the origin along both axes. For example, if you begin with the point (1, 1), applying this transformation will result in the point (5, 5). This dilation affects all points equally, meaning that the relative distances between points are preserved, but the entire figure is made larger by a factor of 5. Therefore, if you have a figure with dimensions of length and width, after the transformation, both dimensions will be increased by five times their original measure.
Final answer:
The transformation (x, y) -> (5x, 5y) represents a dilation, enlarging a figure by a factor of 5 along both the x-axis and y-axis, which alters size but not shape.
Explanation:
The transformation described by the rule (x, y) -> (5x, 5y) is a geometric transformation known as a dilation or scaling. This type of transformation alters the size of a figure without changing its shape. Specifically, the coordinates of each point in the figure are multiplied by 5, which means that the figure is enlarged by a factor of 5 in both the x-axis (east-west direction) and the y-axis (north-south direction). If, for example, we apply this transformation to a point (1, 2), the resulting coordinates will be (5, 10), and similarly, applying it to (3, 7) would yield (15, 35). This illustrates the dependence of y on x as each x-coordinate and y-coordinate are scaled by the same factor, maintaining the shape but increasing the size.
1. Given f(x)=3x+8f(x)=3x+8 and g(x)=6x+6g(x)=6x+6 then what is (f+g)(−1))(f+g)(−1)) ?
2. Given f(x)=6x+4f(x)=6x+4 and g(x)=3x+7g(x)=3x+7 then what is (f−g)(1)) ?
In which of the following quadrilaterals are consecutive angles always congruent? Check all that apply.
Answer:
Rectangle and Square.
Step-by-step explanation:
To know if the angles of a quadrilateral is congruent you must overlap these angles one over the other, if all elements of the angles coincide, the angles are congruent; if the elements do not match, the angles are not congruent. In quadrilateral rectangle and square consecutive angles are always congruent.
In other words, two or more angles are said congruent if and only if they have the same measurement.
PLEASE HELP ME AND TRY TO ANSWER THIS PLS PLS PLS AND IF YOU CAN DO THIS ONE AND HELP ME CAN YOU PLEASE GO BACK TO MY LAST PROBLEM AND TRY TO SOLVE IT IF IT HASNT ALREADY BEEN SOLVED I AM RUSHING SO FAST RIGHT NOW PLEASE TRY TO HELP AND ANSWER IT ASAP IT WOULD BE A HUGE HELP!
1. What is 3/8x < -6 or 5x>2 solved and graphed?
2. What is 2<10 -4d< 6 solved and graphed?
I appreciate your help!
Two trucks leave a warehouse at the same time. one travels due north at an average speed of 4747 miles per hour, and the other travels due south at an average speed of 5050 miles per hour. after how many hours will the two trucks be 388388 miles apart?
AB and BC are tangent to circle D. Find x if AB = 2x + 9 and BC = 3x + 6. Find x.
Answer:
the value of X comes out to be equal to 3
Step-by-step explanation:
since AB and BC are tangent to the circle D
then the length of the tangent will be same
AB will be equal to BC
where,
AB = 2 x + 9
and
BC = 3 x + 6
2 x + 9 = 3 x + 6
3 x - 2 x = 9 - 6
x = 3
hence, the value of X comes out to be equal to 3
the sum of 3 numbers is 26. the second number is twice the first and the third number is 6 more than the second. find the number
Answer:
the numbers are 4, 8, 14
Step-by-step explanation:
If we subtract 6 from the third number and from the total, we find that we now have 5 times the first number for a total of 20.
The first number is 4.
The second number is 2×4 = 8.
The third number is 8 + 6 = 14.
Find the take home percent of the gross pay: net pay $298.76, gross pay $402.38. round to the nearest percent.
Factor the expression.
4r^2 – 64
1)(4r + 5)(r – 16)
2)4(r – 4)(r – 4)
3)(4r – 5)(r + 16)
4)4(r + 4)(r – 4)
What is the slope of the line below
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. x2 + 4x + 3 = 0
On a recent trip, I took a cab from the airport to my hotel. These were the cab fares posted on the door of the cab: $2.20 for the first 1⁄2 mile and 30 cents for each additional 1/5 mile. How far did I travel if my fare was $17.20? What would my fare be if I were to travel 16.8 miles? What would my fare be if I were to travel n miles? What kind of relationship is this? Justify your response and provide a visual representation (a graph) of the relationship.
What is another name for angle 2?
Angle 2 could refer to different things, such as an angular velocity, a direction angle, or a contact angle, depending on its context within a mathematical or physical scenario.
Explanation:In mathematical terms, angle 2 refers to a particular position or orientation, typically specified in degrees. For instance, if points 1 and 2 rotate through the same angle (AO), angle 2 might move through a greater arc length because it is farther from the center of rotation. This concept is related to the mathematical definition of angular velocity, defined as radians per unit time.
Alternatively, angle 2 could also refer to the direction angle, which is the angle measured counterclockwise from the positive direction on the x-axis to a vector. This term is often used when calculating vector components. In this context, a positive angle indicates a counterclockwise rotation, whereas a negative angle implies a clockwise rotation.
Finally, angle 2 might specify the contact angle, which is the angle between the tangent to the liquid surface and the surface itself. To figure out the precise name for angle 2 in your particular context, I would need further information about the specific scenario or diagram you're referring to.
Learn more about Angle Interpretation here:https://brainly.com/question/33518405
#SPJ2
in how many ways can a judge award first, second, and third place in a contest with 10 entries
720. just multiply 10 9 and 8 because first, second, and third, that is means three and that's how many numbers you multiply from 10,so it equals 720.
hope this helps
cheers!
Statistics??? Construct a 95% confidence interval for the population mean. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677.
HELP might fail class
Harry Hoodeen made $24,567.00 net pay last year. His monthly expenses averaged $1,980.00. How much was left over for savings for the year?
In triangle abc, the measure of angle b is 29 degrees° more than three times the measure of angle
a. the measure of angle c is 61 degrees° more than the measure of angle
a. find the measure of each angle.
Answer:
∠a = x
∠b = 3x + 29
∠c = x + 61
x + 3x + 29 + x + 61 = 180
5x = 180 - 29 - 61
5x = 90
x = 90/5
x = 18° ← ∠a
∠b = 3x + 29 = 3*18 + 29 = 83°
∠c = x + 61 = 18 + 61 = 79°
Step-by-step explanation:
How do I do this someone please explain I need help