Which choice is equivalent to the quotient shown here when x ≥ 0?
√27 x + √48
O A. 3√x
OB.
V1 14
о с. 18x-32
O D. 3√x
8
Upon solving the root, the answer for given expression is option D: 3√x / 3.
What does "root" actually mean?In this case, the radical symbol for the number's root is "√". By multiplying the positive integer by itself, the square of the number is represented. By taking the square root of the square of a positive number, the original number can be found. For instance, 32 also equals 9, as does the square of 3 and the square root of 9.
How should the provided expression be calculated?This is the given expression:√27x + √48.
We will first simplify the square roots before simplifying the statement. √27 = 3 and √48 = 6.
Thus, the formula becomes 3√x + 6.
None of the suggested alternatives are equivalent to this statement. However, we can rephrase the expression in a way that is comparable to options A and D.
Let's multiply the expression's two sides by three.
The formula is now:√x + 2
Option D is represented by the formula 3√x/3 = √x + 2.
The solution is therefore option D: 3√x/3.
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You roll a six-sided die.
Event A: Roll an odd number.
Event B: Roll a number less than 5.
Find P(A or B). Express you answer as a fraction in simplest form.
P(A or B) =
Formula: P(AUB)=P(A)+P(B)-P(A n B)
We roll six-sided die.
Then sample space ={1,2,3,4,5,6}
And
Event A: Roll an odd number.
Odd numbers are {1,3,5}
Event B: Roll a number less than 5
Number less than 5 are {1,2,3,4}
So, Probability P(A)=
Probability P(B)=
Now, the odd number which is less than 5 are {1,3}
So, P(A n B)=
Since P(AUB)=P(A)+P(B)-P(A n B)
Therefore, P(A or B) = 1/6
Write an equation in point-slope form of the line that passes through (-3, -2) and (2, -1).
Your goal is to exercise for 15 hours
this month. You exercise for 3 1/2 hours
the first week and 3 3/4 hours the next week. How many more hours do you
need to exercise to reach your goal?
Answer: You need to exercise for 7 3/4 more hours
You need to do more exercise for [tex]7\frac{3}{4}[/tex] hours.
What are words problems?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given that, Your goal is to exercise for 15 hours this month. You exercise for [tex]3\frac{1}{2}[/tex] hours the first week and [tex]3\frac{3}{4}[/tex] hours the next week.
To find how much exercise is left, we will add both the hours and subtract it from 15 hours,
Therefore,
Exercise done = [tex]3\frac{1}{2} + 3\frac{3}{4}[/tex]
= 7/2 + 15/4
= (14 + 15) / 4
= 29/4
Exercise left = 15 - 29/4
= 31/4
= [tex]7\frac{3}{4}[/tex]
Hence, you need to do more exercise for [tex]7\frac{3}{4}[/tex] hours.
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1/8 of a clockwise rotation is how many degrees?
Answer: 45 degrees
Step-by-step explanation:
1 clockwise rotation = 360 degrees
1/8 a clockwise rotation = 360/8 = 45 degrees
Will give brainliest!
Answer:
1. x = 10.46
2. y = 5.2
Step-by-step explanation:
1.
[tex]cos17^{0} =\frac{10}{x}[/tex]
[tex]x=\frac{10}{cos17^{0} }[/tex]
[tex]x=10.46[/tex]
2.
Angle F = 180 - 42 - 48 = 90° (is a right triangle)
[tex]sin48^{0} =\frac{y}{7}[/tex]
[tex]y=7sin48^{0}[/tex]
[tex]y=5.2[/tex]
Hope this helps
What is the area of the shaded region?
Answer:
30 x^2
Step-by-step explanation:
(5x)(7x)-5x^2=30x^2
Simplify the following:
5×7 x x - 5 x^2
5 x×7 x = 5 x^2×7:
5×7 x^2 - 5 x^2
5×7 = 35:
35 x^2 - 5 x^2
35 x^2 - 5 x^2 = 30 x^2:
Answer: 30 x^2
Evaluate the expression below when x = 8 and y = 6.
The value of expression for x = 8 and y = 6 is,
⇒ 25
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (x² + y²) / 4
Here, We have;
⇒ x = 8 and y = 6
Substitute the value of x and y in above expression, we get;
⇒ (x² + y²) / 4
⇒ (8² + 6²) / 4
⇒ (64 + 36) / 4
⇒ (100) / 4
⇒ 25
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Determine what system, graph, colution and the slope and y intercept
4x = y - 6
4y = 3x -5
Answer:
System: A system of two equations that can be written in the form of y = mx + b where m is the slope and b is the y-intercept.
Graph: The graph of these two equations would be two straight lines in a coordinate plane.
Solution: The solution of the system would be the point where the two lines intersect on the coordinate plane, which represents the values of x and y that satisfy both equations.
Slope and y-intercept of 4x = y - 6:
Slope: 4 (m)
y-intercept: -6 (b)
Slope and y-intercept of 4y = 3x -5:
Slope: 3/4 (m)
y-intercept: -5/4 (b)
Note that the slope is the coefficient of x in the equation, and the y-intercept is the constant term in the equation. The solution can be found by equating the two equations and solving for x and y.
Find the discriminant of each quadratic equation
7k² + k + 7 = 0
a. Discriminant=
b. State the number of solutions(how many times the graph hits the x-axis):
(For example type: 1, 2, 0)
The discriminant of the given equation is -195 and the number of real solutions is 0.
What are Quadratic Equations?Quadratic expressions are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
(a) Discriminant of a quadratic equation of the form ax² + b x + c = 0 is b² - 4ac.
Given quadratic equation is 7k² + k + 7 = 0.
Discriminant = 1² - (4 × 7 × 7) = 1 - 196 = -195
(b) Discriminant is negative.
So there are no real solutions for the given quadratic equation.
There are two complex solutions.
Hence the value of the discriminant is negative and there are no solutions.
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Need Explanation on how to solve:
Please help
The denominator for the final answer for fraction in question 2 is 75 and the numerator for the final answer for the fraction in question 3 is 25.
How to evaluate for the denominator and numerator of the fractionsWe shall simplify the fractions to get the final answer for the denominators and numerators as follows:
5/9 + 1/3 = (15 + 1)/9 {simplifying to a single denominator}
5/9 + 1/3 = 16/9
(5/9 + 1/3) ÷ 25/3x = 16/9 × 3x/25 {changing division to multiplication}
(5/9 + 1/3) ÷ 25/3x = 16 × x/75
(5/9 + 1/3) ÷ 25/3x = 16x/75 {denominator 75}
4/5 - 16/(x + 2) = [4(x + 2) - 16(5)]/5(x + 2) {simplifying to a single denominator}
4/5 - 16/(x + 2) = (4x + 8 - 80)/5(x + 2)
4/5 - 16/(x + 2) = (4x -72)/5(x + 2)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 20/(x + 2) ÷ (4x -72)/5(x + 2)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 20/(x + 2) × 5(x + 2)/(4x -72) {changing division to multiplication}
(x + 2) will cancel out and 4 is factored out from (4x -72)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 20 × 5/4(x -16)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 5 × 5/(x - 16)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 25/(x - 16) {numerator 25}
Therefore, the first fraction have 75 as its denominator and the second fraction have 25 as its numerator.
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(Look at picture) ty btw :)!!!!! <3
Answer:
the answer is in the picture
Iris has 120 songs on her playlist. Each week, she downloads 4 new songs. How do I write an expression to show the total number of songs on Iris's playlist after w weeks
The expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that Iris has 120 songs on her playlist. Each week, she downloads 4 new songs.
We can write the expression to show the total number of songs on Iris's playlist after {w} weeks as -
y = 120 + 4w
Therefore, the expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.
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find the perimeter of abcd
The length of a form represents its perimeter. The provided parallelogram's perimeter will therefore be 38 units.
How do you find the perimeter?Quadrilateral's perimeter.The measurement of a shape's perimeter is its length.It takes adding the lengths of all four sides to determine a rectangle's or square's perimeter.
Knowing that the quadrilateral's perimeter equals the sum of its sides (AB + BC + CD + DA), we can write it as ABCD.
The quadrilateral's perimeter is equal to the sum of its four side lengths.
From the accompanying photo,
The supplied parallelogram's perimeter is equal to
AB + BC + CD + DA.= 9 + 10 + 9 + 10
= 38 units
ABCD's circumference is 38 units.
The provided parallelogram's perimeter will therefore be 38 units.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer: 36
Step-by-step explanation: The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
The standard form for finding the equation of a circle is expressed as;
(x-a)^2 + (y-b)^2 = b=r^2
where;
(a, b) is the center of the circle
r is the radius of the circle
Given the following
diameter = 12 units
radius = 12/2 = 6 units
If the centre lies on the y-axis, the center will be at (0, 3)
Substituting into the formula, we will have (x-0)^2 + (y-3)^2 = 6^2 equivalent to x²+ (y-3)² = 36
341.12 to 1 decimal place i did it but I'm not sure 50 points pls full explanation heres pic
The approximation of 341.12 to 1 decimal place is 341.1.
How to Approximate a Number to 1 Decimal Place?To approximate 341.12 to 1 decimal place, you can follow these steps:
Multiply the number by 10 to move the decimal point one place to the right.Round the resulting number to the nearest whole number.Divide the rounded number by 10 to move the decimal point one place to the left.For example, if you want to approximate the number 341.12 to 1 decimal place, follow these steps:
341.12 * 10 = 3411.2
Round 3411.2 to the nearest whole number, which is 3411.
3411 / 10 = 341.1
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Answer:
341.1
Step-by-step explanation:
When you round to the first decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down. If the hundredths digit is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.
341.12
The number in the hundredths place is 2, which means that we would round down the first decimal place by keeping it the same:
341.1
Luke invested $86,000 in an account paying an interest rate of 5 ⅛ % compounded
continuously. Alexander invested $86,000 in an account paying an interest rate of 5 ⅝ % compounded annually. After 8 years, how much more money would Alexander
have in his account than Luke, to the nearest dollar?
Therefore , the solution of the given problem of interest comes out to be
$4,962.93 money more made by Alexander.
What exactly is meant by interest?Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.
Here,
Given :
Luke :
Principal amount = $86,000
and rate of interest = 5 ⅛ % or 41/8% or 5.125%
Alexander :
Principal amount = $86,000
rate of interest = 5 ⅝ % or 45/8% or 5.625%
To find the amount of money after time =8 years.
So ,
using compound formula :
=> A = P[tex](1 + r/n)^{nt}[/tex]
For luke = P=86000[tex](1 + 41/8*1)^{1*8}[/tex] = $42,276.33
For Alexander = P=86000[tex](1 + 45/8*1)^{1*8}[/tex] = $47,239.26
The amount made by Alexander by luke
=> 47,239.26 - 42,276.33 = 4,962.93
Therefore , the solution of the given problem of interest comes out to be
$4,962.93 money more made by Alexander.
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please help me now i need help
The equation that describes the diagram could be; 5 + 9 = 14
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Since Adding a negative number is the same as subtracting a positive number just as subtracting a negative number is the same as adding a positive.
The equation becomes as
5 + 9 = 14
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Amal, Brian, and Cami help clean Ms. Rivers’s house is she gives and $42.00 to share equally. Cami decides to save half her money and spend the other half. How much does Cami have to spend?
Answer:
Each of them will get 42/3 = $14.00
Cami saves half of her money which is 14/2 = $7.00
Cami has 14 - 7 = $7.00 to spend.
It takes Alexa 40 minutes to get to school (14.4 km). What is her speed in km/min?
Answer:
0.36km/
Step-by-step explanation:
speed= distance/time
14.4km/40min
= 0.36km/min
Please help me i do not know
The statements that are true for line 'n' are
a) The slope of line n is equal to BC/AC
d) The slope of line n is equal to DE/AE.
The slope of a line:A line's slope is defined as the ratio of the change in the y-coordinates to the change in the x-coordinate. And the formula for slope is given by
Slope (m) = (y₂ - y₁)/(x₂ - x₁)Here we have
A line 'n' passing diagonally through a coordinate plane
From the given figure,
The points that the line passes are (4, 3) and (-2, 0)
The slope of the line, 'm' = [-0 -3]/[-2 - 4] = 3/6 = 1/2
From the given figure,
BC = 1 unit and AC = 2 units
DE = 4 units and AE = 8 units
a) The slope of line n is equal to BC/AC = 1/2
d) The slope of line n is equal to DE/AE = 4/8 = 1/2
Therefore,
The statements that are true for line 'n' are
a) The slope of line n is equal to BC/AC
d) The slope of line n is equal to DE/AE.
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Complete Question:
Use the graph below to answer the question. Which statements about line n are true? n, Select all that apply.
Answer choices:
a) The slope of line n is equal to BC/AC.
b) The slope of line n is equal to AC/BC.
C) The slope of line n is equal to BC/DE.
d) The slope of line n is equal to DE/AE.
e) The slope of line n is equal to AE/DE.
f) The slope of line n is equal to AC/AE.
rewrite 24/7 as a mixed number
A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To solve this, we would first need to see how many times 7 can fit into 24.
7 + 7 + 7 = 21.
We can see that is fits 3 times into 24, but what about the remaining 3? We can take that 3 and make it into a fraction of 7, making it [tex]\frac{3}{7}[/tex].
Now, putting the 3 and the 3/7 together, we get [tex]3\frac{3}{7}[/tex].
The angles t the right are complementary angles determine the measures of 1 and 2
Look at picture <3 ty btw
Answer:
5, -2
Step-by-step explanation:
NEED HELP ASAP PLS AND THX Picture is attached
We do not obtain a triangle, but rather a straight line with a single side. Contrary to the triangle, which is a closed figure with two sides, the straight line is not closed.
Do Collinear points have to be straight?Two points A and B are here collinear. Points that are parallel to or within a single line are referred to as collinear points. In Euclidean geometry, two or more points are said to be collinear if they are situated on a line that is either close to or far from another.
As opposed to non-collinear points, which do not lie on a single straight line, collinear points are two or more points that are located along a straight line. Collinear points are three or more points on the same line. A, B, and C are on the line m, for instance. The two are parallel. Two lines will coincide if their slopes are the same and they cross at the same location.
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The cost of 3 pairs of sneakers at Store A is $243. The graph below compares the cost of sneakers at Store A with the cost at Store B.
Answer:
Step-by-step explanation: Hello! I can help you if you include the graph!
5.1 mathematics for business
The inverse function would be x = (y + 3) / -3 and the domain of the inverse function would be (-infinity, -1/3].
What is the inverse function?
An inverse function is a function that "undoes" another function. The inverse function, denoted as f^-1, reverses the direction of the original function, so that if the original function maps x to y, the inverse function maps y to x.
To find the inverse function of a given function, you can switch the x and y variables and solve for y. The inverse function will also have a different domain and range than the original function.
For example, for the function y = 1 - 3x, where x belongs to the interval [-2, 2],
First, we need to switch the x and y variables to get x = 1 - 3y.
Now we need to solve for y,
y = (x + 3) / -3
So the inverse function of y = 1 - 3x, where x belongs to the interval [-2, 2], is
x = (y + 3) / -3
The domain of the original function is [-2, 2] and the range is (-infinity, -1/3], whereas the domain of the inverse function is (-infinity, -1/3] and the range is [-2, 2].
Hence, The inverse function would be x = (y + 3) / -3 and the domain of the inverse function would be (-infinity, -1/3].
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Determine if the triangles in each pair are similar. If so, write a similarity statement and state whether AAA, SAS, Or SSS
the triangle are congruent by AAA
What is congruent by AAA?
It can also be stated as the AAA (angle-angle-angle) similarity theorem, which states that two triangles have identical corresponding angles if and only if their corresponding sides are proportionate.given, ABC and XYZ, are congruent according to the AAA rule by looking at the image provided below. According to the AAA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.
In the given two triangles,
The ratio of the sides are similar
And hence the angles are similar.
Hence the triangle are congruent by AAA
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for her average speed in km/h.
11 A train travels from Newcastle to Edinburgh at an average speed of 68 mph, correct
to the nearest whole number. The journey is 80 miles, to the nearest 10 miles.
Bryn says that the journey will definitely take less than an hour and a quarter.
a Show working to explain why Bryn is wrong.
b Calculate the shortest possible time it could take to complete the journey to the
nearest minute.
Bryn is wrong as he says that the journey will definitely take less than an hour and a quarter
time = 1.17 hours = 1 hour 42 minutes
What is speed?
The definition of speed is. a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.
Average speed= distance / time
time= distance /Average speed = 80/68 hours
time = 1.17 hours = 1 hour 42 minutes
So, Bryn is wrong as he says that the journey will definitely take less than an hour and a quarter.
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Please show me how to work out these math problems. Only the ones with stairs next them please. Thank you. Don’t understand how to work it out. Try to give me a good and simple step by of how to do this. Thanks .
Answer: Formulas for Solving Composite Figures
Step-by-step explanation:
The formula for finding the area of a rectangle is length x width.
The formula for finding the area of a square is side x side.
The formula for finding the area of a triangle is base x height/2.
The formula for finding the area of a circle is π x radius x radius
Hope this helps! :)