The radical expression completely:
Square root of [tex]48x^2y^5z[/tex] is 4[tex]xy^2[/tex] × sqrt(3y)
Now, According to the question:
Factor 48 into its prime factors
48 = 24 × 3
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
16 = [tex]2^4[/tex]
Factors which will remain inside the root are :
3 = 3
To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
4 = [tex]2^2[/tex]
At the end of this step the partly simplified SQRT looks like this:
4 × sqrt[tex](3x^2y^5)[/tex]z
Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt[tex](x^8)=x^4[/tex]
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or < (-2) , examples:
(4.1)[tex]sqrt(x^5)=x^2sqrt(x)[/tex]
(4.2) sqrt(x-7)=x-3sqrt(x-1)
Applying these rules to our case we find out that
SQRT[tex](x^2y^5) = xy^2[/tex]SQRT(y)
Simplified root:
4[tex]xy^2[/tex] × sqrt(3y)
Hence, the radical expression completely:
Square root of [tex]48x^2y^5z[/tex] is 4[tex]xy^2[/tex] × sqrt(3y)
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geometry - i need help with this problem and it’s pretty easy. i’m just curious on how i would round the square root of 95 within the problem
Step-by-step explanation:
I am not sure what you mean. you don't round the intermediate numbers and results. only the final result.
you keep the irrational terms (like square root) like variable terms as they are and apply operations on them without actually expressing them as numbers.
only at the very last moment (when the final result is calculated) would you express them as actual number. and then you round the final result.
so, this is solved via Pythagoras :
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
in our case we have
BP² = BN² + NP² = 7² + sqrt(95)² = 49 + 95 = 144
you see ?
no need ever to bring the actual result of sqrt(95) into the picture. just keep it at sqrt(95) and do with it, what you would do with any actual number.
BP² = 144
BP = sqrt(144) = 12
so, we never had to deal with the actual irrational number.
we know how it is created, so we keep using that term to represent it.
a line with slope 3 is 2 units away from the origin. find the area of the triangle formed by this line and the coordinate axes.
The triangle created by the coordinate axes and the line with slope 3 has a 6 square unit area.
Given that the height (distance of the line from the origin) is 2 units, the area of the triangle is equal to
= (1/2)×(hypotenuse)×(height),
=6.66 square units.
The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's slope.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
n = a/b = change in b/change in a
where "n" represents a line's slope.
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The triangle formed by the coordinate axes and the line with slope 3 has a surface area of 4.44 square units.
As per data, we have,
Given a height of 2 units (distance of the line from the origin), the area of the triangle is equal to = (1/2)(hypotenuse) (height)
The solution is the same whether the line passes by the origin on the right or the left.
The sloping line will be the hypotenuse of a triangle whose other two sides are x or y-axis segments terminating at the origin.
The triangle's angles are 71.56 degrees (arctan3), 90 degrees, and 18.44 degrees.
The value of the length of the side opposite the tiny angle will be = 2/sin18.44 = 6.32 units
The hypotenuse length is 6.32/cos18.44 = 6.66.
The area of the triangle is calculated as (1/2)*(hypotenuse)*(height) = 4.44 square units.
The formula for the change in the y-coordinate with respect to the change in x-coordinate is: n = a/b = change in b/change in a
where "n" represents a line's slope.
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Use substitution to solve the system
4x+3y = 2
x-2y = -5
X=
Y=
The solution for linear equations given will be x=-1 and y=2 using substitution method.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now
Given 4x+3y=2 -->1
x-2y=-5 --->2
Using substitution method, In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation.
From 2, x=2y-5
Put x=2y-5 in 1
4(2y-5)+3y=2
11y-20=2
y=22/11
y=2
Hence,
x=2*2-5
x= -1
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A dot plot shows the number of pizza sold at a local restaurant each day one week. One Columbia of dots on the plot is much taller than the others explain what that means in the context of the data and of percents
If one column of dots on the dot plot is much taller than the others, it means that on that particular day, the restaurant sold significantly more pizzas than on the other days of the week.
A dot plot is a simple graphical representation of data where each data point is represented by a dot or mark above a number line. In this context, the dot plot shows the number of pizzas sold at a local restaurant each day for one week. The height of the column of dots represents the number of pizzas sold on that particular day.
If one column of dots is much taller than the others, it means that on that particular day, the restaurant sold significantly more pizzas than on the other days of the week. This could be due to a variety of reasons such as a special promotion, a holiday, or just a generally busy day.
Understanding which days are the busiest for the restaurant can help the management make decisions such as staffing levels, inventory management, and marketing strategies. For example, if a particular day of the week is consistently the busiest, the restaurant may want to offer a special promotion or discount on that day to attract more customers.
In terms of percents, if for example, the restaurant sold 100 pizzas on the day with the tallest column of dots, and the next highest day sold 60 pizzas, the day with 100 pizzas would be 166.6% higher than the day with 60 pizzas. It indicates the significance of the difference between the two days in terms of sales.
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Pls help me on this homework question
The graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24 .
What is trend line?A linear relationship is depicted by a trend line. Y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept, is the equation for a linear relationship.
a graph line indicating the general path that a collection of points appears to take.
When plotting predictions, trendlines, also referred to as lines of best fit or regression lines, are frequently used to graphically represent trends in data series. Typically, a trendline is a line or curve that crosses or links two or more points in a series to indicate a trend.
From the graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24.
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find the value of X.
1. x ÷ 5/6 = 1 and 4/5
2. x ÷ 2 and 1/10 = 1 and 2/3
The value of X are 5/6,1/5
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.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.
Given;
x ÷ 5/6 = 1....1
x ÷ 2 = 1/10....2
Equation.1
(x/5)*6=1
6x/5=1
x=5/6
Equation.2
x/2=1/10
x=2/10
x=1/5
Therefore, the value of x in equations will be 5/6 and 1/5
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alex earns a $35,000 salary in the first year of his career. each year, he gets a 3% percent raise. which expression gives the total amount alex has earned in his first n years of his career?
After n years Alex will earn salary which can be expressed as $(1 + 0.03)^n * 35,000.
The total amount Alex has earned in his first year of his career is $35,000.
In the second year of his career, he gets a 3% raise, which is an increase of 3/100 * $35,000 = $1,050.
So his salary for the second year is $35,000 + $1,050 = $36,050.
In the third year of his career, he again gets a 3% raise, which is 3/100 * $36,050 = $1,081.50
So his salary for the third year is $36,050 + $1,081.50 = $37,131.50
We can see that for each year, his salary is increasing by a fixed percentage of the previous year's salary.
This pattern can be represented by the expression:
(1 + 0.03)^n * 35,000
Where n is the number of years since the start of his career. This expression gives the total amount Alex has earned in his first n years of his career.
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which of the functions in this command can help them determine how strongly related their variables are?
The cor() returns the correlation between two variables.
Correlation shows us how strong the relationship is between two variables.
Hence, option (c) is the correct choice.
Correlation quantifies the intensity of a link between two variables and is symmetrical, meaning that the correlation between A and B is the same as the correlation between B and A.
Correlation is a statistical term that describes the degree to which two variables are linearly connected (meaning they change together at a constant rate). It's a common way of explaining simple interactions without stating a cause and effect relationship.
In R, the cor() function is used to calculate the correlation coefficient between two vectors. Correlations may be generated using the cor() function, while covariances can be generated using the cov() function. The type of correlation is specified.
There are three options: Pearson, Spearman, and Kendall.
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The complete questions should be like:
A data analyst is using statistical measures to get a better understanding of their data. What function can they use to determine how strongly related are two of the variables?
A sd()
B mean()
C cor()
D bias()
what is the volume? please please PLEASE help T0T
The volume of the cuboid is 16 cubic yards.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
Given:
A cuboid with height 2 yards, length 2 yards and width 4 yards.
The volume of the cuboid,
= length x width x height
= 4 x 2 x 2
= 16 cubic yards.
Therefore, the volume is 16 cubic yards.
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Sandra measures the diameter of a hula hoop as 0. 7 m. Write and solve an equation to
determine the radius of the hula hoop.
An equation to determine the radius of the hula hoop is diameter/2 and the radius is 0.35.
The term called equation in math is known as a mathematical statement that is made up of two expressions connected by an equal sign.
Here we know that the Sandra measures the diameter of a hula hoop as 0. 7 m.
Here we need to write and solve an equation to determine the radius of the hula hoop.
As we all know that radius is defined as the distance from the center of the circle to any point on it's circumference.
And the term diameter is defined as a straight line passing through the center of a figure or body.
So, the diameter is calculated by using the formula,
=> d = 2r where r refers the radius.
Then the equation to calculate the radius is written as,
=> r = d/2
then the equivalent radius value is,
=> r = 0.7/2 = 0.35
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Triangle congruence proof
Given the information, the triangle congruence prove is explained below.
Properties of congruent triangles?If the corresponding sides or measure of angles of two or more triangles have common properties, then the triangles are said to be congruent. Such that on comparing their sides and internal angles, some have equal values.
With the given information in the question, the prove is explained below:
STATEMENTS REASONS
1. AB ≅ CD Given
2. <ABD ≅<CDB Given
3. AD ≅ BC Equal sides of a parallelogram
4. <ADB ≅ <CBD Alternate angle theorem
5. <A ≅ <C Opposite property of a parallelogram
Therefore, it can be deduced that;
ΔABD ≅ ΔCDB
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a shade allows light to pass through from a lamp, but reduces the intensity of the light. the intensity of the light is reduced by 15% if the fabric is 1mm thick. each additional millimetre of fabric reduces the intensity by another 15%
a) write an expression that gives percent P, of light which penetrates x mm of fabric. b) use the equation to determine the percentage of light that will pass through a cloth, that is 2.75mm thick
a) The exponential function that gives the percent P is: P = (0.85)^x.
b) The percentage of light that will pass through a cloth that is 2.75mm thick is given as follows: 63.96%.
How to define the exponential function?A decaying exponential function is defined as follows:
y = a(1 - r)^x.
In which the parameters are given as follows:
a is the initial value.r is the decay rate, as a decimal.The parameter values for this problem are given as follows:
a = 1, r = 0.15.
Hence the function is:
y = (0.85)^x.
The percentage passing through a cloth that is 2.75 mm thick is given as follows:
y = (0.85)^2.75
y = 0.6396.
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Adding and subtracting fractions with unlike denominators Find the sum.
1. 1/3+2/3 = 2. 1/2 + 1/3 = 3. 2/5+1/2
Find the difference.
1. 1/2-1/3 = 2. 4/5-2/3 = 3. 4/15-1/10 =
the sum is 1) 5/3, 2) 5/6 , 3) 7/10 and the difference is 1) 1/6 , 2)2/15, 3) 1/30. When adding or subtracting fractions with unlike denominators, the first step is to convert the fractions so that they have a common denominator.
1. 1/3+2/3 = 5/3
2. 1/2 + 1/3 = 5/6
3. 2/5+1/2 = 7/10
1. 1/2-1/3 = 1/6
2. 4/5-2/3 = 2/15
3. 4/15-1/10 = 1/30
When adding or subtracting fractions with unlike denominators, the first step is to convert the fractions so that they have a common denominator. To do this, you can use the lowest common denominator, which is the least common multiple of the denominators. For example, in the first problem, the least common multiple of 3 and 2 is 6, so you can convert the fractions to 2/6 and 4/6, or 1/3 and 2/3. Then, you can add or subtract the fractions as normal. For example, 1/3+2/3 would equal 3/3 or 1.
For subtracting fractions with unlike denominators, the same process is used. For example, in the second problem, the least common multiple of 5 and 3 is 15, so you can convert the fractions to 4/15 and 2/15. Then, you can subtract the fractions as normal. For example, 4/15-2/15 would equal 2/15.
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It takes 2 cups of water to cook 1 cup of rice.
How much rice can you cook with 0.5 cups of water?
How much water does it take to cook 6.5 cups of rice?
Answer:
0.25 cup of rice; 13 cup of water
Step-by-step explanation:
2 cup of water: 1 cup of rice = 2:1 ratio
Someone help please I don’t get it
The scale factors of the shapes are 1.25, 1.25. 5 and 2, respectively
How to determine the scale factorsTo do this, we divide the side length of the larger shape with the corresponding side of the small shape
using the above as a guide, we have the following scale factors calculations
figure 7 = 15/12 = 1.25
figure 8 = 25/20 = 1.25
figure 9 = 40/8 = 5
figure 10 = 10/5 = 2
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HELP ASAP PLS!!
PLSS
Answer:
Step-by-step explanation:
6. XZY
7. YX
Pls help me find the answer to this I could figure it out
Answer: There are 114 red marbles contained in the bag containing 120 marbles.
Step-by-step explanation:
To find the amount of red marbles in the bag:
From the question, we can presume that for every 19 marbles in a bag, there exist a single black marble. This is the same case for the total number of marbles (both red and black) in each set is 20 marbles
Set of marbles: 120/20
Red marbles:
19r = 19 x 6
19r = 114 red marbles.
I hope this helps!
It entered the wrong thing so i js took a picture ….. :)
I’m kinda slow can someone help
Answer:
60
Step-by-step explanation:
You're not slow.
So given was the formula for perimeter
12x + 1/2 - 4x - 8.5 + 2x + 8
They want you to find perimeter is x = 6, so this is a matter of plug and play. so everywhere you see an x, you'll replace it with the number 6
And we will start simplifying what we can
P = 12(6) + 1/2 - 4(6) - 8.5 + 2(6) + 8
P = 72 + 0.5 - 24 - 8.5 + 12 + 8
P = 72 - 24 - 8 + 12 + 8
P = 72 - 12
P = 60
how to go from slope intercept form to standard form
To go from slope intercept form of line to standard form Ax + By + C = 0, collect all terms on the left side of the equation and multiply by the denominator B.
We know that the standard form of equation of line is Ax + By + C = 0. And the slope intercept form of line is y = mx +b, where m is the slope of the line, and b is the y-intercept i.e., the value of y when x = 0.
Converting from slope intercept form to standard form:
⇒ y = mx + b
⇒ y - mx = (mx - mx) + b .........(subtract mx from each side)
⇒ y - mx = b
⇒ y - mx - b = b -b .........(subtract b from each side)
⇒ y - mx - b = 0
⇒ - mx + y - b = 0
Above equation is of the form Ax + By + C = 0
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Angela wants to learn how to rock climb. The Rocky Climbing gym has a special where 5 climbs cost $52.50.
Select the equation that represents the total cost, t, of c climbs. Assume the relationship is proportional.
Answer: t = 10.50c
Step-by-step explanation: The relationship between the number of climbs, c, and the total cost, t, is proportional. This means that the ratio of t to c is constant. One way to represent this relationship is through an equation of the form:
t = kc
where k is a constant of proportionality. In this case, we know that 5 climbs cost $52.50, so we can use this information to find the value of k:
52.50 = k(5)
k = 52.50/5 = 10.50
So the equation that represents the total cost, t, of c climbs is:
t = 10.50c
Where t is the total cost, c is the number of climbs and 10.50 is the constant of proportionality.
which graph shows different numbers of tickets that ellena can sell to raise more than 180$
Amanda explains to a classmate how to find the growth factor of an exponential function, given a table of values. She tells her classmate to choose a f ( x ) f(x) value from the table and divide it by the previous f ( x ) f(x) value.
Analyze Amanda's explanation.
If she is correct, choose one of the following ways to respond.
Create a function and explain how to use Amanda's method.
Create a function, in function notation, and explain how to tell what the growth factor is.
If she is incorrect, respond to the following statement.
Explain what Amanda did wrong and what should be done to correct her explanation
Amanda's explanation is not correct. The growth factor of an exponential function is the constant value that the function is multiplied by for each expansion in the information variable.
It is not determined by dividing one value in the table by the previous value.
To find the growth factor of an exponential function, one ought to take the proportion of any two consecutive f(x) values and distinguish the normal proportion. The growth factor is equivalent to this normal proportion.
For instance, assuming the function is [tex]f(x) = 2^x[/tex], and the table of values is:
x f(x)
0 1
1 2
2 4
3 8
The growth factor can be tracked down by taking the proportion of f(x) values for consecutive x:
f(1)/f(0) = 2/1 = 2
f(2)/f(1) = 4/2 = 2
f(3)/f(2) = 8/4 = 2
For this situation, the growth factor is 2, meaning that the function is multiplied by 2 for each increase in x.
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we have 20 cards including 10 a, 5 b and 5 c. we randomly take a card. if it is not a, what is the probability that it is b?
We randomly take a card, if it is not a, then the probability that it is b, is 1/4.
We have to find the the probability that it is a card of b, if it is not a.
We have total number of cards = 20
The cards of a = 10
The cards of b = 5
The cards of c = 5
We don't select the card a, then;
The probability of choosing card b = The total number of card b/total number of cards
The probability of choosing card b = 5/20
The probability of choosing card b = 1/4
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IXL: S26 (ALGEBRA 1)
The equation of line k is y=9/8x-9. Line I is perpendicular to line k and passes through (-2,2) What is the equation of line I? write the equation in slope intercept form.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{9}{8}}x-9\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{9}{8}} ~\hfill \stackrel{reciprocal}{\cfrac{8}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{8}{9} }}[/tex]
so we're really looking for the equation of a line whose slope is -8/9 and it passes through (-2 , 2)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{8}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{8}{9}}(x-\stackrel{x_1}{(-2)}) \implies y -2= -\cfrac{8}{9} (x +2) \\\\\\ y-2=-\cfrac{8}{9}x-\cfrac{16}{9}\implies y=-\cfrac{8}{9}x-\cfrac{16}{9}+2\implies {\Large \begin{array}{llll} y=-\cfrac{8}{9}x+\cfrac{2}{9} \end{array}}[/tex]
Please help someone with this additional gcse maths 'surds and indices' question :)
The simplest form of the expression is given as 12 + 6√3.
What is the simplest form of the expression?
We know that when we are asked to simplify in mathematics, they are asking us to write the expression in the simplest form that the expression can be in. In this case, we are to simplify 6/2 - √3.
Then we would now have to multiply the numerator and the denominator by the conjugate of the denominator such that we have;
6/2 - √3 * 2 + √3/2 + √3
12 + 6√3/4 +2√3 - 2√3 - 3
12 + 6√3/1
12 + 6√3
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Which of the reasons to network is most important for recent culinary program graduates?
A. Developing friendships that may lead to business referrals
B. Learning best practices from experienced professionals
C. Recommending extensive contacts that can help others
D. Sharing their favorite recipes and stories from their program
Answer:
C. gaining confidence
Robert Wadlow was 8’11” tall. He Pingping was 2’4.7”. what is the difference between their heights in feet and inches?
The difference between their heights in feet and inches is 6'6.3"
How to determine the difference between their heights in feet and inches?From the question, we have the following parameters that can be used in our computation:
Robert Wadlow was 8’11” tall.
Pingping was 2’4.7" tall
The difference in their heights can be calculated by subtracting the smaller height from the larger
So, we have
Difference = 8’11” - 2’4.7"
Evaluate the difference
Difference = 6'6.3"
Hence, the difference is 6'6.3"
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PLEASE HELP I WILL GIVE BRAINLIEST
For the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale
factor and center of dilation.
D(2,-2), E(4, -2), F(1, -4)
k = 1.5,, E(4,-2), centered at E
The coordinates of vertices after dilation by scale factor of 1.5 with center of dilation is D'(3,-3), E'(6,-3) and F'(1.5,-6).
What is the vertices after dilation?A dilation is just a transformation which enlarges or contracts the size of a figure. This means that the preimage and image are similar and are scaled up or down using a factor.
The vertices of the triangle are D(2,-2), E(4,-2), F(1,-4).
The origin-centered dilation with a scale factor of k is defined as,
(x,y) → (kx,ky)
As a result, dilation with a scale factor of 1.5 centered at the origin is defined as,
(x,y) → (1.5x,1.5y)
The image's vertices are
D(2,-2) → D'(3,-3)
E(4,-2) → E'(6,-3)
F(1,-4) → F'(1.5,-6)
Therefore the coordinates of vertices after the dilation by the given scale factor 1.5 is D'(3,-3), E'(6,-3) and F'(1.5,-6).
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What is the distance between PQ?
P: (1,6)
Q: (7,2)
The distance between PQ : 7
Given points P: (1,6)
Q : (7,2)
distance between two points formula is : √(x2-x1)^2 + (y2-y1)^2
(x1,y1)= (1,6)
(x2,y2) = (7,2)
therefore
= √(7-1)^2 +(2-6)^2
= √36+16
= √52
= 7.211