*NEED HELP COMPLETING THIS*
Simplify all radicals using the Perfect Square/Cube Factors Method as demonstrated in class.
Answers
The answers to all parts shown below.
What is Radical?Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root. Radicand - A number or expression inside the radical symbol.
Given:
We have to find the Square/Cube Factors
1. 5/6√3
Now, rationalizing
5/6√3 x √3/ √3
= 5√3 / 18
2. √3/ (7- 3√5)
Now, rationalizing
= √3/ (7- 3√5) x (7+ 3√5) / (7+ 3√5)
= √3(7+ 3√5) / 4
3. 8/ (4 + 5√2)
Now, rationalizing
= 8/ (4 + 5√2) x (4 - 5√2)/ (4 - 5√2)
= -8 (4 - 5√2)/ 34
4. 7 ∛(48 [tex]m^{18} n^{13}[/tex])
= 14 [tex]m^6[/tex][tex]n^4[/tex]∛6n
5.[tex]2\sqrt{\left(-300x^{18}\right)}[/tex]
=[tex]20\sqrt{3}\sqrt{-x^{18}}[/tex]
6. (4+ 7√10)²
= 4² + (7√10)²+ 2 (4)( 7√10)
= 16 + 490 + 56√10
= 506 + 56√10
7. (6- 7√3) x (6+ 7√3)
= 6² - (7√3)²
= 36 - 147
= -111
8. 11√50[tex]x^{12}y^5[/tex]
= 55[tex]x^6[/tex]y²√2y
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Related Questions
(Easy!) The box plot shown displays the data on the response times of one hundred mice to see a flash of light.
What percent of mice responded in 0.8 seconds or more?
A. 25%
B. 50%
C. 75%
D. 100%
Answers
The percent of mice whose response time was 0.8 seconds or more is; Choice B; 50%.
How many mice responded in 0.8 seconds or more?As evident on the box plot; The response time, 0.8 seconds corresponds to the median of the plot.
Since the median represents the 2nd quartile of a distribution or otherwise termed , the 50th percentile;
It can be inferred that the percent of mice who responded in 0.8 seconds or more is; Choice B; 50%.
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=-72[tex]x^{2}[/tex]
Answers
On solving for (x), we get -
x = ±i√(a/72).
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 the equation as -
- 72x² = a
The given equation is -
- 72x² = a
x² = -a/72
x = ±i√(a/72)
Therefore, on solving for (x), we get -
x = ±i√(a/72).
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What is the area of the parallelogram?
Answers
Area of the parallelogram is 65 square meter.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
Area of the parallelogram = Base × Height
From the figure,
Length of base = AB = 3 m + 10 m = 13 m
Height is also given as 5 m.
Area of the parallelogram ABCD = 13 m × 5 m
= 65 m²
Hence the required area of the parallelogram is 65 m².
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I need help with the image below
Answers
The value of x is -29
How to determine the valueIt is important to note that;
a diameter of a circle will always pass through the centertwo diameters of a circle will necessarily intersect at the centerWe have the diameters as;
-9x + 104 and 3x + 82
Also note that angles at the center is 360 degrees
This is then represented as;
-9x + 104 + 3x + 82 = 360
collect the like terms
-6x = 360 - 186
subtract the values
-6x = 174
Make 'x' the subject of formula, we get;
x = 174/-6
x = -29
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will scale factor =12 enlarge, reduce or preserve
Answers
For {K} = 12, the image will remain preserved.
What is image dilation?An enlargement or reduction of a figure that preserves shape but not size.All dilations are similar to the original figure.Dilations have a center and a scale factor.Given is the scale factor of {K} = 12.
We can write the scale factor as -
reduction {for K < 1}
enlargement {for K > 1}
preserved {for K = 1}
For {K} = 12, the image will remain preserved.
Therefore, for {K} = 12, the image will remain preserved.
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What is independent variable dependent variable and constant?
Answers
Independent Variable = A variable that is being changed in an experiment of each trail
Dependent Variable: The one that is being measured
Constant: The one that is constant (still the same) or is unchanged in the experiment
The area of a circle is 49π m². What is the circumference, in meters? Express your answer in terms of
�
π.
Answers
Answer: 14π
Step-by-step explanation:
The area of a circle can be expressed as πr^2. In this case, the area is given as 49π m², so we can write:
πr^2 = 49π
Dividing both sides by π, we get:
r^2 = 49
Taking the square root of both sides, we get:
r = 7
The circumference of a circle is given by 2πr, so the circumference in this case would be:
C = 2π * 7 = 14π
So the circumference of the circle with an area of 49π m² is 14π meters.
evaluate 9.3p + 8.9r when p=7 and r=8
Answers
The value of the expression for the given p and r value is 136.3.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 9.3p + 8.9.
Here, p=7 and r=8
Substitute p=7 and r=8 in 9.3p + 8.9r, we get
9.3×7+8.9×8
= 136.3
Therefore, the value of the expression is 136.3.
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HELPPPPPPPPPPPPPPPPPPPPPPPPP DUE RIGHT NOWWWWWWWWWWWWW
Answers
help due tonight!!!!!!!! 100 points + Brainliest
Answers
The missing numerator are 7, 3, 6, 6, and 2
What are numerators?The Numerator is the number the at top of a fraction.
From the question, the numerators are
21) 2/3 x 7/5 = 14/15
The missing numerator here is 7
22) 5/6 X 3/7 = 5/14
The missing numerator here is 3
23) 3/4 X 6/7 = 9/14
The missing numerator here is 6
24) 6/9 X 2/4 = 1/2
The missing numerator here is 6
25) 9/10 X 2/3 = 3/5
The missing numerator here is 2
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Answer:
21) 7; 22) 3, 23) 6; 24) 6; 25) 2.-------------------------
Substitute ? with x and solve each equation.
21)
2/3 × x/5 = 14/152x/15 = 14/152x = 14x = 722)
5/6 × x/7 = 5/145x / 42 = 5/14x/42 = 1/14x = 42/14x = 323)
3/4 × x/7 = 9/143x/28 = 9/14x/28 = 3/14x/2 = 3x = 624)
x/9 × 2/4 = 1/3x/9 × 1/2 = 1/3x/18 = 1/3x = 18/3x = 625)
9/10 × x/3 = 3/53x/10 = 3/5x/2 = 1x = 2b) From the following data of rainfall and production of rice, find the most likely production corresponding to the rainfall of 40 mm Rainfall Production (mm). (quintals) Mean: 35. 50 s.d. 5. 8 Coefficient of correlation = 0.8
Answers
The most likely production for a rainfall of 40 mm is 56.4 quintals.
How to determine the production that correspond to the rainfallFrom the question, we have the following parameters that can be used in our computation:
Rainfall (mm) Production (quintals)
Mean 35 50
S.D 5 8
Coefficient of correlation = 0.8
First, we need to calculate the regression equation, which is:
y = a + bx
Where
y is the predicted value of production x is the rainfalla is the interceptb is the slope of the regression line.To calculate the intercept and slope, we use the following formulas:
b = r * (SDy / SDx)
a = Ymean - b * Xmean
Plugging in the given values, we get:
b = 0.8 * (8 / 5) = 1.28
a = 50 - 1.28 * 35 = 5.2
Therefore, the regression equation is:
Y = 5.2 + 1.28x
To find the most likely production for a rainfall of 40 mm, we plug in x = 40 into the regression equation:
Y = 5.2 + 1.28 * 40
Y = 56.4
Hence, the most likely production is 56.4 quintals.
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what is 79kg to lbs?
Answers
Answer: 79 kilograms is equal to 173.776 pounds.
Step-by-step explanation:
To convert kilograms to pounds, you can multiply the number of kilograms by 2.20462.
So, to convert 79 kilograms to pounds:
79 kg * 2.20462 = 173.776 lbs
Therefore, 79 kilograms is equal to 173.776 pounds.
A furniture store donated a percent of every sale to hospitals. The total sales were $7,200 so they store donated $288. What percent of $7,200 was donated to hospitals?
Answers
Answer:
Step-by-step explanation:
x% OF 7200 = 288
x/100*7200 = 288
x=288/72=4
4% was donated
How many 65 kg in pounds ?
Answers
65 kg is equivalent to approximately 143.3 pounds and both are unit of measurement of weight.
To convert kilograms to pounds, we multiply the weight in kilograms by the conversion factor of 2.20462. Therefore, to convert 65 kg to pounds, we can multiply 65 by 2.20462, which gives us approximately 143.3 pounds.
It's important to note that kilograms and pounds are both units of weight, but they are used in different parts of the world. Kilograms are the standard unit of weight in most countries, while pounds are commonly used in the United States and some other countries.
Converting between units of measurement is a valuable skill, especially when communicating or traveling internationally. Knowing how to convert from kilograms to pounds, or vice versa, can help you understand weight measurements in different contexts.
Online conversion tools or calculators can be useful resources to quickly and accurately convert between units of measurement as needed.
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What is the formula of arc length of a curve?
Answers
Answer:
Arc Length=∫ba√1+[f′(x)]2dx. Note that we are integrating an expression involving f′(x), so we need to be sure f′(x) is integrable. This is why we require f(x) to be smooth.
Step-by-step explanation:
have a nice day
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
Answers
Answer:
Step-by-step explanation:
y=9700(0.909)^x
# If the base of an exponential function is an element of the set (0,1) the function is decreasing as the value of 'x' is increasing from negative infinity to positive infinity.
the function y=9700(0.909)^x is an exponential function with a coefficient 9700 and base 0.909, as we increase the value of x from negative infinity to positive infinity, the value of y decreases. So the change between two consecutive 'y' values as 'x' increases indicate decay rather than growth.
And it can be written as y=9700(1-0.091)^x, therefore the percentage decrease is 9.1%
A farmer needs to fence a rectangular plot of land with the area of 3000 square yards. He considers several possible length of the plot: 50 yards, 40 yards, 48 yards, and 36 yards. What will be the width of the plot in each case? Do the length and the width of the rectangular plot vary directly or inversely when the same area is needed?
Answers
For length of 50 yards , the width is 60 yards, for length of 40 yards , the width is 75 yards, for length of 48 yards, the width is 62.5 yards , for length of 36 yards, the width is 83.33 yards, they are inversely proportional.
The formula for the area of a rectangle is: Area = Length * Width.
So, for the given case, we have:
Area = 3000 square yards
Length = 50 yards, 40 yards, 48 yards, or 36 yards
Therefore, the width of the plot in each case can be calculated as:
For Length = 50 yards,
Width = Area / Length
= 3000 / 50
= 60 yards
For Length = 40 yards,
Width = Area / Length
= 3000 / 40
= 75 yards
For Length = 48 yards,
Width = Area / Length
= 3000 / 48
= 62.5 yards
For Length = 36 yards,
Width = Area / Length
= 3000 / 36
= 83.33 yards
Therefore, the width of the plot depends on the length chosen and they are inversely proportional. When the length increases, the width decreases, and when the length decreases, the width increases.
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how is the bell shaped histogram?
Answers
A bell-shaped histogram is a type of graph that displays a normal distribution, which is a probability distribution that is symmetrical and has a characteristic bell shape.
The bell-shaped histogram is created by plotting the data on a horizontal axis and the frequency or probability on a vertical axis. The data points are grouped into intervals called bins, and the number of data points that fall into each bin is plotted as a bar. The bars are typically drawn adjacent to one another and connected with lines to create a continuous curve that represents the normal distribution.
The resulting histogram will have a characteristic bell shape, with a high point at the mean, and decreasing frequency or probability as the values move away from the mean in either direction. The width of the curve is determined by the standard deviation of the data, with wider curves indicating greater variation in the data.
The bell-shaped histogram is commonly used in statistical analysis to represent normally distributed data, such as the heights or weights of a population, test scores, or other measurements that tend to cluster around a central value with a predictable range of variation.
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What numbers do i put in the blanks
Answers
The solutions of the system are y = -8 and x = 9.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
Given:
A system of equations,
5x + 6y = -3 {Equation 1}
8x + 8y = 8 {Equation 2}.
Multiply 8 into equation 1 and multiply by 5 into equation 2,
and subtract the equation,
we get,
40x + 48y - 40x - 40y = -24 - 40
8y = -64
y = -8 and x = 9
Therefore, the solutions are y = -8 and x = 9.
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Write an equation that represents the relationship between the distance the car
has traveled in miles, d, and the amount of gas left in the tank in gallons, x.
Answers
Answer: The relationship between the distance a car has traveled in miles, d, and the amount of gas left in the tank in gallons, x, can be represented by the equation:
d = r * m
where r is the fuel efficiency of the car in miles per gallon and m is the amount of gas consumed in gallons.
Since x is the amount of gas left in the tank, we can write:
x = m_0 - m
where m_0 is the initial amount of gas in the tank.
Combining the two equations, we get:
d = r * (m_0 - x)
This equation represents the relationship between the distance the car has traveled in miles, d, and the amount of gas left in the tank in gallons, x.
Step-by-step explanation:
How do you find the percentage of yield in caculator?
Answers
To find the percentage of yield in a calculator, you can follow these steps:
1. Determine the actual yield and the theoretical yield of the reaction. The actual yield is the amount of product that was actually produced in the reaction, while the theoretical yield is the amount of product that should have been produced based on the balanced chemical equation.
2. Divide the actual yield by the theoretical yield to find the decimal form of the percentage yield.
3. Multiply the decimal form of the percentage yield by 100 to find the percentage yield.
For example, if the actual yield of a reaction is 15 grams and the theoretical yield is 20 grams, the percentage yield would be:
(15/20) x 100 = 75%
Therefore, the percentage yield of the reaction is 75%.
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how to write 1/400 as a percent
Answers
Answer:
0.25%
Step-by-step explanation:
Answer:
0.25%
Step-by-step explanation: you`re welcome :)
A student earned the scores in the data set in one course.
{78, 64, 74, 92, 67}
What is the mean of the scores?
75
74
64
28
Answers
Answer:
75.
Step-by-step explanation:
The mean = (78 + 64 + 74 + 92 + 67) / 5
= 375 / 5
= 75.
Answer:A.75
Step-by-step explanation:
i did it in class
The length of the rectangle is (4x + 2) and width of the rectangle 6x. Find the
perimeter of the rectangle.
A.10x + 2
B.20x + 4
C.10x + 4
D.20x - 4
Answers
Answer:
B. 20x + 4
Step-by-step explanation:
Perimeter of a rectangle = 2 × (Length + Width)
= 2 × [(4x + 2) + 6x]
Expand the brackets and bring like terms together:
= 2 × [4x + 2 + 6x]
= 2 × [4x + 6x + 2]
= 2 × [10x + 2]
Expand the brackets by applying the Distributive Law:
= 20x + 4
Option B.
There is a sales tax of $25 on an item that costs $310 before tax. The sales tax on a second item is $10. How much does the second item cost before tax?
Answers
The percentage of sales tariff is 8.06%. Then the second item cost before the tariff will be $124.
What is the percentage?Any product's quantity is given as if it were a percentage of one hundred. The ratio can be written as 100. The word "%" means "100%" in English. The sign for it is the letter "%".
The percentage is given as,
[tex]\text{Percentage (P) }= \dfrac{ \text{Final value - Original value}}{\text{ Original value }} \times 100[/tex]
An item that costs $310 before the tariff carries a $25 sales tariff. The sales tax % is then provided as,
[tex]\rm P = \left ( \dfrac{25}{ 310} \right ) \times 100[/tex]
P = 0.0806 x 100
P = 8.06%
The sales tax on a second object is $10. Then the second object cost before the tariff is given as,
⇒ $10 / 0.0806
⇒ $124
The percentage of sales tariff is 8.06%. Then the second item cost before the tariff will be $124.
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Need help ASAP! Write the inequality to represent the graph.
(didnt mean to put it at highschool, whoops!)
Answers
The inequality that represents the graph is given as follows:
x < 4.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The numbers to the right of 4 that are shaded on the number line are the numbers that are less than 4, with an open interval, due to the open circle at x = 4, hence the inequality is given as follows:
x < 4.
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‼️WILL MARK BRAINLIEST‼️
Answers
a. The inequality for the number of cases they go through in 30 days is:
number of cases > 30 x (15 cans/day) / 24 cans/case
We multiply 30 by 15 to get the total number of cans they use in 30 days, then divide by 24 to get the number of cases they need to buy to have enough cans for 30 days.
Simplifying the expression, we get:
number of cases > 7.8125
Therefore, they need to buy at least 8 cases of sparkling water to have enough cans for 30 days.
b. If they buy 8 cases of sparkling water, the total cost would be:
8 cases x $3.50/case = $28
Therefore, they would spend $28 on sparkling water in 30 days if they buy only full cases.
Junior is looking into buying a new car he has $2000 for a down payment and he wants to pay $250 per month. for Ford mustang has the following equation for a special deal Y equals 275X +2500 and a dodge charger has a special deal of Y equals 250 X +1500. which deal would work better for him? explain your answer.
Answers
Answer:
Step-by-step explanation:
First, we need to calculate the cost of each car after 60 months.
For the Ford Mustang:
Y = 275X + 2500
Y = 275 * 60 + 2500
Y = 16500
For the Dodge Charger:
Y = 250X + 1500
Y = 250 * 60 + 1500
Y = 15000
Next, we can compare the total cost of each car to determine which is the better deal.
In this case, the Dodge Charger is the better deal as it costs $1500 less than the Ford Mustang over the course of 60 months.
It's important to keep in mind that these calculations are based on the assumption that Junior will only make the minimum payments of $250 per month. If he decides to make larger payments or pay off the car early, the total cost of each car will be different.
Additionally, there may be other factors, such as the reliability and maintenance costs of each car, insurance costs, fuel efficiency, and driving experience, that should also be considered before making a decision. Junior should research and weigh all these factors before making a final decision.
In conclusion, the calculation of the cost of each car after 60 months is just one aspect of the decision-making process when buying a car. Junior should consider all relevant factors and weigh the pros and cons of each option before making a final decision.
2. Tell whether each function is linear. If so, graph
the function.
2y = -4x
Answers
The function 2y = -4x is linear and the graph is given below.
What is Linear Function?A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.
Here the given function is 2y = -4x.
The function is linear since the exponent of the two variables x and y are 1.
This can be written as,
y = -4x / 2
y = -2x
This is a proportional function with slope -2.
Graph will be a decreasing function.
The points on the graph includes (-2, 4), (-1, 2), (0, 0), (1, -2) and (2, -4).
Hence the graph of the function is given below.
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Which statement is true of triangles FGH and F'G'H?
Answers
Step-by-step explanation:
I suspect this to be a trick question.
because 2 statements are correct :
B and C.
according to the definition, two triangles are similar if their corresponding angles are congruent (identical) and corresponding sides are proportional (the ratio between the length of corresponding sides is equal for all pairs of corresponding sides, or, in other words, there is one scale factor for all 3 pairs of corresponding sides).
in fact, each criteria alone is sufficient.
if all 3 corresponding angles are identical between both triangles, the corresponding pairs of sides will be proportional.
if all 3 pairs of corresponding sides are proportional, then the corresponding angles are identical.
and the triangles are similar.