The product of ∛3 and 5√3 is 15√3⁸ (Option C).
This question can be easily solved by using the concept of roots. The two terms mentioned in the question are ∛3 ( cubic root of 3 ) and 5√3 (5th root of 3 ). This question can be solved in 4 easy steps
Step 1 : Identify the power of the root and take LCM of those numbers.
In this case, the powers of root for ∛3 and 5√3 are 3 and 5, respectively. Take LCM of 3 and 5.
LCM = 3 x 5 = 15
=> We get the LCM of 3 and 5 as 15.
Step 2 : Write the given numbers in the form of fractional powers
∛3 = 3¹ˡ³ => The power of 3 = 1/3
5√3 = 3¹ˡ⁵ => The power of 5 = 1/5
Step 3 : Multiply and divide the powers of the base number ( in this case 3 ) with a number such that you get the denominator as the LCM ( in this case 15 )
1/3 can be multiplied and divided by 5 to get the denominator as 15
=> 1 * 5 / 3 * 5 = 5 /15
1/5 can be multiplied and divided by 3 to get the denominator as 15
=> 1 * 3 / 5 * 3 = 3 /15
Step 4 : Find the product of the two terms
15√3⁵ x 15√3³ = 15√3³⁺⁵ = 15√3⁸
Therefore, using the concept of roots and fractions, we get the product of ∛3 and 5√3 as 15√3⁸.
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Simplify each number.
6¹/₂ . 12¹/₂
[tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] can be simplified into 8.48.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 6= 2 x 3
Prime factorization of 12= 3 x 2 x 2
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m} )^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]
According to the given condition,
Applying the laws of indices mentioned above,
∴[tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] = [tex](2 X 3)^{\frac{1}{2} } . (3 X 2^{2}) ^{\frac{1}{2} }[/tex]
= [tex](3^{2} X 2^{3})^{\frac{1}{2} }[/tex]
= [tex]\sqrt{72}[/tex] = 8.48.
Thus, [tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] can be simplified into 8.48.
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two rectangles have the exact same area. the measurements of the first rectangle is 3k by 3.calculate the value of k
The value of k is 6.
Given we have length as 3k and the width as 3 of the first rectangle.
length = k₊3 and width = 6 of the second recatngle
Two rectangles has the same exact area.
area = length × breadth
3k × 3 = (k₊3)6
9k = 6k ₊ 18
3k = 18
k = 18/3
k = 6
hence we get the value of k as 6.
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3. Suppose you graph the information in the table. Find the slope of a line drawn through the points.
Answer:
I can't see the information in the table but I can tell you how to do it
Step-by-step explanation:
pick two points on the graph, then do this: (y2-y1)/(x2-x1)
this will help you to find the slope of the line
The point C(4,5) is rotated 270° counterclockwise around the origin. What are the coordinates of the resulting point, C'?
The coordinates of the resulting point C' are (-5, 4).
What are coordinates?A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold, such as Euclidean space. The order of the coordinates matters, and they are sometimes identified by their position in an ordered tuple and other times by a letter, as in "the x-coordinate."Since we know that rotating a point 270° counterclockwise about the origin causes the point (x,y) to become (-y, x), we can swap the positions of the x and y coordinates and make y negative.
We have, using the above transformation:
(x, y) ⇒ (-y, x)(4, 5) ⇒ (-5, 4)Therefore, the coordinates of the resulting point C' are (-5, 4).
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Answer:
Step-by-step explanation:
(5,-4)
In the figure below, /BC/= 2cm, /AB/= 3cm and ZACD= 1500, what is the value of sin A? A D 150° с A√3 B √√3 2 2cm 2/3 3cm B DE 2 3
Answer:
E 1/3
Step-by-step explanation:
m<ACB = 30° because of supplementary angles.
Use the Law of Sines
sin C/AB = sin A/BC
sin 30°/3 = sin A/2
sin A = (2 × sin 30°)/3
sin A = (2 × 0.5)/3
sin A = 1/3
Answer: E 1/3
1. Give two other names for CD.
2. Give another name for plane M.
3. Name three points that are collinear. Then name a fourth point that is not collinear with these three points.
4. Name a point that is not coplanar with points A, C, E.
1. The other two names for CD is DC and line m
2. The another name for plane M is plane AEB , ABE ,BEA ,ACE.
3. The points which are collinear are A ,C , B and the point which is not collinear is D or E .
4. The point that is not coplanar with points A, C, E is D.
A line can be defined as a series of straight lines extending in opposite directions. A collinear point is a point that lies on the same straight line or a single line. Two or more points on a line are said to be collinear if they are close or far apart. The word "coplanar" means "on the same plane".1. CD lies on m so , other name for CD can be DC and line m.
2. As point A , B , E lies on plane M so , other name for plane M can be AEB , ABE , BEA and ACE .
3. As A , C and B are in straight line hence , they are collinear and point D and E are not in collinear with these three points .
4. Only D point is not on the plane hence , it is not coplanar with points A, C, E.
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ace company provided the following data on december 31, 2021: cash 1,500,000 inventories 280,000 prepaid supplies 120,000 land 360,000 furniture & fixtures 60,000 accounts payable 385,000 salaries & wages payable 12,000 net sales and other revenue 770,000 cost and expenses 340,000 retained earnings, jan. 01, 2021 1,100,000 on december 31, 2021, what amount should be reported as current assets
Amount reported as Current Assets = 1,912,000
Current assets are items that a corporation utilizes, replaces, or turns into cash during a typical operating cycle. They are also known as short-term assets (typically less than 12 months). It sets them apart from long-term assets or those that a company utilizes for more than a year. Current assets are referred to as liquid assets since they may be converted into cash more readily than long-term assets.
The balance sheet shows both current and long-term assets, which combined comprise all of the company's assets.
Amounts reported as Current Assets are :
Cash = 1,500,000
Inventories = 280,000
Prepaid Supplies = 120,000
Salaries and Wages Payable = 12,000
Total Amount = 1,500,000 + 280,000 + 120,000 + 12,000 = 1,912,000
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What is the tax due for a single taxpayer reporting a taxable income of 64,725
The tax due for a single taxpayer by virtue of the tax rate for single filers; 22% as required in the task content is; 14,239.5.
What is the tax due for a single tax payer whose taxable income is; 64,725 as required in the task content?It follows from the task content that the taxable income of the single taxpayer as discussed in the task content is; 64,725.
Since, the tax rate which is alloted to such individual single filers is; 22%.
It simply follows that the tax due on the individual can be determined as follows;
Tax due = 22% of 64, 725
= (22/100) × 64,725
= 14,239.5
Ultimately, the tax due for a single taxpayer by virtue of the tax rate for single filers; 22% as required in the task content is; 14,239.5.
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Given g(x) = − 4x + 8, identify the domain, range, and x-intercept of the function.
Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0)
Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (−2, 0)
Domain: −4 < x < 8; Range: − 4 < y < ∞; x-intercept (2, 0)
Domain: −4 < x < 8; Range: −∞ < y < 4; x-intercept (−2, 0)
Domain of a function means all possible inputs or all the numbers that can be put in place of x to get some output
Range of a function means all possible outputs or all the numbers that are the result of all the inputs or value of y
Intercept is the point on graph whose one coordinate is zero. There are two types of intercepts - X intercept where the y coordinate is zero and Y intercept where the value of x coordinate is zero
the function given is g (x) = -4x +8
The domain of the given function is all real numbers or - infinite < x< infinite
The range of the given function is all real numbers or - infinite < x< infinite
The x intercept of of the given function is where y = 0
so, 0 = -4x + 8
-8 = -4x
x = 2
The x intercept is (2,0)
Hence, the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) which is first option
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Step-by-step explanation:
Took test
Write each expression in simplest form. (x³/x⁻¹)⁻¹/₄
The result of simplifying the expression (x³/x⁻¹)⁻¹/₄ using the exponent rules is 1/x
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(x³/x⁻¹)⁻¹/₄
Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:
(x⁽³⁻⁽⁻¹⁾)⁻¹/⁴
(x⁽³⁺¹⁾)⁻¹/⁴
(x⁴)⁻¹/⁴
Using the power of a power rule that indicates that: the exponent result will be the multiplication of these powers, we have:
x⁽⁴*⁻¹/⁴⁾
x⁽⁻⁴/⁴⁾
x⁽⁻¹⁾
As we have a negative exponent, you have to pass the exponent to the denominator:
1/x
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Find 29- 3f + 2g, when f=4 and g=3
29-3f+2g
=29-3(4)+2(3)
=29-12+6
=23
if 251x=100 two, find x
Answer:
X = 102/251
Step-by-step explanation:
251x = 102
/ /
251 251
X= 102/251
Jamar writes 4 x 6 = 24 to find the total number of
marbles he has. How might Jamar describe what each
factor represents in the multiplication equation?
There 6 number of bags and each bag will have 4 marbles in it.
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
4 x 6 = 24
If 24 represents total bof marbles.
So, we can assume that there 6 number of bags and each bag will have 4 marbles in it.
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The supertanker and the iceberg are headed straight toward each other. The supertanker traveling at a speed of 12 miles per hour, while the iceberg is traveling at 0.5 miles per hour. If the two are exactly 50 miles apart, in how many hour will the hit
If the two are exactly 50 miles apart, it will hit in
T=0.25hours
This is further explained below.
If the two are exactly 50 miles apart, in how many hour will they hit?Generally, the equation for Time is mathematically given as
T=v/d
Therefore
T=(12+0.5)/50
T=0.25hours
In conclusion, If the two are exactly 50 miles apart, it will hit in
T=0.25hours
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Write in index form using a unit fraction 10 √ 34
Answer:
2.6
i thank
Step-by-step explanation:
You make $9.25 an hour and want to buy a new watch that’s costs $277.50. Write and solve an inequality to find out how many hours you will have to work to have enough money for the new watch.
The Sierpinski triangle (pictured below) is a fractal image. The original figure is an equilateral triangle. In each step, the computer splits every triangle in the design into 4 congruent equilateral triangles, and removes the center one from the design. The area remaining in a particular design after n steps can be shown using the following expression:
25√3 / 2 * (3/4)^n
What does 25√3 / 2 signify in the expression? (Image Shown Below)
O Each step multiplies the area 25√3 / 2.
O The original figure had an area of 25√3 / 2 square units.
O Each step increases the area of the figure by 25√3 / 2 square units.
O After many steps, the figure will have an area of 25√3 / 2 square units.
The original figure had an area of 25√3 / 2 square units option (B) is correct.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
The Sierpinski triangle is a fractal image:
The original figure is an equilateral triangle.
The area remaining in a particular design after n steps can be shown using the following expression:
= 25√3/2 (3/4)ⁿ
Plug n = 0
= 25√3/2 (3/4)⁰
= 25√3/2 square units
The expression 25√3/2 represents the area of the image of the triangle(shown in the first number image)
Thus, the original figure had an area of 25√3 / 2 square units option (B) is correct.
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Question 1 options:
Find the distance between the points (-10, -2) and (-8,0).
*round to the nearest tenth
The distance between the given pair of points (-10, -2), (-8,0 ) round to the nearest tenth is 2.8.
What is the distance between the given pair of points?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given the data in the question;
Point 1(-10, -2)
x₁ = -10y₁ = -1Point 2( -8,0 )
x₂ = -8y₂ = 0Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √( ( (-8) - (-10) )² + ( 0 - (-2) )² )
D = √( ( -8 + 10 )² + ( 0 + 2 )² )
D = √( ( 2 )² + ( 2 )² )
D = √( 4 + 4 )
D = √8
D = 2.8
Therefore, the distance between the given pair of points (-10, -2), (-8,0 ) round to the nearest tenth is 2.8.
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PLEASE ANSWER RIGHT AWAY
4⁰ + 9 x 2 – 5³
show work please im doing a test
The simplified form of the expression is -106
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
4⁰ + 9 x 2 – 5³
Simplifying
4⁰ + 9 x 2 – 5³
First, evaluate the exponents
5³ = 125
4⁰ = 1
Thus, the expression becomes
1 + 9 x 2 – 125
Simplifying further
1 + 18 - 125
= 19 - 125
= -106
Hence, the simplified form of the expression is -106
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A group of friends wants to go to the amusement park. They have $183 to spend on
parking and admission. Parking is $8, and tickets cost $25 per person, including tax.
Write and solve an equation which can be used to determine x, the number of people
who can go to the amusement park.
The equation is 25x + 8 = 183
The value of x is 7
How to determine the value of x ?The group of friends have $183 to spend
The cost of parking is $8
The tickets cost $25 per person
The equation can be written as follows
25x + 8 = 183
Collect the like terms
25x= 175
Divide by the coefficient of x which is 25
x= 175/25
x= 7
Hence the value of x is 7 and the equation is written as 25x + 8 = 183
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solve for y
-4=-2+y/2
Answer:
y = -4
Step-by-step explanation:
-4 = -2 + y/2
-2 = y/2
2(-2) = y
y = -4
Your robot is 3 inches wide. Its legs are 1 inch apart.
For each robot, enter the distance between the legs.
When the robot width is 6 inches, the distance between the legs will be 2 inches.
When the robot width is 5 inches, the distance between the legs will be 1.67 inches.
How to illustrate the information?It should be noted that from the information, the robot is 3 inches wide and its legs are 1 inch apart.
Therefore, when the robot width is 6 inches, the distance between the legs will be:
= 1/3 × 6
= 2 inches.
When the robot width is 5 inches, the distance between the legs will be:
= 1/3 × 5
= 5/3
= 1.67 inches.
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A typical paper bag at a grocery store cannot hold more than 49 pounds. Let p represent the number of pounds a typical paper bag can hold.
Create an inequality to represent the situation. Move a symbol to the lines to create the inequality.
P___49
Answer: = is it maybe
if not sry
p≤49 is the inequality to represent the situation.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that a typical paper bag at a grocery store cannot hold more than 49 pounds.
Let p represent the number of pounds a typical paper bag can hold.
We have to find the inequality to represent the situation
As grocery store cannot hold more than 49 pounds which means it holds less than or equal to 49.
p≤49
Hence, p≤49 is the inequality to represent the situation.
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In a class of 30 children, 60% of the children are girls. How many boys are there in the class?
Answer:12 boys
Step-by-step explanation:100-60=40 40% of 30 is 12
Solve each trigonometric equation for θ in terms of y .
y=2 cosθ+1
Answer:
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{y-1}{2}[/tex] )
Step-by-step explanation:
y = 2cosΘ + 1 ( subtract 1 from both sides )
y - 1 = 2cosΘ ( divide both sides by 2 )
[tex]\frac{y-1}{2}[/tex] = cosΘ , then
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{y-1}{2}[/tex] )
A grain of rice weighs about 0.03 g.
a) Write the mass of a grain of rice in standard form.
In the USA, about 4.3 million tonnes of rice are eaten each year.
b) 1 tonne = 1 million grams
What is the mass, in grams, of rice eaten in the USA each year?
Give your answer in standard form.
a) The mass of a grain of rice in standard form; 0.3×10⁻¹ gram.
b) The mass, in grams, of rice eaten in the USA each year: 4.6×10¹² grams.
What is described as scientific notation?Scientific notation is a handy way to shorten extremely large numbers with positive exponential values and also very small numbers with negative exponential values. To shorten long numbers in scientific notation, employ positive exponents and decimals.For the given question;
a) Weight of the rice grain is 0.03 g.
Shift the point to one decimal of the right and replace it with 10⁻¹ for this.
= 0.3×10⁻¹
Thus, the number in standard form becomes 0.3×10⁻¹ grams.
b) In USA, the rice eaten per year = 4.3 million tonnes.
1 tonne = 1 million grams
And, we know, one million can be written as.
1 million = 10⁶
4.3 million tonnes = 4.6×10⁶ tonnes.
Now, if 1 tonne = 1 million grams.
Then, multiply both side by 4.6×10⁶.
4.6×10⁶ × 1 tonne = 4.6×10⁶×1 million grams.
4.6×10⁶ tonnes = 4.6×10⁶ million grams.
Again convert million as 10⁶.
= 4.6×10⁶×10⁶
= 4.6×10⁶⁺⁶
= 4.6×10¹²
Thus, in USA 4.6×10¹² grams of rice is eaten each year.
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A police car drives 46 miles in 1 hour and 55 minutes what is the average speed in miles per hour
The average speed of the police is 23.96 miles per hour
How to calculate the average speed ?
The distance is 46 miles
The time is is 1 hour 55 minutes, convert the minutes
= 55/60
= 0.92 + 1
= 1.92
The average speed can be calculated as follows
= distance/time
= 46/1.92
= 23.96
Hence the average speed of the police car is 23.96 miles per hour
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Suppose that every person that sees an image on social media
shares it with 6 people, who each share it with 6 people, who
each share it with 6 people. If two people saw an image, how
many people was it shared to?
Answer:
its 432
(ps. if your having trouble with focusing with school or work, try music. Would recommend lessoning to Wilbur Soot.)
The dimensions of a rectangular prism are shown below with one 1/2 feet with 1 foot high 2 1/2 feet the weight of the size of a small Cubes 1/2 of each how many small cubes can be packing rectangle prism show your work
Final Answer:
Rectangular Prism: A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that all the pairs of the opposite faces are congruent. Like all three-dimensional shapes, a rectangular prism also has volume and surface area.
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Slope intercept form (-6,19) and (3,-2)
Answer:
[tex]y = -\dfrac{7}{3}x +5[/tex]
Step-by-step explanation:
The general equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept is rise over run
[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x₁, y₁) and (x₂, y₂) are any two points on the line
[tex]m = \dfrac{-2 - 19}{3 - (-6)}\\\\[/tex]
[tex]\\\\m= \dfrac{-21}{9}[/tex]
[tex]m = -\dfrac{7}{3}[/tex]
So slope-intercept form is
[tex]y = -\dfrac{7}{3}x +b\\\\[/tex]
[tex]-2 = -\dfrac{7}{3}\cdot 3 +b\\\\\\\\-2 = -7 + b\\\\[/tex]
or 7 -2 = b
==> b = 5
[tex]y = -\dfrac{7}{3}x +5[/tex]