The expressions are not equal and the explanation is wrong because the index forms have different exponential values.
The correct answer is 14^-1/3
How to determine the correct optionEquivalent expressions are known as expressions that are the same solution but differ in the mode of their arrangement.
From the information given, we have the index forms;
(14^0/14^3)^1/3=14^-2/3
It is important to note that exponents with zero equals 1.
Then, we have that;
1/14^1/3 = 14 ^-2/3
Take the inverse of the exponent
14^-1/3 is not equal to 14^-2/3
Hence, the correct answer is 14^-1/3
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How do you multiply fractions with a common denominator?
When multiplying fractions, multiply the numerator (top number), then the denominator (bottom number), and finally reduce to the lowest term if necessary.
Fractions are subsets of wholes. They are made up of a numerator (the number on top) and a denominator (the number on the bottom). The numerator represents the number of parts, while the denominator represents the total number of available parts.
To multiply two fractions, follow these three simple steps:
Step 1: Multiply the numerators of each fraction by themselves (the numbers on top). The answer's numerator is the result.
Step 2: Add the denominators of each fraction together (the numbers on the bottom). The answer's denominator is the result.
Step 3: Simplify or reduce your response.
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HELPPPPPPPPPPPPPPPPPPPP
Answer:
i wish i knew but try just posting the pictures on the math page and boom
Answer: it should just be (x, -y)
Step-by-step explanation:
write the weight of caribou cows in kilograms as a prime factorization
Answer: Female caribou have a wide range of weight. They can average anywhere from 51 (3 x 17) to 156 (2 x 2 x 3 x 13) kg.
Step-by-step explanation:
What is the equation of the line that passes through thé point (-1, 3) and has a
slope of -3?
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of the line that passes through the point (-1, 3) and has a slope of -3, we can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
Substituting the given values, we get: y - 3 = -3(x - (-1))
Expanding the right side, we get: y - 3 = -3x + 3
Adding 3 to both sides, we get: y = -3x + 6
So the equation of the line that passes through the point (-1, 3) and has a slope of -3 is y = -3x + 6.
Hope this helps,
- Jeron :- )
Answer: y=-3x+6
Step-by-step explanation:
The equation for slope intercept form is y=mx+b, and since you are given your y and x values from the point (-1, 3), you can plug those values into it. You are also given your slope of -3, and since m is your slope value, you would plug the -3 in as your m.
After you plug in your given values from the problem, you should should get 3 = -1 (3) + b.
Then, you isolate the b. Multiply the -1 and 3 to get -3.
3 = -1 (3) + b
3 = -3 + b
Next, add the 3 to both sides of the equation, and you should be left with b=6.
3 = -3 + b
+3 +3
--------------
6 = 0 + b
6 = b
Finally, you re-write the slope intercept equation with the y-intercept (b value) you just found along with the slope of -3 given by the problem to get y=-3+6.
2x power of 2 + 3x + 1,Gives the answer 2x power of 3 + x power of 2 - 2x +1
The answer 2x power of 2 + 3x + 1. Therefore, the answer of the equation is x = 2.
Equation:
An equation is a mathematical operator that contains two algebraic expressions on either side of an equals (=) sign. Shows the equivalence between the expression written on the left and the expression written on the right. Every equation in mathematics has L.H.S = R.H.S (left = right). We can solve an equation to find the value of an unknown variable that represents an unknown quantity. If an expression does not have an equal sign, it is not an equation. This is considered an expression.
Now,
It has been given that
[tex]\frac{2^{3x-1} +10}{7} = 6[/tex]
Cross multiplying, we get
[tex]2^{3x-1} +10 = 42[/tex]
Subtract 10 to both sides
[tex]2^{3x-1} = 32[/tex]
Write 32 in exponent form
[tex]2^{3x-1} = 2^{5}[/tex]
Since, base of both sides of the equation is 2. Hence, the exponent must be equal.
3x - 1 = 5
⇒ 3x = 6
⇒ x = 2
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Please work on paper and help me do this
It should be noted that the addition of 1.17+ √63 will give an irrational number.
How to convey the informationIf p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so forth.
All real numbers that are not rational numbers are referred to be irrational numbers in mathematics. In other words, it is impossible to describe an irrational number as the ratio of two integers.
In this case, the answer is irrational, as the square root of 63 is not a rational number and cannot be expressed as a fraction of two integers.
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Please help now I need help ASAP thank you!
Answer:
Top TUV
Bottom: UV, UT, TV
Step-by-step explanation:
The scale factor from the larger to the smaller is 3/4
24(3/4) = 18
12(3/4) = 9
16(3/4) = 12
a committee of congressmen will be selected from a group of democrats and republicans. find the number of ways of obtaining exactly one .
The number of ways of obtaining exactly one Democrat is 504
We are choosing 6 committee members, and exactly 1 of them must be a Democrat, which leaves 5 members to be selected from the Republicans. The number of ways to select 5 Republicans from 9 Republicans is 9 choose 5, which is 9! / (5! * (9-5)!).
Therefore, the total number of ways to form a committee with exactly 1 Democrat and 5 Republicans is 4 * (9 choose 5) = 4 * 126 = 504. or
There are a total of 13 members (4 Democrats and 9 Republicans), so the number of combinations that can be chosen is 13C6, or 1716. Since we are looking for a committee with exactly one Democrat, we need to subtract the total number of combinations with no Democrats (9C6, or 84) from the total number of combinations, giving us 1716-84 = 504 ways of obtaining exactly one Democrat.
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Your question is incomplete but probably the full question was:
A committee of six Congressmen will be selected from a group of four Democrats and nine Republicans. What is the number of ways of obtaining exactly one Democrat?
what is s(t)=0.65(0.48)^t's percent rate of change.
The percent rate of change of s(t) is approximately -26.15%. This means that the function is decreasing at a rate of about 26.15% per unit of time.
The function s(t) = 0.65[tex](0.48)^t[/tex]represents a decreasing exponential function, where t is time and s(t) is the value of the function at time t.
To find the percent rate of change of s(t) at any given time t, we can use the formula:
percent rate of change = [(new value - old value)/old value] x 100%
In this case, the "old value" is s(t) and the "new value" is s(t+1), or the value of the function one unit of time later.
So, the percent rate of change of s(t) is:
percent rate of change = [(s(t+1) - s(t))/s(t)] x 100%
We can substitute the given function into this formula:
percent rate of change = [(0.65[tex](0.48)^(t+1)[/tex]- 0.65[tex](0.48)^t)[/tex]/0.65[tex](0.48)^t][/tex]x 100%
Simplifying, we get:
percent rate of change = [(0.48(0.65)[tex](0.48)^t[/tex]- 0.65[tex](0.48)^t)[/tex]/0.65[tex](0.48)^t][/tex] x 100%
percent rate of change = [-0.17/0.65] x 100%
percent rate of change = -26.15%
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Off track biking charges an hourly rate for mountain bike lessons and adds a charge of $100 for insurance. The overvalued cost (C) is represented by the formula, C=40h + 100 where h is the number of hours of lessons. Ben has 7 hours of lessons with off track biking.
How much does he pay?
Answer:
Step-by-step explanation:
If Ben has 7 hours of lessons with Off Track Biking, we can find the total cost (C) using the formula:
C = 40h + 100
where h is the number of hours of lessons. Substituting h = 7, we get:
C = 40(7) + 100
C = 280 + 100
C = 380
Therefore, Ben pays $380 in total for his 7 hours of lessons with Off Track Biking.
3. Zachary earned $4, 236 in August as a salesman at the racetrack. His earnings include his monthly salary of $700 and commission. If Zachary's sales totaled $10, 654, what is his rate of commission?
-approximately 30.6%
-approximately 28.4%
-approximately 29.8%
-approximately 33.2%
Answer:
approximately 33.2%
Step-by-step explanation:
Find Zachary's commission by subtracting his basic salary from total monthly earnings.
Commission = 4236 - 700
= $ 3536
[tex]\sf rate \ of \ commission = \dfrac{commission}{total \ sales}*100[/tex]
[tex]\sf = \dfrac{3536}{10654}*100\\\\ = 33.19 \%\\ = 33.2 \%[/tex]
given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. determine whether the system has a solution and find the solution(s) to the system, if they exist.
We have solution as:
z =z and y -8-z
The solution set is
x=9, y = -8-z, w = 1, z = z
Matrix:Matrix is an arrangement of numbers into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular arrangement of numbers into rows and columns. For example, matrix A has two rows and three columns.
The augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations.
[ 1 0 0 0 | -9 ]
[ 0 1 1 0 | -8 ]
[ 0 0 0 1 | 1 ]
We find that this is a rectangular matrix 3 rows and 4 columns
i.e. the variables are four but independent equations are only 3.
So only parametric equations can be found out
First row gives x = -9
Last row gives w = 1
II row gives y + z =-8 and we do not have any other equation in y or z
Hence we have solution as:
z =z and y -8-z
The solution set is
x=9, y =-8-z, w =1, z=z
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The given question is incomplete, complete question is :
Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. Determine whether the system has a solution and find the solution(s) to the system, if they exist.
[ 1 0 0 0 | -9 ]
[ 0 1 1 0 | -8 ]
[ 0 0 0 1 | 1 ]
A) x=-9, y=-8, z=-8, w=1
B) No solution.
C) x=-9, y=-8, z=1
D) x=-9, y=-8+z, w=1, z=any real number
E) z=-9, y=-8-z, w=1, z=any real number
F) None of the above.
The width of a rectangle is 4.25y-7.5 feet and its length is 7.5y+8 feet. Find the perimeter of the rectangle.
The perimeter of the rectangle is (23.5y + 1) feet.
The perimeter of the rectangle formula:
The perimeter = the width + the length + the width + the length
The perimeter = 2 × (the width + the length)
The perimeter = 2 × ((4.25y - 7.5) + (7.5y + 8))
The perimeter = 2 × ((4.25y + 7.5y) + (- 7.5 + 8)
The perimeter = 2 × (11.75y + 0.5)
The perimeter = 23.5y + 1
So, the perimeter of the rectangle is (23.5y + 1) feet.
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Work out the percentage change when a price of £50 is decreased to £40.
pls give simple working out :)
Answer: They took away 5%
Step-by-step explanation:
If you get 50 and the you have 40 you get 5%
Maths question attached
(a) The scale factor from shape A to shape B is 3/4.
(b) The value of w is 21/4 cm.
What is sale factor?A scale factor is the ratio of the new object to a given original object.
For example,
The size of original object is A.The size of new object is B.They have the similar shape.The scale factor is A : B.
We have two similar trapezoid as shown in the picture.
Find (a) the scale factor from shape A to shape B, and (b) the value of w!
The scale factor from shape A to shape B can be determined by analyzing one of the side length. We can take the longest side of the trapezoid.
Scale factor = 9/12 = 3/4
The value of w side is correspond to 7. So,
w/7 = 3/4
w = 3/4 × 7
w = 21/4 cm
Hence, the scale factor is 3/4 and the value of w is 21/4 cm.
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hassan built a fence around a square yard. it took 48 m 2 48 m 2 48, start text, space, m, end text, squared of lumber to build the fence. the fence is 1.5 1.51, point, 5 meters tall. what is the area of the yard inside the fence?
The fence surrounds a square yard with an area of 64 square meters. We first have to find length of fence and then multiply it by itself.
Given that it took 48 square meters of lumber to build the fence, and the fence is 1.5 meters tall, we can calculate the area of the yard inside the fence. To do this, we need to determine the total length of the fence. If we assume that the fence is built around a square yard, then the length of each side of the yard will be equal to the total length of the fence divided by 4.
Let's call the length of each side of the yard x. Then, the area of the yard inside the fence is x * x, or x^2. The total length of the fence is 4 * x. Since the fence is 1.5 meters tall, the total area of the lumber used to build the fence is 4 * x * 1.5, or 6x. This is equal to 48 square meters, so we have the equation:
6x = 48.
Solving for x,
x = 8.
Therefore, each side of the yard is 8 meters long.
Area of the yard inside the fence = 8 * 8 = 64 square meters.
This means that the fence surrounds a square yard with an area of 64 square meters.
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To get the echo of a positive integer, we write it twice in a row without a space. For example,
the echo of 2023 is 20232023. Is there a positive integer whose echo is a perfect square? If
so, how many such positive integers can you find? If not, explain why not.
Answer: Yes, but it's extremely hard to find
Step-by-step explanation:
The echo number 20222022202220222022 is the perfect square of 4496890281.
What echo number is a perfect square
An echo number has a perfect square if its square root is also a natural number. After some iterations we found that echo number 20222022202220222022 is a perfect square:
The echo number 20222022202220222022 is the perfect square of 4496890281.
A store employee creates a display of gymnastics mats priced at $73 apiece. The store paid $50 for each gymnastics mat. What percentage is the mark-up?
Suppose you know that ∠S and ∠Y are complementary and that m∠S = 3(m∠Y) − 70°. Find m∠Y. (help pls)
The measure of angle m∠Y as required to be determined given that the two angles S and Y are complementary is; 40°.
What is the measure of angle Y?As evident in the task content; ∠S and ∠Y are complementary.
Therefore; m∠S + m∠Y = 90°.
Also, since; m∠S = 3(m∠Y) − 70°.
By substitution;
3(m∠Y) − 70° + m∠Y = 90°
4m∠Y = 160°
m∠Y = 40°.
Ultimately, the measure of angle Y as required is; m∠Y = 40°.
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Matthew signed up for a streaming music service that costs $14 per moilth. The service allows Matthew to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $1.50 per song. How much total money would Matthew have to pay in a month in which he downloaded 15 songs? How much would he have to pay if he downloaded s songs?
Answer:p-by-step explanation:
15 x$1.50 is $22.50 then add that to the monthly fee of $14.00 for a total of $36.50
find the quotient. simplify your answer. 3b/4 divided by -c/6
The quotient of 3b/4 divided by -c/6 is -9b/2c
What are algebraic expressions?Algebraic expressions are simply defined as those expressions that are made up of coefficients, variables, constants, terms and factors.
They are also seen as expressions that are composed of mathematical or arithmetic operations, such as;
SubtractionAdditionMultiplicationDivisionParenthesesBracketFloor divisionFrom the information given, we have that;
3b/4 divided by -c/6
This is represented as;
3b/4 ÷ -c/6
Take the inverse of the divisor and multiply
3b/4 × 6/-c
18b/-4c
Divide the values
-9b/2c
Hence, the value is -9b/2c
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what information do you need to be given to be able to use trig function to solve for a missing side length of a right triangle?
Rebecca, Meg, and Kristin drive together for their home to visit their grandparents. Kristen drives 65 miles. Rebecca drives two times as far as Kristin. Then Meg drives twice as far as Kristin and Rebecca combined, which gets them to their grandparents house. How far did Meg drive?
Meg has drive 390 miles to visit Grandma.
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.
We are Given Number of miles Kristen drive = 65 miles
Rebecca drives two times as far as Kristin. Then Meg drives twice as far as Kristin and Rebecca combined
This means Number of miles Meg drive is equal to twice the number of miles driven Kristin .
Then equation we get;
Number of miles Meg drive = 2 × Number of miles Kristin drive =
Number of Miles Driven by Rebecca is equal to twice the sum of Number of miles Kristin drive and Number of miles Meg drive.
Then equation we get;
Number of miles Meg drive = 2 × (Number of miles Susie drive + Number of miles Meg drive) =
Hence Meg has drive 390 miles to visit Grandma.
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Rephrasing a question I had because people keep misunderstanding it
write the equation 8-2x= 3(y+1)^2 in x-h=a(y-k)^2 form
Step-by-step explanation:
[tex](8 - 2x) = 3(y + 1) {}^{2} [/tex]
If we factor out -2
[tex] - 2( - 4 + x) = 3(y + 1) {}^{2} [/tex]
[tex](x - 4) = - 1.5(y + 1) {}^{2} [/tex]
Disclaimer: this is a weird question because they would usually have you isolate the quadratic(the term being squared) but this is the answer is you're form you asked about
The vertex of this parabola is (4,-1)
Simplify
Sin A(cos A + sin A tan A)
The equation be Sin A(cos A + sin A tan A) then the trigonometric identities be tan (A).
What is meant by trigonometric identities?Trigonometric Identities are equality conditions that apply to all values of the equation's variables and which require trigonometry functions. There are numerous unique trigonometric identities that involve both the side length and angle of a triangle.
Trigonometry equations known as trig identities are used frequently to solve trigonometry and geometry problems and comprehend a variety of mathematical facts. Understanding and remembering fundamental mathematical concepts and resolving a variety of math issues are made easier by having a solid understanding of key trig identities.
Let the equation be Sin A(cos A + sin A tan A)
Express with sin, cos
[tex]$=\frac{\left(\cos ^2(A)+\sin ^2(A)\right) \sin (A)}{\cos (A)}$$[/tex]
Rewrite using trig identities
= tan (A)
Therefore, the equation be Sin A(cos A + sin A tan A) then the trigonometric identities be tan (A).
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Convert to the unit in brackets 1497 ml
(cm³)
After conversion, 1497 milliliters (ml) is equal to 1497 cubic centimeters (cm³) because 1 milliliter (ml) is equal to 1 cubic centimeter (cm³).
The units of volume, such as milliliters (ml) and cubic centimeters (cm³), measure the amount of space occupied by a substance. A milliliter (ml) is a unit of volume that is commonly used to measure small quantities of liquids. A cubic centimeter (cm³) is a unit of volume that is used to measure the volume of solid objects or substances.
One milliliter (ml) is equal to one cubic centimeter (cm³). This means that one milliliter of a substance takes up the same amount of space as one cubic centimeter of the same substance.
So, to convert 1497 milliliters (ml) to cubic centimeters (cm³), we simply use the conversion factor of 1 ml = 1 cm³:
1497 ml = 1497 * 1 cm³ = 1497 cm³
Therefore, 1497 milliliters (ml) is equal to 1497 cubic centimeters (cm³).
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Element X is a radioactive isotope such that its mass decreases by 8% every year. If an experiment starts out with 600 grams of Element X, write a function to represent the mass of the sample after t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent.
On solving the provided question we cans ay that the half life of the given exponential growth radioactive isotope will be 3.2894067399 years.
What is exponential growth?The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially. The exponential function has the formula f(x)=abx where a and b are positive real values. Sketch exponential functions using the app below for different values of a and b. Describe verbally how modifying a and b changes the graph's form.
Here, Element X starts with 490 grams
After 1 year we have (490 X 0.81 grams) or 396.9 grams
Now, We can solve for half-life by this equation:
Half life = (time X log 2) / log (beginning amount / ending amount)
Half-life = (1 year X 0.30102999566) / log (490 / 396.9)
Half life = (1 year X 0.30102999566) / log (1.2345679012 )
Half life = (0.30102999566) / 0.091514981109
Half-Life = 3.2894067399 years
Thus, the half life of the given exponential growth radioactive isotope will be 3.2894067399 years.
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Helpppppppp please i would like to have some help so i don't have to do it later
Answer:
Math ba yan? Wala ba diyan example kung pano i solvee yan?
Step-by-step explanation:
11 cm
assuming all sides angles are right angles, opposing sides are equal in length or total length.
top bottom.
x = 5 +6 = 11
x = 11 cm
Here is a point on a circle centered (0,0) at .
Which equation defines the circle?
The equation of circle is,
⇒ x² + y² = 100
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
Here is a point (6, 8) on a circle centered (0,0) at.
Now, Distance between the point (6, 8) and (0, 0) is,
⇒ D = √(6 - 0)² + (8 - 0)²
⇒ D = √36 + 64
⇒ D = √100
⇒ D = 10
We know that;
Distance between the point (6, 8) and (0, 0) is the radius of circle.
And, The equation of circle is,
⇒ (x - a)² + (y - b)² = r²
Where, (a, b) is center of circle and r is radius of circle.
Here, Center of circle = (0, 0)
And, Radius of circle = 10
So, We get;
The equation of circle is,
⇒ (x - a)² + (y - b)² = r²
⇒ (x - 0)² + (y - 0)² = 10²
⇒ x² + y² = 100
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for the figures below assume they are made of semicircle quarter circles and squares for each shape find the area and the perimeter. Give your answers as a completely simplified exact value in terms of pie (no approximations)
Thank you
The area of the combined figure is 98.64 sq cm and the perimeter of the combined figure is 91.88 cm.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
What are the area and perimeter of a rectangle?
We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know, The area of a triangle is (1/2)×base ×height and the area of the semicircle is (1/2)πr².
Also, the perimeter of a triangle is the sum of the lengths of all the sides and the perimeter of a semicircle is πr.
From the given figure The right angle triangle is an isosceles therefore, The length of the side BC is also 12 units.
Hence the area is = (1/2)×12×12 = 72 sq cm.
And The area of the semicircle is,
(1/2)×π×(√12² + 12²) sq cm.
= (1/2)×3.14×√(288) sq cm.
= 26.64 sq cm.
Therefore, The total area is (72 + 26.64) sq cm.
= 98.64 sq cm.
And the perimeter is,
= (12 + 12 + 16.97) + (3.14×16.97) cm.
= 91.88 cm.
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