The rewritten expression will be 4a³ and the value of this expression is -500.
Given in the question:
(2a⁴)² / a⁰a⁵
We know that
(xy)ⁿ = xⁿ × yⁿ ... (i)
We can use equation (i) for the next step of our given expression.
In the case of the numerator:
(2a⁴)² = 2² × a⁸ = 4a⁸
Now, we know, any number to the power of zero is 1.
So, for the denominator, we get:
a⁰a⁵ = 1 × a⁵ = a⁵
We know,
pˣ / pʸ = y ⁽ˣ⁻ʸ⁾ ... (ii)
Using this equation, we can further simplify the given expression:
⇒ 4a⁸ / a⁵
⇒ 4 a⁽⁸ ⁻ ⁵⁾
⇒ 4 a ³ ... (iii)
Now, in the second part of the question, we need to find the value of the expression.
Given a = -5
Putting this value in equation (iii) we get:
4 a ³
⇒ 4 (-5) ³
⇒ 4 × (-125)
⇒ -500
Hence, the simplified expression is 4 a ³ and the value of the simplified equation is -500.
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-9 ( x + 6)= -9x + 108
Answer: 0=1620=162
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
Solve for the value of k.
(2k-2)
(k+2)°
Answer:
30
Step-by-step explanation:
( 2k - 2 )°, 90° and ( k + 2 )° are linear pair angles.
Sum of linear pair angle is supplementary ( that is 180 ),
2k - 2 + 90 + k + 2 = 180
2k + k + 90 = 180
3k = 180 - 90
3k = 90
k = 90/3
k = 30
Note : -
□ means 90°
in a tournament there are six teams that play each other twice. a team earns 3 points for a win, 1 point for a draw, and zero points for a loss. after all the games have been played it turns out that the top three teams earned the same number of total points. what is the greatest possible number of total points for each of the top three teams?
The greatest possible number of total points for each of the top three teams is 24.
Given;
Six teams compete against one another twice in a tournament. A team receives three points for a victory, one point for a tie, and no points for a defeat. The top three clubs ended up with the same total number of points when all the games were completed.
After fully understanding the problem, we immediately know that the three top teams, say team A, team B, and team C, must beat the other three teams D, E, F. Therefore, A, B, and C must each obtain (3 + 3 + 3 ) = 9 points. However, they play against each team twice, for a total of 18 points against D, E, and F. For games between A, B, and C, we have 2 cases. There is an equality of points between A, B, and C in the following cases.
Case (I): A team ties the two other teams. For a tie, we have 1 point, so we have (1 + 1) * 2 = 4 points (they play twice).
Therefore, this case brings a total of 4 + 18 = 22 points.
Case (II): A team beats one team while losing to another. This gives equality, as each team wins once and loses once as well. For a win, we have 3 points, so a team gets 3 * 2 = 6 points if they each win a game and lose a game.
This case brings a total of 18 + 6 = 24 points.
Therefore, we use case (II) since it brings the greater amount of points as 24.
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FIND THE SLOPE FROM THE GRAPH
a.
b.
c.
d.
Answer:
A
Step-by-step explanation: Rise/run. is important
it goes up 4 and then over 6 and so we have to simplify which is 2/3 and snice it is going down it is negitive.
Find the measure of the exterior angle.
Answer:
since the degree of the adjacent angles is 180°, we find the answer from that
Answer:
128°
Step-by-step explanation:
it is a right triangle, the bottom right one is, from the drawing, 90 °, the sum of the internal angles of all the triangles is 180 °, so making 180 - 90 - 38 we have the missing internal angle of 52 °.
Then we find the outer angle, the inner-outer sum is 180 °, 180 - 52 = 128 ° (your answer)
Find h in the parallelogram shown.
h= ? ft
The required value of h is 5.29 ft in the parallelogram shown.
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
As per the given figure, the dotted lines create a triangle, and the hypotenuse of that triangle is the opposite base of the parallelogram, indicating that it is likewise 8 feet long.
The base of the newly made triangle is one of the parallelogram's diagonals, which is 6 feet long.
According to Pythagorean's theorem, we have
h² + 6² = 8²
h² + 36 = 64
h² = 28
h = √28
h = 5.29
Thus, the required value of h is 5.29 ft.
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Answer:
4
I did the i-ready, hope this helps! :)
2x² - 9 = 3x
A. {3,-1.5}
B. (-3,-1.5}
C. {-3, 1.5}
D. {3, 1.5}
The roots for the given quadratic equation 2x² - 9 = 3x is {3, -1.5}.
What is a quadratic equation?
The Quadratic equations are second-order polynomial equations such as ax² + bx +c = 0 for x, where a ≠ 0.
It has at least one solution that could be real or complex.
The given equation is 2x² - 9 = 3x.
Now expressing in the form of ax² + bx + c = 0, we get
2x² - 3x - 9 = 0,
a = 2, b = -3, c = -9, Now solving the above equation, we get
2x² - 6x + 3x - 9 =0
2x(x - 3) + 3(x - 3) = 0
(x - 3)(2x + 3) = 0
x - 3 = 0 (or) 2x + 3 = 0
x = 3 (or) x = -1.5
Hence, the roots of the equation are {3, -1.5}.
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How can the dimensions of algebra tile rectangles and area models be used to represent expressions and multiplication?
The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.
What is a Rectangle?This is referred to as a quadrilateral which has four right angles and the area is calculated by multiplying the length with the breadth.
In as situation where the algebra tile rectangles is used , it is best to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 8cm and the breadth is 5cm then the area will be 8cm × 5cm = 40cm²
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Solve the inequalityr divided by negative 2.5 is less than or equal to 8.7 for r.
Answer:
r ≤ -21.75
Step-by-step explanation:
Forming the equation,
→ r ÷ (-2.5) ≤ 8.7
Then the value of r will be,
→ r ÷ (-2.5) ≤ 8.7
→ r ≤ 8.7 × (-2.5)
→ r ≤ -21.75
Hence, value of r is -21.75.
10.7 10.9 11.3 11.6 11.8 12.2 12.3 13
what is the mean of this set
Answer:
11.725
Step-by-step explanation:
Add all the numbers together and divide it by how many numbers are in the set
The equation x=-2 is graphed on the coordinate plane shown.
What is the equation of the line perpendicular to x=-2 that passes through (-9,3)?
What is the parallel line and what is the perpendicular line.
We will see that the linear equations are:
Parallel line: x = -9
Perpendicular line: y = 3
How to get the parallel and perpendicular lines?Here we have the vertical line:
x = -2
A parallel line to this one will also be vertical, of the form:
x = a
And a perpendicular line to this one will be horizontal, of the form:
y = b
We want the parallel line to pass through (-9, 3)
So our line x = a needs to pass through that point, then:
x = -9
Is the parallel line.
And if the perpendicular line y = b needs to pass through that point, then:
y = 3
Is the perpendicular line.
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Write another number puzzle with at least three steps. On a different piece of paper, write
a solution to your puzzle.
Puzzle:
A man walked certain distance first. Then, walked 12 miles. Again walked twice the distance he walked at first. Now, the total distance is 42 miles. what is the initial distance?
The initial distance is 10 miles
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Puzzle:
A man walked certain distance first. Then, walked 12 miles. Again walked twice the distance he walked at first. Now, the total distance is 42 miles. what is the initial distance?
Let x= initial distance
x+12+2(x)=42
3x+12=42
3x=42-12=30
x=30/3=10 miles
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24.15 as a two significant figures?
24.15 as two significant figures is 24.
What are significant figures?All significant figures are those that enhance the overall worth of the number's meaning. Numbers are frequently rounded to avoid repeating quantities that are not significant. When rounding, one must be careful not to lose precision. Sometimes the purpose of rounding numbers is simply to make them simpler.
What are the significant figure's rules?Use the following guidelines to decide which numbers are important and which are not:
1) A decimal number less than 1 is not affected by the zero to the left of it.
2) The placeholders for all trailing zeros are all insignificant.
3. There should be significance between non-zero numbers.
4) Every non-zero number has meaning.
5) A number is rounded if it has more digits than the necessary number of significant ones. For instance, 432,500 is rounded up to 433,000 to three significant digits using the half-up (regular) method.
6) Zeros at the end of numbers that are not important but are left in because eliminating them would change the number's value. The 000 in 433,000 in the example above cannot be removed without converting the number to scientific notation.
Given the number, 24.15
We have to convert it to two significant figures, so we will consider the only two figures before the decimal point. So, the number up to two significant figures is 24.
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I need help like asap !!!
only numbers and decimal points
Now we have to,
→ find the required value of c.
Formula we use,
→ (AC)² = (BC)² + (AB)²
Then the value of a will be,
→ c² = (8.1)² + (8.1)²
→ c² = 65.61 + 65.61
→ c² = 131.22
→ c = √131.22
→ [ c = 11.46 yd ]
Hence, value of c is 11.46 yd.
Where do i start?
This is only a grade 11 math problem thanks
The smallest positive integer is 267 that should be multiply with given series.
What is meaning of series?
A series in mathematics is the total of a given set of terms. Real or complex numbers are typically used in these terms, but considerably more generality is conceivable.
Given series is 3, 6, 9, .... , 2400.
Assume that n should be multiply with the given series.
The series becomes 3n, 6n, 9n, .... , 2400n.
Now add the series:
(3n + 6n + 9n + ....+ 2400n)
Taking common 3n:
= 3n( 1 + 2 + 3 + ...+ 800)
Apply the formula the sum of the first n positive integers is n(n+1)/2
= 3n ×{800(800+1)}/2
=3n × 400 × 801
= 3n × 4 × 100 × 3 × 3 × 89
= (4 × 100 × 3 × 3) × (3 × 89) × n
The product of (4 × 100 × 3 × 3) is a perfect square. But 3 × 89 is not a perfect square. Thus n = 3 × 89 = 267.
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Question 2 of 10 Which of the following is equal to the fraction below? (5/8)
The fraction that is equivalent to the fraction expression given as 5/8 is 40/64
How to evaluate the expression?From the question, we have the following fraction expression that can be used in our computation:
Fraction = 5/8
The above expression is a fraction and at the same time it is a rational number
The denominator of the fraction is 8
So, we start by rationalizing the expression by the fraction
This is represented as
5/8 = 5/8 * 8/8
Evaluate the products of the numerator
So, we have the following representation
5/8 = 40/8 * 1/8
Evaluate the products of the denominator
So, we have the following representation
5/8 = 40/64
The above expression cannot be further simplified
Hence, the equivalent expression of the fraction is 40/64
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Possible question
Which of the following is equal to the fraction below? (5/8)
40/64
0.556
2/5
The equation below describes a function of x . y=−4x+12
The solution for x in the function when the equation y=−4x+12 equals -12 is -6
How to determine the solution for x in the function?From the question, we have the following equation that can be used in our computation:
y=−4x+12
To make the equation legible, we need to rewrite it
So, we have the following representation
y = −4x + 12
Also from the question, we have
y = -12
This means that we calculate x when y = -12
Substitute the known values in the above equation, so, we have the following representation
-12 = -4x + 12
So, we have the following equation
-4x + 12 = -12
Add -12 to both sides of the equation
So, we have the following representation
-4x + 12 - 12 = -12 - 12
Evaluate the like terms in the equation
-4x = -24
Divide both sides of the equation by -4
x = 6
Hence, the solution is 6
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Possible question
The equation below describes a function of x . y=−4x+12
Solve for x when y = -12
PL zz HELP WILL GIVE BRAINILIST
Answer:
n + 2
Step-by-step explanation:
If n is the smallest of three consecutive integers, the largest in the sequence must be only two integers greater.
What are the solutions to the equation?
Finding the value of the given equation's unknown variables is a step in the equation-solving process. The value of the variable satisfies the requirement that the two expressions are equal and is called the solution of that equation.
What Does Solving Equations Mean?Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. When a condition on variable guarantees that two expressions in the variable have the same value, it qualifies as an equation.
The variable's value for which the equation holds true is referred to as the equation's solution If the LHS and RHS are switched, an equation doesn't change. The answer is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are working with, we can solve it. There are several types of equations, including linear, quadratic, rational, and radical ones.
When a linear equation has one variable, there is only one solution; when there are two variables, there are two solutions. A quadratic equation's solution yields two roots. To solve an equation, a variety of techniques and steps are used.
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Help Please!
Solve the inequality and graph it’s solution.
The solution of given inequality is x≤-2.
What is inequality?
Inequality (mathematics), a relation between two numbers or quantities indicating which of them is greater or smaller. An inequality is denoted by the symbol <, which is drawn pointed toward the smaller number.
The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things.
p ≠ q means that p is not equal to q
p < q means that p is less than q
p > q means that p is greater than q
p ≤ q means that p is less than or equal to q
p ≥ q means that p is greater than or equal to q.
Given, inequality
8x - 5x ≤ -6
3x ≤ -6
x≤ -6/3
x≤ -2.
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the option a is the correct option.
XY is an angle bisector of ΔAXN. Find the length of side XN
The length of XN is 6
What is the angle bisector theorem?According to the triangle angle bisector theorem, any angle in a triangle will divide the opposite side in a ratio equal to the ratio of the sides that contain the angle.A line or ray that divides an angle in a triangle into two equal parts is known as an angle bisector. The two fundamental characteristics of an angle bisector are that each point on it is equally spaced from its sides and that it divides the opposite side of a triangle in proportion to its adjacent sides, which is known as the triangle's angle bisector property.Calculation
By angle bisector theorem
[tex]\frac{AX}{NX} =\frac{AY}{NY}[/tex]
[tex]\frac{18}{NX} =\frac{12}{4}[/tex]
[tex]NX=\frac{18*4}{12} =6[/tex]
Therefore, the length of side NX in the given triangle is 6.
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The length of side NX in the given triangle is 6.
What is the angle bisector theorem?According to the triangle angle bisector theorem, any angle in a triangle will divide the opposite side in a ratio equal to the ratio of the sides that contain the angle.A line or ray that divides an angle in a triangle into two equal parts is known as an angle bisector.The two fundamental characteristics of an angle bisector are that each point on it is equally spaced from its sides and that it divides the opposite side of a triangle in proportion to its adjacent sides, which is known as the triangle's angle bisector property.By angle bisector theorem
According to the angle bisector theorem, PQ/PR = QS/RS or a/b = x/y. An angle bisector is a line or ray that divides an angle in a triangle into two equal measures
Therefore, the length of side NX in the given triangle is 6.
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work out the circumferecnce of this cricle take π to be 3.142 and write down all the digits given by your calculator 16.8cm
The circumference of the circle with a radius of 16.8 cm is 105.504 cm
How to calculate the circumference?The given parameters are
Radius = 16.8 cm
As a general rule, radius are represented by the variable r
So, we have the following representation equation
r = 16.8 cm
The circumference of the circle is then calculated as
C = 2πr
Next, we substitute the value of the variable r in the above equation
i.e. r = 16.8 cm
So, we have the following equation
C = 2π * 16.8 cm
From the question, we have
π = 3.14
So, we have the following equation
C = 2 * 3.14 *16.8 cm
Evaluate the products
So, we have the following equation
C = 6.28 *16.8 cm
Evaluate the products
C = 105.504 cm
Hence, the circumference is 105.504 cm
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The difference between an Arithmetic Sequence and a Linear
Function:
O The Linear Function has a y-intercept.
O All the points on a Linear Function connect.
O The Domain of the Linear Function includes negative numbers.
O All of the above
All the statements about Arithmetic sequence and linear function are correct.
What is Arithmetic sequence and linear function?
When used in mathematics, the term "linear function" describes two different but related ideas: A linear function, also known as a polynomial function of degree zero or one, is a function in calculus and related fields that has a graph that is a straight line.
In an Arithmetic Sequence the difference between one term and the next is a constant. In other words, we just add the same value each time.
Since the Linear Function has a y-intercept.
Also all the points on a Linear Function connect.
When a line slopes down from left to right, it has a negative slope. This means that a negative change in y is associated with a positive change in x.
That means the Domain of the Linear Function includes negative numbers when the function is decreasing.
Therefore, all the statements are correct.
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average temperatures were measured at five randomly selected soups. the x-bar and r-bar were found 45.25 degree and 1.05 degree, respectively. the uclr and lclr are:
The UCLR (Upper Control Limit) and LCLR(Lower Control Limit) are 2.22 and 0 respectively.
Given that,
At five soups that were chosen at random, average temperatures were recorded. X-bar and r-bar positions were 45.25 degree and 1.05 degree, respectively.
To find : UCLR (Upper Control Limit) and LCLR (Lower Control Limit)
R-bar = 1.05 Degrees
X-bar = 45.25 Degrees
Sample Size , n=5
D3=0
D4=2.114
3 Sigma control limits of Range Chart
LCLR = D3*R-bar = 0*1.05 =0
UCLR =D4*R-bar = 2.114*1.05 = 2.22
The UCLR (Upper Control Limit) and LCLR (Lower Control Limit) are therefore 2.22 and 0, respectively.
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The map shows a portion of downtown Mapledale. Main Street and 2nd Avenue are parallel. Use the map to answer each question. Question Angle Which angle is an alternate exterior angle to angle 8? Which angle is a same-side interior angle to angle 2? Which angle is a corresponding angle to angle 3?
a. Angle 4 is an alternate exterior angles to angle 8.
b. Angle 3 is same-side interior angle to angle 2.
c. Angle 1 is corresponding angles to angle 3.
What are Corresponding Angles?Corresponding angles are located on the same corner and on the same side of a transversal.
For example, in the given image below, angles 1 and 3 are corresponding angles.
What are Alternate Exterior Angles?Alternate exterior angles are any two exterior angles that lie on two different parallel lines but on alternate sides of the transversal that crosses the two parallel lines.
For example, in the image given, angles 8 and 4 are alternate exterior angles.
What are Same-side Interior Angles?Same-side interior angles are interior angles that are located on the same side of the transversal but on different parallel lines that the transversal cuts across.
For example, angles 2 and 3 are same-side interior angles as seen in the given image.
What are Corresponding Angles?Corresponding angles are located on the same corner and on the same side of a transversal.
For example, in the given image below, angles 1 and 3 are corresponding angles.
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a percentage distribution is given below for the size of families in one u.s. city. size percentage 2 42.8 3 21.1 4 19.2 5 11.6 6 3.3 7 2.0 a family is selected at random. find the probability that the size of the family is 4 or more. round your result to three decimal places.
The probability that the size of the family is 4 or more rounded to three decimal places is 0.361.
Given that families are selected at random, to find the probability that the size of family 4 we need to select and add those probabilities whose family size is more than and equal to 4.
P(X ≥ 4) = P(4) + P(5) + P(6) + P(7)
P(X ≥ 4) = 19.2 + 11.6 + 3.3 + 2.0
P(X ≥ 4) = 36.1
Since we need the answer rounded off to three decimal places, we can divide the answer by 100 which will give the final answer which is 0.361.
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Given that D( x ) = 2 x , select all of the following that are true statements. D( x ) is a direct variation. D( x ) is a function. D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). x is the dependent variable. D(6) = 3 1 Attempts Remain
The true statements are:
D(x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4).D(x) is a direct variation.x is the dependent variable.D(x) is a function.How to determine the true statements?The function is given as D(x) = 2x
The function D(x) is a linear function, and it is also a proportional function
Proportional functions represent direct variation
This means that (b) and (e) are true
Also set x = 5, 6 and -2
So, we have the following equations
D(5) = 2 x 5 = 10
D(6) = 2 x 6 = 12
D(-2) = 2 x -2 = -4
This means that (a) is true
Lastly, the function D(x) is dependent on x for its value
This means that x is the dependent variable.
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7. A bag of marbles contains 3 green, 7 red, 2 white
and 8 black marbles. If a marble is randomly
chosen, what is the probability that the marble will
NOT be green or white?
a. 25%
b. 50%
C. 60%
d. 75%
e. 80%
Answer: 50%
Step-by-step explanation:
Answer:
D. 75%
Step-by-step explanation:
There are 20 marbles, so each 1 has a chance of 5% If you were to choose randomly 75% of the time you will get either red or black and 25% you will get green or white
Lines n and o are parallel and are cut by the transversal p.
What is the value of x?
Answer:
Step-by-step explanation:
here the alternally exterior angle sum property:
48°+(2x+2)°=180°
⇒2x+2°=180°-48°
⇒2x+2°=132°
⇒2x=130°
⇒x=65°
or Line p has an equation of y= – 8x+6. Line q, which is perpendicular to line p, includes the point (2, – 2). What is the equation of line q?
Answer:
y = 1/8 x - 9/2
Step-by-step explanation:
slope of line q = 1/8
y-(-2)= 1/8(x-2)
y+2 = 1/8 x - 1/4
y = 1/8 x - 1/4 - 2
y = 1/8 x + (-1-8)/2
y = 1/8 x -9/2
