(-4mn)³*(-2m²)³ How do I simplify this?
Simplifying the given expression can be rewritten as: [tex](512m^9n^3)[/tex].
Power RulesThe main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents. Power. For this rule, you should repeat the base and multiply the exponents.Exponent negative - For this rule, you should write the reciprocal number with the exponent positive. Zero Exponent. When you have an exponent equal to zero, the result must be 1.For simplifying the given expression, it is necessary to apply the presented power rules previously.
The given expression is (-4mn)³*(-2m²)³. Thus,
Applying the rule - Power, you have:(-64m³n³) * [tex](-8m^6)[/tex]
Note that the rule should be apply in numbers and letters.
After that, you should apply the rule of Multiplication. See below:[tex](512m^9n^3)[/tex]
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Anu brought an air cooler, its water tank is in the shape of a cuboid and can take 40 liters of water. Its dimensions are 50 cm x 20 cm. What will be the height of the water tank?.
The height of the water tank given the volume, length and width is 40 cm
What is the height of the water tank?Volume of the water tank= 40 liters
Length of the water tank= 50 cm
Width of the water tank= 20 cm
Height of the water tank= x
convert liters to centimeters
1 liter= 1000 cm
40 liters= 40,000 cm
Volume of the water tank= length × width × height
40,000 = 50 × 20 × x
40,000 = 1000x
divide both sides by 1000
x = 40,000 / 1000
x = 40 cm
Therefore, the height of the water tank is 40 cm
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a = [1 0 -4 0 3 -2 -2 6 3] b = [4 1 -4] Denote the columns of A by a1, a2, a3, and let W = Span {a1, a2, a3,}. a) is b in {a1, a2, a3,}? how many vectors are in {a1, a2, a3,}? is b in W?
If a = [tex]\left[\begin{array}{ccc}1&0&-4\\0&3&-2\\-2&6&3\end{array}\right][/tex] , b = [tex]\left[\begin{array}{ccc}4\\1\\-4\end{array}\right][/tex] and we denote the columns of A by a₁, a₂, a₃, and let W = Span {a₁, a₂, a₃,} , then b is not in {a₁, a₂, a₃} .
The Span of set of vectors is set of all linear combinations of those vectors. In other words, it's the set of all possible vectors that can be created by taking a weighted sum of the original vectors.
The span of a set of vectors is a subspace of the vector space in which the vectors lie, and it's the smallest subspace that contains all of the original vectors.
The vector b is not in {a₁,a₂,a₃} because "b" is not equal to any of the column vectors of A. Clearly, there are only 3 vectors in {a₁,a₂,a₃}.
The given question is incomplete , the complete question is
a = [tex]\left[\begin{array}{ccc}1&0&-4\\0&3&-2\\-2&6&3\end{array}\right][/tex] , b = [tex]\left[\begin{array}{ccc}4\\1\\-4\end{array}\right][/tex] . Denote the columns of A by a₁, a₂, a₃, and let W = Span {a₁, a₂, a₃,}. Is b in {a₁, a₂, a₃} ?
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the sum of eleven and a number c
Answer:
11 + C
Step-by-step explanation:
Sum= +
You add 11 and C
what's the difference between discrete math and continuous math like calculus?
Discrete mathematics is focused on discrete objects and the relationships between them, while calculus is focused on continuous change and motion.
Discrete mathematics and calculus are two branches of mathematics that deal with different types of mathematical objects and concepts. Discrete mathematics studies discrete objects, such as integers, graphs, and algorithms, while calculus deals with continuous and smooth objects and their derivatives and integrals.
Discrete mathematics provides the mathematical foundations for computer science, especially in areas such as algorithm design, data structures, and complexity theory.
In contrast, calculus is a branch of mathematics that focuses on continuous change, and provides a foundation for many other branches of mathematics and science, including physics, engineering, and economics.
In discrete mathematics, concepts are studied in a finite and countable manner, meaning that the objects and structures being studied can be counted and identified.
For example, in graph theory, discrete mathematical structures like vertices and edges are studied and their properties are analyzed. In discrete mathematics, the focus is on finding relationships between discrete objects and how they can be manipulated, such as in combinatorics and number theory.
On the other hand, calculus deals with the study of change and motion, specifically the rate at which objects change and the accumulation of these changes over time.
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Find the best approximation to a solution of the following systems of equations. What the value for x? 4x 2y = 0 x +y = 11 -2 2 1
The best approximation to a solution of the system of equations is x = -11 and y = 22.
A system of equations is a collection of two or more equations with the same variables. Solving a system of equations means finding the values of the variables that satisfy all the equations in the system.
In this case, you have a system of two equations:
4x + 2y = 0 and x + y = 11.
To find the best approximation to a solution of the system, we can use substitution or elimination methods.
First, we can isolate one of the variables in one of the equations.
=> 4x + 2y = 0.
Dividing both sides by 2, we get:
=> 2x + y = 0.
Now we have one equation in terms of one variable, which is y.
Next, we can substitute the expression for y from this equation into the second equation:
=> x + y = 11.
Replace y with -2x
=> x + (-2x) = 11.
=> -x = 11.
=> x = -11.
Finally, we can substitute the value for x back into one of the original equations to find the value of y.
Let's substitute x = -11 into the first equation:
=> 4(-11) + 2y = 0.
=> -44 + 2y = 0.
=> 2y = 44.
=> y = 22.
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Given A(2,1), B(6,3), C(8,1), D(4,2) and E(5,1), shown below, prove that.
Note that the hint to demonstrating the above proof (that ΔABC ≅ ΔADE) is to compare the slopes of DE and BC. See the computation below.
What is a slope?The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
Comparing both slopes, we have:
Slope of DE = 2-1/4-5 = 1/-1 = -1
Slope of BC = 3-1/6-8 = 2/-2 = -1
Since the slope of DE and BC are the same an they are not intersection, it means they are parrallel lines.
Since DE || BC
In ΔABC and ΔADE
∠DAE = ∠BAC
∠ADE ≈ ∠ABC (Correspoinding Angle)
∠AED = ∠ACB (Corresponding Angles)
Thus, ΔABC ≅ ΔADE.
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Full Question:
Given A(2,1), B(6,3), C(8,1), D(4,2) and E(5,1), shown below, prove that ΔABC ≅ ΔADE
-1 = 2x - y, 8x - 4y = -4 using substitution
Answer:
Infinitely many solutions
Explanation:
1) subtract “1” from both sides to get y by itself
Y=-2x-1
2) 4y+8x=-4 share a gcf of “4” so you can divide the whole equation by 4
y+2y=-1
Now substitute “-2x-1” as y
(-2x-1)+2x=-1
-2x and 2x cancel each other and so does -1 and -1
Hence, this system has infinitely many solutions
Answer:
x = 0, y = 1.
Step-by-step explanation:
We can solve for the variables x and y by using substitution. Let's start by solving the first equation for one of the variables:
-1 = 2x - y
y = 2x + 1
Next, we'll substitute y = 2x + 1 into the second equation:
8x - 4y = -4
8x - 4(2x + 1) = -4
Expanding the second equation:
8x - 8x - 4 = -4
-8x - 4 = -4
-8x = 0
x = 0
Finally, we can use one of the equations to find y:
y = 2x + 1
y = 2(0) + 1
y = 1
So, the solution is x = 0, y = 1.
If 3 lbs of fertilizer will cover 408 square feet of lawn, how many pounds would be needed to cover 1088
square feet?
One pound of nitrogen or mixed fertilizer is recommended per 1,000 square feet of lawn and your particular fertilizer contains 20% nitrogen.
How many pounds would be needed to cover 1088 square feet?
In order to calculate pounds per square foot you just need to do some simple math. Simply take the area (in square feet) you want to use as a measurement and divide the number of pounds you want to place on the area by that number.Two gallon cans of paint cover up to 800 square feet, which is enough to cover an average size room. This is the most common amount needed, especially when considering second coat coverage. Three gallon cans of paint cover up to 1200 square feet.Pounds or Pounds Force per Square Foot is a British (Imperial) and American pressure unit which is directly related to the psi pressure unit by a factor of 144 (1 sq ft = 12 in x 12 in = 144 sq in). 1 pound per square foot equals 47.8803 pascals.To learn more about pounds refers to:
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Solve for x in the diagram below
The value of the variable x in the given right angle expression is; x = 11
How to solve right angle problems?We know that a right angle simply means an angle that is equal to 90 degrees.
Now, we see that the sum total of the angle in the diagram is 90 degrees and as such the sum of the two internal angles will be 90 degrees.
Thus;
5x + 35 = 90
Subtract 35 from both sides to get;
5x = 55
x = 55/5
x = 11
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find the equation of the tangent line to the graph of the function f(x)=x 1x−4 at the point (0,−14)
The equation of the tangent line to the graph of the function f(x)=x 1x−4 at the point (0,−14) is 4x + y +14 = 0.
To find the tangent equation we need slope and intercept for the equation.
To find slope we need to differentiate the given function as the differentiation at a given point gives us the slope :
firstly differentiate the given function :
f(x)=x(x−4)
= x^2 - 4x
f'(x) = 2x - 4
f'(x) at (0,-14) = 2(0) - 4
= -4
Hence , the slope is -4
Use the formula to find the equation of the tangent line that passes through a point (x1, y1) with the slope m, that is, y-y1=m(x-x1).
y-y1=m(x-x1) at a point (0,−14)
y - (-14) = -4 (x-0)
y+14 = -4x
therefore, 4x + y +14 = 0 is the required equation of the tangent.
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[02.03]
Solve for x: -3|2x + 61 = -12 (1 point)
O x = 1 and x = 5
O x = -1 and x = -5
O x = -9 and x = 3
O No solution
For, -3 |2x + 6| = -12 the value of x = -1 and - 5
Correct option is: x = -1 and x = -5. This can be solved using the concept of equation.
What is an equation?Equations simultaneously, or a system of equations Multiple equations in algebra must be solved simultaneously. There must be an equal number of equations and unknowns for a system to have a singular solution. When two or more equations use the same variables, they are said to be in a system of equations. Graphing, substitution, and elimination are the three techniques used to solve systems of equations.
-3 |2x + 6| = -12
or, 2x + 6 = 4
or, 2x + 6 = ± 4
or, 2x + 6 = 4
or, 2x = -2
or, x = -1
on the other hand,
2x + 6 = -4
or, 2x = - 10
or, x = -5
So, the value of x = -1, and -5
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Mr adbul made tuna and curry potato filling for ome puff. 3/5 of the filling he made wa tuna and the ret wa curry potato
Answer is 2 5/8 tuna filling at first.
How much tuna filling did he make at first?At first, he made 2 5/8 kg of tuna filling.
M r Abdul made tuna and curry potato filling for some puffs.
3/5 of the filling he made was tuna and the rest was curry potato.
So, amount of curry potato = 1- 3/5 = 2/5
Ratio of tuna & curry potato = tuna : curry potato
= 3/5 : 2/5 = 3 : 2
Let amount of tuna = 3x & amount of curry potato = 2x
After he used 1/8kg of the tuna filling and made another 3/4 kg of curry potato filling.
According to the question, he then had equal amounts of tuna filling and curry potato filling left.
So, 3x - 1/8 = 2x + 3/4
Multiplying 8 in both sides we get,
⇒ 24x - 1 = 16x +6
⇒ 24x - 16x = 7
⇒ 8x = 7
⇒ x = 7/8
So, 3x = (3×7/8) = 21/8 kg = 2 5/8 tuna filling at first.
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the isosceles trapezoid is part of an isosceles triangle with a 42 vertex angle. what is the measure of an acute base angle of the trapezoid? of an obtuse base angle? the diagram is not to scale
The measure of the acute base angle is 69°
The measure of the obtuse base angle is 111°
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Isosceles triangles mean two sides are equal and the angles opposite to the equal sides are also equal.
Now,
Isosceles trapezoid
Vertex angle = 42
This means,
The other two angles will be the same.
x + x + 42 = 180
2x = 180 - 42
2x = 138
x = 69
Now,
The opposite angles of an isosceles trapezoid are supplementary.
So,
Obtuse base angle + Acute base angle = 180
Obtuse base angle + 69 = 180
Obtuse base angle = 180 - 69 = 111
Thus,
Acute base angle = 69°
Obtuse base angle = 111°
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The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:
Triangle ABC has length of BC equal to 12 inches. A line segment DC joins the point D on AB with point C. Measure of angle ABC is 90 degrees, ACD is 15 degrees, and measure of angle DCB is 30 degrees.
What is the length of the wood that is needed to replace AD?
A. 6.2
B. 4.2
C. 6.9
D. 5.1
The length of the side AD that needed to be replaced is D. 5.1
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.
We know, tan = opposite/adjacent.
tan30° = DB/12.
DB = 12×tan30°.
DB = 6.93.
Now, m∠BCA = 30° + 15° = 45°.
Therefore,
tan45° = (AD + DB)/12.
AD + DB = 12.
AD = 12 - 6.93.
AD = 5.1.
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Answer:
5.1
Step-by-step explanation: got right on test
The function f(x)=x√ is horizontally stretched by a factor of 2 to form function g(x).
What is the equation of g(x)?
The solution is , The equation of g(x) is g(x) = 2*x^(1/2).
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
The original function f(x) is defined
as f(x) = x^(1/2)
which is the square root of x.
When the function is stretched horizontally by a factor of 2,
the x term becomes 2x.
So the new function g(x) is defined
as g(x) = 2*x^(1/2)
Hence, The solution is , The equation of g(x) is g(x) = 2*x^(1/2).
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If 5 glue sticks cost $9.65., then which equation would help determine the cost of 21 glue sticks?
.
5/$9.65 =21/
.
21/5=$9.65/
.
5/=21/$9.65
.
21/= $9.65/5
The equation which would help determine the cost of 21 glue sticks is 5 / 9.65 = 21 / x, where x is the cost of 21 glue sticks.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
Given that,
Cost of 5 glue sticks = $9.65
Let x be the cost of 21 glue sticks.
Using proportional concept,
5 / 9.65 = 21 / x
Hence the equation is 5 / 9.65 = 21 / x
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A basketball player has made 13 out of 20 free throws so far this season. How many
consecutive free throws must the basketball player make to raise the free throw average
to 0.75? Justify your answer.
Answer:
Step-by-step explanation:
x=8
Assume 2. 0 kg of apples is 1 dozen and that each apple has 8 seeds. How many seeds are in 14 kg of apples?.
Answer:56
Step-by-step explanation:
You divide 14kg by 2kg and get 7kg. So then you times 7kg by 8 seeds.
Hope this helps :)
Find the circumference of the circle
Answer:
C
Step-by-step explanation:
the circumference of a circle is
2×pi×r
r being the radius, which is half of the diameter.
in our case
r = 18/2 = 9 mm
so, the circumference is
2×3.14×9 = 18×3.14 = 56.52 mm
ochala bought a music system on hire purchase. He paid a total of sh 5,200 .if he started by paying a deposit of sh 2,300 for how many months did he pay the remaining money if each monthly installment was sh 2,900
Jackie is looking on a map at the distance between her campsite and a trail which she plans to hike. The distance between the two points on the map is 1.8 centimeters. If the map uses a scale in which 1 centimeter represents 5 miles, find the actual distance in miles that Jackie’s campsite is from the trail.
The actual distance in miles between the campsite and the trail is 9 miles.
What is map?Map can be defined as a symbolic depiction emphasizing relationships between elements of some space such as objects and regions.
To convert from centimeters on the map to miles, we use the scale of 1 centimeter represents 5 miles.
So, 1.8 centimeters on the map represents 1.8 * 5 = 9 miles in real life.
Therefore, The actual distance in miles between the campsite and the trail is 9 miles.
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The population of a city grew from 23,000 in 2010 to 25,000 in 2015. What was the average rate of change during this time interval
The average rate of change for a city population of the city was growing steadily and can be used to predict future population growth.
The average rate of change for a city can be calculated by subtracting the initial population (23,000 in 2010) from the final population (25,000 in 2015) and then dividing that number by the total number of years (five). The equation for this calculation is:
(Final Population - Initial Population) / (Number of Years)
Using this equation, the average rate of change for the city is calculated as follows:
(25,000 - 23,000) / 5 = 2,000 / 5 = 400
Therefore, the average rate of change for the city between 2010 and 2015 was 400 people per year. This means that on average, the population of the city increased by 400 people each year during this time interval. This calculation shows that the population of the city was growing steadily and can be used to predict future population growth.
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Which meaurement repreent the ide length of a right triangle?
Right Triangle
NOT a Right Triangle
6 cm, 8 cm, 10 cm
12 cm, 35 cm, 37 cm
4 cm, 6 cm, 10 cm
10 cm, 24 cm, 26 cm
6 cm, 8 cm, 10 cm meaurement repreent the ide length of a right triangle.
Which dimension best describes a right triangle?A right triangle, like the triangle below, is one in which one of the angles measures 90 degrees (a right angle). In most cases, right angles are shown by drawing a square at the angle's vertex.
For a right triangle, where c is the hypotenuse and a and b are the smaller sides, the Pythagorean Theorem gives us a2 + b2 = c2.
The hypotenuse is usually the longest. Any triple would still represent the sides of a right triangle if we multiplied it by a constant. Therefore, the sides of a right triangle would be 6, 8, and 10.
a2 + b2 = c2.
= 6^2 + 8^2 = 10^2
36 + 64 = 100.
so,
6 cm, 8 cm, 10 cm meaurement repreent the ide length of a right triangle.
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X^2-5x+2=0 select the two values of x that are roots of this equation
Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.
what is discriminant ?When use the formula to solve a problem, the "discriminant" is the value that helps in recognizing the various sorts of solutions. In a mathematical formula (a quadratic equation), it is a special function of a cross that reveals information out about bases of the equation. The "b" term must be square-rooted before the "a" term and "c" term may be isolated by four times to calculate the discriminant. It has a (delta) next to the letter "D" that stands for discrimination. Positive discriminant describes a quadratic equation with two unique real number solutions. Repeated positive integer solutions exist for a quadratic equation with a characteristic of zero. A negative discriminant reveals that none of the solutions is a real number.
given
x2 - 5x + 2 = 0
the roots of the equation
x = -b ±[tex]\frac{\sqrt{b^{2} - 4ac} }{2a}[/tex]
x = 5 ± [tex]\sqrt{17} / 2[/tex]
Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.
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a new cell phone design from samsung has demonstrated a constant failure rate of 0.06 fpmh. assuming customers will use their devices 5 hours per day, every day, what will the probability of failure after one year of use?
The probability of failure after 1 year of use will be approximately 109/1,000,000 = 0.000109 or 0.0109%.
The failure rate (fpmh) is the number of failures per million hours. If a device is used for 5 hours per day, every day, it will be used for 365 days * 5 hours/day = 1,825 hours in a year.
The probability of failure after 1 year of use can be calculated as:
Failure rate * total hours used = 0.06 fpmh * 1,825 hours = 0.06 * 1,825 failures = 109.35 failures
So, there will be approximately 109 failures after 1 year of use. Since the failure rate is per million hours, and there were 1,825 hours of use, the probability of failure after 1 year of use will be approximately 109/1,000,000 = 0.000109 or 0.0109%.
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Compare the rates to find which is greater.
49 meters in 28 hours or 56 meters in 40 hours
Answer:
Step-by-step explanation:
Equivalent rates can be used to compare different sets of quantities that have the same value. A rate that compares a quantity to one is called a unit rate. The unit rate has a denominator equal to one when written as a fraction. Unit rates can be used to find larger equivalent rates.In a unit rate, the denominator is always 1. So, to find unit rate, divide the denominator with the numerator in a way that the denominator becomes 1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09 km/hour
Caroline has two pieces of fabric, one is 90 inches wide and the other is 36 inches wide. If she wishes to cut the fabric into equal pieces that are as wide as possible, how wide should she cut the pieces?
Caroline should cut the fabric into 63 inches wide each
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
For example if a number is added to 20 and gives 50. what is the numbers
x+20 = 50
x = 50-20
x = 30
The total width of the pieces of fabrics = 90 + 36 = 126 inches
To cut the pieces into two equal part with maximum width, we divide the total width by 2
= 126/2
= 63 inches
therefore the fabric should be cut into 63 inches wide each
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4. You are painting the roof of a
boathouse. You are going to
place the base of a ladder
3.2 feet from the boathouse.
How long does the ladder
need to be to reach the
roof of the boathouse?
K
3.2 ft
12.6 ft
Answer:
ladder has to be at least 13 ft long
Step-by-step explanation:
l = length of the ladder
12.6² + 3.2² = l²
l² = 158.76 + 10.24 = 169
√l² = l = √169 = 13
The ladder is the hypotenuse of a right triangle with sides 12.6 and 3.2
help this is literally due today
If the diameter of the pool is 24ft, the area is 452.16 ft²
How to find the area of the pool?Here we have a circular pool and we want to find its area.
Remember that the area of a circle of radius R is given by:
A = pi*R²
Where pi = 3.14
Here we want to define the diameter as a value between 12 and 24 ft, so I will use 24 ft.
The radius is half of that, then we have:
R = 24ft/2 = 12ft
Then the area of the pool is:
A = 3.14*(12 ft)² = 452.16 ft²
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I dont understand may you please help me
Answer:4
Step-by-step explanation:
3