1)Substituting the given values, we get:
xyz = 3(-1)(2) = -6
Therefore, when x=3, y=-1, and z=2, the value of xyz is -6.
2)y^2 = (-1)^2 = 1
Therefore, when x = 3, y = -1, and z = 2, y^2 = 1.
3) 2
Let A= (2 1)
(6 4)
(a) ExpressA−1as a product of elementary matrices. (b) ExpressAas a product of elementary matrices.
E1 x E2 x E4 = (2 0) (0 1) (1 0) (3 1)
(a) A-1 can be expressed as a product of elementary matrices by following these steps:
1. Create a matrix A' = A (2 0)
(0 1)
2. Create an elementary matrix E1 = (1 -2)
(0 1)
3. Multiply A' and E1 to get matrix E2 = (2 -4)
(0 1)
4. Create an elementary matrix E3 = (1 0)
(-3 1)
5. Multiply E2 and E3 to get matrix E4 = (2 0)
(-6 1)
6. Create an elementary matrix E5 = (1 0)
(0 2)
7. Multiply E4 and E5 to get A-1 = (2 0)
(-3 2)
Therefore, A-1 can be expressed as a product of elementary matrices, E1 x E3 x E5 = (2 0) (-6 1) (1 0) (0 2).
(b) A can be expressed as a product of elementary matrices by following these steps:
1. Create an elementary matrix E1 = (2 0)
(0 1)
2. Create an elementary matrix E2 = (1 1)
(0 1)
3. Multiply E1 and E2 to get matrix E3 = (2 1)
(0 1)
4. Create an elementary matrix E4 = (1 0)
(3 1)
5. Multiply E3 and E4 to get A = (2 1) (6 4)
Therefore, A can be expressed as a product of elementary matrices, E1 x E2 x E4 = (2 0) (0 1) (1 0) (3 1).
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HELP i have a exponential functions nd i need to know if my word problem is solve able pls
The Population of salmonella
doubles in size every 25 hours.
There are about 1.35 million
infections every year, determine
how many bacteria is present
every year.
Yes, this word problem is solvable using exponential functions.
To solve this problem, we need to use the formula for exponential growth:
P(t) = P0 * e^(rt)
where P(t) is the population after t hours, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.
In this problem, we are given that the population doubles in size every 25 hours. This means that the growth rate is 1/25, since the population is multiplying by 2 each time.
We are also given that there are about 1.35 million infections every year. Since there are 365 days in a year, this means there are about 1.35 million/365 = 3699.18 infections per day.
We can now use this information to find the initial population:
P0 = 3699.18 / e^(1/25 * 24 * 365)
P0 ≈ 2135.05
So the initial population is about 2135.05 bacteria.
To find the population after one year, we can use the formula again:
P(365 * 24) = 2135.05 * e^(1/25 * 24 * 365)
P(365 * 24) ≈ 3.89 x 10^18
Therefore, there are approximately 3.89 x 10^18 bacteria present after one year.
measure the height of the tin in mm
The measure of the height of the tin in mm can be found using the steps below.
What are Measurements?
Measurement is the method of comparing the properties of a quantity or object using a standard quantity.
Measurement is essential to determine the quantity of any object.
Here, the activity is to measure the height of a tin.
Height of the tin is the vertical distance from the base of the tin to the top of the tin.
The height of the tin is the exact straight line measurement when the tin is placed upright on a flat surface.
The measurement has to be in millimeters.
So the best tool is the ruler.
Place the ruler vertically with point 0 at the baseline of the tin.
Mark the point in millimeters that the ruler coincides with the top of the tin.
Read the height to the nearest millimeter.
Hence, the height of the tin can be measured as above.
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The complete Question:
Measure the height of the tin in the mm and write down the real height in mm
Can y’all please help a gurl out thanks
Answer:
The answer is B
Step-by-step explanation:
To solve this, we need to combine like terms.
(9c-8d) + (2c-6) + (-d+3)
9c + 2c - 8d - d - 6 + 3
11c - 8d - d - 6 + 3
11c - 9d - 6 + 3
11c - 9d - 3
pleaseweeee helppppp
Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
Answer:
A
[tex]2y {}^{4} \div x {}^{4} [/tex]
Step-by-step explanation:
Divide 14 by 7 it will be 2.
Now divide the variables.
X variable will give you X{}^{-4} and y{}^{4}.
So bring X variable in the denominator to make it positive.
So your answer will be option A.
Answer:
A
Step-by-step explanation:
It was right for me
$8,374.78 $6,741.75 What are the complex solutions to the following equation? 2x^(2)+4x+6=0
The complex solutions to the given equation are -1 + i√2 and -1 - i√2.
To determine the complex solutions to the equation, we can first simplify the quadratic equation by dividing each term by 2. This gives x² + 2x + 3 = 0.
The discriminant (b² - 4ac) can be calculated to find the nature of roots.
b² - 4ac = 2² - 4(1)(3) = 4 - 12 = -8
As the discriminant is less than 0, the roots are imaginary roots. That is, the roots are complex numbers.
To find the roots of this quadratic equation, the following steps can be followed.
Since the coefficient of x² is 1, the quadratic formula can be used to solve the given quadratic equation. The quadratic formula is given by
x = [-b ± √(b² - 4ac)] / 2a
Substitute the given values into the formula.
x = [-2 ± √(-8)] / 2
On simplifying the above expression,
x = [-2 ± 2i√2] / 2= -1 ± i√2
Therefore, -1 + i√2 and -1 - i√2 are the complex roots or solutions of the given quadratic equation.
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There are 15 students in Mrs. Jones’ class who are going to the band competition. If 60% of her students are going to the competition, how many students are there in the class in all?
15 - 60%
x - 100%
1500 = 60x
x = 25
∴ There are 25 students in the class in all.
Identify the terms, the degree of each term and the degree of the polynomial. Then identify the leading term, the leading coefficient, and the constant term. -5s^(7)-8s^(4)+6s^(3)+4s-6
Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6
Degree of each term: 7, 4, 3, 1, and 0
Degree of the polynomial: 7
Leading term: -5s^(7)
Leading coefficient: -5
Constant term: -6
The terms of the polynomial are -5s^(7), -8s^(4), 6s^(3), 4s, and -6. The degree of each term is 7, 4, 3, 1, and 0, respectively. The degree of the polynomial is the highest degree of any of its terms, which is 7.
The leading term is the term with the highest degree, which is -5s^(7). The leading coefficient is the coefficient of the leading term, which is -5. The constant term is the term with a degree of 0, which is -6.
So, the terms are -5s^(7), -8s^(4), 6s^(3), 4s, and -6; the degree of each term is 7, 4, 3, 1, and 0; the degree of the polynomial is 7; the leading term is -5s^(7); the leading coefficient is -5; and the constant term is -6.
Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6
Degree of each term: 7, 4, 3, 1, and 0
Degree of the polynomial: 7
Leading term: -5s^(7)
Leading coefficient: -5
Constant term: -6
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1.Solve 3^2x−1=27, showing steps 2 Solve 3^x∧2−3x=81, showing work
3 Solve 4^x+1=64, showing steps as 4 Solve 4^x+1=1/64, showing work as
1. To solve 3^(2x-1)=27, we first need to simplify 27 to power of 3: 27=3^3
3^(2x-1)=3^3
Next, we can use the property that if the bases are the same, the exponents must be equal:
2x-1=3
Solving for x, we get:
2x=4
x=2
2. To solve 3^(x^2-3x)=81, we first need to simplify 81 to the power of 3: 81=3^4
3^(x^2-3x)=3^4
Next, we can use the property that if the bases are the same, the exponents must be equal:
x^2-3x=4
Solving for x, we can use the quadratic formula:
x=(-b±√(b^2-4ac))/(2a)
x=(-(-3)±√((-3)^2-4(1)(-4)))/(2(1))
x=(3±√(9+16))/2
x=(3±5)/2
x=4 or x=-1
3. To solve 4^(x+1)=64, we first need to simplify 64 to the power of 4: 64=4^3
4^(x+1)=4^3
Next, we can use the property that if the bases are the same, the exponents must be equal:
x+1=3
Solving for x, we get:
x=2
4. To solve 4^(x+1)=1/64, we first need to simplify 1/64 to the power of 4: 1/64=4^(-3)
4^(x+1)=4^(-3)
Next, we can use the property that if the bases are the same, the exponents must be equal:
x+1=-3
Solving for x, we get:
x=-4
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A regular hexagon is a polygon that has six sides with equal length and six interior angles with equal measure. In Figure 1, regular hexagon ABCDEF has side length 2x and its vertices lie on the circle with centre O. The diagonals AD, BE and CF divide ABCDEF into six congruent equilateral triangles. (a) In terms of x, what is the radius of the circle?
radius of the circle is sqrt(3)x.
The radius of the circle can be found by using the Pythagorean Theorem. The side lengths of each equilateral triangle created by the diagonals is 2x, so the hypotenuse of the triangle is sqrt(3)x. Since the hypotenuse of each triangle is the same as the radius of the circle, the radius of the circle is sqrt(3)x.
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HELP A GIRL OUT PLEASEEEEEEEEEE
Answer: C
Step-by-step explanation:
replace n=1 with f(n)= 5n-2 we have
f(1)=3 => remove answers B and D
f(n)= 5n-2 so f(n-1)= 5(n-1) -2=5n-7
Try with answers C and D to see if it satisfies this
f(n)= f(n-1)+5= 5n - 7+5=5n-2 => C is correct
Unit rates.
Calista ran 6.75 miles in 45 minutes. At this rate, his far can she run per minute?
Answer:0.15 miles a minute
Step-by-step explanation:
Her pace is 6 minutes and 40 seconds a mile, she is going 0.15 miles per minute and will go 9 miles an hour
Write an equation for the nth term of the arithmetic seqeuence. Then find a10-
-6,-9, -12,-15, ...
an
11
a10
Given- A sequence as -6,-9,-12,-15
To find- The equation for the nth term of the arithmetic sequence and to find the value of [tex]a_{10}[/tex].
Explanation- The common difference is [tex]-9-(-6)=-3[/tex]
We know the arithmetic sequence formula is
[tex]a_n=a_1+(n-1)d\\a_n=-6+(n-1)(-3)[/tex]
When n=10
[tex]a_{10}=-6+(10-1)(-3)\\a_{10}=-6+9(-3)\\a_{10}=-6-27\\a_{10}=-33[/tex]
Final answer- The value of 10th term is -33.
Compute the area of triangle, if x equals 3 less than 6
Answer:
C
Step-by-step explanation:
I think its c because it said x = 3 less than 6, what is three less than 6? 3 so if you were to plug in 3 for x so bc = 3 and ab = 6 you multiply those two together but when you are doing area for a triangle its 1/2 bh so how i do this is i multiply 6 and 3 and get 18 and divide that by 2 and my final answer is 9. Hope this works, let me know if it doesnt!
Abstract Algebra: Let ???? be the group of all real-valued functions with domain ℝ under addition. Let H be the subset of ???? consisting of all functions that are differentiable. Determine if H is a subgroup of ????.
Yes, H is a subgroup. We can prove this by using the subgroup criterion, which states that a subset H of a group G is a subgroup if and only if it satisfies the following three conditions:
1. The identity element of G is in H.
2. If h1 and h2 are in H, then h1*h2 is in H.
3. If h is in H, then h^(-1) is in H.
Let's check if these conditions are satisfied for H:
1. The identity element of ???? is the zero function, f(x) = 0, which is differentiable. Therefore, the identity element is in H.
2. If h1 and h2 are in H, then they are both differentiable functions. The sum of two differentiable functions is also differentiable, so h1 + h2 is in H.
3. If h is in H, then it is a differentiable function. The inverse of a differentiable function under addition is its negative, which is also differentiable. Therefore,[tex]h^{-1} = -h[/tex] is in H.Since all three conditions are satisfied, H is a subgroup.
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when f(x)=4 what is the of x
When f(x) = 4, then, the value of x = 2 (domain = 2, range = 4).
How did we determine the value of x?According to the mapping above, the given relationship is bijective (one-to-one and onto or one-to-one correspondence) because each element of the range is mapped to by exactly one element of the domain.
When we say a relationship is bijective, it means the satisfies both the injective (one-to-one function) and surjective function (onto function) properties. Therefore, as a result, f(x)=4 implies f(2)=4 or simply x=2.
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I need help on this asap!
The inequalities that represent the regular price of eyeglass frames will be 0.4r ≤ 120 and r ≥ 4(360/5).
How to calculate the InequalitiesIf we let r represent the regular price of the eyeglass frames, then we can write the following two inequalities based on the given information:
0.4r ≤ 120
This inequality represents the fact that the lowest regular price for the eyeglass frames is $120. We use 0.4 because a 60% discount means that the price paid is 40% of the regular price.
Also, r ≥ 4(360/5) as this inequality represents the fact that the highest regular price for the eyeglass frames is $360. We use 4(360/5) because a 75% discount means that the price paid is 25% of the regular price, which is equivalent to multiplying the regular price by 0.25. Then, 4 times that amount gives us the regular price, which is $360 in this case.
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Y varies inversely as x. If x = 8 when y = 30, find x when y = 20
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=30 \end{cases} \\\\\\ 30=\cfrac{k}{8}\implies 240=k\hspace{9em}\boxed{y=\cfrac{240}{x}} \\\\\\ \textit{when y = 20, what's "x"?}\qquad 20=\cfrac{240}{x}\implies x=\cfrac{240}{20}\implies x=12[/tex]
Easton has a goal to complete 70% of the jumps on a skateboard course. If he has completed 18 out of 30 jumps already, how many more jumps does Easton need to complete to reach his goal?
Easton needs to complete 3 more jumps to reach his goal of completing 70% of the jumps on the skateboard course.
How to determine the additional number of jumps neededEaston's goal is to complete 70% of the jumps on the skateboard course. This means he needs to complete 70% of the total number of jumps.
We know that Easton has already completed 18 jumps out of 30, which is equivalent to completing 60% of the jumps.
The total number of jumps on the skateboard course is 30.
Easton's goal is to complete 70% of the jumps, which is:
0.7 x 30 = 21 jumps
Easton has already completed 18 jumps, so he needs to complete:
21 - 18 = 3 more jumps
So, he needs 3 more jumps
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A toolbox is 2 ft high, and its width is 3 ft less than its length. If its volume is 80 ft³, find the length and width of the box.
The length and width of the toolbox are 8 feet and 5 feet respectively.
What is the length of the toolbox?The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length.
Given that the volume of the toolbox is 80 cubic feet, so we can write:
V = w × h × l = 80ft³
Next, we know that the width is 3 feet less than the length, so we can write:
w = l - 3
Now we can substitute the second equation into the first equation to get an equation with just one variable:
V = w × h × l = l(l - 3)(2) = 80
Simplifying this equation, we get:
2l² - 6l - 80 = 0
We can solve this quadratic equation using the quadratic formula:
l = (-b ± √(b² - 4ac)) / 2a
where a = 2, b = -6, and c = -80. Plugging in these values, we get:
l = (6 ± √(6² - 4(2)(-80))) / 4
l = (6 ± √(676)) / 4
We take the positive value of l since the length must be positive, so we get:
l = (6 + 26) / 4
l = 8
Now we can use the second equation (w = l - 3) to find the width:
w = l - 3
w = 8 - 3
w = 5
Therefore, the length of the toolbox is 8 feet and the width is 5 feet.
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Evaluate. Write your answer as a fraction or whole number without exponents. 5^-4
Answer:
1 / 625
Step-by-step explanation:
To write 5^-24 without exponents, simplify.
5^-4
1 / 5^4
1 / 625 or .0016
A bag of mixed nuts contains almonds and hazelnuts. There are (6x+13) nuts in this particular bag, and (3x-7) of there are hazelnuts.
Which expression represents the number of almonds in the bag?
The expression that represents the number of almonds in the bag is (6x+13) - (3x-7)
What is Linear Equation?
A linear equation is a mathematical equation that represents a straight line on a graph. It is an equation in which the highest power of the variable is one. A general linear equation can be represented as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
Linear equations can be solved algebraically using techniques like substitution or elimination, and they can be used to model real-world situations involving linear relationships.
The expression that represents the number of almonds in the bag is (6x+13) - (3x-7) which simplifies to 3x + 20.
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What is the solution, if any, to the equation 3(x-2)+4=3x+6
Answer:
if I'm correct it's 3(4x5)
BUT RECHECK JUST INCASE
Step-by-step explanation:
I need help like gosh
Answer:
The outputs are in order:
5
2
1
2
5
Answer:
5.2.1.2.5
Step-by-step explanation:
Write down the value of the digit in colour as a fraction with a denominator that is a power of 10. a) 0,453 b)43,1 c)92,303 d)2,3214
Answer:
a) The digit in the hundredths place in 0.453 is 3. Therefore, the value of the digit in color is 3/100.
b) The digit in the tenths place in 43.1 is 1. Therefore, the value of the digit in color is 1/10.
c) The digit in the thousandths place in 92.303 is 3. Therefore, the value of the digit in color is 3/1000.
d) The digit in the ten-thousandths place in 2.3214 is 1. Therefore, the value of the digit in color is 1/10,000.
help me below??? dont guess
Answer:
C is your answer
Step-by-step explanation:
Wite the first five terms of the sequence whose general term, a_(n), is given as a_(e)=2n-8.
The first five terms of the sequence whose general term is given as a_(n)=2n-8 are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.
To explain this in more detail, the general term for a sequence is given by an equation in the form a_(n)= some expression. In this case, the expression is 2n-8, so it can be read as “2 times the term number minus 8”.
To calculate the first term, we substitute n=1 into the equation and solve, so a_1=2*1-8=-6. To calculate the second term, we substitute n=2 into the equation and solve, so a_2=2*2-8=-4. Continuing in this manner, we calculate the third term as a_3=2*3-8=-2, the fourth term as a_4=2*4-8=0, and the fifth term as a_5=2*5-8=2.
Therefore, the first five terms of the sequence are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.
In conclusion, to find the first five terms of a sequence given by a general term a_(n)= some expression, substitute the values n=1, n=2, n=3, n=4, and n=5 into the expression and solve to get the desired terms.
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Graph the solution to the following system of inequalities.
2x+3y<9
Y>_ - 2/3x-4
Then give the coordinates of one point in the solution set.
Point in the solution sets D
The graph of 2x + 3y < 9 and y≥ - 2/3x-4 is given in the attachment.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
For the first inequality, 2x + 3y < 9, we will start by graphing the line 2x + 3y = 9, which is the boundary line of the inequality.
To do this, we will solve for y:
2x + 3y = 9
3y = -2x + 9
Divide both sides by 3
y = (-2/3)x + 3
For the second inequality, Y≥ - 2/3x-4
Hence, the graph of 2x + 3y < 9 and y≥ - 2/3x-4 is given in the attachment.
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Can someone help with this please?
According to the Synthetic Division, the Quotient is equal to 7x² -4x + 5 and the Remainder is equal to 8.
Synthetic Division: What is it?Synthetic division can divide two polynomials more quickly than the standard long division algorithm.
With this method, the dividend and divisor polynomials are reduced to a set of numerical numbers.
Given:
(7x³-25x² +17x -7) ÷ (x-3).
So, Synthetic Division for this is as follows:
(x-3) | (7x³-25x² +17x -7) | 7x² -4x + 5
7x³-21x²
_________
-4x² + 17x
-4x² + 12x
_______________
5x - 7
5x - 15
________
8
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Solve. Check for extraneous solutions. 7y+3−6y+9=0
The solution of the given expression is y = -12 and there are no extraneous solutions.
What in algebra is a superfluous solution?A solution to an equation that appears during the solving process but does not fulfil the original problem is known as an extraneous solution. In other words, it is a solution that, when inserted back into the original equation, yields an untrue assertion. Extraneous solutions typically result from certain algebraic operations, such squaring an equation's two sides, which might introduce new solutions that don't truly satisfy the original problem.
The given expression is:
7y+3−6y+9=0
y = -12
Substitute y = -12 back into the original equation:
7y + 3 - 6y + 9 = 0
7(-12) + 3 - 6(-12) + 9 = 0
-84 + 3 + 72 + 9 = 0
The left-hand side simplifies to:
0 = 0
Hence, the solution of the given expression is y = -12 and there are no extraneous solutions.
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