which graph represents exponential decay?

This statement is false.

Every real matrix has real eigenvalues or comes in pairs of complex conjugate eigenvalues.

In general, the eigenvalues of a 2x2 matrix A can be found by solving the characteristic equation det(A - lambda*I) = 0, where I is the 2x2 identity matrix and lambda is the eigenvalue. The characteristic equation is a quadratic equation in lambda, and its solutions are the eigenvalues of A.

For a real 2x2 matrix, the coefficients of the characteristic equation are real, and so the solutions to the characteristic equation are either real or complex conjugate pairs. This follows from the fact that complex roots of real polynomials always come in complex conjugate pairs.

Now, suppose that a real 2x2 matrix A has eigenvalues i and 2i. Since these eigenvalues are not real, they must be complex conjugates of each other. That is, 2i is also an eigenvalue of A, and the other eigenvalue must be the complex conjugate of i, which is -i.

However, the characteristic equation of a 2x2 matrix with eigenvalues i and 2i is given by:

det(A - lambda*I) = (a - lambda)(d - lambda) - bc = (a - lambda)(d - lambda) - b*c

where A = [[a,b],[c,d]], and lambda = i or 2i.

If we substitute lambda = i into the above equation, we get:

(a - i)(d - i) - b*c = 0

Expanding this equation, we get:

ad - ai - di + i^2 - bc = 0

Simplifying, we get:

(ad - bc) - i(a + d) = 0

Since the matrix A has real entries, the imaginary part of this equation must be zero, which implies that a + d = 0. But this contradicts the assumption that A has eigenvalues i and 2i, since the sum of the eigenvalues of A is equal to the trace of A, which is a + d. Therefore, there cannot exist a real 2x2 matrix with eigenvalues i and 2i.

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When chosen 2 of the 16,701 mathematics degrees at random, the probability that at least 1 of the 2 degrees was earned by a woman is P(at least 1 women out of 2)= 70.4064%

P(women)=0.4560

We know the rule: P(not A) = 1−P(A)

We can then determine the probability of individuals who earned a degree but are not women:

P(not women) =1−P(women)=1−0.4560=0.5440

when we multiply we get,

P(A and B) = P(A)×P(B)

now we can then determine the probability of obtaining 2 individuals who earned a degree but are not women:

P(2 not women) = P(not women) × P(not women)

= 0.5440 × 0.5440 = 0.295936

now we can use the complement rule, and with this now we can then determine the probability of at least 1 degree earned by women:

P(at least 1 women out of 2) = 1−P(2 not women) = 1−0.295936

=0.704064

=70.4064%

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Using law of sine and triangle rule, the value of n is 443 inches

The law of sines establishes the relationship between the sides and angles of an oblique triangle(non-right triangle). Law of sines and law of cosines in trigonometry are important rules used for "solving a triangle". According to the sine rule, the ratios of the side lengths of a triangle to the sine of their respective opposite angles are equal.

The law of sines relates the ratios of side lengths of triangles to their respective opposite angles. This ratio remains equal for all three sides and opposite angles. We can therefore apply the sine rule to find the missing angle or side of any triangle using the requisite known data.

The formula is given as

a / sin A = b / sin B = c / sin C

In this triangle NOP, we can find the value of angle P

∠N +  ∠O  +  ∠P = 180

57 + 55 +  ∠P = 180  : Sum of angles in a triangle is equal 180 degrees

∠P= 180 - 112

∠P = 68

Using law of sine

p / sin P = n / sin N

490 / sin68 = n / sin57

n = [(490 * sin 57) / sin 68]

n = 443 inches

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Answer:

7.a) 5

7.b) 1/2

8. 1

Step-by-step explanation:

7.

a)

Read the points on the graph (0, 0) and (1, 5).

slope = (5 - 0)/(1 - 0) = 5/1 = 5

b)

read the points on the graph (0, 0) and (4, 2).

slope = (2 - 0)/(4 - 0) = 2/4 = 1/2

8.

Points (1, 4) and (5, 8)

slope = (8 - 4)/(5 - 1) = 4/4 = 1

The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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Answer:

-8a(a-5)

Step-by-step explanation:

-8a^2+40a

-8a(a-5)

Answer:

y= -2x-3

Step-by-step explanation:

y-5 = -2x-8

y = -2x-8+5

y = -2x-3

Answer:

4x+y=17 that the answer  

Step-by-step explanation:

Answer:

-4x-17=y

Step-by-step explanation:

Distribute the -4 into the parenthises. Then subrtract the 1 from both sides.

Answer:

\(\mbox{\large $0.5 + 0.16 \bar {3}$ = \boxed{\dfrac{199}{300}}}\)

Step-by-step explanation:

\(0.16\bar{3} = 0.16333333333\\\)

the 3 repeats until infinity

Let's multiply this by 100 to move the non-repeating part to the left of the decimal point

0.1633333333...... x 100 = 16.333333333333333...

.333333 = 1/3

Therefore the recurring number multiplied by 100 is
\(16 + \dfrac{1}{3} = \dfrac{16 \times 3 + 1}{3}=\dfrac{49}{3}\)

Since this fraction was arrived at by multiplying by 100, divide this fraction by 100 to get back the fraction in its original decimal value of 0.163333

\(\dfrac{49}{3} \div 100\)

To divide by a number, multiply by the reciprocal of that number

Reciprocal of 100 is 1/100:

\(\dfrac{49}{3} \div 100 = \dfrac{49}{3} \times \dfrac{1}{100} = \dfrac{49}{300}\)

(You can verify this by dividing 49 by 300 in a calculator and seeing that the result is 0.163333333333333333333 i.e. 0.16333 recurring

We want to add 0.5 to this.

0.5 = \(\dfrac{1}{2}\)

so
0.5 + 0.16333333 = 0.6633333

\(= \dfrac{1}{2} + \dfrac{49}{300}\)

We can write \(\dfrac{1}{2}\) as \(\dfrac{150}{300}\)  by multiplying numerator and denominator by 150

So we get

\(0.5 + 0.1633333 = \dfrac{150}{300} + \dfrac{49}{300} = \dfrac{150+49}{300} = \dfrac{199}{300}\)

If you perform this division on a calculator you will get the answer as 0.663333 = \(0.66\bar{3}\) which is what you get when you add 0.5 and \(0.16\bar{3}\)

The exact value of sin(θ/2) is ±(3/√10).

To find the exact value of sin(θ/2), we can use the half-angle formula for sine:

sin(θ/2) = ±√[(1 - cosθ) / 2]

Given that cosθ = -4/5 and 90° < θ < 180°, we can determine the value of sin(θ/2) using the half-angle formula.

First, let's find sin(θ) using the Pythagorean identity:

sinθ = ±√(1 - cos²θ)

sinθ = ±√(1 - (-4/5)²)

= ±√(1 - 16/25)

= ±√(9/25)

= ±3/5

Since 90° < θ < 180°, we know that sinθ < 0. Therefore, sinθ = -3/5.

Now we can substitute this value into the half-angle formula:

sin(θ/2) = ±√[(1 - cosθ) / 2]

= ±√[(1 - (-4/5)) / 2]

= ±√[(1 + 4/5) / 2]

= ±√[(9/5) / 2]

= ±√(9/10)

= ±(3/√10)

Thus, the exact value of sin(θ/2) is ±(3/√10).

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Answer:

i think it's B, I'm not 100% sure

Answer: 135

Step-by-step explanation:

took it on edg2020

Answer:

135

Step-by-step explanation:

Just took the test and got it right

If 4 - 5i is a zero of a quadratic function with real coefficients, then 4 + 5i is also a zero. The zeros of a quadratic function with real coefficients always occur in conjugate pairs.

In a quadratic function with real coefficients, the complex zeros occur in conjugate pairs due to the nature of the quadratic equation. The quadratic equation can be factored as (x - a)(x - b), where "a" and "b" represent the zeros of the function. If 4 - 5i is one of the zeros, it means that (x - (4 - 5i)) is a factor of the quadratic equation.

By expanding this factor, we get x - 4 + 5i. To ensure the coefficients remain real, the conjugate of 4 - 5i must also be a zero. Therefore, the other zero will be 4 + 5i. This property of complex zeros occurring in conjugate pairs is essential when dealing with quadratic functions with real coefficients.

When a quadratic function with real coefficients has a complex zero of 4 - 5i, it will also have a complex zero of 4 + 5i. This is due to the conjugate pair property, where complex zeros occur in pairs that differ only in the sign of the imaginary part.

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Yes, monotone is a sequence.

We say that a sequence (xn) is increasing if xn ≤ xn+1 for all n and strictly increasing if xn < xn+1 for all n.

Similarly, we define decreasing and strictly decreasing sequences. Sequences which are either increasing or decreasing are called monotone.

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Answer:

43

Step-by-step explanation:

2 significant figures means we keep the first 2 and round the 1 place

42.598 we round to 43 since next to the 2 is a 5 so we round up

And 43 are 2 significant figures since none of them are zero

Hopes this helps please mark brainliest

The diameter of circle C is \(x\), which is \(5\).

A circle is the collection of all points on a plane that are at a specified distance from another point (the radius) (the centre). A radius is any distance separating a point on a circle from its center. Any two radii are equal in length under the concept of a circle.

A semicircle is a half circle produced by splitting a circle into two equal parts. It is created when a line pierces the circle's center and touches its two ends.

Since \(CE\) is a radius of the circle and the diameter is \(30\) units long, we know that \(CE\)is half the length of the diameter:

\(CE = 1/2\)(diameter)\(= 1/2(\)30 units)\(= 15\) units

We are given that \(CE = 6x\), so we can solve for \(x\):

\(CE = 6x = 15\)

\(x = 15/6\)

\(x = 2.5\)

Now, we can use the fact that angle \(CED\), where \(D\) is the center of the circle, is a central angle that intercepts arc \(CD\), to find the measure of angle \(CED\).

Since the diameter of the circle is a straight line, it forms a \(180\) degree angle at its endpoints. Therefore, angle \(CED\) is half of this angle, which is:

angle \(CED = 1/2(180 degrees) = 90\)degrees

We are given that angle \(CED\) is \(30\) degrees, so we can set up an equation:

angle \(CED = 30 = 6x\)

Simplifying and solving for \(x\):

\(6x = 30\)

\(x = 30/6\)

\(x = 5\)

Therefore, \(x\) is equal to \(5\).

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The solutions to the equation \(x^{\frac{2}{3} } -2x^{\frac{1}{3} } -8=0\) are x = 64 and x = -8.

In Mathematics and Geometry, an exponent is a mathematical operation that is commonly used in conjunction with an expression, so as to raise a given quantity to the power of another.

Mathematically, an exponent can be modeled by this mathematical expression;

bⁿ

Where:

the variables b and n are numerical values, letters, or an expression.

n is known as a power.

By applying the law of indices for powers to the given equation, we would have the following simplified expression:

\(a^{\frac{n}{m} }=a^{(\frac{1}{m})n }\\\\x^{(\frac{1}{3} )2} -2x^{\frac{1}{3} } -8=0\\\\n^2 -2n - 8=0\)

n² - 4n + 2n - 8 = 0

n(n - 4) + 2(n - 4) = 0

(n + 2)(n - 4) = 0

n = -2 or n = 4.

Now, we can solve for x as follows;

\(x^{\frac{1}{3} }=4\\\\x = 4^3\)

x = 64.

\(x^{\frac{1}{3} }=-2\\\\x = -2^3\)

x = -8.

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Therefore , the solution of the given problem of inequality comes out to be x = 12.5°.

An inequality in mathematics is a linear relationship or a set of integers even without equal sign. Equilibrium follows equity ineluctably. Inequality exists between two variables when they are not equal. There are distinctions between equality and inequality. I've selected the most prevalent symbol because when variables aren't identical or comparable (). Any number of inequalities, no matter how little or large, can be used to compare values.

Here,

Given :4x -10 = 40

=> 4x = 40 + 10

=>  4x =50

=> x  =50/4

=>x= 12.5°

Therefore , the solution of the given problem of inequality comes out to be x = 12.5°.

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If speed is important and the array is large, the a. Binary search algorithm should be used. This algorithm is designed to efficiently search through sorted arrays by repeatedly dividing the search interval in half.

It has a time complexity of O(log n), which means that as the size of the array increases, the time it takes to search for an item will not increase at the same rate.
On the other hand, ascending bubble sort and other sorting algorithms such as selection sort and insertion sort have a time complexity of O(n^2), which means that as the size of the array increases, the time it takes to sort the array will increase exponentially. Therefore, these algorithms are not efficient for large arrays and should not be used if speed is important.
In summary, when dealing with large arrays and speed is important, binary search is the best algorithm to use for searching, while ascending bubble sort and other sorting algorithms with a time complexity of O(n^2) should be avoided.

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Answer:37oF/hr

Step-by-step explanation:

Recall the definition of the sine of an angle on a right triangle:

On the other hand, according to this diagram, the values for tan(A) and cos(A) are given by:

Since 180≤A≤270, the right triangle that corresponds to the angle A on the coordinate plane looks as follows:

Where a and b are negative distances.

Since sin(A)=-4/7, we can assume that a=-4 and c=7. Use the Pythagorean Theorem to find the exact value of b:

We know that b should be negative. Then:

Substitute b=-sqrt(33) and c=7 to find the exact values for cos(A) and tan(A):

Therefore, the exact values for cos(A) and tan(A) are:

Answer:

f(5) = 22; f(9) = 34

Step-by-step explanation:

f(5) = 3(5) +7

f(5) = 22

f(9) = 3(9) +7

f(9) = 34

Answer:

760

Step-by-step explanation:

Answer:

760 of course

Step-by-step explanation:

3 is below 5 so its 760

If the last digit was a 5 or higher,it'll be 770

Answer:

1.049

Step-by-step explanation:

Divide 103 into 108

The solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

To simplify the equation 3(x-6) - 1/2(8x+10) = -25, we can start by applying the distributive property and then combining like terms.

First, let's distribute the 3 and the -1/2 to the terms inside the parentheses:

3(x-6) - 1/2(8x+10) = 3x - 18 - (4x + 5)

Now, let's simplify further by combining like terms:

3x - 18 - 4x - 5 = -x - 23

So, the simplified equation is -x - 23 = -25.

To solve for x, we can isolate the variable by adding 23 to both sides of the equation:

-x - 23 + 23 = -25 + 23

This simplifies to:

-x = -2

Finally, we can solve for x by multiplying both sides of the equation by -1:

(-1)(-x) = (-1)(-2)

This gives us:

x = 2

Therefore, the solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

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Answer:

0.5

\(points \: of \: best \: fit \: are \\ (9, 5) \: and \: (1, 1) \\ slope = \frac{(1 - 5)}{(1 - 9)} \\ = \frac{ - 4}{ - 8} \\ = \frac{1}{2} \\ = 0.5\)

The coordinates of midpoint M is (3,-4)

It is given that AB is a line segment whose end points A ( 4,6) and B (2.-14) and M is the midpoint

We need to find out the coordinates of midpoint  M which can be found out using the mid point formula  which is (x1 + x2/2 , y1 +y2/2)

the x coordinate of the midpoint M of line segment AB = 4 + 2/2

                                                                                               = 6/2

                                                                                                = 3

the y coordinate of the midpoint M of line segment AB = 6+ (-14) /2

                                                                                               = -8/2

                                                                                               = -4

Hence the coordinates of the midpoint M of line segment AB is (3,-4)

In geometry, the midpoint is the center point of a line section. it's far equidistant from each endpoints, and it's far the centroid each of the segment and of the endpoints. It bisects the section.

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Answer:

For question 3b the answer is no because the common difference is 4

Step-by-step explanation:

6,10,14,18,22,26,30,34

It will be 34 not 33