I forgot to post the actual question LOL my points :')

SIMPLIFY the expression, don't solve it! Explain too please!

Answer:

center of the circle is (5, -3) and radius of the circle is 8 units

Step-by-step explanation:

Find the center of the circle given by this equation:

x²-10x+y²+6y-30=0

for x

b= -10

for y

b=+6

complete the square

for x

(-10/2)² = 25

for y

(6/2)²=9

x²-10x+25

y²+6y+9

(x²-10x+25)+(y²+6y+9)+30=0+25+9

(x²-10x+25)+(y²+6y+9)=25+9+30

(x-5)²+(y+3)²=64

This is the form of a circle. Use this form to determine the center and radius of the circle

(x − h)² + (y − k)² = r²

Circle Equation

(x-a)² + (y−b) ² = r² is the circle equation with a radius r, centered at (a, b)

Rewrite x² - 10x + y² + 6y - 30 = 0 in the form of the standard circle equation

(x − h)² + (y − k)² = r²

(x - 5)² + (y-(-3))² = 8²

(x-5)² + (y+3)² = 8²

r=8

h=5

k=-3

signs of h and k are opposite of what they are inside the parenthesis

Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x- offset from the origin, and k represents the y-offset from origin.

r=8

h=5

k=-3

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expii

Brian McLogan

Alex Federspiel

The correct answer is option (d), where X is 9 and Y is 3. Option (a), where X is 9 and Y is 6, is incorrect because Y is modified in the third step of the pseudo-code. Option (b), where X is 0, is also incorrect because X is modified in the second step. Option (c), where X is 9 and Y is still 9, is also incorrect because Y is modified in the third step.

The given pseudo-code consists of three steps:

Set Z = X

Set X = Y

Set Y = Y - Z

Using the initial values X = 6, Y = 9, and Z = 0, we can work through each step to determine the final values of X, Y, and Z:

Set Z = X, so Z = 6 and the values are X = 6, Y = 9, and Z = 6.

Set X = Y, so X = 9 and the values are X = 9, Y = 9, and Z = 6.

Set Y = Y - Z, so Y = 3 and the final values are X = 9, Y = 3, and Z = 6.

Therefore, the correct answer is option (d), where X is 9 and Y is 3. Option (a), where X is 9 and Y is 6, is incorrect because Y is modified in the third step of the pseudo-code. Option (b), where X is 0, is also incorrect because X is modified in the second step. Option (c), where X is 9 and Y is still 9, is also incorrect because Y is modified in the third step.

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Answer:

17000 grams

Step-by-step explanation:

A kilogram is 1000 grams so if you want to find out what 17 kilograms in grams is, you have to multiply the kilograms by 1000:

17 * 1000 = 17000 grams

Answer:

17000

Step-by-step explanation:

multiply the mass value by 1000

I hope this helps!

Answer:

the answer is the first option, A) 2x-7

Step-by-step explanation:

Answer:

"Ay Cuz!" get it no okay but A is the answer

Step-by-step explanation:

To convert the following second-order differential equation into a system of coupled equations, the following steps should be followed:d2y/dt2 + dy/dt + 2x - 5y = 9cos(4t)This is a second-order differential equation.

To transform the second-order differential equation to a system of two first-order differential equations, we will use the following notation:y1 = y, y2 = y'First, we'll find y1' and y2', as follows:y1' = y' (since y1 = y)y2' = y'' = -2y' + 5y - 9cos(4t)Using our notation for y1 and y2, we can rewrite the second-order differential equation as follows:y2' + 2y1 - 5y2 = 9cos(4t)y1' = y2

In matrix form, the system of coupled equations x1' 0 1 x1 = x2' 3 -2 x2 is written as x' = Ax, where A = 0 1 -2 3.We need to find the eigenvalues, eigenvectors, characteristic equation, general solution, and response type expected of this system of coupled equations.

Let us take each of these steps one at a time.i) Characteristic equation:The characteristic equation can be obtained as det(A - λI) = 0, where I is the identity matrix of size 2 x 2. By substituting A and I into the above expression, we get det 0 - 1 2 - λ 3 - λ = 0 Simplifying the above equation gives λ2 - 3λ + 2 = 0.

ii) Eigenvalues: Using the quadratic formula, we can solve for the eigenvalues: λ = (3 ± sqrt(9 - 8))/2 = 2, 1iii) Eigenvectors:

Substituting λ = 2 into (A - λI)x = 0 gives (-2 1 2 -1)x = 0, which is equivalent to the system of linear equations -2x1 + x2 + 2x3 = 0 x1 - x2 - x3 = 0 By solving this system of equations, we get the eigenvector (1 1/2)T.

Substituting λ = 1 into (A - λI)x = 0 gives (-1 1 2 -2)x = 0, which is equivalent to the system of linear equations -x1 + x2 + 2x3 = 0 x1 - x2 + 2x3 = 0 By solving this system of equations, we get the eigenvector (2 -2)T.

iv) The general solution of the system x' = Ax is given by x(t) = c1e2t(1 1/2)T + c2e1t(2 -2)T, where c1 and c2 are constants that are determined by the initial conditions of the system.

v) Response type expected:The system is a stable node because both eigenvalues are negative and the eigenvectors point towards the origin.

We have transformed a second-order differential equation into a system of coupled equations and found the characteristic equation, eigenvalues, eigenvectors, general solution, and response type expected of the system of coupled equations. The system is a stable node, which means that it returns to the equilibrium state after being disturbed.

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The domain of the function f(x) = log_b(x) in interval notation is (0, +∞). The range of the function depends on the base b.

The domain of the logarithmic function f(x) = log_b(x) is determined by the requirement that the argument of the logarithm, x, must be positive. Since the logarithm is undefined for zero and negative numbers, the domain excludes these values. Therefore, the domain is expressed in interval notation as (0, +∞), where the parentheses indicate that zero is not included and the positive infinity symbol indicates that the domain extends indefinitely towards positive numbers.

The range of the logarithmic function depends on the base b. If the base b is greater than 1, the function can output any real number as the exponent increases or decreases, leading to a range of (-∞, +∞), covering all possible real numbers. However, if the base b is between 0 and 1, the logarithmic function only outputs negative numbers. As the exponent increases or decreases, the value of the logarithm approaches negative infinity, resulting in a range of (-∞, 0). This signifies that the range consists of all negative real numbers, but does not include zero or positive numbers.

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Answer:

15

Step-by-step explanation:

Answer:

The smallest number is  

14

Explanation:

Let: x= the 1st con.even number

x+2=the 2nd con.even number

x+4=the 3rd con.even number

Add the terms and equate it with the total, 48

x + ( x + 2 ) + ( x + 4 ) = 48 , simplify

x + x + 2 + x + 4 = 48 , combine like terms

3 x + 6 = 48 , isolate x

x = 48 − 6 3 , find the value of x

x = 14

Answer:

Yes its very sad (the words)

Step-by-step explanation:

Not going to lie but it does kind of sound like camila cabeo sang it.

I really like the tune and the singing too

==================================================

Explanation:

We'll start things off by computing the inner function u(2)

Plug x = 2 into the u(x) function

u(x) = -x-1

u(2) = -2-1

u(2) = -3

This tells us that w(u(2)) is the same as w(-3). I replaced u(2) with -3.

We'll plug x = -3 into the w(x) function

w(x) = 2x^2-1

w(-3) = 2(-3)^2 - 1

w(-3) = 2(9) - 1

w(-3) = 18-1

w(-3) = 17

Therefore, w(u(2)) = 17

------------------------

Here's a slightly different approach:

Let's find what w(u(x)) is in general

w(x) = 2x^2 - 1

w(u(x)) = 2(u(x))^2 - 1

w(u(x)) = 2(-x-1)^2 - 1

Then we can plug in x = 2

w(u(x)) = 2(-x-1)^2 - 1

w(u(2)) = 2(-2-1)^2 - 1

w(u(2)) = 2(-3)^2 - 1

w(u(2)) = 2(9) - 1

w(u(2)) = 18 - 1

w(u(2)) = 17

The value of the variable x in the given right angle expression is; x = 11

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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The Solution:

Given the linear function below:

So, the slope of the linear function above is the coefficient of x in the given linear function. Therefore, the slope of the given function is 4.6

The interpretation of the slope is 4.6% of the people graduate from college every year after the year 1998.

Answer: 2:3

Step-by-step explanation:

25/75 beads are square. Thus, 1 out of every 3 beads (1/3) is square. With this information, 2/3 of the beads are round because 1 - 1/3 = 2/3.

This means that the ratio of round to square beads is 2:3.

Answer:

1/12 or 0.0833

Step-by-step explanation:

P(Coin) = 1/2

P(Dice) = 1/6

1/2 × 1/6 = 1/12

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

The volume of a parallelepiped is equal to the product of the magnitudes of its three adjacent edges. In this case, the three adjacent edges are given by the vectors <6,-9>, <5,-2,9> and <7,6,-2>.

Therefore, the volume of the parallelepiped is equal to |<6,-9>| x |<5,-2,9>| x |<7,6,-2>|

We can find the magnitudes of each vector using the formula for the magnitude of a vector, which is the square root of the sum of the squares of its components.

|<6,-9>| = sqrt(6^2 + (-9)^2) = sqrt(36 + 81) = sqrt(117)
|<5,-2,9>| = sqrt(5^2 + (-2)^2 + 9^2) = sqrt(25 + 4 + 81) = sqrt(110)
|<7,6,-2>| = sqrt(7^2 + 6^2 + (-2)^2) = sqrt(49 + 36 + 4) = sqrt(89)

Therefore, the volume of the parallelepiped is sqrt(117) x sqrt(110) x sqrt(89) = 834.45.

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The volume of the parallelepiped whose adjacent sides are the vectors =6 −9, =5−2 9, and =7 6−2 is 387.

To find the volume of a parallelepiped given three adjacent vectors, we can take the scalar triple product of the three vectors.

The scalar triple product of three vectors a, b, and c is given by:   a · (b x c)

where · represents the dot product and x represents the cross product.

In other words, the scalar triple product is the dot product of the first vector with the cross product of the second and third vectors.

So in this case, we can find the volume of the parallelepiped whose adjacent sides are the vectors a=6−9, b=5−2 9, and c=7 6−2 by computing:

V = a · (b x c)

To compute the cross product b x c, we can use the following determinant:

i   j   k

5 -2 9

7 6 -2

Expanding this determinant, we get:

(−2×9−6×7)i−(5×−2−7×9)j+(5×6−−2×5)k

= −60i − 83j + 40k

So b x c = -60i - 83j + 40k, and:

a · (b x c) = (6)(-60) + (-9)(-83) + (0)(40) = 387

Therefore, the volume of the parallelepiped is 387 cubic units.

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The statement "Pr(E ∪ F) = Pr(E) + Pr(F)" is generally false. The probability of the union of two events, E and F, is not always equal to the sum of their individual probabilities. It holds true only if the events E and F are mutually exclusive.

The probability of the union of two events, E and F, denoted as Pr(E ∪ F), represents the probability that at least one of the events E or F occurs. When events E and F are mutually exclusive, it means that they cannot occur simultaneously. In this case, the probability of their union is equal to the sum of their individual probabilities: Pr(E ∪ F) = Pr(E) + Pr(F).

However, if events E and F are not mutually exclusive, meaning they can occur together, then the formula Pr(E ∪ F) = Pr(E) + Pr(F) does not hold. In such cases, the formula overcounts the probability by including the intersection of the events twice. To account for the overlapping portion, we need to subtract the probability of their intersection: Pr(E ∪ F) = Pr(E) + Pr(F) - Pr(E ∩ F).

In conclusion, the equation Pr(E ∪ F) = Pr(E) + Pr(F) holds true only if events E and F are mutually exclusive. Otherwise, the formula should include the probability of their intersection as well.

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Answer:

RT = 26

Step-by-step explanation:

Based on the figure we can say :

Scale factor :

Hence, as the proportions are the same :

The triangle ABC and RST will be similar triangles. Then the length of RT will be 26 units.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If the two triangles are similar, the ratio of the corresponding sides will be constant.

The triangle ABC and RST will be similar triangles.

RT / 13 = 24 / 12

      RT = 26

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The life length in hours is exceeded by 95/5% of the light bulbs is 1329 hours.

To find the life length in hours that is exceeded by 95% of the light bulbs, we need to determine the corresponding z-score for the 95th percentile and use it to calculate the value.

Since the distribution is assumed to be normal, we can use the standard normal distribution (z-distribution) to find the z-score. The z-score represents the number of standard deviations an observation is above or below the mean.

To find the z-score corresponding to the 95th percentile, we look for the z-value that corresponds to a cumulative probability of 0.95. This value can be obtained from standard normal distribution tables or using a statistical software/tool.

For a cumulative probability of 0.95, the corresponding z-score is approximately 1.645.

Once we have the z-score, we can calculate the exceeded life length as follows:

Exceeded life length = Mean + (Z-score * Standard deviation)

Exceeded life length = 1000 + (1.645 * 200)

Exceeded life length ≈ 1000 + 329

Exceeded life length ≈ 1329 hours

Therefore, approximately 95% of the light bulbs will have a life length that exceeds 1329 hours.

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Answer:

70°

Step-by-step explanation:

m ∠L = 180-(55+55)

= 180-110

=70°

Answer:

x = 9

Step-by-step explanation:

The perimeter of the first triangle is x + 3 + x + 3 + x + 3 = 3x + 9 and the perimeter of the second triangle is x + 3 + 2x - 3 + x = 4x. We know that the perimeters are equal, therefore, we can write the following equation:

3x + 9 = 4x

x = 9

Answer:

16870

Step-by-step explanation:

Answer: um 16870 I guess

Step-by-step explanation: I hope I help and can you plz give me a brainliest

1950:12

1990:70

70-12:58

58/40:1.45

1.45x40 :58

cada año le sumaban 1.45 a la barrita de cereal

saben que no me hagan caso ni yo se que acabo de hacer xd

Thus, the linear equation models the increase in the price of a loaf of bread will be 50x+12=70.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that, the average cost of a loaf of bread in 1950 was approximately 12 cents, and by 1990 the cost was about 70 cents.

(Let x represent the number of years since 1900.)

The linear equation models the increase in the price of a loaf of bread will be.

y = bx + +c

70 = 50x + 12

The linear equation models the increase in the price of a loaf of bread will be 50x+12=70.

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Answer and Step-by-step explanation:

4. We are finding line AC.

AB is congruent to BC because the angles at the top are both 30 because of angle bisector. BD is congruent to BD, so triangles are congruent by SAS theorem. That means AB is congruent to BC by CPCTC (Congruent Parts of Congruent Triangles are Congruent).

With that being said, we can equal the expressions together.

-x + 25 = 3(2x - 8)

-x + 25 = 6x - 24

49 = 7x

7 = x

-(7) + 25 = 18

3(2(7) - 8) = 3(14 - 8) = 3(6) = 18

18 + 18 = 36

AC = 36

6. We are finding measure of angle UTW.

We have another angle bisector, so that side is equal to itself (TV ≅ TV)

We have UV and VW having the same length, so those are congruent.

Since this is a right triangle, these triangles are congruent by the HL (Hypotenuse-Leg) Theorem.

So, now we can equal the angles together.

2x + 3 = 5x - 24

27 = 3x

9 = x

2(9) + 3 = 18 + 3 = 21

5(9) - 24 = 45 - 24 = 21

21 + 21 = 42

m∠UTW = 42

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(Sorry for the late response, this took some time).

Answer:

3x+6

Step-by-step explanation:

just multiply 3*x=3x and 3*2=6 so  3x+6

Answer:

x=3y-29/y-8

Step-by-step explanation:

3(y-10)+1=x(y-8)

xy-8x=3y-29

x(y-8)=3y-29

/y-8        /y-8

x=3y-29/y-8

Answer:

I believe there are four terms in this expression.