) Which of the following expressions has a coefficient of 6 and a constant of 9?
6x + 9
9-6
9 +6
6 + 9.2

Answer:

2x + y = 3

Step-by-step explanation: because if you do 2x1 you'll get 2

Given that a || b, m∠2 = 63° and m∠9 = 105°.

Now, all the angles are as follows:

m∠5= m∠2 = 63° [vertically opposite angle]

m∠7= m∠9=105° [vertically opposite angle]

m∠8= 180°-m∠9=180°-105°=75° [Supplementry angles, m∠8+m∠9=180°]

m∠10= m∠8= 180° [vertically opposite angle]

m∠6= m∠8=75° [ Alternate angles]

m∠3= m∠6=75° [vertically opposite angle]

m∠1= 180°-(m∠2+m∠3)=180°-(63°+75°)=42° [as m∠1+m∠2+m∠3=180°]

m∠4= m∠1=42° [vertically opposite angle]

m∠11=m∠4=42° [ Alternate angles]

m∠13= m∠11=42° [vertically opposite angle]

m∠12= 180°-m∠11=180°-42°=138° [as m∠8+m∠9=180°]

m∠14 = m∠12=138° [vertically opposite angle]

The scale factor that was used to create triangle J′K′L′ include the following: A. 1/3.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)

By substituting the given parameters into the formula for scale factor, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

Scale factor = 2/6 = 3/9 = 4/12

Scale factor = 1/3.

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Sequences can start at either 0 or 1, depending on the specific sequence and the conventions used.

In mathematics, there are two main ways to number the elements of a sequence: zero-indexing and one-indexing. In zero-indexing, the first element of a sequence is assigned the index 0, the second element is assigned the index 1, and so on. This is the standard convention used in computer science and programming.

On the other hand, in one-indexing, the first element of a sequence is assigned the index 1, the second element is assigned the index 2, and so on. This is the standard convention used in mathematics and many other fields.

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According to the question The local sidereal time (LST) at noon on March 21st is approximately 12:00 (option c).

To determine the LST, we need to consider the rotation of the Earth and its relation to the stars. LST is based on the apparent motion of the vernal equinox, which completes a full cycle in approximately 24 hours.

Since noon is halfway through the day, we can estimate that the LST at noon would be approximately half of 24 hours, which is 12:00. This assumes that we are considering a location where the local time is synchronized with the standard time zone and there are no factors like daylight saving time or variations in the location's longitude that can affect the LST calculation.

Therefore, the correct answer is option c) 12:00 local sidereal time.

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9514 1404 393

Answer:

  (x, y, z) = (5, 11, 6)

Step-by-step explanation:

To solve this problem, you need to understand "row operations". The ones we're concerned with are multiplying a row by a scalar, and adding rows together.

You also need to understand what the solution looks like, and the usual way that is achieved. The solution will have the 3×3 matrix left of the vertical line be a diagonal of 1s (the identity matrix). Then the numbers to the right of the vertical line represent the solution.

__

In the following, we will use the notation [a]+b[c]⇒[d] to mean that row 'a' is added to the product of row 'c' and the scalar 'b' and that sum replaces row [d]. Multiplying a row by a scalar multiplies each element in the row by that scalar.

The first several operations look like this. Notice we have made the upper left 2×2 matrix an identity matrix. Steps will continue to take care of the 3rd column.

  \(\left[\begin{array}{ccc|c}1&1&1&22\\6&1&8&89\\-6&4&4&38\end{array}\right] \qquad\text{given}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&-5&2&-43\\0&5&12&127\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ 6[1]+[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ $-\frac{1}{5}$[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[1]-[2]$\rightarrow$[1]}\)

Now, we normalize the third column.

  \(\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&1&6\end{array}\right] \qquad\text{$\frac{1}{14}$[3]$\rightarrow$[3]}\\\\\left[\begin{array}{ccc|c}1&0&0&5\\0&1&0&11\\0&0&1&6\end{array}\right] \qquad\text{$-\frac{7}{5}$[3]+1$\rightarrow$[1];\ $\frac{2}{5}$[3]+[2]$\rightarrow$[2]}\)

This is the target of our row operations. It tells us the solution to the system of equations is ...

  (x, y, z) = (5, 11, 6)

_____

A number of online calculators and phone or tablet apps are available for putting a coefficient matrix into this "reduced row-echelon form." Many graphing calculators will do this, too.

In the end, this is not terribly different from ad hoc solution using "elimination" methods. That is precisely what we did when we created the zeros in the first two columns of row 3.

We have the inverse Laplace transform of \((5s + 2) / (s^2 + 3s + 2) as 3e^_(-t)\)\(- e^_(-2t).\)

To find the Laplace transform of 2t sin(2t), we can use the formula for the Laplace transform of \(t^n f(t)\), where n is a non-negative integer. Applying this formula, we have:

L{2t sin(2t)} = \(-d/ds [L{sin(2t)}]\)

Now, the Laplace transform of sin(2t) can be found using the formula:

L{sin(at)} = \(a / (s^2 + a^2)\)

Substituting a = 2, we have:

L{2t sin(2t)} = \(-d/ds [2/(s^2 + 2^2)]\)

Taking the derivative and simplifying, we get:

\(L{2t sin(2t)}\) = \(-2(2s) / (s^2 + 4)^2\)

=\(-4s / (s^2 + 4)^2\)

Therefore, the Laplace transform of 2t sin(2t) is \(-4s / (s^2 + 4)^2.\)

To find the Laplace transform of 3H(t-2) - 8(t-4), we need to split it into two terms: one corresponding to the Laplace transform of 3H(t-2) and the other corresponding to the Laplace transform of -8(t-4).

The Laplace transform of H(t-a) is given by:

L{H(t-a)} =\(e^(-as) / s\)

Substituting a = 2, we have:

L{3H(t-2)} = \(3e^_(-2s)\)\(/ s\)

For the second term, we can use the linearity property of the Laplace transform:

L{-8(t-4)} = -8L{t-4}

The Laplace transform of t-a is given by:

L{t-a} =\(1 / s^2\)

Substituting a = 4, we have:

L{-8(t-4)} =\(-8 / s^2\)

Combining the two terms, we have:

L{3H(t-2) - 8(t-4)} = \(3e^(-2s) / s - 8 / s^2\)

Therefore, the Laplace transform of \(3H(t-2) - 8(t-4) is 3e^(-2s) / s - 8 / s^2\).

5.2 To find the inverse Laplace transform of \((5s + 2) / (s^2 + 3s + 2)\), we need to decompose the expression into partial fractions.

First, we factor the denominator as (s + 1)(s + 2).

Then, we write the expression as:

\((5s + 2) / (s^2 + 3s + 2) = A / (s + 1) + B / (s + 2)\)

Multiplying both sides by (s + 1)(s + 2), we have:

5s + 2 = A(s + 2) + B(s + 1)

Expanding and combining like terms, we get:

5s + 2 = As + 2A + Bs + B

Matching coefficients, we find A = 3

and B = -1.

Therefore, we have:

\((5s + 2) / (s^2 + 3s + 2) = 3 / (s + 1) - 1 / (s + 2)\)

Now, we can use the linearity property of the inverse Laplace transform

to find the inverse transform of each term. The inverse Laplace transform of 3 / (s + 1) is \(3e^_(-t)\), and the inverse Laplace transform of

\(-1 / (s + 2) is -e^_(-2t).\)

Combining these, we have the inverse Laplace transform of

\((5s + 2) / (s^2 + 3s + 2) as 3e^_(-t)\)\(- e^_(-2t).\)

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Using  cylindrical coordinates ∫∫∫ (r^3cos^2θ) dz dr dθ, where r ranges from 0 to 2, θ ranges from 0 to 2π, and z ranges from 0 to √(36r^2).

To evaluate the integral ∫∫∫ x^2 dV over the solid e, using cylindrical coordinates, we need to express the integral in terms of cylindrical coordinates and determine the appropriate bounds for the variables.

In cylindrical coordinates, the solid e can be defined as follows:

Radius: r ranges from 0 to 2 (from x^2 + y^2 = 4, taking the square root).

Angle: θ ranges from 0 to 2π (full revolution around the z-axis).

Height: z ranges from 0 to the height of the cone, which is determined by z^2 = 36x^2 + 36y^2.

To convert the integral, we need to express x^2 in terms of cylindrical coordinates:

x^2 = (rcosθ)^2 = r^2cos^2θ

The integral in cylindrical coordinates becomes:

∫∫∫ (r^2cos^2θ) r dz dr dθ

Now we can determine the bounds for the variables:

r ranges from 0 to 2.

θ ranges from 0 to 2π.

z ranges from 0 to the height of the cone, which can be determined by setting z^2 = 36r^2.

Substituting the bounds and integrating, we can evaluate the integral to find the desired result.

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The value of y at x = 0 is -9/7 for the given differential equation y' = 10x⁴ − 12x³ + 8⁻⁴ˣ + 7 . Therefore, option C is correct.

Given the differential equation y' = 10x⁴ − 12x³ + 8⁻⁴ˣ + 7 and (0) = −9,

we are to find the value of y at x = 0.

The given differential equation is,

y' = 10x⁴ − 12x³ + 8⁻⁴ˣ + 7

It is in the form y' = f(x)

Now, we integrate the given differential equation with respect to x,

∫y' dx = ∫(y' = 10x⁴ − 12x³ + 8⁻⁴ˣ + 7) dx

Integrating the right hand side w.r.t x, we get

y = 10x⁵/5 − 12x⁴/4 + 8⁻⁴ˣ²/2 + 7x + c

where c is the constant of integration.

Now, we have (0) = −9 i.e. y = -9 when x = 0.

Substituting the values of x and y, we have

-9 = 0 + 0 + 0 + 7c

Therefore,

c = (-9 - 0 - 0)/7

= -9/7

Hence, the value of c is -9/7

Putting the value of c in the equation of y, we have

y = 2x⁵ - 3x⁴ + 4x² - 9/7

The value of y at x = 0 is

y = 0 - 0 + 0 - 9/7

= -9/7.

Therefore, option C is correct.

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Given data

The length of the square L = 25 in

Use the formula for the perimeter of a square below, to find the perimeter.

Use the formula for the area of a square below, to find the area.

The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.

What is algebra ?

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It includes the study of operations such as addition, subtraction, multiplication, division, and the extraction of roots, as well as the properties of operations such as commutativity, associativity, and distributivity.

The method proposed by Alan is not fair because it does not take into account the probability of each outcome. The product of the outcomes being even or odd does not guarantee an equal probability of winning for both siblings. To make it fair, each sibling should have an equal chance of winning. A fair method could be to have the arrow spun once, and the sibling whose number is spun gets to choose the new pet. Another fair method could be to have a coin flipped, and the sibling whose side of the coin is facing up gets to choose the new pet.

So , The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.

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Answer:

D is correct

Step-by-step explanation:

A graph of that sort will make a perfectly mirrored "V" shape, and with no offset, the bottom point will be on the y axis.  This means that the first equation will intercept the y axis at zero, the second will intercept the y-axis at -15.

"A" may seem correct also, as the second graph will intercept the x-axis at -15, but it is not complete, as it will intercept that axis at +15 as well.

Answer:

j=7

Step-by-step explanation:

11j-20=6j+15

-6j          -6j  

5j-20=15  Isolate the variable:

  +20  +20

5j=35 Divide to get variable by itself

j=7  

Hope this helps :)

Answer:

1) \(\frac{12.2}{sin(54)}\) which rounds to 15.1

2) \(\frac{12.2}{cos(54)}\) which rounds to 20.8

Step-by-step explanation:

1) We're going to have to use the trig ratios for this. We know that sin(x) = \(\frac{opposite}{hypotenuse}\) (opposite side over the hypotenuse). In this case, we know that angle h = 54 and the side opposite to angle h = 12.2, and we're trying to find the hypotenuse. If we label the hypotenuse as x, then we can say that sin(H) = \(\frac{MI}{HI}\). We can plug in the values we know to get sin(54) = \(\frac{12.2}{x}\). From there, we multiply by x on both sides to get x out of the denominator, and then we divide by sin(54). So, we end up with x = \(\frac{12.2}{sin(54)}\) which, if you put it in your calculator (and make sure the calculator is in degree mode) we get approximately 15.1 mi.

2) Follow the same steps that are described in 1), but instead of sin, we're using cos.

Hope this helps! Let me know if you have any further questions!

Hey there! I'm happy to help!

To find the surface area of a sphere, here is what you do.

You square the radius.

4²=16

You multiply by 4.

16×4=64

And you multiply by pi!

64×π=64π

Therefore, the surface area of the sphere is A. 64π units². It's that easy!

Now you can find the surface area of a sphere! Have a wonderful day! :D

Question :-

Answer :-

\( \rule{180pt}{3pt}\)

Diagram :-

\(\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{4 \: units}}\end{picture}\)

Solution :-

As per the provided information in the given question, we have been given that the radius of the sphere is 4 units. We have been asked to find or calculate the surface area of the sphere.

To calculate the surface area of the sphere, we will use the formula below :-

\(\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}\)

Substitute the given values into the above formula and solve for surface area:

\(\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2\)

\(\sf:\implies Surface \: Area_{(Sphere)} = 4 \times \pi \times (4 \: units)^2\)

\(\sf:\implies Surface \: Area_{(Sphere)} = (4 \: units)^2 \times 4 \times \pi\)

\(\sf:\implies Surface \: Area_{(Sphere)} = 16 \: units^2 \times 4 \times \pi\)

\(\sf:\implies \bold{Surface \: Area_{(Sphere)} = 64\pi \: units^2}\)

Therefore :-

\(\\\)

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The required coordinates of endpoint S are (8, -2).

Given that the midpoint of Rs is M (1, 2) and one endpoint is R(-6, 6). We need to find the coordinates of endpoint S.Let the coordinates of the endpoint S be (x, y).Now, the formula for the midpoint of a line is:(x₁+x₂/2 , y₁+y₂/2)M(1, 2)=R(-6, 6)+ S(x, y)/2⇒ (x - 6)/2 = 1 ....(1)and (y + 6)/2 = 2....(2)

Solving the above equations we get,x - 6 = 2⇒ x = 8and y + 6 = 4⇒ y = -2So, the coordinates of endpoint S are (8, -2).

Hence, the required coordinates of endpoint S are (8, -2).

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The probability of selecting exactly 2 white marbles out of 5 marbles from container b is approximately 0.144 or 14.4%.

To calculate the probability of selecting exactly 2 white marbles out of 5, we can use the binomial coefficient formula, which is given by:

P(X=k) = (n choose k) × \(p^{k}\) × \(1-p^{n-k}\)

where n is the total number of trials (in this case, 5), k is the number of successful outcomes (in this case, 2), p is the probability of success (in this case, the probability of selecting a white marble), and (n choose k) is the binomial coefficient.

First, let's find the probability of selecting a white marble from container B, which is given by:

p = (number of white marbles) / (total number of marbles) = (300 + 1) / (300 + 100 + 1) = 301 / 401

Next, we can use the formula to find the probability of selecting exactly 2 white marbles:

P(X=2) = (5 choose 2) × p² * (1-p)⁽⁵⁻²⁾ = (10) × (301/401)² × (100/401)³ = 0.144

So the probability of selecting exactly 2 white marbles out of 5 is approximately 0.144 or 14.4%.

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The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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The correct representation of the inequality are:

1 ≥ 2x

6x ≥ 3 + 8x – 4

A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.

6x ≥ 3 + 4(2x – 1)?

6x ≥ 3 + 8x - 4  ---- correct

6x - 8x ≥ 3 - 4

-2x ≥ - 1

1 ≥ 2x ----- correect

The number line would be A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.

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Answer:

The answer is explained below

Step-by-step explanation:

Given that:

mean (μ) = 7 and standard deviation (σ) = 1.5.

The z score is used in statistic used to measure the number of standard deviation by which the raw score is above or below the mean value. It is given by:

\(z=\frac{x-\mu}{\sigma}, where\ x\ is\ the \ raw\ score\)

To find the Probability that x < 8.8, we first find the z score using:

\(z = \frac{x-\mu}{\sigma}=\frac{8.8-7}{1.5}=1.2\)

From the z tables, P(x < 8.8) = P(z < 1.2) = 0.8849 = 88.49%

Answer:

3) 7:8  7 to 8   4) 40/100 = 2/5   5) 60 mph   6) 300 kph   7) Jane  8) Jon can go faster

Step-by-step explanation:

5) 120/2 =60

6) 900/3 =300

7) Tim =50/5= $10 an hour

Jane= 24/2 =$12 an hour

Answer:

look at explanation, oh and pls give brainlist

Step-by-step explanation:

3.   7:8  \(\7\frac{7}{8}\) ,7 to 8

4.  \(\frac{100 l}{40 w}\), \(\frac{25}{10}\), \(\frac{50}{20}\)

5.  \(\frac{2 hrs}{120 m}\), unit rate= 60 miles per hour, \(\sqrt[2]{120}\)=60

6.  \(\sqrt[3]{900}\)= 300, 300x3=900, unite rate= 300km per hour

7.  \(\frac{50}{5}\)=\(\frac{10\\}{1}\), unit rate for Tim= $10 for 1 hour, \(\frac{24}{2}\)=\(\frac{12}{1}\), unit rate for Jane= $12 for 1 hour, Jane has the higher rate of pay.

8. \(\frac{65}{4}\)=\(\frac{16.25}{1}\) , \(\sqrt[4]{65}\)= 16.25, unit rate for Jon is 16.25ths of a pushup per minute.

\(\frac{45}{3}\)=\(\frac{15}{1}\), \(\sqrt[3]{45}\)=15, unit rate for Paul is 15 pushups per minute.

Jon can do more pushups in 1 minute

The growth rate of a bacterial colony after 2 hours can be found by calculating the derivative of the population function with respect to time and substituting t = 2. The growth rate after 2 hours is 4.

The population function of the bacterial colony is given as p(t) = 4t^2 - 20t + 150. To find the growth rate after 2 hours, we need to calculate the derivative of this function with respect to time (t).

Taking the derivative of the population function, we get p'(t) = 8t - 20.

To find the growth rate after 2 hours, we substitute t = 2 into the derivative:

p'(2) = 8(2) - 20

     = 16 - 20

     = -4.

Therefore, the growth rate after 2 hours is -4.

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Answer:

(5,2) and (6,5)

length of side = sqrt10 ~= 3.16 units

Area = 12 sq units

Step-by-step explanation:

It really helps to graph the given information. See image. The sides have the same slope bc they are parallel. If you go UP3 & OVER1 to get from the first point to the second point, then do that again on the right side. See image. Use distance formula or pythagorean thm to find the length:

c^2 = 3^2 + 1^2

c^2 = 9+1

c^2 = 10

c = root10 ~= 3.16

Area of a parallelogram is b•h

A = 4•3

= 12

see image.

Answer:

26

Step-by-step explanation:

Problem: f(x) = 28 + x + 7

Plug in f(-9)

New equation: f(-9) = 28 + (-9) + 7

Simplify: f(-9) = 26

Answer: f(-9) = 26

Here is the answer for the question

Answer:

D

Step-by-step explanation:

D is the correct answer

The total area of the figure in this problem is given as follows:

41.3 ft².

The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.

The figure in this problem is composed as follows:

Then the area of the triangle is given as follows:

At = 0.5 x 6 x 3 = 9 ft².

The area of the semicircle is given as follows:

Ac = π x 3² = 28.3 ft².

The area of the square is given as follows:

As = 2² = 4 ft².

Then the total area of the figure is given as follows:

9 + 28.3 + 4 = 41.3 ft².

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