Factor 2a–4b. Write your answer as a product with a whole number greater than 1.

The speed of light in diamond is approximately 1.24 x 10⁸ meters per second.

The index of refraction (n) of a given media affects how fast light travels through it. The refractive is given as the speed of light divided by the speed of light in the medium.

n = c / v

Rearranging the equation, we can solve for the speed of light in the medium,

v = c / n

The refractive index of the diamond is given to e 2.42 so we can now replace the values,

v = c / 2.42

Thus, the speed of light in diamond is approximately 1.24 x 10⁸ meters per second.

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Step-by-step explanation:

f(-7)= (-7)^2 + 6×(-7)=49-42= 7

f(-6)=36-36= 0

f(-5)=25-30= -5

f(-4)=16-24= -8

Answer:

60$ and 10$ dollar maybe

The length from point A to point B on the clock is approximately 24.083 cm, which is closest to 24 cm. This is calculated using the Pythagorean theorem.

Using the Pythagorean theorem, we can calculate the length from point A to point B as follows

First, we need to find the length of the vertical line segment from point D to point A. This is equal to the radius of the clock, which is 24 cm.

Next, we can find the length of the horizontal line segment from point D to point B. This is equal to the distance from the top of the clock at point D to the hanger at point B, which is given as 2 cm.

Now, we can use the Pythagorean theorem to find the length from point A to point B

AB² = AD² + DB²

AB² = (24 cm)² + (2 cm)²

AB² = 576 cm² + 4 cm²

AB² = 580 cm²

AB ≈ 24.083 cm

Therefore, the length from point A to point B is approximately 24.083 cm, which is closest to 24 cm.

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Answer:

The length from point A to point B on the clock is approximately 24.083 cm, which is closest to 24 cm. This is calculated using the Pythagorean theorem.

Hope this helps :)

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The number of outcomes in the complement of the event is 163

The statement is given as:

Out of 301 apartments in a complex, 138 are available for rental.

This means that

Apartments = 301

Rental = 138

The complement is calculated as:

Complement = Apartment - Rental

So, we have

Complement = 301 - 138

Evaluate

Complement = 163

Hence, the number of outcomes in the complement of the event is 163

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4x+4y..........................

The function in this graph is constant in the range of -4 ≤x≤-2 , Option D is the correct answer.

A function is a mathematical statement which identifies relation between independent and dependent variable.

A graph is given

The graph will be considered constant when the y value is constant for any value of x

The value of y is constant in the range of

-4 ≤x≤-2

Therefore Option D is the correct answer.

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the function in this graph is constant. from -4 ≥ x ≤ -2.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.

Given a graph, by observing that graph we can determine that

Since The graph of a constant function can never be a curve. The graph of a constant function is always a horizontal line. An algebraic function is a constant function if there is no variable in its definition.

x < -4 it is a linear function

-4 ≥ x ≤ -2 graph is constant

-2 ≥ x ≤ 3 linear with positive slope

x > 3 graph is linear with a negative slope

Therefore, From -4 ≥ x ≤ -2 the function in this graph is constant.

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The expression 2z^4 - 2 can be factored as 2(z^2 + 1)(z^2 - 1), which is option C.

The expression 2z^4 - 2 can be factored as:

2(z^2 - 1)(z^2 + 1)

To understand why this is the case, we need to notice that the expression has the form of a difference of squares. Specifically, 2z^4 can be written as (z^2)^2 * 2, and -2 can be written as (-1)^2 * 2. So, we have:

2z^4 - 2 = (z^2)^2 * 2 - (-1)^2 * 2

Now, we can use the formula for the difference of squares:

a^2 - b^2 = (a + b) * (a - b)

where a = z^2 and b = 1, to get:

2z^4 - 2 = 2(z^2 + 1)(z^2 - 1)

So, the expression 2z^4 - 2 can be factored as 2(z^2 + 1)(z^2 - 1), which is option C.

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Answer:

x

=

±

√

5

−

6

Decimal Form:

x

=

−

3.76393202

…

,

−

8.23606797

…

Step-by-step explanation:

Answer:

Step-by-step explanation:

Look at the coefficients of x: One is a multiple of the other. This makes it easy to eliminate the x terms.

Multiply the first equation by 2:

10x - 8y = 6

Then add it to the second equation:

 10x - 8y = 6

-10x + 7y = -4

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

 0x - y = 2,  therefore, y = -2.

Now substitute -2 for y in either of the equations and solve for x:

5x - 4(-2) = 3

5x = -5

x = -1

(x,y) = (-1,-2)

Hi! Your answer is x = -1, y = -2. We can write in coordinate form as (-1,-2)

Please see an explanation for a better and clear understanding to your problem.

Any questions about my answer and explanation can be asked through comments! :)

Step-by-step explanation:

\(\large{\begin{cases} 5x-4y=3 \\ -10x+7y=-4 \end{cases}}\)

By elimination method, we can eliminate either x-term or y-term. It depends on your choice or desire. Notice that both equations cannot be eliminated because if we add x-term up, we would get -5x which doesn't even eliminate x-term. Same goes to y-term. Now the question will pop up in your head - Then how do we eliminate either x-term or y-term?

Simple, multiply the whole equation to make one of the terms have same absolute value. Notice if we multiply the whole first equation by 2, we would get x-term from 5x to 10x. Then we add 10x and -10x up, we would get 0 and finally get x-term to be eliminated.

Therefore, multiply the whole first equation by 2.

\(\large{5x-4y=3}\\\large{5x(2)-4y(2)=3(2)}\\\large{10x-8y=6}\)

Next, rewrite the equation.

\(\large{\begin{cases} 10x-8y=6 \\ -10x+7y=-4 \end{cases}}\)

Then we are able to eliminate x-term by adding up between first and second equation.

\(\large{(10x-10x)+(-8y+7y)=6-4}\\\large{0-y=2}\\\large{-y=2}\\\large{y=-2}\)

We've finally got the y-value. But we are not done yet. What we are going to do next is to find x-value.

Simply substituting y = -2 in any given equations. You can either substitute y = -2 in one equation only if you are pretty certain enough or two equations if you think that you value safety/quality more than time. I'll be substituting y = -2 in two equations to demonstrate how substituting the solution in two equations get you to the same answer.

Substituting in First Equation

\(\large{5x-4y=3}\)

Substitute y = -2 in the equation. It's the best to use an original equation instead of rewritten equation.

\(\large{5x-4(-2)=3}\\\large{5x+8=3}\\\large{5x=3-8}\\\large{5x=-5}\\\large{x=-1}\)

Substituting in Second Equation

\(\large{-10x+7y}=-4\)

Substitute y = -2 in the equation.

\(\large{-10x+7(-2)=-4}\\\large{-10x-14=-4}\\\large{-14+4=10x}\\\large{-10=10x}\\\large{-1=x}\)

Notice how substituting in two equations give the exact same answer in the end. We've finally got the solution.

We can conclude that when x = -1, y =-2.

To answer this question we will set and solve a system of equations.

Let A be the speed (in miles per hour) of the airplane in still air, and W be the wind speed (in miles per hour).

Since the airplane flying with the wind takes 4 hours to travel a distance of 1200 miles and flying against the wind takes 5 hours to travel the same distance, then we can set the following equation:

Dividing the first equation by 4 we get:

Subtracting A from the above equation we get:

Substituting the above equation in the second one we get:

Simplifying the above result we get:

Adding 1500 to the above equation we get:

Dividing the above equation by 10 we get:

Finally, substituting A=270 at W=300-A we get:

Answer:

The speed of the airplane in still air is 270 miles per hour.

The wind speed is 30 miles per hour.

Answer:

B. (-3, -17)

Step-by-step explanation:

Plotting them out on a graph, the other 3 points are able to be connected as a parallelogram. If you don't have graph paper at home, you can do an online search for "online graph paper" and use that. I personally find it very helpful to be able to see these kinds of things with my eyes.

Answer:

1/16   2/16  3/16  4/16  5/16  6/16  7/16  8/16 9/16 10/16  11/16 12/16

Step-by-step explanation:

Para la identificación de las brocas tenemos dos consideraciones:

1.- Fracciones de igual denominador son mas grandes en orden creciente según vayan creciendo los numeradores, de tal forma que entre

9/16   3/16    7/16     5/16   11/16    el orden es como sigue ( de menor a mayor)

3/16     5/16     7/16     9/16     11/16

2.- Las fracciones con denominadores distintos pueden llevarse a denominador común /16  amplificando la fracción es decir por ejemplo

1/4   =  1*4/4*4   =  4/16

Con ese procedimiento las convertimos todas al caso señalado en el punto anterior y ordenamos

1/4   = 4/16

3/8  = 6/16

1/2  = 8/16

5/8 =  10/16

1/8  =  2/16

Entonces hay diez brocas la primera será 1/16 y la número 12   12/16

Y finalmente el orden es:

1/16   2/16  3/16  4/16  5/16  6/16  7/16  8/16 9/16 10/16  11/16 12/16

Answer:

1.71 pounds of sugar per dollar.

Step-by-step explanation:

To calculate how many pounds of sugar Keisha got per dollar, we divide the total amount of sugar by the total amount of money spent. In this case, she bought 12 pounds of sugar for $7, so we divide 12 by 7:

12 ÷ 7 = 1.71

So, Keisha got 1.71 pounds of sugar per dollar.

According to the image, the table shows a relationship that is not proportional. First of all, you cannot multiply a number by 0 and get something other than 0. Anything multiplied by 0 is always 0.

Second, the rule is different for each row.

2x5=10

4x4=16

6x3.6=22

A proportional relationship must increase by the same amount, and this does not, which means it is not proportional.

Find common ratio

Yes they are proportional

The given system of equation is,

consider the equation (2),

consider the quation (3) and mulitply with 2,

then subract them,

Thus, the system of equation are, infinitely many solution.

The answer is (x,y) = (oo,oo).

To find the greatest common factor, we take these numbers and analyze them into prime numbers

Example : 48 = 2^4 x 3
112 = 2^4 x 7
80 = 2^4 x 5

Now, the greatest common factor of them all will be the prime number (with power) that they all have in common.

So, they all have 2^4 -> Their greatest common factor is 2^4


Side note : Example with 10 and 80, we analyzed to 2 x 5 and 2^4 x 5, here their common prime numbers are actually 2 and 5 -> 2 x 5 = 10
(So, if there is a prime number and a prime number that is powered, we take the original one)

Answer:

t = -1

Step-by-step explanation:

  Distribute (-2) to each term of (t + 4) in the RHS

10t + 4 - 2t = 2 - 2(t + 4)

10t - 2t + 4 = 2 - 2 *t - 2*4

10t - 2t + 4 = 2 - 8 - 2t

Combine the like terms in the LHS and RHS,

        8t + 4 = - 6 - 2t

Subtract 4 from both sides,

        8t      = -6 - 2t - 4

            8t  = -10 - 2t

Add 2t to both sides,

         8t + 2t = -10

           10t    = -10

                 t = -10 ÷ 10

                 \(\sf \boxed{t =-1}\)

T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).

To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.

For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).

As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).

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Answer: If two forecasters have unbiased forecasts, then they should have the same average error over many forecasts. In that sense, they would be equally good at forecasting.

Step-by-step explanation:

The statement that is true regarding evaluating the quality of a forecast is:

If both forecasters have an unbiased forecast, then they are equally good at forecasting.

Explanation:

A biased forecast can have a zero forecast error if the bias happens to offset the error in the forecast. However, a zero forecast error does not necessarily indicate that the forecast is unbiased.

In the mean squared error (MSE) evaluation, one single observation can make a very large difference because the errors are squared before they are averaged. Therefore, outliers can have a large impact on the MSE.

If we are evaluating the same forecaster, then the mean squared error is not always lower than the mean absolute error. It depends on the specific forecast and the distribution of errors.

However, if two forecasters have unbiased forecasts, then they should have the same average error over many forecasts. In that sense, they would be equally good at forecasting.

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Triangle KVM is similar to triangle BVG because angle M = angle G = 90° and angle V is common to both triangles.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two triangles to be similar, the corresponding angles must be congruent i.e equal.. Also the ratio of the corresponding sides of similar triangles are equal.

angle M and G are both 90° , this means they are equal.

angle KVM = BVG

therefore angle K = angle B

Since all the corresponding angles are equal, we can say triangle KVM is similar to triangle BVG

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51 degrees is the measure of the angle D from the given diagram

The given diagram is a circle with angles. The measure of the angle 'd' can be determined using the equation below:

m<d = 1/2(arcIM - arcNX)

Substitute the given parameters into the formula

m<d = 1/2(152- 50)

m<d = 1/2(102)

m<d = 51 degrees

Hence the measure of the angle m<D from the given circle is 51 degrees.

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Answer:

your answer is 12

Step-by-step explanation:

Base 7 Area 42

Using the formula

A= hb over 2

Solving for hb

hb=2A

b=2·42

7=12

hope this is not to confusing but the answer is 12.

answer : x≤-6

steps:

3x+2≥4x+8

-x≥6

x≤-6

Answer:

x≤−6

View graph below

Step-by-step explanation:

x≤−6

Solution Steps

3x+2≥4x+8

Subtract 4x from both sides.

3x+2−4x≥8

Combine 3x and −4x to get −x.

−x+2≥8

Subtract 2 from both sides.

−x≥8−2

Subtract 2 from 8 to get 6.

−x≥6

Divide both sides by −1. Since −1 is negative, the inequality direction is changed.

x≤−6

X could be from -6 to -infinity.

Answer:

2nd option

{(-8, -2), (-4, 1), (0, -2), (2, 3), (4, -4)}

Step-by-step explanation:

For a function to exist, every value of input must have exactly one value of output.

The rest of the relations(1, 3, and 4) have 2 outputs for 1 input so they dont make a function.

Answer:

(B)

Step-by-step explanation:

If you noticed, all the other input values have one input value that has two output values. This doesn't represent a function. Only (B) has one output for each input.

Hope that helps (●'◡'●)