find the slope of each line 5x-y=-7

Answer:

Step-by-step explanation:

Given , two air craft carriers are A and B . The carrier A is longer than the carrier B in length.

Total length of two carriers =4178 feet

Difference of two carriers = 14 feet

Let

Length of carrier A =x  feet

And

Legth of carrier B =y feet

According to question  

The I equation is

x+y=4178

The II equation is

x-y= 14

Substitution method:  In this method step I :  we  find value of x or y from the equation I

Step II:  put the value of x or y in II equation then we get the value of another  varaiable x or y  

Step : Again put the obatined value of variable x or y  from  step II   in equation I then we get value of other variable x or y .

By  using substitution method ,

we find value of x from equation I

x= 4178-y

Now, put the value of x in equation II then we get

4178-y-y=14

4178-2y=14

4178-14=2y

4164=2y

[tex]y=\frac{4164}{2}[/tex]

y= 2082

Again , put the value of y in equation I

2082 +x=4178

x= 4178-2082

x=2096

Hence, the length of carrier A = 2096 feet

The length of carrier B= 2082 feet

Final answer:

To solve the problem, we set up two equations based on the given total length and the length difference of the two aircraft carriers. By solving these equations, we find that carrier A is 2096 feet long and carrier B is 2082 feet long.

Explanation:

The student's question involves solving a system of linear equations to find the lengths of two aircraft carriers, A and B. Given that the total length is 4178 feet and the length difference is 14 feet, we can set up the following equations:

Equation 1: A + B = 4178

Equation 2: A - B = 14

To solve for A and B, we can add the two equations together to eliminate B.

This gives us 2A = 4192, hence A = 2096 feet.

Substituting A back into one of the equations, we find B = 2082 feet.

Therefore, carrier A is 2096 feet long and carrier B is 2082 feet long.

Final answer:

Your expected monthly earnings in 10 years, with a 2.3% annual increase, would be $4424.10, rounded to the nearest cent.

Explanation:

To calculate your expected monthly earnings in 10 years, taking into account a 2.3% annual increase, we will use the formula for compound interest: P(1 + r)^n, where:

P is the principal amount (your current earnings)

r is the annual raise rate

n is the number of years

Your current monthly earnings are $3500. The annual raise rate is 2.3%, so r is 0.023 when expressed as a decimal. The number of years, n, is 10.

Plugging the values into the formula, we get:

Earnings in 10 years = $3500 * (1 + 0.023)^10

Calculating the result, we find that your expected monthly earnings in 10 years are:

$4424.10

The cosine value of cos(15) is [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2

The trigonometry identity of half angles is given as:

cos([tex]\theta[/tex]/2) = [tex]\sqrt{[/tex](1 + cos([tex]\theta[/tex]))/2

Substitute 30 for [tex]\theta[/tex]

So, the equation becomes

cos(30/2) = [tex]\sqrt[/tex](1 + cos(30))/2

In trigonometry, we have:

cos(30) = [tex]\sqrt[/tex]3/2

So, we have:

cos(30/2) = [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2

Divide 30 by 2

cos(15) = [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2

Hence, the cosine value of cos(15) is [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2

Read more about trigonometry identities at:

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Answer:

d

Step-by-step explanation:

took the test yahoot

Answer:11.5

Step-by-step explanation: 11.5

To find 1/4 of 268, you divide 268 by 4. The result of this operation is 67.

Calculating 1/4 of a number involves a simple mathematical operation known as division. In this case, we want to find out what is 1/4 of 268. To do this, you simply divide 268 by 4.

The calculation is as follows:

This means that 1/4 of 268 is 67.

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Answer:

[tex]x=+/-i\sqrt{13}[/tex]

Step-by-step explanation:

To find the roots, factor and set equal to 0 or use the quadratic formula. This quadratic equation does not factor and must be solved using the quadratic formula.

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

where a = 2, b=0, and c=26

[tex]x=\frac{0+/-\sqrt{0^2-4(2)(26)} }{2(2)} \\x=\frac{+/-\sqrt{-208)} }{4} \\x=\frac{+/-i\sqrt{16*13)} }{4}\\x=\frac{+/4i\sqrt{13} }{4}\\x=+/-i\sqrt{13}[/tex]

Answer:

Step-by-step explanation:

X=-i√13,x=i√13

The question is about finding the value of a determinant for matrices, a fundamental concept in Mathematics, especially linear algebra. For 2 × 2 matrices, the determinant calculation is straightforward and essential for various applications.

The subject of this question is clearly Mathematics, specifically it pertains to linear algebra and the concept of determinants. The task involves finding the value of a determinant for a given matrix. For a 2 × 2 matrix, the determinant is found using a simple formula: if the matrix is given by

\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}\]

then the determinant is calculated as \(ad - bc\). Additionally, the determinant provides important information about the matrix, such as whether the matrix is invertible and the product of its eigenvalues.

To understand determinants for larger matrices, a recursive approach is often used, breaking down the determinant into smaller matrices until 2 × 2 matrices are reached, where the simple formula can be applied. Also of note is that the determinant of the product of two matrices is equal to the product of their determinants (det(AB) = det(A)det(B)).

This fundamental concept is crucial for many applications in mathematics, including solving systems of linear equations, finding eigenvalues, and understanding linear transformations.

Both functions log(n + 1) and log(n^2 + 1) are not o(log n). For large values of n, log(n + 1) is approximately equal to log n, and log(n^2 + 1) behaves like 2*log n, none of which grows strictly slower than log n.

To determine whether the functions log(n + 1) and log(n2 + 1) are o(log n), we'll use the definition of little-o notation. A function f(n) is said to be o(g(n)) if for any positive constant c > 0, there exists a threshold n0 such that for all n > n0, f(n) < c * g(n). In other words, f(n) grows slower than any constant multiple of g(n) as n approaches infinity.

Analysis for log(n + 1)

When n is very large, the +1 becomes negligible, and log(n + 1) behaves similarly to log n. Therefore,

log(n + 1) ≈ log n when n is large.

This implies that log(n + 1) is not o(log n) because it does not grow strictly slower than any multiple of log n.

Analysis for log(n2 + 1)

Using logarithm properties:

log(n2 + 1) < log(n2 + n2) = log(2n2) = log 2 + 2*log n.

As n grows, the constant term (log 2) becomes insignificant, and the function approaches the behavior of 2*log n. However, since there is a multiple of log n (which is 2*log n), this still means that log(n2 + 1) is not o(log n) because it grows faster, not slower, than log n.

The constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].

The equilibrium solutions of the given differential equation [tex]\(ay'' + by' + cy = d\)[/tex] are found by setting the derivatives equal to zero.

1. Setting [tex]\(y'' = 0\)[/tex]: When [tex]\(y'' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Solving for y, we get [tex]\(cy = d\)[/tex], and therefore, [tex]\(y = \frac{d}{c}\)[/tex].

2. Setting [tex]\(y' = 0\)[/tex]: When [tex]\(y' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Again, solving for y, we obtain [tex]\(cy = d\)[/tex], and hence, [tex]\(y = \frac{d}{c}\)[/tex].

So, the constant solutions are [tex]\(y = \frac{d}{c}\)[/tex], and this is the equilibrium solution for the given differential equation.

Therefore, the constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].

Final answer:

The price of a dozen eggs in Ensley is $1.21.

Explanation:

To find the price of a dozen eggs in Ensley, we need to consider that the eggs in Ensley cost 10% more than in Dover. If a dozen eggs in Dover cost $1.10, we can calculate the 10% increase by multiplying $1.10 by 1.10:

$1.10 x 1.10 = $1.21

Therefore, a dozen eggs in Ensley cost $1.21.

Answer:

C) 100

Step-by-step explanation:

The given equation is x(x + 8) = 9

Distributing x insides, we get

x^2 + 8x = 9

Now set the equation equal to zero.

x^2 + 8x - 9 =0

Here a = 1, b = 8, and c = -9

b^2 - 4ac = (8)^2 - 4*1*-9

= 64 + 36

= 100

Therefore, b^2 - 4ac = 100.

Answer: C) 100

Hope this will helpful.

Thank you.

Answer:

C. 100

Step-by-step explanation:

Answer : The volume blue prism in Model 1 is, [tex]32in^3[/tex]

Step-by-step explanation :

As we are given that:

Volume of Model 1 = Volume of Model 2

Given:

Volume of blue prism in Model 2 = [tex]36in^3[/tex]

Volume of orange prism in Model 2 = [tex]12in^3[/tex]

Volume of orange prism in Model 1 = [tex]16in^3[/tex]

Now we have to calculate the total volume of Model 2.

Total volume of Model 2 = [tex]36in^3+12in^3[/tex] = [tex]48in^3[/tex]

Now we have to calculate the volume blue prism in Model 1.

Volume of Model 1 = Volume of Model 2

Volume of orange prism in Model 1 + Volume blue prism in Model 1 = Total volume of Model 2

[tex]16in^3[/tex] + Volume blue prism in Model 1 = [tex]48in^3[/tex]

Volume blue prism in Model 1 = [tex]48in^3-16in^3[/tex]

Volume blue prism in Model 1 = [tex]32in^3[/tex]

Thus, the volume blue prism in Model 1 is, [tex]32in^3[/tex]

1220/1.65 = 739.39 pounds of potatoes were sold

1 pound = 0.453592 kilograms

739.39 x 0.453592 = 335.38 kilograms

Final answer:

By dividing the total sales of $1220 by the price per pound ($1.65), we find that approximately 739.39 pounds were sold, which converts to roughly 335.38 kilograms of potatoes purchased by grocery shoppers.

Explanation:

To calculate the number of kilograms of potatoes grocery shoppers bought, we need to use the given prices and total sales. Since the price of 1 lb of potatoes is $1.65, we can find the total weight of the potatoes sold by dividing the total sales amount by the price per pound:

Total weight in pounds = Total sales                      
                     = $1220                      
                     = $1220 / $1.65                
                     = 739.39 pounds approximately

Next, we need to convert pounds to kilograms. There are approximately 2.20462 pounds in 1 kilogram. The conversion is:

Total weight in kilograms = Total weight in pounds / 2.20462

                         = 739.39 / 2.20462
                         = 335.38 kilograms approximately

Therefore, grocery shoppers bought approximately 335.38 kilograms of potatoes.