A rectangle has a perimeter of 60 inches. The length of the rectangle is 3 inches less than twice the width
What is the length of the rectangle?

Here is the correct format for the question.

[tex]x'_1 = 7x_1 +4x_2+ 12x_3 , \ \ x'_2 = x_1 + 2x_2 + x_3 , \ \ x'_3 = -3x_1 -2x_2 -5x_3[/tex] . Then find the solution that satisfies  [tex]x \limits ^{\to} = \left[\begin{array}{c}0\\1\\-2\end{array}\right][/tex]

Answer:

[tex]\mathbf{c_1 = -3, c_2 = 2, c_3 = 2}[/tex]

Step-by-step explanation:

From the figures given above:

the matrix can be computed as,

[tex]\left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right] x \limits ^{\to} = \left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right] = x \limits ^{\to} = \left[\begin{array}{c}x_1'\\x_2'\\x_3'\end{array}\right][/tex]

The first thing we need to carry out is to determine the eigenvalues of A,

where:

[tex]A = \left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right][/tex]

[tex]|A-rI|=0[/tex]

[tex]\begin {vmatrix} 7-r&4&12\\1&2-r&1\\-3&-2&-5-r \end {vmatrix}=0[/tex]

the eigenvalues are r = 0, 1, 3

However, the eigenvector correlated to each eigenvalue can be calculated as follows.

suppose  r = 0

(A - rI) x = 0

[tex]\left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right] \left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right] = \left[\begin{array}{c}0\\0\\0\end{array}\right][/tex]

now the eigenvector is [tex]\left[\begin{array}{c}-4\\1\\2\end{array}\right][/tex]

However, for eigenvalue = 1, we have :  [tex]\left[\begin{array}{c}-4\\1\\2\end{array}\right][/tex]

for eigenvalue = 3, we have:[tex]\left[\begin{array}{c}-2\\-1\\1\end{array}\right][/tex]

The solution now can be computed as :

[tex]x(t)= c_1 \left[\begin{array}{c}-4\\1\\2\end{array}\right] + c_2e^t \left[\begin{array}{c}-4\\3\\1\end{array}\right]+ c_3e^{3t} \left[\begin{array}{c}-2\\-1\\1\end{array}\right][/tex]

Similarly, the fundamental matrix solution is:

[tex]\left[\begin{array}{ccc}-4&-4e^t&-2e^{3t}\\1&3e^t&-e^{3t}\\2&e^t&e^{3t}\end{array}\right][/tex]

[tex]-4c_1 -4c_2-2c_3 =0 \\ \\ c_1 + 3c_2 -c_3 = 1\\ \\ 2c_1+c_2 +c_3 = -2[/tex]

Solving the above equation, we get:

[tex]\mathbf{c_1 = -3, c_2 = 2, c_3 = 2}[/tex]

Answer:

If 12 granola bars are nine dollars,

(12/9)

We divide the amount by the price!

Twelve divided by nine is about $1.33.

The image is rounded to the nearest thousandth

Answer:

4/16 pieces are in 2/8, 5/8 pieces are in 10/16, 8/8 pieces are in 4/4

Step-by-step explanation:

multiply or divide both the numerator (top number) and the denominator (bottom number) by a number that will give you a common denominator

[tex]\frac{2*2}{8*2} =\frac{4}{16} \\\frac{10/2}{16/2} =\frac{5}{8} \\\frac{4*2}{4*2}=\frac{8}{8}[/tex]

Answer:

y = 120º

Step-by-step explanation:

180 - (33 + 87) = 60

x = 60

180 - 60 = 120

y = 120º

or y = 33 + 87, because the outer angle of one angle equals the other two inner angles.

Answer: 120°

Step-by-step explanation:

If you add up all the triangles angles, it always is 180. So, when you add 33+87, you get 120. This means that x=60 because 120+60 =180.

Then, you also know that x and y together, make a 180° also because it is a straight line. So, y is equal to 120° because 60+120 = 180°.

Hope this helps! :)

Answer:

x = 9 or x = -21

Step-by-step explanation:

Solve for x over the real numbers:

x^2 + 12 x - 189 = 0

The left hand side factors into a product with two terms:

(x - 9) (x + 21) = 0

Split into two equations:

x - 9 = 0 or x + 21 = 0

Add 9 to both sides:

x = 9 or x + 21 = 0

Subtract 21 from both sides:

Answer: x = 9 or x = -21

Answer:

The equation of a sphere with endpoints at (4, 1, 6) and (8, 3, 8) is [tex](x-6)^{2}+(y-2)^{2}+(z-7)^{2} = 6[/tex].

Step-by-step explanation:

Given the extremes of the diameter of the sphere, its center is the midpoint, whose location is presented below:

[tex]C(x,y,z) = \left(\frac{4+8}{2},\frac{1+3}{2},\frac{6+8}{2}\right)[/tex]

[tex]C(x,y,z) = (6,2,7)[/tex]

Any sphere with a radius [tex]r[/tex] and centered at [tex](h,k,s)[/tex] is represented by the following equation:

[tex](x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}[/tex]

Let be [tex](x,y,z) = (4,1,6)[/tex] and [tex](h,k,s) = (6,2,7)[/tex], the radius of the sphere is now calculated:

[tex](4-6)^{2}+(1-2)^{2}+(6-7)^{2}=r^{2}[/tex]

[tex]r = \sqrt{6}[/tex]

The equation of a sphere with endpoints at (4, 1, 6) and (8, 3, 8) is [tex](x-6)^{2}+(y-2)^{2}+(z-7)^{2} = 6[/tex].

Answer:

y = 7(1 + x/5)

Step-by-step explanation:

7x - 5y = -35

-5y = -35 - 7x

5y = 35 + 7x

y = (35 + 7x) / 5

y = 7 + 7x/5

y = 7(1 + x/5)

Answer:

A function is a mathematical device that converts one value to another in a known way. ... The set of allowable inputs to a given function is called the domain of the function. The set of possible outputs is called the range of the function.

Step-by-step explanation:

Hopefully this was mindfull

The input set of a function is called the "Domain" of the function.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

For any function, the values which we are putting form a set of intervals called domain.

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.

Hence "The input set of a function is called the "Domain" of the function".

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Answer:

Each book costs 26 dollars

Step-by-step explanation:

Let b be the price of each book

8*b +17 = 225

Subtract 17 from each side

8b+17-17 = 225-17

8b =208

Divide by 8

8b/8 = 208/8

b =26

Each book costs 26 dollars

Answer:

0.66

Step-by-step explanation:

Rosalia passed out fliers that say, “Vote for Rosalia!” She gave out 85 fliers on Monday, 66 fliers on Tuesday, and 99 fliers on Wednesday.

Total fliers shared= 85+66+99

Total fliers shared= 250 fliers

Fraction of the fliers she gave out on Wednesday= fliers on Wednesday/total fliers

=99/150

= 33/50

= 3.3/5

= 0.66

Answer:

0.66

Step-by-step explanation:

Answer:

  $1108.25

Step-by-step explanation:

Danielle's commission on $4300 in sales is ...

  0.0775 × $4300 = $333.25

That, added to her base salary, gave her weekly earnings of ...

  $333.25 +775 = $1108.25 . . . . Danielle's pay last week

Answer:

-13v^4 + v^3 - 10v (if simplified)

Step-by-step explanation:

combine like terms

(-7v^4 - 5v) - (-5v^3 - 2v)+ ( - 7v - 6v^4 - 4v^3)

-7v^4 + -6v^4 = -13v^4

-5v^3 + -4v^3 = v^3 (the five becomes positive because of the negative sign infront of the parenthesis) Example: -(-5v^3) = +5v^3

-13v^4 + v^3 -5v -(-2v) -7v (now we have the -2 left alone in the parenthesis which means it becomes positive too) Example: -(-2v) = +2v

-5v +2v - 7v = -3v -7v = -10v

Answer: -13v^4 + v^3 - 10v

Answer:

The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.

Step-by-step explanation:

Answer: (3,-10)

Step-by-step explanation:

Using the translated rule that x is increase by 5 and y  is decreased by 7 put it into the equation and solve for  the coordinates of k.

(-2 +5 ) = 3

(-3 -7) = -10

So now the coordinates will be (3,-10)

Answer:

its the 3rd 1

Step-by-step explanation:

Answer:

10.95 or 11 if rounded up

Step-by-step explanation:

The side length of a pool shaped like a square with an area 120ft² is

S = [tex]\sqrt{120}= 10.954[/tex]

Given,

 Let side of the pool = S

      Area of the pool = S² = 120

      Hence, the side of the pool = S = [tex]\sqrt{120}= 10.954[/tex] ft

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Answer:I believe the answer is C

Step-by-step explanation:

The y-intercept is 2

Answer:

B. Ordinal

Step-by-step explanation:

The level of measurement used for a variable in statistical analysis determines what summary statistics and analysis are possible. In statistical analysis, we have three types of level of measurement.

Nominal , Ordinal  , Interval/ Ratio

The nominal is the most basic level of measurement. It is the  qualitative level of measurement such as color or number.  Data in Nominal scale of measurement are  stored as a word or  as numerical code.

Ordinal level of measurement  are variables based on ranks or hierarchy. Ordinal level of measurement posses a sequential step-wise order but the intervals between the variables are not  equal. They are usually expressed in frequencies.

Therefore, the level of measurement of variable that determines the livability rankings for cities based on their ranks or hierarchy is Ordinal.

The interval/ratio level of measurement  is the highest  level of measurement where  data are  being measured and ordered in a sequential process.

Answer:

The teacher woll award the student 96 points for studying for 4 hours

Step-by-step explanation:

The student receives 72 point for preparing a test as long as 3 hours.

If she prepares for another test for 4 hours.

3 hours= 72 points

4 hours=( 72*4)/3

4 hours=72/3 *4

4 hours = 24*4

4 hours= 96 points

The teacher woll award the student 96 points for studying for 4 hours

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{62}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{x ° + 118 ° = 180 ° }[/tex]

( Sum of angle in straight line )

Move 118 to right hand side and change it's sig

⇒[tex] \sf{x ° = 180 ° - 118 °}[/tex]

Calculate

⇒[tex] \sf{x = 62 °}[/tex]

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

Hello, the sum of the roots is -9=-4-5 and the product is 20=(-4)*(-5) so we can write

[tex]x^2+9x+20=(x+4)(x+5)[/tex]

thanks

Answer:

( x + 4 ) ( x + 5 )

Step-by-step explanation:

For this polynomial, we will factor the coefficient of the x^2 term and the constant.

The coefficient of x^2 is 1, which just factors to 1.

The constant 20 factors into 2 * 2 * 5.

Note, that our middle term coefficient is 9 and thus we want a pairing of 1 with either 2, 4, or 5 to make 9.   4 + 5 = 9, so we will choose that.

Using the standard binomials, we will factor the polynomial:

( x^2 + 9x + 20 )

= ( x + 4 ) ( x + 5)

We can check by performing foil:

= ( x + 4 ) ( x + 5 )

= ( x * x + x * 5) + ( 4 * x + 4 * 5)

= ( x^2 + 5x ) + ( 4x + 20 )

= ( x^2 + 9x + 20 )

Thus, we have successfully factored our polynomial.

Cheers.

Answer:

63 is greater than 48.1 ...

63 > 48.1

Step-by-step explanation:

63 is greater than 48 remember. So you need to remove the [.1] and focus on the 63 and 48.

Thanks!!!!❤❣❤

Answer:

The first and the fourth one.

The ones that could be rationalized are automatically the ones you should pick.

Answer:

The direction cosines are:

[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex]  and  [tex]\frac{4}{\sqrt{42} }[/tex]  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

Step-by-step explanation:

For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.

If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.

Where;

cos α = [tex]\frac{a . i}{|a| . |i|}[/tex]               ---------------------(i)

cos β = [tex]\frac{a.j}{|a||j|}[/tex]               ---------------------(ii)

cos γ = [tex]\frac{a.k}{|a|.|k|}[/tex]             ----------------------(iii)

And from these we can get the direction angles as follows;

α =  cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )

β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )

γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )

Now to the question:

Let the given vector be

a = 5i + j + 4k

a . i =  (5i + j + 4k) . (i)

a . i = 5         [a.i is just the x component of the vector]

a . j = 1            [the y component of the vector]

a . k = 4          [the z component of the vector]

Also

|a|. |i| = |a|. |j| = |a|. |k| = |a|           [since |i| = |j| = |k| = 1]

|a| = [tex]\sqrt{5^2 + 1^2 + 4^2}[/tex]

|a| = [tex]\sqrt{25 + 1 + 16}[/tex]

|a| = [tex]\sqrt{42}[/tex]

Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e

cos α = [tex]\frac{5}{\sqrt{42} }[/tex]

cos β =  [tex]\frac{1}{\sqrt{42} }[/tex]              

cos γ =  [tex]\frac{4}{\sqrt{42} }[/tex]

From the value, now find the direction angles as follows;

α =  cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )

α =  cos⁻¹ ( [tex]\frac{5}{\sqrt{42} }[/tex] )

α =  cos⁻¹ ([tex]\frac{5}{6.481}[/tex] )

α =  cos⁻¹ (0.7715)

α = 39.51

α = 40°

β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )

β = cos⁻¹ ( [tex]\frac{1}{\sqrt{42} }[/tex] )

β = cos⁻¹ ( [tex]\frac{1}{6.481 }[/tex] )

β = cos⁻¹ ( 0.1543 )

β = 81.12

β = 81°

γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )

γ = cos⁻¹ ([tex]\frac{4}{\sqrt{42} }[/tex])

γ = cos⁻¹ ([tex]\frac{4}{6.481}[/tex])

γ = cos⁻¹ (0.6172)

γ = 51.89

γ = 52°

Conclusion:

The direction cosines are:

[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex]  and  [tex]\frac{4}{\sqrt{42} }[/tex]  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

Answer:

0.0893

Step-by-step explanation:

Let A be the event that the individual has the disease

Let Aⁿ be the event that the individual doesn't have the disease

Let B be the event of a positive result showing.

Now,

We are told One in 1000 adults is afflicted with the disease.

Thus;

P(A) = 1/1000 = 0.001

P(Aⁿ) = 1 - 0.001 = 0.999

Also,we are told that when an individual has the disease, a positive result will occur 98% of the time.

Thus;

P(A|B) = 98% = 0.98

Also, we are told that an individual without the disease will show a positive result only 1% of the time. Thus;

P(Aⁿ|B) = 1% = 0.01

Now, from fundamental rule, let's find P(B). Thus;

P(B) = [P(A|B) × P(A)] + [P(Aⁿ|B) × P(Aⁿ)]

P(B) = (0.98 × 0.001) + (0.01 × 0.999)

P(B) = 0.01097

Now, from Baye's theorem, If a randomly selected individual is tested and the result is positive, the probability that the individual has the disease is given by;

P(A|B) = [P(A|B) × P(A)]/P(B)

P(A|B) = (0.98 × 0.001)/0.01097

P(A|B) = 0.0893

Answer:

The tree is approximately 22.707 meters tall.

Step-by-step explanation:

The geometric diagram of the problem is included below as attachment. The height of the tree is found by means of trigonometric functions:

[tex]\tan \alpha = \frac{h}{w}[/tex]

Where:

[tex]\alpha[/tex] - Elevation angle, measured in sexagesimal degrees.

[tex]h[/tex] - Height of the tree, measured in meters.

[tex]w[/tex] - Length of the tree shadow, measured in meters.

The height of the tree is cleared in the equation:

[tex]h = w\cdot \tan \alpha[/tex]

If [tex]w = 51\,m[/tex] and [tex]\alpha = 24^{\circ}[/tex], the height is:

[tex]h = (51\,m)\cdot \tan 24^{\circ}[/tex]

[tex]h \approx 22.707\m[/tex]

The tree is approximately 22.707 meters tall.

Answer:

Step-by-step explanation:

[tex]5^3\times\:5^5\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times\:a^c=a^{b+c}\\5^3\times\:5^5=5^{3+5}\\\\=5^8=390625[/tex]

The solution of the expression will be 5⁻².

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 5³ x 5⁻⁵. The expression will be solved as below,

E = 5³ x 5⁻⁵

E = 5³⁻⁵

E = 5⁻²

Hence, the expression will be E = 5⁻².

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Answer:

Hello your question has some missing parts attached is the missing part

answer : slightly skewed to the right ( B )

Step-by-step explanation:

From the attached histogram related to the question above, it can be seen that the the right tail is longer than the left tail and this can help us draw the conclusion that the overall shape of the distribution is slightly skewed to the right

Step-by-step explanation:

Two of the sides are 4 and 5.  The other four sides are 1, 2, 3, and 6.

The probability of rolling a number other than 4 or 5 on any roll is 4/6, or 2/3.

The probability of rolling no 4s or 5s six times is:

P = (2/3)⁶

P ≈ 0.088

Step-by-step explanation:

hope it will help you.......