Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)

[1 0 0 1]
[0 0 1 0]
[0 0 0 0]

(x1, x2, x3, x4) = _________

Answer:

The equation of the line is [tex]y = -\frac{2}{5}x + \frac{24}{5}[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Slope:

Having two points, the slope is given by the change in y divided by the change in x. Points (2,4) and (7,2)​, so:

Change in y: 2 - 4 = -2

Change in x: 7 - 2 = 5

Slope: [tex]m = \frac{-2}{5} = -\frac{2}{5}[/tex]

So

[tex]y = -\frac{2}{5}x + b[/tex]

(2,4)

This means that when [tex]x = 2, y = 4[/tex]. So

[tex]y = -\frac{2}{5}x + b[/tex]

[tex]4 = -\frac{2}{5}(2) + b[/tex]

[tex]b = 4 + \frac{4}{5} = \frac{20}{5} + \frac{4}{5} = \frac{24}{5}[/tex]

The equation of the line is [tex]y = -\frac{2}{5}x + \frac{24}{5}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: ( {x - 7})^{2} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] {x}^{2} - 14x + 49[/tex]

[tex] = {x}^{2} - 7x - 7x + 49[/tex]

Taking "[tex]x[/tex]" as common from first two terms and "7" from last two terms, we have

[tex] = x \: ( \: x - 7 \: ) - 7 \: ( \: x - 7 \: )[/tex]

Taking the factor [tex](x-7)[/tex] as common,

[tex] = ( \: x - 7\:) \: (\: x - 7\: )[/tex]

[tex] =( {x - 7})^{2} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

7 x 1/10 = 7/10

Step-by-step explanation:

There are 7 "bumps" on the number line, and each "bump" moves the line 1/10.

This can also be modeled as

1/10 + 1/10 + 1/10 +1/10 +1/10 +1/10 +1/10 = 7/10

Answer:

its a three in seven chance, since there are seven total outcomes and there is only one favorable outcome. Hope that helps.

Step-by-step explanation:

Answer:

x = 14 is your answer

Step-by-step explanation:

76 = 7x-22, so to figure it out, you first move -22 to the other side and get

76+22 = 7x.

add them together and you get 98 = 7x

7x would be your equation, so divide 98 by 7 and you get your solution

x = 14 is your answer

Answer:

2/3

Step-by-step explanation:

2/3 is 66 2/3%

Answer:

Step-by-step explanation:

18x-6=120

18x=120+6

18x=126

    x=126÷18

    x=7

Answer:

Incomplete question, but you can use the formulas given to solve it.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniform distribution over an interval from 0 to 0.5 milliseconds

This means that [tex]a = 0, b = 0.5[/tex]

Determine the probability that the interarrival time between two particles will be:

Considering [tex]a = 0, b = 0.5[/tex], and the question asked, you choose one of the three formulas above.

Both figures r similar (given )

[tex] \frac{5}{2.5} = \frac{3}{1.5} = \frac{2}{1} = \frac{4}{x} \\ \frac{2}{1} = \frac{4}{x} \\ \frac{ \cancel{2}}{1} = \frac{ \cancel{4}^ { \tiny{2}}}{x} \\ x = 2 \: \: ans[/tex]

Answer:

A and D

Step-by-step explanation:

Total ice cream bars sold = sum of chocolate sold , vanilla and strawberry ice-creams sold.

=(1/2)x2 + (6/11)x + 8 + (5/9)x2 + (2/3) +(1/3)x2 + 4x +(4/3) (Given in the question)

=(25/18)x2 + (50/11)x + 10 (Adding terms corresponding to x2,x ,constant respectively)

Difference in chocolate and strawberry bars =[ (1/2)x2 + (6/11)x + 8] - [(1/3)x2 + 4x +(4/3)]

= (1/6)x2 - (38/11)x +(20/3)

So, the correct options are A and D

Answer:

2b^2

Step-by-step explanation:

according to the question equation is

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

a^2 + b^2 - a^2 + b^2

plus a square and minus a square gets cancel

b^2 + b^2

since they are like terms they can be added

2b^2

Answer:

2b^2

Step-by-step explanation:

according to the question equation is

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

a^2 + b^2 - a^2 + b^2

= b^2 + b^2

like terms can be added

+2b^2

Answer:tu culo

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

9 is the difference

9 times 4 is 36

Subtraction is a mathematical operation. The statement "Four times the difference of 15 and 6" is equal to 36.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The statement "Four times the difference of 15 and 6" can be expressed as,

= 4 × (15 - 6)

= 4 × (9)

= 36

Hence, The statement "Four times the difference of 15 and 6" is equal to 36.

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Answer:

[tex]x = 24.75[/tex]

Step-by-step explanation:

Required

Find x

To find x, we have:

[tex]\angle PQR + \angle RPQ + \angle QRP = 180[/tex] -- angles in a triangle

Because [tex]\bar {PR}[/tex] is extended to S, then:

[tex]\angle QRS = \angle QRP[/tex]

So, we have:

[tex]2x + 6 + x - 7 + 5x -17 = 180[/tex]

Collect like terms

[tex]2x + x + 5x = 180 + 17 + 7-6[/tex]

[tex]8x = 198[/tex]

Divide by 8

[tex]x = 24.75[/tex]

Answer:

D. 7:10

Step-by-step explanation:

The Correct Answer

Answer:

Step-by-step explanation:

sin x° = [tex]\frac{17}{19}[/tex]

x° = [tex]sin^{-1}[/tex] [tex]\frac{17}{19}[/tex]

x° ≈ 63°

Answer:

See explaation

Step-by-step explanation:

Given

Represent the balls with the first letters

[tex]W =1[/tex]

[tex]R =2[/tex]

Solving (a): P(F) --- White balls twice

The event of F is:

[tex]F = \{(W,W)\}[/tex]

So:

[tex]P(F) = P(W) * P(W)[/tex]

[tex]P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(F) = \frac{1}{3} * \frac{1}{3}[/tex]

[tex]P(F) = \frac{1}{9}[/tex]

Solving (b): P(G) --- two different colors

The event of G is:

[tex]G = \{(W,R),(R,W)\}[/tex]

So:

[tex]P(G) = P(W) * P(R) + P(R) * P(W)[/tex]

[tex]P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(G) = \frac{1}{3} * \frac{2}{3} + \frac{2}{3} * \frac{1}{3}[/tex]

[tex]P(G) = \frac{2}{9} + \frac{2}{9}[/tex]

[tex]P(G) = \frac{4}{9}[/tex]

Solving (c): P(H) --- White picked first

The event of H is:

[tex]H = \{(W,R),(W,W)\}[/tex]

So:

[tex]P(H) = P(W) * P(R) + P(W) * P(W)[/tex]

[tex]P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(H) = \frac{1}{3} * \frac{2}{3} + \frac{1}{3} * \frac{1}{3}[/tex]

[tex]P(H) = \frac{2}{9} + \frac{1}{9}[/tex]

[tex]P(H) = \frac{3}{9}[/tex]

[tex]P(H) = \frac{1}{3}[/tex]

Solving (d): F and G, mutually exclusive?

We have:

[tex]F = \{(W,W)\}[/tex]

[tex]G = \{(W,R),(R,W)\}[/tex]

Check for common elements

[tex]n(F\ n\ G) = 0[/tex]

Hence, F and G are mutually exclusive

Solving (e): G and G, mutually exclusive?

We have:

[tex]G = \{(W,R),(R,W)\}[/tex]

[tex]H = \{(W,R),(W,W)\}[/tex]

Check for common elements

[tex]n(G\ n\ H) = 1[/tex]

Hence, F and G are not mutually exclusive

Answer:

First one and Third one

Step-by-step explanation:

Answer is correct from Plato

The correct expressions are:

[tex]17^{-1/4}[/tex] [tex]= \frac{1}{17^{1/4}}[/tex]

[tex]y^{1/2}[/tex] [tex]= \frac{1}{y^{-1/2}}[/tex]

In the given expression,

Since we know that the rule of exponent,

[tex]a^{-n} = \frac{1}{a^n}[/tex]

Therefore,

For the given expression,

[tex]17^{-1/4}[/tex]

Using the above property of exponent we can write it,

[tex]= \frac{1}{17^{1/4}}[/tex]

Hence this is the correct expression.

For the given expression,

[tex]y^{1/2}[/tex]

Using the above property of exponent we can write it,

[tex]= \frac{1}{y^{-1/2}}[/tex]

Hence this is the correct expression.

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Answer:

False

Step-by-step explanation:

Rational number :

A rational number is a number which can be represent as p/q of two integers where q is not equal to zero

Example: 2/3

[tex]\sqrt{3}[/tex] = 17320508075........ and it keeps extending. Since it does not terminate or repeated after the decimal point.

Therefore [tex]\sqrt{3}[/tex] is an irritational number,

Hence given statement is FALSE

Step-by-step explanation:

1.x³y²

2. 6x²y³

hope it helps

Answer:

Step-by-step explanation:

tan(30) = x/1

sqrt(3) / 3 = x/1

x= sqrt(3) / 2

[tex]7 - 3x = 2x - 3 \\ 7 - 3x - 2x = - 3 \\ 7 - 5x = - 3 \\ - 5x = - 3 - 7 \\ - 5 = - 10 \\ x = \frac{ - 10}{ - 5} \\ x = 2[/tex]

Answer:

so that you will multiply 15 * 4.

Step-by-step explanation:

15*4 = 60 now you divide 60 by 4 and the answer will be 15.

Answer: hello your question lacks some information attached below is the complete question

answer :

a) attached below

b) 65 students aged 1-2 years

Step-by-step explanation:

For a Leslie matrix ; there is a relation

Pn = L^n Po  where ; Pn = population vector after n years , Po = initial population vector .

a) Initial population vector

attached below

[tex]\left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]

b) Number of birds aged 1-2 years are available after 10 years

i.e. P10 = L^10 Po

note : Po = Xo

∴ P10 = [tex]\left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right][/tex]   [tex]\left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]

we will apply  MATLAB to resolve the above matrix

P10  = [tex]\left[\begin{array}{ccc}217.91\\65.24\\31.911\end{array}\right][/tex]

∴ Number of children between 1-2 years left after 10 years  = 65.24 ≈ 65

The total number of birds aged between 1-2 years which are available after 10 years is 65 and this can be determined by using the Leslie matrix relation.

Given :

According to the given data, the initial population vector is given by:

[tex]x_0 = \left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]

Now, the total number of birds aged between 1-2 years which are available after 10 years is:

[tex]\rm P_{10} = \left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right] \left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]

Now, solve the above matrices in order to determine the value of [tex]\rm P_{10}[/tex].

[tex]\rm P_{10} = \left[\begin{array}{ccc}217.91\\65.24\\31.911\end{array}\right][/tex]

Therefore, the total number of birds aged between 1-2 years which are available after 10 years is 65.

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5 ÷ 1/2 => 5 x 2/1 => 10/1 => 10

Answer:

10

Step-by-step explanation:

In the pic, it shows ten half squares.  

Answer:

20

Step-by-step explanation:

l*w*h

4*5*1= 20

Answer:

-2 and -2

Step-by-step explanation:

The probability of rolling any one number on a 6 sided die is 1/6

The probability of rolling a 4 is 1/6

The probability of rolling a 5 is 1/6

The probability of rolling a 4 or a 5 is the probability of rolling a 4 plus the probability of rolling a 5:

1/6 + 1/6 = 2/6 = 1/3

The answer is 1/3