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2 years ago

Write an equation of a line through (4,-1), parallel to y = 1x – 5

Mathematics

1 answer:

Mashcka [7]2 years ago

5 0

Y=1x -1

this is because you only change the z intercept when lines are parallel

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Find the number of paths of length 4 between two different vertices in K5

Mkey [24]

K₅ is the 5-complete graph, with adjacency matrix

$A = \begin{bmatrix} 0 & 1 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 1 & 0 \end{bmatrix}$

The (i, j)-th entry of the matrix A⁴ gives the number of length-4 paths from vertex i to vertex j. Computing A⁴ isn't so bad:

$A^2 = \begin{bmatrix} 0 & 1 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} 0 & 1 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 1 & 0 \end{bmatrix} = \begin{bmatrix} 4 & 3 & 3 & 3 & 3 \\ 3 & 4 & 3 & 3 & 3 \\ 3 & 3 & 4 & 3 & 3 \\ 3 & 3 & 3 & 4 & 3 \\ 3 & 3 & 3 & 3 & 4 \end{bmatrix}$

$A^4 = \begin{bmatrix} 4 & 3 & 3 & 3 & 3 \\ 3 & 4 & 3 & 3 & 3 \\ 3 & 3 & 4 & 3 & 3 \\ 3 & 3 & 3 & 4 & 3 \\ 3 & 3 & 3 & 3 & 4 \end{bmatrix} \begin{bmatrix} 4 & 3 & 3 & 3 & 3 \\ 3 & 4 & 3 & 3 & 3 \\ 3 & 3 & 4 & 3 & 3 \\ 3 & 3 & 3 & 4 & 3 \\ 3 & 3 & 3 & 3 & 4 \end{bmatrix} = \begin{bmatrix} 52 & 51 & 51 & 51 & 51 \\ 51 & 52 & 51 & 51 & 51 \\ 51 & 51 & 52 & 51 & 51 \\ 51 & 51 & 51 & 52 & 51 \\ 51 & 51 & 51 & 51 & 52 \end{bmatrix}$

We want the paths between two distinct vertices, so we ignore the entries on the diagonal and take the total of the non-diagonal entries, 20 • 51 = 1020.

4 0

2 years ago

Which expression is equivalent to (StartFraction 4 Superscript five-fourths Baseline time 4 Superscript one-fourth Baseline Over

Tpy6a [65]

The expression is equivalent to 4 Superscript five-fourths Baseline time 4 Superscript one-fourth Baseline Over 4 Superscript one-half baseline is,

$x=2$

<h3>What is equivalent expression?</h3>

Equivalent expression are the expression whose result is equal to the original expression, but the way of representation is different.

Given information-

The expression given in the problem is,

$\left((4^{\dfrac{5}{4}}\times4^{\dfrac{1}{4}}\div 4^{\dfrac{1}{2}} \right)^{\frac{1}{2}}$

Let the result of the given expression is <em>x</em>. Rewrite the given expression as,

$x=\left(\dfrac{4^{\dfrac{5}{4}}\times4^{\dfrac{1}{4}}}{4^{\dfrac{1}{2}}} \right)^{\frac{1}{2}}$

When the two number is multiplies with the same base, the powers of the number is added in result. Thus,

$x=\left(\dfrac{4^{(\dfrac{5}{4}+\dfrac{1}{4})}}{4^{\dfrac{1}{2}}} \right)^{\frac{1}{2}}\\x=\left(\dfrac{4^{(\dfrac{3}{2})}}{4^{\dfrac{1}{2}}} \right)^{\frac{1}{2}}$

When the two number is divided with the same base, the powers of the number is subtracted in result. Thus,

$x=\left(4^{\dfrac{3}{2}-\dfrac{1}{2}} \right)^{\frac{1}{2}}$

$x=\left(4^1} \right)^{\frac{1}{2}}\\x=\left(4} \right)^{\frac{1}{2}}\\x=(2^2)^{\dfrac{1}{2}} \\x=2$

Thus the expression is equivalent to 4 Superscript five-fourths Baseline time 4 Superscript one-fourth Baseline Over 4 Superscript one-half baseline is,

$x=2$

Learn more about the equivalent expression here;

brainly.com/question/2972832

5 0

2 years ago

If 12% of the total amount is 108. What is the total amount?

weqwewe [10]

Answer: 900

Step-by-step explanation:

12% means 0.12

total amount means X

"of" means multiply

"is" means equal sign

0.12 * X = 108 / Divide both sides by 0.12

X = 108 / 0.12 = 900

6 0

2 years ago

Please answer the question and leave an explanation on how to solve each part. Thank you in advance!

horsena [70]

The solutions are

it is going to take 15.9 months to raise 10000 dollars

You will have $37.31 after you have bought the car
The money deficit would be $37.31

<h3>How to solve the question</h3>

a. 10000 = 9359.08e(0.05)

e⁰⁰⁵ = 10000/9359.08

= 0.05 = ln(10000/9359.08)

= 1.325 years

convert to months = 15.9 months

Hence it is going to take 15.9 months to raise 10000 dollars

b. 9359.08 x e^(0.05 x1.25)

= 9962.69

10000 - 9962.69

= $37.31

You will have $37.31 after you have bought the car

c. The money loss and the deficit would be same as above $37.31

d. ln(e^a) = a

We can clearly see that the money cannot be raised in the 15 months from $ 9359.08. there is a deficit amount of $37.31

Read more on compound interest here: brainly.com/question/24924853

#SPJ1

3 0

1 year ago

Answer this asap also show work c;;

Oduvanchick [21]

Answer:

D. Expression for Nick's distance from starting point= 6+(-4)+2

Step-by-step explanation:

Finding expression for each scenario:

Number of boxes processed on on Monday =6 boxes

Number of boxes processed on on Tuesday =4 boxes

Number of boxes processed on on Wednesday =2 boxes

Expression for total boxes processed on these 3 days = $6+4+2$

Temperature of Suma's city at noon = 6°C

Temperature of Suma's city at 8pm = 4°C

Temperature of Suma's city at noon next day = 2°F

Total temperature change = cannot be determined as all measurements are not in same units.

Money put on Monday = $6

Money put in Wednesday =$4

Money withdrew on Saturday = $2

Expression for balance of Re'onna's piggy bank = $6+4-2$

Distance ran north =6 miles

Distance ran south(back) = 4 miles

Distance ran north again = 2 miles

Expression for Nick's distance from starting point= 6+(-4)+2

5 0

2 years ago

Write an equation of a line through (4,-1), parallel to y = 1x – 5​

Write an equation of a line through (4,-1), parallel to y = 1x – 5