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3 years ago

which is the equation of a line in point slope form that passes through the point 2,5 and has a slope of 1/2

Mathematics

1 answer:

VMariaS [17]3 years ago

8 0

Answer:

see below

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y - 2 = 4(x- -1)

y - 2 = 4(x+1)

slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = 4x+b

Substituting the point in

2 = 4(-1)+b

2 = -4+b

6 =b

y = 4x+6

standard form

Ax +by = c where A is a positive integer and b and c are integers

y = 4x+6

Subtract 4x from each side

-4x+y = 6

Multiply by -1

4x -y = 6

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Read 2 more answers

e) Given the following: Let X = {1, 2, 3, 4) and a relation R on X as R= {(1,2), (2,3), (3,4)}. Find the reflexive and transitiv

Naddika [18.5K]

Answer:

The answer is $\{(1,1),(2,2),(3,3),(4,4),(1,2)(2,3)(3,4),(1,3),(1,4)\}$

Step-by-step explanation:

Remember that a reflexive relation $R\subset \mathcal{P}(X)$ , where $\mathcal{P}(X)$ is the power set of $X$ , is one which conteins the ordered pairs of the form $(a,a)$ , for $a\in X$ .

So, As the reflexive and transitive closure of $R$ (that we will denote by $\overline{R}$ ) is in particular reflexive, we must add to $R$ the elements $\{(1,1) , (2,2),(3,3),(4,4) \}$

A transitive relation $R$ is one in which if the pair $(a,b)$ and the pair $(b,c)$ are in there, then the pair $(a,c)$ must be there too.

So, to complete the relation $R$ to be reflexive and transitive we must add the pair $(1,3)$ (because $(1,2),(2,3)$ are in $R$ ), the pair $(2,4)$ , and the pair $(1,4)$ because we added the pair $(2,4)$ .

Therfore we have that $\overline{R}=\{(1,1),(2,2),(3,3),(4,4),(1,2)(2,3)(3,4),(1,3),(1,4)\}$ .

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3 years ago

Consider Z1= 4-4 radical 3i and Z2= -16 i. What is Z1-Z2?

goldfiish [28.3K]

Answer:

Option (3)

Step-by-step explanation:

$Z_1=4-4\sqrt{3}i$

$Z_2=-16i$

$Z_1-Z_2=(4-4\sqrt{3}i)-(-16i)$

$=4-4\sqrt{3}i+16i$

$=4-(4\sqrt{3}i-16i)$

$=4-4(\sqrt{3}-4)i$

Therefore, Option (3) will be the correct option.

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2 years ago

Each pound of food C contains 6 ounces of ingredient P and 3 ounces of ingredient Q. Each pound of food D contains 4.5 ounces of

GuDViN [60]

So hmm the food C = 6p + 3q and the food D = 4.5p + 1.5q

now, if we check how much is the ratios of C/D for each component, then, mixture M = 144p + 60q, must contain the same ratio for each "p" and "q" component

$\bf \textit{ratio of "p"}\implies \cfrac{6}{4.5}\implies \cfrac{4}{3}
\\\\\\
\textit{ratio of "q"}\implies \cfrac{3}{1.5}\implies \cfrac{2}{1}$

so, if we divide the 144p by 4+3, or 7 even pieces, 4 must belong to food C and 3 to food D, retaining the ratio of 4/3

and we do the same for 60q, we divide it in 2+1 or 3 even pieces, but that one is very clear, 2 must belong to food C and 1 to food D, 60/3 is clear ends up with a ratio of 40 and 20

now the "p" part... ends up as $\bf \cfrac{144}{7}\cdot 4\qquad and\qquad \cfrac{144}{7}\cdot 3\implies \cfrac{576}{7}\qquad and\qquad \cfrac{432}{7}$

that's what I see it, as the ratio of 4/3 and 2/1 being retained in the mixture M

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3 years ago