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ra1l [238]
3 years ago
9

Find the constant of proportionality k. Then write an equation for the relationship between x and y

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
6 0

Question:

Find the constant of proportionality k. Then write an equation for the relationship between x and y

\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}

Answer:

(a) k = 5

(b) y = 5x

Step-by-step explanation:

Given

\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}

Solving (a): The constant of proportionality:

Pick any two corresponding x and y values

(x_1,y_1) = (2,10)

(x_2,y_2) = (6,30)

The constant of proportionality k is:

k = \frac{y_2 - y_1}{x_2 - x_1}

k = \frac{30-10}{6-2}

k = \frac{20}{4}

k = 5

Solving (b): The equation

In (a), we have:

(x_1,y_1) = (2,10)

k can also be expressed as:

k = \frac{y- y_1}{x- x_1}

Substitute values for x1, y1 and k

5 = \frac{y- 10}{x- 2}

Cross multiply:

y - 10 = 5(x - 2)

Open bracket

y - 10 = 5x - 10

Add 10 to both sides

y - 10 +10= 5x - 10+10

y = 5x

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(4x-10)<br> Use the diagram above to determine the mCE<br> The mCE-
BabaBlast [244]

Answer: Arc CE measures 62 units

Step-by-step explanation: What we have in the question is a circle with two secants ABC and ADE. The two secants have been extended such that two arcs have been formed which are, major arc CE (that is, 4x - 10) and minor arc BD (that is 26).

When you have a circle with two intersecting secants, the angle x (that is angle CAE) is derived as half of the difference of the two intercepted arcs. That is;

Angle x = 1/2 [CE - BD)

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On sunday 1/16 people who visit were senior citizens, 3/16 were infants, 3/8 were children and 3/8 were adults, how many of each
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Answer:

Out of total people visited the zoo on Sunday , 6.25% was senior citizen ,  18.75% were infants , 35% were children and 35% were adult.

Step-by-step explanation:

let total number of people visited the group  = x

so number of senior citizens = x × 1/16 = x/16

Percentage of  senior citizens = (number of senior citizens ÷ total number of people visited the group) × 100

= (x/16 ÷ x)  × 100 = 100/16 = 6.25%

number of infants = 3/16 × x = 3x/16

Percentage of  infants =(number of infants  ÷ total number of people visited the group) × 100 = (3x/16 ÷ x)  × 100 = 300/16 = 18.75%

number of  children = 3/8 × x = 3x/8

Percentage of  children =(number of children ÷ total number of people visited the group) × 100 = (3x/8 ÷ x)  × 100 = 300/8 = 37.5%

number of  adults = 3/8 × x = 3x/8

Percentage of  adults =(number of adults ÷ total number of people visited the group) × 100 = (3x/8 ÷ x)  × 100 = 300/8 = 37.5%.

Hence we can conclude that Out of total people visited the zoo on Sunday , 6.25% was senior citizen ,  18.75% were infants , 35% were children and 35% were adult.






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