1/4 of a pizza is split equally between three sisters. How much of a whole pizza will each sister get?

Is this linear relationship a direct variation?

Talja [164]

Since the ratio of of second variable to the ratio of first variable remains constant i.e y/x =8 so, the linear relationship is direct variation.

Step-by-step explanation:

A relationship is said to have direct variation if ratio of second variable to the ratio of first variable remains constant.

A relationship is direct variation if $y=kx\,\,or\,\, \frac{y}{x} =k$ where k is the constant.

Now checking if the given data is having direct variation or not.

x y

3 24

4 32

5 40

6 48

Now finding y/x

if y=24 and x = 3 then y/x = 24/3 = 8

if y=32 and x = 4 then y/x =32/4=8

if y=40 and x = 5 then y/x =40/5 =8

if y=48 and x = 6 then y/x =48/6= 8

Since the ratio of of second variable to the ratio of first variable remains constant i.e y/x =8 so, the linear relationship is direct variation.

Keywords: Direct Variation

Learn more about Direct Variation at:

#learnwithBrainly

5 0

3 years ago

A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes

Alenkinab [10]

The relationship between the sides MN, MS, and MQ in the given regular heptagon is $\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}$

The area to be planted with flowers is approximately <u>923.558 m²</u>

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

$A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )$

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

$\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}$

$s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69$

$The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52$

The area of the heptagon MNSRQPO is therefore;

$A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94$

$MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08$

By sine rule, we have

$\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}$

$sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})$

$\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}$

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

$Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}$

The area of the of the garden plated with flowers, $A_{req}$ , is given as follows;

$A_{req}$ = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

$A_{req}$ = 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, $A_{req}$ ≈ <u>923.558 m²</u>

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

6 0

3 years ago

Convert 4.5 kg into g

ryzh [129]

Step-by-step explanation:

1 kg = 1000 g

4.5 kg = 4.5 × 1000

4500 g

4 0

3 years ago

Read 2 more answers

Use the zeros of the following quadratic to find the x-value of the vertex.

frez [133]

(x-1)^2 is the factored version, so vertex is at 0, which is 1, so, A

6 0

3 years ago

Hich rule about the sign of the quotient of positive and negative decimals is correct?

MrRissso [65]

B is the right answer

3 0

3 years ago

Read 2 more answers