The cost table shows the average cost, a(x), of producing x number of earbuds.

4 (X+7) = 38 WHAT IS X AND EXPLAIN HOW YOU KNOW

xxMikexx [17]

Answer:

X=2.5

Step-by-step explanation:

38÷4 = 9.5

9.5 - 7=2.5

Divide each side by four to get rid of that numbr from the elft and subtract seven from both sides to get rid of the seven so your left with x=2.5

7 0

3 years ago

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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 923.558 m²

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, $A_{req}$ ≈ 923.558 m²

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

6 0

3 years ago

Which of the following illustrates the truth value of the given conditional statement?

Blababa [14]

Answer:

Option A. F T → F

Explanation:

A conditional is represented by:

p → q

Where p is called the antecedent, and q is the consequent.

Thus, a conditional states that if the antecedent is true, its consequent is also true; also, if the consequent is false, then the antecedent must be false.

On the other hand, if the antecedent is true, the consequent can be either true or false.

1. State the antecedent of the conditional and is truth value

Antecedent: 6 > 10

Truth value: False, because 6 is not greater than 10.

2. State the consequent of the conditional and its truh value

8 • 3 = 24

Truth value: True, because 8 times 3 is 24.

3. Truth value of the conditional

Hence, the truth value of the conditional is:

False Truth → Truth, or

F T → T

Which is the option A.

6 0

3 years ago

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A scuba diver descends 80 feet, rises 25 feet, descends 12 feet, and then

cluponka [151]

Answer: That would be 15ft

3 0

3 years ago

Please simplify: 5x + 2 (x - 3) = -2 (x - 1)

zysi [14]

Answer:

x= 8/9

Step-by-step explanation:

Open everything up to get 5x+2x-6=-2x+2. Move numbers with an x to the left side and without to the right to have 5x+2x+2x=2+6. Simplify to have 9x=8. Divide by 9 which leaves you with x= 8/9

3 0

3 years ago