Solve the equation. -9x + 1 = -x + 17 O x=-8 O x= -2 Ox=2 O x= 8

If a train travels at 78 mph for 10 min, what is the distance traveled?

Marina CMI [18]

Answer:

13

Step-by-step explanation:

78 (Miles Per Hour) divided by 60 (Minutes in an hour)= 1.3 (Miles traveled per Minute). 1.3 (Miles traveled per minute) x 10 (minutes traveled) = 13 miles traveled in 10 minutes.

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

2 years ago

4 friends went to the movies and each ordered a container of popcorn.They spent $24 on popcorn.How much did each container of po

alexandr402 [8]

Answer: $6

Step-by-step explanation:

24/4 = 6

5 0

3 years ago

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Explain how you can use the distributive property to check the binomial factors when a trinomial has been factored. Include an e

erica [24]

What you can do is split one of the binomials and then apply the distributive property if f(x) = (x + 3)(x -2) split the 1st binomial f(x) = x(x -2) + 3(x -2) now apply the distributive property to get
f(x)=x2−2x+3x−6
which simplifies to
f(x)=x2+x−6

4 0

2 years ago

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Daca a = 3-5 si b= 4:3*9:2

Thepotemich [5.8K]

A={2,3,5}
B={1,3,4}
A∩B={3}
R: a. {3}

5 0

2 years ago