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2 years ago

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Zack and Antonio are on the track team. Zack ran 108 miles over 9 weeks, running the same distance each week. Antonio ran 91 mil

es over 7 weeks, running the same distance each week. Which statement correctly compares the numbers of miles per week they ran?

1 answer:

lina2011 [118]2 years ago

6 0

Answer:

zack ran 17 more miles per week than antonio

Step-by-step explanation:

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Consider the probability distribution shown below.

rusak2 [61]

Answer:

it is b

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2 years ago

I need help with this, plz help

antoniya [11.8K]

Answer:

<AFB

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2 years ago

The coordinates of the vertices of a rectangle are (−3, 4) , (7, 2) , (6, −3) , and (−4, −1) . What is the perimeter of the rect

ki77a [65]

Answrer

Find out the what is the perimeter of the rectangle .

To prove

Now as shown in the figure.

Name the coordinates as.

A(−3, 4) ,B (7, 2) , C(6, −3) , and D(−4, −1) .

In rectangle opposite sides are equal.

Thus

AB = DC

AD = BC

Formula

$Disatnce\ formula = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2}}$

Now the points A(−3, 4) and B(7, 2)

$AB = \sqrt{(7- (-3))^{2} +(2- 4)^{2}}$

$AB = \sqrt{(10)^{2} +(-2)^{2}}$

$AB = \sqrt{100+4}$

$AB = \sqrt{104}$

$AB = 2\sqrt{26}\units$

Thus

$CD= 2\sqrt{26}\units$

Now the points

A (−3, 4) , D (−4, −1)

$AD = \sqrt{(-4 - (-3))^{2} +(-1- 4)^{2}}$

$AD = \sqrt{(-1)^{2} +(-5)^{2}}$

$AD = \sqrt{1 + 25}$

$AD = \sqrt{26}\units$

Thus

$BC = \sqrt{26}\units$

Formula

Perimeter of rectangle = 2 (Length + Breadth)

Here

$Length = 2\sqrt{26}\ units$

$Breadth = \sqrt{26}\ units$

$Perimeter\ of\ rectangle = 2(2\sqrt{26} +\sqrt{26})$

$Perimeter\ of\ rectangle = 2(3\sqrt{26})$

$Perimeter\ of\ rectangle = 6\sqrt{26}$

$\sqrt{26} = 5.1 (Approx)$

$Perimeter\ of\ rectangle = 6\times 5.1$

Perimeter of a rectangle = 30.6 units.

Therefore the perimeter of a rectangle is 30.6 units.

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3 years ago

Please answer fast please

kvv77 [185]

Answer:

you can use a website called calculator soup the answer is -9/14 please mark me branlist

Step-by-step explanation:

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3 years ago

Find the values of the sine, cosine, and tangent for ZA C A 36ft B <br> 24ft

Reptile [31]

<h2>Question:</h2>

Find the values of the sine, cosine, and tangent for ∠A

a. sin A = $\frac{\sqrt{13} }{2}$ , cos A = $\frac{\sqrt{13} }{3}$ , tan A = $\frac{2 }{3}$

b. sin A = $3\frac{\sqrt{13} }{13}$ , cos A = $2\frac{\sqrt{13} }{13}$ , tan A = $\frac{3}{2}$

c. sin A = $\frac{\sqrt{13} }{3}$ , cos A = $\frac{\sqrt{13} }{2}$ , tan A = $\frac{3}{2}$

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Answer:</h2>

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Step-by-step explanation:</h2>

The triangle for the question has been attached to this response.

As shown in the triangle;

AC = 36ft

BC = 24ft

ACB = 90°

To calculate the values of the sine, cosine, and tangent of ∠A;

<em>i. First calculate the value of the missing side AB.</em>

<em>Using Pythagoras' theorem;</em>

⇒ (AB)² = (AC)² + (BC)²

<em>Substitute the values of AC and BC</em>

⇒ (AB)² = (36)² + (24)²

<em>Solve for AB</em>

⇒ (AB)² = 1296 + 576

⇒ (AB)² = 1872

⇒ AB = $\sqrt{1872}$

⇒ AB = $12\sqrt{13}$ ft

From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of $12\sqrt{13}$ ft (43.27ft).

<em>ii. Calculate the sine of ∠A (i.e sin A)</em>

The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e

sin Ф = $\frac{opposite}{hypotenuse}$ -------------(i)

<em>In this case,</em>

Ф = A

opposite = 24ft (This is the opposite side to angle A)

hypotenuse = $12\sqrt{13}$ ft (This is the longest side of the triangle)

<em>Substitute these values into equation (i) as follows;</em>

sin A = $\frac{24}{12\sqrt{13} }$

sin A = $\frac{2}{\sqrt{13}}$

<em>Rationalize the result by multiplying both the numerator and denominator by </em> $\sqrt{13}$ <em />

sin A = $\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }$

sin A = $\frac{2\sqrt{13} }{13}$

<em>iii. Calculate the cosine of ∠A (i.e cos A)</em>

The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e

cos Ф = $\frac{adjacent}{hypotenuse}$ -------------(ii)

<em>In this case,</em>

Ф = A

adjacent = 36ft (This is the adjecent side to angle A)

hypotenuse = $12\sqrt{13}$ ft (This is the longest side of the triangle)

<em>Substitute these values into equation (ii) as follows;</em>

cos A = $\frac{36}{12\sqrt{13} }$

cos A = $\frac{3}{\sqrt{13}}$

<em>Rationalize the result by multiplying both the numerator and denominator by </em> $\sqrt{13}$ <em />

cos A = $\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }$

cos A = $\frac{3\sqrt{13} }{13}$

<em>iii. Calculate the tangent of ∠A (i.e tan A)</em>

The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e

tan Ф = $\frac{opposite}{adjacent}$ -------------(iii)

<em>In this case,</em>

Ф = A

opposite = 24 ft (This is the opposite side to angle A)

adjacent = 36 ft (This is the adjacent side to angle A)

<em>Substitute these values into equation (iii) as follows;</em>

tan A = $\frac{24}{36}$

tan A = $\frac{2}{3}$

6 0

3 years ago