$Answer: \\ 4(2y - 20) + 2y = 720 \\ \Leftrightarrow 2(2y - 20) + y = 360 \\ \Leftrightarrow 4y - 40 + y = 360 \\ \Leftrightarrow 5y = 400 \\ \Leftrightarrow y = 80°$

8 0

4 years ago

Out of 45 times at bay Raul got 19 hits, find Raul's batting average as a decimal and round it to the nearest thousandth

gladu [14]

Out of 45 times at bat, Raul got 19 hits. Find Rauls batting average as a decimal rounded tothe nearst thousandth.

4 0

3 years ago

Sarah plants 760 vines in rows containing either 20 vines or 25 vines. There are 3 times as many rows containing 25 vines as the

bogdanovich [222]

Answer: 27 rows contain 25 vines.

Step-by-step explanation:

Let x represent the number of rows that contain 20 vines.

Let y represent the number of rows that contain 25 vines.

Sarah plants 760 vines in rows containing either 20 vines or 25 vines. This means that

20x + 25y = 760- - - - - - - - - - -1

There are 3 times as many rows containing 25 vines as there are rows containing 20 vines. This means that

y = 3x

Substituting y = 3x into equation 1, it becomes

20x + 25 × 3x = 760

20x + 75x = 760

95x = 760

x = 760/95

x = 9

y = 3x = 3 × 9

y = 27

6 0

3 years ago

A certain bridge arch is in the shape of half an ellipse 106 feet wide and 33.9 feet high. At what horizontal distance from the

nata0808 [166]

Answer:

The horizontal distance from the center is 49.3883 feet

Step-by-step explanation:

The equation of an ellipse is equal to:

$\frac{x^2}{a^{2} } +\frac{y^2}{b^{2} } =1$

Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.

Then, replacing a by 106/2 and b by 33.9, we get:

$\frac{x^2}{53^{2} } +\frac{y^2}{33.9^{2} } =1\\\frac{x^2}{2809} +\frac{y^2}{1149.21} =1$

Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:

$\frac{x^2}{2809} +\frac{y^2}{1149.21} =1\\\frac{x^2}{2809} +\frac{12.3^2}{1149.21} =1\\\\\frac{x^2}{2809}=1-\frac{12.3^2}{1149.21}\\\\x^{2} =2809(0.8684)\\x=\sqrt{2809(0.8684)}\\x=49.3883$

So, the horizontal distance from the center is 49.3883 feet

8 0

4 years ago