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3 years ago

6

Coach Jeffries had forty-six students sign up for after-school soccer. Then some students decided to join after-school basketbal

l instead. Coach Jeffries had twenty-five players left on the soccer team. How many students switched to after-school basketball?

1 answer:

Natasha_Volkova [10]3 years ago

7 0

21

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Find the value of sin(a/2) if cosa= 12/13<br>

daser333 [38]

Answer: sin $\frac{a}{2}$ = ± $\frac{1}{\sqrt{26} }$

Step-by-step explanation:

We very well know that,

cos2A=1−2sin²A

⟹ sinA = ± $\sqrt{(1-} \frac{cos2A}{2} )$

As required, set A = $\frac{a}{2}$ & cos a= $\frac{12}{13}$ ,thus we get

sin $\frac{a}{2}$ =± $\sqrt{\frac{1-cos a}{2} }$

∴ sin $\frac{a}{2}$ =± $\sqrt{\frac{1-\frac{12}{13} }{2} }$ = ± $\frac{1}{\sqrt{26} }$

since ,360° < $\frac{a}{2}$ <450°

,180° < $\frac{a}{2}$ <225°

Now, we are to select the value with the correct sign. It's is obvious from the above constraints that the angle a/2 lies in the III-quadrant where 'sine' has negative value, thus the required value is negative.

hope it helped!

5 0

3 years ago

Find the volume of the cylinder. Use 3.14 for π. Round to the nearest tenth.

lakkis [162]

Answer:

62.8 m^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

V = (3.14) ( 2)^2 *5

V = 62.8 m^2

8 0

3 years ago

Read 2 more answers

Which angle corresponds to < 8?

Yuri [45]

Answer:

b

Step-by-step explanation:

7 0

3 years ago

Lorico [155]

1. For this item we just refer to the prompt to know the conjectures of Ernest and Denise. According to Ernest, they should swim 1 kilometer on the first week then add 0.25km every week while Denise believes that they should swim 1 kilometer on the first week then add 0.5km every week.

2. Yes, these distances make an arithmetic sequence. It's because an arithmetic sequence is defined as a group of increasing or decreasing numbers where the difference between any two consecutive numbers is constant. This just means that every number has the same interval. In the case of their schedule, this is true.

3. For this item we just follow the descriptions of Ernest's and Denise's schedule in item number 1. For Ernest, we just keep adding 0.25 from 1 kilometer until we added it thrice. For Denise, we also keep adding a number thrice but this time it's 0.5 instead of 0.25.

Ernest's Schedule: 1, 1.25, 1.5, 1.75
Denise's Schedule: 1, 1.5, 2, 2.5

4. Here we are asked to determine a formula that will describe the schedules of Ernest and Denise. In the given formula $a_{n}= a_{n-1}+d$ , $a_{n}$ refers to the next term in the sequence, $a_{n-1}$ refers to the previous term, while $d$ refers to the common difference. In the recursive formula all we need is to insert the value of d to the equations.

Ernest: $a_{n}= a_{n-1}+0.25$
Denise: $a_{n}= a_{n-1}+0.5$

5. For this item we basically do the same thing but this time we are given another formula. Our formula is in the form $a_{n}= a_{1}+(n-1)d$ where $a_{n}$ is still the nth term of the sequence, $a_{1}$ is the very first time, $n$ is the number of terms, and $d$ is the common difference.

Ernest: $a_{n}= 1.0+0.25(n-1)$
Denise: $a_{n}= 1.0+0.5(n-1)$

6. In this item we will just basically substitute numbers to one of the equations that we've set up in item #5. For this we need Ernest's explicit formula first. To know how far they will be swimming on week 10, the number of elements (n) must be 10.

$a_{10}= 1.0+0.25(10-1)$
$a_{10}= 1.0+0.25(9)$
$a_{10}= 1.0+2.25$
$a_{10}= 3.25$

7. Here, we just do the same thing as item #6 but this time we will consider Denise's explicit formula. Since we are also asked how far the students will be swimming on week 10, the number of elements would also be 10 and this would also be our value for n.

$a_{10}= 1.0+0.5(10-1)$
$a_{10}= 1.0+0.5(9)$
$a_{10}= 1.0+4.5$
$a_{10}= 5.5$

8. The answer for this question is obvious. You would just need to look at the 10th element in Ernest's and Denise's sequences and tell whose schedule had more than or equal to 5 as an answer. Following Ernest's schedule, you will just get 3.5 kilometers on the 10th week so it's definitely a no. Denise's schedule, on the other hand, would get you to 5.5 kilometers on week 10 so her training schedule should be followed.

7 0

3 years ago

Which equation has infinitely many solutions? A) 4x + 3 3 = 4x + 5 B) 10x + 8 2 = 5x + 4 C) 8x − 5 3 = 2x − 2 D) 8x − 5 2 = 4x −

abruzzese [7]

Answer: If the left side and the right side of the equation are equal, the equations has infinitely many solutions.

Step-by-step explanation:

The options are not clear, so I will give you a general explanation of the procedure you can use to solve this exercise.

The Slope-Intercept form of the equation of a line is the following:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

For this exercise you need to remember that, given a System of Linear equations, if they are exactly the same line, then the System of equations has Infinitely many solutions.

If you have the following system:

$\left \{ {{y=2x+1} \atop {y=\frac{12}{6}x+1}} \right.$

You can simplify the second one:

$y=2x+1$

Then, both equations are the same line.

By definition you can also write the systemf making both equations equal to each other:

$2x+1=2x+1$

So, if the left side and the right side are equal, the equations has infinitely many solutions.

3 0

3 years ago