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2 years ago

There are a total of 64 students in a drama club and a yearbook club. The drama club has 10 more students than the yearbook club

Mathematics

1 answer:

ivolga24 [154]2 years ago

8 0

Answer:

The system of equations are $x+y=64$ and $x=y+10$

Step-by-step explanation:

Given : There are a total of 64 students in a drama club and a yearbook club. The drama club has 10 more students than the yearbook club.

To find : Write a system of linear equations that represents the situation.

Solution :

Let x represent the number of students in the drama club

and y represent the number of students in the yearbook club.

There are a total of 64 students in a drama club and a yearbook club.

i.e. $x+y=64$ ....(1)

The drama club has 10 more students than the yearbook club.

i.e. $x=y+10$ ....(2)

Substitute the value of (2) in (1),

$y+10+y=64$

$2y=54$

$y=\frac{54}{2}$

$y=27$

Substitute in (2),

$x=27+10$

$x=37$

Therefore, the system of equations are $x+y=64$ and $x=y+10$

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80% of what # is 16?

liraira [26]

80% of x = 16
"of" translates to multiplication and 80% becomes 80/100.

80/100 × x = 16

0.8x = 16

0.8x/0.8 = 16/0.8

x = 16/0.8

x = 20

Your final answer is 80% of 20 is 16.

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2 years ago

What is the unit rate for 15 apples eaten in 5 minutes for 15 apples eaten in 5 minutes

USPshnik [31]

The unit rate is 3 apples per minute

Step-by-step explanation:

Unit rate will be calculated by dividing the total number of apples by the time

Given

Total number of apples = 15

Time = 5 min

So, The unit rate will be:

$Unit\ rate=\frac{Apples}{Time}\\=\frac{15}{5}\\=3\ apples\ per\ min$

Hence,

The unit rate is 3 apples per minute

Keywords: Unit rate, Division

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2 years ago

On a coordinate plane, a line goes through (negative 12, negative 2) and (0, negative 4). A point is at (0, 6).

mariarad [96]

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st

Step-by-step explanation:

Parallel lines have:

Same slopes
Different y-intercepts

The formula of the slope of a line which passes through points $(x_{1},y_{1})$ and $(x_{1},y_{1})$ is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ The given line passes through points (-12 , -2) and (0 , -4)

∴ $x_{1}$ = -12 , $x_{2}$ = 0

∴ $y_{1}$ = -2 , $y_{2}$ = -4

- Use the formula of the slope above to find the slope of the given line

∵ $m=\frac{-4-(-2)}{0-(-12)}=\frac{-4+2}{12}=\frac{-2}{12}=\frac{-1}{6}$

∴ The slope of the given line is $\frac{-1}{6}$

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = $\frac{-1}{6}$

∵ The parallel line passes through point (0 , 6)

- The form of the linear equation is y = mx + b, where m is the slope

and b is the y-intercept (y when x = 0)

∵ m = $\frac{-1}{6}$ and b = 6

∴ The equation of the parallel line is y = $\frac{-1}{6}$ x + 6

Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line

Point (-12 , 8)

∵ x = -12 and y = 8

∵ y = $\frac{-1}{6}$ (-12) + 6

∴ y = 2 + 6 = 8

- The value of y is equal the y-coordinate of the point

∴ Point (-12 , 8) is on the line

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/9527422

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4 0

3 years ago

Read 2 more answers

A transformation describes a change in location, orientation, or size of a figure. Translations, reflections, and rotations belo

marshall27 [118]

Answer: These are called rigid transformations because the structure and shape of the shape remains the same.

Step-by-step explanation: The word rigid and rigidity is often used to describe something that is tough or the strength of something. The transformations might be called a rigid transformation because the rigidity of the shape remains the same because the size is the exact same, it is the exact same shape it is just moved.

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2 years ago

What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

Maksim231197 [3]

Hello,
the first step should be to distribue:
-4(3-5x)= -12+20x

Teh resolution may be:

-4(3-5x)>=-6x+9
==>-12+20x>=-6x+9
==>20x+6x>=9+12
==>26x>21
==>x>=21/26

But an other way may be used:

-4(3-5x)>=-6x+9
==>3-5x<= -6x/(-4)+9/(-4)
==>-5x-3/2 x<=-9/4 -3

==>-13/2 x <=-21/4

==>x>= -21/4 *(-2/13)
==>x>=21/(2*13)
==>x>=21/26

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2 years ago

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