Solve for y in the following equation. x+2y=z

a zoo charges an admission price of $85 for the first 12 members of a group and $6 for each additional member of the group. What

elena-14-01-66 [18.8K]

The largest group that can go to the zoo is 23 members

Step-by-step explanation:

The given is:

A zoo charges an admission price of $85 for the first 12 members of a group and $6 for each additional member of the group
We need to find the largest group that can go to the zoo and spend less than $155 on admission

Assume that the number of members in the group is x

∵ There are x members in the group

∵ The zoo charges an admission price of $85 for the first 12

members of a group and $6 for each additional member

of the group

- Take 12 members from x and multiply the rest members by

6 and then add 85 to the product

∴ The group will spend = 6(x - 12) + 85

∵ The group wants to spend less than 155 to go to the zoo

- use the symbol < between the expression above and 155

∴ 6(x - 12) + 85 < 155

- Simplify the left hand side

∴ 6x - 72 + 85 < 155

- Add like terms in the left hand side

∴ 6x + 13 < 155

- Subtract 13 from both sides

∴ 6x < 142

- Divide both sides by 6

∴ x < 23.67

- Take the largest integer less than 23.67

∵ 23 is the largest integer less than 23.67

∴ The group has 23 members

The largest group that can go to the zoo is 23 members

Learn more:

You can learn more about the inequalities in brainly.com/question/1465430

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6 0

2 years ago

What is the greatest common factor of 34 and 58

Stella [2.4K]

The greatest common factor is 2

8 0

3 years ago

Read 2 more answers

How to solve 76×327 step by step

hram777 [196]

Here's a method that takes advantage of the values of these particular numbers.

... 76 = 80 - 4

so

... 76 × 327 = (80 -4)×327

... = 80×327 - 4×327

Repeated doubling will give us values that are 2, 4, and 8 times 327.

... 2×327 = 327+327 = 654

... 2×654 = 4×327 = 654+654 = 1308 . . . . we'll use this later

... 2×1308 = 8×327 = 2616

We want 80×327, so we can add a zero to the end of this last:

... 80×327 = 26160

Now, we can subtract 4×327 to get 76×327

... 80×327 - 4×327 = 26160 -1308 = 24852 = 76×327

_____

More conventionally, you would multiply every digit of one number by every digit of the other and add the products according to their respective place values.

327 × 076 = (3×0)×10000 + (3×7 +2×0)×1000 +(3×6 +7×0 +2×7)×100 +(2×6 +7×7)×10 +(7×6)×1

... = 0 +21,000 +3,200 + 610 +42

... = 24,852

Note the pattern of partial products here. This is a method taught to/by practitioners of Vedic mathematics, and can be done in your head. At most, you would write down the partial product sums 21, 32, 61, and 42 to keep from having to carry more than one number in your head at a time.

5 0

3 years ago

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

Harrizon [31]

Answer:

Equation of the line that passes through the given point and is (a) parallel is: $\mathbf{y=-2x+11}$

Equation of the line that passes through the given point and is (b) perpendicular is: $\mathbf{y=\frac{1}{2}x+1}$

Step-by-step explanation:

We need to Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

First we will find slope of the line given in graph

The slope can be found using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have points (1,6) and (2,2)

Slope is:

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{2-6}{2-1}\\Slope=\frac{-4}{2}\\Slope=-2$

Part a)

Write an equation of the line that passes through the given point and is (a) parallel

When the lines are parallel, they have same slope. So, slope of required line: m = -2

Using slope m =-2 and point(4,3) we can find y-intercept b

$y=mx+b\\3=-2(4)+b\\3=-8+b\\b=3+8\\b=11$

The equation of line will be:

$y=mx+b\\y=-2x+11$

Equation of the line that passes through the given point and is (a) parallel is: $\mathbf{y=-2x+11}$

Part b)

Write an equation of the line that passes through the given point and is (b) perpendicular

When the lines are perpendicular they have opposite slope. So, slope of required line: m = 1/2

Using slope m =1/2 and point(4,3) we can find y-intercept b

$y=mx+b\\3=\frac{1}{2}(4)+b\\3=2+b\\b=3-2\\b=1$

The equation of line will be:

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

Equation of the line that passes through the given point and is (b) perpendicular is: $\mathbf{y=\frac{1}{2}x+1}$

6 0

2 years ago

Simplify the expression show work<br> -3(4a-5b)

galben [10]

Answer:

$- 3(4a - 5b) \\ - 12a - 15b \: \: answer$

Step-by-step explanation:

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6 0

2 years ago

Solve for y in the following equation. x+2y=z​

Solve for y in the following equation. x+2y=z