For an upcoming school field trip, there must be one adult supervisor for every five children.If the bus seats 40 people, how many children can go on the trip?

Answers

Answer 1

Answer: the answer is 30, i did 6(the number of kids and adult combined) times 6( the highest number i could get to without going over the limit 40) hope this helped

Answer 2

Answer:

Answer: 32 Childrens maximum I think

Step-by-step explanation: I believe it is 32 because there will be 8 adults for every 32 children (ratio 1 adult:5 children) then convert the ratio to ?adult: availaible seats (40) so multiply by 8 since 5×8 equals 40 and 8×1 equals 8 but the adults have their spots too so 40-8=32

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A hallway measuring 90 feet x 7 feet requires 1/2 a fluid oz of cleaning solution per sq ft. How much cleaning solution is needed to clean the hallway?

Answers

You want area of the floor to know how many square feet you have 90x7=630 630sq. ft of floor and it takes 1/2 an oz to clean one of them 630(1/2)=315oz

A square and a rectangle have the same area. The length of the rectangle is twelve more than twice times the side of the square. The width of the rectangle is eight less than the side of the square. Let x be the length of the side of the square. Using the information above, what is the value of x?

Answers

Answer:

$x = 12$

Step-by-step explanation:

Given

Shapes: Square and Rectangle

Square:

$Length = x$

Rectangle:

$Length = 12 + 2x$

$Width = x- 8$

Required

Find x

First, we calculate the area of the square.

$Area = x * x$

$Area = x^2$

Next, we calculate the area of the rectangle

$Area = (12 + 2x) * (x - 8)$

$Area = 12x -96 + 2x^2 - 16x$

$Area = 2x^2 - 16x + 12x -96$

$Area = 2x^2 -4x -96$

Since both areas are equal, we have:

$x^2 = 2x^2 -4x -96$

Equate to 0

$2x^2 -x^2 -4x -96= 0$

$x^2 -4x -96= 0$

Expand:

$x^2 - 12x + 8x -96 = 0$

$x(x - 12) + 8(x - 12) = 0$

$(x + 8)(x - 12) = 0$

$x + 8 = 0$ or $x - 12 = 0$

$x = -8$ or $x = 12$

But x can't be negative.

Hence:

$x = 12$

Which statement best describes a solution to the system of equations 3x+Y=17 X+2y=49 A. It has no solution B. It has infinite solutions C. It has a single solution x=15 y=17 D. It has a single solution x=-3 y=26

Answers

Answer:

It has a single solution x=-3 y=26

Step-by-step explanation:

The ratios of coefficients of x and y are different, so the pair of equations has one solution. It is easy to tell the first offered solution (15, 17) does not satisfy the first equation, so that choice is eliminated.

Fortunately, the second offered solution, (x, y) = (-3, 26), satisfies both equations.

The equations have a single solution: (x, y) = (-3, 26).

Answer: The equation has a single solution x = -3 , y = 26.

( -3, 26 )

Step-by-step explanation:

3x + y =17 ---------------------(1)

x + 2y = 49 -------------------(2)

Using substitution approach

From (2)

x = 49 - 2y --------------------(3)

Now put (3) in equation (1) and solve.

3(49 - 2y) + y = 17

Open the bracket and solve

3 x 48 - 3 x 2y + y = 17

147 - 6y + y = 17

Gather like terms

-5y = 17 - 147

-5y = -130

Multiple through by (-1)

5y = 130

Divide by 5

y = 130/5

y = 26.

Substitute for y now in equation (3) to get the value of x

3x + y = 17

3x + 26 = 17

3x = 17 - 26

3x = -9

Now , divide by 3

x = -3

The equation had a single solution of x = -3 , y = 26

Chech.

3 x -3 + 26

-9 + 26

= 17

The perimeter of a rectangle is 70 cm. If its length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 cm2. Find the length and the width of the original rectangle.

Answers

x=length of the original rectangle. (in cm)
y=width o f the original rectangle. (in cm)

Perimeter of a rectangle=sum of the all sides.
Perimeter of the original rectangle=x+x+y+y=2x+2y

Area of a rectangle=length x width
Area of the original rectangle=xy

x-5=length decreased by 5 cm
y+5=width increase by 5 cm.

We can suggest this system of equations:
2x+2y=70
(x-5)(y+5)=xy+50

We solve this system of equations by susbstitution method:
2x+2y=70 ⇒x+y=35 ⇒ y=35-x

(x-5)(35-x+5)=x(35-x)+50
(x-5)(40-x)=35x-x²+50
40x-x²-200+5x=35x-x²+50
40x-35x+5x=200+50
10x=250
x=250/10
x=25

y=35-x
y=35-25
y=10

Answer: the lenght and the width of the original rectangle is :
lenght=25 cm
width=10 cm.

The length of the rectangle is 25cm and the width of the rectangle is 45cm and this can be determine by forming the linear equations.

Given :

Perimeter of a rectangle is 70 cm.

Rectangle length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 $\rm cm^2$ .

Let 'a' be the length of the rectangle and 'b' be the width of the rectangle. Than the perimrter of the rectangle will be:

a + b = 70 ---- (1)

Now, the area of the rectangle will be:

$\rm (a-5)(35-a+5)=a(35-a)+50$

$\rm 35a -a^2+5a-175+5a-25=35a-a^2+50$

$\rm10a -200=50$

a = 25

Now, put the value of 'a' in equation (1).

b = 70 - 25 = 45

b = 45

Therefore, the length of the rectangle is 25cm and the width of the rectangle is 45cm.

For more information, refer the link given below:

brainly.com/question/919810

How to get the base of a parallelogram that has a area of 26 1/2 and a height of 6 5/8?

Answers

the area of all paralellograms can be found by
area=base times height

so
area=26 and 1/2
height=6 and 5/8
convert to improper fractions for ease of use
26 and 1/2=52/2+1/2=53/2
6 and 5/8=48/8+5/8=53/8
so

area=height times base
53/2=53/8 times base
multiply both sides b 8/53 so that we clar the fraction (53/8 times 8/53=424/424=1)
(53 times 8)/(53 times 2)=1base
8/2=1base
4=base

answer is base=4 units

Well you start of in reverse. The formula to find the Area of a parallelogram is A = bh so since you already have the Area all you would have to do is divide the area by the height like so 26 1/2 / 6 5/8 = 4. So to make sure you have the right answer you would just Multiply 4 by 6 5/8 to see if it equals 26 1/2.
4 X 6 5/8 = 26 1/2
I hope this helped

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