Mathematics High School

1. An open box is to be made from a sheet of card 40cm by 30cm. A square of side x cm is to be
cut from each corner, as shown in the diagram, and then the sides will be folded up so that the
depth of the box will be x cm.

(a) Find in terms of x the length and width of the base of the box (ie AB and AD).
(b) The volume of the box is y. Write down an equation expressing y in terms of x.

Answers

Answer 1

Step-by-step explanation:

AB = DC = 40 - 2x

AD = BC = 30 - 2x

there is not more explanation possible, I think.

we cut off from each side 2 pieces of x cm. so, AB, DC, AD, BC are the the remaining lengths.

the volume of the box is ground area times height (x is the length of the remaining flaps after the cut, so, when folding up these flaps/sides, they will be x cm high).

Volume = y = AB×AD×x

=> y = (40-2x)×(30-2x)×x = (1200 - 60x - 80x + 4x²)×x =

= (1200 - 140x + 4x²)×x = 4x³ - 140x² + 1200x

Related Questions

HELP DUE IN 15 MINS!

Assume that any lines that appear to be tangent are tangent.

x=??

Answers

Answer:

Step-by-step explanation:

arc TS = 360 - 90 - 150

Arc TS = 120

The central angle is also 120

x is 1/2 of the central angle

x = 1/2 * 120

x = 60

Find the slope of the line that passes through (7, 1) and (2, 8).

Answers

Answer:

-7/5

Step-by-step explanation:

(1-8)/(7-2)= -7/5

Answer:-1.4

Step-by-step explanation: The slope or gradient is given by

Slope=y2-y1÷x2-x1.

From the problem

X1=7

Y1=1

X2=2

Y2=8

Thus we will have

Slope=(8-1)÷(2-7)

=7÷(-5)

=-1.4

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Answers

Answer:

:;;;,,,

Step-by-step explanation:

^^^^^^^^^!!~~~

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*.-_-.*
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HELP BRAINLIEST PLEASE!!!!!!!!

Answers

Answer:

12/25

Step-by-step explanation:

there are 24 'T's out of 50

ILL BRAINLIEST YOU PLEASE HELP ME

Answers

Answer:

1.) 15

2.) 12.5

Step-by-step explanation:

hi can someone explain what does consecutive angles are supplementary mean

Answers

Answer:

key note is that when the angles are added it equals 180 degrees

Ariana has a collection of 100 coins. How many coins represent 10% of her collection?

Answers

Answer: 10

Step-by-step explanation:

10% is the same as 10/100

10% would equal 10 (out of the 100) coins

Translate the sentence into an equation.
Five more than the product of a number and 6 equals 4.
Use the variable w for the unknown number.

Answers

Answer:

The to your question is 5w+6=4

Answer:

Below,

Step-by-step explanation:

Produce of w and 5 = 6w

Adding 5 gives 6w + 5 so the equation is:

6w + 5 = 4.

Write a rule to describe each reflection.
Rule:r() (x,y)=()

Who ever answers this question will get 25 points.

Answers

Answer: ok so if it is ok im sorry but like how is it like is there supposed to be a number? im sorryyy i thught i had it before i saw the picture

Step-by-step explanation:

Hurry please !! It’s timed...

Answers

The links don’t work.

Of the last 20 balloons sold at a party store, 2 were red. What is the experimental probability that the next balloon sold will be red? Write your answer as a fraction or whole number.

Answers

Answer : 1 of 4 ( 1 of every 4 )
| ||||||||

I dont know sorry 2/4 or 18

which point on the graph would best represent unemployment (underutilizing labor)?

Answers

Answer:

i think the right one is H

The following table displays the number of sofas sold in a furniture store during certain months of the year.
Furniture Store Sofa Sales
January 255
February 234
March 263
April 229
May 248

Based on these data, which statement is correct?

A. There are outliers.

B. The mean best describes the data.

C. The median best describes the data.

D. The measure of variability that best describes the data is the IQR, 27.5.

Answers

I think answer should be d. Please give me brainlest let me know if it’s correct or not okay thanks bye

Can anyone help me with this?

Answers

Answer:

Link Is A Virus. Do Not Search! Have A Nice Day! Owa Owa! UwU

Step-by-step explanation:

what is 4 /25 in a whole number

Answers

Step-by-step explanation:

4/25 cannot be converted into a whole number, it is less than 1

Answer:

decimal = 0.15

whole number (rounded) = 0

Part A
What is the volume of the gift shown?
Part B
Which equation was used to find the volume in Part A?

Answers

Answer:

Part A:

1120 inches cubed

Part B:

Base X Height

Step-by-step explanation:

Es una division el cociente es 14, el divisor 19, calcule el dividiendo si se sabe que el residuo resutó ser el maximo.

Answers

Answer:

266

Step-by-step explanation:

En Matemáticas, al realizar la operación de División, la regla es la siguiente:

Dividendo ÷ Divisor = Cociente

En la pregunta anterior, se nos da:

Divisor = 19

Cociente = 14

Dividendo =?

Para encontrar el dividendo,

Dividendo = Divisor × Cociente

Por eso,

Dividendo = 19 × 14

= 266

Por lo tanto, el Dividendo = 266

Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.

Answers

The greatest common factor is 2x^3y^2
Hope that helps!!! :)

A line intersects the point (-3,-7) and has a slope of -3. what is the slope intercept equation for this line?

Answers

Answer:

-3

Step-by-step explanation:

y = -3x + b

-7 = -3(-3) + b

-7 = 9 + b

-16 = b

y = -3x - 16

What is the explanation please help me

Answers

Answer:

Yes. If the first friend descended 0.11 mile (-0.11) and the second friend descended 0.12 mile (-0.12), then the second friend had to have caught up to the first friend knowing that the second friend descended at least 0.11 mile. Hope this helps :)

Step-by-step explanation:

Find the equation of the line that passes through (1,3) and is perpendicular to y=2x−1. Leave your answer in the form y=mx+c

Answers

Answer:

y = -1/2x + 3.5

Step-by-step explanation:

In order to pass through the point (1, 3), and is perpendicular to y = 2x - 1, then the line must be y = -1/2x + 3.5. Hope this helps!

a parallelogram shaped patio has a rectangular rug in the middle jwhat is the area of the patio around the rug?

Answers

Answer:

12" 15"

Step-by-step explanation:

The answer would be 127

Please help!!! in need of help, will mark brainliest!

Answers

Answer:

minimum value : -1

Step-by-step explanation:

y= 2x^2- |0x+1|

y=2x^2-1

0x has no value they're just putting that in there to trip you up. Also you can view the graph on Desmos graphing calc online to see the minimum value of this function.

x is positive so parabola opens up: meaning minimum value

y-intercept is (0, - 1) so minimum value = -1

I DONT WANT TO GO TO SUMMER SHCOOL
PLEASE IF YOU HAVE ANY KNOWLEDGE OF THIS TEACH ME BC MY TEACHER DIDN'T TEACH ME ANYTHING

Answers

Answer:

Yes, both are radii.

Step-by-step explanation:

Assume S lies in the center of the circle. If so, when drawing a line from S to Y, it can be counted as half a diameter, or a radii. Same goes for line ST.

the person above me is correct i just took that test

NEED HELP ASAP DUE SOON!!!! This scatter plot shows the relationship between the amount of time, in hours, spent working on an essay and the grade, as a percent, earned.
Enter the approximate slope of the estimated line of best fit.

Answers

Answer:

5 % per hour

Step-by-step explanation:

Pick two of the grid points the line seems to go through. I'm using (0, 50) and (4, 70).

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{70-50}{4-0}=\frac{20}{4}=5[/tex]

Shelia works at the ice cream shop and makes $8.00 an hour during the day, and one and a half times that rate in the evening. Last week she worked 12 hours during the day and 6 hours at night. How much was her paycheck?

Answers

12 x 8 = 96
+
6 x 1.5 = 9

ANSWER: $105

This should be right and I hope it helps :)

what is the equation for this graph pls help me and pls make sure it’s right:))

Answers

Answer:

y = 5x + 4

Step-by-step explanation:

First I found the slope by using the the definition that slope is rise/run so I saw that the y value went up from 4 to 9 which is 5 units and then the x value went up one in that same time. This means that the slope is 5/1. Then I found the y intercept by seeing where x = 0. On the graph you can see the line touches the y - axis at a value of 4 which means that the y - intercept is 4. Plugging these values into the y = mx + b equation you get y = 5x + 4.

Answer:

y = 5x + 4

Step-by-step explanation:

Slope-intercept form uses the formula y = mx + b where m is the slope and b is the y-intercept.

The slope is 5, because from one point to another, you go up 5 and over one (5/1)

So you can substitute the slope into the formula:

y = (5)x + b

The y intercept is 4 because that is where the line crosses the y axis.

So substitute that:

y = (5)x + (4)

y = 5x + 4

20 points help asap!!!

Find B n C Given
B

Answers

Answer:

Step-by-step explanation:

Sets B and C have nothing in common and therefore B ∩ C = empty set

Sunshine Raisin Company sells snack-sized boxes of raisins. Twenty boxes were randomly selected and the raisins we counted. The results are shown in the list below. What frequency table BEST represents the Sunshine Raisin data? Sunshine Raisins

Answers

Answer:

Step-by-step explanation:

mrk me brainliest

Answer:

the correct answer is A

Step by step explanation

area of a circle of radius is 6.5?

Answers

Answer:

see below

Step-by-step explanation:

The area of a circle is given by

A = pi r^2 where r is the radius

A = pi (6.5)^2

A =42.25 pi

If we approximate pi by 3.14

A = 42.25 * 3.14 =132.665

If we use the pi button

A = 132.7322896

Answer:

132.73

Step-by-step explanation:

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