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3 years ago

8

joe measured a brick using a ruler with centimeters and got 9 cm. he then measured the same brick using a ruler with millimeters

and got 90 mm. are these measurements equivalent?

1 answer:

max2010maxim [7]3 years ago

8 0

Answer:

yes

Step-by-step explanation:

1 cm=10mm. if 1cm=10mm what about 9cm

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A rectangular box has the dimensions shown in the diagram. The volume of the box is given by the function V(x) = x3 – 4x, where

marta [7]

Answer:

$Height =3$

Step-by-step explanation:

Given

$Length = x + 2$

$Width = x - 2$

$Height = x$

$Volume = 15$

Required

Find the height

The volume is calculated as thus:

$Volume = Length * Width * Height$

This gives

$15 = (x + 2) * (x - 2) * x$

Apply difference of two squares

$15 =(x^2 - 4 ) * x$

$15 = x^3 - 4x$

Subtract 15 from both sides

$x^3 - 4x - 15 = 0$

Using a calculator to factorize, we have:

$(x-3)(x^2+3x+5) = 0$

Split

$x - 3 = 0$ or $x^2 + 3x + 5 = 0$

$x = 3$ or $x^2 + 3x + 5 = 0$

x has complex roots for $x^2 + 3x + 5 = 0$

Hence:

$x = 3$

Recall that:

$Height = x$

$Height =3$

3 0

2 years ago

a train travels 288km at a uniform speed.if the speed has been 4km per hour more it would have taken one hour less for the same

Lostsunrise [7]

Given:

A train travels 288 km at a uniform speed.

If the speed has been 4 km per hour more it would have taken one hour less for the same journey.

To find:

The initial speed of the train.

Solution:

Let x km/h be the initial speed on the train.

New speed of train = (x+4) km/h

We know that,

$Time=\dfrac{Distance}{Speed}$

Time taken by the train initially to cover 288 km is $\dfrac{288}{x}$ hours.

New time taken by the train to cover 288 km is $\dfrac{288}{x+4}$ hours.

It is given that If the speed has been 4 km per hour more it would have taken one hour less for the same journey.

$\dfrac{288}{x}-\dfrac{288}{x+4}=1$

$\dfrac{288(x+4)-288x}{x(x+4)}=1$

$288x+1152-288x=x^2+4x$

$1152=x^2+4x$

$0=x^2+4x-1152$

Splitting the middle term, we get

$x^2+36x-32x-1152=0$

$x(x+36)-32(x+36)=0$

$(x+36)(x-32)=0$

$x=-36,32$

We know that the speed cannot be negative. So, the only possible value of x is 32.

Therefore, the speed of the train is 32 km/h.

3 0

2 years ago

What are all the solutions to the following<br> equation?<br> |10x + 2| =48

Greeley [361]

$\huge \boxed{\mathfrak{Question} \downarrow}$

What are all the solutions to the following

equation?

|10x + 2| =48

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$| 10 x + 2 | = 48$

Combine like terms and use the properties of equality to get the variable on one side of the equals sign and the numbers on the other side. Remember to follow the order of operations.

$|10x+2|=48$

Use the definition of absolute value.

$10x+2=48 \\ 10x+2=-48$

Subtract 2 from both sides of the equation.

$10x=46 \\ 10x=-50$

Divide both sides by 10.

$\boxed{ \boxed{ \bf \: x=\frac{23}{5} = 46}} \\ \boxed{\boxed{ \bf \: x=-5 }}$

7 0

2 years ago

Read 2 more answers

Purina dog food costs $43 for a $20 pound bag. A 41 pound bag of Puppy Cow

zhannawk [14.2K]

It is better to buy the Purina dog food

3 0

2 years ago

Kindly i need solution of these both parts a and b which are attached below

Nikitich [7]

9514 1404 393

Answer:

a) 252 cm³, 252 cm², 705.6 g

b) 240 cm³, 252 cm², 672 g

Step-by-step explanation:

The volume of each figure can be computed as the product of the base area (the side facing the viewer) and the "height" of the prism (the distance between bases).

The surface area of the prism is the sum of the two base areas and the "lateral area" consisting of the product of the base perimeter and the "height" of the prism.

The mass will be the product of volume and density.

__

ai) The base is a 3 cm by 8 cm rectangle together with a trapezoid with bases 3 cm and 6 cm, and height 7 - 3 = 4 cm.

B = (3 cm)(8 cm) +(1/2)(3 cm +6 cm)(4 cm) = 24 cm² +18 cm² = 42 cm²

The "height" is 6 cm, so the volume is ...

V = Bh = (42 cm²)(6 cm) = 252 cm³

__

aii) The perimeter of the base is the sum of its side lengths. Clockwise from left, the lengths are ...

(8 +3 +2 +5 +3 +7) cm = 28 cm

Then the lateral area is ...

LA = Ph = (28 cm)(6 cm) = 168 cm²

Adding this to the areas of the two bases, we get the total surface area:

A = LA +2B = (168 cm²) + 2(42 cm²) = 252 cm²

__

aiii) The mass is the product of volume and density:

M = ρV = (2.8 g/cm³)(252 cm³) = 705.6 g

____

bi) This trapezoidal prism has a base that has bases of 6 and 9 cm, and a height of 4 cm. The area of the base is ...

B = (1/2)(b1 +b2)h = (1/2)(6 cm + 9cm)(4 cm) = 30 cm²

Then the volume is ...

V = Bh = (30 cm²)(8 cm) = 240 cm³

__

bii) The lateral area is the perimeter of the base times the height of the prism:

LA = Ph = (4 +6 +5 +9 cm)(8 cm) = 192 cm²

The total area is this area plus that of the two bases:

A = LA +2B = (192 cm²) +2(30 cm²) = 252 cm²

__

biii) M = ρV = (2.8 g/cm³)(240 cm³) = 672 g

3 0

3 years ago