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2 years ago

What is the volume of a shoe box with length 13 inches, width 7 inches, and height 5 inches? V = lwh in3

Mathematics

2 answers:

Sati [7]2 years ago

4 0

The volume is 13*7*5. Therefore, the answer is 455 in^3

Mademuasel [1]2 years ago

3 0

A shoe box is in the shape of cuboid.

The formula to find volume of cuboid is given by:

Volume of a cuboid = (length × breadth × height) cubic units.

We are given:

length = 13 inches

width = 7 inches and

height = 5 inches.

Plugging these values in the formula of volume,

Volume of cuboid = L * W * H = 13 *7 *5 = 455 cubic inches.

Answer : The volume of shoe box is 455 cubic inches.

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find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0

Citrus2011 [14]

Answer:

Radius: $r =\frac{\sqrt {21}}{6}$

$Center = (-\frac{3}{2}, -\frac{2}{3})$

Step-by-step explanation:

Given

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Solving (a): The radius of the circle

First, we express the equation as:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

So, we have:

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Divide through by 9

$x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0$

Rewrite as:

$x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}$

Group the expression into 2

$[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}$

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

Next, we complete the square on each group.

For $[x^2 + 3x]$

1: Divide the $coefficient\ of\ x\ by\ 2$

2: Take the $square\ of\ the\ division$

3: Add this $square\ to\ both\ sides\ of\ the\ equation.$

So, we have:

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

$[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Factorize

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Apply the same to y

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}$

Add the fractions

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}$

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

By comparison:

$r^2 =\frac{7}{12}$

Take square roots of both sides

$r =\sqrt{\frac{7}{12}}$

Split

$r =\frac{\sqrt 7}{\sqrt 12}$

Rationalize

$r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}$

$r =\frac{\sqrt {84}}{12}$

$r =\frac{\sqrt {4*21}}{12}$

$r =\frac{2\sqrt {21}}{12}$

$r =\frac{\sqrt {21}}{6}$

Solving (b): The center

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

From:

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

$-h = \frac{3}{2}$ and $-k = \frac{2}{3}$

Solve for h and k

$h = -\frac{3}{2}$ and $k = -\frac{2}{3}$

Hence, the center is:

$Center = (-\frac{3}{2}, -\frac{2}{3})$

6 0

2 years ago

Courtney receives a mailer to a local store. In the mailer, there are two coupons which cannot be combined. One coupon is for $2

STatiana [176]

Answer:

B, Courtney should use the 15% off coupon

8 0

3 years ago

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Find the measure of angel 3

Elena-2011 [213]

Answer:

100

Step-by-step explanation:

Remark

If two opposite arcs are given by being opposite vertically opposite angles, then the value of both the vertically opposite angles are equal to

Vertically opposite angle = 1/2 (arc1 + arc2)

Givens

Arc1 = 60

Arc2 = 100

Solution

The red dot angle = 1/2 (60 + 100)

The red dot angle = 1/2(160)

The red dot angle = 80

Because the red dot angle and <3 are on the same line with the same common point, they are supplementary.

<3 and red dot = 180

<3 + 80 = 180 Subtract 80 from both sides

<3 = 180 - 80

<3 = 100

8 0

3 years ago

QUESTION: Josephine put a frame round his picture which measured 36 cm by 34 cm. A margin 4cm wide was left all the way round. W

Mandarinka [93]

36x34= 1224cm²
(36-4)x(34-4)= 32x30= 960cm²

Area of frame= 1224
Area of picture inside frame= 960
So border = 1224-960= 264

ANSWER = 264cm²

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2 years ago

Solve the inequality m + 2 < -4

jeka57 [31]

Answer:

m < - 6

Step-by-step explanation:

Given

m + 2 < - 4 ( subtract 2 from both sides )

m < - 6

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2 years ago

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