For the value of the constant n is Q(x)=x^3+(n-9)x^2+(2n-5)x+4 divisible by(x+4)?

Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'

Virty [35]

Scale factor is a ratio. The correct option is C.

<h3>How are scale drawings formed?</h3>

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

$\rm 1\: ft : \dfrac{s}{k}\: in.$

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

The length of AB can be written as,

AB = √[(1-4)²+ (1-1)²]

AB = 3

Since the length A'B' is 6 units, therefore, the scale factor will be,

Scale factor = (Length after transformation)/(Length before transformation)

Scale factor = 6 /3 = 2

Hence, the correct option is C.

Learn more about Scale factors:

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8 0

2 years ago

Find the common difference for the sequence shown: [1/5, 13/40, 9/20...)

bazaltina [42]

<h3>Answer: 1/8</h3>

Explanation:

Pick any term and subtract off the previous term to get the common difference.

So,

13/40 - 1/5 = 13/40 - 8/40 = (13-8)/40 = 5/40 = 1/8

Or

9/20 - 13/40 = 18/40 - 13/40 = (18-13)/40 = 5/40 = 1/8

The positive common difference value indicates this arithmetic sequence is increasing.

6 0

3 years ago

What is f(0)?<br> 4<br> 5<br> 6<br> 7

Nutka1998 [239]

Answer with a Step-by-step explanation: We are given the table as:

x f(x)

0 6

2 7

4 0

7 5

i.e. corresponding to different values of x we are given the values of f(x)

we have to find the value of f(0)

i.e. we have to find the value of f(x) when x=0

As we can see from the table the value of f(x) at x=0 is 6

Hence, Correct option is:

C) 6

4 0

3 years ago

The two rectangular prisms are similar. What is the volume of the larger rectangular prism? 240 cm³ 540 cm³ 1620 cm³ 3240 cm³ A

Andreas93 [3]

Volume of a figure is measure of the space it occupies. The volume of the larger rectangular prism is given as: Option C: 1620 cm³

<h3>How to calculate volume of a rectangular prism?</h3>

If a rectangular prism has dimensions <u>a</u> unit, <u>b</u> unit, and <u>c</u> units, then its volume is given as

$V = a \times b \times c \: \rm unit^3$

<h3>What are similar figures?</h3>

They are scaled. It means, if two figures are similar, then we can get one figure from another by multiplying some constant value(same for one pair of similar figure) to its dimensions.

For example,

if for given case, one rectangular prism has got dimensions a, b, and c centimetres, then

the second rectangular prism, which is similar, let the scale factor is 'd',t then second prism's dimensions will be a x d units, b x d units, and c x d units.

For first prism(smaller), its one side is given to be 5 cm, let its other two sides be 'b' cm, and 'c' cm, then,

$60 \: \rm cm^3 = 5\times b\times c \\\\b\times c = \dfrac{60}{5} = 12$

Now, the larger prism has 15 cm corresponding side, thus, scale factor was 3 (since 15 is 3 times 5).

Thus, its dimensions would be 15, 3 x b, 3 x c

Thus, its volume would be

$15 \times 3 \times b \times 3 \times c = 135 \times b\times c = 135 \times 12 = 1620 \: \rm cm^3$

Thus,

The volume of the larger rectangular prism is given as: Option C: 1620 cm³

Learn more about volume of rectangular prism here:

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5 0

3 years ago

Can someone help me pls

Gekata [30.6K]

Answer:

C, D

Step-by-step explanation:

6 0

3 years ago

For the value of the constant n is Q(x)=x^3+(n-9)x^2+(2n-5)x+4 divisible by(x+4)?​

For the value of the constant n is Q(x)=x^3+(n-9)x^2+(2n-5)x+4 divisible by(x+4)?