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2 years ago

Two negative integers are 8 units apart on the number line and have a product of 308. What equation could be used to determine x

Mathematics

1 answer:

forsale [732]2 years ago

5 0

Answer:

Therefore the two negative integers are - 22, - 14.

Step-by-step explanation:

Given that, two negative number are are 8 units apart.

Let x be a negative integer one of them.

Then the another integer be (x+8)

Given that the product of them is 308.

According to the problem,

$x(x+8)=308$

$\Rightarrow x^2+8x=308$

$\Rightarrow x^2+22x-14x-308=0$

$\Rightarrow x(x+22)-14(x+22)=0$

$\Rightarrow (x+22)(x-14)=0$

$\Rightarrow x=-22,14$

Since x is a negative integer.

∴x = - 22.

Then another integer is =( - 22+8) = -14

Therefore the two negative integers are - 22, - 14.

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Which expression is equivalent

Tatiana [17]

Given expression is

$\sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6}}$

Radical is fourth root

first we simplify the terms inside the radical

$\frac{x^{11}}{x^7}=x^4$

$\frac{y^(8)}{y^6}=y^2$

So the expression becomes

$\sqrt[4]{\frac{16x^4y^2}{81}}$

Now we take fourth root

$\sqrt[4]{16} = 2$

$\sqrt[4]{81} = 3$

$\sqrt[4]{x^4} = x$

We cannot simplify fourth root (y^2)

After simplification , expression becomes

$\frac{2x\sqrt[4]{y^2}}{3}$

Answer is option B

8 0

2 years ago

A jewelry company prints a hidden logo watermark. The watermark is a chord that is 0.8 cm from the center of a circular ring tha

Sergeeva-Olga [200]

Answer:

length of chord is 6cm

Step-by-step explanation:

Here, we are to calculate the length of the chord.

It should be understood that the chord has a length of 0.8cm from the center of the circle of radius 3cm, thereby forming two right-angled triangles with the radius 3cm being the hypotenuse of each and 0.8cm being the height of each.

Now, the chord is divided into 2 by this height dropping from the center of the circle. To calculate the first half, we use Pythagoras’ theorem with 3cm being hypotenuse and 0.8cm being the other side.

mathematically;

3^2 = 0.8^2 + l^2

9 = 0.64 + l^2

l^2 = 9-0.64

l^2 = 8.36

l = √(8.36)

l = 2.89 approximately

The length of the chord would be 2l = 2 * 2.89 = 5.78 cm which is 6cm to the nearest length

5 0

2 years ago

a) Work out the next term in this sequence. 4 12 16 b) Describe the rule for continuing this sequence. 44 41 38 35 32 c) The seq

horsena [70]

Answer:

1. Next sequence = 20

2. Tn = 47 - 3n

3. Common number: 32

Step-by-step explanation:

Given

Sequence 1: 0, 4, 8, 12, 16

Sequence 2: 44, 41, 38, 35, 32

a. Write out the next sequence in (1)

The pattern followed by sequence 1 is that, each successive sequence is and addition of 4 to the previous sequence..

See observation below

4 = 0 + 4

8 = 4 + 4

12 = 8 + 4

16 = 12 + 4

Definitely, the next sequence will be 4 + the previous sequence.

Next sequence = 16 + 4

Next sequence = 20

2. The rule for continuing sequence 2

It'll be observed that sequence 2 follows an arithmetic progression.

To get the rule for continuing the sequence, the following data are needed.

I. The first term of the sequence.

This is often represented by letter a.

a = 44

II. The common difference.

This is the difference between two successive sequence

This is often represented by letter d.

d = 41 - 44 = -3

d = 38 - 44 = -3

Using the arithmetic progression formula

Tn = a + (n - 1)d

By substituting 44 for a and -3 for d.

Tn = 44 + (n - 1)(-3)

Tn = 44 - 3n + 3

Tn = 44 + 3 - 3n

Tn = 47 - 3n

Hence, the rule for continuing the sequence is 47 - 3n where n is the current term of the sequence

III. Work out a number in common in both sequence

It'll be observed that the visible data of sequence 2 are bigger than that of sequence 1.

To get a common number, we have to extend sequence 1 until we arrive at a common number in both sequence

Sequence 1: 0, 4, 8, 12, 16

This becomes

Sequence 1: 0, 4, 8, 12, 16, 20, 24, 28, 32.....

32 is common in sequence (1) and (2).

If the sequence is extended, we'll arrive at another common number. But we have to stop, since we've arrived at a common number.

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2 years ago

-7=-x <br><br> One step equations ( Find X)

Marysya12 [62]

Answer:

answer of your question is

-x= -7

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2 years ago

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abruzzese [7]

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2 years ago