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3 years ago

Determine which situation(s) best describes operations with the numbers 4.58 and -0.145. Select all situations that apply.

1 answer:

7 0

The product and the quotient of the decimal numbers are both negative
(because when multiplying/dividing, and ur signs are different, then ur answer will be negative)

The sum of the decimal numbers is positive
(because when adding, if the signs are different, u subtract and take the sign of the larger number)

The difference of the decimals is positive
(because ur subtracting a negative...4.58 - (- 0.145) = 4.58 + 0.145...and that equals a positive)

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The nth term of a sequence is 3n^2- 1

Thepotemich [5.8K]

Answer: The number that belongs to both sequences is 26.

Step-by-step explanation:

We have two sequences, let's call one as A and the other as B.

The n-th term of sequence A is written as:

aₙ = 3*n^2 - 1

the nth term of sequence B is written as:

bₙ = 30 - n^2

We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)

Then we want to find:

aₙ = bₓ

where n and x are integer numbers.

Then we will heave:

3*n^2 - 1 = 30 - x^2

To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.

Let's isolate n.

3*n^2 = 30 - x^2 + 1

3*n^2 = 31 - x^2

n^2 = (31 - x^2)/3

n = √( (31 - x^2)/3)

Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.

Then let's start with x = 1.

n(1) = √( (31 - 1^2)/3) = √(30/3) = √10

We know that √10 is not an integer.

now with x = 2,

n(2) = √( (31 - 2^2)/3) = √( (31 - 4)/3) = √(27/3) = √9 = 3

then if x = 2, we have n = 3.

Both of them are integers, then we get:

a₂ = 3*(3)^2 - 1 = 27 - 1 = 26

b₃ = 30 - 2^2 = 30 - 4 = 26

The number that belongs to both sequences is 26.

5 0

3 years ago

2. Mr. Terrific Teacher recorded the scores of unit

vesna_86 [32]

Oooo this a little bit to hard for me I’m sorry

3 0

3 years ago

Which transformation of Figure A results in Figure A' ?

MariettaO [177]

Option B: a counterclockwise rotation of 90° about the origin

Explanation:

From the graph, we can see the coordinates of the figure A are (0,2), (-1,6) and (-4,4)

The coordinates of the figure A' are (-2,0), (-6,-1) and (-4,-4)

<u>Option B: a counterclockwise rotation of 90° about the origin </u>

The transformation rule for a coordinate to reflect a counterclockwise rotation of 90° about the origin is given by

$(x,y)\implies (-y,x)$

Let us substitute the coordinates of the figure A

Thus, we have,

$(0,2)\implies(-2,0)$

$(-1,6)\implies (-6,-1)$

$(-4,4)\implies(-4,-4)$

Thus, the resulting coordinates are equivalent to the coordinates of the figure A'.

Therefore, the figure is a counterclockwise rotation of 90° about the origin .

Hence, Option B is the correct answer.

3 0

3 years ago

Read 2 more answers

I have 3 slots left and 3 answers left. Fill them in pls and u get a brainlist :)

gulaghasi [49]

Answer:

Water (one oxygen atom bonded to two hydrogen atoms)

Step-by-step explanation:

The chemical formula for water is H²O. The H is the chemical symbol for Hydrogen and O is the chemical symbol for Oxygen. The 2 is a subscript which represents how many atoms of a certain element are in a molecule. In this case, the subscript ² comes after H, indicating that there are two Hydrogen atoms inside water. There is no subscript after O, meaning there is only one Oxygen atom. Therefore, there are two Hydrogen atoms and one Oxygen atom that bond to form water. Hope this helps :))

4 0

3 years ago

PLZ HELP, GIVING BRAINLIEST!!

Alex

Answer: the diameter of the circle is 226 cm

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Length of arc = 88π

θ = 140 degrees

Therefore,

88π = 140/360 × 2 × π × r

Dividing both sides of the equation by π, it becomes

88 = 140/360 × 2r

88 × 360 = 140 × 2r = 280r

280r = 31680

r = 31680/280

r = 113 cm

Diameter = radius × 2

Diameter = 113 × 2 = 226 cm

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4 years ago