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3 years ago

write the following algebraically using x as your unknown “i think of a number, multiply it by 3, add 4 and square the result”

Mathematics

1 answer:

beks73 [17]3 years ago

6 0

Answer:

(3x +4)²

Step-by-step explanation:

I think of a number x, then i multiply it by 3, add 4 and square the result.

Representing this mathematically,

x * 3= 3x

Then add 4 which will be 3x + 4

Squaring the result would be (3x +4)².

So, if we give our unknown which is x the value of say, 3.

Substituting the value of x into that equation would be easy.

(3 (3) +4)²

= (9 + 4)²

= (11)²

=132.

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Please someone help me to prove this.

morpeh [17]

Answer: see proof below

Step-by-step explanation:

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

Proof LHS → RHS

LHS: 2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]

Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]

Distribute: cos²2A + 2cos2A·sin2A + sin²2A

Pythagorean Identity: 1 + 2cos2A·sin2A

Double Angle: 1 + sin4A

LHS = RHS: 1 + sin4A = 1 + sin4A $\checkmark$

6 0

3 years ago

Which graph represents a function? A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative

Jet001 [13]

The ordered pair that represents a function is:

⇒ (-3, 3), (-2, -2), (1, 1), (2, -2)

What are Coordinates?

A pair of numbers that describe the exact position of a point on a cartesian plane by using horizontal and vertical lines are called the coordinates.

The given points are;

(-3, 3), (-3, -3), (-1, 1), (1, 4)

(-3, 3), (-2, -2), (1, 1), (2, -2)

(-3, 3), (-3, -3), (1, -4), (1, 1)

(-4, 4), (-4, 1), (-2, 1), (2, 1)

Now, For an ordered pair to be a function, either of the following must be true:

Each x-value has exactly one corresponding y-value.

More than one x-values have the same corresponding y-values.

And, If any of the following conditions is true, then the ordered pair is not a function,

One x-value has multiple corresponding y-values.

More than one x-values have multiple corresponding y-values.

From the given options, only ordered pair (-3, 3), (-2, -2), (1, 1), (2, -2) satisfies the condition to be a function.

Because none of its x-values have multiple corresponding y-values.

And, Other ordered pairs are either one-to-many or many-to-many.

So, The ordered pair that represents a function is:

⇒ (-3, 3), (-2, -2), (1, 1), (2, -2)

To learn more about ordered pairs visit:

brainly.com/question/19267542

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4 0

1 year ago

Which expression is equivalent to (2g^5)^3/(4h^2)^3

9966 [12]

$\cfrac{(2g^5)^3}{(4h^2)^3} = \cfrac{2^3 \cdot g^{5\cdot3}}{4^3 \cdot h^{2\cdot3}} = \cfrac{8 g^{15}}{64 h^{6}} =\cfrac{g^{15}}{8h^{6}}$

First option

7 0

3 years ago

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nydimaria [60]

Answer:

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3) 56

4) 9

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Step-by-step explanation:

For the day blanks, you just multiply the number of weeks by 7.

For the week blank, you divide 63 by 7

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3 years ago

The following octagon is formed by removing four congruent triangles from a rectangle. What is the area of the rectangle?

prisoha [69]

Area= length times width. 10×6 is 60. Answer is 60 cm^2

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3 years ago

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