[tex] \sf \: If (3x-1) ^{7} = a _{7} x ^{7} + a _{6} x ^{6} + a _{5} x ^{5}+.... \\ \sf + a₁x + a _{0}, then \: \: a_0 + a₁ + a₂ + a_3 + a_4 + a_5 + a_6 + a7 = [/tex]
a)0
b)1
c)128
d)64

Please solve this for me. Need step-by-step explanation. Spam free answer required. Thank you in anticipation.

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Answer:

4^n-1

Step-by-step explanation:

So given sequence is a geometric sequence where terms increase or decrease by a constant common ratio(r)

Formula to find terms in Geometric sequence is " ar^n-1 where a is first term , r is common ratio and n is number of items

In this case , first term (a) is 1 , common ratio(r) is succeeding term/preceding term = 4/1 = 4 and number of items be (n).

Applying "ar^n-1 " we get,

1*4^n-1 which is , 4^n-1

Thats the formula which represents the situation....

Answer:

1. To solve a one-variable equation, it may be necessary to first multiply by using the Distributive Property

2. The next step is to combine like terms as needed.

3. Then solve for the variable by applying inverse operations.

4. If solving lead to a true equation, then the equation has infinitely many solutions.

5. if solving leads to an untrue equation, then the equation has no solution.

Answer:

38

Step-by-step explanation:

38.23 is closest to 28, because neither the .2 or .03 is high enough to round the last whole number up

Answer:

Rounding 38.23 to the nearest whole number would be 38

Step-by-step explanation:

Rounding 38.23 to the nearest whole number would be 38 because the extra 0.23 is less than 0.50

If it was 0.50, the answer would go up to 39.

Answer:

what are the statements we pick from?

Step-by-step explanation:

most likely look out for angles and lengths that go against the established ratio

Answer:

Step-by-step explanation:

△ RST ≅ △ TXY

We are given ΔRST and ΔTXY are congruent to each other.

If two triangles are congruent to each other then their corresponding parts are equal.

Please see the attachment of two triangles.

∠R is corresponding to ∠T

∵  ∠R=∠T By CPCT

∠XYT is corresponding to ∠STR

∵  ∠XYT=∠STR By CPCT

∠XTY is corresponding to ∠SRT.

∵  ∠XTY=∠SRT By CPCT

∠TXY is corresponding to ∠RST

∵  ∠TXY=∠RST By CPCT

CPCT: Congruent part of congruence triangle.

Answer:

∠ DAB = 48°

Step-by-step explanation:

The sum of the 3 angles in Δ ACD = 180° , then

∠ CAD + 60° + 90° = 180° , that is

∠ CAD + 150° = 180° ( subtract 150° from both sides )

∠ CAD = 30°

Then

∠ DAB + ∠ CAD = ∠ CAB

∠ DAB + 30° = 78° ( subtract 30° from both sides )

∠ DAB = 48°

Answer:

7.5.

Step-by-step explanation:

A square has 4 equal sides so:

4x =  9  + 10 + 11    where x is the length of one side of the square.

4x = 30

x = 7.5.

Answer:

do it got a picture

Step-by-step explanation:

Hope it helps.

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Answer:

x = ± [tex]\sqrt{\frac{7y+8}{5} }[/tex]

Step-by-step explanation:

5x² - 3y = 4y + 8 ( add 3y to both sides )

5x² = 7y + 8 ( divide both sides by 5 )

x² = [tex]\frac{7y+8}{5}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{7y+8}{5} }[/tex]

Answer:

Look at step-by-step explanation

Step-by-step explanation:

Side-side-angle is not a congruence rule because a side cannot be in between an angle and a side. Angle-side-side is the same thing, a side cannot be in between an angle and a side.

Answer:

K (-1,-1)

Step-by-step explanation:

Answer:  A:  3x^2y^(3/2)

Step-by-step explanation:

This can be written as

(81*x^8*y^6)^(1/4)

Then multiply each exponent by (1/4):

81^(1/4)*x^(8(1/4))y^6(1/4))

81^(1/4) = 3

x^(8(1/4)) = x^2

y^6(1/4)) = y^(3/2)

The result:  3x^2y^(3/2)

We are given –

[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf x² = 4x -4[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf x² -4x +4 = 0[/tex]

Let's find it's discriminant.

We know –

[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf Discriminant = b² - 4ac}[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf Discriminant = (-4)² - 4 \times 1 \times 4[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf Discriminant = 16-16[/tex]

[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\sf Discriminant =0 }[/tex]

As we got –

Answer:

X=9

Step-by-step explanation:

2x-7=11

Add 7 each side

2x - 7 +7 =11 + 7

2x=18

Divide by 2 each side

2x/2=18/2

x=9

Answer:

x = 9

Step-by-step explanation:

2x - 7 = 11

Add 7 to both sides: 2x = 18

Divide by 2: x = 9

Answer:

35 degrees.

Step-by-step explanation:

Answer:

35 degrees

Step-by-step explanation:

27 - 35 = -8

Answer:

x = 3/2 or 1.5

Step-by-step explanation:

(9(4x-1))/2x = 15

simplify the 9(4x-1) = 36x-9

(36x-9)/2x = 15

multiply both sides by 2x to take out the fraction

36x-9 = 15(2x)

36x-9 = 30x

subtract by 30x on both sides, and add 9 on both sides

36x-9-30x = 0

36x-30x = 9

6x = 9

x = 9/6 = 3/2 or 1.5

Answer:

7:1

Step-by-step explanation:

Answer:

2*2*2*3*5

Step-by-step explanation:

It is saying that 120 is the same as 24*5, and that 24* 5 is the same as 5 *2*12, which is that same as 5*2*3*4, which is then the same as 5*2*3*2*2.

Answer:

2 x 2 x 2 x 3 x 5

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

1. Group all x terms on the left side of the equation

1/3· x+4=-2/3·x+12

Add  2/3x to both sides:

1/3x+4+2/3·x=-2/3x+12+2/3·x

Group like terms:

1/3·x+2/3·x+4=-2/3·x+12+2/3·x

Combine the fractions:

1+2/3·x+4=-2/3·x+12+2/3·x

Combine the numerators:

3/3·x+4=-2/3·x+12+2/3·x

Find the greatest common factor of the numerator and denominator:

1·3/1·3·x+4=-2/3·x+12+2/3·x

Factor out and cancel the greatest common factor:

1x+4=-2/3·x+12+2/3·x

Simplify the left side:

x+4=-2/3·x+12+2/3·x

Group like terms:

x+4=-2/3·x+2/3·x+12

Combine the fractions:

x+4=-2+2/3·x+12

Combine the numerators:

x+4=0/3·x+12

Reduce the zero numerator:

x+4=0x+12

Simplify the arithmetic:

x+4=12

2. Group all constants on the right side of the equation

Subtract 4 from both sides:

x+4-4=12-4

Simplify the arithmetic:

x=12-4

Simplify the arithmetic:

x=8

Answer:

x=8

Step-by-step explanation:

1/3x +4= -2/3 +12

Subtract 4 from both sides: 1/3x + 4-4 = -2/3x + 12 -4

Simplify: 1/3x = 2/3x + 8

Add 2/3x to both sides: 1/3x + 2/3x = -2/3x + 8 + 2/3x

Simplify: x=8

[tex]\huge \bf༆ Answer ༄[/tex]

At first Divide the figure into two rectangles, I and Il

Area of figure l is ~

Area of figure ll is ~

Area of whole figure = Area ( l + ll )

that is equal to ~

The volume of the prism, in cubic units is 1/2x³ + x²

The volume of the oblique prism is given as:

V = Base area * Height

Given the following

Base area = 1/2 (x*x)

Base area = 1/2 x²

Get the volume of the prism;

Volume of the prism = 1/2(x²)(x+2)

Volume of the prism = 1/2(x³+2x²)

Volume of the prism = 1/2x³ + 1/2(2x²)

Volume of the prism = 1/2x³ + x²

Hence the volume of the prism, in cubic units is 1/2x³ + x²

Learn more on the volume of prism here: https://brainly.com/question/23963432

Answer:

1/2x³ + x²

Step-by-step explanation:

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