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3 years ago

What is the coefficient of x^2 in the expansion of (x+2)^3

Mathematics

1 answer:

goldenfox [79]3 years ago

3 0

(x+2)^3=x^3+2^3+3*x^2*2+3x*2^2=x^3+8+6x^2+12x

The coeficient of the x^2 is 6.

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The ski club wants to take in at least $100 in profit for the bus to Holiday Valley. Students pay $5 to ride the bus and chapero

laiz [17]

Answer:

x + y < 20

5x + 10y ≥ 100

Step-by-step explanation:

The ski club wants at least $100

Student pays $5

Chaperone pays $10

Maximum number of seats = 20

Assumption:

Assumed number of students = x

Assumed number of chaperone = y

Equation:

Maximum number of seats = 20

⇒ x + y < 20

The club wants $100

⇒ 5x + 10y ≥ 100

4 0

4 years ago

What is the standard form of the points (-3,4) (2,-6)

Bas_tet [7]

The standard form equation of the line connecting the two points is $2x + y = -2$

Linear equation in a standard form is given as $Ax + By = C$

where,

A, B, and C are constants or numbers

x and y are the variables.

To solve this problem, the following steps would be taken:

Step 1: Find the slope of the line connecting points (-3,4) and (2,-6)

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1}$

where,

$(x_1, y_1) = (-3,4)\\(x_2, y_2) = (2,-6)$

Substitute

$slope (m) = \frac{-6 - 4}{2 -(-3)} \\m = \frac{-10}{5}\\m = -2$

Step 2: Find the y-intercept (b) of the line by substituting $(x, y) = (-3,4)$ and $m = -2$ into $y = mx + b$ (slope-intercept form)

$4 = -2(-3) + b\\4 = 6 + b\\4 - 6 = 6 + b - 6\\-2 = b\\b = -2$

Step 3: Write the equation of the line in slope-intercept form by substituting $m = -2$ and $b = -2$ into $y = mx + b$

$y = -2x + (-2)\\y = -2x - 2$

Step 4: Rewrite the equation in standard form $(Ax + By = C)$

$y = -2x - 2\\$

Add $2x$ to both sides

$2x + y = -2x - 2 + 2x\\2x + y = -2$

The standard form equation of the points (-3,4) and (2,-6) is $2x + y = -2$

Learn more about standard form of two points of a linear equation here:

brainly.com/question/18446164

6 0

3 years ago

Which is a reasonable frist step that can be used to solve the equation 4x+3(x+2)=5(2x-3)

vagabundo [1.1K]

Answer:

they are not equal if that was what you were looking for

Step -by-step explanation:

8 0

3 years ago

Read 2 more answers

(a) 3 - 2/3÷4/3 × 7<br>(b) [(2/3)/(5/6)]-2/5<br>(c) {(-3/4) +( 1/2)}/{(2/5)-(5/2)}<br>

BartSMP [9]

Step-by-step explanation:

a. (3 - 2/3) ÷ (4/3 x 7)

= [(3 x 3) / (1 x 3) - 2/3] ÷ 28/3

= (9/3 - 2/3) ÷ 28/3

= 7/3 x 3/28

= 21/84

= (21 x 1) / (21 x 4)

= 1/4

b. 2/3 ÷ 5/6 - 2/5

= 2/3 x 6/5 - 2/5

= 12/15 - 2/5

= (3 x 4) / (3 x 5) - 2/5

= 4/5 - 2/5

= 2/5

c. (- 3/4 + 1/2) ÷ (2/5 - 5/2)

= [- 3/4 + (1 x 12) / (2 x 2)] ÷ [(2 x 2) / (5 x 2) - (5 x 5) / (2 x 5)]

= (- 3/4 + 12/4) ÷ (4/10 - 25/10)

= 9/4 ÷ (- 21/10)

= 9/4 x - 10/21

= - 90/84

= (6 x - 15) / (6 x 14)

= - 15/14.

If you have any doubt, then you can ask me in the comments.

6 0

3 years ago

Read 2 more answers

Triangle EFG is dilated by a scale factor of 1/4 to form triangle E'F'G'. Side E'F' measures 12.512.5. What is the measure of

WINSTONCH [101]

Answer: 3.125

Step-by-step explanation:

Given

Triangle is dilated by a factor of $\frac{1}{4}$ i.e. each side multiplies to 0.25.

Side E'F' becomes 0.25 times the original length

$\Rightarrow E'F'=\dfrac{1}{4}\times 12.5=3.125$

6 0

3 years ago