Explain how to use Pascal's Triangle to expand the binomial (3x-4y)^11

Answer:

B (5,9)

Step-by-step explanation:

when working with fractions as slopes we use rise over run (broken down)

3 (numerator)--rise-how unit to go up or down

--

4 (denominator)--run--how many units to the left or right

since our slope is positive we will be going up 3 and 4 to the right.

if the slope is negative we go down and to the left.

hope this explanation helps for future questions

Answer:

Step-by-step explanation:

Use identity:

Substitute values:

Answer:

(a - b)² = 9

Step-by-step explanation:

Expand (a - b)²:

[tex]\begin{aligned}\implies (a-b)^2&=a^2-2ab+b^2\\&=a^2+b^2-2ab\end{aligned}[/tex]

Given:

Substitute the given values into the expanded equation:

[tex]\begin{aligned}\implies (a-b)^2&=a^2+b^2-2ab\\&=15-2(3)\\&=15-6\\&=9\end{aligned}[/tex]

Therefore, (a - b)² = 9.

Answer:

x= -2, -10

Step-by-step explanation:

(x+6)^2-16=0

(x+6)(x+6)-16=0

x^2+6x+6x+36-16=0

x^2+12x+20=0

10+2=12

10(2)=20

(x+2)=0

(x+10)=0

x= -2, -10

Answer:

A 35%

Step-by-step explanation:

take the higher number (27) and subtract the smaller number (20) from it. there's your difference. afterwards, take the difference (7) and divide it by the smaller number (20). this gives you .35. convert it into percentage move the decimal point to the right two spots and slap a percentage sign onto it (shift+3). giving you 35%, or A.

Answer:

a) 35%

Step-by-step explanation:

Given information,

→ 20 guests attended the 1st party, and 27 guests attended the 2nd party.

Now we have to,

→ find the % increase of number of guests from first party to second party.

Let's solve the problem,

→ ((27 - 20)/20) × 100

→ (7/20) × 100

→ 0.35 × 100

→ 35%

Hence, the answer is 35%.

The difference in lengths is 9 cm and the length of the carrot is 9 cm longer than the pea pod.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have to determine the difference in lengths

The length of the carrot = 14 cm

The length of the pea pod = 5 cm

The difference in lengths = maximum length - minimum length

The difference in lengths = 14 cm - 5 cm

Apply the subtraction operation, and we get

The difference in lengths = 9 cm

We conclude that the length of the carrot is 9 cm longer than the pea pod.

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The simplified expression is 3a + 5ay - 3y -52 .

(a) There are 4 terms in the simplified expression

(b) there are 2 negative terms in the simplified expression .

In the question ,

the algebraic expression is given as 3a+2y+5ay-2y-52-3y

to simplify it , we first group them in like terms

the expression becomes .

= 3a [tex]+[/tex] 2y [tex]+[/tex] 5ay -2y - 52 -3y

= 3a + 5ay + 2y - 2y - 3y - 52

= 3a + 5ay - 3y -52

Part(a)

the number of terms in the simplified expression is 4 ,

Part(b)

as we can see that the terms -3y and  -52 are negative

So , there are 2 negative terms in the expression.

Therefore , (a) There are 4 terms in the simplified expression

(b) there are 2 negative terms in the simplified expression .

The given question is incomplete , the complete question is

Write the expression 3a+2y+5ay-2y-52-3y in simplest form. Then, answer the following questions using complete sentences.

a. How many terms are in the simplified expression?

b. How many of the terms in the simplified expression are negative?

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The proposition ~ (~ q ⇒ p) ⇒ ~ q represents a tautology, as it is true for all combinations of p and q.

Propositions are constructions that contains a truth value, which are two according to classical logic (T - true, F - false). There are simple propositions and compound propositions. Compound propositions are formed by combining simple propositions and operators. There are the following operators:

A tautology is a compound proposition that is always true. We can prove whether a proposition is a tautology by the use of a truth table:

p        q      ~ q       ~ q ⇒ p        ~ (~ q ⇒ p)       ~ (~ q ⇒ p) ⇒ ~ q

T        T        F              T                      F                           T

T        F        T              T                      F                           T

F        T        F              T                      F                           T

F        F        T              F                      T                           T

The proposition ~ (~ q ⇒ p) ⇒ ~ q is a tautology.

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Answer: (0.4k+0.6w)

Step-by-step explanation:

the answer would be (0.4k+0.6w) Since we do not know the values of k nor w, their coefficients cannot be added together.

The total volume of the solution as an algebraic expression is

0.4k + 0.6w.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount of acid added to the solution = 40% of k  

Amount of water added to the solution= 60% of w

Now,

The total volume of the solution.

= 40% of k + 60% of w

= 40/100 x k + 60/100 x w

= 0.40k + 0.60w

Thus,

The volume is 0.4k + 0.6w.

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x = 3

Step-by-step explanation:

[tex]{ \blue{ \sf{n(x) = 4x + 4}}}[/tex]

[tex]{ \blue{ \sf{16 = 4x + 4}}}[/tex]

[tex]{ \blue{ \sf{16 - 4 = 4x}}}[/tex]

[tex]{ \blue{ \sf{12 = 4x}}}[/tex]

Divide both the sides with 4

[tex]{ \blue{ \sf{ \frac{12}{4} = \frac{4}{4}x}}}[/tex]

[tex]{ \green{ \boxed{ \red{ \sf{x = 3}}}}}[/tex]

The exponential function will be written as y = 14⁰.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given exponential function is [tex]y = ab^x[/tex]. The equation of the exponential function passing through the point is,

[tex]y = ab^x \\[/tex]

14 = ab⁰

a = 14

The equation will be written as,

y = 14b⁰

y = 14⁰

Therefore, the exponential function will be written as y = 14⁰.

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a) The value  sets of n(A) = 5, n(B) = 8

b)  33 ∈ A is false, -4 ∈ B is true, 25 ∈ A is true, 5 ∉ B is true.

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.

A = { 25, 26, 27, 28, 29}

B ( is greater or equal to -6 and equal to 1) = { -6, -5, -4, -3, -2, -1, 0, 1}

n(A) = number of elements in A which is 5 and n(B) = 8

33 ∈ A The symbol ∈ means element of. so 33 is not an element of A.

-4 is an element of B so it is true, -4 ∈ B is true

25 ∈ A is true because 25 is an element of A

5 ∉ B is true because 5 is not an element of B

In conclusion, n(A) = 5, n(B) = 8

-4 is an element of B so it is true, -4 ∈ B is true

25 ∈ A is true because 25 is an element of A

5 ∉ B is true because 5 is not an element of B

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Answer:

394,200

Step-by-step explanation:

You have to multiply the house value by 1.08 or 108%

365,000*1.08=394,200

The angle measurements are 5.38°, 87.31° and 87.31°.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are the sides of triangle as AB = 18cm, BC = 18cm, AC = 16cm.

The given triangle is a isosceles triangle with two sides equivalent. Angles opposite to these sides will be equal. So, we can write -

2∠x + ∠y = 180°

from the figure, it can be seen that angle B is 5.38 degrees.

2∠x + 5.38 = 180

2∠x = 174.62

∠x = 87.31°

Therefore, the angle measurements are 5.38°, 87.31° and 87.31°.

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The number of months required to pay off the loan will be 15.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30.

The number of the months will be calculated as,

N = ( 1178.8 - 547.30) / 42.10

N = 631.5 / 42.10

N = 15

Therefore, the number of months required to pay off the loan will be 15.

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Answer:

1) 7:4

2) 11: 7

Step-by-step explanation:

By using the concept of proportionality, it can be concluded that

y = 5x is the proportional relation

Third option is correct

What is proportionality?

Suppose there are two quantities. Proportionality indicates that if there's a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio

Proportionality are often direct or inverse

Direct proportion

Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.

For example cost of an article and quantity of an article are in direct proportion

Inverse proportion

Two quantities are said to be in inverse proportion if on increasing the value of one quantity,  the value of other quantity decreases and vice versa.

For example Number of men and number of days taken by those men to complete a work are in inverse proportion

For the first option

7x - 2 = y

y = 7x - 2

Here a non zero constant (-2) is added after the term with variable x

So this relation is not proportional

For the second option

y = 2x + 4

Here a non zero constant (4) is added after the term with variable x

So this relation is not proportional

For the third option

y = 5x

Here, no non zero constant is added after the term with variable x

So this relation is proportional.

For the fourth option

y + 1 = 3x

y = 3x - 1

Here a non zero constant (-1) is added after the term with variable x

So this relation is not proportional

So the correct option is the third option

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let the number be = x

[tex] = > \frac{3x}{5} = 150[/tex]

[tex] = > 3x = 150 \times 5[/tex]

[tex] = > 3x = 750[/tex]

[tex] = > \frac{3x}{3} = \frac{750}{3} [/tex]

[tex] = > x = 250[/tex]

The number can be found by multiplying 150 by 5 and then dividing the result by 3. Therefore, the number is 250 by solving equations.

To find the number, we can set up the equation: (3/5) * x = 150. To isolate x, we multiply both sides of the equation by 5/3, resulting in x = 250. This means that the number is 250.

Start with the equation: (3/5) * x = 150.

To isolate x, multiply both sides of the equation by the reciprocal of (3/5), which is 5/3. This yields (5/3) * (3/5) * x = (5/3) * 150.

Simplify the left side of the equation: x = (5/3) * 150.

Multiply 5 by 150 and divide the result by 3: x = (750/3).

Simplify the fraction by dividing the numerator (750) by the denominator (3): x = 250.

Therefore, the number is 250.

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Answer:

Angle 1: 27

2: 153

3: 58

4: 138

Step-by-step explanation:

1. 180-(116+37)=27

2. 180-27=153

3. 180-(48+74)=58

4. 122+16=138

180-138=42

180-42=138

Answer: x=25/4 or 6.25, y=79/16 or 4.9375

Step-by-step explanation:

Normally, we would have to set up a system of linear equations, but in this case we can solve for x and plug in from there. x=5/2 or 2.5 when solving for the variable. Now we go to the second equation, plug for x, and solve for y. 5/2 times 5/2 is 25/4, multiplied by 3 is 75/4. Subtract 75/4 from -1, and divide both sides by -4.

Using the corresponding angle theorem, the value of x is 15 and y is 12.

In the given question we have to find the value of x and y.

From the graph we can see that

From the corresponding angle theorem

4x+2=62

Subtract 2 on both side, we get

4x=60

Divide by 4 on both side, we get

x=15

So the value of x is 15.

Similarly from the corresponding angle theorem

12y=144

Divide by 12 on both side, we get

y=12

So the value of y is 12.

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The five number summary from the given box plot is presented as follows:

A box and whisker plot shows five things of a distribution, listed as follows:

These values are the values marked from left to right on the box plot, from the minimum value to the maximum value, passing through the first quartile, the median and the third quartile, and form the five number summary.

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Answer:

the answer to 2dp is 2536.02

The equation that relates x and y is given as y = 2.5x

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a.

The formula for direct variation is in the form of

y = kx

where we have the value of y = 5, the value of x = 2

we have to put this in the formula above

5 = 2k

to get the value of k we would have to divide through by 2

k = 5 / 2

k = 2.5

Hence we would have y = 2.5x

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Answer:

Step-by-step explanation:

step 1 of 2:  

We got pairs: (-3, y) and (x, 2), to compute the missing x and y values, we plugin the number into the equation.

(-3, y)

y = -3x - 1

y = -3(-3) - 1

y = 9 - 1

y = 8

So we solve this pair as (-3, 8).

(x, 2)

y = -3x - 1

2 = -3x - 1

3 = -3x

x = -1

So we solve this pair as (-1, 2).

Sorry that I cannot see the following questions.

Distance travelled by the particle from time t = 0 to t = 3 in x-direction and y-direction is 27 units and 54 units respectively.

How to get distance/displacement using velocity?

According to given data:

A particle moves with velocity (dx)/(dt) = 3t² in x- direction

and (dy)/(dt) = 12t in y-direction

Integrating both sides of these derivatives with respect to t

x=  ∫3t² dt = (3t³)/3 + A = t³ + A

where A is integration constant

y= ∫12t d t = (12t²)/2 + B = 6t² + B

where B is integration constant

At t = 0 we get x = A and at t = 3 we get x = 3³ + A = 27 + A.

Therefore, the difference in position of a from t = 0 t = 3 is

27 + A - (0 + A) = 27 units.

Similarly,

At t = 0 , we get y = B and at t = 3 we get

y = 6 * 3² + B = 54 + B

Therefore, the difference in position of y from t = 0 tot t = 3 is

54 + B - (0 + B) = 54 units.

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The quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.

According to the question,

We have the following information:

([tex]x^{2} -25[/tex]) is divided by (x+5)

Now, we can solve this using two ways. First method is to use the long division method and second is to solve the expression using an identity.

We know that the following identity can used to expand the dividend:

[tex]a^{2} -b^{2} = (a+b)(a-b)\\[/tex]

In this case, we have a = x and b = 5.

[tex]x^{2} -(5)^{2} = (x-5) (x+5)[/tex]

Now, we have the following expression:

(x+5)(x-5)/(x+5)

(x-5)

Now, the remainder is 0.

Hence, the quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.

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Equation for the perpendicular bisector of the line segment is  

2y = 3x +20.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.

Given coordinates of the endpoints of a line segment  (-9, 3) and (-3,-1).

In order to find the equation of perpendicular line, we need to find the slope between given coordinates.

Slope between  (-9, 3) and (-3, -1). :

slope = [tex]\frac{-1-3}{-3+9} =\frac{-2}{3}[/tex]

Slope of the perpendicular line is reciprocal and opposite in sign.

Therefore, slope of the perpendicular line = 3/2

Now, we need to find the midpoint of the given coordinates.

[tex]Mid points : \\x= \frac{ -9-3}{2} =-6\\ y= \frac{3-1}{2} = 1\\ pint = (-6,1)[/tex]

Let us apply point-slope form of the linear equation:

y-y1 = m(x-x1)

y - 1 = 3/2 (x + 6)

2y = 3x +20

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