Algebra

I'm sorry, but I cannot access specific pages from books, including the Punchline Algebra book B. However, I can help with algebra concepts or problems if you provide more details or context!

To solve this problem, let ( x ) be the ounces of the 13% alcohol solution and ( y ) be the ounces of the 42% alcohol solution. We have two equations:

1. ( x + y = 58 ) (total volume)
2. ( 0.13x + 0.42y = 0.15(58) ) (total alcohol content)

Solving these equations, we find ( x = 24 ) ounces of the 13% solution and ( y = 34 ) ounces of the 42% solution.

x^(3) X x^(5) = x^(3+5) = x^(8)

Remember the coefficient 'x' MUST remain the same for both numbers.

NNB

x^(3) X y(5) is NOT allowed , because the coefficients 'x' & 'y' are different.

This multiplication is expressed as x^(3)y^(5). The indices are NOT added.

The power of '1/3' is another way of expressing the 'cube root'.

Hence 8^(1/3) = 2

Remember

2x2x2 = 8 .

2^(3) 8

Hence

8^(1/3) = 2

(-1/4)^(3) =

-1/4 x -1/4 x -1/4 =

(+)1/16 x -1/4 = -1/64 = -0.015625

(-4)^(4) = (+)256

-4x-4x-4x-4 = (+)16X (+)16 = 256

(256^(1/3))^(4) =

256^(4/3) =

256^(1.3333...... =

1625.498674..... ( The answer)

NB 256 raised to the power of 1/3 , means the 'cube root'. The answer is then raised to the fourth power.

However, under the rules for indices you can muktiply the indices together.

NNB Here are the indices rules.

a^(n) X a^(m) = a^(n+m)

a^(n) / a^(m) = a^(n - m)

(a^( n ))^(m) = a^(nm)

In all cases THE COEFFICIENT 'a' must be the same.

256^(1/4) = '4'

Remember

4x4x4x4 = 256

Hence the fourth root is '4'.

The equation (3v + x = w) represents a linear relationship between the variables (v), (x), and (w). In this equation, (w) is the sum of three times the variable (v) and the variable (x). To isolate any variable, you can rearrange the equation accordingly, such as solving for (x) by subtracting (3v) from both sides, giving (x = w - 3v).

To calculate simple interest, you use the formula: Interest = Principal × Rate × Time. For a principal of $200, an interest rate of 4% (or 0.04), and a time period of 1 year, the calculation would be: $200 × 0.04 × 1 = $8. Therefore, the simple interest earned in one year is $8.

To solve the expression (9x^0 y - 3), first recognize that (x^0) equals 1 for any non-zero (x). Therefore, the expression simplifies to (9y - 3). To further simplify or solve, you would need a value for (y) or additional equations if you are solving for (y).

It seems there might be a typographical error in your question, particularly with the functions you've provided. If ( f(x) = x^2 + 1 ) and ( g(x) = x - 4 ), to find the equivalent values, you would typically need to evaluate either ( f(g(x)) ) or ( g(f(x)) ). Please clarify your question so I can provide a more accurate response!

This is Simultaneous equ'ns.

3x + 5y = -1

2x -5y = 16

Add the two eq'ns. This will eliminate 'y'

Hence

5x = 15

x = 3

When x = 3 , substitute into either eq'n to yimnd 'y'.

Hence

3)3) + 5y = -1

9 + 5y = -1

5y = -10

y = -10/5 = -2

So the solution in ( x,y) form is ( 3, -2).

35

y = x/2 + 1

This is a line of the form y = mx + c

When c = 1 it passes through the y-axis at y = 1

When m= 1/2 ( 0.5) it has a gradient of 1/2 )0.5) . For every two places along in 'x', you go up one place in 'y'.

So to plot two point

s

When x = 1 ; y = 1/2 + 1 = 3/2 ( 1,3/2)

When x - 2 ; y = 2/2 + 1 =. 1 + ` = 2 (2,2)

et seq.,

The line y = x is a straight line of gradient '1' passing through the origin (0,0)

The line/curve y = x^(2) is 'bowl' shaped curve(parabola). with varying gradients, and just touching the origin (0,0).

Pythagoras was a Classical Greek mathematician , who intorduced his famous eq;'n to western civilisation. .

He lived in about 500 BC on the island of Samos ( now in modern Greece).

Her a pre=Socratean philosopher and mathematician .

The expression (x^3 + 1) can be factored using the sum of cubes formula, which states that (a^3 + b^3 = (a + b)(a^2 - ab + b^2)). Here, (a = x) and (b = 1). Thus, the factorization of (x^3 + 1) is ((x + 1)(x^2 - x + 1)).

Form left to right:

(14): Ten trillion

(13): One trillion

(12): Hundred billion

(11): Ten billion

(10): One million

(9): Hundred million

(8): Ten million

(7): One million

(6): Hundred thousand

(5): Ten thousand

(4): Thousand

(3): Hundred

(2): Ten

(1): Unit

The expression "five squared" refers to the mathematical operation of raising the number five to the power of two, which is written as (5^2). This calculation results in (5 \times 5 = 25), not 52. The confusion may arise from the notation, but 52 is simply the number fifty-two and does not have a direct correlation to "five squared."

The product of p and 7 is the result of multiplying the value of p by 7. In mathematical terms, this can be represented as p * 7. Multiplying a number by 7 is equivalent to adding that number to itself 7 times, or using the distributive property, which states that a(b + c) = ab + ac.

The inbreeding coefficient (F) can be calculated using several methods, the most common being the pedigree method. This involves tracing the ancestry of an individual and identifying the genes inherited from common ancestors. The formula for calculating F is: F = Σ (1/2)^n, where n is the number of generations to a common ancestor. Alternatively, software tools like PLINK or pedigree analysis software can automate this calculation for complex pedigrees.

Firstly , it is 'pi' NOT 'pie'. 'pie' is what you eat ; apple pie.

Secondly ; make sure your calculator is in 'Radian' mode; NOT degree mode. Otherwise you will have an incorrect answer!!!!!

Type in ' Tan, Bracket 'pi', divide, '3', Close Bracket, equals (=) the answer should appear on your calculator screen as ' 0,01827908761,,,,'

NB Many students/people forget to correct the mode of their calculator, and thereby have an incorrect answer.

Degrees ; degrees mode

'pi' ; Radian mode.

tan(135 degrees) = negative 1.

Functions that exhibit asymptotes are typically rational functions, where the degree of the numerator and denominator determines the presence of vertical and horizontal asymptotes. Additionally, logarithmic functions and certain types of exponential functions can also have asymptotes. Vertical asymptotes occur where the function approaches infinity, while horizontal asymptotes indicate the behavior of the function as it approaches infinity. Overall, asymptotes characterize the end behavior and discontinuities of these functions.