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3 years ago

Use factoring to write an expression that is equivalent to 25b^16-64c^2

1 answer:

4 0

We can write this as the difference of squares:
(5b⁸+8c)(5b⁸-8c)

To write as the difference of squares, take the square root of each term first:
√25b¹⁶ = 5b⁸; √64c² = 8c

Now we write this as a sum in one binomial and a difference in the other:
(5b⁸+8c)(5b⁸-8c)

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Hi, can someone help with this 8th grade math question?

Norma-Jean [14]

They multiplied 3 by itself 4 times, so it’s 3^4

3 0

3 years ago

What is 3/2=9/10k im having troble lots rly

tigry1 [53]

Answer:

k= 5 over 3 =1.667

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(3)/(2)-((9)/(10)*k)=0

simplify 9/10

3 9

— - (—— • k) = 0

2 10

simplify 3/2

3 9k

— - —— = 0

2 10

Find the Least Common Multiple

The left denominator is : 2

The right denominator is : 10

Least Common Multiple:

Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 5

Right_M = L.C.M / R_Deno = 1

Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 3 • 5

—————————————————— = —————

L.C.M 10

R. Mult. • R. Num. 9k

—————————————————— = ——

L.C.M 10

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3 • 5 - (9k) 15 - 9k

———————————— = ———————

10 10

Pull out like factors :

15 - 9k = -3 • (3k - 5)

-3 • (3k - 5)

————————————— = 0

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

-3•(3k-5)

————————— • 10 = 0 • 10

Now, on the left hand side, the 10 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

-3 • (3k-5) = 0

Solve : -3 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solve : 3k-5 = 0

Add 5 to both sides of the equation :

3k = 5

Divide both sides of the equation by 3:

k = 5/3 = 1.667

one solution was found

k = 5/3 = 1.667

hope it helps sry its so long

7 0

4 years ago

Let f(x) = Square root x. Find g(x), the function that is f(x) shifted up 7 units and left 1 units.

Rudik [331]

$~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill$

$\bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}$

$\bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}$

keeping in mind that template, let's take a looksie

$f(x) = \sqrt{x}\implies f(x) = A\sqrt{Bx + C}+D\implies f(x) = 1\sqrt{1x+0}+0 \\\\\\ \begin{cases} D = \stackrel{\textit{shifted up}}{+7}\\ C = \stackrel{\textit{left shift}}{+1} \end{cases}~\hspace{4em}g(x) = 1\sqrt{1x+1}+7\implies g(x) = \sqrt{x+1}+7$

8 0

3 years ago

Can someone plzzzzz helppp

Ann [662]

Y>(with the line underneath)1/3x-2 I think

5 0

3 years ago

Find an explicit formula for the arithmetic sequence -5, 13, 31,

Lynna [10]

Answer:

b(n) = -23 + 18n

Step-by-step explanation:

NOTE - This is an arithmetic sequence, so each number is increasing by addition. If you were in a geometric sequence, however, you'd be multiplying. This means that the explicit formula for the geometric sequence you'll be learning later on will be different.

The formula for explicit formula is b(n)=b(1)+d(n-1). The variable d represents the common difference and the a is whatever number of the term you are using.

Since you have b(1), you look at what your first term is. Plug -5 into a(1).

To find your common difference, find 13-(-5). This is 18, and adding it to the others you can see that it continues.

So, plugging in what you have so far it looks like b(n) = -5 + 18(n - 1)

All we need to do now is simplify.

1. Distribute: -5 + 18n - 18

2. Add like terms: -23 + 18n

Hope this helped and made sense lol.

8 0

3 years ago