All categories

2 years ago

What is the range of f(x) = (three-fourths) Superscript x – 4?

1 answer:

8 0

{y | y > –4}

Left-brace y vertical line y greater-than three-fourths right-brace

{y | y < –4}

Left-brace y vertical line y less-than three-fourths right-brace

You might be interested in

Which expression correctly displays the calculations to find the a^5b^4 term of (a+b)^8

LUCKY_DIMON [66]

Answer:

Step-by-step explanation:

THE BINOMIAL THEOREM shows how to calculate a power of a binomial -- (a + b)n -- without actually multiplying.

For example, if we actually multiplied out the 4th power of (a + b) --

(a + b)4 = (a + b)(a + b)(a + b)(a + b)

-- then on collecting like terms we would find:

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 . . . . (1)

Note: The literal factors are all possible terms in a and b where the sum of the exponents is 4: a4, a3b, a2b2, ab3, b4.

The degree of each term is 4.

The first term is actually a4b0, which is a4 · 1.

Thus to "expand" (a + b)5, we would anticipate the following terms, in which the sum of all the exponents is 5:

(a + b)5 = ? a5 + ? a4b + ? a3b2 + ? a2b3 + ? ab4 + ? b5

The question is, What are the coefficients?

They are called the binomial coefficients. In the expansion of

(a + b)4, the binomial coefficients are

1 4 6 4 1

line (1) above.

Note the symmetry: The coefficients from left to right are the same right to left.

The answer to the question, "What are the binomial coefficients?" is called the binomial theorem. It shows how to calculate the coefficients in the expansion of (a + b)n.

The symbol for a binomial coefficient is The binomial theorem. The upper index n is the exponent of the expansion; the lower index k indicates which term, starting with k = 0.

For example, when n = 5, each term in the expansion of (a + b)5 will look like this:

The binomial theorema5 − kbk

k will successively take on the values 0 through 5.

(a + b)5 = The binomial theorema5 + The binomial theorema4b + The binomial theorema3b2 + The binomial theorema2b3 + The binomial theorem ab4 + The binomial theoremb5

Note: Each lower index is the exponent of b. The first term has k = 0 because in the first term, b appears as b0, which is 1.

Now, what are these binomial coefficients, The binomial theorem ?

The theorem states that the binomial coefficients are none other than the combinatorial numbers, nCk .

The binomial theorem = nCk

(a + b)5 = 5C0a5 + 5C1a4b + 5C2a3b2 + 5C3a2b3 + 5C4ab4 + 5C5b5

= 1a5 + The binomial theorema4b + The binomial theorema3b2 + The binomial theorema2b3 + The binomial theoremab4 + The binomial theoremb5

= a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

The binomial coefficients here are

1 5 10 10 5 1.

8 0

2 years ago

In 1975 1000 tons of coal was manufactured. It is 10% greater in 1976 and 5% less in 77. What is the final about of coal in 1977

Digiron [165]

In 1975 it was 1000tons, ok, well, in 1976 it went up by 10%, how much is a 10% increase?

$\bf \begin{array}{ccllll}
coal&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
1000&100\\
x&100+10
\end{array}\implies \cfrac{1000}{x}=\cfrac{100}{100+10}\implies \cfrac{1000\cdot 110}{100}=x
\\\\\\
1100=x$

well, in 1976 it was 1100 tons then, and in 1977 it went down by 5% of 1100, well, if we take 1100 to be the 100%, then what is a 5% decrease?

$\bf \begin{array}{ccllll}
coal&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
1100&100\\
x&100-5
\end{array}\implies \cfrac{1100}{x}=\cfrac{100}{100-5}\implies \cfrac{1100\cdot 95}{100}=x$

5 0

3 years ago

Find the measure of angle A

Lapatulllka [165]

Answer:

Step-by-step explanation:

AB and DC are parallel, so ∠B and ∠C are supplementary angles.

∠B = 180°-∠C = 79°

AD and BC are congruent. ∠A = ∠B = 79°

3 0

2 years ago

Find the missing measure in each pair of similar shapes.

Vikki [24]

If your missing a sid but you have the other side opisite sides are the same

7 0

2 years ago

Find the equation of the line the line is perpendicular to the graph of x - 5y=6 and contains 2,-10

qaws [65]

<h3>Answer: </h3><h3>y + 10 = - 5 (x - 2) [point-slope form] OR</h3><h3>y = - 5 x [slope-intercept form]</h3><h2 /><h3>Step-by-step explanation:</h3>

<u>Identify the slope of the given line</u>

If we rewrite the equation given, we can easily identify the slope

x - 5y = 6

- 5y = - x + 6

y = ¹/₅ x - ⁶/₅

∴ the slope of x - 5y = 6 is ¹/₅

<u>Find the slope of the perpendicular line</u>

When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.

⇒ since the slope of this line = ¹/₅

then the slope of the perpendicular line (m) = - 5

<u>Determine the equation of perpendicular line</u>

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

⇒ y - (-10) = - 5 (x - 2)

We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

since y + 10 = - 5 (x - 2)

<h3> y = - 5 x</h3><h3 /><h3>∴ the slope-intercept equation of the perpendicular line is y + 10 = - 5 (x - 2) OR y = - 5 x. </h3><h3 /><h3 />

<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>

4 0

2 years ago