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2 years ago

Which equation is the correct translation of the following statement?

Mathematics

1 answer:

leonid [27]2 years ago

8 0

<h3>hello!</h3>

Let the number be x.

subtract 4:-

x-4 (4 less)

this expression equals 9:-

x-4=9 (Option C)

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

You might be interested in

Recursive formula for a geometric sequence with a starting value of 8 and a common ratio of 5

Alexxx [7]

$a_2=5a_1$
$a_3=5a_2$
$a_4=5a_3$
...
$a_n=5a_{n-1}$

So the recursive formula is

$\begin{cases}a_1=8\\a_n=5a_{n-1}&\text{for }n>1\end{cases}$

5 0

2 years ago

Identify the conclusion of the conditional statement.

gogolik [260]

<h2>Answer:</h2>

The conclusion of the given conditional statement is:

You live in Arizona

<h2>Step-by-step explanation:</h2>

We know that a conditional statement is a statement in which with the help of some valid hypothesis we can reach to a valid conclusion.

The conditional statement is written in the form:

If p then q

where p is the hypothesis of the statement

and q is the conclusion of the statement.

We are given a conditional statement as:

If you live in Phoenix, then you live in Arizona.

Here

Hypothesis-- You live in Phoenix

and Conclusion-- You live in Arizona

8 0

3 years ago

Read 2 more answers

Determine whether each equation is True or False. In case you find a "False" equation, explain why is False.

elixir [45]

Answer:

(1) TRUE.

(2) FALSE.

(3) FALSE.

(4) TRUE.

(5) FALSE.

Step-by-step explanation:

(1) $\sqrt{32} = 2^{\frac{5}{2} }$

$2^{\frac{5}{2} } = (\sqrt{2} )^5 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 4\sqrt{2}\\\\\sqrt{32} = \sqrt{16 \ \times \ 2}\ = \ \sqrt{16} \ \times \ \sqrt{2} \ = \ 4\sqrt{2}$

Thus, the equation is TRUE.

(2) $16^{\frac{3}{8} } = 8^2$

$16^{\frac{3}{8} } =(2^4)^{\frac{3}{8} } = 2^\frac{3}{2} }= (\sqrt{2} )^3 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 2\sqrt{2} \\\\8^2 = 64$

Thus, the equation is FALSE.

(3) $4^{\frac{1}{2} } = \sqrt[4]{64}$

$4^{\frac{1}{2} }= \sqrt{4} = 2\\\\\sqrt[4]{64} = (64)^{\frac{1}{4} } = (2^6)^{\frac{1}{4} }= 2^{\frac{6}{4} } = 2^{\frac{3}{2} }=(\sqrt{2} )^3 = (\sqrt{2} \times \sqrt{2} \times \sqrt{2} ) = 2\sqrt{2}$

Thus, the equation is FALSE.

(4) $2^8 = (\sqrt[3]{16} )^6$

$2^8 = 256\\\\ (\sqrt[3]{16} )^6 = (16)^{\frac{6}{3} } = (2^4)^{\frac{6}{3} } = (2)^{\frac{24}{3} } = 2^8 = 256$

Thus, the equation is TRUE.

(5) $(\sqrt{64} )^{\frac{1}{3} } = 8^{\frac{1}{6} }\\\\$

$8^{\frac{1}{6} } = (2^3)^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} } = \sqrt{2} \\\\(\sqrt{64} )^{\frac{1}{3} } = (2^6)^{\frac{1}{3} } = 2^{\frac{6}{3} } = 2^2 = 4$

Thus, the equation is FALSE.

4 0

3 years ago

Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (E

xxTIMURxx [149]

Answer:

(-∞,-3) and (3,∞)

Step-by-step explanation:

f(x) = x³ − 27x + 3

1. Find the critical points

(a) Calculate the first derivative of the function.

f'(x) = 3x² -27

(b) Factor the first derivative

f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)

(c) Find the zeros

3(x + 3) (x - 3) = 0

x + 3 = 0 x - 3 = 0

x = -3 x = 3

The critical points are at <em>x = -3</em> and x = 3.

2. Find the local extrema

(a) x = -3

f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57

(b) x = 3

f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51

The local extrema are at (-3,57) and (3,-51).

3, Identify the local extrema as maxima or minima

Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)

f'(-4) = 3x² -27 = 3(4)² - 27 = 21

f'(0) = 3(0)² -27 = -27

f'(4) = 3(4)² - 27 = 51

The function is increasing on the intervals (-∞,-3) and (3,∞).

The graph below shows the critical points of your function.

6 0

3 years ago

Josie took a road trip. She drove for 45 minutes at 70 miles per hour. Then she drove 15 minutes at 20 miles per hour. How far d

Hunter-Best [27]

Answer:

Therefore Josie drove 57.5 miles.

Step-by-step explanation:

Speed: The ratio of distance to time.

To find the distance we use the following formula

$Distance= time \times speed$

Given that Josie drove 45 minutes at 70 miles per hour.

$45 \ minutes= \frac{45}{60}\ h=\frac34\ h$

In 45 minutes, she traveled = $(70\times \frac34) \ miles$

=52.5 miles.

The she drove 15 minutes at 20 mile per hour.

$15 \ minutes= \frac{15}{60}\ h=\frac14\ h$

In 15 minutes, she traveled $=(20\times \frac 14) \ miles$

=5 miles

Therefore Josie drove (52.5+5) miles= 57.5 miles.

3 0

3 years ago