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3 years ago

Which logarithmic equation is equivalent to the exponential equation below 9x = 27

1 answer:

7 0

You are asking to write $9^x=27$ in logaritmic form

Remember that $log_{a}(b)=c$ translates to $a^c=b$

So therefore $9^x=27$ translates to $log_{9}(27)=x$

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Which equation can be used to solve for m, the greater integer? m(m – 3) = 108 m(m + 3) = 108 (m + 3)(m – 3) = 108 (m – 12)(m –

nata0808 [166]

Answer:

m(m-3)=108

Step-by-step explanation:

Complete question below:

Two positive integers are 3 units apart on a number line. Their product is 108.

Which equation can be used to solve for m, the greater integer?

m(m – 3) = 108

m(m + 3) = 108

(m + 3)(m – 3) = 108

(m – 12)(m – 9) = 108

Solution

On the number line,

Let

m= larger integer

The integers are 3 numbers apart on the number line, so

m-3=smaller integer

The product (×) of the larger and smaller integers=108

(m)*(m-3)=108

m(m-3)=108

Therefore, the equation that can be used to solve for m, the larger integer is:

m(m – 3) = 108

5 0

3 years ago

What is the length of the shortest altitude in a triangle, if the lengths of the sides are 24 cm, 25 cm, 7 cm?

AfilCa [17]

Answer:

The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

24 cm, 25 cm, 7 cm

The area of a triangle =

$A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}$

Where;

s = Half the perimeter = (24 + 25 + 7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A = 1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

4 0

3 years ago

Have 15 minutes please help!!

Marina86 [1]

Anything which have their degree as 0 is always equal to 1
=> 5^0=1
Option 3 is the answer..!!
Hope this helps you!!

Good Luck!

3 0

3 years ago

Which is the value of x

vodka [1.7K]

16.5 is what I got for x you add them up and equal them to 180 because its a straight line

5 0

3 years ago

Read 2 more answers

In the geometric progression 1, 2, 4… what term is 512?

Levart [38]

The next term is double the previous term, so that the $n$ -th term is given recursively by

$\begin{cases}a_1=1\\a_n=2a_{n-1}&\text{for }n>1\end{cases}$

This rule tells us that

$a_2=2a_1$

$a_3=2a_2=2^2a_1$

$a_4=2a_3=2^3a_1$

and so on, with the explicit rule

$a_n=2^{n-1}a_1=2^{n-1}$

for $n\ge1$ .

If 512 is the $k$ -th term in the sequence, then

$512=2^{k-1}\implies\log_2512=\log_22^9=\log_22^{k-1}\implies9=k-1\implies k=10$

8 0

3 years ago