All categories

2 years ago

Which expression is equivalent to log5(X/4)^2

Mathematics

2 answers:

saw5 [17]2 years ago

4 0

Answer: Applying properties of logarithm, the expression equivalent to

log5 (x/4)^2 is: 2 (log5 x - log5 4)

Solution:

log5 (x/4)^2

Using loga b^c = c loga b; with a=5, b=(x/4), and c=2

log5 (x/4)^2 = 2 log5 (x/4)

Using loga (b/c) = loga b - loga c; with a=5, b=x, and c=4

log5 (x/4)^2 = 2 (log5 x - log5 4)

zzz [600]2 years ago

3 0

2log(base 5)x - 2log(base 5)4

You might be interested in

An artist cuts 4 squares with sides of length x ft from the corners of a 12 ft-by-18 ft rectangular piece of sheet metal. She be

ehidna [41]

Answer:

$V = 216x - 60x^2 + 4x^3$

Step-by-step explanation:

The volume V of the fountain is equal to:

V = L*W*h

Where L is the lenght of the fountain, W is the width of the fountain and h is the high of the fountain

We already know that h is equal to x. On the other hand, if we cut a square with side of length x, L and W are calculated as:

L = 18 - 2x

W = 12 - 2x

So, replacing L, W and h on the equation of the volume, we get:

V = (18-2x)*(12-2x)*x

Finally, simplifying the function we get:

$V = ((18*12)+(18*(-2x))+(-2x*12)+((-2x)*(-2x)))*x$

$V = (216-36x-24x+4x^2)*x\\V = (216-60x+4x^2)*x\\V = 216x - 60x^2 + 4x^3$

6 0

2 years ago

Triangle ABC is translated to image A′B′C′. In this translation, A(5, 1) maps to A′(6, –2). The coordinates of B′ are (–1, 0). W

tatiyna

Answer:

please mark my answer brainliest

Step-by-step explanation:

while solving this sum the main steps are...

make sure

area of 1st triangle =area of the new....tria..

5 0

2 years ago

Read 2 more answers

Triangle A has a height of 2.5\text{ cm}2.5 cm2, point, 5, start text, space, c, m, end text and a base of 1.6\text{ cm}1.6 cm1,

konstantin123 [22]

Answer:

Option A

Option D

Option E

Step-by-step explanation:

we know that

If the height and base of triangle B are proportional to the height and base of triangle A

then

Triangle A and Triangle B are similar

Remember that

If two triangles are similar then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

$\frac{h_A}{h_B} =\frac{b_A}{b_B}$

where

h_A and h_B are the height of triangle A and triangle B

b_A and b_B are the base of triangle A and triangle B

In his problem we have

$h_A=2.5\ cm\\b_A=1.6\ cm$

substitute

$\frac{2.5}{h_B} =\frac{1.6}{b_B}$

Rewrite

$\frac{2.5}{1.6} =\frac{h_B}{b_B}$

$\frac{h_B}{b_B}=1.5625$

<u><em>Verify all the options</em></u>

A) we have

$h_B=2.75\ cm\\b_B=1.76\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{2.75}{1.76}=1.5625$

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B

B) we have

$h_B=9.25\ cm\\b_B=9.16\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{9.25}{9.16}=1.0098$

The ratios are not equal

That means that are not proportional

therefore

These values could not be the height and base of triangle B

C) we have

$h_B=3.2\ cm\\b_B=5\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{3.2}{5}=0.64$

The ratios are not the same

That means that are not proportional

therefore

These values could not be the height and base of triangle B

D) we have

$h_B=1.25\ cm\\b_B=0.8\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{1.25}{0.8}=1.5625$

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B

E) we have

$h_B=2\ cm\\b_B=1.28\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{2}{1.28}=1.5625$

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B

8 0

2 years ago

Show that the three points whose position vectors are 7j+ 10k,-i + 6j+6k and - 4i + +9j + 6k form an isosceles right

Novay_Z [31]

Answer:

AB = √18 , BC=√18 and CA =4

AB²+BC² = CA² and AB=BC

ΔABC isosceles right angled triangle.

Step-by-step explanation:

Given vectors are 7j+ 10k,-i + 6j+6k and - 4i + +9j + 6k

A( 0,7,10), B( -1,6,6) C(-4,9,6)

AB⁻ = OB-OA = -I+6j+6k-(7j+10k) = -I-j-4k

AB = $\sqrt{1+1+16} = \sqrt{18}$

BC = OC-OB = -4i+9j+6k-(-I+6j+6k) = -3i+3j

BC= $\sqrt{9+9} =\sqrt{18}$

CA = OA-OC = 7j+10k - (- 4i + +9j + 6k ) = 4i-2j+4k

CA = $\sqrt{16+4+16} =\sqrt{36} =4$

Since AB²+BC² = CA²

And AB=BC

Therefore it follows that ΔABC is a right angled isosceles triangle

3 0

2 years ago

The store sells a 9 ounce jar of mustard for $1.53 and a 15 ounce for $2.55 explain whether the cost of the mustards have the sa

astraxan [27]

Answer:

same amount of money

Step-by-step explanation:

3 0

2 years ago