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3 years ago

Solve log(base 2) (x+1) + log (base 2) (x-5)= 4

1 answer:

6 0

(x+1)(x-5)= 2^4=16

x^2 -4x -5 =16

x^2-4x-21=0

x= -3 or 7
but we would choose 7 as the answer as -3 gives negative value at (x+1) and we know that log of negative number is not defined.

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You’ve bought a cylindrical thermos 8 in. high with a base 6 in. across. How much coffee can you put in the thermos?

lana66690 [7]

Answer:

3.706 liters

Step-by-step explanation:

Hello

assuming that these measures correspond to the internal measures of the thermos,

we can calculate the volume as, the volume of a cylinder, which is given by

$V=\pi r^{2} h$

where r is the radius of the base, and h the height

also

Diameter=2r

r=Diameter/2

Step 1

let

h=8 in

base = diameter = 6 inch

r=diameter/2

r=6/2 inch,r=3 inch

Step 2

Put the values into the equation

$V=\pi r^{2} h\\V=\pi (3in)^{2} (8 in)\\V=\pi *72 \ in^{3} \\\\V=72\pi\ in^{3} \\\\$

Step 3

Now, the unit (cubic inches) is not an usual unit for measuring coffee, let´s convert cubic inches into liters by knowing

1 inch = 2.54 cm

1 litro = 1000 cubic centimeters

$if\ 1\ inch\ = 2.54\ cm\\(1\ inch)^{3} =(2.54\ cm)^{3}\\\\1\ inch^{3}=16.3870\ cm^{3}$

1 cubic inch = 16.3870 cubic centimeters

$1\ cubic\ inch\ = 16.3870\ cubic\ centimeters\\\\\\72\pi =x?\ cubic\ centimeters\\\\x=\frac{72\pi \cubic \ inch\ \*16.3870 }{1\ cubic\ inch} \\\\x=3706.65\ cubic\ centimeters$

Step 4

Finally, convert cubic centimeters into liters $1000\ cubic\ centimeters =1\ liter \\\\\\3706.65\ cubic\ centimeters = x?\ liters\ centimeters\\\\x=\frac{3706.65 \cubic \ centimeters\ \*1 liter}{1000 cubic centimeters} \\\\x=3706.65\ cubic\ centimeters\\x=3.706 Liters$

I can put 3.706 liters in the thermos

Have a good day

4 0

4 years ago

Equivalent fraction of 6/126

Mice21 [21]

Answer:

1/21

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What is the measure, in degrees, of angle 1?

ra1l [238]

Answer:

Think simple.

angle 1 and the angle with the measurement of 110° are subplementary angles, therefore:

∠1 + 110° = 180°

∠1 = 180° - 110° = 70°

7 0

3 years ago

A restaurant sells tea for $1.50 plus $0.05 per refill a gas station store sells tea for $0.50 plus $0.50 per refill?

lutik1710 [3]

Answer:

Part a) $y=0.05x+1.50$

Part b) $y=0.50x+0.50$

Part c) The graph in the attached figure

Part d) see the explanation

Step-by-step explanation:

The complete question is

A restaurant sells tea for $1.50 plus $0.05 per refill. A gas station store sells tea for $0.50 plus $0.50 per refill.

Part a) Write a linear function for the price of tea at restaurant

Part b) Write a linear function for the price of tea at gas station store

Part c) Graph both equations

Part c) Compare the lines in terms of slope and y-intercept

Let

y -----> the price of tea in dollars

x -----> the number of refills

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value (value of y when the value o x is equal to zero)

Part a)

At restaurant

we have that

The slope or unit rate is equal to

$m=\$0.05\ per\ refill$

The initial value or y-intercept is equal to

$b=\$1.50$

substitute

$y=0.05x+1.50$

Part b)

At gas station store

we have that

The slope or unit rate is equal to

$m=\$0.50\ per\ refill$

The initial value or y-intercept is equal to

$b=\$0.50$

substitute

$y=0.50x+0.50$

Part c) Graph both equations

we know that

The easiest way to graph a line is with two points

Find the intercepts of the line

At restaurant

$y=0.05x+1.50$

The y-intercept is the point (0,1.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

$0=0.05x+1.50$

$x=-30$

The x-intercept is the point (-30,0)

Plot the points and join to graph the line

see the attached figure

At gas station store

$y=0.50x+0.50$

The y-intercept is the point (0,0.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

$0=0.50x+0.50$

$x=-1$

The x-intercept is the point (-1,0)

Plot the points and join to graph the line

see the attached figure

Part c) Compare the lines in terms of slope and y-intercept

The slope or unit rate at the restaurant is less than the slope at the gas station store

$\$0.05\ per\ refill < \$0.50\ per\ refill$

The initial value or y-intercept at the restaurant is greater than the initial value at the gas station store

$\$1.50 > \$0.50$

3 0

3 years ago

The price of an item has been reduced by 10%. The original price was $46. Find the price of the item now.

miss Akunina [59]

41.4

Step-by-step explanation:

Hope this helps ∞<3

let me know if its right or wrong

6 0

3 years ago