Starting at 1:00 p.M., The temperature changes -4 degrees Fahrenheit per hour. Write and solve an equation to find how many hours (x) it will take to reach -1 °F.

Step-by-step explanation:

If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.

Let a = log82x, b = log4x and c = log2x

If a = log8 2x; 8^a = 2x... (1)

If b = log4 x; 4^b = x ... (2)

If c = log2 x; 2^c = x...(3)

Since a, b c are in GP, then b/a = c/b

Cross multiplying:

b² = ac ...(4)  

From eqn 1, x = 8^a/2

x = 2^3a/2

x = 2^(3a-1)

From eqn 2; x = 4^b

x = 2^2b

From eqn 3: x = 2^c

Equating all the values of x, we have;

2^(3a-1) = 2^2b = 2^c

3a-1 = 2b = c

3a-1 = c and 2b = c

a = c+1/3 and b = c/2  

Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;

(c/2)² = c+1/3×c

c²/4 = c(c+1)/3

c/4 = c+1/3

Cross multiplying;

3c = 4(c+1)

3c = 4c+4

3c-4c = 4

-c = 4

c = -4  

Substituting c = -4 into equation 3 to get the value of x we have;

2^c = x

2^-4 = x

x = 1/2^4

x = 1/16    

Since the number x can be written as m/n, then x = 1/16 = m/n

This shows that m = 1, n = 16

m+n = 1+16

m+n = 17  

The required answer is 17.  

The value of m+n in which m and n are relatively prime positive integers is 17.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,

[tex]\log_82 x,\log_4x, \log_2x[/tex]

The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,

[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]

Using the base rule of logarithmic function,

[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]

Using the Power rule of logarithmic function,

[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]

The number x can be written as

[tex]\dfrac{m}{n}[/tex]

Here, m and n are relatively prime positive integers. Thus, the value of m+n is,

[tex]m+n=1+16=17[/tex]

Hence, the value of m+n in which m and n are relatively prime positive integers is 17.

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Answer:

the right answer is : A

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

im smort

Answer: x = 2

Step-by-step explanation:

[tex]10x - 15x + 5= -45 + 40[/tex]

subtract 5

[tex]10x - 15x= -45 + 40-5[/tex]

Combine like terms;

[tex]-5x=-10[/tex]

Divide by -5

[tex]x=\frac{-10}{-5}\\ x=2[/tex]

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]

Answer:

4

Step-by-step explanation:

A rectangle has a shorter side and a longer side.

The longer side is called the length and the shorter side is called width.

with the 24 tiles you can make the following rectangles (consider the first number the length and the second number the width, and that each unit represents a tile):

24 x 1

12 x 2

8 x 3

6 x 4

A total of 4 different rectangles.

I am not counting the rectangles than have the same sides shifted, for example 2 x 12 because it is the same as 12 x 2 and we are asked for the rectangles to be different.

I attache an image of the sketch of each rectangle with the labels of length and width (not to scale).

i think this is the method for solving it

40π

You dont need paper hw since we're in quarantine

Answer:40

Step-by-step explanation:

Answer:

Therefore the largest number that these fractions can be divided by to give them a whole number is

a) 8/15 = The largest number is 8/15

b) 18/35 = The largest number is 18/35

Step-by-step explanation:

A quotient is the result obtained by dividing two numbers.

So that the quotient obtained is a whole number we have to find out, what number they can be divided by to give them that.

Let's assume the whole number is 1

a. 8/15

8/15 ÷ x = 1

8/15 × 1/x = 1

8/15x = 1

We would cross multiply

8 = 15x

We would divide both sides by 15

8/ 15 = x

Hence the largest number that would divide 8/15 and give it a whole number = 8/15

b) 18/35

18/35÷ x = 1

18/35 × 1/x = 1

18/35x = 1

We would cross multiply

18 = 35x

We would divide both sides by 35

18/ 315 = x

Hence the largest number that would divide 18/35 and give it a whole number = 18/35

Answer:

The answer is 2/105

Step-by-step explanation:

first we have to find the LCM of both denominators. IN this case, the LCM of 15 and 35 is 105. Then we have to find the GCF of these numerators. IN this case, the GCF of 8 and 18 is 2.

Now, put the GCF you found over the LCM.

ANSWER: 2/105

This fraction is the largest number you can divide both numbers by to get a whole number.

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Answer:

A and B

Step-by-step explanation:

The lines are both in slope intercept form:

y=Mx+b

Where m is the slope and b is the y intercept.

We have 2 lines:

y=1/3x+3

y=1/3x-2

1/3 is the coefficient of x, which means the slope is 1/3. Both of these lines have the same slope of 1/3. Since they both have the same slope, they are also parallel lines.

Therefore, A: the same slopes and B: parallel lines is correct.

In the photo, the red line is 1/3x+3 and the blue like is 1/3x-2

Answer:

It is A because due to the slope it is a parallelogram.

Step-by-step explanation:

Answer:

its a

Step-by-step explanation:

Answer:

9.958

Step-by-step explanation:

The thousandths spot is where the 8 is so you round 8 with the number behind it 1. Since 1 is below 5, you keep 8 the same and get rid of the 1.

Answer:

9.958

Step-by-step explanation:

find the number in the thousands place, 8 and then look 1 place to the right for the rounding digit 1. Round up if this number is greater than or equal to 5 and round down if it is less then 5.

Answer:

-15

Step-by-step explanation:

3(2 - 7)​

PEMDAS says parentheses first

Subtract

3 (-5)

Multiply

-15

Answer:

(B)[tex]\dfrac{1}{m^8}[/tex]

StartFraction 1 Over m Superscript 8 EndFraction

Step-by-step explanation:

We want to find the simplified form of: [tex]m^{-8}p^0[/tex]

[tex]m^{-8}p^0=m^{-8}$ X p^0\\p^0=1\\m^{-8}=\frac{1}{m^8} \\$Therefore:\\m^{-8}$ X p^0=\dfrac{1}{m^8} X 1\\=\dfrac{1}{m^8}[/tex]

The correct option is B.

Answer:

I am 80% sure its 1 if not then its 1/p

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

because 7x2 is 12

Answer:

3n+7

Step-by-step explanation:

Let's say the variable n stands for how many recyclable bottles Natasha collected.

Enrique collected 7 more than double of what Natasha has.

SO

2n+7

We also need to include Natasha's share

(2n+7) + n

OR 3n+7

Answer:

[tex]9 \dfrac12 m^2[/tex]

Step-by-step explanation:

Tanya has a garden with a trench around it.

Tanya's garden is a rectangle with length [tex]\dfrac12 \text{m}[/tex] and width 2m.

The trench and garden together make a rectangle with length [tex]3 \dfrac12 \text{m}[/tex] and width 3m.

We are to determine the area of just the trench.

Area of just the trench = Area of the trench and garden together-Area of the garden

[tex]=(3 \dfrac12 X 3)-(\dfrac12 X 2)\\\\=( \dfrac72 X 3)-1\\\\=\dfrac{21}{2}-1\\\\=9 \dfrac12 m^2[/tex]

The area of the trench is [tex]9 \dfrac12 m^2[/tex]

Answer:

Find the area of the shape

First the two triangles

3 x 4 = 12 so the area of both triangles is twelve

Now it is only 1 big rectangle left

The side lengths can be added 3 + 4 + 5 = 12

12 x 11 = 132

132+12=144

144 is the surface area/area

If you have any questions please ask

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-2, 2)   (2, -3)

(-3 - 2)/(2 + 2)

-5/4 the slope

y - 2 = -5/4(x + 2)

y - 2 = -5/4x - 5/2

y- 4/2 = -5/4x - 5/2

y = -5/4x - 1/2

Answer:

f(x) = 4^x

f(4) = 4^4 = 256

Hope this helps!

:)

the answer is 256 but i am not sure

hope this helps and be safe :)

Answer: 49.5 and -0.5

Step-by-step explanation:

a  + b =49

a -  b = 0.5

a= 49.5

b= -0.5

The two numbers are approximately 24.25 and 24.75.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

Let's call the two numbers x and y.

According to the problem, we have two equations:

x + y = 49 (since their sum is 49)

x - y = 1/2 (since their difference is 1/2)

We can solve this system of equations using the method of substitution.

First, we can rearrange the second equation to solve for one of the variables in terms of the other:

x - y = 1/2

x = y + 1/2

Now we can substitute this expression for x into the first equation:

(y + 1/2) + y = 49

2y + 1/2 = 49

2y = 48.5

y = 24.25

Now we can use this value of y to solve for x:

x = y + 1/2 = 24.25 + 1/2 = 24.75

Therefore, the two numbers are approximately 24.25 and 24.75.

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Hey!!!

Here's your answer:

Hope it will help u.

Answer:

432

Step-by-step explanation:

To get volume you need to multiply all of the numbers together (Length, height, and width). You need to multiply 6 and 6 (You get 36) and multply the answer by 12 to get 432.

Hope this helps!

(Also can I get Brainliest? Please?)

Answer:

5.3

Step-by-step explanation:

Answer:

The answer is 5.3

Step-by-step explanation:

5.3x3-2= 13.9 but when you round its 14

Answer:

36°.

Step-by-step explanation:

To find this, we will simply need to know that the sum of the angles of a triangle is 180°. This means that in order to find the measure of the third angle, we will need to subtract the others from 180°.

180 - 99 - 45 = 36°.

The measure of the third angle is 36°.

Answer:

angle of depression = -12 degrees

Step-by-step explanation:

Sin = opposite/hypotenuse

sin = -208/1000

inv sin 0.208 = -12

To solve this problem, we just need to use trigonometric ratio and use the ratio that best fits this problem. The angle of depression is equal to 76.23 degrees.

Using SOHCAHTOA, we can easily solve this problem, but we need to first know which ratio to use

Data;

since we have the value of opposite and adjacent, we can solve this using the tangent of the angle

[tex]tan\theta = \frac{opposite}{adjacent} \\tan \theta = \frac{1000}{208} \\tan\theta = 4.807\\\theta = sin^-^1 (4.0807)\\\theta = 76.23^0[/tex]

From the calculation above, the angle of depression is equal to 76.23 degrees.

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Answer:

3 cones

Step-by-step explanation:

This is why the formula for the volume of a cone is 1/3 (π×r^2)× h, while the volume for a cylinder is (π× r^2)× h, respectively.

Answer:

C) 3 Cones.

Explanation:

Hope this helps! :)

There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)

There's no solution to this particular system because the two lines are parallel.

How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.

The line on the left passes through the points (-1, 0) and (0, -2), so it has slope

(-2 - 0)/(0 - (-1)) = -2/1 = -2

The line on the right passes through (0, 2) and (1, 0), so its slope is

(0 - 2)/(1 - 0) = -2/1 = -2

The slopes are equal, so the lines are parallel.

Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.

Answer:

We need the segments but which ever one has the segment that is 2/3 times the length of segments xy

Step-by-step explanation:

Answer: line c

Step-by-step explanation: I got it correct

Answer:

Side AB has a length of 4, and side BC has a length of 11.7