the graphs of f(x)=-2x and g(x)=(1/2)^x are shown. what are the solutions to thr equation -2x=(1/2)^x? select each correct answer.
-2
-1
2
4

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:

[tex]6x + 42[/tex]

Step-by-step explanation:

Apply the distributive property:

[tex]6x + 6 \times 7[/tex]

Multiply 6 by 7

[tex]6x + 42[/tex]

Answer:

Step-by-step explanation:

43feet

Answer:

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

Answer:

The number of batches of paving stones Eric needs is 5 batches

Step-by-step explanation:

Here we have the size of of one paving stone = 1 ft²

The dimensions, size, of one patio = 7 ft × 8 ft = 56 ft²

Therefore, the number of paving stones Eric needs per patio is given by the relation;

[tex]Number\, of\ paving\ stones \ required =\frac{size\, of \, one\, patio}{size \, of \, one\, paving\, stone} = \frac{56 \, ft^2}{1 ft^2/(paving \, stone)} = 56 \, paving \, stones[/tex]

Since the paving stones are sold in batches of one dozen, we have ;

4 batches = 48 paving stones and 5 batches = 60 paving stones

Therefore, the number of batches of paving stones Eric needs = 5 batches.

Answer: The volume is 480 in^3

Step-by-step explanation:

v= lwh

v= 12 * 5 * 8

v= 480 in^3

Answer:

Volume of the rectangular prism = [tex]480in.^{3}[/tex]

Step-by-step explanation:

Formula for the volume of a rectangular prism= Ah, where A= base area

                                                                                               & h= height

Base area(A)= Length×Width

                    = 12in.×8in.

                    = [tex]96in.^{2}[/tex]

Since height=5in.,

Volume= [tex]96in.^{2}[/tex]×5in.

            = [tex]480in.^{3}[/tex]

Hope this helps!!!

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Answer:

area=250.12. perimeter=3380

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

3(2 - 7)​

PEMDAS says parentheses first

Subtract

3 (-5)

Multiply

-15

40π

You dont need paper hw since we're in quarantine

Answer:40

Step-by-step explanation:

Answer:

The answer would be {y|y>0}

Step-by-step explanation:

hope this helps

Answer:grjjrd

Step-by-step explanation:fdfgdjj

Answer:

m = 17

Step-by-step explanation:

[tex]4(m - 13) - 8 = 8 \\ 4(m - 13) = 8 + 8 \\ 4(m - 13) = 16 \\ (m - 13) = \frac{16}{4} \\ m - 13 = 4 \\ m = 4 + 13 \\ \huge \red { \boxed{m = 17}}[/tex]

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.

Learn more about algebra here:

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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:

[tex]73\%[/tex]

Step-by-step explanation:

Given: Present weight of Caleb’s puppy = 2,250 grams

Puppy weighed 600 grams at his last visit to the veterinarian’s office.

To find: percent increase in the puppy’s weight rounded to the nearest whole number

Solution:

Increase in puppy's weight = 2250 - 600 = 1650 grams

Percent increase in the puppy’s weight =( Increase in puppy's weight/Present weight of Caleb’s puppy) × 100 = [tex]\frac{1650}{2250}(100)=73.33 \%[/tex]

[tex]73.33\%[/tex] is rounded to [tex]73\%[/tex]

Answer:

2x+2(x+5)) = 24

Step-by-step explanation:

2x+ 2(x+5) = 24

x is represented by the shorter side. Multiply by 2 because of the 2 sides. For the longer side, since it is 5m longer than the shorter side, you have to write (x+5). Multiply by 2 because of the 2 sides. Finally, add them both together since it is the area and set it equal to 24.

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:

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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30x and 12 have a common factor of 6.   So yes, this might have been the result of distributing the 6 in

6(5x - 2)

Answer:

30x - 12 = 2(15x - 6)

30x - 12 = 3(10x - 4)

30x - 12 = 6(5x - 2)

Step-by-step explanation:

30 and 12 have these factors in common: 2, 3, 6

There are three possible answers.

30x - 12 = 2(15x - 6)

30x - 12 = 3(10x - 4)

30x - 12 = 6(5x - 2)

Answer:

38

Step-by-step explanation:

3 x {10 +1} +5.

PEMDAS

Parentheses first

3 x {11} +5.

Then multiply and divide

33+5

38

Answer:

38

Step-by-step explanation:

3 x {10 +1} +5             Following PEMDAS, solve in the parentheses

3 x 11 + 5                   Multiply 3 x 11

33 + 5                       Add

38

Answer:

Step-by-step explanation:

Hard to figure out huh

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 times

Step-by-step explanation:

Answer:

4.8333333 or 4 5/6 times

Step-by-step explanation:

29/6 = 4.83333333

Answer:

192

Step-by-step explanation:

Add 8 started from 2 and keep going till you hit 192.

Answer:

a1 = 2      d = 8

n = 13

an = a1 + d(n-1)

a(13) = 2 + 8(13-1)

2 + 8(12)

2 + 96 = 98

Step-by-step explanation:

1. identify the terms

2. write down the arithmetic sequence formula and then replace the letters with their values.

3. do parenthesis first, then multiply by d.

4. add them together to get the 13th term

Answer:

The correct answer is 11 ft.

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. This means that the portion marked x+4 is the same length as the portion marked 2x-7; this gives us the equation x+4=2x-7.

Subtract x from each side:

x+4-x=2x-7-x

4=x-7.

Add 7 to both sides:

4+7=x-7+7

11=x

Answer:

11

Step-by-step explanation:

On edge

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 parabola is wider than the parent function

Step-by-step explanation:

If "a" is a fraction less than one, then the parabola becomes wider.

See graph (attached)