How many lines of symmetry does the shape below appear to have?

For exercise a), f and g are the same function. So,

[tex] f(g(x)) = g(f(x)) = f(f(x)) = f\left(\dfrac{2}{x}\right) = \dfrac{2}{\frac{2}{x}} = x [/tex]

This means that f and g are inverse (i.e., f is the inverse of itself). In fact, if f(g(x)) = g(f(x)) = x, then f and g are inverse.

As for exercise b), you have

[tex] f(g(x)) = f(6x-1) = 6(6x-1)+1 = 36x-6+1 = 36x-5 [/tex]

[tex] g(f(x)) = g(6x+1) = 6(6x+1)-1 = 36x+6-1 = 36x+5 [/tex]

So, f and g are not inverse of each other.

30 days. This is because everyday, the magician only climbs 1 foot since 3-2=1

The answer would be 2.4 meters per second. To find this, you would divide the 50 meters by 21 seconds. It equals 2.380952, and rounds to 2.4m/s.

Answer:

2.4 meter per second

Step-by-step explanation:

A swimmer swam the 50-meter freestyle in a time of 21 seconds.

Since a swimmer swam in 21 seconds = 50 meters

To calculate his speed in 1 second we will divide the total distance by the total  time.

Therefore, he swam in 1 second =  [tex]\frac{50}{21}[/tex]

                                                     = 2.380952 rounded to 2.4 meter/sec

The speed of the swimmer is 2.4 meter per second.

A ray is a line with one end. It starts at a given point and goes off in a certain direction forever to infinity. The point where the ray starts is called the endpoint.

Answer:

any of a set of straight lines passing through one point.

Step-by-step explanation:

turn it into a fraction for example (i know i am making it harder than it seems with variables) x:y you turn it into [tex]\frac{x}{y}[/tex] then you take the top number in the fraction and put it in the "house"

                         y  ⟌x

-hope this helps

÷

Hey there!

Given equation :

... 0.2 ( x + 50 ) - 6 = 0.4 ( 3x + 20 )

Using the distributive property.

... 0.2x + 10 - 6 = 1.2x + 8

... 0.2x + 4 = 1.2x + 8

Subtract 4 on both sides.

... 0.2x = 1.2x + 4

Subtract 1.2x on both sides.

... - x = 4

... x = -4

Hence, the answer is -4.

Hope it helps!!

To solve this problem you would distribute the 0.2 and 0.4 inside of the parentheses first. Then you would combine like terms and solve from there on. We are solving for the variable x.

Start by distributing (multiplying) 0.2 and 0.4 inside the parentheses that they are "attached" to (parentheses on their right). After distributing, rewrite the problem.

0.2x + 10 - 6 = 1.2x + 8

1] Combine like terms on the left side of the equation.

0.2x + 4 = 1.2x + 8

2] Subtract 4 from both sides of the equation.

0.2x = 1.2x + 4

3] Subtract 1.2x from both sides of the equation.

-x = 4

4] Divide both sides of the equation by -1 to make the variable x a positive.

3(x+4)

Three times -> 3()

the sum of a number and four x+4

3(x+4)

Answer:

3(x+4)

D is correct

Step-by-step explanation:

81 1/4 should be the answer

ANSWER

[tex]\frac{3}{7}(-21x-49)= -9x- 21[/tex]

EXPLANATION

To expand

[tex]\frac{3}{7}(-21x-49)[/tex], we use the distributive property of multiplication over subtraction.

According to the distributive property of multiplication over subtraction, if we have any three real numbers,

[tex]a,b,\:and\:c[/tex].

Then;

[tex]a(b-c)=a\times b-a\times c[/tex]

Applying this property to the given expression, we obtain;

[tex]\frac{3}{7}(-21x-49)= \frac{3}{7}\times (-21x)- \frac{3}{7}\times (49)[/tex]

If we cancel out common factors we obtain;

[tex]\frac{3}{7}(-21x-49)= 3\times (-3x)- 3\times (7)[/tex]

If we simplify further, we obtain;

[tex]\frac{3}{7}(-21x-49)= -9x- 21[/tex]

QUESTION 1

Let [tex]n[/tex] represent the number of years.

Then each year the number of people added is given by the function

[tex]N(n)=8.7\times 10^5(n)[/tex]

Therefore after [tex]25[/tex] years,

[tex]N(25)=8.7\times 10^5(25)[/tex]

[tex]N(25)=21750000[/tex]

In scientific notation,

[tex]N(25)=2.175\times 10^7[/tex]

ANSWER TO QUESTION 2

The population after 25 years can be calculated by adding the increment in population to the initial population.

The initial population

[tex]P_0=9.7\times 10^7[/tex]

The population  after 25 years

[tex]P(25)=9.7\times 10^7+2.175\times 10^7[/tex]

[tex]P(25)=(9.7+2.175)\times 10^7[/tex]

[tex]P(25)=(11.875)\times 10^7[/tex]

[tex]P(25)=1.1875\times 10^1 \times 10^7[/tex]

[tex]P(25)=1.1875\times 10^1 \times 10^7[/tex]

[tex]P(25)=1.1875\times 10^8[/tex]

Answer:

1. [tex]2.175*10^{7}[/tex]

2. [tex]1.1875*10^{8}[/tex]

Step-by-step explanation:

We are given that population of a country is [tex]9.7*10^{7}[/tex] , and is increasing by [tex]8.7*10^{5}[/tex] people each year.

1. To find number of people added after 25 years we will multiply 25 by [tex]8.7*10^{5}[/tex].

[tex](2.5\cdot 10^{1})\cdot (8.7\cdot 10^{5})[/tex]

[tex](2.5\cdot 8.7)\cdot (10^{1+5})[/tex]

[tex](21.75)\cdot (10^{6})=(2.175)\cdot (10^{7})[/tex]

Therefore, [tex]2.175\cdot 10^{7}[/tex] will be added after 25 years.

2. To find out population after 25 years we will add population added in 25 years to initial population.

[tex]9.7*10^{7}+2.175\cdot 10^{7}[/tex]

[tex]11.875\cdot 10^{7}[/tex]

[tex]1.1875\cdot 10^{8}[/tex]

Therefore, population after 25 years will be [tex]1.1875\cdot 10^{8}[/tex].

first side is 7cm

second is 12cm

third is 14cm

The lengths of the sides are 7 cm, 12 cm, and 14 cm, respectively.

Let's denote the lengths of the sides as follows:

First side: x centimeters

Second side: y centimeters

Third side: z centimeters

According to the problem, we can set up a system of equations based on the given information:

The perimeter is the sum of all three sides, so:

x + y + z = 33

The first side is 5 centimeters shorter than the second:

x = y - 5

The third side is twice the first:

z = 2x

Now, we can use these equations to solve for the lengths of the sides. Substituting the second and third equations into the first, we get:

(y - 5) + y + 2(y - 5) = 33

y - 5 + y + 2y - 10 = 33

4y - 15 = 33

4y = 48

y = 12

Plugging y back into the second equation, we find:

x = 12 - 5

x = 7

And using the third equation:

z = 2x

z = 2(7)

z = 14

So, the lengths of the sides are:

x = 7 centimeters

y = 12 centimeters

z = 14 centimeters.

To learn more about lengths

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Answer: The point A is 26m above from the ground.

Explanation:

It is given that the maximum drop Is 65m over a horizontal distance of 65m in two sections. So, the maximum value is (65,65) and the value is (0,0) when it stops.

From the given information it is noticed that the first section has a gradient of 3 and the second section has a gradient of 1/2.

The equation of line passing through the point [tex](x_1,y_1)[/tex] with slope m is define as,

[tex]y-y_1=m(x-x_1)[/tex]

For first section the slope is 3 and the point is (65,65).

[tex]y-65=3(x-65)[/tex]

[tex]y=3x-130[/tex]    ..... (1)

For second section the slope is 1/2 and the point is (0,0).

[tex]y=\frac{1}{2}x[/tex]  .....(2)

Put [tex]y=\frac{1}{2}x[/tex] in equation (1), we get,

[tex]\frac{1}{2}x=3x-130[/tex]

[tex]\frac{5}{2}x=130[/tex]

[tex]x=52[/tex]

Put this value in equation (2)

[tex]y=26[/tex]

Therefore, the point A is 26m above the ground and the horizontal distance is 52m from the endpoint.

The graph for the line y=4/7 x -2 is added in the attachment.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that the line is,

y=4/7 x -2

Comparing the given equation with the standard equation we get the slope of the line is 4/7 and the intercept is -2.

Plot the (0,-2) value of the y-intercept first. Then, add another point to the sloping plot by moving it up 4, to the right 7, and so forth. The point should be (2,7), and if you need to add another point, draw a line through it at (6,14).

Thus the graphs for the line y=4/7 x -2 are added in the attachment.

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3445 divided by 13 is 265.

If l correctly understand your question, you would subtract 18 - 12 to get 6. Was this the answer you were looking for??

Answer:

2.077 x 10^-4

Step-by-step explanation:

Move decimal point over 4 spaces

The scientific notation for the given number is 20.77 × 10⁻⁵

A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10 is called the scientific notation.

Given that, express the number 0.0002077 in scientific notation.

0.0002077 = 20.77 / 100000

= 20.77 × 10⁻⁵

Hence, the scientific notation for the given number is  20.77 × 10⁻⁵

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Solution

Here we have to use compound interest formula for half year.

6 months = 1/2 years

Amount = [tex]P(1 + \frac{r/2}{100})^2n[/tex]

R = Rate

P = Principle

n = number of years

Here P = 6000, r/2 = 3.5/2 = 1.75, n = 1/2

Plug in the given values into the formula, we get    

A  = 6000(1 + 1.75/100)^2(1/2)

A = 6000(1 + 0.0175)^1

A = 6000(1.0175)

A = $6105

Compound interest = A - P

= $6105 - $6000

Interest = $105

Thank you :)

Given expression in exponential form : [tex]a^{\frac{4}{9} }[/tex].

We need to convert it into radical form.

Please note: When we convert an exponential to radical form, the top number goes in the exponent of the term and bottom number of the fraction goes in the radical sign to make it nth radical.

We can apply following rule:

[tex](a)^{\frac{m}{n}}= \sqrt[n]{x^m}[/tex].

Therefore,

[tex]a^{\frac{4}{9} }= \sqrt[9]{a^4}[/tex].

Therefore, correct option is : D. ninth root of a to the fourth power.

Answer: 30 feet per second

========================================

x = diameter, y = speed of water

y varies inversely with respect to x, so, y = k/x for some constant k

If x = 0.6 and y = 5 pair up, then y = k/x turns into 5 = k/0.6 which solves to k = 3 when you multiply both sides by 0.6

So the equation y = k/x turns into y = 3/x

Now plug in the diameter x = 0.1 to find the speed to be...

y = 3/x

y = 3/0.1

y = 30 feet per second

If you want each side it will equal to 18 in. 18*4=72

-5, -4 -1, 3, 5,  if i am correct

Lildude216001,

In order to solve this question you an just order them from least to greatest.

Remember when dealing with negative numbers the one that is usually greater then the other number is shorter.

Therefore your answer is "-5, -4, -1, 3, and 5."

Hope this helps!

let the wigth =x

then the length =2x

You can get

2·(2x+x)=60

2·(2x+x)÷2=60÷2

2x+x=30

3x=30

x=10

So 2x=2×10=20

The width of the garden is 10 feet, the length is 20 feet and the area is 200 square feet.

Final answer:

To find the dimensions of the garden, set up equations based on the perimeter formula and the given relationship between length and width. Solve to find that the width is 10 feet, and therefore the length is 20 feet.

Explanation:

To find the dimensions of a rectangular garden with a perimeter of 60 feet where the length is twice the width, we first need to set up two equations based on what we know about perimeters and the relationship between the garden's length and width. The perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given that P = 60 feet and the length is twice the width (l = 2w), we can substitute the latter into the perimeter formula and get 60 = 2(2w) + 2w, simplifying to 60 = 4w + 2w, which further simplifies to 60 = 6w. Dividing both sides by 6 gives us w = 10 feet. Therefore, the width is 10 feet and since the length is twice the width, the length is 20 feet.

The answer should be D, divide by 6.78.

Answer:

is it 1.50? I got it wrong tho

When the price of bus tickets is raised, Alphonso's new budget constraint will be affected and he will be able to purchase fewer bus tickets. The opportunity cost of bus tickets increases as Alphonso has to give up more burgers to purchase bus tickets.

When the price of bus tickets is raised to $1 per trip, Alphonso's new budget constraint will be affected. The new budget line will have a steeper slope, indicating that he can purchase fewer bus tickets for the same amount of money. The opportunity cost of bus tickets increases because now Alphonso has to give up more burgers in order to purchase bus tickets.

Amount of chemical A mixed in medicine = 9.357 g

Amount of chemical B mixed in medicine = 12.082 g

Amount of chemical C mixed in medicine = 7.502 g

We have to determine the total amount of medicine he prepared in grams.

Total amount of medicine

= 9.357 + 12.082 + 7.502

= 28.941 grams

So, he prepared 28.941 grams of medicine.

Now, we have to round each chemical to the nearest tenth.

Amount of chemical A mixed in medicine = 9.357 g

Rounding to nearest tenth = 9.4 grams

Amount of chemical B mixed in medicine = 12.082 g

Rounding to nearest tenth = 12.1 grams

Amount of chemical C mixed in medicine = 7.502 g

Rounding to nearest tenth = 7.5 grams

By adding the amounts of Chemical A, B, and C after rounding to the nearest tenth, we find that Dr. Manion made a total of approximately 29 grams of medicine.

To find the total amount of medicine made by Dr. Manion, we need to add the amounts of Chemical A, Chemical B, and Chemical C. But before that, we must round each of these to the nearest tenth of a gram.

So, Chemical A is about 9.4g, Chemical B is approximately 12.1g, and the Chemical C is about 7.5g.

Adding these together: 9.4g + 12.1g + 7.5g = 29.0 gragramsms.

This implies that Dr. Manion made a total of approximately 29.0 grams of medicine.

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To estimate the difference between 17/18 and 3/7, one could use benchmark figures. These fractions are approximated as 1 and 1/2 respectively. Therefore, the estimated difference is typically around 1/2 or 0.5.

The student is asking for help to estimate the difference between the fractions 17/18 and 3/7. To estimate this, we first need to understand fractions and benchmark values. A benchmark value is a value that's easy to handle in calculations. For fractions, often 0, 1/2, and 1 are used as benchmarks.

Looking at the given fractions, 17/18 is close to 1 (our benchmark) and 3/7 is about 1/2 (another benchmark). Therefore, to estimate the difference, we subtract our rough approximation of 1/2 from 1, giving us an estimate of 1/2 or 0.5 as the difference.

This is a fairly quick way to estimate the difference between two fractions using benchmark values. It won't provide you with the exact answer, but it will give you a ballpark figure that's usually quite close to the actual result.

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