Which statements about the graph of the function y=(1/3)^x are true?

The function is increasing.

The function is decreasing.

The x-intercept is (1, 0).

The y-intercept is (0, 1).

The range of the function is all real numbers.

Options 1, 2, and 3 are valid based on the given information and calculations.

1. When added, the sum of the y-intercepts must be 8:

  - If the y-intercepts are denoted as b₁ and b₂ for f(x) and g(x) respectively, then . [tex]b_1 \times b_2 = 8[/tex].

2. When multiplied, the product of the y-intercepts must be 8:

  - This translates to [tex]b_1 \times b_2 = 8[/tex].

3. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change:

  - This implies that the slopes of the lines have opposite signs.

Checking the given U-turn points (-2, 8) and (8, 2). The slope (rate of change) between these points can be calculated as:

[tex]\[ m = \frac{change\:in\:y}{change\:in\:x} \][/tex]

[tex]\[ m = \frac{2 - 8}{8 - (-2)} = \frac{-6}{10} = -\frac{3}{5} \][/tex]

4. f(x) could have a rate of change equal to 3 and g(x) could have a rate of change of -3:

  - This statement is inconsistent with the calculated slope.

5. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of -1:

  - This statement is also inconsistent with the calculated slope.

Therefore, options 1, 2, and 3 are valid based on the given information and calculations.

Answer:

1 When multiplied the product of the y intercepts must be 8

2 Either f(x) or g (x) has a positive rate of change and the other has a negative rate of change

3 f (x) could have a rate of change equal to 2 and g (x) could have a rate change of -1

Answer:

the correct option is C.

Step-by-step explanation:

The x-intercept of both functions g(x) and f(x) occur at point (1, 0).

Now, we need to find where g(x) > f(x) and f(x) > g(x)

We know that the greater the base of a logaritmic function is, the faster it will grow/decay.

For that reason, we can say that g(x) > f(x)  on (1, +inf).

Now, when x<1 then y<0. So on the interval (0, 1) the function g(x) will decay much faster than the function f(x), so we can say that f(x) > g(x) on (0, 1). So the correct option is C.

Check the graph, to verify all this.

B

12 is equal to 4y, or 4(3)

you can multiply 4 by x to get 9 since they’re inversely proportionate.

Answer:

A) 1.

Step-by-step explanation:

y is inversely proporcional to x so the equation has the form:

y = c/x

With c been any constant, to find the value of c we use y=4 and x=3:

4 = c/3

c=4*3

c=12

So the equation is

y=12/x

Using y=12 to find x:

12=12/x

(12/12)=x

x=1

Answer:

[tex]\large\boxed{Domain:\ x\in\mathbb{R}\to\text{the set of all real numbers}}[/tex]

Step-by-step explanation:

The domain of roots:

[tex]\sqrt[n]{p(x)}[/tex]

If n is an odd number, then p(x) can be any real number.

If n is an even number, then p(x) must be a non-negative number.

We have

[tex]f(x)=\sqrt[3]{2x^2-3x-9}[/tex]

n = 3 → odd number.

Therefore the domain is the set of all real numbers.

Answer:

8(3 + 8)

Step-by-step explanation:

Note that 8 is a factor common to both 24 and 64.

Thus, 8(3 + 8) is equivalent to 24 + 64.

Answer is number a

First you find the common factor between 24 and 64 and you factor it out and divide both numbers by it

8(3+8)

Answer:

4/45

Step-by-step explanation:

When you convert 2/10 to 1/5, you get 1/5*4/9. If you multiply the numerator and the denominator, you get 1*4/5*9, which simplifies to 4/45.

Answer:

your answer should be 4/45, if I'm correct.

Answer: A- 6 inches

Step-by-step explanation:

since the triangle has an area of 36in you would reverse the formula of finding the area of a triangle which is bh divided by 2 so i divided 36 by 2 to get 18 then 18 divided by 3= 6

Answer:

B: 12inches

Step-by-step explanation:

Ueuhshsjaksjdsnygwhwhwhwhwg bdbehd jeuwjsnz ,judj

Answer:

B

Step-by-step explanation:

The mean is the average found by adding the sum of the data points and dividing by the number of them. Here there are 3 cars whose speeds are 109, 111, and Z or unknown. The mean of them is 100. Solve for Z.

100 =(109+111+Z)/3

300=220+Z

80=Z

The speed of Car Z is less than 100.

The correct answer is B. The speed of Car Z is less than 100 miles per hour.

To estimate the speed of Car Z, we can use the given mean speed of the three cars. The mean speed is given as 100 miles per hour. Since Car X is driving at 109 miles per hour and Car Y is driving at 111 miles per hour, both of these speeds are above the mean. To maintain an average of 100 miles per hour, Car Z must be driving at a speed less than 100 miles per hour to balance the speeds of Car X and Car Y, which are pulling the average up.

To find the actual speed of Car Z, we can use the formula for the mean speed of the three cars:

[tex]\[ \text{Mean speed} = \frac{\text{Speed of Car X} + \text{Speed of Car Y} + \text{Speed of Car Z}}{3} \][/tex]

Given that the mean speed is 100 miles per hour, we can plug in the known values and solve for the speed of Car Z:

[tex]\[ 100 = \frac{109 + 111 + \text{Speed of Car Z}}{3} \][/tex]

Multiplying both sides by 3 to clear the denominator:

[tex]\[ 300 = 109 + 111 + \text{Speed of Car Z} \][/tex]

Adding the speeds of Car X and Car Y:

[tex]\[ 300 = 220 + \text{Speed of Car Z} \][/tex]

Subtracting 220 from both sides to isolate the speed of Car Z:

[tex]\[ \text{Speed of Car Z} = 300 - 220 \] \[ \text{Speed of Car Z} = 80 \text{ miles per hour} \][/tex]

Thus, the actual speed of Car Z is 80 miles per hour, which confirms our initial estimation that it is less than 100 miles per hour.

Answer:

[tex]1,715\ in^{2}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> surface area of the enlarged figure

y----> surface area of the original figure

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=7[/tex]

[tex]y=35\ in^{2}[/tex]

substitute

[tex]7^{2}=\frac{x}{35}[/tex]

[tex]x=7^{2}(35)=1,715\ in^{2}[/tex]

____________________________________________________

Answer:

Your answer would be 1,385.44 ft²

____________________________________________________

Step-by-step explanation:

To find the area of a circle, we would use the equation [tex]\pi r^2[/tex]

In this case we have the diameter, and that's 42.

The radius of a circle is half of the diameter, therefore the radius would be 21.

Now we know the radius,we can plug that in to our equation.

Your equation should look like this:

[tex]\pi (21)^2[/tex]

Pi would be 3.14159

Now, you can solve.

[tex]3.14159(21)^2\\\\3.14159*441\\\\=1,385.44[/tex]

When you'r edone solving, you should get 1,385.44

1,385.44 ft² would be your FINAL answer.

____________________________________________________

Answer:

1384.74

Step-by-step explanation:

diameter = 42

radius = 42/2 = 21

area of a circle = πr2 (pie r square)

= 3.14 X 21 X 21

=1384.74 sq.ft

Answer:

The possible values of x are:

x= [tex]\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18[/tex]

and

x= [tex]\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68[/tex]

Step-by-step explanation:

[tex]8x^2+4x+1=0[/tex]

Using Quadratic formula to solve this equation:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\a = 8 \,\, b = 4\,\, c = -1\\Putting \,\, values \,\, in \,\, the\,\, equation\\x= \frac{-4\pm\sqrt{(4)^2-4(8)(-1)}}{2(8)}\\x= \frac{-4\pm\sqrt{16+32}}{16}\\x= \frac{-4\pm\sqrt{48}}{16}\\x= \frac{-4+ \sqrt{48}}{16} \,\, and \,\, x= \frac{-4- \sqrt{48}}{16}\\x= \frac{-1+ \sqrt{3}}{4} \,\, and \,\, x= \frac{-1- \sqrt{3}}{4}[/tex]

The possible values of x are:

x= [tex]\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18[/tex]

and

x= [tex]\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68[/tex]

Answer:

the answer is true im pretty sure i really hope this helps

Step-by-step explanation:

Answer:

Alternate Exterior

Step-by-step explanation:

The simplification form of the number expression 70 -7.7 is 62.3 after using the concept of the BODMAS the answer is 62.3.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

The number expression is:

= 70 -7.7

The expression can be defined as the combination of constants and variables with mathematical operators.

Using the rule of BODMAS

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56 etc. are the numbers.

On simplification

= 62.3 [after subtracting 7.7 from 70]

Thus, the simplification form of the number expression 70 -7.7 is 62.3 after using the concept of the BODMAS the answer is 62.3.

Learn more about the arithmetic operation here:

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Final answer:

To subtract 7.7 from 70, align the decimal points and subtract to find the result is 62.3.

Explanation:

The problem at hand requires us to subtract a decimal number from a whole number. Here's the step-by-step calculation for 70 - 7.7:

Therefore, the subtraction of 7.7 from 70 gives us 62.3.

The area of the circle with [tex]\(r = 1\)[/tex] is [tex]\(\pi\)[/tex].

The area ([tex]\(A\)[/tex]) of a circle is given by the formula:

[tex]\[A = \pi r^2\][/tex]

Where [tex]\(r\)[/tex] is the radius of the circle.

Given that [tex]\(r = 1\)[/tex], we can substitute this value into the formula:

[tex]\[A = \pi \times (1)^2\][/tex]

[tex]\[A = \pi \times 1\][/tex]

[tex]\[A = \pi\][/tex]

Therefore, the area of the circle with [tex]\(r = 1\)[/tex] is [tex]\(\pi\)[/tex].

Answer:

$451.5

Step-by-step explanation:

For saturdays, Edward will earn 1.5 times the normal (10.50). So saturday hourly pay is 1.5 * 10.5 = $15.75

For sundays, Edward will earn twice the normal (10.50). So sunday hourly pay is 2 * 10.5 = $21

Edward's hours:

Regular 25 hours: 25 * 10.5 = $262.5

Saturday 4 hours: 4 * 15.75 = $63

Sunday 6 hours: 6 * 21 = $126

Total Pay = 262.5 + 63 + 126 = $451.5

Final answer:

Lisa Edwards' total pay for the week is $451.50, which is the sum of her regular pay for 25 hours, time-and-a-half pay for 4 hours on Saturday, and double-time pay for 6 hours on Sunday.

Explanation:

Lisa Edwards' total pay for the week can be calculated by considering her regular hourly wage, her time-and-a-half pay for Saturday, and her double-time pay for Sunday. Her regular hourly rate is $10.50 per hour. For her regular 25 hours of work, she would earn $10.50 x 25 = $262.50.

On Saturday, Lisa earns time-and-a-half. This means she gets $10.50 x 1.5 = $15.75 per hour for 4 hours, which totals to $15.75 x 4 = $63.00.

On Sunday, Lisa earns double-time pay, which amounts to $10.50 x 2 = $21.00 per hour. For 6 hours of work on Sunday, she will earn $21.00 x 6 = $126.00.

To find out Lisa's total weekly pay, add her earnings from all the days: $262.50 (regular hours) + $63.00 (Saturday) + $126.00 (Sunday) = $451.50.

Answer: -3(5t+2

Step-by-step explanation:

Answer:

−3(5t+2)

Step-by-step explanation:

lets factor out "3" from -15t-6

so factoring out "3" would give you -3(5t+2)

you can check ur work by distributing "3" hope this helps!

Answer:

The first part is A then the second part is B 1/19

Step-by-step explanation:

If you add all together you get 20 then you get a green marble since you removed one that would make the odds into 1 out of 19 that's how you get the next answer. Hope this Helped! ʢ◉ᴥ◉ʡ

Answer:

C. 1/9

Step-by-step explanation:

Blue/Fish

White/Fish

Green/Fish (SELECTED CARD)

Blue/Insect

White/Insect

Green/Insect

Blue/Bird

White/Bird

Green/Bird

There are 9 so the chances of getting one is 1/9.

Answer:

The answer is c

Step-by-step explanation:

The correct answer to the question is option (2): [tex]\( h\left(\frac{x}{3}\right) \).[/tex]

To address the question about the horizontal stretching of the graph of a function [tex]\( f(x) \)[/tex] by a factor of 3, we need to understand how transformations affect the graph of a function. Here are the steps to determine the correct transformation:

1. Identify the Base Function: Recognize that the graph in question is of some function [tex]\( f(x) \)[/tex]. We don't need to know the form of \( f(x) \) to understand how it will be transformed.

2. Understand Horizontal Stretching: A horizontal stretch by a factor of [tex]\( a \)[/tex] is achieved by replacing every [tex]\( x \)[/tex] in the function with [tex]\( \frac{x}{a} \)[/tex]. In this case, [tex]\( a = 3 \).[/tex]

3. Apply the Stretch to the Function: Replace [tex]\( x \)[/tex] with [tex]\( \frac{x}{3} \)[/tex]in the function [tex]\( f(x) \).[/tex]

4. **Write Down the Transformed Function**: The new function after the horizontal stretch will be [tex]\( f\left(\frac{x}{3}\right) \).[/tex]

5. **Choose the Correct Answer**: Look for the choice that represents the transformation [tex]\( f\left(\frac{x}{3}\right) \).[/tex]

The correct transformation that indicates a horizontal stretch by a factor of 3 is:

[tex]\[ f\left(\frac{x}{3}\right) \][/tex]

This means that for any given value of [tex]\( x \)[/tex] in the original function, its corresponding point on the graph will now be three times further away from the y-axis, thus stretching the graph horizontally. If the original function had a point at [tex]\( (x, y) \)[/tex], the new function after the stretch will have a corresponding point at [tex]\( (3x, y) \)[/tex], which means the x-values have been stretched out.

Now, from the options given in the image:

1. [tex]\( h(3x) \)[/tex] represents a horizontal compression by a factor of 3, not a stretch.

2. [tex]\( h\left(\frac{x}{3}\right) \)[/tex] is the correct representation of a horizontal stretch by a factor of 3.

3. [tex]\( h(x) + 3 \)[/tex] represents a vertical shift upwards by 3 units.

4. [tex]\( 3h(x) \)[/tex] represents a vertical stretch by a factor of 3.

Therefore, the correct answer to the question is option (2): [tex]\( h\left(\frac{x}{3}\right) \).[/tex]

Answer:

Step-by-step explanation:

y=mx+b

8=-7m+b

2=0m+b

subtract

6=-7m

-6/7=m

2=0m+b

2=b

y=-6/7x+2

change to standard from

y+6/7x=2

Answer:

-26

Step-by-step explanation:

Plug in 12 for n.

-4-2(12-1)

-4-2(11)

-4-22

-26

-26 !!!!!!!!!!!!!!!!!!!!!

Answer:

3,172

Step-by-step explanation:

The "Money saved that week" is an arithmetic progression, where the next term is found by adding a constant value to the previous term. In this case, the variation is 2.

So that could be modeled with this equation: [tex]a_{n} = a_{1} + (n-1)V[/tex]

Where a1 is the first term of the series, in our case: 10, and the V is the variation each week, in our case: 2.

To be able to calculate the overall sum and answer the question, we first need to calculate the amount she will save on the last week (n=52).

[tex]a_{52} = 10 + (52-1) * 2 = 10 + 102 = 112[/tex]

Now that we know she'll save $112 on the 52nd week, let's calculate the total, using this formula:

[tex]S_{n} = \frac{(a_{1} + a_{n}) * n}{2}[/tex]

We know n (52), a1 (10) and an (112), so...

[tex]S_{52} = \frac{(10 + 112) * 52}{2} = \frac{122 * 52}{2} = 3,172[/tex]

At the end of the year, she will have saved $3,172

To find out how many minutes it takes for 1 person to paint 1 wall, we can set up a proportion using the rate of 6 people painting 6 walls in 23 minutes. Cross-multiplying and solving for the unknown, we find that it would take approximately 3.83 minutes for 1 person to paint 1 wall.

This question falls under the subject of Mathematics and is suitable for students in Middle School. To solve this problem, we can use the concept of rate. We know that 6 people can paint 6 walls in 23 minutes.

We can set up a proportion to find out how many minutes it would take for 1 person to paint 1 wall. Let x represent the unknown time:

6 people / 23 minutes = 1 person / x minutes

Cross-multiplying, we get 6x = 23. Dividing both sides by 6, we find that x = 23/6. Therefore, it would take approximately 3.83 minutes for 1 person to paint 1 wall.

Remember to always read the question carefully and identify the given information and the unknown variable in order to solve the problem accurately.

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The time that it would take for 8 people to paint the walls would be 18 minutes.

The number of walls painted is proportional to the number of people painting, and the time it takes to paint the walls is inversely proportional to the number of people painting.

Using the following formula, we can calculate the amount of time it will take 8 people to paint the 6 walls:

Time = (Number of walls) / (Number of people) * Time per wall

Time = (6 walls) / (8 people) * 23 minutes/wall

Time = 18 minutes

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The full question is:

It takes 23 minutes for 6 people to paint 6 walls​. How long would it take 8 people to paint those same 6 walls

Answer:

The perimeter of a shape is the sum of the measurements of all sides. Since a rectangle have equal lengths and widths, you can just add the numbers twice.

So, 15 + 15 + 8 + 8. So the perimeter is 46 cm.

Answer:

E. 46

Step-by-step explanation:

The perimeter of a square or rectangle can be found by using the following formula:

(length + legnth) + (width + width) = perimeter

Our length here is 15 and the width is 8, so substitute the values into the equation.

(15 + 15) + (8 + 8) = perimeter

Now solve

(15 + 15) + (8 + 8)

(30) + (8 + 8)

(30) + (16)

=46

Therefore, the perimeter (and answer) is E. 46

I hope this helps!

Answer:

I would say the second car.

Step-by-step explanation:

372/15.2 = 24 miles per gallon

198/7.2 = 27.5 miles per gallon

So the answer is the second car is better on gas mileage!

Answer:

The first term is 28.

Step-by-step explanation:

Given: 8th term of Geometric sequence , [tex]a_8=-3584[/tex]

and 3rd term of Geometric Sequence, [tex]a_3=112[/tex]

We have to find First term of given geometric Sequence.

Let a be the first term of geometric sequence.

We know that,

[tex]a_n=ar^{n-1}[/tex]

So,

[tex]\frac{a_8}{a_3}=\frac{ar^{8-1}}{ar^{3-1}}=\frac{-3584}{112}[/tex]

[tex]\frac{r^{7}}{r^{2}}=-32[/tex]

[tex]r^5=-32[/tex]

[tex]r=-2[/tex]

So, 3rd term = 112

a × (-2)² = 112

a = 112 / 4

a = 28

Therefore, The first term is 28.

Answer:

1 and a8 =16,384

Step-by-step explanation:

ANSWER

[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]

EXPLANATION

[tex] \sin(x) = \frac{Opposite}{hypotenuse} [/tex]

[tex]\sin(x) = \frac{3}{4} [/tex]

This means the opposite side is 3 units and the hypotenuse is 4 units.

We use Pythagoras Theorem to find

[tex] { |ZX| }^{2} + {3}^{2} = {4}^{2} [/tex]

[tex]{ |ZX| }^{2} +9=16[/tex]

[tex]{ |ZX| }^{2} =16 - 9[/tex]

[tex]{ |ZX| }^{2} = 7[/tex]

[tex]{ |ZX| } = \sqrt{7} [/tex]

[tex] \tan(x) = \frac{opposite}{adjacent} [/tex]

[tex] \tan(x) = \frac{3}{ \sqrt{7} } [/tex]

[tex] \tan(x) = \frac{3}{ \sqrt{7} } \times \frac{\sqrt{7}}{\sqrt{7}} [/tex]

[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]

Final answer:

Given sin(X) = 3/4 in a right-angled triangle XYZ, by using trigonometric identities and the Pythagorean theorem, we find that tan(Y) is 1/3.

Explanation:

In triangle XYZ with angle Z being a right angle (90 degrees or π/2 radians), if we are given that sin(X) = 3/4, we can use trigonometric identities to find tan(Y). Since sin(X) is the ratio of the opposite side to the hypotenuse in a right-angled triangle, we have a side opposite angle X which is 3 units long and a hypotenuse that is 4 units long. From this, we can deduce that the side adjacent to angle X, which is also the side opposite to angle Y, is 1 unit long (using the Pythagorean theorem, as the square of the hypotenuse is equal to the sum of the squares of the other two sides: 3² + 1² = 4²).

Now, to find tan(Y), which is the ratio of the side opposite to Y to the side adjacent to Y, we just take the length of the side opposite to X (which is the same as the side adjacent to Y) and the length of the hypotenuse. Therefore, tan(Y) = opposite side / adjacent side, which in this case is 1/3.

Answer:

X= O.8 or 10 over 12.5

Step-by-step explanation: Hope this helps darling