Amy wants to construct a fence around her sand -box.

The sand -box is circular in shape with a diameter of 3 ft.

What is the length of fencing material she will need to fence one complete circle around her sand -box?



(Use 3.14 for the value of ∏ (pi))

Answer:

y = -2/3x + 2

Step-by-step explanation:

2x + 3y = 6 to y = mx + b form.

1. Subtract 2x from both sides.

3y = -2x + 6

2. Divide each side by 3.

y = -2/3x + 2

Answer:

y = -2/3x + 2

Answer:

K is the best estimate.

Step-by-step explanation:

This is just common sense, not much math.

J: No, that is smaller than an essential oils bottle, which is as tall as a finger.

K: Probably, the range is from the size of a medicine bottle to a small/medium water bottle.

L: No, that much is the size of a bottle of detergent.

M: No, that much water is 6 kg.

Answer:

Option b. [tex]h=21.6\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle FGH

The function cosine of angle F is equal to divide the adjacent side angle F by the hypotenuse

[tex]cos(F)=\frac{FG}{FH}[/tex]

substitute the values and solve for h

[tex]cos(35\°)=\frac{h}{26.4}[/tex]

[tex]h=(26.4)cos(35\°)=21.6\ units[/tex]

Answer:

35x6=210

Step-by-step explanation:

The 5 in 35 and times that by 6 is 30. So the ones place is 0.

Set aside the 3 and do 3x6 which is 18. but add 3 is 21. So the answer is 210.

Answer:

The answer is 420 people.

Step-by-step explanation:

Over the course of two days, the play was performed 6 times. So multiply 6 times 2 to get 12. The play was performed a total of 12 times in two days. Now multiply 12 times the number of maximum people who watched on both days to get 420.

Answer

Domain of the function:

In interval notation: [6, ∞)

In set notation: {x: x∈R, x≥6}

Explanation

Remember that the the domain of the square root function are all the  values such is is bigger than zero. We can express the later in set notation: {x: x∈R, x≥0}, or in interval notation: [0, ∞)

This is because the square root is not defined, in the real numbers, for negative values.

So, to find the domain of our function, we just need to set the thing inside the radical grater or equal than zero and solve for x:

The domain of the function is all the numbers bigger than 6, including 6.

Answer:

[6, infinity (use the symbol)

Step-by-step explanation:

i got this answer by graphing

Answer:

$188.50

Step-by-step explanation:

i got this answer by dividing $1,508 by 8 and you would get 188.5 which would turn into $188.50 and that is how much each person would get.

I hope this helps.

[tex] - 4 - (( - 4 + 6) \div ( - 2))( - 5) = \\ = - 4 - (2 \div ( - 2))( - 5) = \\ = - 4 - ( - 1)( - 5) = - 4 - 5 = \\ = - 9[/tex]

The answer is M-5

See the image

ANSWER

The correct choice is C.

EXPLANATION

The given graph has vertical asymptote at x=1.

Therefore , the denominator of the function represented by the graph should be 1-x

The graph also has a horizontal asymptote at y=-6. The numerator should be of the form

b+6x,

where b is a constant.

So that the horizontal asymptote will be

[tex]y = \frac{6}{ - 1} = - 6[/tex]

Our rational function now becomes

[tex]y = \frac{b + 6x}{1 - x} [/tex]

The function also has a y-intercept of 3,

[tex]3 = \frac{b + 6(0)}{1 - 0} = b[/tex]

Therefore the required function is

[tex]y = \frac{3 + 6x}{1 - x} [/tex]

The triangle was only rotated. The size did not change, so the corresponding angles would remain identical.

Because C is 28 degrees C' would also be 28 degrees.

Answer:

Step-by-step explanation:

(x-1)(x+2)/x^2(x-1)+2(x-1)

(x-1)(x+2)/(x-1)(x^2+2)

(x+2)/(x^2+2)

Answer:

[tex]\frac{(x+2)}{(x^2+2)}[/tex]

Step-by-step explanation:

[tex]\frac{x^2+x-2}{x^3-x^2+2x-2}[/tex]

To simplify the given expression , factor both numerator and denominator

Numerator : [tex]x^2+x-2[/tex]

Product is -2 and sum is +1. factors are 2 and -1

[tex]x^2+x-2=(x+2)(x-1)[/tex]

Denominator : [tex]x^3-x^2+2x-2[/tex]

Group first two terms and last two terms

Factor out GCF from each term

[tex](x^3-x^2)+(2x-2)[/tex]

[tex]x^2(x-1)+2(x-1)[/tex]

[tex](x^2+2)(x-1)[/tex]

Replace the factors in the given expression

[tex]\frac{(x+2)(x-1)}{(x^2+2)(x-1)}[/tex]

Cancel out x-1 at the top and bottom

[tex]\frac{(x+2)}{(x^2+2)}[/tex]

Answer:

(i) Exponential Decay

(ii)linear

(iii)Exponential Growth

Step-by-step explanation:

(i)

Cost of the van=$25,000.

After 2 years, value of van=$17,500.

After 4 years, value of van = $12,250.

Its a decay but to be a exponential decay it must have constant rate.

As its known the exponential decay formula is [tex]C=C_{0} e^{-kt}[/tex]

Now substitute the values in the above formula

[tex]17500=25000 e^{-k*2}[/tex]

Now on simplification, we get

[tex]k=0.1783[/tex]

Now again apply the same formula for the next time interval

[tex]12250=25000 e^{-k*4}[/tex]

Now on simplification, we get

[tex]k=0.1783[/tex]

Since the value of k is constant for both the time interval. Hence the decays is exponential.

(ii)

At the beginning, battery life=100%.

After 3 Hours, battery life=60%.

After 6 Hours, battery life = 20%.

Since the value of battery life decreases by 40% in each interval. Hence the decay of battery life is linear.

(iii)

Initial population=20.

After 5 years, population=30.

After 10 years, population = 45.

Its a growth but to be a exponential growth it must have constant rate.

As its known the exponential growth formula is [tex]P=P_{0} e^{kt}[/tex]

Now substitute the values in the above formula

[tex]30=20 e^{-k*5}[/tex]

Now on simplification, we get

[tex]k=-0.081[/tex]

Now again apply the same formula for the next time interval

[tex]45=20 e^{-k*10}[/tex]

Now on simplification, we get

[tex]k=-0.081[/tex]

Since the value of k is constant for both the time interval. Hence the decays is exponential.

We first would divide the Pentagon into two shapes, one a square and the other a triangle. To find the height of the triangle we must minus the 15cm to the 10cm, which gives us 5cm.

5cm= height of triangle

7cm= base of triangle

Then, apply the area of triangle formula

which is: A=(b×h)÷2

so the area would be 17.5cm squared.

For the square, 10= height and the 7=base

The formula for rectangles is:

A=b×h

so, the area is 70cm squared.

if you want the total area add the two area together, which equals 87.5cm squared.

I hope this helps.

To find the area of each figure, we can use different formulas depending on the shape. If the figure is a square or rectangle, we can use the formula A = length x width. If the figure is a circle, we can use the formula A = πr², where r is the radius.

To find the area of each figure, we can use different formulas depending on the shape. If the figure is a square or rectangle, we can use the formula A = length × width. If the figure is a circle, we can use the formula A = πr², where r is the radius. For triangles, we can use the formula A = ½base × height. For irregular shapes, we can approximate the area by breaking it down into simpler shapes and summing up their areas.

Let's say we have a square with side length 5 cm. Using the formula A = length × width, the area would be A = 5 cm × 5 cm = 25 cm². If we have a circle with a radius of 2 cm, using the formula A = πr², the area would be A = 3.14 × 2 cm × 2 cm = 12.56 cm² (rounded to the nearest tenth).

The answer is 7.3 mi I think

Answer:D

Step-by-step explanation: The vertex is (-1, -3), and since it's in terms of y, the y-coordinate is in the parentheses. D is the only choice with -3 as the y-coordinate.

The equation of the parabola with vertex (-1, -3) is y = a(x + 1)^2 - 3.

The equation of a parabola in vertex form is y = a(x - h)^2 + k, where the vertex is (h, k). In this case, the vertex is (-1, -3), so the equation could be y = a(x + 1)^2 - 3. The coefficient a determines the shape of the parabola.The vertex of a parabola is the point where the parabola crosses its axis of symmetry.   If the coefficient of the x2  term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.  If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.

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Answer:

See attachment

Step-by-step explanation:

The given parametric equations are;

[tex]x=2t[/tex] and [tex]y=t+5[/tex], [tex]-2\le t\le 3[/tex].

We can graph this by plotting some few points within the given range or eliminate the parameter to identify the type of curve.

Plotting points;

When [tex]t=-2[/tex],

[tex]x=2(-2)=4[/tex] and [tex]y=-2+5=3[/tex]

This gives the point (-4,3).

When [tex]t=0[/tex]

[tex]x=2(0)=0[/tex] and [tex]y=0+5=5[/tex]

This gives the point (0,5).

When [tex]t=3[/tex]

[tex]x=2(3)=6[/tex] and [tex]y=3+5=8[/tex]

This gives the point (6,8).

We plot these points and draw a straight line through them.

Eliminating the parameter.

[tex]x=2t[/tex]

[tex]y=t+5[/tex]

Make t the subject in the second equation;

[tex]t=y-5[/tex]

Substitute into the first equation;

[tex]x=2(y-5)[/tex]

This implies that;

[tex]x=2y-10[/tex]

[tex]y=\frac{1}{2}x+5[/tex]

This is an equation of a straight line with slope [tex]\frac{1}{2}[/tex] and y-intercept 5 on the interval

[tex]-4\le x \le 6[/tex]

Answer:

The answer is in attachment

Step-by-step explanation:

First step finde a function t(x) ⇒ t=x/2;

Now we need to finde the limits of that function:

if t=-2 ⇒ x=-4 and t=3 ⇒ x=6. That means -4≤x≤6

Now replace on y(t) ⇒ y(x)= x/2+5, 4≤x≤6

Answer:

2π/3, 4π/3

Step-by-step explanation:

I interpret your question as asking us to solve the equation

2cos(x) + 1 = 0

2cos(x) = -1

cos(x) = -½x  

x = arccos(-½), 0 ≤ x ≤2π

Since the cosine is negative, x must be in the second or third quadrant.

Referring to the unit circle, we find that

x = 2π/3 (120°) or x = 4π/3 (240°)

answer is: a number to the third power divided by ten. pls mark brainliest!!

Answer:

height  = (x^3 – 3x^2 + 5x – 3) / (x^2 – 2)

Step-by-step explanation:

We know that the volume of a rectangular prism is the product of its base area and height

Volume_prism = area_base *  height

height =  Volume_prism /  area_base

Volume_prism  = (x^3 – 3x^2 + 5x – 3)

area_base = (x^2 – 2)

height =  Volume_prism /  area_base

height  = (x^3 – 3x^2 + 5x – 3) / (x^2 – 2)

Please see attached image

Answer:

The answer is A

Step-by-step explanation:

The way that you get this answer is by divided x2 to x3 and you get x and then you multiply x to x2-2 and you get x3-2x and the you subtract that from x3-3x2+5x-3 and then you repeat that process and the final answer is x-3 + 7x-9/x2-2

Answer:

B) translation 2 units to the right

B) reflection across the y-axis

Step-by-step explanation:

If you move ABCD over to the right by 2, then reflect it over the y axis. Then you get the A'BCD.

ABC goes through a sequence of transformations to form A'B'C'. The sequence of transformations involved are

B) translation 2 units to the right  and followed by a

B) reflection across the y-axis

This can be explained by using the graph and the definition of transformation

Thus, from the graph it is clear that the sequence of transformations involved is B) translation by 2 units to the right and followed by a B) reflection across the y-axis.

Learn more about transformations here:

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Answer:

D

Step-by-step explanation:

The answer is D, since there is no correlation in the data (meaning that it is scattered all over the plot with no pattern or anything).

Answer:

[tex]p=6b[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

The perimeter of rectangle is equal to

[tex]P=2(x+y)[/tex]

[tex]P=p\ cm[/tex]

so

[tex]p=2(x+y)[/tex] -----> equation A

[tex]y=b\ cm[/tex] ----> given problem

[tex]x=2y[/tex] -------> [tex]x=2b\ cm[/tex]

substitute the value of x and the value of y in the equation A

[tex]p=2(2b+b)[/tex]

[tex]p=2(3b)[/tex]

[tex]p=6b[/tex]

Answer:

h = 12x^5y^3

Step-by-step explanation:

The area of a parallelogram is found using A = b*h. Substitute the values given and solve for h.

A = b*h

36x^6 y^5 = 3xy^2 * h

36x^6 y^5 ÷ 3xy^2 = h

12x^5y^3 = h

To solve the system of equations, start by isolating one variable in one equation. Substitute the value of the variable into the other equation, and solve for the remaining variable. The solution to the system of equations is x = 118/17 and y = -42/17.

To solve the given system of equations:

4x - 5y = 10

-x - 8 = 3y

Therefore, the solution to the system of equations is x = 118/17 and y = -42/17.

Final answer:

The solution to the system is x = -10/7 and y = -22/7.

Explanation:

To solve the given system of equations, 4x-5y=10 and -x-8=3y, we can use the method of substitution or elimination. Let's use the substitution method:

Step 1: Solve one equation for one variable in terms of the other. From the second equation, we can rearrange it to get x in terms of y: x = 3y + 8.

Step 2: Substitute the expression for x in terms of y into the other equation.

Substituting 3y + 8 for x in the first equation gives us 4(3y + 8) - 5y = 10.

Step 3: Simplify and solve for y.

Expanding the equation and solving for y gives us 12y + 32 - 5y = 10.

Combining like terms yields 7y + 32 = 10.

Subtracting 32 from both sides gives us 7y = -22.

Dividing both sides by 7 gives us y = -22/7.

Step 4: Substitute the found value of y back into the equation x = 3y + 8 to solve for x.

Substituting -22/7 for y gives us x = 3(-22/7) + 8.

Simplifying the expression gives us x = -66/7 + 56/7, which equals -10/7.

Therefore, the solution to the system of equations is x = -10/7 and y = -22/7.

Answer:

it is b

Step-by-step explanation:

B.) The area is 3 times greater I think

yes, 0.64 is a rational number. it can be expressed as the fractions 64/100, 32/50, 16/25.

Answer:

yes 0.64 is a rational number

Step-by-step explanation:

1) 0.64 = 64/100

2) Divide by 4

64 divided by 4 is 16 (Numerator)

100 divided by 4 is 25 (Denominator)

3) 16/25

It is a rational number because it can be written as a fraction.

Hopes this helps!

Answer:

45

Step-by-step explanation:

Use the geometric sum formula for in infinite sum. 20 terms of this basic formula is close enough The 20th term is 8.6 * 10^-10 which means this goes out to a number with 9 zeros after the decimal and before the 8.

Put another way, the tenth number of this series is the only one affected.

When you use a spreadsheet, it seems to know that the answer is 3/2 as the solution to the sum.

Solution.

Sum = a / (1 - r)

a = 1

r = 1/3

Sum = 1 / (1 - 1/3)

Sum = 1 // 2/3

sum =  3/2

Now you can worry about the 30.

30 * sum(1/3)^n = 30* 3/2 = 45

If there is something you want more information on, leave a note.

The sum of a finite geometric sequence can be calculated using the formula S = a1(1 - r^n) / (1 - r), where S is the sum, a1 is the first term, r is the common ratio, and n is the number of terms.

The student's question pertains to the summation of a finite geometric sequence. A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. Considering the information provided doesn't match the exact question, we would educate the student on how to find the sum of a finite geometric sequence using the standard formula for such a sum, which is S = a1(1 - r^n) / (1 - r), where S is the sum of the sequence, a1 is the first term, r is the common ratio, and n is the number of terms.

Unfortunately, specific values were not provided in the question. Therefore, to calculate the sum, we'd need the initial term, the ratio, and the number of terms. This formula is only applicable if the common ratio r is not equal to 1. Essential to note is that if the common ratio is greater than 1, the terms in the sequence increase, and if the ratio is between 0 and 1, the terms decrease.

Answer:

a) As x decreases within bound, f(x) increases without bound.  

c) as x increases without bound,f(x) approaches the line y = - 4

Step-by-step explanation:

From the graph, we can see, as x becomes more negative, y gets larger and larger.  

As x→ -∞, y → ∞

As x decreases without bound, y increases without bound

We can also see as x gets larger and larger, y gets closer to -4

As x →∞, y → -4

As x increases without bound, y approaches -4

As x decreases within a limit, f(x) increases without bound.

The correct statement in this question is a) As x decreases within bound, f(x) increases without bound.

To understand this concept better, we can look at the graph of the function y = 1/x. As x approaches zero (within the bound), the value of y increases without bound, meaning it becomes very large and approaches infinity.

Other functions can also exhibit similar behavior where as x decreases within a limit, the corresponding values of f(x) increase without bound.

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x2 + 5x + 6 = 0

(x + 2)(x + 3) = 0

x = -2 or -3

Answer:

x = - 3, x = - 2

Step-by-step explanation:

Given

x² + 5x = - 6 ( add 6 to both sides )

x² + 5x + 6 = 0 ← in standard form

(x + 3)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x + 2 = 0 ⇒ x = - 2

Answer:

-8i

Step-by-step explanation:

To multiply numbers is polar form

z1 = r1 ( cos theta 1 + i sin theta 1)

z2 = r2 ( cos theta 2 + i sin theta 2)

z1*z2 = r1*r2 (cos (theta1+theta2) + i sin (theta1+theta2)

z1 = 2(cos 70° + i sin 70°)

z2 = 4(cos 200+ i sin 200)

z1z2 = 2*4 (cos (70+200) + i sin (70+200)

z1z2 = 8 (cos(270) + i sin (270))

       = 8 (0 + i (-1))

       =-8i

The product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°), is found by multiplying the moduli and adding the angles, resulting in -8i.

To find the product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°), we use the properties of complex numbers in trigonometric form. According to the properties, the product of two complex numbers in this form is given by multiplying their moduli (or absolute values) and adding their angles.

The product is: |z1||z2| e[tex]^{(i(angle1+angle2)),}[/tex] where |z1|, |z2| are the moduli of z1 and z2, and angle1, angle2 are the angles of z1 and z2 respectively.

For z1 and z2, we have:

The product is:

|z1||z2| = 2 * 4 = 8

Sum of the angles: angle1 + angle2 = 70° + 200° = 270°

Therefore, z1z2 = 8(cos 270° + i sin 270°), and since cos 270° = 0 and sin 270° = -1, the product simplifies to z1z2 = 8i(-1) = -8i.