Review the geometric sequence below and determine the pattern: 1/4, 1/2, 1, 2, 4, 8

By using the division property of equality we can divide both sides by -12 to get the solution x = -4

An equation:

A = B

Says that the number A is equal to the number B, so basically, are the same number.

So, if we divide both A and B by the same number C, we will get:

A/C and B/C

And A and B are the same numbers, then A/C and B/C also are the same numbers.

So in an equation, we can divide both sides by the same number (except 0) and the equation will not change.

In this case we have:

-12*x = 48

We could divide both sides by -12, so we will get:

-12*x/-12 = 48/-12

x*(-12/-12) = -4

x = -4

And thus we used the division property of equality to solve the equation.

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Answer:

Step-by-step explanation:

This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:

ln(e^x) = x-1

In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:

ln(10^(x-1)) = x-1

e^(x-1) = 10^x

The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.

Answer:

\(6x^4y^8\sqrt{5x}\)

Step-by-step explanation:

\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)

\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)

\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)

\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)

\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)

\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)

\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)

\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)

\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)

\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)

\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)

\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(6 \sqrt{5x}\;x^4\;y^8\)

\(\textsf{Rearrange:}\)

\(6x^4y^8\sqrt{5x}\)

\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)

\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)

The period of the function f(t) = 2.3cos(0.25t) is 8π. Hence, the correct answer is d) period 8π.

To determine the period of the function f(t) = 2.3cos(0.25t), we need to consider the coefficient of t inside the cosine function.

In this case, the coefficient is 0.25, which represents the frequency of the cosine function. The period of a cosine function is given by the formula T = 2π/frequency.

Using this formula, we can calculate the period of the function f(t) as follows

T = 2π / 0.25

T = 8π

Therefore, the period of the function f(t) = 2.3cos(0.25t) is 8π.

Hence, the correct answer is d) period 8π.

The period of a function represents the length of one complete cycle or the distance between two consecutive identical points on the graph of the function. In this case, the function is a cosine function, and the period determines how long it takes for the function to repeat its values

The coefficient 0.25 in the function f(t) = 2.3cos(0.25t) affects the frequency of the cosine function. A smaller coefficient results in a slower oscillation, while a larger coefficient leads to a faster oscillation. In this case, since the coefficient is 0.25, it means that the function completes one full cycle within 8π units of time.

Understanding the period of a function is crucial for analyzing its behavior, identifying the frequency of oscillation, and studying its repetitive patterns.

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Answer:

The zeroes are at (-2, 0), (0, 0) and (2, 0).

The (0, 0) is a double root as the graph just touches the x axis at (0, 0).

The zero at (0, 0) is sometimes referred as  x = 0 (multiplicity 2).

I think the duplicate roots are counted as 2 distinct roots but im not sure.

So the answer is either a or c.

Step-by-step explanation:

The zeroes are the points where the graph cuts the x axis.

Answer:

a

Step-by-step explanation:

The angle of sinθ between the horizontal vector (1, 0) and the slant vector (15/17, -8/17) is sin⁻¹(8/17), which is approximately 29.11 degrees.

To find the angle of sinθ between a horizontal vector and a slant vector, we can use the dot product formula:

a · b = |a| |b| cos(θ)

where a and b are vectors, |a| and |b| are their magnitudes, and theta is the angle between them.

In this case, the horizontal vector is (1, 0) and the slant vector is (15/17, -8/17).

The magnitude of the horizontal vector is 1, and the magnitude of the slant vector is:

|b| = sqrt((15/17)² + (-8/17)²) = sqrt(225/289 + 64/289) = sqrt(289/289) = 1

The dot product of the two vectors is:

a · b = (1)(15/17) + (0)(-8/17) = 15/17

So we have:

15/17 = (1)(1) cos(θ)

cos(θ) = 15/17

To find sin(θ), we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

sin²(θ) = 1 - cos²(θ) = 1 - (15/17)² = 64/289

Taking the square root of both sides, we get:

sin(theta) = sqrt(64/289) = 8/17

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The value of 6 1/2 divided by 1 2/3 is 3 9/10

From the question, we have the following parameters that can be used in our computation:

6 1/2 divided by 1 2/3

When represented as an expression, we have

6 1/2 / 1 2/3

Convert to improper fractions

13/2 / 5/3

Express as products

13/2 * 3/5

So, we have

39/10

Express as mixed number

3 9/10

Hence, the solution is 3 9/10

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Answer:

25

Step-by-step explanation:

it is alternate interior

same thing

65-25=40

2×25-10=40

Answer:

\(92.05^{\circ}\)

Step-by-step explanation:

By the exterior angle theorem, the answer is \(m\angle Y+m\angle Z=92.05^{\circ}\).

Answer:

A

Step-by-step explanation:

exterior angle = sum of the other two angles

63.25 + 28.8

92.05°

Explanation

In the question, we are given that Mrs.Singh purchased 31 softcover books and hardcover books. Let softcover books and the hardcover book be x and y respectively.

Therefore;

Also, each softcopy book costs $3.50 and hard copy books cost $14.50.

The next step is to solve the simultaneous equation.

Substitute equation iii into ii

Next, we substitute the value of y in equation iii

Therefore the answers are:

Soft cover books: 19 books

Hard coverbooks: 12 books

Answer:

7/8 is larger than 5/6

Step-by-step explanation:

If you divide the numerator by the denominator of each given fraction:

7/8 = 0.875

5/6 = 0.833

We can easily see that 0.875 > 0.833.

Therefore, 7/8 is larger than 5/6.

Answer:

7/8 is bigger than 5/6, I hope this helps :)

Answer:

Step-by-step explanation:

Formula: A=πr2

3.14 x 17^2 = 907.46 in2

Answer:

x=4

Step-by-step explanation:

The value of x from the given similar triangles is 7 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

The given triangles ABC and DEF are similar triangles.

Here, AB/DE =AC/DF =BC/EF

4/12 =8/3(x+1)

8/3(x+1) =1/3

24=3x+3

3x=24-3

3x=21

x=7

Therefore, the value of x is 7 units.

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Answer:

The correct answer is D. 0 + 1 = 1

Step-by-step explanation:

To determine the correct option, we must first perform the calculation raised in the question:

2/9 + 10/11 = X

0.22 + 0.9 = X

1.12 = X

Thus, rounded to the nearest whole number, this mathematical operation would be similar to option D, which raises the sum of 0 + 1. This is because 0.22 is rounded to 0, while 0.90 is rounded to 1.

The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

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Answer:

\(h(x)=-5x^2+10x-2\)

Step-by-step explanation:

\(h(x) = -5 (x - 1)^2 + 3\\\\\implies h(x) = -5 (x - 1)^2 + 3\\\\\implies h(x)=-5(x^2-2x+1)+3\\\\\implies h(x) = -5x^2+10x-5+3\\\\\implies h(x)=-5x^2+10x-2\)

Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

\( - 16 = a - 19\)

\(a = - 16 + 19\)

\(a = 3\)

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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Answer:

0.0555 meter =

55.5 millimeters

Answer:

55.5mm

Step-by-step explanation:

60 is thaks for points

Step-by-step explanation:

I think

Answer:

The top choice

Step-by-step explanation:

1/2 x -2 > 0

Add 2 to each side

1/2 x -2+2 > 0+2

1/2 x > 2

Multiply each side by 2

1/2 x *2 > 2*2

x > 4

There is an open circle at 4 and the line goes to the right

Answer:

It is the first option everything to the right of 4.

Step-by-step explanation:

Answer:

8xy

Step-by-step explanation:

Subtract -13xy from -5xy

-5xy - (-13xy) =

-5xy + 13xy =

8xy

good luck, i hope this helps:)

Answer:

-3/2

Step-by-step explanation:

the constant of variation is commonly known as k .

y/x= k

so -3/2 is your answer

Answer:

it is a

Step-by-step explanation:

Answer:

What percent of the large square is shaded? The grid is divided into 10 rectangles. For percents, you need to look at 100 equal-sized parts of the whole

Step-by-step explanation:

First, we need to find the z-value for a probability of 95%.

Looking at the z-table, for p = 0.95 we have z = 1.645.

Then, to find the table clearance, we can use the formula below:

Since the mean is equal to 21.5 inches and the standard deviation is equal to 1.3 inches, we have:

Rounding to one decimal place, we have x = 23.6 inches.