Which of the following options is an equivalent function to f(x) = 3(2)3x?

f(x) = 3(8)x
f(x) = 24x
f(x) = 27(8)x
f(x) = 3(8x)

The height of the sail in feet is 24 feet.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

Look at the triangle ABC below, where we have

BC² = AB² + AC²​​.

The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation. It should be remembered that a right-angled triangle's hypotenuse is its longest side.

Given:

Base = 10 feet

Hypotenuse = 26 feet

Using Pythagoras theorem

H² = P² + B²

P²= (24)² - (10)²

P² = 676 - 100

P² = 576

P=√576

P= 24 feet

hence, height of the sail in feet is 24 feet.

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Answer:

its 282.6 sq cm

Step-by-step explanation:

AL=2πrh=2·π·3·15≈282.74334

The question's topic is about converting volume from cups to quarts. In this particular case, 15 cups of chicken stock is equal to 3.75 quarts.

The subject of this question is the conversion of volume from cups to quarts. In this case, the chicken soup recipe calling for 15 cups of chicken stock needs to be converted into quarts. We know that 1 quart is equal to 4 cups, so we can set up the equation:

4 cups/1 quart = 15 cups/x quarts

To solve for x, we multiply 15 (cups) by 1 (quart) and then divide by 4 (the number of cups in a quart).

Therefore, x = (15*1)/4 = 3.75 quarts. So, 15 cups of chicken stock is equal to 3.75 quarts.

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The number 0.2 x 10⁶ in scientific notation is written as 2 x 10⁵.

To write the number 0.2 x 10⁶ in scientific notation, we need to convert it into a format that has one non-zero digit to the left of the decimal point, followed by the appropriate exponent of 10.

The given number, 0.2 x 10⁶, is already close to scientific notation, however, we typically want the first number to be between 1 and 10. In this case, we can express 0.2 as 2 x 10⁻¹. Multiplying this by 10⁶ gives us:

2 x 10⁻¹ x 10⁶ = 2 x 10⁽⁶⁻¹⁾ = 2 x 10⁵.

So, the number 0.2 x 10⁶ in scientific notation is 2 x 10⁵.

Answer:

Given function is [tex]y=a(x-h)^2+k[/tex] ...........(1)

We re write the function,

transfer k to LHS,

[tex]y-k=a(x-h)^2[/tex]

Since, One variable has degree 2 and one variable has degree 1.

⇒ Function Represent the equation of Parabola.

In given Function,

Coordinates of vertex is ( h , k )

So To, find the vertex of the function.

First we rewrite the function in vertex form that is like equation (1) then we compare them and write the coordinate of the vertex.

For Example,

1. y = 2(x - 2)² + 6 then vertex of the function is ( 2 , 6 )

2. y = -3 ( x + 3 )² - 6

    y = - 3 ( x - (-3) )² + ( -6) then vertex of the function is ( -3 , -6 )

The solution is store A

The store which sells the bicycle with a better rate is store A with a price of  $ 40.00 for two bicycles

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first store be represented as A

Let the second store be represented as B

Now , the equation will be

The price of 2 bicycles at store A = $ 40.00

So ,

The price of 1 bicycle at store A = price of 2 bicycles at store / 2

Substituting the values in the equation , we get

The price of 1 bicycle at store A = 40/2

The price of 1 bicycle at store A = $ 20

Now ,

The price of 5 bicycles at store B = $ 110

So ,

The price of one bicycle at store B = The price of 5 bicycles at store B / 5

Substituting the values in the equation , we get

The price of one bicycle at store B = 110/5

The price of one bicycle at store B = $ 22

And ,

The price of one bicycle at store B > The price of 1 bicycle at store A

22 > 20

Hence , the store A provides better rate for the price of one bicycle

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- Independent quantity: Number of hours worked per week

- Dependent quantity: Earnings per week

- Domain: 20 ≤ hours ≤ 25

- Range: $180 ≤ earnings ≤ $225

In this situation:

- Independent quantity: The number of hours Wendy plans to work per week

- Dependent quantity: The amount of money she earns per week

Reasonable domain and range values:

- Domain: The reasonable range of values for the number of hours Wendy works per week is between 20 and 25 hours. This is because she plans to work between 20 and 25 hours per week.

- Range: The amount of money Wendy earns per week depends on the number of hours she works. The range of values for her earnings can be calculated by multiplying the number of hours worked by her hourly rate of $9. Therefore, the range of values for her earnings per week will be between $180 (20 hours * $9) and $225 (25 hours * $9).

To summarize:

- Independent quantity: Number of hours worked per week

- Dependent quantity: Earnings per week

- Domain: 20 ≤ hours ≤ 25

- Range: $180 ≤ earnings ≤ $225

The unit rate is calculated by dividing the distance run by the time taken. In this case, the unit rate is 5.4 miles per hour, indicating that the student runs 5.4 miles for every hour they run.

To find the unit rate, we first convert the distance to a decimal. So, 3 3/5 miles becomes 3.6 miles. Unit rate is the ratio of the amount of a single unit of an item to its cost. In this case, your unit rate is the distance you run (in miles) per unit of time (in minutes).

Now, you should divide the total distance (3.6 miles) by the time (40 minutes). 3.6 miles / 40 minutes = 0.09 miles per minute.

If you want the unit rate per hour (commonly used), you should multiply this result by 60 (as there are 60 minutes in an hour). 0.09 miles per minute * 60 minutes/hour = 5.4 miles/hour.

So, your unit rate is 5.4 miles per hour, meaning you run 5.4 miles for every one hour of running.

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The perimeter of the figure is 58 feet if the missing side length is 10 feet.

It is defined as the length of the circumference or outline of the geometry. It is the sum of the all side measures.

We have a two-dimensional geometry in the picture with dimensions.

The missing side length  = 15 - 5 = 10 ft

The perimeter of the figure = 5+7+10+10+15+11

= 58 feet

Thus, the perimeter of the figure is 58 feet if the missing side length is 10 feet.

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A polygon can grow from one-dimensional objects, which are lines. Zero-dimensional objects, which are points or vertices, also play a role as they define the positions where lines meet, but a polygon cannot directly grow from three-dimensional objects because polygons are two-dimensional shapes.

A polygon can grow from one-dimensional objects, specifically from lines. In geometric terms, a polygon is a two-dimensional shape that is formed by connecting straight line segments. Each line segment connects to two others to form the polygon's perimeter. Moreover, the line segments join at their endpoints, known as vertices, which are zero-dimensional objects that contain only a single coordinate pair.

The formation of a polygon from lines is analogous to constructing a shape on a piece of paper by drawing lines that connect to form a closed loop. In this process, the lines are the sides of the polygon, and the points where the lines meet are the vertices. It is not possible for a polygon to directly grow from three-dimensional objects, as polygons are inherently two-dimensional.

For example, to represent a soccer ball in a simplified manner such as in geographic information systems (GIS), we can use polygons in the shape of pentagons and hexagons. The soccer ball itself is a three-dimensional object but the representation involving pentagons and hexagons is a two-dimensional schematic, emphasizing the importance of polygons in various mapping and modeling applications.

A scatter plot depicting height and age reveals trends: positive correlation if points slope up, negative if down, none if scattered. Regression lines aid age prediction from height. The plot guides decisions by identifying patterns and outliers, supporting informed conclusions based on observed relationships.

Steps to interpret a scatter plot of a person's height and age:

1. **Scatter Plot Description:**

  - Axes: Height on the y-axis, Age on the x-axis.

  - Each point represents an individual's height and age.

  - Scatter points may form a pattern or cluster.

2. **Trends and Interpretation:**

  - **Positive Correlation:** If the points generally slope upward from left to right, it suggests a positive correlation—taller people tend to be older.

  - **Negative Correlation:** If the points slope downward, it implies a negative correlation—taller people tend to be younger.

  - **No Correlation:** If the points seem randomly scattered, there may be no apparent correlation.

3. **Predicting Age from Height:**

  - Fit a regression line to the data. A linear regression line can be used to predict age given height.

  - For a given height, find the corresponding point on the regression line to estimate the age.

4. **Identifying Trends and Decision Making:**

  - **Patterns:** Identify patterns and correlations between variables.

  - **Outliers:** Notice any data points significantly deviating from the trend.

  - **Decision Support:** Use the trends to make informed decisions. For instance, if there's a correlation between height and age, you might anticipate certain health issues associated with age.

Scatter plots are powerful visual tools to analyze relationships between variables, identify trends, and make predictions or informed decisions based on observed patterns.

The area and the circumference of the given circle are 38.5 cm² and 20 cm respectively.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given that, a circle with radius 3.5 cm, we are asked to find the circumference and the area of the given circle,

Area of a circle = π × radius²

Circumference of a circle = 2π × radius

1) Area =

π × 3.5²

= 3.14 × 12.25

= 38.465

≈ 38.5 cm²

2) Circumference =

2π × 3.5

= 2 × 3.14 × 3.5

= 21.98

≈ 20 cm

Hence, the area and the circumference of the given circle are 38.5 cm² and 20 cm respectively.

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The reciprocal of the fraction 5/8 is 8/5.

We have,

Fraction:

5/8

Now,

To find the reciprocal of a fraction we write as,

x = 1/x

Now,

x = 5/8

So,

1/x

= 1/(5/8)

= 8/5

Thus,

The reciprocal of the fraction 5/8 is 8/5.

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To find out the different orders four cars can finish a race, we calculate the permutations, which is 4 factorial, resulting in 24 different orders.

The student is asking about the number of different ways that four cars can finish a pinewood derby race, which is a question of permutations in mathematics. In this case, we want to find out the number of possible arrangements for the four cars crossing the finish line. Since each car is distinct, the number of permutations of four items is given by 4! (4 factorial), which is calculated as 4 × 3 × 2 × 1.

Therefore, there are 24 different orders in which the cars can cross the finish line. Remember, factorial is a mathematical operation that involves multiplying a sequence of descending natural numbers.

The exact value of cos 15° is (√6 - √2)/4.

To find the exact value of cos 15°, we can use the trigonometric identities and special angles to determine its value.

One of the key identities that can be used is the cosine addition formula: cos (A + B) = cos A x cos B - sin A x sin B.

We can rewrite 15° as the sum of two special angles: 15° = 45° - 30°.

Using the cosine addition formula, we have:

cos 15° = cos (45° - 30°) = cos 45° x cos 30° - sin 45° x sin 30°.

Now, we know the exact values of cos 45° (which is (√2)/2), cos 30° (which is (√3)/2), sin 45° (which is (√2)/2), and sin 30° (which is 1/2).

Substituting these values into the equation, we get:

cos 15° = (√2)/2 x (√3)/2 - (√2)/2 x 1/2.

Simplifying further, we have:

cos 15° = (√6 - √2)/4.

This means that cos 15° can be expressed exactly as (√6 - √2)/4 without any decimal approximation.

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Answer:

the answer is check2+check6/4

Step-by-step explanation:

i took an exam and got it right

(i dont know what those check mark things are called or how to put the actual thing on a computer so hopefully you understand the check part)