Write the equation of the exponential function that has a y-intercept of 3 and a growth factor of 1.25.

The total surface area of the triangular figure is S = 160 m²

Given data ,

Let the total surface area of the triangular figure be S

Now , the area of the base be A

where the side length of the base a = 8 m

So , the area of base A = 8²

A = 64 m²

Now , the height of the triangle = 6 m

The base of the triangle = 8 m0

Now , the area of the four triangles = 4 ( 1/2 ) ( 6 ) ( 8 )

Area of four triangles = 96 m²

Therefore , the total surface area S = 64 + 96

S = 160 m²

Hence , the surface area of figure is 160 m²

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Answer: 17/5 or 3 2/5

Step-by-step explanation:

You separate the whole numbers from the fractions.

8-5=3 and 4/5-2/5=2/5

Then you combine the fraction with the whole number:

3 2/5 or 17/5 as a mixed fraction.

The best descriptions that suits a pyramid is option B.

Pyramids have triangular faces and a polygonal base.

A pyramid is a 3D figure built with a base of a polygon and triangular faces all connected together. A pyramid connects each vertex of the base to a common tip or apex giving it the typical shape.

A pyramid is made by connecting the base to the apex. Sometimes, the triangular sides are also called lateral faces to distinguish them from the base. In a pyramid, each edge of the base is connected to the apex that forms the triangular face.

Hence the correct option is B.

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The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable

We need 1.5 or 3/2 full cones to fill the cylinder completely.

We have,

Let's assume that the diameter and height of the cylinder are D and H, respectively.

Since the cone has the same diameter as the cylinder, its radius is half of the diameter or D/2.

Since the cone has half of the height of the cylinder, its height is H/2.

The volume of the cylinder is given by the formula.

V cylinder = π(D/2)² H.

The volume of the cone is given by the formula.

V cone = 1/3 π(D/2)² (H/2).

To fill the cylinder completely with water using the cone, we need to find out how many cones are required to fill the cylinder.

Let's set up an equation using the volumes of the cylinder and cone:

Number of cones needed = V cylinder / V cone

Substituting the formulas for the volumes.

Number of cones needed = [π(D/2)² H] / [1/3 π(D/2)² (H/2)]

Simplifying this expression, we get:

Number of cones needed = 3(H/2) / H

Number of cones needed = 3/2

Therefore,

We need 1.5 or 3/2 full cones to fill the cylinder completely.

Since we cannot have half a cone, we need 2 full cones to fill the cylinder completely.

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The calculated value of x in the right triangle is 8

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

The right triangle

The value of x can be calculated by using the corresponding sides of similar triangles

Using the similarity theorem of triangles, we have the following equation

x/2√6 = 2√6/3

When both sides are cross muliplied, we have the following equation

3x = 4 * 6

Divide both sides by 3, we get

x = 4 * 2

Evaluate the product of 4 and 2

x = 8

Hence, the value of x is 8

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The value of x is given as follows:

x = 26.

To obtain the value of x, first we must consider that the angle between the two lines, to the left of the transversal line, is congruent to the angle of 5x - 7.

Then the angle stated above is a consecutive interior angle with the angle of (2x + 5)º, meaning that they are supplementary angles, that is, the sum of their measures is of 180º.

Hence the value of x is obtained as follows:

5x - 7 + 2x + 5 = 180

7x = 182

x = 182/7

x = 26.

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The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable

The solutions of the equation are p = -7 + √87 and p = -7 - √87.

We have,

To solve by completing the square, we want to rearrange the equation so that the left side is a perfect square trinomial.

Here are the steps:

- Move the constant term (-38) to the right side:

p² + 14p = 38

- Take half of the coefficient of p (which is 14) and square it:

(14/2)² =  49

- Add and subtract this value to the left side of the equation:

p² + 14p + 49 - 49 = 38

- Simplify the left side by factoring the perfect square trinomial:

(p + 7)² - 49 = 38

- Add 49 to both sides of the equation:

(p + 7)² = 87

- Take the square root of both sides of the equation, remembering to include both positive and negative roots:

p + 7 = ±√87

Solve for p:

p = -7 ± √87

Therefore,

The solutions are p = -7 + √87 and p = -7 - √87.

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The solution to the logarithmic equation log₂(x + 4) + log₂(3) = log₂(8) + log₂(2x − 5) is x = 4

Consider the logarithmic equation,

log₂(x + 4) + log₂(3) = log₂(8) + log₂(2x − 5)

We need to solve this equation for x.

Here, the base of logarithm is 2.

Applying product rule of logarithm to log₂(x + 4) + log₂(3) we get,

log₂(x + 4) + log₂(3) = log₂(3(x + 4))

So, our equation becomes,

log₂(3(x + 4)) = log₂(8) + log₂(2x − 5)

log₂(3x + 12) = log₂(2³) + log₂(2x − 5)             .......(2³ = 8)

log₂(3x + 12) = 3log₂(2) + log₂(2x − 5)

log₂(3x + 12) = (3 × 1) + log₂(2x − 5)

log₂(3x + 12) -  log₂(2x − 5) = 3

Applying power identity of logarithm to  -log₂(2x − 5) we get,

-log₂(2x − 5) = 1 / [log₂(2x − 5)]

So, our equation becomes,

log₂(3x + 12) + [1 / log₂(2x − 5)] = 3

Applying product rule of logarithm to  log₂(3x + 12) + [1 / log₂(2x − 5)] we get,  log₂(3x + 12) + [1 / log₂(2x − 5)] =  log₂[(3x + 12) / (2x − 5)]

So, our equation becomes,

log₂[(3x + 12) / (2x − 5)] = 3

Now, exponentiate both sides.

(3x + 12) / (2x - 5) = 2³

(3x + 12) / (2x - 5) = 8

(3x + 12) = 8(2x - 5)

3x + 12 = 16x - 40

13x = 52

x = 4

This is the required value of x.

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The complete question is:

Solve the logarithmic equation.

log₂(x + 4) + log₂(3) = log₂(8) + log₂(2x − 5)

A catfish with a length of 45 inches would weigh 50 pounds.

From the attached scatter plot, the line of best fit passes through the points (25, 14) and (30, 23)

Using the two point form, the equation of line passing through points (25, 14) and (30, 23) would be,

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(y - 14)/(23 - 14) = (x - 25)/(30 - 25)

(y - 14)/(9) = (x - 25)/(5)

y - 14 = (9/5)x - (9 × 5)

y - 14 = (9/5)x - 45

y = (9/5)x - 45 + 14

y = (9/5)x - 31

For a length of 45 inches, the weight would be,

y = (9/5)(45) - 31

y = (9 × 9) - 31

y = 81 - 31

y = 50

Thus, the weight of the catfish = 50 pounds

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Find the complete question below.

The Inequality which ensure triangle exists is A. 7/4 < x < 11/2

Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.

Theorem used In ΔABC,

AB + BC >AC

AC+ BC >AB

AC + AB > BC

According to the question,

In triangle ABC.

AC = 18units

BC = 6x units,

AB = 2x + 4 units

Substitute the value in the inequality to ensure triangle exists we get 7/4 < x < 11/2. The correct option is A.

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2 pounds 6 ounces in ounces is equivalent to 38 ounces.

The given measurement is -

2 pounds 6 ounces

In 1 pound, there are 16 ounces.

So, we can write that -

2 pounds 6 ounces = 2 x 16 + 6

2 pounds 6 ounces = 38 ounces

So, 2 pounds 6 ounces in ounces is equivalent to 38 ounces.

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The area of the parallelogram is 35 square millimeters.

To find the area of a parallelogram, we multiply the base by the height. Given that the base of the parallelogram is 10 mm and the height is 3.5 mm, we can calculate the area as follows:

Area = base * height

Area = 10 mm * 3.5 mm

Area = 35 mm²

Therefore, the area of the parallelogram is 35 square millimeters.

It is also important to remember to include the units when giving the answer, which in this case is square millimeters (mm²).

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The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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The combination is solved and the number of ways of choosing 7 cards from a set of 48 cards is ⁴⁸C₇ = 85,900,584 ways

Given data ,

Let the number of ways of choosing 7 cards from a set of 48 cards be C

Now , the number of cards = 48 cards in deck

The number of selected cards = 7

From the combination , we get

The number of ways that a player can have 7 cards from a 48-card deck, we can use the formula for combinations:

n choose r = n! / (r! * (n-r)!)

where n is the total number of items and r is the number of items chosen.

In this case, n = 48 (the number of cards in the deck) and r = 7 (the number of cards dealt to each player). So we can plug in these values and simplify:

⁴⁸C₇ = 48! / (7! * (48-7)!)

Hence , the combination is ⁴⁸C₇ = 85,900,584 ways

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Answer:

Step-by-step explanation:

We know this is a combinations problem, so we have 48C7:

48C7=48!7!(48−7)!=48!7!41!=48⋅47⋅46⋅45⋅44⋅43⋅42⋅41!7⋅6⋅5⋅⋅⋅2⋅1⋅41!=73,629,072

That is, there are 73,629,072 ways to choose seven cards from forty-eight.

this is pt 2 of the knewton answer

To create a three-column table, draw three vertical lines and label each column with the appropriate category. Enter the information row by row, be consistent with formatting, and consider using shading or color to improve readability.

To create a three-column table

A three-column table is a way of organizing information into three columns or columns. Each column represents a different category or piece of information. For example, a three-column table might be used to show a list of names, ages, and cities.

Here's how to create a three-column table, Draw three vertical lines on a piece of paper or in a document to create three columns. Label the columns with the appropriate categories. For example, if you're creating a table to show names, ages, and cities, you would label the columns "Name," "Age," and "City."

Enter the information into the table. Start by entering the information for the first row, then move on to the next row until you have entered all the information. Be consistent with your formatting. Use the same font and font size for all the text in the table.

Align the text in the columns so that it is easy to read and compare information. Consider using shading or color to make the table more visually appealing and easier to read.

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

let me know if there's anything that's still confusing

The probability of rolling a 3 or getting heads is 0.67

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

Using the above as a guide, we have the following:

P(3) = 1/6

This is because there is only 1 face with number 3 in a die

Also, we have

P(Head) = 1/2

Using the above as a guide, we have the following:

P(3 and Head) = 1/6 + 1/2

Evaluate

P(3 and Head) = 0.67

Hence the probability is 0.67

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Answer:

56

Step-by-step explanation:

Kaden has 7 bags of animal toys.

Each bag has these animal toys in it.

• 1 whale toy

• 5 dolphin toys

• 2 turtle toys

Total number of toys in each bag: 1 + 5 + 2 = 8

Number of bags: 7

Total number of animals: 7 × 8 = 56

Answer: 7x 8=t and 7x(1+5+2)=t

Step-by-step explanation:

7x8=t. There are 7 bags with 8 (1+5+2) toys in each.

7x (1+5+2).  There are 7 bags with 1+5+2 (8) toys in each.

The money multiplier is the inverse of the reserve requirement ratio. If the Federal Reserve sets the reserve rate to 2%, the reserve requirement ratio is 0.02, and the money multiplier is 1/0.02, which equals 50. Therefore, the correct answer is A. 50.

The total surface area of the given triangular prism is: 72.5 in²

To get the surface area of this prism, what we will do is to find the area of each of the surfaces and add up to get the total surface area.

The formula for the area of a triangle is:

Area = ¹/₂ * b * h'

where:

b is base length

h is height

Total Surface Area = (¹/₂(5 * 5)) + 3(¹/₂*5*8)

Total Surface Area = (25/2) + 60

Total Surface Area = 72.5 in²

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The required simplified value of x is -377.

To solve for x in the given equation:

7 + √(-36 - 5x) = 250/5

First, simplify the right-hand side:

7 + √(-36 - 5x) = 50

√(-36 - 5x) = 43

Square both sides to eliminate the square root:

-36 - 5x = 1849

Solve for x:

x = (-1849 - 36)/5

x = -377

Therefore, the value of x is -377.

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Answer:

First, we need to isolate the radical term on one side of the equation:

7 + V(-36 - 5x) = 250

V(-36 - 5x) = 243    (subtract 7 from both sides)

-36 - 5x = 243^2     (square both sides)

-36 - 5x = 59049

-5x = 59049 + 36

-5x = 59085

x = -11817

Therefore, x = -11817.

After calculating the area of figure, we can conclude that it's area is 38.4 cm².

To find the figure of this area, we need to first divide the composite figure into two parts so that we can find it's area. So, it will be divided into a parallelogram and a rectangle.

Firstly, we will find the area of the parallelogram.

For parallelogram,

base = 4cm

height = 3.6 cm

area of parallelogram = base × height

= 4 × 3.6

= 14.4 cm²

Now, we will find the area of the rectangle:

We have been given Its length as 4cm and breadth as 6 cm

Area of rectangle = length × breadth

= 4 × 6

= 24 cm²

Now, to find the area of composite figure, we will add both the areas

Area of figure = Area of rectangle + area of parallelogram

= 24 + 14.4

= 38.4 cm²

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The exponential function in the form y= ab^x is y = 16(2)^7

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

Function that goes through points (0,16) and (7,2048)

An exponential function is represented as

y = ab^x

Where

a = y when x = 0

This means that

a = 16

So, we have

y = 16b^x

Using the other point, we have

16b^7 = 2048

Divide

b^7 = 128

So, we have

b = 7

So, the function is y = 16(2)^7

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