Evaluate the expression. (7 − 3)!

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)

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

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.

Learn more about inequalities on

https://brainly.com/question/24372553

#SPJ1

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

Read more about right triangle at

brainly.com/question/2437195

#SPJ1

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.

To know more about three-column table:

https://brainly.com/question/30422989

#SPJ1

The incorrect statement is the reflection is over x-axis.

Given that an image has been reflected to form another image, we need to find the incorrect statement from the given options,

A reflection is known as a flip.

A reflection is a mirror image of the shape.

An image will reflect through a line, known as the line of reflection.

A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

Learn more about transformations, click;

https://brainly.com/question/11709244

#SPJ1

The incorrect statement is the reflection is over x-axis.

Given that,

an image has been reflected to form another image, we need to find the incorrect statement from the given options,

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

Learn more about transformations, click;

brainly.com/question/11709244

#SPJ1

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.

Learn more about the equation here:

https://brainly.com/question/28243079

#SPJ1

The complete question is:

Solve the logarithmic equation.

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

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

Read more about surface area of prism at: https://brainly.com/question/1297098

#SPJ1

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.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1

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.

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

Read more about probability at

https://brainly.com/question/251701

#SPJ1

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 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.

Learn more about solutions of equations here:

https://brainly.com/question/545403

#SPJ1

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 balloon's vertical distance above the ground is given as follows:

h = 10.7 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 24º, we have that:

Hence the height is obtained as follows:

tan(24º) = h/24

h = 24 x tangent of 24 degrees

h = 10.7 ft.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

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).

To learn more about : area

https://brainly.com/question/25292087

#SPJ11

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.

To solve more questions on unit conversion, visit the link-

brainly.com/question/11805053

#SPJ1

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

To know more about area of figure:

https://brainly.com/question/23718948

#SPJ1

a. The range of data is 37 (max: 83, min: 46).

b. The box-and-whisker plot:

Min: 46  Q1: 53  Median: 61  Q3: 68  Max: 83

---|----|----|----|----|----|----|----|----|---

46  53  61  68  83

c. The five-number summary:

Minimum (46): Lowest speed recorded.

First Quartile (Q1 - 53): 25% of the cars were traveling at 53 mph or below.

Median (61): The middle value in the dataset, meaning 50% of cars were traveling at or below 61 mph.

Third Quartile (Q3 - 68): 75% of the cars were traveling at 68 mph or below.

Maximum (83): Highest speed recorded.

d. The IQR (Q3-Q1 = 68-53 = 15) tells you the spread of the middle 50% of the speeds. It gives an idea of how varied the speeds are in the dataset.

e. Since the majority of recorded speeds (more than 50% - based on the median) are above the 50 mph speed limit, the residents should be concerned about speeding.

Read more about range here:

https://brainly.com/question/24326172

#SPJ1

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

Read more about exponential function at

https://brainly.com/question/2456547

#SPJ1

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.

More can be learned about consecutive interior angles at https://brainly.com/question/24839702

#SPJ1

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.

To learn more on angle click:

brainly.com/question/28451077

#SPJ1

complete question:

Find the value of each variable

The value of the k is; 1/12

The proportion is given by the expression;

y = kxz

Given the values;

y=6 when x=4 and z=12

To find the constant, k;

6 = k*4*12

6= 48k

k = 4/48

k = 1/12

More can be learned about proportions at;

brainly.com/question/24372153

#SPJ1

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

Learn more about the line of best fit here:

https://brainly.com/question/29250235

#SPJ1

Find the complete question below.

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

To learn more about combinations click :

https://brainly.com/question/28065038

#SPJ1

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

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.

Learn more about pyramids, click;

https://brainly.com/question/13057463

#SPJ1