20!!!!! POINTS!!!!!!! The bar graph shows the strengths of tornadoes that occurred in Alabama in 2011. What percent of the tornadoes were EF1s?

Answers

Answer 1

The percentage of tornadoes that were EF1s is 40%.

What is the percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. The acronyms pct., pct., and occasionally pc are also used to indicate it, however, the percent sign is most frequently used. A % is a number without dimensions and without a standard measurement.

Here, we have

Given: the strengths of tornadoes that occurred in Alabama in 2011.

We have to find the percentage of tornadoes that were EF1s.

EF1s = 58

Total = 145

percentage of tornadoes = 58/145 = x/100

5800/145 = x

x = 40%

Hence, the percentage of tornadoes that were EF1s is 40%.

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Related Questions

Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)


What is the total net amount (in $) the supermarket owes the wholesaler for the order?

Answers

The total net amount the supermarket owes the wholesaler for the order is $231.31.

What does discount mean?

A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.

According to the given information

To find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.

The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:

Discounted cost = List price - (Discount rate x List price)

For the soup, the discounted cost per case is:

$18.90 - (0.39 x $18.90) = $11.51

For the baked beans, the discounted cost per case is:

$33.50 - (0.39 x $33.50) = $20.42

Now we can calculate the total net amount owed by the supermarket to the wholesaler:

Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)

Total net amount = (13 x $11.51) + (4 x $20.42)

Total net amount = $149.63 + $81.68

Total net amount = $231.31

Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.

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Chloe claims that Point A=−6 and Point B=1 . Which of the following statements provide support for Chloe's claim? Select ALL that apply. A A<0 because A is to the left of zero B A>0 because A is to the left of zero C A 0 because B is to the left of zero F B>0 because B is to the right of zero

Answers

The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.

Describe Comparison Algebra?

Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.

Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.

In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.

The statements that provide support for Chloe's claim are:

A. A<0 because A is to the left of zero.

F. B>0 because B is to the right of zero.

Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.

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Rewrite 6x2 + 2xy + 9x + 3y in factored form. (2x + 3)(3x + y) (2x + y)(3x + 3) (3x + 2)(3x + y) (3x + y)(2x + 1)

Answers

Answer:

(3x + y)(2x + 3)

Step-by-step explanation:

Factorizing the expression:

6x² = 2 * 3 * x * x

2xy = 2*x * y

Common factor = 2x.

        9x = 3 * 3 * x

        3y = 3 * y

Common factor = 3

Take out the common factor 2x from the first and second term & take out the common factor 3 from third and fourth term.

6x² + 2xy + 9x + 3y = 2x(3x + y) + 3(3x + y)

                              = (3x + y)(2x + 3)

Answer is (2x + 3) (3x + y)

Explanation
When this is distributed we get

6x^2 + 2xy + 9x + 3y

So the first set of factors is correct

Mohal plans to repaint some classroom bookcases. He has 1 1 /8​ gallons of paint. All of the bookcases are the same size and each requires 1/8gallon of paint. How many bookcases will he be able to paint?

Answers

Mohal will be able to paint 9 bookcases for the amount of paint.

What is fraction?

An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.

Given that, he has 1 1 /8​ gallons of paint.

Thus, number of bookcases are:

1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9

Hence, Mohal will be able to paint 9 bookcases for the amount of paint.

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What is the solution to the equation 3/5x-4-3√7x+8?
A x = -6
B x=-1
C x = 1
D x = 2

Answers

The solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.

What is equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To solve the equation 3/5x - 4 - 3√7x + 8 = 0:

First, simplify the expression by combining like terms:

3/5x - 3√7x + 4 = 0 + 8

3/5x - 3√7x + 4 = 8

Next, move the constant term to the right side:

3/5x - 3√7x = 8 - 4

3/5x - 3√7x = 4

Factor out x from the left side:

x(3/5 - 3√7) = 4

Divide both sides by (3/5 - 3√7):

x = 4 / (3/5 - 3√7)

To simplify the expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (3/5 + 3√7):

x = 4(3/5 + 3√7) / [(3/5 - 3√7)(3/5 + 3√7)]

x = 12/5 + 12√7/5 / (9/25 - 63/25)

x = 12/5 + 12√7/5 / (-54/25)

x = -10√7/9

Therefore, the solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.

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Please help me please tysm and have a great day :)

Answers

Answer:

mean: 20mins

Step-by-step explanation:

add them all together to get 240

then divide by how many there are

240÷12=20

so the mean is 20mins

3. In a sports centre, the ages of 100 people were recorded as follows: Age Under 20 years 20 to 29 years 30 t0 39 years 40 to 59 years 60 years and over Number of people 30 15 12 14 29 Fri, 24 Mar 2023 Angle (i) complete the table above to show the angle for each categ rounded off to the nearest degree. (ii) construct a pie chart using the circle below.​

Answers

100 people = 360° of circle

For n people, the degree for the circle is (n×360)÷100

30 people = (30×360)÷100 = 108°

15 people = 54°

12 people = 43.2° ≅ 43°

14 people = 50.4° ≅ 50°

29 people = 104.4° ≅ 104°

Find the equation of the linear function
represented by the table below in slope-intercept
form.
X: -3,1,5,9
y: -8,0,8,16

Answers

By answering the presented question, we may conclude that As a result, the linear function denoted by the table is y = 2x - 2.

what is slope?

A line's slope shows how steep it is. A mathematical equation for the gradient is referred to as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of vertical change (rise) to horizontal change between two points (run). The slope-intercept form of an equation is used to represent the equation of a straight line, which is written as y = mx + b. The y-intercept is located where the line's slope is m, b is b, and (0, b). The slope and y-intercept of the equation y = 3x - 7 are two examples (0, 7). The line's slope is m. b is b at the y-intercept, and (0, b).

To obtain the slope and y-intercept of a linear function in slope-intercept form, we must first establish the slope and y-intercept.

With two locations on the line, we can first determine the slope. Let us start with the first and last points in the table:

slope = (y change) / (change in x)

slope = (16 - (-8)) / (9 - (-3))

slope = 24 / 12

slope = 2

We can now use the slope and one of the points to get the y-intercept. Let's take the point (1, 0) as an example:

y = mx + b 0 + b b = 2(1) + b b = -2

Hence the linear function's slope-intercept equation is:

y = 2x - 2

As a result, the linear function denoted by the table is y = 2x - 2.

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ii) The door is 0.9 m wide and 2.1 m high. Each of the four windows is 1.5 m wide and 1.2 m high work out the toral area of the door and the four windows ​

Answers

Answer: The area of the door can be calculated as:

Area of door = width x height

= 0.9 m x 2.1 m

= 1.89 square meters

The area of one window can be calculated as:

Area of window = width x height

= 1.5 m x 1.2 m

= 1.8 square meters

Since there are four windows, the total area of the four windows is:

Total area of four windows = 4 x Area of window

= 4 x 1.8 square meters

= 7.2 square meters

Therefore, the total area of the door and the four windows is:

Total area = Area of door + Total area of four windows

= 1.89 square meters + 7.2 square meters

= 9.09 square meters

Hence, the total area of the door and the four windows is 9.09 square meters.

Step-by-step explanation:

What is the average of these numbers?
45 46 50 52 51 59 55 51 42 44
51 55 60 62 52 54 47 74 52 52
59 52 65 45 58 59 59 52 54 65

Answers

The average of these numbers is 54.0666667 and if you rounding it is 54.

Explanation: Add all the numbers together and divide by the number of numbers.

Becky ate 7.5 x 10^5 milligrams of rice. Carter ate 3.1 x 10^6 milligrams of rice. who ate more?​

Answers

Answer:

The Correct answer is Carter

carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet

Answers

A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

How to determine the amount of carpet needed for a rectangular room?

To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.

The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),

18 feet ÷ 3 feet/yard = 6 yards

So the dimensions of the room in yards are 10 yards by 6 yards.

To find the total area of the room, we need to multiply the length and width,

10 yards × 6 yards = 60 square yards

Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

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4)
Northbrook Middle School surveyed 325 students to learn more about their after-schoo
activities. They found that 90 students are in a club and play a sport. 140 total students
play a sport and 200 total students are in a club. Construct a two-way relative freques
table summarizing the data.
Plays a Sport
In a Club
Not In a Club
Total
Doesn't Play a
Sport
Total

Answers

Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).

What is frequency?

Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.

90 students are in a club and play a sport.

140 total students play a sport.

Therefore, 140 - 90 = 50 students play a sport but are not in a club.

The total number of students who play a sport is 140 + 50 = 190.

200 total students are in a club.

Therefore, 200 - 90 = 110 students are in a club but do not play a sport.

The total number of students who do not play a sport is 325 - 190 = 135.

The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.

This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.

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A man bought two pencils and three biros at a cost of 50, Again he bought three pencils and four biros for 70. find the cost of a pencil and a biro​

Answers

Let the cost of a pencil be "x" and the cost of a biro be "y".

From the first statement, we can write:

2x + 3y = 50 ...(1)

Similarly, from the second statement, we can write:

3x + 4y = 70 ...(2)

We now have two equations with two unknowns. We can solve for x and y using elimination or substitution method. Let's use the elimination method:

Multiplying equation (1) by 3 and subtracting it from equation (2) multiplied by 2, we get:

(2)(3x + 4y) - (3)(2x + 3y) = (70)(2) - (50)(3)

Simplifying, we get:

2x + 5y = 40 ...(3)

Now we have two equations with two unknowns:

2x + 3y = 50 ...(1)
2x + 5y = 40 ...(3)

Subtracting equation (1) from equation (3), we get:

2y = -10

Therefore, y = -5

Substituting y = -5 in equation (1), we get:

2x + 3(-5) = 50

Simplifying, we get:

2x = 65

Therefore, x = 32.5

Hence, the cost of a pencil is 32.5 cents and the cost of a biro is -5 cents.

However, it is not possible for the cost of a biro to be negative, so there must be an error in the calculations or in the problem statement. Please check the numbers and the problem statement again.

solve for r if $425.83=400(1+r)^5 ? (show explanation please)

Answers

Answer: 0.0295

Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.

Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:

$1+r=\sqrt[5]{1.064575}$.

Subtracting 1 from both sides gives $r\approx 0.0295$.

Therefore, your answer would be 0.0295.

In order to develop a more appealing​ cheeseburger, a franchise uses taste tests with 11 5 different​ buns, 3 different​ cheeses, 4 types of​ lettuce, and types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each​ cheeseburger, approximately how long would it take the tester to eat all possible​ cheeseburgers?

Answers

It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.

Write an absolute value equation that has the following solution set.

-8 and -2

Thank you!

Answers

The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3

What is an absolute value equation?

An absolute value equation can be written as |expression| = value

To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.

We can write,

|x + 5| = 3

To solve for x, we have two cases,

Case 1: x + 5 is positive

If x + 5 is positive, then the equation becomes x + 5 = 3

Solving for x,

x = -2

This matches one of the solutions we want.

Case 2: x + 5 is negative

If x + 5 is negative, then the equation becomes -(x + 5) = 3

Solving for x,

x = -8

This also matches the other solution we want.

Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.

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When two sample means are significantly different
Group of answer choices

The pooled variance estimate should not be used

The difference is too great to attribute to chance

The corresponding population means are significantly different

The difference is of practical importance

Answers

When two sample means are significantly different, "the difference is too great to attribute to chance".

What is statistical significance?

The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).

Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.

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A rectangular pyramid is shown in the figure.
A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.
What is the surface area of the pyramid?

Answers

The surface area of the pyramid is 113 cm².

What is rectangular pyramid?

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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Could someone help me find the answers and show me how they got it it’s a review for a quiz I have to take for tomorrow

Answers

Area of composite shape = 12 + 9

                                         = 21 cm²    

How to solve

Area of composite shapes:

13) Figure 1:

        Figure1 is a rectangle.

        l = 4 cm & w = 2 cm

Area of figure1 = l * w

                        = 4 * 2

                        = 8 cm²

Figure2:

             Figure2 is a parallelogram

              base = b = 4 cm

                 h = 4 cm

  Area of figure2 = b * h

                            = 4 * 4

                           = 16 cm²

Area of composite shape = 8 + 16

                                         = 24 cm²

14) Figure1:

      Figure 1 is a trapezium. a & b are parallel sides and h is the height

      a = 4 cm ; b = 6 cm; h = 4 -2 = 2 cm

               

Figure2:

  Figure2 is a rectangle. l = 6 cm ; w = 2 cm

 Area of figure2 = 6*2

                            = 12 cm²

Area of composite shape = 10 + 12

                                         = 22 cm²

15) Figure 1 & figure 2:

          Figure 1 and  figure 2 are congruent triangles

            base = b = 3 cm & h= 4 cm

= b *h

= 3 * 4

= 12 cm²

Figure3:

   Figure 3 is a square.

     side =  3 cm

 Area of figure3 = side *side

                            = 3 * 3

                           = 9 cm²

Area of composite shape = 12 + 9

                                         = 21 cm²                      

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A container in the shape of a rectangular prism has a height of 2 feet. Its length is four
times its width. The volume of the container is 200 cubic feet. Find the length and width of
the container.

Answers

Answer: length = 20 feet and width = 5 feet

Step-by-step explanation: Volume is equal to volume = height * width * length. The questions tells us the total volume is 200 cubic feet and that the lenght is equal to length = 4w. Set up the equation 4w * w * 2 = 200 cubic feet. Multiply to get 8w^2 = 200 and solve for w.

60°
y
Find the value of y.
A. y = 2
B.
4√√3
3
y = 4
C.
D. y = 4√3
8
30°

Answers

The value of y is 4, so the answer is option A: y = 4.

What is trigonometric ratios ?

Trigonometric ratios are mathematical relationships between the angles and sides of a right triangle. There are three primary trigonometric ratios: sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

Using the given diagram, we can use the trigonometric ratios to find the value of y.

First, we can find the length of the side opposite the 30-degree angle by using the sine ratio:

sin(30°) = opposite/hypotenuse

sin(30°) = y/8

y/8 = 1/2

y = 8/2

y = 4

Therefore, the value of y is 4, so the answer is option A: y = 4.

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Given f’(x)=4x-3 compute f(5)-f(-1)

Answers

Answer:

To solve this problem, we need to integrate the derivative f'(x) to obtain the function f(x).

∫f'(x) dx = ∫(4x - 3) dx

f(x) = 2x^2 - 3x + C

where C is the constant of integration.

To find the value of C, we need to use the fact that f(0) = 5. Substituting x = 0 into the above equation, we get:

f(0) = 2(0)^2 - 3(0) + C = C

Therefore, C = 5.

Hence, the function f(x) is:

f(x) = 2x^2 - 3x + 5

Now, we can find f(5) and f(-1) and compute their difference:

f(5) - f(-1) = (2(5)^2 - 3(5) + 5) - (2(-1)^2 - 3(-1) + 5)

f(5) - f(-1) = (50 - 15 + 5) - (2 + 3 + 5)

f(5) - f(-1) = 35 - 10

f(5) - f(-1) = 25

Therefore, f(5) - f(-1) = 25.

Divide and give your answer as a decimal. Round your answer to the nearest thousandth (3 digits behind the decimal).

2/9

Answers

Answer:

0.222

Step-by-step explanation:

2 divided by 9 is:

0.222 (rounded to the nearest thousandth)

2/9 as a fraction to decimal form is= .222

find the factors to this polynomials i need help SHOW YOUR WORK.

Answers

Answer:

hope this will help you...

Which expresion has the greatest value when n is equal to 4

Answers

The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.

How do we calculate?

To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.

A. 5n = 5(4) = 20

B. n + 30 = 4 + 30 = 34

C. 50 - n = 50 - 4 = 46

D. 80 ÷ n = 80 ÷ 4 = 20

The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n

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What is the perimeter of the triangle?

Answers

Answer:

40 units

Step-by-step explanation:

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

Answer:

  40 units

Step-by-step explanation:

You want the perimeter of the triangle shown in the graph.

Dimensions

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

  c² = a² +b²

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17

The long side of the triangle is 17 units.

Perimeter

The perimeter of the triangle is the sum of the lengths of its sides:

  P = 8 + 15 + 17 = 40

The perimeter is 40 units.

__

Additional comment

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

Prove: DC = 6 units
A
6 units
D
Statements
AD || BC
ZDAC ZBCA
C
?
DC BA
DC = BA
given
alternate interior angles theorem
AC AC
reflexive property of congruence
ZDCA ZBAC alternate interior angles theorem
DC = 6 units
Which step is missing?
B
O A. ADAC
OB. ADCA
O C. ADCA
Reasons
?
CPCTC
definition of congruent sides
substitution property of equality
ABCA by SAS
ABCA by ASA
ABCA by SAS

Answers

The missing step in the proof is: D. ADCA

What is the missing step and reason of the proof?

In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).

Therefore, we have the following proportional sides:

DC/AC = AC/BC

Given that DC = BA (given statement), we can substitute BA for DC in the proportion:

BA/AC = AC/BC

Now, we can cross-multiply to get:

BA * BC = AC²

Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:

BA * BC = AC * AC

Use the definition of congruent sides to replace BA with DC:

DC * BC = AC * AC

And finally, use the substitution property of equality to replace BC with 6 units (given statement):

DC * 6 = AC * AC

From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.

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The expression 12x +8 is equivalent to the expression a(bc+c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4). Which statement best explains whether the students answer is correct or incorrect

Answers

The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

What is expression?

Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.

This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.

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Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).

Which statement best explains whether the student's answer is correct or incorrect?

OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).

C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).

OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).

The supply and demand for a product are related to price by the following​ equations, where y is the​ price, in​ dollars, and x is the number of​ units, in thousands. Find the equilibrium point for this product.
y=300+40x
y=9300-50x

helpp..

Answers

Answer: At equilibrium, the supply and demand are equal, so we can set the two equations equal to each other:

300 + 40x = 9300 - 50x

Simplifying and solving for x:

90x = 9000

x = 100

Now that we know x, we can use either equation to find y:

y = 300 + 40(100) = 4300

So the equilibrium point is when x = 100 and y = 4300.

Step-by-step explanation:

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