Given the following segment lengths,
find the value of x.

1) The area of the first figure is 99 square units, 2) Total area = Area of rectangle + Area of triangle = 30 + 6 = 36 square units, 3) Total area = Area of rectangle + Area of triangle = 13.5 + 10.5 = 24 square units.

i) The first figure is a trapezium with height 9 units, bottom base 9 units and top base 13 units.
To find the area of the trapezium, we can use the formula:
Area of trapezium = h/2[a + b]
where h is the height, a and b are the lengths of the parallel sides.
Substituting the given values, we get:
Area = 9/2[13 + 9] = (9 x 22)/2 = 99 square units
Therefore, the area of the first figure is 99 square units.

ii) The second figure is composed of a rectangle with sides 6 and 5 units and a right-angled triangle with base 3 and height 4 units.
To find the area of the rectangle, we can use the formula:
Area of rectangle = length x breadth
Substituting the given values, we get:
Area of rectangle = 6 x 5 = 30 square units
To find the area of the right-angled triangle, we can use the formula:
Area of right-angled triangle = 1/2 x base x height
Substituting the given values, we get:
Area of right-angled triangle = 1/2 x 3 x 4 = 6 square units
Therefore, the total area of the second figure is:
Total area = Area of rectangle + Area of triangle
= 30 + 6 = 36 square units

iii) The third figure is made up of a rectangle with length 9 and breadth 1.5 units and a right-angled triangle with base 6 (9-3) and height 3.5 (5-1.5) units.
To find the area of the rectangle, we can use the formula:
Area of rectangle = length x breadth
Substituting the given values, we get:
Area of rectangle = 9 x 1.5 = 13.5 square units
To find the area of the right-angled triangle, we can use the formula:
Area of right-angled triangle = 1/2 x base x height
Substituting the given values, we get:
Area of right-angled triangle = 1/2 x 6 x 3.5 = 10.5 square units
Therefore, the total area of the third figure is:
Total area = Area of rectangle + Area of triangle
= 13.5 + 10.5 = 24 square units
Thus, the areas of all three figures have been determined.

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Complete question is in the image provided.

1) Note that the ratio of the Area of the Trapezoid to that of the Triangle is 3:1 (Option D)

2) No. Ivan is not correct. He multiplied the base by the length of the side of the parallelogram to get 99cm the correct answer, however, is 90cm.

1) To determine the ratio of the Trapezoid to that of the Triangle, we need to first find the Areas of both.

a) To find the area of a trapezium, we use the formula:

Area = (1/2) × (sum of the parallel sides) × (height)

In this case, the trapezium has bases of length 9 cm and 18 cm, and a height of 10 cm. So, we can substitute these values into the formula to get:

Area = (1/2) × (9 + 18) × 10

Area = (1/2) × 27 × 10

Area = 135 square cm

Therefore, the area of the trapezium is 135 square cm

b) To find the area of an isosceles triangle, we can use the formula:

Area = (1/2) × base × height

In this case, the base of the triangle is 9 cm and the height is 10 cm. So, we can substitute these values into the formula to get:

Area = (1/2) × 9 × 10

Area = 45 square cm

Therefore, the area of the isosceles triangle ACE is 45 square cm.

c) To find the ratio of the area of the trapezium to that of the isosceles triangle, we need to calculate the area of the isosceles triangle using the given dimensions and then divide the area of the trapezium by the area of the triangle.

The ratio of the area of the trapezium to the area of the triangle is:

Ratio = Area of trapezium / Area of triangle

Ratio = 135 / 45

Ratio = 3

Therefore, the ratio of the area of the trapezoid to that of the triangle is 3:1.

d) Note that the area of a parallelogram is given by the formula:

Area = base x height

In this case, the base of the parallelogram is 9 cm and the height is 10 cm. So, we can substitute these values into the formula to get:

Area = 9 cm x 10 cm

Area = 90 square cm

Therefore, the area of the parallelogram is 90 square cm, not 99cm as indicated by Ivan.

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Answer:

25.85 cubic feet

Step-by-step explanation:

Volume of a cylinder is

Base Area • height

The Base Area of a cylinder is a circle. The area of a circle is pi•r^2.

Vol = pi•r^2•h

They gave the diameter of the circle as 2.8, so the radius is half of that.

r = 1.4

The height was given

h = 4.2

Fill in radius and height and 3.14 for pi. Square the radius and then multiply everything.

see image.

Round to two decimal places.

hi i just did the test and the answer is 25.85 cubic feet

and it was correct btw other person deserves brainly have a nice day!

The shark is fed during the feeding at night is 1/6 tons.

What is a proper fraction?

A proper fraction is one that doesn't contain any whole numbers and has a smaller numerator than a denominator. A fraction that represents a number greater than one and has a larger numerator than the denominator is said to be improper.

Given that during the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning.

The shark fed (2/15 + 1/15) ton during the afternoon.

Assume that the shark fed x tons at night.

Therefore, the total fed is 2/15 + (2/15 + 1/15) + x

The equation is:

2/15 + (2/15 + 1/15) + x = 1/2

Add like terms:

5/15 + x = 1/2

1/3 + x = 1/2

Subtract 1/3 from both sides:

x = 1/2 - 1/3

x = (3-2)/6

x = 1/6

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The number is 2. To find the unknown number that satisfies the equation "4x = 8x - 8," we can simplify and solve for x, which gives us the answer x = 2.

Let's call the unknown number "x".
According to the problem statement, "A certain number is multiplied by 4 and the result equals 8 less than 8 times of the number" can be translated into the following equation:
4x = 8x - 8
Simplifying this equation, we can move 4x to the right side of the equation:
4x - 8x = -8
Simplifying further, we get:
-4x = -8
Dividing both sides by -4, we find:
x = 2
Therefore, the number is 2.

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Student 2 has lower percentage of likes as compare to student 1 ,it is equal to 71.5%.

Number of likes of student 1 is equal to 147

Number of likes of student 2 is equal to 42

147 > 42

⇒Number of likes of student 1 is greater than student 2

Difference between number of likes

= 147 - 42

= 105

Percentage difference = ( 105 / 147 ) × 100

                                     = 71.5%

Student 2 has 71.5% lower percentage of likes than student 1

Therefore, student 2 has lower percentage of likes than student 1 which is equal to 71.5%.

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Answer:

164 cm^2

Step-by-step explanation:

lets find square of triangle first

corner ABD is 90 degrees coz corner ABC is 180 degrees and EBC is 90

(sum of all angles of a quadrilateral is 360,

B = 360 - C - F - E

360 - 90 - 90 - 90 = 90)

BD = CF - DE

BD = 16 - 8 = 8 cm

S ABD = AB * BD / 2 (coz corner B is 90 degrees)

S ABD = 13 * 8 / 2 = 13 * 4 = 52 cm^2

lets find square of BEFC next

S BEFC = CF * EF ( B = C = F = E = 90 so thats a rectangle)

S BEFC = 16 * 7 = 70 + 42 = 112 cm^2

finally lets find total area

S = S ABD + S BEFC = 52 + 112 = 164 cm^2

Answer:

30%

Step-by-step explanation:

100-70=30

During assignment, the result of the calculation on the right side of an equals sign is assigned to a variable on the left of the equals sign. Where as, equality is a logical test that evaluates whether two values are equivalent.

In the given question, the first option is correct among the four.

An assignment operator assigns the result of the calculation on the right side of an equals sign to a variable on the left of the equals sign. It is indicated by ' = '.

Example: s = 4 + years, then the operator assigns the value of the sum of 4 and years to the variable s.

On the other hand, equality is a logical test that evaluates whether two values are equivalent or not. It is indicated by ' == '. The results obtained by this operator is either true or false.

Example: If f == s, it checks whether the value stored in f equals the value stored in s. If they are equal it returns output as true else false.

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Answer: There would be a higher rate on the 2250 labels on 150 sheets.

Step-by-step explanation:

1080/90 = 12

2250/150 = 15

There would be a higher rate on the 2250 labels on 150 sheets.

Check the picture below.

[tex]\cfrac{8^2}{6^2}~~ = ~~\cfrac{A_1}{A_2}\implies \cfrac{8^2}{6^2}~~ = ~~\cfrac{A_1}{(36)}\implies \cfrac{8^2(36)}{36}=A_1\implies 8^2=A_1\implies \stackrel{ mm^2 }{64}=A_1[/tex]

We can solve steps in expressions with many operations in accordance with the order of operations. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. The fourth rule is that we always add and subtract from left to right.

Use the acronyms PEMDAS or BODMAS to determine the sequence of operations. PEMDAS: Parentheses ⇒  (3+4)

Exponents ⇒ 3², Multiply ⇒ 8*4, Divide ⇒ 12÷4, Add ⇒ 6+6, Subtract ⇒ 10-5. BODMAS: Brackets, Order, Divide, Multiply, Add, Subtract .A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Using PEMDAS, we can retain the following order: Exponents, parentheses, addition, subtraction, multiplication, and division (from left to right) Parentheses, exponents, multiplication, division, addition, and subtraction are the orders in which operations must be performed, according to the order of operations. Both BODMAS and PEMDAS are valid and in use in various parts of the globe.

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(i) The function that predicts your expected payroll for the day is,

For first person; y = $50 + $10.50x

For second person; y = $60 + $10.50x

Where, y is total amount and x is number of working hours.

(ii) In Wednesday; The amount expect to pay your employees is,

For first person;

⇒ y = $102.50

For second person;

⇒ y = $112.50

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The first employee scheduled to work next Wednesday makes $10.50 per hour and averages $50 per day for commission.

And, The other person that is scheduled earns $10.50 per hour and averages $60 per day for commission.

Let total amount earn = y

And, Number of working hours = x

Hence, We can formulate;

The function that predicts your expected payroll for the day is,

For first person;

⇒ y = $50 + $10.50x

For second person;

⇒ y = $60 + $10.50x

And, For 5 hours, the amount is,

For first person;

⇒ y = $50 + $10.50x

⇒ y = 50 + 10.50 × 5

⇒ y = 50 + 52.50

⇒ y = $102.50

For second person;

⇒ y = $60 + $10.50x

⇒ y = 60 + 10.50 × 5

⇒ y = 60 + 52.50

⇒ y = $112.50

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Answer:

sin(35)

Step-by-step explanation:

Because of the co-function identity [tex]\cos(\theta)=\sin(90^\circ-\theta)[/tex], then [tex]\cos(55^\circ)=\sin(90^\circ-55^\circ)=\sin(35^\circ)[/tex].

Answer:

a the answer for angle 1 is also 52

b the answer for angle 3 is 180- 112= 68

Answer:   900 x (2.5 x t) = y

900 hundred dollars originally invested, times the number of years multiplied by the yearly interest rate, equals Y, or the amount of the investment in dollars.

I hope this helps & good luck <3 !!!

======================================================

Explanation:

Let's label the sides of the triangle a, b, and c.

Furthermore, let's have 'a' & b represent known sides and  [tex]b \ge a[/tex] be the case. For a triangle to be possible, the missing side c must have these restrictions placed on it:

b-a < c < b+a

This inequality is valid because of a modification to the Triangle Inequality Theorem. I'll leave the proof to the reader.

-------

In this case we have a = 3 and b = 8 which lead to...

b-a < c < b+a

8-3 < x < 8+3

5 < x < 11

The third side is between 5 and 11, excluding both endpoints. We cannot have x = 5. Furthermore, we cannot have x = 11 either. If x were either of those endpoints, then we'd form a straight line rather than a triangle.

Having x be an integer leads to the roster set notation {6,7,8,9,10} to represent all possible values of x. For instance, we could have a triangle with side lengths 3, 8, and 6. I recommend getting slips of paper of these lengths to try it out yourself. Or you can use software such as GeoGebra to see why this works.

Answer:

In 6 seconds: 180 m

20 m: in 2 seconds

Step-by-step explanation:

y = distance

x = time

y is proportional to x:

y = kx

y is proportional to the square of x:

y = kx²

We are given: (3, 45)

45 = k × 3²

45 = 9k

k = 5

The equation is:

y = 5x²

When x = 6,

y = 5(6²)

y = 180

180 m in 6 seconds

When y = 20,

20 = 5x²

x² = 4

x = 2

2 seconds for 20 m

Answer:

258cm

it is the vertex's hieght as well as the length of the sides to multiply together and also divide since there is 5 sides

Answer:

Step-by-step explanation:

the probability of drawing a face card=12/52

drawing the king of diamonds=1/52

Answer:

Probability of face is 12/52

The hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in, rounded to the nearest tenth. This is calculated by using the Pythagorean Theorem, which states that a2 + b2 = c2 and plugging in the values for a and b.

The hypotenuse of a right triangle is the longest side of the triangle and is always opposite of the right angle. To calculate the length of the hypotenuse, you need to use the Pythagorean Theorem. The theorem states that a2 + b2 = c2, where a and b are the legs of the triangle and c is the hypotenuse. In this case, a is 18 inches and b is 26 inches, so the equation would be 182 + 262 = c2. Plugging in the values, we get 324 + 676 = c2, which simplifies to 1000 = c2. To find the length of the hypotenuse, we need to take the square root of 1000, which is 31.6 inches. Rounded to the nearest tenth, the hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in.

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"Choose" means "select". Finding the number of possible methods to choose k items out of n items is done using the "n choose k formula."

C (n, k) represents "n select k" (or) [tex]_n C_k[/tex] (or) (n k) . A binomial coefficient is another name for it. It is used to determine how many different ways there are to choose k distinct items from n distinct items.

The combination formula is another name for the n select k formula (as we call a way of choosing things to be a combination). Factorials are used in this formula.

The n Choose k Formula is:

C (n , k) = n! / [ (n-k)! k! ]

"Choose" means "select". Finding the number of possible methods to choose k items out of n items is done using the "n choose k formula." We occasionally prefer choosing than ordering things.

When preparing for a trip, for instance, you decide to bring five of your ten brand-new clothes. There are several ways you can achieve this; it doesn't matter what sequence you choose them in, but it does matter which dresses you picked.

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Answer: A=71°

Step-by-step explanation:

A+B+C=180°

A+38°+C=180°

A+C=180°-38°

A+C=142°

142°/2=71°

∴A=71°

∴C=71°

The farmer needs to purchase 66 feet of fencing to enclose the rectangular region.

Let's call the length of the side of the rectangle that is parallel to the barn "2x" (since it is twice the length of the adjacent side), and let's call the length of the adjacent side "x". The length of the side opposite the barn is also "x", since it is opposite to the adjacent side.

We know that the area of the rectangle is 242 ft^2. The formula for the area of a rectangle is:

area = length * width

So we can write an equation for the area of the rectangle in terms of "x":

242 = 2x * x

Simplifying this equation, we get:

242 = 2x²

Dividing both sides by 2, we get:

121 = x²

Taking the square root of both sides, we get:

11 = x

So the adjacent side of the rectangle is 11 feet, and the side parallel to the barn is twice as long, or 22 feet.

To find the amount of fencing needed, we need to add up the lengths of all three sides that are not parallel to the barn. The formula for the perimeter of a rectangle is:

perimeter = 2 * length + 2 * width

Since one of the sides is the barn, we only need to add up the lengths of the two sides opposite the barn:

Perimeter = 2 * length + 2 * width

Therefore, the farmer needs to purchase 66 feet of fencing to enclose the rectangular region.

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The correct option for a parabola with given details is D i.e. A curve declines through (negative 1, 6), (0, 4), (1, 2), (2, 1), (4, 0) and (6, 1) on the x y coordinate plane.

What exactly is a parabola?

A parabola is a U-shaped plane curve in which any point is an equal distance from both a fixed point (known as the focus) and a fixed straight line (known as the directrix).

In general, if the directrix is parallel to the y-axis, the typical parabola equation is: y² = 4ax.

If the parabola is sideways, i.e., the directrix is parallel to the x-axis, the conventional parabola equation is x² = 4ay.

Aside from these two, if the parabola is in the negative quadrants, the equation can also be y²= -4ax and x² = -4ay.

Now,

The Graph is drawn for option D in the image and it matches the

details provided in the question.

Hence,

           The correct option for a parabola with given details is A curve declines through (negative 1, 6), (0, 4), (1, 2), (2, 1), (4, 0) and (6, 1) on the x y coordinate plane.

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The required we can save $13.86 annually by buying all your turkey at the discount store.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's call the price of turkey per pound at the supermarket "x". Then the price of turkey per pound at the discount store would be x - $0.99.

Since we consume 14 pounds of turkey annually, the cost of the turkey at the supermarket would be 14 × x dollars.

And the cost of the turkey at the discount store would be 14 × (x - $0.99) dollars.

Therefore, the amount you would save annually by buying all your turkey at the discount store is,

= 14 × x - 14 × (x - $0.99) = 14 × $0.99
= $13.86

So, we would save $13.86 annually by buying all your turkey at the discount store.

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All the numbers less than -10 and upto negative infinity will make the mentioned statement true.

Let us assume the number to be x. So, twice the number will be 2x. Then, nine more will be represented as: 2x + 9. Now, the total is less than -11, so representing the information in expression along with sign.

2x + 9 < - 11

Rewriting the expression according to 2x

2x < - 11 - 9

Performing subtraction on Right Hand Side of the equation

2x < - 20

x < - 20/2

Performing division on Right Hand Side of the equation

x < - 10

So, the numbers below -10 will make the statement true.

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The difference between rational algebraic expressions and fractions is discussed above.

In mathematics, an expression or mathematical expression is a combination of terms, both variables and constants.

For example → 2x + 3y + z

Given is to explain how is rational algebraic expressions different with fractions.

In a rational algebraic expressions, the expression function in the numerator and denominator both are non - zero polynomials. A fraction is of the form {x/y}, in which it is not necessary that {x} and {y} should be polynomials only. They can be numbers also.

Therefore, the difference between rational algebraic expressions and fractions is discussed above.

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