How do you multiply polynomials step by step?

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°

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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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.

Answer:

0 over 12

Step-by-step explanation:

3/4 is equal to 9/12

so your basically taking 9/12 from 9/12

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 equivalent expression with combined like terms is -5.5t + 6.3.

What is Equivalent expression?

Equivalent equations are algebraic equations with the same roots or solutions. We get an analogous equation by adding or subtracting the same number or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same non-zero value.

To combine like terms, we can group the terms with the variable t together, and group the constant terms together:

(-3.6t) + (-1.9t) + (1.2 + 5.1)

We can simplify the constant terms:

(-3.6t) + (-1.9t) + 6.3

Finally, we can combine the terms with the same variable by adding their coefficients:

-5.5t + 6.3

Therefore, the equivalent expression with combined like terms is -5.5t + 6.3.

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The student can combine like terms in the given expression by adding and subtracting the corresponding pairs. This gives the equivalent expression as 3.2t - 2.4.

To combine like terms in the equation -3.6 - 1.9t + 1.2 + 5.1t, you need to group together the like terms. The two like terms we have are the terms with the variable t, -1.9t and +5.1t, and the two constant terms -3.6 and +1.2 without the variable t.

When you add and subtract these pairs accordingly, you get:
-1.9t + 5.1t = 3.2t
-3.6 + 1.2 = -2.4

So, the equivalent expression that combines these like terms is: 3.2t - 2.4.

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Step-by-step explanation:

so, it starts (year 0 after 2000) with 350 foxes.

after 1 year the number had increased by 5%.

that means : 350×1.05

because 5% is represented by 0.05.

5% of 350 is 350×0.05 (= 17.5)

and to add 5% means that this is added to the original 100% (= 1).

100% + 5% = 105%

means

1 + 0.05 = 1.05

so, again, after the first year we have

350×1.05

foxes.

after the second year we have to multiply that by 1.05 again :

350×1.05×1.05

and so on.

so, what we are doing is multiplying the original number of foxes by powers of 1.05 (with the exponent being the number of years after 2000).

f(x) = 350 × (1.05)^x

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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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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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.

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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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 !!!

Answer: 25 inches

Step-by-step explanation:

cos60 = adjacent over hypotenuse

cos60 = a/50

50cos60 = 25

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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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].

Neglecting friction, a similar ride with 12 passengers aboard would take 6 minutes.

The time it takes for a roller coaster ride is directly proportional to the mass of the passengers. If we assume that each passenger has the same mass, then the time it takes for the ride is proportional to the number of passengers.

Let T1 be the time for the ride with 6 passengers, and T2 be the time for the ride with 12 passengers. Then, we have:

T2 = (12/6) * T1

Simplifying this expression, we get:

T2 = 2 * T1

We are given that T1 = 3 minutes, so we can substitute this value into the equation above to find T2:

T2 = 2 * 3 minutes = 6 minutes

Therefore, a similar roller coaster ride with 12 passengers aboard would take 6 minutes, as opposed to the 3 minutes it takes with 6 passengers aboard. The answer is 6 minutes.

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Answer:

a the answer for angle 1 is also 52

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

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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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]

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.

The Olap operations for a data warehouse of a train company contains information about train segments is performed in order to answer the queries with dimension hierarchies when needed.

OLAP operation for first case is Filter on the train dimension to select only Alstom trains. Filter on the departure station dimension to select only French or Belgian stations. Filter on the year dimension to select only 2012. Aggregate the number of kilometers measure across the selected dimensions

Dimension hierarchies for this case is Station dimension: Country > City > Station,  Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for the second case is Filter on the departure station and arrival station dimensions to select only trips that cross country borders. Filter on the year dimension to select only 2012. Aggregate the duration measure across the selected dimensions

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for third case is Filter on the departure station and arrival station dimensions to select only trips that involve Paris. Filter on the month dimension to select only July 2012. Aggregate the number of trips measure across the selected dimensions.

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for fouth case is Filter on the departure station and arrival station dimensions to select only trips that involve Belgian stations. Filter on the year dimension to select only 2012.Aggregate the duration measure across the selected dimensions. Calculate the average duration of the segments

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for fifth case is Aggregate the number of passengers measure across all segments of each trip. Divide by the number of segments per trip to get the average number of passengers per segment

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

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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:

654

Step-by-step explanation:

An increase of 9% would mean 1.09 times 600 which equals 654

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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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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Answer:
11i√√3

Step-by-step explanation:

The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.

a) Probability of a student being from other majors = (150-90) / 150 = 0.40

b) Probability of a student majoring only math = (30 - 20) / 150 = 0.13

c) Probability of a student not majoring engineering = (150 - 40 - 20) / 150 = 0.73

Probability = Number of Favorable Outcomes / Total Number of Outcomes

For part a)

Number of Favorable Outcomes = 150-90 = 60

Total Number of Outcomes = 150

Therefore, Probability = 60 / 150 = 0.40

For part b)

Number of Favorable Outcomes = 30-20 = 10

Total Number of Outcomes = 150

Therefore, Probability = 10 / 150 = 0.13

For part c)

Number of Favorable Outcomes = 150-40-20 = 90

Total Number of Outcomes = 150

Therefore, Probability = 90 / 150 = 0.73

The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.

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Answer:

2(fx-2cosx)

Step-by-step explanation:

regroup terms

factor out the common term 2