Tüm alıştırma soruları

Soru 461Soru →

A naval architect creates a scale drawing for a new submarine. The drawing uses a scale of $\frac{3}{16}\text{ inch} = 15\text{ feet}$ . If the pressure hull measures $4\frac{1}{8}\text{ inches}$ long on the drawing, what is the actual length, in feet, of the pressure hull?

Cevabı ve açıklamayı göster

Cevap: 330

Cevap

330

The scale establishes that every inch on the drawing represents

80

actual feet (

15 \div \frac{3}{16} = 80

). Multiplying the drawing length of

4\frac{1}{8}

inches (or

\frac{33}{8}

inches) by

80

feet per inch yields the correct actual length of

330

feet.

Adım Adım Çözüm

1

Find the unit rate for

1\text{ inch}

of the drawing.

15 \div \frac{3}{16} = 15 \times \frac{16}{3} = 5 \times 16 = 80\text{ feet}

per inch.

Establishing a unit rate simplifies finding actual dimensions for any measurement on the scale drawing.

2

Convert the drawing measurement from a mixed number to an improper fraction.

4\frac{1}{8} = \frac{4 \times 8 + 1}{8} = \frac{33}{8}\text{ inches}

.

Improper fractions are required to properly multiply the scale factor with the drawing measurement.

3

Calculate the actual length by multiplying the map measurement by the unit rate.

\frac{33}{8} \times 80 = 33 \times 10 = 330\text{ feet}

.

Multiplying the measurement on the drawing by the actual distance per inch yields the total actual distance.

Anahtar Kavram

Scale Drawings and Map Measurements

Soru 462Soru →

An algebraic relationship is given by the equation:

\frac{3}{5}(10k - 25) - \frac{1}{4}(8 - 16k) = \frac{1}{2}(14k - 10) - 2(k - 9)

What value of $k$ balances the given equation?

Cevabı ve açıklamayı göster

Cevap: 6

Cevap

The value that satisfies the equation is 6.

The correct value is found by carefully distributing the fractional multipliers and negative signs to eliminate all parentheses, simplifying both sides to get

10k - 17 = 5k + 13

, and finally isolating

k

by performing balanced operations to find

k = 6

.

Adım Adım Çözüm

1

Distribute the fractional coefficients into the parentheses on both sides of the equation.

(6k - 15) - (2 - 4k) = (7k - 5) - 2(k - 9)

Distribution eliminates the parentheses and clears the fractional multipliers, allowing the terms to be evaluated and combined.

2

Distribute the negative signs for the remaining terms in the equation.

6k - 15 - 2 + 4k = 7k - 5 - 2k + 18

Properly applying the negative sign ensures all terms are correctly added or subtracted, especially noting that

- \frac{1}{4}(-16k) = +4k

and

-2(-9) = +18

.

3

Combine the constant terms and the variable terms independently on each side.

10k - 17 = 5k + 13

Simplifying each side makes it easier to isolate the variable.

4

Isolate the variable term by moving all terms containing k to one side and constants to the other side.

10k - 5k = 13 + 17 \Rightarrow 5k = 30 \Rightarrow k = 6

Solving for k provides the final numerical value that balances the equation.

Anahtar Kavram

Solving complex one-variable linear equations by distributing fractional coefficients, managing negative signs, and combining like terms.

Soru 463Soru →

The sum of three consecutive negative even integers is $-102$ . What is the absolute value of the smallest of these integers?

Cevabı ve açıklamayı göster

Cevap: 36

Cevap

36

By defining the consecutive even integers algebraically, the smallest integer is correctly identified as

-36

. Taking the absolute value of

-36

yields

36

.

Adım Adım Çözüm

1

Define variables for the three consecutive even integers.

Let the smallest integer be

x

. The next consecutive even integers are

x + 2

and

x + 4

.

Consecutive even integers are always 2 units apart.

2

Set up the equation.

x + (x + 2) + (x + 4) = -102

The sum of the three integers is given as

-102

.

3

Solve for

x

.

3x + 6 = -102

leads to

3x = -108

, yielding

x = -36

.

Isolating

x

provides the value of the smallest integer.

4

Calculate the absolute value.

|-36| = 36

The question specifically asks for the absolute value of the smallest integer.

Anahtar Kavram

Consecutive integers and absolute value properties

Soru 464Soru →

Find the value of the following expression for $x = -3$ , $y = -2$ , and $z = \frac{1}{2}$ :

\frac{x^2 y - y^3}{x - y} + 4z

Cevabı ve açıklamayı göster

Cevap: 12

Cevap

12

The correct result of 12 is obtained by substituting the given values, correctly applying exponents to negative bases, properly combining terms with double negatives, and following the standard order of operations.

Adım Adım Çözüm

1

Substitute the values of x, y, and z into the algebraic expression.

\frac{(-3)^2(-2) - (-2)^3}{(-3) - (-2)} + 4(\frac{1}{2})

Direct substitution establishes the numerical expression to be evaluated.

2

Evaluate the terms containing exponents.

(-3)^2 = 9

and

(-2)^3 = -8

Following the order of operations, exponents are calculated before multiplication or addition.

3

Multiply the factors in the numerator and the separate z-term.

The numerator term becomes

9(-2) = -18

. The z-term becomes

4(\frac{1}{2}) = 2

.

Multiplication is the next step in simplifying the expression according to the order of operations.

4

Simplify the fraction's numerator and denominator by performing the subtractions.

Numerator:

-18 - (-8) = -10

. Denominator:

-3 - (-2) = -1

.

The fraction bar acts as a grouping symbol; the numerator and denominator must be simplified completely before division.

5

Divide the simplified numerator by the simplified denominator.

\frac{-10}{-1} = 10

Completing the division of the rational part of the expression.

6

Add the result of the division to the remaining term.

10 + 2 = 12

Addition is the final operation required to find the total value.

Anahtar Kavram

Evaluating complex algebraic expressions using substitution and the order of operations with negative integers and fractions.

Soru 465Soru →

A military supply shipment contains $3.4 \times 10^4$ ready-to-eat meals. What is the total number of meals written in standard numerical form?

Cevabı ve açıklamayı göster

Cevap: 34000

Cevap

34000

The expression

3.4 \times 10^4

represents

3.4

multiplied by

10,000

. Shifting the decimal point 4 places to the right results in exactly

34,000

.

Adım Adım Çözüm

1

Identify the exponent on the base 10.

The exponent is 4.

The exponent determines the number of places the decimal point must be shifted.

2

Move the decimal point 4 places to the right.

3.4 becomes 34000.

Multiplying by 10^4 is equivalent to shifting the decimal to the right by 4 places to convert the scientific notation into standard form.

Anahtar Kavram

Converting from scientific notation to standard form involves shifting the decimal point based on the value and sign of the exponent.

Soru 466Soru →

A mechanical engineer is determining the load factor for a support beam. The calculation requires evaluating the equation below.

\text{Load Factor} = \left( 5 \frac{5}{8} - 2 \frac{3}{4} \right) \div \left( 1 \frac{1}{3} \times \frac{3}{8} \right)

What is the final load factor? Express your answer as an exact decimal.

Cevabı ve açıklamayı göster

Cevap: 5.75

Cevap

The final load factor is exactly 5.75.

The expression evaluates to exactly 5.75. This is found by first converting all mixed numbers to improper fractions, calculating the values inside the parentheses (

\frac{23}{8}

and

\frac{1}{2}

respectively), and then performing fraction division by multiplying by the reciprocal (

\frac{23}{8} \times 2 = \frac{23}{4} = 5.75

).

Adım Adım Çözüm

1

Convert the mixed numbers in the expression to improper fractions.

5 \frac{5}{8} = \frac{45}{8}

,

2 \frac{3}{4} = \frac{11}{4}

, and

1 \frac{1}{3} = \frac{4}{3}

.

Fraction multiplication and division require working with improper fractions rather than mixed numbers.

2

Perform the subtraction inside the first set of parentheses:

\frac{45}{8} - \frac{11}{4}

.

Convert

\frac{11}{4}

to

\frac{22}{8}

. Then,

\frac{45}{8} - \frac{22}{8} = \frac{23}{8}

.

To subtract fractions, they must have a common denominator. The lowest common denominator for 8 and 4 is 8.

3

Perform the multiplication inside the second set of parentheses:

\frac{4}{3} \times \frac{3}{8}

.

Multiply the numerators and denominators:

\frac{4 \times 3}{3 \times 8} = \frac{12}{24}

. This simplifies to

\frac{1}{2}

.

Following the order of operations (PEMDAS), operations inside parentheses must be evaluated first.

4

Divide the result of the first parentheses by the result of the second parentheses.

\frac{23}{8} \div \frac{1}{2} = \frac{23}{8} \times \frac{2}{1} = \frac{46}{8}

.

Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.

5

Simplify the final fraction and convert it to a decimal format.

\frac{46}{8} = \frac{23}{4} = 5 \frac{3}{4}

. As a decimal,

5 \frac{3}{4} = 5.75

.

The question specifically requests the final load factor expressed as a decimal.

Anahtar Kavram

Compound Fraction Operations and Order of Operations

Soru 467Soru →

A cybersecurity team analyzes network traffic and categorizes detected threats into low, medium, and high severity in a ratio of $9:5:2$ . If the team logged exactly $145$ medium severity threats during a shift, what was the total number of threats logged across all three categories?

Cevabı ve açıklamayı göster

Cevap: 464

Cevap

464

The correct answer is found by first determining the value of a single ratio part. Since

5

parts represent

145

medium threats, one part equals

29

threats. Multiplying this base unit by the total number of parts (

16

) gives the total of

464

threats.

Adım Adım Çözüm

1

Determine the total number of parts in the ratio.

9 + 5 + 2 = 16

parts

To find the total amount of threats, we first need to know how many total parts make up the complete ratio.

2

Find the numerical value of a single part.

145 \div 5 = 29

threats per part

We know that

5

parts equal

145

medium threats. Dividing the count by the parts gives the baseline value of one part.

3

Calculate the total number of threats.

29 \times 16 = 464

threats

Multiplying the value of one part by the total number of parts yields the total count across all categories.

Anahtar Kavram

Solving Part-to-Whole Ratio Problems

Soru 468Soru →

A renewable energy company is installing a chain-link fence around a newly constructed rectangular solar farm. The solar farm measures $120$ yards in length and $85$ yards in width. The fence will enclose the entire perimeter, with the exception of two access gates that each measure $5$ yards wide. If the fencing material costs $\$22$ per linear yard, what is the total cost of the fencing material in dollars?

Cevabı ve açıklamayı göster

Cevap: 8800

Cevap

The total cost of the fencing material is 8800 dollars.

The total perimeter of the solar farm is

410

yards (

120 + 120 + 85 + 85

). Subtracting the

10

yards for the two

5

-yard gates leaves

400

yards of fencing to be installed. Multiplying

400

yards by the

\$22

per yard cost gives a total of

\$8800

.

Adım Adım Çözüm

1

Calculate the total perimeter of the rectangular solar farm.

P = 2 \times (120 + 85) = 2 \times 205 = 410

yards.

The perimeter formula for a rectangle is

P = 2(L + W)

, which represents the total boundary length before any openings are considered.

2

Determine the total width of the two access gates.

2 \times 5 = 10

yards.

Since there are two gates and each is

5

yards wide, their combined width must be subtracted from the total perimeter.

3

Calculate the actual length of fencing needed.

410 - 10 = 400

yards.

The fencing covers the perimeter minus the space left open for the access gates.

4

Calculate the total cost of the fencing material.

400 \times 22 = 8800

.

Multiplying the total yards of fencing by the cost per yard gives the total cost in dollars.

Anahtar Kavram

Calculating the perimeter of a rectangle, subtracting openings, and finding the total cost based on a unit price.

Soru 469Soru →

A network engineer is configuring a load balancer to distribute traffic across two servers. The equation below models the traffic distribution, where $t$ represents the number of active connections:

5(2t - 4) - 3t = 4(t + 2) - (t - 8)

Calculate the required number of active connections, $t$ , to successfully balance the server loads.

Cevabı ve açıklamayı göster

Cevap: 9

Cevap

9

By successfully applying the distributive property on both sides, combining the variable and constant terms, and isolating the variable, the equation perfectly balances when the variable is exactly 9.

Adım Adım Çözüm

1

Distribute the coefficients and negative signs across the parentheses on both sides of the equation.

10t - 20 - 3t = 4t + 8 - t + 8

Distribution removes the parentheses, allowing individual terms to be combined.

2

Combine like terms on each side of the equation.

7t - 20 = 3t + 16

Simplifying each side individually makes it easier to balance the equation.

3

Subtract

3t

from both sides of the equation.

4t - 20 = 16

This groups all the variable terms on one side of the equation.

4

Add 20 to both sides and divide by 4.

4t = 36 \implies t = 9

Isolating the variable determines the final numerical solution.

Anahtar Kavram

Solving multi-step linear equations involving the distributive property and combining like terms.

Soru 470Soru →

A botanist has $120$ tulip bulbs, $168$ daffodil bulbs, and $216$ crocus bulbs. She wants to plant them in separate rows such that each row contains only one type of flower, and every row has the exact same number of bulbs. What is the greatest number of bulbs she can plant in a single row?

Cevabı ve açıklamayı göster

Cevap: 24

Cevap

24

The greatest number of bulbs per row must perfectly divide the total count of each flower type without remainders. Therefore, we calculate the Greatest Common Factor (GCF) of 120, 168, and 216. The prime factorizations reveal the common factors are

2^3

and

3^1

, which multiply to 24.

Adım Adım Çözüm

1

Identify the mathematical operation required by the scenario.

The problem asks for the greatest number that divides 120, 168, and 216 evenly. This means finding the Greatest Common Factor (GCF).

Each row must have the same number of bulbs and only one flower type, meaning the row size must be a common divisor of all three total quantities.

2

Find the prime factorization of 120, 168, and 216.

120 = 2^3 \times 3 \times 5

,

168 = 2^3 \times 3 \times 7

, and

216 = 2^3 \times 3^3

.

Prime factorization is a systematic method to determine the common factors of multiple large numbers.

3

Identify the common prime factors and select their lowest powers.

The common prime factors are 2 and 3. Their lowest powers across the three numbers are

2^3

and

3^1

.

The GCF is formed by multiplying the lowest powers of all prime factors that appear in every number's factorization.

4

Calculate the GCF.

2^3 \times 3 = 8 \times 3 = 24

.

Multiplying the selected prime factors yields the greatest possible number of bulbs per row.

Anahtar Kavram

Greatest Common Factor (GCF)

Soru 471Soru →

What is the value of the following expression?

$|-4 - |-9||$

Cevabı ve açıklamayı göster

Cevap: 13

Cevap

13

The correct answer is found by first evaluating the innermost absolute value,

|-9| = 9

. Substituting this value back into the expression gives

|-4 - 9|

. Simplifying the subtraction inside yields

|-13|

. Finally, the absolute value of

-13

is

13

.

Adım Adım Çözüm

1

Evaluate the inner absolute value.

|-9| = 9

According to the order of operations, we must simplify the expression from the inside out. The absolute value of a negative number is its positive counterpart.

2

Substitute and simplify the remaining expression.

|-4 - 9| = |-13|

Replacing

|-9|

with

9

gives the subtraction

-4 - 9

, which simplifies to

-13

.

3

Evaluate the outer absolute value.

|-13| = 13

The absolute value represents the distance from zero on the number line, which is always non-negative.

Anahtar Kavram

Absolute Value

Soru 472Soru →

If $4(k - 3) = 28$ , what is the value of $k$ ?

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

10

Applying inverse operations to isolate the variable results in

k = 10

. This can be verified by substituting 10 back into the original equation:

4(10 - 3) = 4(7) = 28

, which makes the statement true.

Adım Adım Çözüm

1

Divide both sides by 4.

k - 3 = 7

Dividing by the coefficient outside the parentheses simplifies the equation and isolates the binomial.

2

Add 3 to both sides of the equation.

k = 10

Using the inverse operation of subtraction isolates the variable

k

.

Anahtar Kavram

Solving One-Variable Linear Equations

Soru 473Soru →

A military engineering unit is installing a security fence around a rectangular vehicle depot. The depot is $150$ yards long and $80$ yards wide. The fencing plan includes leaving a single $30$ -foot wide opening for a main access gate. If the fencing material costs $\$15$ per linear foot, what is the total cost of the fencing material needed? (Do not include commas or dollar signs in your answer)

Cevabı ve açıklamayı göster

Cevap: 20250

Cevap

20250

To find the total cost, first determine the total perimeter of the depot in yards:

2 \times (150 + 80) = 460

yards. Since the fencing cost and gate width are in feet, convert the perimeter to feet:

460 \times 3 = 1380

feet. Next, subtract the

30

-foot gate opening where no fencing is needed:

1380 - 30 = 1350

feet of fencing. Finally, multiply the required fencing by the cost per foot:

1350 \times \$15 = \$20,250

.

Adım Adım Çözüm

1

Calculate the perimeter of the rectangular depot in yards.

2(150 + 80) = 2(230) = 460

yards.

The fencing will enclose the boundary of the rectangular area.

2

Convert the perimeter from yards to feet.

460 \times 3 = 1380

feet.

The cost of the fencing is given per linear foot and the gate is measured in feet, so all measurements must be in feet.

3

Subtract the gate opening from the total perimeter.

1380 - 30 = 1350

feet.

Fencing material is not needed for the gate opening.

4

Calculate the total cost of the fencing material.

1350 \times 15 = 20250

dollars.

The total length of fencing required is multiplied by the cost per linear foot.

Anahtar Kavram

Calculating perimeter, converting units (yards to feet), and determining total cost based on a linear rate.

Soru 474Soru →

An event coordinator is setting up a temporary security perimeter for an outdoor festival. The secured VIP zone is rectangular, measuring $30$ yards in length and $20$ yards in width. An un-fenced opening of $5$ yards must be left on one side for the main entrance gate. If the temporary fencing costs $\$4.50$ per linear foot, what is the total cost, in dollars, of the fencing required?

Cevabı ve açıklamayı göster

Cevap: 1282.5

Cevap

1282.5

The correct total cost is

1282.50. To find this, the full perimeter of the 30-by-20 yard rectangle is calculated as 100 yards. After subtracting the 5-yard opening, 95 yards of fencing are needed. Because the fencing is priced per foot, the 95 yards must be converted to 285 feet by multiplying by 3. Finally, multiplying 285 feet by the

4.50 per foot cost yields 1282.50.

Adım Adım Çözüm

1

Calculate the total perimeter of the rectangular zone in yards.

100 yards

The perimeter represents the total distance around the rectangle before accounting for any openings.

2

Subtract the gate opening from the perimeter.

95 yards

Fencing is not required for the 5-yard entrance gate.

3

Convert the required fencing length from yards to feet.

285 feet

The cost of the fencing is provided per linear foot, so the length must be in feet.

4

Calculate the total cost by multiplying the length in feet by the price per foot.

1282.5

Total cost equals the total amount of material multiplied by the unit price.

Anahtar Kavram

Calculating perimeter of a rectangle, adjusting for openings, and converting units for cost calculation.

Soru 475Soru →

A military motor pool maintains a fleet of tactical trucks, transport vans, and passenger cars in a ratio of $8:5:3$ . If there are exactly $112$ total vehicles in this fleet, how many transport vans does the motor pool maintain?

Cevabı ve açıklamayı göster

Cevap: 35

Cevap

The motor pool maintains 35 transport vans.

The problem outlines a part-to-part-to-part ratio of

8:5:3

and a total quantity of

112

. To solve this, first add the parts of the ratio together (

8 + 5 + 3 = 16

). Next, divide the total quantity by the total ratio parts (

112 \div 16 = 7

) to determine that each 'part' represents

7

actual vehicles. Since the ratio for transport vans is the middle number (

5

), multiply

5

by

7

to correctly get

35

transport vans.

Adım Adım Çözüm

1

Determine the total number of parts in the given ratio.

8 + 5 + 3 = 16

parts

Since the total number of vehicles in the fleet is given, we must find the total sum of the ratio parts to determine the size of a single part.

2

Calculate the exact value of a single ratio part.

112 \div 16 = 7

vehicles per part

Dividing the total quantity of vehicles by the total number of ratio parts gives the multiplier for the ratio.

3

Find the number of transport vans.

5 \times 7 = 35

transport vans

The ratio value specifically assigned to transport vans is

5

. Multiplying this by the value of one part gives the final count.

Anahtar Kavram

Solving part-to-whole ratio problems by establishing the total parts before finding specific component quantities.

Tahmini Süre:1m 0s

Soru 476Soru →

A supply clerk is organizing copper wire. A spool initially contains $15\frac{4}{5}$ meters of wire. If a technician uses $6\frac{1}{2}$ meters of wire from the spool, how many meters of wire remain? Express your answer as a decimal.

Cevabı ve açıklamayı göster

Cevap: 9.3

Cevap

9.3

The initial length of the wire is

15\frac{4}{5}

meters and the used portion is

6\frac{1}{2}

meters. By converting these to decimals, you get

15.8

meters and

6.5

meters. Subtracting the used portion from the initial portion yields

15.8 - 6.5 = 9.3

meters. Alternatively, using a common denominator of 10 gives

15\frac{8}{10} - 6\frac{5}{10} = 9\frac{3}{10}

, which also equals 9.3.

Adım Adım Çözüm

1

Convert the mixed numbers to decimals or find a common denominator.

15\frac{4}{5} = 15.8

and

6\frac{1}{2} = 6.5

Numbers must be in a uniform format to perform subtraction easily.

2

Subtract the length of wire used from the initial length.

15.8 - 6.5 = 9.3

The remaining length is the difference between the starting amount and the used amount.

Anahtar Kavram

Fraction Operations

Tahmini Süre:45s

Soru 477Soru →

Calculate the value of the algebraic expression $x^2 - 4y$ given that $x = -5$ and $y = -2$ . What is the final value?

Cevabı ve açıklamayı göster

Cevap: 33

Cevap

33

By correctly applying substitution and the order of operations, squaring

-5

gives

25

, and multiplying

4

by

-2

gives

-8

. Subtracting

-8

from

25

results in

33

.

Adım Adım Çözüm

1

Substitute the given variable values into the expression

(-5)^2 - 4(-2)

To replace the variables with their corresponding numerical values.

2

Evaluate the exponent

25 - 4(-2)

Following the order of operations (PEMDAS), exponents must be calculated before multiplication and subtraction. The square of a negative number is positive.

3

Evaluate the multiplication

25 - (-8)

Multiply 4 by -2 to find the term to be subtracted.

4

Perform the final subtraction

25 + 8 = 33

Subtracting a negative number is equivalent to adding its positive counterpart.

Anahtar Kavram

Evaluating Algebraic Expressions

Soru 478Soru →

Solve for $n$ in the equation below:

8n - 11 = 37

Enter the exact value of $n$ .

Cevabı ve açıklamayı göster

Cevap: 6

Cevap

6

To find the value of

n

, first perform the inverse operation of subtraction by adding 11 to both sides, which simplifies the equation to

8n = 48

. Then, perform the inverse operation of multiplication by dividing both sides by 8, yielding

n = 6

.

Adım Adım Çözüm

1

Isolate the variable term.

8n = 48

Adding 11 to both sides neutralizes the -11 on the left side of the equation.

2

Solve for the variable.

n = 6

Dividing both sides by 8 isolates n completely.

Anahtar Kavram

Solving two-step linear equations using inverse operations.

Soru 479Soru →

What is the sum of all distinct prime factors of the integer $546$ ?

Cevabı ve açıklamayı göster

Cevap: 25

Cevap

25

The integer

546

factors completely into the prime numbers

2

,

3

,

7

, and

13

. Since the question asks for the sum of all distinct prime factors, adding these together yields

2 + 3 + 7 + 13 = 25

.

Adım Adım Çözüm

1

Find the prime factorization of

546

by continuously dividing by the smallest possible prime numbers.

546 = 2 \times 273 = 2 \times 3 \times 91 = 2 \times 3 \times 7 \times 13

To identify all prime factors, we must break the number down into its foundational prime components.

2

Identify the distinct prime factors from the factorization.

The distinct prime factors are

2

,

3

,

7

, and

13

.

The question specifically asks for the sum of the 'distinct' prime factors.

3

Calculate the sum of these distinct prime factors.

2 + 3 + 7 + 13 = 25

Adding the identified distinct prime factors yields the final requested value.

Anahtar Kavram

Prime Factorization and Properties of Integers

Soru 480Soru →

What is the coefficient of the $k$ term in the expanded product of $(3k - 2)$ and $(k + 5)$ ?

Cevabı ve açıklamayı göster

Cevap: 13

Cevap

13

When expanding

(3k - 2)(k + 5)

, the

k

terms are generated by multiplying the outer terms

(3k \times 5 = 15k)

and the inner terms

(-2 \times k = -2k)

. Combining these gives

15k - 2k = 13k

. Therefore, the coefficient of the

k

term is 13.

Adım Adım Çözüm

1

Identify the terms that will produce a

k

term when multiplied.

The outer terms are

3k

and

5

. The inner terms are

-2

and

k

.

Only the product of a variable term and a constant term will result in a term with degree 1 (

k

).

2

Multiply the outer terms.

(3k)(5) = 15k

This is the 'Outer' multiplication step in expanding two binomials.

3

Multiply the inner terms.

(-2)(k) = -2k

This is the 'Inner' multiplication step in expanding two binomials.

4

Combine the resulting like terms.

15k + (-2k) = 13k

Combining like terms gives the final

k

term of the expanded polynomial.

5

Identify the coefficient.

13

The coefficient is the numerical factor of the

k

term.

Anahtar Kavram

Multiplying polynomials and combining like terms

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