Use the Distributive Property to expand the following expressions.

a.) 2 ( y + 5x) = _______________

b.) 0.4 ( x + 2) = ______________

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

Step-by-step explanation:

5 is in the hundreds place.

The answer should be 213500

Answer:

Step-by-step explanation:

"to the nearest hundreds" requires rounding off the hundreds place.  We get 213,500 because the 48 is less than 50, indicating rounding down.  

Answer: Nick and Pablo

Step-by-step explanation:

6 feet and 2 yards are the same distance because each yard is 3 feet

Answer:

6 feet 2 yards

Step-by-step explanation:

Answer:

How many feet does a car travel in 1 second if it is moving at a rate of 75 mph? So you're going 110 ft per second. In other words, the car travels 110 feet in 1 second (and does so each second assuming you maintain the speed of 75 mph).

The distance (in feet) travelled by the car moving at 75 mph in one second is 110 feet

Speed is the distance travelled per unit time. Mathematically, it can be expressed as:

Speed = distance / time

1 mph = 1.467 fps

Therefore,

75 mph = 75 × 1.467

75 mph = 110.025 fps

Distance = speed × time

Distance = 110.025 × 1

Distance ≈ 110 feet

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Answer:

ez b no doubt

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

1. Triangle inequality theorem.

3. The missing lengths and angles are:

<B = 27.07, <C = 98 and c = 32.64.

1. According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. To determine the number of triangles that can be formed, we can use the given measurements and check if the triangle inequality theorem is satisfied.

3. We have,

a = 27, b = 15, and A = 55°,

Using the Law of Sines,

sin A/ a = sin B/ b

sin 55 /27 = sin B / 15

0.81915204428 / 27 = sin B /15

0.4550844690444 = sin B

<B = 27.07

Now, <C = 180 - <A - <B = 180 - 55 - 27.07 = 98

Now, Using the Law of Sines

sin A/ a = sin C/ C

0.81915204428 / 27 = sin 98 / c

0.030338964602963 = 0.99026807 /c

c = 32.64

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Answer:B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

               3x = -6 --->  x = -2

Answer:

1/3 = 0.3333 = 33.33% experimental probability of rolling a 9​.

Step-by-step explanation:

The experimental probability is given by the number of desired outcomes divided by the number of total outcomes, after a number of experiments is made.

In this question:

Cube rolled 78 times.

9 appeared 26 times

26/78 = 1/3 = 0.3333 = 33.33% experimental probability of rolling a 9​.

Answer:

true

Step-by-step explanation:

Answer:

TRUE is the answer.

The unit for density is a derived unit.

The number 2000 is 10 times as much as the number 200.

The number 0.5 is 1/10 as much as the number 5.

The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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9514 1404 393

Answer:

  48 kg

Step-by-step explanation:

(40 sacks)×(30 kg/sack)/(25 households) = (1200/25) kg/household

  = 48 kg/household

Each household will receive 48 kg of rice.

Answer:18

Step-by-step explanation:

first : 8-2 =6 gallons

he gave 6 to 7 students

then he needs : 18 gallons for 21 students

Answer:

10.00

Step-by-step explanation:

because 2.00 x 5 is 10 which is a hundred percent hope this helps!

Answer:

Proof:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

Step-by-step explanation:

Analyze and ensure the answer is correct.

Answer:

Step-by-step:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

The number of Caroline's textbook is 8

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.

Represent the Notebook bought by Bert as q

q = p-5

p-2= 2q

p = 2q +2

substitute 2q +2

q = 2q+2-5

2q-q = 3

q = 3

substitute 3 for q

3 = p-5

p = 5+3

p= 8

Therefore Caroline's number of notebook is 8

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Answer:

A=base×height

A=20×60

A=1,200yd

Answer:

Step-by-step explanation:

4. D- Nachos are .11 cents an ounce which is the cheapest from all the other options. do this by dividing the money amount by the ounces!

5. B- Al's tomates (.90/6) is .15 cents, Barbra (1.54/11) is .14 cents, so Barbs has a better price

6. C- 1 hour (60 minutes) divided by 12, the minutes we read = 5. Next we multiple 5x5.5(the pages she reads in 12 minutes) and we get 27 1/2!

hope i helped!

Answer:

Step-by-step explanation:

1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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The missing value in the proportion is C- 10

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that 2/5 = ?/25

Let x be the unknown number.

Here first we have the bottom half of type equation equal each other

5x=25 (2)

x= 25 (2) / 5

x = 5 (2)

x = 10

10 is the answer

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A) the average speed  of the journey from my home town to A is 30 miles per hour

B) the average speed of the journey from my home town to B is 40 miles per hours.

C) The average time is 36 miles per hours.

Average speed = distance /   time

So the answers is

A) Average speed = 10 miles ÷ (1/3 hour) = 30 miles per hour

B) Average speed = 20 miles ÷ 0.5 hours = 40 miles per hour.

C) Average speed = 30 ÷ (50/ 60) = 30 ÷ 0.8333 = 36 miles per hour.

Average Speed is essential for understanding the rate at which a travel occurs.

The speed of a vehicle may change from time to time throughout a travel. In that instance, determining the average speed is critical in order to determine the pace at which the voyage will be completed.

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Full Question:

The diagram shows the distance between my home, H, and two towns, A and B. It also shows information about journey times. See same attached.

The value of the equation is y = 4c + 18 , where c is the cost of each teacup and c = $ 6

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total cost Rebecca spend on teacups = $ 42

The cost of the large teapot = $ 18

The cost of small teacups be = c

The number of small teacups = 4

So , the equation will be

Total cost Rebecca spend on teacups = cost of the large teapot + ( number of small teacups x cost of small teacups )

Substituting the values in the equation , we get

42 = 18 + 4c

y = 4c + 18   be equation (1) , where y is the total cost

On simplifying the equation , we get

Subtracting 18 on both sides of the equation , we get

4c = 24

Divide by 4 on both sides of the equation , we get

c = $ 6

Therefore , the cost of each teacup is $ 6

Hence , the equation is y = 4c + 18

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Answer:

\(40m^4n^{10}\) units is the area of the triangle

Skills needed: Combining Like Terms, Triangle Area

Step-by-step explanation:

1) First, let's understand two important concepts:

---> The area of a triangle:

\(\frac{1}{2} * b * h\) is the area

The base is one of the sides of the triangle, and the height is perpendicular to the base and connects to a vertex usually opposite of the base.

Perpendicular means to intersect at a right angle (that square thing that is drawn into the diagram signifies a right angle).

---> Combining Like Exponent Terms

Let's say we have: \(a^b\) and \(a^c\)

If we are multiplying, we are doing \(a^b * a^c\)

\(a^b*a^c=a^{b+c}\)

Example: \(2^4*2^2=2^{4+2}=2^6\)

Think about it: 2 to the 4th power is 16, and 2 squared is 4. When multiplying those together you get 16 * 4  = 64. The method above yields the same answer.

2) Now, let's apply these two concepts to the problem shown. We are given a base (\(20m^3n^5\)) and a height perpendicular to the base (\(4mn^5\)).

---> Let's substitute in for the formula: \(\frac{1}{2} * 20m^3n^5 * 4mn^5\)

Let's combine like terms now:

\(\frac{1}{2} * 20 * 4\) can be combined and multiplied as they are all constant numbers.

\(\frac{1}{2} * 20 * 4 = 10 * 4 = 40\)

Now let's combine the exponent parts

We can split into two groups for the two different variables (\(m, n\))

---> \(m^3*m\) can be combined (remember \(m = m^1\)) --> \(m^3*m=m^3*m^1=m^4\)

---> \(n^5*n^5\) can be combined --> \(n^5*n^5=n^{10}\)

So we have: \(40*m^4*n^{10}\) as the answer.

You can take out the multiplication signs: \(40m^4n^{10}\)

(When you have unlike terms, you do not need to separate with multiplication signs)

Step-by-step explanation:

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Step-by-step explanation:

21x²-2x +1/2 = 0

x² - 2x ×21 + 1/2× 21 = 0

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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The elements using rooster-method:

A){3,4,5,6,7,8,9,10}

B){5,6,7,8,9,10,11,12,13,14}

What is rooster-method?

By listing the items of a set inside brackets, the roster method may be used to display the elements of a set. One of three ways to describe a set is in rooster form. The items of a set are listed in the roster form between curly or following brackets, with commas separating each element. When items repeat in the set, the roster approach actually has an issue. Because the elements do not follow a pattern or have a specific order, it is impossible to describe the elements in roster notation if the set has a significant number of elements or any repeated elements.

A)Set of natural odd numbers greater than 2 but less than 11:

Let us represent the set using symbol O:

O = {3,4,5,6,7,8,9,10}

B){x| x∈ N and 4<x<15}

Given that x is a natural number greater than 4 but less than 15.

X={5,6,7,8,9,10,11,12,13,14}

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