a table is 6 feet long and 3 feet wide. You extend the table by inserting two identical table leaves. The longest side length of each rectangular leaf is 3 feet. The extended table is rectangular with an area of (18+6x) square feet. a) write an algebraic expression that represents the length of the extended table b) what does your variable represent?

Answer:

15

Step-by-step explanation:

You have to multiply 0.60 by 25 in order to get 15! Easy, right?

To evaluate 8[tex]a^3b^{-2[/tex] for a=4 and b=-5, substitute the given values into the expression and simplify to obtain the final result, which is 16.32.

To evaluate 8[tex]a^3b^{-2[/tex] for a=4 and b=-5, we substitute the given values into the expression. Plugging in these values, we have:

8[tex](4)^3(-5)^{(-2)[/tex]

Simplifying this expression, we get:

8(64)(1/[tex](-5)^2)[/tex]

The next step is to calculate the value of [tex](-5)^2[/tex], which equals 25. So the expression becomes:

8(64)(1/25)

Then, multiplying 64 by 1/25, we get:

8(64/25)

Finally, multiplying 8 by 64/25, we obtain:

16.32

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After 8 movie rentals, will the cost of renting movies with the membership be less than the cost of renting movies without the membership.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the information given in the question,

There are two options for renting movies.

As per the first option,

Pay $4 per movie, so the equation will be,

y = 4x     (i)

Where y is the total cost and x is the number of movies.

As per the second option,

Take a membership of $20, and they pay $1.50 per movie.

So, the equation will be,

y = 1.5x + $20   (ii)

Where y is the total cost and x is the number of movies.

Now, solve equations (i) and (ii)

4x = 1.5x + $20

4x - 1.5x = 20

2.5x = 20

x = 20/2.5

x = 8

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Answer:

For the proof, check the explanation part.

Step-by-step explanation:

In the given figure, the lines PQ and RS are parallel and line t is transversal.

It is required to prove that measure of angle 4 is equal to measure of angle 8.

Now, measure of angle 4 will be equal to measure of angle 6 because they are the alternate interior angles.

Now, the measure of angle 6 will be equal to measure of angle 8 because they are the vertically opposite angles.

So, form the above information, it can be concluded that,

[tex]\angle 4=\angle 6\\\angle 6=\angle 8\\\angle 4=\angle 8[/tex]

Hence proved.

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Answer: Our required probability is 12%.

Step-by-step explanation:

Since we have given that

Probability of being selected as the captain of the baseball team= P(A) = 60%

Probability of being selected as elected student body president = P(B) = 20%

We need to find the probability of being selected as the captain of the baseball team and will be elected student body president.

Since both the events A and B are independent events.

So, it becomes,

[tex]P(A\cap B)=P(A)\times P(B)=0.6\times 0.2=0.12\times 100\%=12\%[/tex]

Hence, our required probability is 12%.

Answer:

The given product is

[tex]3.4 \times 0.5 = 1.7[/tex]

This results was showed by the calculator, which doesn't shows the two decimal numbers that it should have.

The reason why the calculator only shows one decimal number, it's because the second decimal number is zero, and it would be the same if we express [tex]1.7[/tex] or [tex]1.70[/tex], that zero doesn't change the value that the number represents.

However, if we solve without calculator, we would have [tex]1.70[/tex], because the multiplication rule states that we should add to the result as many decimal number have both factor of the multiplication, which in this case they have two.

When multiplying or dividing decimals, the number of decimal places in the product or quotient may not be the same as the factors or dividend and divisor. The product or quotient should have the same number of decimal places as the factor/dividend or divisor with the fewest decimal places.

When multiplying or dividing decimal numbers, the number of decimal places in the product or quotient may not be the same as the number of decimal places in the factors or dividend and divisor. This happens because the calculator does not consider significant figures and simply performs the operation.

To determine the number of decimal places in the product or quotient, look at the decimal places in the factors or dividend and divisor. The product or quotient should have the same number of decimal places as the factor/dividend or divisor with the fewest decimal places.

In Tony's example, 3.4 x 0.5 = 1.7, the factor with the fewest decimal places is 0.5 with one decimal place. Therefore, the product should also have one decimal place.

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Answer: 15

Step-by-step explanation: k12 Interim Checkpoint: Grade 6 Checkpoint 1 - Part 1

Final answer:

The other rational number is 384/7.

Explanation:

To find the other rational number, we can set up a proportion by setting the two ratios equal to each other. The given ratio is 66/7, and the product of the two ratios is 48/5.

Let the other rational number be represented by w. Writing the proportion, we have:

66/7 = w/(48/5)

Cross multiplying and solving for w:

w = (66/7) * (48/5)

w = 8*48/7

w = 384/7

Hence, the other rational number is 384/7.

The total amount of money spent on sandwiches is $26.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Twenty-five students go to lunch. The pizza costs $3 and the sandwiches cost $2.

Twelve students buy pizza.

∴ 13 students bought sandwiches.

So, The total money they spent on Pizza and Sandwiches is (3×12) + (2×13) = 36 + 26 = $52.

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Answer:

The answer is 24.28 square meters.

Step-by-step explanation:

Kwan bought three rolls of regular wrapping paper with 6.7 square meters of paper each.

The paper in three rolls become = [tex]3\times6.7=20.1[/tex] square meter

He also bought a roll of fancy wrapping paper containing 4.18 square meters.

So, total paper that Kwan had is = [tex]20.1+4.18=24.28[/tex] square meter.

Therefore, the answer is 24.28 square meters.

Answer: The answer is 20.1

Step-by-step explanation: To find out how much paper Kwan had altogether, we need to calculate each type's total square meters of wrapping paper and then add them together.

Kwan bought three rolls of regular wrapping paper, each with 6.7 square meters of paper. To find the total square meters for the traditional wrapping paper, we can multiply the number of rolls (3) by the square meters per roll (6.7):

3 rolls * 6.7 square meters/roll = 20.1 square meters

So, Kwan has 20.1 square meters of regular wrapping paper.

In addition, Kwan also bought a roll of fancy wrapping paper, which contains 4.18 square meters.

To find the total amount of wrapping paper Kwan has, we can add the square meters of regular wrapping paper to the square meters of fancy wrapping paper:

A. For this to be a linear situation, we must assume that Marisa is walking a straight path so that the time needed to cover a distance is constant.

B. The equation of the line is given as:

y = m x + b

where in this case y is the distance, m is the slope or the time it takes for each block, x is the time, and b is the y intercept or the initial position of Marisa

C. The slope m can be calculated using the formula:

m = (y2 – y1) / (x2 – x1)

m = (8 – 12) / (6 – 0)

m = -0.67

The negative sign means that the distance between Marisa and Sanjay’s home is decreasing by time. It further means that there is a decrease in 0.67 blocks per minute.

D. y = - 0.67 x + b

The initial point of Marisa is at 12 blocks away from Sanjay’s home, hence b = 12.

Finding for time x when distance is 0 (y = 0):

0 = -0.67 x + 12

x = 17.9 minutes

Hence it takes around 17.9 minutes to reach Sanjay’s home.

Answer:

Option (a) is correct.

The area of triangle is 24 m²

Step-by-step explanation:

Given : A  triangle with base 6 m and height  8 m

We have to find the area of the triangle and choose the correct option from the given options.

Area of triangle = [tex]\frac{1}{2}\cdot base\cdot height[/tex]

Given Base = 6 m

and height = 8 m

Therefore, Area of triangle = [tex]\frac{1}{2}\cdot 6\cdot 8=24[/tex]

Thus, The area of triangle is 24 m²

The correct option is [tex]\boxed{\bf option A}[/tex] i.e., the area of triangle is [tex]\boxed{\bf 24\text{\ \bf m}^{2}}[/tex].

Further explanation:

We are given the base and height of the triangle as shown in the given figure.

If the height and base of a triangle is given then the area of the triangle can be calculated by the formula given below,

[tex]\boxed{\text{Area of Triangle}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}}[/tex]               .....(1)

Calculation:

Here, the height of the triangle is [tex]8\text{ m}[/tex] and base of the triangle is [tex]6\text{ m}[/tex].

Substitute the value of height that as [tex]8\text{ m}[/tex] and the value of base that as [tex]6\text{ m}[/tex] in equation (1) to obtain the area of the triangle as follows:

[tex]\begin{aligned}\text{Area of Triangle}&=\dfrac{1}{2}\cdot 6\cdot 8\\&=\dfrac{48}{2}\\&=24\end{aligned}[/tex]  

Therefore, the area of the triangle is [tex]\boxed{\bf 24\text{\ \bf m}^{2}}[/tex].

This implies that the correct option is [tex]\boxed{\bf option A}[/tex].

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1. Problem on the rotation of the triangle   about the origin https://brainly.com/question/7437053.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Triangle

Keywords: Triangles, area, height, base, volume, heron’s formula, edges, vertices, collinear, non-collinear, geometry, equilateral triangles, isosceles triangle, right angled triangle, angles, Pythagoras theorem, acute angle, obtuse triangle, congruent triangles, similar triangles.

Answer:

The total cost of a pencil from the student store is $ 1.188

Step-by-step explanation:

Given,

The original cost or wholesale cost of each pencil = $ 0.50,

Markup percentage = 120 %,

So, the cost of the pencil after markup = 0.50 + 120% of 0.50

[tex]=0.50+\frac{120\times 0.50}{100}[/tex]

[tex]=0.50+\frac{60}{100}[/tex]

[tex]=0.50+0.6[/tex]

[tex]=1.1[/tex]

Now, sales tax = 8 %,

Hence, the final total cost of a pencil = 1.1 + 8 % of 1.1

[tex]=1.1 + \frac{8\times 1.1}{100}[/tex]

[tex]=1.1+\frac{8.8}{100}[/tex]

[tex]=1.1+0.088[/tex]

[tex]=\$1.188[/tex]

Answer:

564

Step-by-step explanation:

80            x        7        =        560      +             4               =         564

Divsor          Answer                                  Remainder                Divident

Therefore, the number is 564.

Final answer:

Seth's table is not square because it has different side lengths of 36' and 18'. For a rectangle to be a square, all four sides must be of equal length. Additionally, the side lengths and the diagonal of Seth's table do not satisfy the Pythagorean relation for a square.

Explanation:

To determine whether Seth's table is square or not, we need to recognize that a square is a rectangle with equal sides. Since the table has sides measuring 36' and 18', we can immediately conclude that it is not square because the lengths of the sides are different. In a square, the lengths of all four sides would be equal.

To further illustrate this point, let's consider the diagonal of a square. For a square, the diagonal can be determined using the Pythagorean Theorem, where the diagonal is the square root of twice the side squared, because a square is essentially two identical right-angle triangles put together.

In Seth's table, if we were to apply the Pythagorean Theorem (a² + b² = c²), we would find that the square of one side plus the square of the other should equal the square of the diagonal. By doing the calculation:

36'² + 18'² = 1296' + 324' = 1620',

which does not equal the square of the diagonal given, which is 43'² = 1849'. This further confirms that the table cannot be square since the sides and the diagonal do not satisfy the Pythagorean relation for a square.

Solution-

Two cars leave the same location traveling in opposite directions.

The first car leaves at 3 p.m and has a speed of 55 mph

The second car leaves at 4 p.m and has a speed of 75 mph

Let x hours after the first car leaves, the two cars are 380 miles apart from each other.

[tex]Speed =\frac{Distance}{Time}[/tex]

[tex]\Rightarrow Distance=Speed\times Time[/tex]

In this x hours, distance covered by the first car,

[tex]\Rightarrow Distance_1=Speed_1\times Time_1[/tex]

[tex]\Rightarrow Distance_1=55\times x[/tex]

As the second car leaves at 4 p.m i.e 1 hour late as compared to the first car, so distance covered by the second car in (x-1) hours,

[tex]\Rightarrow Distance_2=Speed_2\times Time_2[/tex]

[tex]\Rightarrow Distance_2=75\times (x-1)[/tex]

According to the question,

[tex]Distance_1+Distance_2=380[/tex]

[tex]\Rightarrow 55\times x+75\times (x-1)=380[/tex]

[tex]\Rightarrow 55x+75x-75=380[/tex]

[tex]\Rightarrow 130x=455[/tex]

[tex]\Rightarrow x=3.5[/tex]

∴ After 3.5 hours from 3 p.m i.e at 6.5 p.m the cars will have a distance of 380 miles.

The expression which is obtained on factorising it completely is:

         [tex]x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)[/tex]

We are asked to factorize the expression which is given by:

               [tex]x^6-64y^3[/tex]

This expression could also be written as:

[tex]x^6-64y^3=(x^2)^3-(4y)^3[/tex]

Now, we know that:

[tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex]

Here we have:

[tex]a=x^2\\\\and\\\\b=4y[/tex]

Hence,

[tex]x^6-64y^3=(x^2-4y)((x^2)^2+(4y)^2+x^2\times 4y)[/tex]

i.e.

[tex]x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)[/tex]