what is the surface area of this triangular prism

You can calculate that, since all children and horses have two eyes, and that children have two legs and horses have four, and the total number of eyes is 20 and the total number of legs is 30, there were 5 children and 5 horses.

This problem can be solved using basic algebra. We need to count the numberOfChildren and numberOfHorses in a manner where each child and each horse contribute two eyes and with each child having two legs while each horse has four legs.

Let's make two assumptions:

So, we can write two equations according to the question:

By solving these two equations, we find that the numberOfChildren = 5 and numberOfHorses = 5.

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Answer:

3360

Step-by-step explanation:

45 plus 50 plus 55 plus 60 equals 3360 !

We have defined two variables, bookshelves (b) and tables (t), to reflect the number of each that Andrew can make. The constraints representing time and cost are given by two inequalities and these produce a feasible region of possible combinations of bookshelves and tables. Within this region, Andrew can determine the combination that gives maximum profit.

Let's define the variables: Let's say 'b' is the number of bookshelves Andrew makes and 't' is the number of tables he makes.

B. The constraint inequalities are: b + t <= 25 due to the time constraint, and 20b + 45t <= 675 due to the cost constraint. These inequalities represent the limit on the number of pieces he can make due to time and the limit due to money available to buy materials.

C. In this system of inequalities, the feasible region would be determined by finding the intersecting points (vertices) of our inequalities. The feasible region is the set of all points that satisfy all the constraints of the problem.

To ascertain the maximum profits, Andrew should calculate his profit for each possible combination of bookshelves and tables within the feasible region to find the combination with the maximum profit.

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D

It provides concise information which is derived from the question.

Answer: 28.26 inches

Step-by-step explanation:

We know that the circumference of a circle is given by :-

[tex]\text{Circumference}=\pi d[/tex], where d is the diameter of the circle.

Given: The diameter of pie dish (d)= 9 inches

Then the circumference of the pie dish is given by :_

[tex]\text{Circumference}=\pi (9)\\\\\Rightarrow\text{Circumference}=(3.14)(9)\text{Circumference}=28.26\ inches[/tex]

The measure of an edge of a cube = 4.7 in

We have to determine the surface area of the cube.

The surface area of a cube is the area of the six squares that cover it. The area of one square is [tex] a^{2} [/tex]. Therefore, area of six squares = [tex] 6a^{2} [/tex].

Surface area of cube = [tex] 6a^{2} [/tex] , where a is the edge of a cube

Therefore, Surface area of this cube

= [tex] 6a^{2} [/tex]

= [tex] 6 \times (4.7)^{2} [/tex]

= 132.54 square inches.

Therefore, surface area of the cube is 132.54 square inches.

Answer:256

Step-by-step explanation:

Answer:

265 miles.

Step-by-step explanation:

The reason why it is more difficult to use repeated addition when multiplying two mixed numbers than it is to use repeated addition when you are multiplying a mixed number by a whole number is:

This refers to the mathematical operation that involves to find the product of a set of numbers.

This refers to the type of number that is made up of a whole number and a proper fraction, for example,2 [tex]1/4[/tex].

With this in mind, if we have mixed numbers like  1 1/2 x 2 1/2, and we were to use repeated addition to multiply them, we would have 2 whole groups of 1 1/2, but then we would need to represent 1/2 group which requires multiplying or dividing first.

Read more about multiplication here:
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A triangle with side lengths of 22, 32, and 55 units is an obtuse triangle.

A triangle with side lengths of 22, 32, and 55 units is an obtuse triangle.

To determine the type of triangle, we can use the Pythagorean theorem. If the sum of the squares of the lengths of the two shorter sides is greater than the square of the length of the longest side, then the triangle is obtuse. In this case, 22^2 + 32^2 = 484 + 1024 = 1508, which is greater than 55^2 = 3025, so the triangle is obtuse.

An obtuse triangle is a triangle with one angle greater than 90 degrees. In this case, the angle opposite the longest side will be greater than 90 degrees.

To find the number of field trips Cornell's class took last year, we set up the equation 3x + 1 = 7, where x represents the number of trips last year. Solving this, we find that Cornell's class took 2 field trips last year.

The question involves a basic mathematical equation to determine the number of field trips taken by Cornell's class last year. Since this year Cornell's class took 7 trips, and this number is one more than three times the amount of the previous year, we can set up the equation as x being the number of trips taken last year:

3x + 1 = 7

To find x, subtract 1 from both sides of the equation:

3x = 7 - 1

3x = 6

Now divide both sides by 3 to solve for x:

x = 6 / 3

x = 2

So, Cornell's class took 2 field trips last year.

The value 0.75 is 100 times larger than the value 0.0075.

To solve the problem, we need to determine how many times larger 0.75 is compared to 0.0075. This can be done by dividing the larger number by the smaller number and then simplifying the result.

First, write both numbers as fractions to make the division easier:

[tex]\[ 0.75 = \frac{75}{100} \][/tex]

[tex]\[ 0.0075 = \frac{75}{10000} \][/tex]

Now, divide the fraction representing 0.75 by the fraction representing 0.0075:

[tex]\[ \frac{0.75}{0.0075} = \frac{\frac{75}{100}}{\frac{75}{10000}} \][/tex]

When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction:

[tex]\[ \frac{\frac{75}{100}}{\frac{75}{10000}} = \frac{75}{100} \times \frac{10000}{75} \][/tex]

The 75s in the numerator and denominator cancel out:

[tex]\[ \frac{75}{100} \times \frac{10000}{75} = \frac{10000}{100} \][/tex]

Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 100:

[tex]\[ \frac{10000}{100} = \frac{100 \times 100}{100} = 100 \][/tex]

Answer:  Another root of the same function is 7-2i.

Step-by-step explanation:  Given that 7+2i is a root of a polynomial function.

We are to find the another root of the same function.

We know that

if a complex number a+ib is one of the roots of a polynomial function f(x), then the conjugate a-ib is another root of the same polynomial f(x).

According to the given information, the conjugate of 7+21, that is, 7-2i is another root of the same polynomial function.

Thus, another root of the same function is 7-2i.