Choose the correct factorization for the polynomial 21xy+15x+35ry+25r

Answer:

Correct answer is option C (√61)

Step-by-step explanation:

in this question we have given a right triangle in which

∠C=[tex]90^{0}[/tex]

BC = 6 and AC = 5

we have to find the length of the hypotenuse, AB=?

To find the the hypotenuse we will apply Pythagoras theorem (According to Pythagoras theorem, "in a right angle triangle, square of hypotenuse is equal to the sum of square of other two sides")

In ΔABC by Pythagoras theorem

[tex]AB^{2}=AC^{2}+BC^{2}[/tex]...................(1)

put values of BC and AC in equation 1

[tex]AB^{2}=5^{2}+6^{2}[/tex]

[tex]AB^{2}=25+36[/tex]

[tex]AB^{2}=61[/tex]

AB=√61

False. A Fermi estimate doesn't rely on geometry. It's a method for approximating large numbers using basic assumptions and math.

False. A Fermi estimate is not reliant on geometry to estimate measurements of real-world objects.

Instead, it's a method for making quick, rough approximations of quantities or numbers, especially when precise data is unavailable or impractical to obtain. Named after physicist Enrico Fermi, this approach involves breaking down complex problems into simpler components, making reasonable assumptions, and using basic mathematics to arrive at an estimate.

While geometry might be employed in some cases, Fermi estimates primarily focus on leveraging broad understanding and educated guesses to reach ballpark figures rather than precise calculations based on specific measurements.

The required 1/8 divided by 6 is equal to 1/48.

To solve 1/8 divided by 6, we can rewrite it as a fraction. The reciprocal of 6 is 1/6, so the division problem becomes (1/8) * (1/6). To multiply fractions, we multiply the numerators together and the denominators together.

Step 1 is given as:
= (1/8) * (1/6)

Step 2(simplification) is given as:

= 1 * 1 / 8 * 6
= 1/48

Therefore, the required 1/8 divided by 6 is equal to 1/48.

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The correct statement is that if two polygons are similar, their corresponding sides are proportional while their corresponding angles are congruent. Similar polygons have the same shape but can have different sizes, and this applies across various geometrical figures and principles, like the Pythagorean theorem in the context of right triangles.

The correct statement among the given options is: If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. When polygons are similar, this means their shapes are geometrically the same but they may differ in size. The ratios of the lengths of corresponding sides of similar polygons are equal, which is true for any pairs of similar polygons, not just triangles. The corresponding angles, on the other hand, are congruent, which means they have the same measure in both polygons.

To explain this concept, we use different examples in geometry. For instance, in similar triangles, not only are the three angles in one triangle congruent to the three angles in the other, but also the sides are proportional, which can be expressed as the ratio of any two corresponding sides in the two triangles being equal. This proportional relationship is a key characteristic of similarity in geometry.

Moreover, a statement like the Pythagorean theorem applies to right triangles, stating that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is connected to similarity because one can generate a family of similar right triangles by scaling a single right triangle.

The opposite of 890 is -890, which means -890 added to 890 equals zero.

The opposite of a number is defined as a number that, when added to the original number, results in zero. To find the opposite of a number, you simply change its sign. If the number is positive, the opposite is negative, and if the number is negative, the opposite is positive. Therefore, the opposite of 890 is -890.

Answer:

Solution-

∵ cotx = (cosx÷sinx)

∴ The given expression can be written as

sinx + cotx·cosx = sinx + ( cosx÷ sinx).cosx

⇒sinx +(cosx)²÷sinx = [ (sinx)² + (cosx)²] ÷ sinx

⇒ 1÷ sinx = cosecx = cscx

using the identity (sinx)²+(cosx)²=1

∴ option B is correct.

The expression that is equal to the rational expression when x does not equal to 5 or -1 is; (x - 7)/(x -5)

We want to simplify the algebraic expression;

(x - 7)(x + 1)/(x + 1)(x - 5)

Now, looking at the given expression, we see that (x + 1 ) is common to both numerator and denominator and as such they will cancel out to leave us with;

(x - 7)/(x -5)

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In the given set, the mean is 64, the median is 66, there is no mode, and the range is 62.

To find the mean, median, mode, and range of the given set of numbers: 83, 75, 74, 40, 85, 64, 23, 68.

1. Mean:

[tex]\[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}} \][/tex]

[tex]\[ \text{Mean} = \frac{83 + 75 + 74 + 40 + 85 + 64 + 23 + 68}{8} \][/tex]

[tex]\[ \text{Mean} = \frac{512}{8} \][/tex]

[tex]\[ \text{Mean} = 64 \][/tex]

2. Median:

The median is the middle number when the numbers are arranged in ascending order.

Arranging the numbers in ascending order: 23, 40, 64, 68, 74, 75, 83, 85

Since there are 8 numbers, the median is the average of the two middle numbers:

[tex]\[ \text{Median} = \frac{64 + 68}{2} \][/tex]

[tex]\[ \text{Median} = 66 \][/tex]

3. Mode:

The mode is the number that appears most frequently.

In this set, there is no number that appears more than once.

So, there is no mode.

4. Range:

The range is the difference between the largest and smallest numbers.

[tex]\[ \text{Range} = \text{Largest number} - \text{Smallest number} \][/tex]

[tex]\[ \text{Range} = 85 - 23 \][/tex]

[tex]\[ \text{Range} = 62 \][/tex]

So, for the given set of numbers, the mean is 64, the median is 66, there is no mode, and the range is 62.

The Ratio of the square feet to the per flower type is 14 : 1.

A Ratio shows the relative size of two or more value.

According to the question,

Area of a flower garden = 70 square feet

Number of flower plants varieties = 5

Formula for Perimeter of square = 4a where 'a' is sides of a square

4(a) = 70

a=70/4

a=15

To find the Ratio of the square feet to the per flower type

70 : 5

14 : 1.

Hence,  the Ratio of the square feet to the per flower type is 14:1

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Answer: Permutation

Permutation is a way, in which a set or number of things can be ordered or arranged. It is a listing where order matters and each thing in the list of things appears only once.

 In Mathematics, permutation is the action of changing the arrangement of a set of items. .It is also called an "arrangement number" or "order 

0.0003840

Written in scientific notation!

Move the decimal point.

.00384 x 10^1

.0384 x 10^2

.384 x 10^3

3.84 x 10^4

38.4 x 10^5

Answer:

[tex]41\%[/tex]

Step-by-step explanation:

we have the ratio

[tex]\frac{41}{100}[/tex]

To write as percent, multiply the ratio by 100

so

[tex]\frac{41}{100}*100=41*100/100=41\%[/tex]

Given mean = 24.5 and standard deviation = 1.7

Within 1 standard deviations, x ∈ [24.5 - 1.7 , 24.5 + 1.7] or [22.8 , 26.2].

Within 2 standard deviations, x ∈ [24.5 - 2(1.7) , 24.5 + 2(1.7)] or [21.1 , 27.9].

Within 3 standard deviations, x ∈ [24.5 - 3(1.7) , 24.5 + 3(1.7)] or [19.4 , 29.6].

Given values are 24, 23, 28, 23, 24, and 25.

So {24, 23, 23, 24, 25} fall within 1 standard deviation and {28} falls within 3 standard deviations.