Which expression is the simplest form of 3x³ – x² + 2 (x³ − 4x²)?

The answer to the given question is length is 17m and width is 6m

Given that a rectangle's length is 7 meters less than its width.

And also given the perimeter of the rectangle is 46 meters.

We know that the rectangle's perimeter is twice the sum of its length and width.

l - length of the rectangle

w - width of the rectangle

P - perimeter of the rectangle

Then we have P = 2 × (l + w)

Given that a rectangle's length is 7 meters less than its width.

⇒ l = 4 × w - 7

Given the perimeter of the rectangle is 46 centimeters.

⇒ 2 × ( l + w) = 46

⇒ 2 × (4w - 7 + w) = 46 (using the value of length given in terms of width)

⇒ 4w - 7 + w = 23 (dividing by 2 on both the sides)

⇒ 5w - 7 = 23

⇒ 5w = 23 + 7

⇒ 5w = 30

⇒ w = 6 (dividing both sides by 5)

Using the width value in the length equation, we get

l = 4 × 6 - 7

⇒ l = 24 - 7

⇒ l = 17

Therefore, The rectangle is 17 meters in length and 6 meters in width.

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Answer: 53.7

I hope this helps!

The expression for the product of s and t, plus r will be (s × t) + r which is st + r.

This can be illustrated as an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Therefore, the expression for the product of s and t, plus r will be:

= (s × t) + r.

= st + r.

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Using integrals, the probabilities and desired measures are given as follows:

a) P(0 < X) = 0.5.

b) P(0.6 < X) = 0.392.

c) P(-0.5 ≤ X ≤ 0.5) = 0.125.

d) P(X < -2) = 0.

e) P(X < 0 or X > -0.5) = 1.

f) x = 0.965.

The distribution is given by:

f(x) = 1.5x², -1 < x < 1.

The integral of this function will be used to find the probabilities.

In item a, the probability is given by:

[tex]P(0 < X) = \int_{0}^{1} f(x) dx[/tex]

[tex]P(0 < X) = \int_{0}^{1} 1.5x^2 dx[/tex]

[tex]P(0 < X) = 0.5x^3|_{x = 0}^{x = 1}[/tex]

Applying the Fundamental Theorem of Calculus:

P(0 < X) = 0.5(1)³ - 0.5(0)³ = 0.5 - 0 = 0.5.

Item b is similar as item a, just with lower limit 0.6, hence:

P(0.6 < X) = 0.5(1)³ - 0.5(0.6)³ = 0.5 - 0.108 = 0.392.

For item c, the lower limit is -0.5 and the upper limit is of 0.5, hence:

P(-0.5 ≤ X ≤ 0.5) = 0.5(0.5)³ - 0.5(-0.5)³ = 0.125.

For item d, values of -2 and less are not on the range of the distribution, which is between -1 and 1, hence the probability is of 0.

For item e, the intersection of the intervals is the entire range of the function, hence the probability is of 1.

For item f, we have that:

0.5(1)³ - 0.5(x)³ = 0.05

0.5x³ = 0.45

x³ = 0.9.

x = (0.9)^(1/3) -> cubic root

x = 0.965.

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By using the definition of perimeter and addition and subtraction of sides, the perimeter of the composite figure is 22 centimeters.

According to the image attached aside, we find a composite figure created by adding three quadrilaterals. The perimeter is the sum of the lengths of all sides of the composite figure, that is, we need to add the lengths of the eight sides of the figure.

p = AB + BC + CD + DE + EF + FG + GH + AH

GH = AB - EF - CD

GH = 7 cm - 3 cm - 1 cm

GH = 3 cm

AH = BC - DE + FG

AH = 3 cm - 2 cm + 1 cm

AH = 2 cm

p = 7 cm + 3 cm + 1 cm + 2 cm + 3 cm + 1 cm + 3 cm + 2 cm

p = 22 cm

The perimeter of the composite figure is 22 centimeters.

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The location rotates 24.9 miles in 1 day

It is a method in which one finds the value of a unit from the value of a number of units and the value of a number of units from the value of a  unit.

In the unit method, we always count the value of a unit or quantity first, and then we calculate the value of more or less quantities. This is why this method is called the unitary method.

Earth equator moves 2.075 miles in 2 hours, We need to find how far does this location rotate in 1 day

Using Unitary Method

2 hours = 2.075 miles

1 hour = 2.075/2 mile

1 hour = 1.0375 mile

1 day = 24 hours

24 hours = 1.0375 *24

= 24.9 miles

The location rotates 24.9 miles in 1 day

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Using multiplication, Correct option is B. The amount of solution that can be made from 15 L of concentrate is 16.5L.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.

Given,

Total ant killers added in the water is 5 × 20mL = 100mL = 0.1L (using 1L = 1000mL)

Total quantity of solution is 0.1L + 1L = 1.1L

It takes 0.1 mL of ant killer to make 1.1L of solution.

⇒ Total solution that can be made from 15L of concentrate is -

⇒ 15L × 0.1L = 16.5L

∴ The solution that can be made from 15L of concentrate is  16.5L

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Answer:

C) Positively skewed, and the mean is to the right of the median.

Step-by-step explanation:

A histogram is a graphical representation of the distribution of numerical data.

A histogram is:

Since the long tail of the given histogram is on the positive side of the peak, the histogram is positively skewed (right-skewed).

The mode is the value that occurs most often in a set of data.

In a histogram, the mode is the highest point.

The median and mean fall to the right of the mode in a right-skewed (positively skewed) histogram, and the mean is always to the right of the median: mode < median < mean.

The median and mean fall to the left of the mode in a left-skewed (negatively-skewed) histogram, and the mean is always to the left of the median: mean < median < mode.

So the correct definition of the given histogram is:

Answer:

Step-by-step explanation:

[tex]A=64\pi ft^2[/tex]

[tex]r=\sqrt{\frac{A}{\pi } }[/tex]

[tex]r=\sqrt{\frac{64\pi }{\pi } }[/tex]

[tex]r=\sqrt{64}[/tex]

[tex]r=8[/tex]

So the radius is 8 ft.

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Answer:

5

Step-by-step explanation:

The correct answer is $3000.

It is quite effective to compare two or more values using the division approach. Therefore, it would be accurate to state that a ratio is a comparison or simplification of two quantities of the same type. This relationship illustrates how many times one quantity is equivalent to the other. The ratio may be defined as the number we use to represent one quantity as a percentage of the others.

As given ratio A:B:C = 2:3:5

let, A=2x, B=3x, C=5x

2x=600

x=600/2

x=$300

Total money = 2x+3x+5x

=x(2+3+5)

=x(10)

=300×10

=$3000

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Answer:

Step-by-step explanation:

34 with a remainder of 5. so basically you can say 34 1/2

Answer:

350

Step-by-step explanation:

Rounding 345=350

345 to the nearest thousands is 0

345 to the nearest hundreds is 300

345 to the nearest tens is 350

345 to the nearest whole number is 345

345 to the nearest tenths is 345.0

The square's diagonal length is (E) d = 5√2.

So, we must determine the length of the square's diagonal.

Therefore, the square's diagonal length is (E) d = 5√2.

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The correct question is given below:
What is the length of the diagonal of the square shown below? 5 45° 5 5 90° 5 O A. 5

B. 10

C. 5

D. 5/5

E. 5√2

F. 25​

Based on the fact that Lines a and m are parallel, the degree measure of angle 3 is 127

Based on the fact that a and m are parallel lines, then this means that the angle 127 degrees is corresponding to angle 1.

This means that the measure of angle 1 is 127 degrees as well because corresponding angles are congruent.

Angle 1 and Angle 3 are vertical angles. Vertical angles are also congruent. This means that if Angle 1 is 127 degrees then angle 3 will be 127 degrees as well.

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Answer:b

Step-by-step explanation:

The area of circle S will be 50.24 mm². Then the correct option is A.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius of circle S is half the radius of circle L.

Let 'r₁' be the radius of circle S and 'r₂' be the radius of circle L. Then the equation is given as

r₁ = r₂ / 2

The radius of circle L is 8 millimeters. Then the radius of the circle S is calculated as,

r₁ = 8 / 2

r₁ = 4 mm

The area of the circle S is calculated as,

A = πr₁²

A = 3.14 x (4)²

A = 50.24 mm²

The range of the circle S is 4 mm. Then the region of the circle S will be 50.24 mm². Then the right choice is A.

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Answer: the answer is 42.5

Answer:

253

Step-by-step explanation:

512-15×14-49

512-210-49

302-49

= 253 Ans

The ratio of squares to circles is 1/ 2

A ratio is defined as the comparison of two or more numbers or elements indicating their sizes in relation to each other.

From the information given, we have that;

To determine the ratio of the squares to circles, we take the quotient of squares to circles, we have;

= 3/ 6

Reduce to simpler form

= 1/ 2

Thus, the ratio of squares to circles is 1/ 2

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Answer:O 18+3

O-18+3

O-18+(-3)

Step-by-step explanation:O 18+3

O-18+3

O-18+(-3)

Answer:

m+6n+5

Step-by-step explanation:

Let's simplify step-by-step.

m+8+6n−3

=m+8+6n+−3

Combine Like Terms:

=m+8+6n+−3

=(m)+(6n)+(8+−3)

=m+6n+5

The length of the side x of the triangle ADE is 16.5 units.

If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be similar (corresponding sides). When compared individually, similar triangles may have different side lengths, but they must all have the same ratio of their side lengths and equal angles.

From figure, it is given that:

AB = 3 units

BC = 2 units

AD = x units

DE = 11 units

We know that the triangle ABC ~ ADE.

Therefore, the ratio of corresponding sides of the triangles will be same.

Now,

AB/ AD = BC/ DE

3/x = 2/11

Cross multiply to get:

2x = 3(11)

2x = 33

x = 33/2

x = 16.5 units

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Answer:

well wheren is the question

Answer:

maximum = (2,-3)

Step-by-step explanation:

the domain of the function y = 56.35 x is 0.27 ≤ x ≤ 0.44.

We are given a function:

y = 56.35 x

We are also given that at least 15 but no more than 25 students go to the water park.

This means that the range of y is:

Range = 15 ≤ y ≤ 25.

Now, we need to find the domain of the function.

Put y = 15 in the equation:

15 = 56.35 x

x = 15 / 56.35

x = 0.27

Put y = 25 in the equation:

25 = 56.35 x

x = 25 / 56.35

x = 0.44

So, the domain becomes:

Domain = 0.27 ≤ x ≤ 0.44.

Therefore, we get that, the domain of the function y = 56.35 x is 0.27 ≤ x ≤ 0.44.

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Answer:

asdfasdf

Step-by-step explanation:

asdfasdfasdfasdfasdf

[tex]9x = 81+4[/tex]

[tex]9x = 85[/tex]

[tex]x = 85/9[/tex](divide using calculator)

Observe that

[tex]\dfrac{(n!)^2}{(2n+1)!} = \dfrac{n!(2n-n)!}{(2n+1)(2n)!} = \dfrac1{(2n+1)\binom{2n}n}[/tex]

Starting with a well-known series

[tex]\displaystyle 2\arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}[/tex]

we take some (anti)derivatives to find a sum that more closely resembles ours.

Let [tex]f(x)=2\arcsin^2(x)[/tex]. Then

[tex]\displaystyle f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{n \binom{2n}n}[/tex]

[tex]\displaystyle x f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{n \binom{2n}n}[/tex]

[tex]\displaystyle x f''(x) + f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{\binom{2n}n}[/tex]

[tex]\displaystyle x^2 f''(x) + x f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{\binom{2n}n}[/tex]

Noting that both sides go to zero as [tex]x\to0[/tex], by the fundamental theorem of calculus we have

[tex]\displaystyle \sum_{n=1}^\infty \frac{2^{2n} x^{2n+1}}{(2n+1)\binom{2n}n} = \frac14 \int_0^x (t^2 f''(t) + t{}f'(t)) \, dt[/tex]

so that when [tex]x=\frac12[/tex], and rearranging some factors and introducing a constant, we recover a useful sum.

[tex]\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac12 \int_0^{1/2} (x^2 f''(x) + x f'(x)) \, dt[/tex]

Integrate by parts.

[tex]\displaystyle \int_0^{1/2} x^2 f''(x) \, dx = \frac14 f'\left(\frac12\right) - 2 \int_0^{1/2} x f'(x) \, dx[/tex]

[tex]\displaystyle \int_0^{1/2} x f'(x) \, dx = \frac12 f\left(\frac12\right) - \int_0^{1/2} f(x) \, dx[/tex]

Then our sum is equivalent to

[tex]\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac18 f'\left(\frac12\right) - \frac14 f\left(\frac12\right) + \int_0^{1/2} \arcsin^2(x) \, dx[/tex]

The remaining integral is fairly simple. Substitute and integrate by parts.

[tex]\displaystyle \int_0^{1/2} \arcsin^2(x) \, dx = \int_0^{\pi/6} u^2 \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} - 2 \int_0^{\pi/6} u \sin(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 2 \int_0^{\pi/6} \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1[/tex]

Together with

[tex]f\left(\dfrac12\right) = 2 \arcsin^2\left(\dfrac12\right) = \dfrac{\pi^2}{18}[/tex]

[tex]f'\left(\dfrac12\right) = \dfrac{4\arcsin\left(\frac12\right)}{\sqrt{1-\frac1{2^2}}} = \dfrac{4\pi}{3\sqrt3}[/tex]

we conclude that

[tex]\displaystyle \sum_{n=0}^\infty \frac{(n!)^2}{(2n+1)!} = \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} \\\\ ~~~~~~~~~~~~~~~~~~ = 1 + \left(\frac18\cdot\frac{4\pi}{3\sqrt3}\right) - \left(\frac14\cdot\frac{\pi^2}{18}\right) + \left(\frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \boxed{\frac{2\pi}{3\sqrt3}}[/tex]

[tex](f/g)(7)=-\frac{9}{26}[/tex].

[tex]f(a)=-2a-4\\ \\g(a) =a^ 2+3[/tex]

[tex]\frac{-2a-4}{a^ 2+3}[/tex]

For this, we substitute a by 7 throughout the entire expression and calculate.

[tex]f/g(7)=\frac{-2(7)-4}{(7)^ 2+3}=\frac{-18}{52} =-\frac{9}{26}[/tex]

[tex](f/g)(7)=-\frac{9}{26}[/tex].