Using the principle of
mathematical induction show that 10^(2n-1 ) + 1 is divisible by 11 for all z

We conclude that the width of the rectangular garden is 80 feet.

Let's define the variables:

The perimeter of a rectangle of length L and width W is given by the simple formula:

P = 2*(L + W)

The perimeter is equal to 400ft, then:

400ft = 2*(L + W)

And we know that the length is 120ft, then:

L = 120ft.

Replacing the length in the perimeter equation we get:

400ft = 2*(120ft + W)

Now we can solve this linear equation for W.

400ft/2 = 120ft + W

200ft = 120ft + W

200ft - 120ft = W

80ft = W

We conclude that the width of the rectangular garden is 80 feet.

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Split up [0, 16] into 4 equally-spaced subintervals of length [tex]\frac{16-0}4=4[/tex],

[0, 16] = [0, 4] U [4, 8] U [8, 12] U [12, 16]

with midpoints 2, 6, 10, and 14, respectively.

Then with the midpoint rule, we approximate the integral to be about

[tex]\displaystyle \int_0^{16} \sin(\sqrt x) \, dx \approx 4 \left(\sin(\sqrt2) + \sin(\sqrt6) + \sin(\sqrt{10}) + \sin(\sqrt{14})\right) \approx \boxed{4.1622}[/tex]

The given statement that's true about the function is g(-13) = 20 is true for g.

From the information given, the function, g, has a domain of -20 < x < -5 < g(x) <45 and that g(0)= -2 and g(-9)= 6.

Let's analyze the options that are given in the scenario. g(7) = -1. It should be noted that 7 isn't in our domain. Therefore, this isn't possible.

g(-13) = 29

x = 13 is in our domain and 20 is also is in our range. Therefore, this is true for g.

g(0) = 2.

This isn't true because it is given that g(0) = 2

In conclusion, the given statement that's true about the function is g(-13) = 20 is true for g.

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(infinity -1/2]u [-1/2 -1/2] u [1/2 infinity)

Answer:

Step-by-step explanation:

(1400x14.5x5%) + 1400 =2415

Answer: 14.5 months

Answer:

Step-by-step explanation:

The correct value of w is 20 as the width of a rectangle must be positive. A quadratic function always has 2 zeroes and in a case like this the negative one is ignored.

Answer:

B

Step-by-step explanation:

Cos is the adjacent side over the hypotenuse.  The adjacent side to <E is side ED.  The hypotenuse is side EF.  ED/EF.  They do not go right out and give you this choice, but you see that B says the same thing.

Answer:

2

Step-by-step explanation:

Substitute:

2(1)(3)+2 / 2(1)(3)-2 =

6 + 2 / 6 - 2 =

8 / 4 =

2.

Hey there!

2ab + 2 / 2ab - 2

= 2(1)(3) + 2 / 2(1)(3) - 2

= 2(3) + 2 / 2(3) - 2

= 6 + 2 / 6 - 2

= 8 / 4

= 2

Therefore, your answer should be: 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

If Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

Given that Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb.

We are required to find the inequality that represents the number movies and songs that Caisse downloads each month.

Inequality is like an equation that shows the relationship between variables that are expressed in greater than, less than , greater than or equal to , less than or equal to sign.

let the number of movies be x and the number of songs be y.

According to question Caisse cannot download more than 1000 mb, so we will use less than towards equation.

It will be as under:

85x+4y<1000.

Hence if Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \:6 = 2(y + 2)[/tex]

[tex] \qquad❖ \: \sf \:(y + 2) = \cfrac{6}{2} [/tex]

[tex] \qquad❖ \: \sf \:y + 2 = 3[/tex]

[tex] \qquad❖ \: \sf \:y = 3 - 2[/tex]

[tex] \qquad❖ \: \sf \:y = 1[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

The answer is t ≤ 11.

If we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.

Given two equations x-2y=5 and 4x+12y=-20.

We are required to find the value of x and y through substitution method.

Equation is like a relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Equation can be a linear equation,quadratic equation, cubic equation or many more depending on the power of variable.

They can be solved as under:

x-2y=5---------------1

4x+12y=-20--------2

Finding value of variable x from equation 1.

x=5+2y--------------3

Use the value of variable  x in equation 2.

4x+12y=-20

4(5+2y)+12y=-20

20+8y+12y=-20

20y=-20-20

20y=-40

y=-40/20

y=-2

Use the value of variable y in equation 3.

x=5+2y

x=5+2*(-2)

x=5-4

x=1

Hence if we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.

Question is incomplete as it should include one more equation x-2y=5.

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The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000

We have x + y + z = 1000000

((1+0.03)x - x)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000

4z + x + z = 1000000

((1+0.03)4z - 4z)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000

((1+0.03)4z - 1)+ ((1+0.04)y - 1) + ((1 + 0.02)z-1) = 34000

12/100z + 4/100y +2/100z = 34000

2y + 7z = 1700000

-2y - 10z = -2000000

2y + 7z = 1700000

Solve through the use of the simultaneous linear equation

z = 100000

y = 500000

x = 400000

The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000

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Step-by-step explanation:

second one

explanation: trust me bro

The vector in component form is given by:

V = i - j.

A vector is given by the terminal point subtracted by the initial point, hence:

(3,-4) - (2, -3) = (3 - 2, -4 - (-3)) = (1, -1)

A vector (a,b) in component form is:

V = a i + bj.

Hence, for vector (1,-1), we have that:

V = i - j.

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Answer:

x = 46 degrees

Step-by-step explanation:

180 - 134 = 46

Answer:

46°

Step-by-step explanation:

134 + x   add to a straight line angle = 180

134+x = 180

x = 46

The 4.2 inches base length and 36 in.² area of the given triangle and the 5.6 inches base length of the similar triangle gives the area of the similar triangle as 64 square inches

Area of a triangle = (Base length × Height)/2

Area of the given triangle = 36 in.²

Base length of the given triangle = 4.2 inches

Base length of the similar triangle = 5.6 inches

Therefore;

Area of the given triangle = (Base length × Height)/2

Which gives;

36 = (4.2 × h)/2

Where;

h = Height of the given triangle

36 × 2 = 4.2 × h

[tex]h = \mathbf{\frac{36 \times 2}{4.2}} = 17 \frac{1}{7} [/tex]

Height of the given triangle, h = 17+ 1/7

The ratio of corresponding sides of similar triangles are the same, which gives;

[tex] \frac{5.6}{4.2} = \frac{h'}{17 \frac{1}{7}} [/tex]

Where;

h' = The height of the similar triangle

Which gives;

[tex] h' = \frac{5.6}{4.2} \times 17 \frac{1}{7} = 22 \frac{6}{7} [/tex]

The area, A', of the similar triangle is therefore;

[tex] A' = \frac{1}{2} \times 5.6 \times 22 \frac{6}{7} = 64 [/tex]

The area can also be obtained using the scale factor of area as follows;

Which gives;

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Answer:

[tex]3x^{2} - 4xy + 2y { }^{2} - 1 \\ 3 \times ( - 3) { }^{2} - 4 \times ( - 3) \times 5 + 2 \times 5 {}^{2} - 1 \\ (3 \times 9) - ( - 60) + 50 - 1 \\ 27 + 60 + 50 - 1 \\ 165 [/tex]

Answer: 136

Substitute -3 for x and 5 for y.

[tex]3x^2 - 4xy + 2y^2 - 1[/tex]

[tex]3(-3)^2-4(-3)(5)+2(5)^2-1[/tex]

[tex]3(9)-4(-15)+2(25)-1[/tex]

[tex]27+60+50-1[/tex]

[tex]87+50-1[/tex]

[tex]137-1[/tex]

[tex]136[/tex]

hope this helped!

Answer: -1

Step-by-step explanation:

Here, we are subtracting two fractions; therefore, we must make the denominators the same by finding the least common multiple. Since we have x - 3 for one denominator and x + 2 for the other, we don't have any common factors. Hence, the least common multiple would be their product.

[tex](x-3)(x+2)\\x(x-3)+2(x-3)\\x^2-3x+2x-6\\x^2-x-6[/tex]

The question is looking for the coefficient of the second term. Since there is just a negative sign in front of the x, the "?" can be filled with either a negative sign or a -1.

The ratio of grenadine syrup to 7-Up will be 1:8.

From the information given, we are told that Shirley Temple" drink is made by a 5 mixing 2 cups of 7-Up with 4 tablespoons of grenadine syrup.

The ratio of grenadine syrup to 7-Up will be:

4 tablespoon : 2 cups

Note that 1 cup = 16 teaspoon

4 : (2 × 16)

= 4:32

= 1:8

Therefore, the ratio of grenadine syrup to 7-Up will be 1:8.

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The least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors. This can be obtained by simply giving colors to the small shapes according to the criteria.

From the question the figure, the number of colored sections with which are not colored with respect to a "touching" colored section, would not be half of the total colored sections since the sections are not alternating as they still meet at a common point.

After all, it notes no two touching sections, not adjacent sections.

There is no equation to calculate this requirement with respect to the total number of sections.

Taking one triangle or square as the starting we can give colors to each small units. This figure will be the start of sequence of other small figures.

If a square were to be this starting shape that have same color as that color of the square.

Now from the remaining given another color to the starting figure. We will get that shapes, that will have same color.

Like that the remaining figures are given colors.          

Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.

Hence the least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors.

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The derivatives of the functions are listed below:

(a) [tex]f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}[/tex]    

(b) [tex]f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }[/tex]

(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²    

(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]

(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶

(f) [tex]f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}][/tex]

(g) [tex]f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)[/tex]

(h) f'(x) = cot x + cos (㏑ x) · (1 / x)

In this question we must obtain the first derivatives of each expression by applying differentiation rules:

(a) [tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}[/tex]

(b) [tex]f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}[/tex]

(c) f(x) = (sin x - cos x) / (x² - 1)

(d) f(x) = 5ˣ · ㏒₅ x

(e) f(x) = (x⁻⁵ + √3)⁻⁹

(f) [tex]f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}[/tex]

(g) [tex]f(x) = \arccos^{2} x - \arctan (\sqrt{x})[/tex]

(h) f(x) = ㏑ (sin x) + sin (㏑ x)

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The time it would take for the print to reach 100 percent completion is 12,101 minutes 9 seconds.

The mathematical operations that would be used to determine the required value are division and multiplication. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is  ÷. Multiplication is the process of determining the product of two or more numbers. The sign used to denote multiplication is ÷.

Other mathematical operations that are used to solve problems include addition and subtraction.

Time it would take to reach 100% completion = (minutes it takes to print 87% of the words x 100%) / 87%

Time it would take to reach 100% completion = (10,528 x 1) / 0.87 =

10.528 / 0.87

= 12,101. 15

= 12,101+ (0.15 x 60)

= 12,101 minutes 9 seconds

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Answer:

(10,10)

Step-by-step explanation:

y = .5x + 5

If you put in 10 for x, we get 10 for y.

y = .5(10) + 5

y =5 + 5

y = 10

When x is 10, y is 10 (10,10)

Answer: 57 cm²

Step-by-step explanation:

We can split this figure into two shapes: the rectangle on the left and the triangle on the right. We can find the area of each separately and add them to get the total area.

The area of a rectangle is [tex]lw[/tex], where l is the length and w is the width. We can just multiply 8 and 6 to get the area of the rectangle.

[tex]A=8*6\\A=48[/tex]

The area of the triangle is [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle and h is the height. Here' the base would be 6 cm as opposite sides of a rectangle have the same measure, and the height is 3.

[tex]A=\frac{1}{2}(6*3)\\A=\frac{1}{2}(18)\\A=9[/tex]

The total area would just be the sum of the two separate areas.

[tex]48+9=57[/tex]

Hence, the area of the figure is 57 cm².

Answer: 57 cm^2

Step-by-step explanation:

To find the entire area of the figure, we have to find the area of the rectangle and the triangle and sum it up

The area of the rectangle is 6 * 8 = 48 cm^2

The area of the triangle is 1/2 * 3 * 6(Opposite sides of a rectangle have equal lengths) = 9 cm^2

So the area of the figure is 48 + 9 = 57 cm^2

The shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle

The shapes are given as:

The lines of symmetry are the lines that, when the shape is rotated through this line, the shape remains the same

As a general rule:

An Isosceles trapezoid and an Isosceles triangle have two lines of symmetry

Hence, the shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle

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Use the quotient and chain rules. If

[tex]y = \dfrac{\cos(2x)}{\tan(2x)}[/tex]

then the derivative is

[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) \frac d{dx}\cos(2x) - \cos(2x) \frac d{dx}\tan(2x)}{\tan^2(2x)}[/tex]

[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) (-\sin(2x)) \frac d{dx}(2x) - \cos(2x)\sec^2(2x) \frac d{dx}(2x)}{\tan^2(2x)}[/tex]

[tex]\dfrac{dy}{dx} = \dfrac{-2\sin(2x)\tan(2x) - 2 \sec(2x) }{\tan^2(2x)}[/tex]

and we can rewrite this by

• multiplying by [tex]\frac{\cos^2(2x)}{\cos^2(2x)}[/tex],

[tex]\dfrac{dy}{dx} = \dfrac{-2\sin^2(2x)\cos(2x) - 2 \cos(2x) }{\sin^2(2x)}[/tex]

• factorizing,

[tex]\dfrac{dy}{dx} = -\dfrac{2\cos(2x) \left(\sin^2(2x) + 1\right)}{\sin^2(2x)}[/tex]

etc

Answer:

8+8+12+5= 33

Step-by-step explanation:

8+8+12+5=33

The graph is shown in the attached image.