Explain why cos(−3π4)=cos(5π4).

Answer:

[tex]\frac{\left(3x^2-6x+3\right)}{\left(x-1\right)3x-93x^2-3x^3x-33x^2-6}: -\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]
[tex]\frac{3x^2-6x+3}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{-3\left(x^4+41x^2+x+2\right)}[/tex]
[tex]\frac{\left(x-1\right)^2}{-\left(x^4+41x^2+x+2\right)}[/tex]
[tex]-\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]

Answer:

3x-3

Step-by-step explanation:

use synthetic division

When the height of the prism doubles, the percentage increase in the volume is 100%

The volume of a prism is:

V₁ = BH

Where:

B represents the base area and H represents the height.

When the height doubles, the volume becomes

V₂ = 2BH

The percentage increase is then calculated using:

%Increase = (V₂ - V₁)/V₁

So, we have:

%Increase = (2BH - BH)/BH

Evaluate

%Increase = 1

Express as percentage

%Increase = 100%

Hence, the percentage increase is 100%

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The bearing of R from P is 019 and the distance |PR| is 8.75

A cyclist set out from a town P on a bearing of 060 to a town Q, 5 km away. He then moves on a bearing of 345 to a town R, 6km from Q.

See attachment

Start by calculating the distance PR using the following cosine ratio

PR² = PQ² + QR² - 2 * PQ * PR cos(Q)

Substitute known values

PR² = 5² + 6² - 2 * 5 * 6 cos(105)

Evaluate

PR² = 76.53

Take the square root of both sides

PR = 8.75

Next, calculate angle R using the following sine ratio

PQ/sin(R) = PR/sin(Q)

Substitute known values

5/sin(R) = 8.75/sin(105)

Evaluate the quotient

5/sin(R) = 9.06

Multiply both sides by sin(R)

9.06 * sin(R) = 5

Divide both sides by 9.06

sin(R) = 0.5519

Take the arc sin of both sides

R = sin⁻¹(0.5519)

Evaluate

R = 34

Calculate angle P using:

P = 180 - 34 - 105

P = 41

The bearing of R from P is then calculated as:

Bearing = 060 - 41

Evaluate

Bearing =  019

Hence, the bearing of R from P is 019

In (b), we have:

PR = 8.75

Hence, the distance |PR| is 8.75

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Answer:-8.3

Step-by-step explanation:-8.3

Answer:

-8.3333333333

Step-by-step explanation:

First you want to start by multiplying (-2) * 3.

Next you want to multiply 1/2 * 1/3

Finally you add you answers together to get what you need.

Also this was very very very easy so go to summer school if you are this dum.

half the diagonal is shown as 20cm.

The full diagonal would be 20 x 2 = 40 cm.

area of a square using the diagonal is 1/2 x diagonal^2

Area = 1/2 x 40^2 = 800 square cm

answer: 800 square cm.

Answer:

20 for $8

Step-by-step explanation:

The functions and their descriptions are:

The functions are given as:

[tex]y = \frac{5x^3}{8}[/tex]

[tex]y = 6 + 0.25\ln(x)[/tex]

[tex]y = \frac{18}{1 + 6e^{-0.25x}}[/tex]

[tex]y = 5x^3 + 8[/tex]

The functions would be described based on the type of function they represent.

Functions that use the "ln" keyword are logarithmic functions, while functions that use the "e" keyword are exponential functions.

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Answer:

Select the correct word to describe the function.The equation  represents ✔ a powera logistica logarithmican exponential function.The equation y = 6 + 0.25 ln x represents X a logistica polynomial✔ a logarithmican exponential function.The equation  represents a power✔ a logistica polynomiala logarithmic function.The equation y = 5x3 + 8 represents a powera logistic✔ a polynomialan exponential function.

Step-by-step explanation:

you are so welcome

Answer:

26 degrees.

Step-by-step explanation:

The angles of triangles will always add up to 180 degrees.

The first angle is 50 degrees.

The second angle, is shown with a 76 degree angle next to it.

Since this is a 180 degree line, we can find the angle of the bottom right corner by doing 180 - 76. 180 - 76 is 104.

104 + 50 = 154 degrees.

The remaining 26 degrees is the answer to the value of y.

Answer:

x^2-12x+36

Step-by-step explanation:

The first step in solving this equation is to expand the square which makes the equation (x-6)(x-6). Then you distribute the x to both parentheses which leaves you with x^2-6x, and then you distribute the 6 to both parentheses which gives you 6x+36. Then add both binomials which leaves you with x^2-12x+36. The reason it is +36 and not -36 is because you are multiplying a negative 6 by another negative 6.

All the valid statements are,

⇒ Statement 1; By definition of parallel lines

⇒ Statement 3; Because of alternate interior angle theorem.

⇒ Statement 4; Because it is linear

⇒ Statement 5; because of substitution

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Mr. Hussey prove that the sum of interior angle of triangle is 180 degree.

Now, For all the statements al the correct postulate are,

⇒ Statement 1; By definition of parallel lines

⇒ Statement 3; Because of alternate interior angle theorem.

⇒ Statement 4; Because it is linear

⇒ Statement 5; because of substitution

Thus, All the valid statements are,

⇒ Statement 1; By definition of parallel lines

⇒ Statement 3; Because of alternate interior angle theorem.

⇒ Statement 4; Because it is linear

⇒ Statement 5; because of substitution

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The value of x when f(x) = -4 is 3

The function is given as:

f(x) = -3x + 5

When f(x) = -4, we have:

-4 = -3x + 5

Subtract 5 from both sides

-3x = -9

Divide both sides by -3

x = 3

Hence, the value of x when f(x) = -4 is 3

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Answer:

x = 3

Step-by-step explanation:

Hello!

Think of this as a linear equation: y = -3x + 4.

If f(x) = -4, it means that y = -4.

Plug in the value for y and solve for x.

The value of x is 3.

Answer:

i don't know

Step-by-step explanation:

i don't know

Answer:

10

Step-by-step explanation:

x/20= 5/x

x²= 100

x=√100

X=±10

x=10

Answer:

x = 10

Step-by-step explanation:

expressing the ratios in fractional form

[tex]\frac{x}{20}[/tex] = [tex]\frac{5}{x}[/tex] ( cross- multiply )

x² = 100 ( take square root of both sides )

x = ± [tex]\sqrt{100}[/tex] = ± 10

the positive solution is x = 10

Answer:

the area is 168

Step-by-step explanation:

the formula for trapezoids is a+b/2 multiplied by the height

Answer / Step-by-step explanation:

(300.500+40.60+8.2)=348.562

                  [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

         [refer to attachment for question] ~

    [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

✫ First of all, Slope-intercept form is written as follows:-

                                        [tex]\longmapsto\Large\textbf{y=mx+b}[/tex]

Where:-

To find:-

Solving,

           Replace m with -1/5 And b with -3:-

                 [tex]\large\text{$y=-\displaystyle\frac{1}{5} x-3$}[/tex]

[tex]\Uparrow[/tex]  [tex]\sf{the\:equation}[/tex]

#TogetherWeGoFar

[tex]\rule{300}{1}[/tex]

Answer:

[tex]r \: = \: \boxed{ \bold{\frac{2}{3} }}[/tex]

Step-by-step explanation:

[tex]r \: = \: \frac{36}{54} \\ \\ r \: = \: \frac{24}{36} \\ \\ r \: = \: \frac{16}{24} [/tex]

[tex]r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} [/tex]

Since the ratio is the same, that is the common ratio.

Answer:

Step-by-step explanation:

Remark

Anything multiplied by 0 = 0. So the whole right side is 0.

(6x - 9)*3 - 1  = 0                       Add 1 to both sides.

(6x - 9)*3 - 1 + 1 = 0 + 1             Combine

(6x - 9)*3 = 1                             Divide both sides by 3

(6x - 9)*3/3 = 1/3                      Simplify

(6x - 9) = 1/3                             Remove brackets. Add 9 to both sides

6x - 9+9 = 9 1/3                        Combine

6x = 9 1/3

6x = 28/3                                   Divide both sides by 6

6x / 6 = 28/3 // 6                       Invert the 6 and multiply.

x = 28/3 * 1/6

x = 28/18

Answer

x = 14/9

Answer: 8.8

Step-by-step explanation:

Because [tex]\angle S \cong \angle S[/tex] by the reflexive property, we know that [tex]\triangle STU \sim \triangle SQR[/tex] by AA.

So, by the triangle proportionality theorem,

[tex]\frac{x}{5.3}=\frac{11.1}{6.7}\\x=(11.1/6.7)(5.3) \approx \boxed{8.8}[/tex]

Answer:

8

Step-by-step explanation:

Income = 0

  so    0   = 9x^2 - 54x - 154  

             you can go straight to the Quadratic Formula to find the answer, or you can try factoring as follows ....

    divide both sides of the equation by 9 to get

           x^2 -6x -16   = 0  which easily factors to :

          (x -8)(x+2) = 0     <===== this shows x = 8   or -2(throw out)

Answer:

4

Step-by-step explanation:

A fundamental theorem of algebra,  the degree of a polynomial is the maximum number of roots the polynomial has.
The degree of the polynomial s 4 so it has 4 roots.

Answer:

  11.6 ft²

Step-by-step explanation:

We assume the 1/8 scale factor is the ratio of the linear dimensions of the smaller of the prisms to the larger. The ratio of areas will be the square of the ratio of the linear dimensions.

__

The ratio of areas will be ...

  smaller area / larger area = (scale factor)²

  smaller area = (larger area)×(scale factor)² . . . multiply by the denominator

  smaller area = (740 ft²) × (1/8)² = 11.5625 ft² . . . use given values

The surface area of the smaller prism is about 11.6 square feet.

Step-by-step explanation:

6y + 2(3x + 5) + 2y + 3 = 8r + 3r² + 6r² + 2r + r

6y + 6x + 10 + 2y + 3 = 9r² + 11r

8y + 6x + 13 = 9r² + 11r

Answer:

Step-by-step explanation:

Equation of area:

Substitute values and calculate:

The equation can be used to find the time in hours, [tex]\dfrac{t}{4}+\dfrac{t}{7}=1[/tex] and the time will be 2.5 hours. So the correct answer is option A.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Layna can paint a 350-square-foot room in 4 hours.It takes Bebe 7 hours to paint the same room.

Let t be the total time taken by both to paint.They are completing 1 job so the equation will be :

[tex]\dfrac{t}{4}+\dfrac{t}{7}=1[/tex]

Further solving it we get;

7 t + 4 t = 28

11t  =  28

t = 2.5 hours.

Therefore the equation can be used to find the time in hours, [tex]\dfrac{t}{4}+\dfrac{t}{7}=1[/tex] and the time will be 2.5 hours. So the correct answer is option A.

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The distance around the perimeter would be 120 ft.

Perimeter is the distance around the edge of a shape.

The complete question is

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

A rhombus is shown. Lines are drawn from each point to the opposite point to form 4 right triangles. The other 2 angle measures are 30 and 60 degrees. The base length of each triangle is 15 feet.

What is the distance around the perimeter of the garden?

let AE is the half of the diagonal AC.

AC = 30 ft.

So, AE = ½ * 30

AE = 15 ft

Now, using trigonometry

sin 30 = 15/AD

0.5= 15/AD

AD= 30 ft

Hence, distance around the perimeter would be: AD+AD+AD+AD=

=30 ft + 30 ft + 30 ft + 30 ft

= 120 ft.

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Answer:A

Step-by-step explanation: just took it

The distance the airplane can travel before it runs out of diesel is 15.67.

The first step is to convert gallon to kilogram

1 gallon = 3.79 kg

62 x 3.79 = 234.98 kg

Now, divide 234.98 by 15.: 234 . 98 / 15 = 15.67 kilogram

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Answer:

119 4/7

Step-by-step explanation:

Perimeter is all of the lengths of the sides added together. I started by adding all of the whole numbers:

35+10+12+15+24+12+10=118

Then I added the fractions (after making the denominators equal by multiplying the 3/7, 1/7, 2/7 all by 2)

6/14+2/14+4/14+3/14+1/14+4/14+2/14= 22/14

Then I subtracted 14 from 22 to take out our whole number (which would be 14/14 or 1), and see that we are left with 8.

This means that our answer is 119 8/14 or 119 4/7

Answer:

For no solution,

2x + 9 + 3x + x = 6x

For one solution,

2x + 9 + 3x + x = 15

For infinitely many solutions,

2x + 9 + 3x + x = 6x + 9

Step-by-step explanation:

Step-by-step explanation:

1.  2x + 9 + 3x + x = 6x

6x + 9 = 6x

Subtract 6x from both sides,

9 = 0 which is absurd and hence the equation has no solution.

2.  2x + 9 + 3x + x = 15

6x + 9 = 15

Subtract 9 from both sides.

6x = 6

Divide both sides by 6.

x = 1 and this is the only solution.

3. 2x + 9 + 3x + x = 6x + 9

6x + 9 = 6x + 9

Subtract 6x from both sides,

9 = 9, both sides are balanced which means, the equation has infinitely many solutions.

First simplify

#No solution

#One solution

#Infinitely many solution