Boden conjectures that in a right triangle, the sine of one acute angle is always equal
to the cosine of the other acute angle. Is Boden's conjecture correct? Choose the best
answer.

Answer:

15×w

Step-by-step explanation:

15 times w is a number bigger 15 times or added up again and again 15 times:

w+w+w+w+w+w+w+w+w+w+w+w+w+w+w or 15×w

The expression to represent "15 times a number w" is written as 15w. Substituting ½ for w would lead to the multiplication 15 × ½, resulting in 7.5.

To represent the phrase "15 times a number w," you would write the algebraic expression 15w. This is accomplished by using the coefficient 15 to indicate that the number w is being multiplied by 15. So, if you were to substitute the value ½ for w into this expression, you would perform the multiplication 15 × ½ to get the result, which simplifies to 7.5.

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Answer:

A - 110

Step-by-step explanation:

So if it is 6% increase you would times the number by 1.06. So you would do this like 5 times:

1,625 x 1.06 = 1722.5

1722.5 x 1.06 = 1825.85

1825.85 x 1.06 = 1935,401

1935.401 x 1.06 = 2051,52506

2051.52506 x 1.06 = 2174,6165636

Now you have the total number of bottles after 5 years, you would find the increase which is 2174.6165636 - 1,625 ≈ 550. 550 / 5 = 110

A

⭐ Answered by Foxzy0⭐

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The average increase in bottles purchased per year over that time is c) 110 bottles.

What is percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is generally denoted using the percent sign ''%''.

Now it is given that,

Number of bottles purchased per year, a = 1,625

Percentage increase per year, r = 6% = 0.06

Total time period, n = 5 years

Since, the equation of a exponential growth function is given as,

y = a(1 +r)ⁿ

⇒ y = 1625(1 +0.06)⁵

⇒ y = 1625(1.06)⁵

⇒ y = 1625*1.338

⇒ y = 2,175

Therefore, average increase in bottles purchased per year over that time   = (2175 - 1625) / 5

= 550 / 5

= 110 bottles

Thus, the average increase in bottles purchased per year over that time is c) 110 bottles.

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Use the distance formula: sqrt((x2-x1)^2+(y2-y1)^2)

Plug in variables:

sqrt((-3-2)^2+(5-8)^2)

sqrt((-5)^2+(-3)^2)

sqrt(25+9)

sqrt(34)

Rounded to the nearest tenth is 5.8 units

Hope this helped.

Incomplete Question Consider here NS = SQ then we may solve for NQ

Answer:

Therefore,

[tex]NQ=54\ units[/tex]

Step-by-step explanation:

Consider N -S -Q as a Straight line as shown in the figure below such that,

[tex]NS = 2x + 7[/tex]

[tex]SQ = 5x -23[/tex]

[tex]NS =SQ[/tex] ..............Consideration

To Find:

NQ = ?

Solution:

[tex]NS =SQ[/tex]   .....Given Consideration

Substituting the values we get

[tex]2x+7=5x-23\\\\3x=30\\\\x=\dfrac{30}{3}=10[/tex]

Therefore,

[tex]NS = 2\times 10 + 7 = 27[/tex]

[tex]SQ = 5\times 10 -23=27[/tex]

N -S-Q is a Straight Line,

Then BY Line Addition Postulate,

[tex]NQ=NS+SQ[/tex]       ...............N-S-Q

Substituting the values we get

[tex]NQ=27+27=54\ units[/tex]

Therefore,

[tex]NQ=54\ units[/tex]

Final answer:

The number halfway between 0.2 and 0.3 is 0.25, which is found by adding the two numbers and dividing the total by 2.

Explanation:

The number halfway between 0.2 and 0.3 can be found by calculating the average of the two numbers. To find the average, you add the two numbers together and then divide by 2.

To show the steps:

Therefore, the number that is halfway between 0.2 and 0.3 is 0.25.

The number halfway between 0.2 and 0.3 is 0.25.

To find the number halfway between 0.2 and 0.3, you calculate the average of the two numbers. Here's the step-by-step process:

So, the number halfway between 0.2 and 0.3 is 0.25. This method ensures that you find the exact midpoint between two values.

Answer:

Sally need  [tex]5\frac{1}{3}[/tex]  cups of orange juice.

Step-by-step explanation:

Given:

Sally makes a fruit drink using ⅔ of a cup of orange juice for every ¼ of a cup of pineapple juice.

If she uses 2 cups of pineapple juice.

Now, to find the cups of orange juice.

So, to solve by using unitary method:

As, ¼ of a cup of pineapple juice is needed for orange juice of = ⅔ cup.

So, 1 cup of pineapple juice is needed for orange juice of = [tex]\frac{2}{3}\div \frac{1}{4}[/tex]

[tex]=\frac{2}{3}\times \frac{4}{1}[/tex]

[tex]=\frac{8}{3}[/tex]  cups.

Thus, 2 cups of pineapple juice is needed for orange juice  of  = [tex]\frac{8}{3} \times 2[/tex]

= [tex]\frac{16}{3}[/tex]

= [tex]5\frac{1}{3}[/tex] cups.

Therefore, Sally need [tex]5\frac{1}{3}[/tex] cups of orange juice.

Answer:

v = 13

b = 23

Step-by-step explanation:

To solve this system of equations, we can negate one equation and add it to other to cancel out one variable.

Looking at v and b, the coefficients are 6, 4 and 13, 9, respectively.

It would be easier to use the LCM of 6 and 4

[tex]E_1 : 6v + 13b = 377\\E_2: 4v + 9b = 259\\\\4E_1 + (- 6)E_2:\\24v + 52b = 1508\\-24v - 54b=-1554\\\\0v -2b = -46\\-2b = -46\\b = 23\\\\4v + 9(23) = 259\\4v + 207 = 259\\4v = 52\\v = 13\\\\6(13) + 13(23)\\78 + 299\\377[/tex]

Answer: t = 4.5

Step-by-step explanation: 13.5/3 = 4.5

Answer:

T = 4.5

Step-by-step explanation:

The way to solve this is simple.

You just have to divide 13.5 by 3

and then you get the answer of 4.5!

Hope this helped!

~Oreo!!

The area of a triangle is 1/2*base*height

So make your equation: 1/2*b*12=42

6*b=42

b=7

So the base is 7 inches long

Hope that helped!

Answer:

  (-2, -3)

Step-by-step explanation:

A careful graph shows the point (-2, -3) is at the intersection of the circles whose radii are the given distances from the receiving stations.

_____

The simultaneous equations for the circles can be solved algebraically.

The epicenter is 10 units from X, so lies on the circle ...

  (x -4)^2 +(y -5)^2 = 10^2

  x^2 -8x +16 +y^2 -10y +25 = 100

  x^2 +y^2 -8x -10y = 59

__

The epicenter is 5 units from Y, so lies on the circle ...

  (x +6)^2 +(y +6)^2 = 5^2

  x^2 +12x +36 +y^2 +12y +36 = 25

  x^2 +y^2 +12x +12y = -47

__

The epicenter is 13 units from Z, so lies on the circle ...

  (x +14)^2 +(y -2)^2 = 13^2

  x^2 +28x +196 +y^2 -4y +4 = 169

  x^2 +y^2 +28x -4y = -31

__

Subtracting the second equation from each of the other two, we get ...

  (x^2 +y^2 -8x -10y) -(x^2 +y^2 +12x +12y) = (59) -(-47)

  -20x -22y = 106 . . . . eq1 -eq2

  (x^2 +y^2 +28x -4y) -(x^2 +y^2 +12x +12y) = (-31) -(-47)

  16x -16y = 16 . . . . . . . .eq3 -eq2

These simultaneous linear equations can be solved a variety of ways. We might use substitution:

  x = y+1 . . . . . from eq3 -eq2 divided by 16

  10(y +1) +11y = -53 . . . . . from eq1 -eq2 divided by -2

  21y = -63 . . . . . . . . . . . . simplify, subtract 10

  y = -3

  x = y+1 = -2

The epicenter is located at (x, y) = (-2, -3).

3^15 = 14,348,907

Which means...

x^5 = 14,348,907

If we execute [tex]\sqrt[5]{14348907}[/tex] and do the same with x^5 we get...

x = 27

So the 5th power of 27 is equal to 3^15.

⭐ Answered by Hyperrspace (Ace) ⭐

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The fifth power of the number 27 is equal to 3¹⁵.

To find the fifth power of a number that is equal to 3¹⁵, we need to determine what number raised to the power of 5 gives us 3¹⁵.

Let's call the number we are looking for "x." So, we need to solve the equation:

x⁵ = 3¹⁵

To find x, we can take the fifth root of both sides of the equation:

x = (3¹⁵[tex])^{(1/5)[/tex]

x = 3³

x = 27

This means that if we raise 27 to the power of 5 (27⁵), we will get 3¹⁵ (3 raised to the power of 15).

In conclusion, the number we are looking for is 27, as 27^5 is equal to 3¹⁵.

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Answer:

[tex]\text{Inverse property of multiplication: For all real numbers except }0,\text{ }a\cdot 1/a=1[/tex]

Explanation:

These are the examples given to illustrate the inverse property of multiplication:

         [tex]1/5\cdot 5=1\\\\ \sqrt{2}\cdot (1/\sqrt{2})=1[/tex]

And you must complete the statement to describe the property.

In the first example, 1/5 and 5 are reciprocal numbers of each other, also known as multiplicative inverses. And the example is showing that the product of 1/5 and its reciprocal is 1.

In the second example,    [tex]\sqrt{2}\text{ and }(1/\sqrt{2})[/tex]    are reciprocal of each other. Again, the example is showing that the product of those a number at its reciprocal is 1.

That is a general property, that can be written as:

             [tex]a\cdot 1/a=1[/tex]

That property is satisfied by any number except 0, because the reciprocal of    [tex]0[/tex]  , i.e.    [tex]1/0[/tex]    is not defined.

Then, the statemen is:

[tex]\text{For all real numbers except }0,\text{ }a\cdot 1/a=1[/tex]

The statement that best describes the inverse property of multiplication is: Inverse property of multiplication: For all real numbers except 0, a * a⁻¹ = 1.

This means that if you multiply a number by its reciprocal, you will always get 1.

The examples you provided illustrate this property nicely:

5 * 1/5 = 1

√2 * 1/√2 = 1

Note that the inverse property of multiplication does not hold for the number 0, because the reciprocal of 0 is undefined.

Here is another example of the inverse property of multiplication:

3 * 1/3 = 1

You can check any other real number and its reciprocal, and you will always find that the product is 1.

The inverse property of multiplication is a useful property in mathematics, and it is used in many different areas, such as algebra, calculus, and physics.

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The output y is [tex]y=22[/tex]

Explanation:

The expression is [tex]y=5 x-3[/tex]

We need to determine the output y, when the value of input is x is 5.

That is, substituting [tex]x=5[/tex] in [tex]y=5 x-3[/tex], we get,

[tex]y=5(5)-3[/tex]

Multiplying the value within the bracket, we have,

[tex]y=25-3[/tex]

Subtracting the terms, we get,

[tex]y=22[/tex]

Thus, the value of output y is [tex]y=22[/tex]

Answer:

19.9

Step-by-step explanation:

divide 199000 by 10000

=19.9

Answer:

19.9

Step-by-step explanation:

Add in Morse code is :

.—..-..

There are 8 total symbols, 5 of them are dots.

The fraction would be 5/8 are dots.

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

The Morse Code for Add is:

.__.._..

There are 5 dots and 3 dashes, so there are 8 figures in total. The fraction is 5 divided by the total number of symbols, which is 8. So the answer is [tex]\frac{5}{8}[/tex]

Answer:

Figure 1: Option A :   [tex]$ \sqrt{\frac{\textbf{3}}{\textbf{2}}} $[/tex] ;   [tex]$ \frac{\textbf{1}}{\textbf{2}} $[/tex] ;  [tex]$ \sqrt{\textbf{3}}} $[/tex]

Figure 2: Option B: [tex]$ \frac{\sqrt{\textbf{19}}}{\textbf{10}} $[/tex] ;     [tex]$ \frac{\textbf{9}}{\textbf{10}} $[/tex] ;  [tex]$ \frac{\sqrt{\textbf{19}}}{\textbf{9}} $[/tex]

Figure 3: Option C:  [tex]$ \frac{\textbf{4}}{\textbf{5}} $[/tex]  ;  [tex]$ \frac{\textbf{3}}{\textbf{5}} $[/tex] ;  [tex]$ \frac{\textbf{4}}{\textbf{3}} $[/tex]

Step-by-step explanation:

[tex]$ \textbf{Sin A} \hspace{1mm} \textbf{= } \hspace{1mm} \frac{\textbf{opp}}{\textbf{hyp}} $[/tex]

[tex]$ \textbf{Cos A} \hspace{1mm} {\textbf{=} \hspace{1mm} \frac{\textbf{adj}}{\textbf{hyp}} $[/tex]

[tex]$ \textbf{Tan A} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{Sin A}}{\textbf{Cos A}} $[/tex]

We can simply follow these three formulas to solve the problem.

Figure 1:

Sin A = [tex]$ \frac{6\sqrt{3}}{12} $[/tex]  = [tex]$ \frac{\sqrt{3}}{2} $[/tex]

Cos A = [tex]$ \frac{6}{12} = \frac{1}{2} $[/tex]

Tan A = [tex]$ \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}} $[/tex]  = [tex]$ \sqrt{3} $[/tex]

Figure 2:

Sin A = [tex]$ \frac{2\sqrt{19}}{20} $[/tex]  = [tex]$ \frac{\sqrt{19}}{10} $[/tex]

Cos A = [tex]$ \frac{18}{20} = \frac{9}{10} $[/tex]

Tan A = [tex]$ \frac{\frac{\sqrt{19}}{10}}{\frac{10}{9}} $[/tex] = [tex]$ \frac{\sqrt{19}}{9} $[/tex]

Figure 3:

Sin A =   [tex]$ \frac{16}{20} $[/tex]   = [tex]$ \frac{4}{5} $[/tex]

Cos A = [tex]$ \frac{12}{20} = \frac{3}{5} $[/tex]

Tan A = [tex]$ \frac{\frac{4}{5}}{\frac{3}{5}} $[/tex]  = [tex]$ \frac{4}{3} $[/tex]

Hence, the answer.

Answer:

30

Step-by-step explanation:

Answer:

C. 11

Step-by-step explanation:

First, find the value of "x" by solving the first equation. You need to move every other number to the other side of "x". When you move a number, you have to do the opposite operation to both sides.

5x + 6 = 10     The opposite of +6 is -6.

5x + 6 - 6 = 10 - 6     Subtract 6 from both sides

5x = 10 - 6       The "6" on the left cancelled out. Simplify the right side

5x = 4          The opposite of multiply by 5 is divide by 5

5x/5 = 4/5           Divide both sides by 5

x = 4/5           Value of "x"

Substitute the value of "x", which is 4/5, in the "x" for the second equation.

10x + 3

= 10(4/5) + 3             Multiply 10 and 4/5

= [tex]\frac{10*4}{5}[/tex] + 3        Combine into the numerator

= [tex]\frac{40}{5}[/tex] + 3         Divide the top by the bottom

= 8 + 3             Add

= 11                  Value of second equation

Therefore the value of 10x + 3 is 11.

Answer:

60

Step-by-step explanation:

15*4=60

The 15x when x = 5 will be 60.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given,

x = 4

Now,

15x is nothing but we need to multiply 15 with x

So,

15x = 15 × 4

15x = 60

Hence,The 15x when x = 5 will be 60.

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Answer:

Step-by-step explanation:

400-65=335

To find 20% of 950, first convert the percentage to a decimal (20% becomes 0.20) and then multiply that value by 950. The mathematical expression representing this calculation is 0.20 x 950, which yields the result: 190.

The question is asking about how to find 20% of 950 in mathematics. Here's how you do that:

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To find 20% of 950, convert 20% to decimal form as 0.20 and multiply it by 950. The result of this calculation is 190, which represents 20% of 950.

The expression to find 20% of 950 is obtained by multiplying 950 by the percentage in decimal form. Since 20% as a decimal is 0.20, you multiply 950 by 0.20 to find the answer. The calculation is as follows:

So, 20% of 950 is 190.

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Answer: Y = 9

Step-by-step explanation:

Y & X

Y = KX

K = Y / X = - 15 / - 5 = 3

X = 3

K= 3

Y=?

Y = KX = 3 x 3 = 9

Therefore, when X = 3, Y = 9

Answer:

the sum of the 2 expressions is -11+2i.

Step-by-step explanation:

-1-10=-11

-i+3i=2i

-11+2i

Answer:

y = - 4

Step-by-step explanation:

The output is the value of y for a given input x

For an input of - 1, substitute x = - 1 into the equation.

y = (- 1)² - 5 = 1 - 5 = - 4 ← output

Answer:

Senior citizen tickets = $9

Student tickets = $11

Step-by-step explanation:

We begin by converting these into simultaneous linear equation;

Senior citizen tickets = a

Student tickets = b

5a + 9b = 144

14a + 6b = 192

5a = 144 - 9b

a = 144/5 - 9b/5

a = 28.8 - 1.8b

We now substitute this into the first equation

14(28.8 - 1.8b) + 6b = 192

403.2 - 25.2b +6b = 192

-19.2b = 192 - 403.2

b = -211.2/-19.2

b = 11

Put the value of b into either equation

5a + 9b = 144

5a + 9(11) = 144

5a +99 = 144

5a = 144-99

5a = 45

a = 9

Answer:    ✔ 281.25

Step-by-step explanation:

Answer:

281.25

Step-by-step explanation:

It is correct E d g e n u i t y

There are about 124.29 acres in this parcel woods

Step-by-step explanation:

The given is:

We need to find how many acres are in this parcel of woods

∵ The population density = 3.5 deer per acre

- That means 1 acre for every 3 dears

∵ There are a total of 435 deer

∴ [tex]\frac{3.5}{1}=\frac{435}{x}[/tex] , where x is the number of acres

- By using cross multiplication

∴ 3.5 × x = 1 × 435

∴ 3.5 x = 435

- Divide both sides by 3.5

∴ x = 124.29

There are about 124.29 acres in this parcel woods

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Check the picture below.

the idea being, that if we run an altitude segment from a right-angle in a triangle, and parallel to the opposite side, like in thise case, we end up with 3 similar triangles, a Large one, containing the other smaller ones, a Medium and a Small.

now, let's simply use proportions for those similar triangles.

[tex]\bf \stackrel{Large}{\cfrac{12}{4+x}}=\stackrel{Small}{\cfrac{4}{12}}\implies \cfrac{12}{4+x}=\cfrac{1}{3}\implies 36=4+x\implies \boxed{32=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Small}{\cfrac{4}{y}}=\stackrel{Medium}{\cfrac{y}{x}}\implies 4x=y^2\implies 4(32)=y^2\implies 128=y^2\implies \sqrt{128}=y \\\\\\ \sqrt{64\cdot 2}=y\implies \sqrt{8^2\cdot 2}=y\implies \boxed{8\sqrt{2}=y} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{Large}{\cfrac{z}{4+x}}=\stackrel{Medium}{\cfrac{x}{z}}\implies z^2=(4+x)x\implies z^2=4x+x^2\implies z = \sqrt{4x+x^2} \\\\\\ z = \sqrt{4(32)+32^2}\implies z = \sqrt{128+1024}\implies z = \sqrt{1152} \\\\\\ z = \sqrt{576\cdot 2}\implies z = \sqrt{24^2\cdot 2}\implies \boxed{z = 24\sqrt{2}}[/tex]