if the relationships below are given in the form(input, output) which paring always describes a function

We can make 64 different equations using the power of ten.

The power of a number identifies how many times that particular number is multiplied by itself.

Here, let us assume that the different equations = x

Using a power of 10, we have 10x making a total of 640.

Divide both sides by 10

10x/10 = 640/10

x = 64

Therefore, we can conclude that we can make 64 different equations using the power of ten.

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Answer:

9

Step-by-step explanation:

The Pythagorean Theorem is a² + b² = c². c² is the hypotenuse while a² and b² are the legs.

So plugging it into the equation,

a² + 12² = 15²

a² + 144 = 225

a² = 81

a = 9

steps:

1. square the values

2. isolate the missing value

3. take the square root of both sides

The best buy is (d) a 9 oz box of rice $1.25

The best buy is the product that has the least unit rate.

The unit rate is calculated as:

Unit = Price/Weight

So, we have:

Box 1:

Unit rate = $0.90/6 oz = $0.150 per oz

Box 2:

Unit rate = $1.93/12 oz = $0.161 per oz

Box 3:

Unit rate = $2.42/16 oz = $0.151 per oz

Box 4:

Unit rate = $1.25/9 oz = $0.139 per oz

The least unit price is $0.139 per oz for box 4

Hence, the best buy is (d) a 9 oz box of rice $1.25

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Answer:

C

Step-by-step explanation:

a = 4

b = 5

c = 2

C = arccos((a² + b² - c²) / 2ab)

C = arccos((16 + 25 - 4) / 2(4)(5))

C = arccos(37 / 40)

C = 22.33°

2abcosC

2(4)(5)cos(22.33)

40(0.925)

37

Option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have from law of cosines that a² + b² - 2abcosC = c²

We have to find the value of 2abcosC.

Now let us find the value of C

C = arccos((a² + b² - c²) / 2ab)

C = arccos((16 + 25 - 4) / 2(4)(5))

C = arccos(37 / 40)

C = 22.33°

Now plug in the value of C in  2abcosC.

2abcosC

=2(4)(5)cos(22.33)

=40(0.925)

=37

Hence, option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.

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Answer:

y = 4(x+6)(x-2)

Step-by-step explanation:

y = 4x² + 16x - 48, factor out the 4

y = 4(x² + 4x - 12), find factors of 12

Factors of 12:

1*12, 2*6, 3*4; find a pair that sums to 4x or 4

6-2 = 4, since 12 is a negative number, a number in the factor must be negative, in this case, making 2 negative, would make 6-2 = 4

y = 4(x+6)(x-2)

After all the conditions you applied from the statement given you will get the original number as 16.08.

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.

Given that, if you subtract 0.3 from a certain number, add 0.4 times the original number to the result and then add another 2.78, you'll get 25.

We need to find the original number.

Let us take the original number as x.

Now, subtract 0.3 from the original number.

That is x-0.3.

0.4 times the original number is 0.4x.

Add 0.4 times the original number to the result.

That is, x-0.3+0.4x=1.4x-0.3

Now, add 2.78 to the result. That is 1.4x-0.3+2.78=1.4x+2.48.

As a result, you'll get 25. That is 1.4x+2.48=25

⇒1.4x=22.52

⇒x=16.08

There, the original number is 16.08.

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Answer:

CI = $182.25

Step-by-step explanation:

Compound interest formula:

[tex]Compound \space\ Interest= P(1 + \frac{r}{100})^{n} - P[/tex]  ,

where P is the principal amount ($4000), r is the interest rate (2%), and n is the time period (2 years and 3 months = 2.25 years).

Using formula:

CI = [tex]4000(1 + \frac{2}{100} )^{2.25} - 4000[/tex]

CI = $182.25

Answer:

[tex] \boxed{f(6) =2 4}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x) = x² - 2x[/tex]

Solution:

ATP,it is that x = 6. So substitute 6 on the function.

[tex]f(6) = 6 {}^{2} - 2(6)[/tex]

Simplifying using PEMDAS,we obtain:

[tex]f(6) = 6 \times 6- 12[/tex]

[tex]f(6) = 36 - 12[/tex]

[tex] \boxed{f(6) =2 4}[/tex]

Hence,f(6) = 24.

Answer:

the answer to this problem is 703.7 in^2

Answers:

=======================================================

Work Shown:

n = number of sides = 26

S = sum of the interior angles of a polygon with n sides

S = 180(n-2)

S = 180(26-2)

S = 180(24)

S = 4320 degrees is the sum of the interior angles.

i = measure of one interior angle of a regular polygon

i = S/n

i = 4320/26

i = 166.1538 approximately

i = 166.15 degrees is the approximate measure of each interior angle.

Side note: The formula to determine the interior angle i only works for regular polygons. This is because each angle is the same measure.

Answer:

x = ±5

Step-by-step explanation:

x² - 25 = 0

x² = 25

√x² = √25

x = ±5

Check:

5² - 25 = 0

-5² - 25 = 0

25 - 25 = 0

The pounds of corn in the second month is 390

We have:

First month, a = 300

Rate, r = 35%

The pounds of corn in the second month is calculated using:

Pound = a * (1 + r)

So, we have:

Pound = 300 * (1 + 30%)

Evaluate the sum

Pound = 300 * 1.3

Evaluate the product

Pound = 390

Hence, the pounds of corn in the second month is 390

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Answer:

10

Step-by-step explanation:

Answer:

y=3x-21

Step-by-step explanation:

Given points A(2,5) and B(8,3), line AB must contain them.

To calculate the slope, [tex]m_{\text{AB}}[/tex], of line AB, use the slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m_{\text{AB}}=\dfrac{(3)-(5)}{(8)-(2)}[/tex]

[tex]m_{\text{AB}}=\dfrac{-2}{6}[/tex]

[tex]m_{\text{AB}}=-\frac{1}{3}[/tex]

Since the slope isn't undefined, line AB must cross the y-axis somewhere.  To find the y-intercept, build and equation in slope-intercept form:

[tex]y=m_{\text{AB}}x+b_{\text{AB}}[/tex]

[tex]y=\left(-\frac{1}{3} \right) x+b_{\text{AB}}[/tex]

Substituting values for a known point (point A) on line AB...

[tex](5)=\left(-\frac{1}{3} \right) (2)+b_{\text{AB}}[/tex]

[tex]5=-\frac{2}{3} +b_{\text{AB}}[/tex]

[tex](5)+\frac{2}{3} =(-\frac{2}{3} +b_{\text{AB}})+\frac{2}{3}[/tex]

Finding a common denominator...

[tex]\frac{3}{3}*5+\frac{2}{3} =b_{\text{AB}}[/tex]

[tex]\frac{15}{3}+\frac{2}{3} =b_{\text{AB}}[/tex]

[tex]\frac{17}{3}=b_{\text{AB}}[/tex]

So, the equation for line AB is  [tex]y=-\frac{1}{3} x +\frac{17}{3}[/tex]

Since line AB and line BC form a right angle, they are perpendicular.  Perpendicular lines have slopes that are opposite (opposite sign) reciprocals (fraction flipped upside-down) of each other.  Stated another way, the slopes multiply to make negative 1.

[tex]m_{\text{AB}}*m_{\text{BC}}=-1[/tex]

[tex]\left( -\frac{1}{3} \right) *m_{\text{BC}}=-1[/tex]

[tex]-3*\left( -\frac{1}{3} *m_{\text{BC}} \right) =-3*(-1)[/tex]

[tex]m_{\text{BC}} =3[/tex]

Since the slope isn't undefined, line BC must also cross the y-axis somewhere.  To find the y-intercept, build and equation in slope-intercept form:

[tex]y=m_{\text{BC}}x+b_{\text{BC}}[/tex]

[tex]y=(3) x+b_{\text{BC}}[/tex]

Substituting values for a known point (point B) on line BC...

[tex](3)=3 * (8)+b_{\text{BC}}[/tex]

[tex]3=24+b_{\text{BC}}[/tex]

[tex](3)-24=(24+b_{\text{BC}})-24[/tex]

[tex]-21=b_{\text{BC}}[/tex]

So, the equation for line BC is  [tex]y=3 x -21[/tex]

Answer:

28 feet

Step-by-step explanation:

Area of a rectangle is :

A = L × W

We are given A and a expression for L, so let's substitute :

448 = (2W-4) × W

Now we expand the left side :

2W²-4w = 448

Subtract 448 from both sides :

2W²-4W-448 = 0

Divide everything by 2 :

W²-2W-224 = 0

Now we factorise :

Find 2 numbers that multiply to give -224 and add to give -2 :

-16 and 14

Rewrite -2W with -16W and +14W :

W² - 16W + 14W -224 = 0

W(W-16)  +14(W-16) = 0

(W+14)(W-16) = 0

W = -14 ,  W = 16

Only take positive value since this is lengths :

W = 16

Now we substitute W into the expression to find L :

L = (2W -4)

L = 2(16) - 4

L = 32 - 4

L = 28

Units will be feet since it is a length

Hope this helped and have a good day

Answer:

F.  31.4 ft

Step-by-step explanation:

The distance around the edge of a circle is called the circumference.

Formula for the circumference of a circle

[tex]\sf Circumference\:of\:a\:circle=2 \pi r[/tex]

(where r is the radius)

Given values:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \sf circumference & = \sf 2 \cdot 3.14 \cdot 5\\ & = \sf 31.4\:ft \end{aligned}[/tex]

Therefore, the distance around the edge of the circular patio is 31.4 ft.

The distance around the edge of the patio is 31.4 feet, which is determined by the circumference of a circle. The correct answer is option (F).

To find the distance around the edge of the circular patio, we need to calculate the circumference of the circle.

The formula for the circumference of a circle is given by:

Circumference = 2 × π × radius

Given that the radius of the patio is 5 feet and using the approximate value of π as 3.14, we can now calculate the circumference:

Circumference = 2 × 3.14 × 5

Circumference = 31.4 feet

Therefore, the distance around the edge of the patio is 31.4 feet.

Hence, the correct answer is option (F).

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Considering the result of the expression of the square of the sum,  2(2n² + 2)  is always an even number, then when 1 is added it will always be an odd number.

It is given as follows:

(a + b)² = a² + 2ab + b².

In this problem, the expression is:

(2n + 1)² = (2n)² + 2(2n)(1) + 1²

             = 4n² + 4n + 1

             = 2(2n² + 2) + 1

The term 2(2n² + 2) will always be even(multiplication by 2), and when 1 is added to an even number it will always be odd, hence it is proved that an  odd number squared is an odd number.

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Answer:

11 + x = 28

Step-by-step explanation:

The number of books they bought must add to 28.

Answer:the equations are

y = x + 4 and y = 3x + 6

Now we can use substitution method to solve the system

So we can substitute value of y from one equation into other

So we get

x+4 = 3x+6

So Option B is correct

Step-by-step explanation:

Answer:

2x + 4 = 3x + 1

Explanation:

Equation A: y = 2x + 4

Equation B: y = 3x + 1

Simultaneously solving :

⇒ y  =  y

⇒ 2x + 4 = 3x + 1

⇒ 2x - 3x = 1 - 4

⇒ -x = -3

⇒ x = 3

Solve for y :

⇒ y = 2x + 4

⇒  y = 2(3) + 4

⇒ y = 10

(a) The parabola opens downward.

(b) The axis of symmetry is at x = -2.

(c) The vertex is at (-2,0).

(d) The x-intercepts is (-2,0), and the y-intercept is at (0,-1).

The function of f(4) = g(x+1) gives the value of x that is -1/5.

It is the addition of two functions similar to the addition of any two polynomial functions.

Given;

F(x)=x+1

g(x)=5x+1

We need to find f(4)=g(x+1)

First substitute x = 4 in f(x)

F(x)=x+1

F(4) = 4 + 1

F(4) =  5

Now substitute x = x + 1 in g(x)

g(x)=5x+1

g(x + 1) = 5(x + 1) + 1

g(x + 1) = 5(x + 1) + 1

g(x + 1) = 5x + 5 + 1

g(x + 1) = 5x + 6

Then ,

F(4) = g(x + 1)

5 = 5x + 6

5x = 5 - 6

5x = -1

x = -1/5.

The function of f(4) = g(x+1) gives the value of x that is -1/5.

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Answer:

x is 130°,y is 60°

Step-by-step explanation:

x is corresponding to 130° therefore they are equal to find y since the angle on a straight line is 180° you subtract 180 from 130 and get 50 then you have gotten the other interior angle then add both interior angles and subtract by180 then you get the y

Answer:

both the lines are parallel

therefore, X= 130° ( if two lines are parallel their corresponding angles are equal)

Y + 70° = X ( sum of tow interior angle is equal to exterior)

Y + 70= 130

Y = 130 - 70

Y = 60°

Answer:

Step-by-step explanation:

The domain is the set of x values, and the range is the set of y values.

Answer:

Total Miles he  drives first day      = 8 miles

Total Miles he drive second day   = 12miles

Total Miles he drives third day    =    18miles

Total Miles he drives fourth day    =  27 miles

Step-by-step explanation:

This is a problem of linear equations in 1 variable:

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

It is given in the question that ,

This week his goal is to drive bike about 65 total miles over four days. Each day, he wants to ride 1.5 times as far as he rode the day before.

Let, on the first day, he drives x miles. On second day, he drives 1.5x. On the third day, he drives 1.5(1.5x) and on the fourth day, he drives 1.5(1.5(1.5x)).

So the equation is :

x +1.5x + 1.5(1.5x) + 1.5(1.5(1.5x)) = 65miles

x + 1.5x + 2.25x + 3.375x   = 65miles

            8.125x   =    65 miles

                  x   =  65/8.125  miles

                  x   = 8 miles

so after solving the equation we get, on the first day Gavin drives 8 miles

similarly, on the second day he drives 12miles

               on third day 18 miles

   and     on the fourth day  27miles

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Answer:

[tex]\tan(\beta)[/tex]

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something.  If you have options that you're building toward, aim toward one of them.

[tex]{\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]    and   [tex]{\sec(\theta)}={\dfrac{1}{\cos(\theta)}[/tex]

Recall the following reciprocal identity:

[tex]\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}[/tex]

So, the original expression can be written in terms of only sines and cosines:

[tex]\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)[/tex]

[tex]\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }[/tex]

[tex]\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}[/tex]

[tex]\sin(\beta) *\dfrac{1 }{\cos(\beta) }[/tex]

[tex]\dfrac{\sin(\beta)}{\cos(\beta) }[/tex]

Working toward one of the answers provided, this is the tangent function.

The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero.  However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to [tex]\tan(\beta)[/tex].

Answer:

arc QM = 38°

Step-by-step explanation:

the inscribed angle NQM is half the measure of its intercepted arc NM , so

arc NM = 2 × 90° = 180°

the sum of the arcs in a circle = 360° , then

QN + NM + MQ = 360° , that is

142° + 180° + QM = 360°

322° + QM = 360° ( subtract 322° from both sides )

QM = 38°

Answer:

314 in²  (nearest whole number)

Step-by-step explanation:

Radius of a regular polygon: The distance from the center of the polygon to any vertex.  The radius of a hexagon is equal to the length of one side.

Therefore, from inspection of the given diagram:

To find the area of a regular polygon, we first need to calculate the apothem.   The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.

[tex]\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]

where:

Given:

Substitute the given values into the formula and solve for a:

[tex]\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}[/tex]

Area of a Regular Polygon

[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}[/tex]

[tex]\implies \sf A=314.3672216...[/tex]

[tex]\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)[/tex]