Each pair of values is from an inverse variation. Find the missing value. (2,5),(4, y)

The standard form for the linear equation is y=6a+38.

An equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=5x+3. Where:

a= the slope.

b= the constant term that represents the y-intercept.

For the given example: a=5 and b=3.

The question gives:

- the value of the slope (a) = 6

- the coordinates of a point = (-3,20)

Thus, you can write from the question information :

y=ax+b

20=6*(-3)+b

20=-18+b

b=20+18=38

Therefore, the standard form for the linear equation is:

y=6a+38

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The graph that shows the  relationship between the number of miles the truck is driven and the cost for transporting the equipment is option c.

The $2000 fee that is charged by the company represents a fixed cost. Fixed cost is the cost that remains constant regardless of the mile travelled. The $2 per mile represents the variable cost. Variable cost is the cost that increases as the mile travelled increases. The total cost is the transporting the equipment is the sum of the fixed cost and the variable cost.

A graph can be described as a pictorial representation of data. A graph is made up of a x-axis and a y-axis. The graph should start at $2000 and slope upward. The graph would slope upward representing the increasing variable cost function.

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Step-by-step explanation:

[tex]23 - 7x = 3x + 8 \\ - 7x - 3x = 8 - 23 \\ - 10x = - 15 \\ - 10x = - 15 \\ - 10 \: \: \: \: \: \: \: \: \: \: \: \: - 10 \\ x = \frac{15}{10 \\ } \\ x = 1.5[/tex]

The value of the Equation 23 - 7x = 3x + 8 is x = 3.1

A mathematical statement that shows that two mathematical expressions are equal.

Given an equation, 23 - 7x = 3x + 8

7x + 3x = 23 + 8

10x = 31

x = 3.1

Hence, The value of the Equation 23 - 7x = 3x + 8 is x = 3.1

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The inverse of function y=6-x is y = -x+6.

given that the function is y=6-x.

A function that can reverse into another function is known as an inverse function or anti function. A function takes in values, applies specific operations to them, and produces an output. In order to find y when x is swapped with another variable, we must first determine the inverse function. On the other hand, the inverse function and the original function likewise have interchangeable domains and ranges.

Here,inverse is a function

now, interchange the x and y places.

x = 6 - y

x - 6 = -y

y = -(x-6)

y = -x + 6

Hence, the inverse of function y=6-x is y = -x+6

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If the approximated number is given as 6.3 Then the error interval of x is 6.24≤x≤6.35

A value or quantity that is nearly but not exactly correct.

The number is given as x.

So, we have:

x = 6.3

The smallest number that can be approximated to 6.3 is 6.25 (to 1 decimal place), while the largest number is 6.34

Given that there are possibilities of error, the lower and upper bound of the error interval would be:

6.25-0.01≤x≤6.34+0.01

6.24≤x≤6.35

Hence, the error interval of x is  6.24≤x≤6.35

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The proof of DE is parallel to BC in the given triangle is shown.

As per the given data in the question;

A, B and C are the vertices of a triangle.

Whereas,

D lies at the midpoint of AB.

E lies at  the midpoint of AC.

The mid piont formula is;

Mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)

The coordinates of D is found by the mid point formula of coordinates.

Put the coordinates of A (4, 6) and B (2,-2).

D = (4 + 2 / 2, 6 - 2 / 2)

D = (3, 2)

The coordinates of E is found by the mid point formula of coordinates.

Put the coordinates of A (4, 6) and C (-2,-4)

E = (4 - 2 / 2, 6 - 4 / 2)

E = (1, 1)

Now, the slope is calculated by;

m of DE = (y₂ -  y₁)/(x₂ - x₁)

The slope of E is

m of DE = (1 - 2)/(1 - 3) = 1/3

Slope of BC

M of BC = (-4 + 2)/(-4 - 2)

M of BC = 1/2

As, the slope of both line DE and BC are equal. Thus, both line are parallel to each other.

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The value of  h(-2), h(4), and h(0) in the given function is 11, 29 and 9 respectively.

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.

To determine if a graph represents a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line touches it at more than one location.

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The distance between points A and B is 9.22units, approximately.

This is further explained below.

Generally, In the image attached, you can observe a representation of the problem.

We have to find the distance between points A and B, which have coordinates (7,0) and (0,6), respectively.

The definition of distance between two given points is

[tex]d=\sqrt{\left(y_2-y_1\right)^2+\left(x_2-x_1\right)^2}[/tex]

Using points A and B, the distance between us

[tex]&d_{A B}=\sqrt{(7-0)^2+(0-6)^2}\\\\d_{A B}=\sqrt{49+36}\\\\\ d_{A B}=\sqrt{85} \\\\&d_{A B} \approx 9.22[/tex]

In conclusion, the distance between points A and Ais 9.22 units, approximately.

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The price of the computer if the discount is applied before the rebate is $1225. The composite function is (g.f)(x) = g(f(x))

(g.f)(x) = g(f(x))

f(1500) = 0.95(1500)

= 1425

g(1425) = 1425-20

= 1225

= $1225

Therefore, The price of the computer if the discount is applied before the rebate is $1225. The composite function is (g.f)(x) = g(f(x))

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We can multiply 67 x 5 using distributive property and answer will be 335.

What is the distributive property of multiplication ?

The distributive property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

It is given that we have to multiply 67 x 5.

We can multiply the two numbers using the distributive property.

We know that , the distributive property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

Distributive property is written in form : A × (B + C) = AB + AC

So , 67 x 5 can be written as : 5 × (60 + 7)

or

5 × (60 + 7)

= (5 × 60) + (5 × 7)

= 300 + 35

= 335

Therefore , we can multiply 67 x 5 using distributive property and answer will be 335.

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Answer:

1. 32/80  2. 9/3  3. 1/3  4. 12/4   5. 4/1  6. 3/6 or 1/2  7. 21/18  8.  24/15  9. 25/5  10. 7/21

Step-by-step explanation:

good fraction brain

The only option that is not viable to solve the systems of equations is:

D. Substitute y = 6/5x - 12 into the first equation

Given the systems of equations,

2x + y = 20 ----> equation 1

6x - 5y = 12 ----> equation 2

In order to solve the system of equations using the substitution method, rewrite 2x + y = 20:

2x + y - 2x = 20 - 2x

y = 20 - 2x

Or

2x = 20 - y

x = 10 - 1/2y

Or

6x - 5y = 12

-5y = -6x + 12

y = -6/5x - 12/5

or

6x = 12 + 5y

x = 2 + 5/6y

Therefore, the only option that is not viable to solve the systems of equations is:

D. Substitute y = 6/5x - 12 into the first equation

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Answer:

You draw the exact same shape but at a different scale

Step-by-step explanation:

You just draw it bigger.

The factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

The given parameters are

f(x) = x^3 + 5x^2 - 16x - 80

x = -4 is a root

To set up the synthetic division, we start by writing out the coefficient of each term

So, we have

-4 |  1    5    -16    -80

Bring down the first coefficient

-4 |  1    5    -16    -80

      1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)

      1

Add

-4 |  1    5    -16    -80

           (-4)

      1     1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1

Add

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1     -20

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20

Add

So, we have

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20    0

This means that,

Quotient = x^2 + x - 20

Remainder = 0

Expand x^2 + x - 20

x^2 + x - 20 =x^2 + 5x - 4x - 20

Factorize

x^2 + x - 20 = (x + 5)(x - 4)

Recall that the initial root is

x = -4

Rewrite as

x + 4 = 0

So, we have the complete factor to be

f(x) = (x + 4)(x + 5)(x - 4)

Set to 0

(x + 4)(x + 5)(x - 4) = 0

Solve for x

x = -4,  = -5 and x = 4

Hence, the factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

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Answer:

14.5

Step-by-step explanation:

Answer:0.33

Step-by-step explanation:

I used a calculator

The expected number of balls in the first bin would be (1/n)^n

It is given that,

The number of balls and bins is same

If so, then there should always be one ball in each container. The likelihood that every ball will land in the first bin is (1/n)^n.

For example -

Let there be three balls and three bins. Put an A, B, and C next to each ball. The bins are marked 1, 2, and 3. Ball A is likely to land in bin 1 with a 1/3 chance. However, there is a 1/3 chance that ball B will land in bin 1, and there is a 1/3 chance that ball C will land in bin 1. As a result, bin 1 should have a value of 1/3 + 1/3 + 1/3 = 1. The expected values of bins 2 and 3 follow a similar rationale.

By the same reasoning, bins 2 and 3 should likewise have anticipated values of 1.

How likely is it that all three balls will fall into bin one?

1/3 x 1/3 x 1/3 = 1/27, or in the general situation, (1/n)^n, which equals (1/3)^3.

Hence, the expected number of balls in the first bin would be (1/n)^n

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The statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2  for n > 2

The function definition is given as

f(n) = -4 +2n for n > 1

Start by calculating f(2), f(3) and f(4)

So, we have

f(2) = -4 +2(2)

f(2) = 0

f(3) = -4 +2(3)

f(3) = 2

f(4) = -4 +2(4)

f(4) = 4

In the above computation, we can see that the sequence is an arithmetic sequence with a common difference of 2

So, we have

f(n) = f(n - 1) + 2

Also, we have

f(1) = -4 +2(1)

f(1) = -2

Hence, the statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2  for n > 2

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The equation of the parabola is y = (x + 3)^2 - 1

Parabolic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The given parameters are

Vertex = (-3, -1)

X-intercept = (-4, 0)

A parabolic equation has the form y = a(x - h)^2 + k

Where the vertex is (h, k)

This means that, (h, k) is given as

(h, k) = (-3, -1)

Substitute (h, k) = (-3, -1) in the equation y = a(x - h)^2 + k

So, we have

y = a(x + 3)^2 - 1

Next, we substitute (-4, 0) for (x, y) in y = a(x + 3)^2 - 1

So, we have

0 = a(-4 + 3)^2 - 1

This gives

0 = a - 1

Solve for a

a = 1

Substitute a = 1 in y = a(x + 3)^2 - 1

y = (x + 3)^2 - 1

So, the required equation of the parabola is y = (x + 3)^2 - 1

Hence, the equation of the parabola is y = (x + 3)^2 - 1

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Using logarithmic expansion, we get expansion for the function log₃(2x+1) is f(x) = {1/log (3)} [2x - 2² . x²/2 + 2³ . x³/3 -  2⁴. x⁴/4 + ....]

According to the question, we need to expand  log₃(2x+1) using logarithmic expansion,

Let f(x) =  log₃(2x+1)

Using change base rule →logₐ b = logₓ (b) / logₓ (a), x > 0. We get

⇒ log (2x+1) /log (3)      

= {1/log (3)} [log (1+2x)]         →(1)

Logarithmic expansion: log (1+x) = x - x²/2 + x³/3 - x⁴/4.....∞

Replace '2x' in the place of 'x' in the above logarithmic expansion, we get

log (1+2x) = 2x - (2x)²/2 + (2x)³/3 - (2x)⁴/4.....∞     →(2)

Substitute (2) in equation (1), we get

f(x) = {1/log (3)} [2x - 2² . x²/2 + 2³ . x³/3 -  2⁴. x⁴/4 + ....]

Hence, using logarithmic expansion we get expansion for the function log₃(2x+1) is f(x) = {1/log (3)} [2x - 2² . x²/2 + 2³ . x³/3 -  2⁴. x⁴/4 + ....]

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No we can not  expand the given logarithmic expression log₃(2x+1).

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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Answer:

1

Step-by-step explanation:

[tex]\sin 2x=2\sin x \cos x \\ \\ \sin 90^{\circ}=2\sin 45^{\circ} \cos 45^{\circ} \\ \\ =2(1/\sqrt{2})(1/\sqrt{2}) \\ \\ =2(1/2) \\ \\ =1[/tex]

The system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a total of 35 pounds of apples and strawberries.

Suppose the number of pounds of apples and strawberries is x and y respectively.

If the total of 35 pounds of apples and strawberries as a result,

x + y = 35-------(1)

If each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 then,

2x + 3y = 80---------(2)

Multiply equation 1 by 2 and subtract from equation 2 as

2x + 3y -2(x+y) = 80 - 2(35)

y = 10

Substitute the value of y we get x = 25

As a result, there are 25 pounds of apples and 10 pounds of strawberries in all.

Thus, the system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

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Answer:

AB = 7.28 units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]

From inspection of the given graph:

Substitute the given points into the formula:

[tex]\begin{aligned}\impliesAB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(-3-(-5))^2+(3-(-4))^2}\\& =\sqrt{(2)^2+(7)^2}\\& =\sqrt{4+49}\\& =\sqrt{53}\\ & = 7.28\; \sf units \; (nearest \: hundredth)\end{aligned}[/tex]

Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.

You may also hear the simplest form called "lowest term."

In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:

Expand the following:

(9×4 x sqrt(y)) ^(3/2)

9×4 = 36:

(36 x sqrt(y))^(3/2)

(36 x sqrt(y))^(3/2) = 36^(3/2) (x sqrt(y))^(3/2):

36^(3/2) (x sqrt(y))^(3/2)

36^(3/2) = 36^(2/2 + 1/2) = 36^(2/2)×sqrt(36):

36^(2/2) sqrt(36) (x sqrt(y))^(3/2)

2/2 = 1

Answer:

36 sqrt(36) (x sqrt(y))^(3/2).

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No extraneous solution to the equation:

The equation is:

[tex]x^{1/2}[/tex] - [tex](x- 5)^{1/2}[/tex] = 2

To know whether the equation has an extraneous solution first we need to find the value of x.

[tex]x^{1/2}[/tex] - 2 = [tex](x - 5)^{1/2}[/tex]

[tex]x^{1/2} - 2[/tex] = [tex](x - 5)^{1/2}[/tex]

Now squaring both sides of the equation we have:

[tex](x^{1/2} - 2)^{2}[/tex] = x - 5

x - 4[tex]x^{1/2}[/tex] + 4 = x -5

[tex]x^{1/2}[/tex] = -9/4

x = 81/16

Now we have to put the value of x in the equation.

[tex](81/16)^{1/2}[/tex] - [tex](81/16 - 5)^{1/2}[/tex] =2

9/4 - 1/4 =2

8/4 = 2

2 =2

Therefore we get to know that there is no extraneous solution to the equation.

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The length of each side will be 14.8 inches approx.

It's given that an Octagon sign is drawn out of a square by cutting out triangles from its corners and the total length of the stop sign is 36 inches. We know that squares are Right Angled at each side so in the picture mentioned below, we apply Pythagoras' theorem to find an equation for the side of the sign.

                     =>  [tex]s^{2} = x^{2} + x^{2}[/tex]

                     =>  [tex]s^{2} = 2x^{2}[/tex]                  ----> Eq. 1

Also, it is a square. So, the measurement of length from side to side

                     => 2x + s = 36 inch      ----> Eq. 2

By solving Eq.1 we get s = (√2)(x), Putting this value in Eq.2

                    => s = 36 - 2x    =>    (√2)(x) = 36 - 2x

                    => x(2 + √2 ) = 36   =>  x = 36/(2+√2)

Putting this value of x in Eq.1 , s^2 = 2(x^2)

                   => s = √2.(x)       =>  s = √2 (36/(2 + √2)

                   => s = 14.8

Hence, the length of each side of the sign will be 14.81-inch approx.

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k, q, r, t are directly proportional to p and s is inversely proportional to p.

The inversely proportional property state that two values are opposite to each other. If there will increase in one value or quantity then the another quantity will automatically decrease with the same ratio and if one quantity will decrease then another will increase with that ratio.

Say if x and y are inversely proportional, then mathematically

x ∝ 1 / y

The directly proportional property state that two values are same to each other. If there will increase in one value or quantity then the another quantity will automatically increase with the same ratio and if one quantity will decrease then another will also decrease with that ratio.

Say if x and y are directly proportional, then mathematically

x ∝  y

In the given equation,

k, q, r, t are directly proportional to p and s is inversely proportional to p.

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The area of the aerial banner which is to fly over a professional football game is 201600square inches and can be written as 2.06 ×[tex]10^{5}[/tex] square inches.

The length of the banner is given as 2× 103 inches which are 206 inches

the height of the banner is 100 inches tall

The banner is in the shape of a rectangle

the area of Rectangle = length × breath

So, the area of the banner = 206 ×100

                                               = 20600 square inches

Hence the area of the aerial banner which is to fly over a professional football game is 20600 square inches

As we need to write the area in in scientific notation, we need to use exponents

So, the area of the aerial banner which is to fly  over a professional football game is 201600square inches  and can be written as 2.06 ×[tex]10^{5}[/tex] square inches

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