Mr. Jackson drove 40 miles in June. He drove 6 times as many miles in August as he did in June. He drove 2 times as many miles in July as he did in August. How many miles did Mr. Jackson drive in July?

The standard form of this expression is equal to 10 + 20i.

Complex numbers are those numbers that contain the imaginary and the real part.

Complex value z is written in a rectangular form as; z = x+iy where (x, y) is the rectangular coordinates.

r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

We are given that the expression as (1+7i)(3-i)

Solving it;

(1+7i)(3-i)

3 - i + 21i - 7i^2

3 - i + 21i + 7

10 + 20i

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Answer:

Step-by-step explanation:

(2/3)x - 4 > 1

(2/3)x  > 5

x is larger or equal 15/2

Answer:

9.71 ÷ 9.82 = .9987 or 1% .

The percentage increase is 1.1% to the nearest tenth

The calculation can be done as follows

Original price= $9.82

increase= $9.71

Change in price= 9.82-9.71

= 0.11

percent increase= 0.11/9.82 × 100

= 1.12

= 1.1 (to the nearest tenth)

Hence the percent increase is 1.1%

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Answer:

C and E on edge

Step-by-step explanation:

The equations that correspond to the rectangular equation is option B, C, and E.

The equations in which the dependent and the independent variable are written in terms of an individual parameter are called Parametric Equations.

The rectangular equation is

y = -|x|

x = t² and y = –|t²|

x = 2t and y = –|2t|

x = t + 4 and y = –|t + 4|

These three equations will not change the original value.

It seems that your question is incomplete, the complete question is as follows:

x = –t and y = |–t|

x = t2 and y = –|t2|

x = 2t and y = –|2t|

x = t3 and y = |t3|

x = t + 4 and y = –|t + 4|

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Step-by-step explanation:

in equation 1

y=4x+12

so now

eqs 2

2y=4+3x

then

-y=x+8

y= -x-8

so

-x-8=4x+12

-20=5x

-4=x

so

y= 4-8

y=-4

To rotate a point (x, y) by 270 degrees clockwise about the origin, we can use the following formula:

(x', y') = (y, -x)

where (x', y') are the coordinates of the rotated point.

Using this formula for each of the vertices of RSQ, we get:

R' = (yR, -xR) = (-1, -4)

S' = (yS, -xS) = (-3, -5)

Q' = (yQ, -xQ) = (-1, -3)

Therefore, the coordinates of the vertices of the image RSQ after rotating 270 degrees clockwise about the origin are R'(-1, -4), S'(-3, -5), and Q'(-1, -3).

Thus, an equation to show the overall price y of renting shoes and bowling x equipment is: y=4x+b.

The task is to create an equation that use the total expense (y) and the total number of bowled games (x). Hence, the way that we will begin is by entering the knowing into the formula of slope intercept form:  y=mx+b.

Thus, we include them in the formula: y=4x+b.

14 = 4(3)+b

Find b

14 = 12+b

14 - 12=b

b = 2

Thus, an equation to show the overall price y of renting shoes and bowling x equipment is: y=4x+b.

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Complete question:

The total cost for bowling includes the fee for shoe rental plus a fee per game. The cost of the game increases the price by $4. After 3 games, the total cost with shoe rental is $14.

a.write an equation to represent the total cost y to rent shoes and bowl x games.

Convert the problem to standard form and write the initial tableau with slack variables:

Maximize

\(Z = 7*3 + 6*4 + 18*5 + 14*6 - 3*1 - 3*2 - 4*5 - 4*6\)

Subject to:

\(x1 + x2 + s1 = 4000\\x3 - (1/3)*1 + (1/3)*5 = 0\\x4 - (1/3)*2 + (1/2)*6 = 0\\x3*1 + 3*2 + 3*3 + 3*4 + 3*5 + 2*6 + s2 = 6000\)

All variables are non-negative.

Tableau

 x1  x2  x3  x4  x5  x6  s1  s2   b

Z -3 -3 7 6 18 14 0 0 0

s1 1 1 0 0 0 0 1 0 4000

s2 3 3 3 3 3 2 0 1 6000

x5 0 0 1 0 1/3 0 0 0 0

x6 0 0 0 1 0 1/2 0 0 0

The basic variables are s1, s2, x5, and x6.

Step 1: Choose  entering variable. The most positive coefficient in objective row is 18, corresponding to x5. x5 enters the basis.

Step 2: Choose the leaving variable. The minimum ratio of right-hand side to coefficient of x5 is 12000/(1/3) = 36000,

corresponding to s1. s1 leaves the basis.

Step 3: Perform, pivot operation to make x5 the basic variable for s1. Divide, pivot row by 1/3 and subtract appropriate multiples of the pivot row from other rows to make other entries in column 5 zero.

 x1    x2    x3    x4     x5     x6   s1    s2       b

Z -3 -3 7 6 18 14 0 0 0

x5 0 0 1 0 1/3 0 0 0 0

s2 3 3 3 3 2 2/3 2/3 0 1/3 24000

x3 1 0 1/3 0 1/3 0 -1/3 0 0

x4 0 1 0 1/3 0 1/2 -1/6 0 0

The basic variables are x5, x3, x4, and s2.

Step 4: Choose the entering variable. The most positive coefficient in the objective row is 7, corresponding to x3. x3 enters the basis.

Step 5: Determine the leaving variable. The right-hand side's minimum ratio to the coefficient of x3 is 0, indicating that x3 can be increased without bound. This implies that the optimal solution is unbounded and that there is no finite optimal value for the problem.

As a result, the simplex algorithm demonstrates that the given linear programming problem lacks a feasible solution. This means that it is not possible to meet all of the constraints at the same time.

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Answer:

y = - \(\frac{1}{3}\) x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 3 ← is in slope- intercept form

with slope m = 3

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{3}\) , then

y = - \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (- 6, 9 ) into the partial equation

9 = - \(\frac{1}{3}\) (-6) + c = 2 + c ( subtract 2 from both sides )

7 = c

y = - \(\frac{1}{3}\) x + 7 ← equation of perpendicular line

The complete factor is (2x+1)/(2x+1)^2

(2x+1)^-2/3+(2x+1)^1/3

X= 1/(2x+1)^2/3+(2x+1)^1/3

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

The complete factor form is

x/(2x+1)^2/3+(2x+1)^1/3

=1 x+(2x+1)^2/3×(2x+1)^1/3/

(2x+1)^2/3

x+(2x+1)^2/3+1/3 =3/3=1

/

(2x+1)^2/3

X+(2x+1)/(2x+1)/(2x+1)^2/3

3x+1/(2x+1)^2/3 (Ans)

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Answer:

12

Step-by-step explanation:

PEMDAS is the order

P = parenthesis

E = exponent

M = *

D = division

A = +

S = -

so first 8*2 = 16

and then -8/2 = -4

and then -4 + 16

= 12

Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Answer:

60.5 m

Step-by-step explanation:

We can use the arc length formula to calculate the length of highlighted arc. Let the numerical measure of the highlighted arc be known as C, the angle measure be known as \(\theta\), and r as the radius of the circle.

Given variables:

Plug in all the variables into the formula and solve for the letter C.

\(\boxed{\text{Formula: C = }{2\pi r\huge{\text(}\frac{\theta}{360}\huge\text{)}}}\)

\(\implies C = }{2\pi (11)\huge{\text(}\dfrac{315}{360}\huge\text{)}}}\)   \(\implies C = }{22\pi \huge{\text(}\dfrac{315}{360}\huge\text{)}}} = 60.5 \ \text{m}\)

Therefore, Option A is the correct option.

Answer:

-73

Step-by-step explanation:

i think

Step-by-step explanation:

it is then simply scanned (multiplied).

the new point is

(-8 × 1/4, 0 × 1/4) = (-2, 0)

The area of the rectangular field is 70000 square m if the rectangular field is 0.35 kilometers long and 0.2 kilometers wide.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Area of rectangle = 0.35x0.2 = 0.07 square km

1 km = 1000 m

1 square km = 1000000 square m

Area of rectangle = 0.07x1000000 square m

Area of rectangle = 70000 square m

Thus, the area of the rectangular field is 70000 square m if the rectangular field is 0.35 kilometers long and 0.2 kilometers wide.

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Answer:   6

Step-by-step explanation:   You'll need to substitute x for 12 in the expression, which will be 12 - 2 + 2(4) - 12, and using BODMAS/BIDMAS/PEDMAS (or whatever you use), you should get 6 if you did it correctly.

Answer:

18

Step-by-step explanation:

using bodmas rule by working out brackets first

Answer:

D.

Step-by-step explanation:

is a equilateral triangle ( has all the lengths  equal)

The ratio of x to y is given by 3 : 1

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

6 ( y + 3 ) = 2 ( x + 9 )

On simplifying , we get

6y + 18 = 2x + 18

Subtracting 18 on both sides , we get

6y = 2x

Divide by 2 on both sides , we get

x = 3y

Divide by 3 on both sides , we get

x/y = 3/1

Therefore , the proportion is x : y : : 3 : 1

Hence , the ratio is 3 : 1

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The graph of the function is attached below.

The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.

Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.

We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.

In the given problem;

The graph of the function f(x) = 1 + x / x² - 1 is attached below;

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By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

What is the parallel lines?

Parallel lines are two lines in a plane that never intersect.

1. Orientation of Lines:

Parallel lines are lines that never intersect and remain equidistant from each other at all points.

When constructing parallel lines, the lines are drawn in the same direction and maintain the same distance between them throughout their entire length. They do not meet or cross each other.

On the other hand, perpendicular lines are lines that intersect at a right angle (90 degrees). When constructing perpendicular lines, the lines are drawn so that they intersect at a right angle, forming four right angles at the point of intersection.

2. Tools/Methods Used:

Constructing parallel lines and constructing perpendicular lines may require different tools or methods.

To construct parallel lines, one common method is to use a straightedge and a compass. A straightedge is used to draw a straight line, and a compass is used to measure and transfer distances to create additional parallel lines.

Therefore, By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

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Answer:

Area = 110.88 m²

Step-by-step explanation:

Total area = area of the two triangles + area of the rectangle

Total Area = ½bh + L*W × ½*by

= ½*7*7.2 + 7.6 × 7.2 + ½*8.6*7.2

= 25.2 + 54.72 + 30.96

Total Area = 110.88 m²

The cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

To find the cost of one hosta and one geranium, we can set up a system of equations based on the given information.

Let's assume the cost of one hosta is represented by 'h' and the cost of one geranium is represented by 'g'.

From the information given, we can set up the following equations:

Eugene's spending:

18h + 6g = $150

Jessica's spending:

7h + 16g = $113

We can now solve this system of equations to find the values of 'h' and 'g'.

Multiplying the first equation by 2 and the second equation by 3 to eliminate 'g', we get:

36h + 12g = $300

21h + 48g = $339

Now, we can subtract the second equation from the first to eliminate 'h':

(36h + 12g) - (21h + 48g) = $300 - $339

36h - 21h + 12g - 48g = -$39

15h - 36g = -$39

Simplifying further, we have:

15h - 36g = -$39

Now we can solve this equation for 'h' and substitute the value back into any of the original equations to find 'g'.

Let's solve for 'h':

15h = 36g - $39

h = (36g - $39) / 15

Substituting this value of 'h' into Eugene's equation:

18[(36g - $39) / 15] + 6g = $150

(648g - $702) / 15 + 6g = $150

648g - $702 + 90g = $150 * 15

738g - $702 = $2250

738g = $2250 + $702

738g = $2952

g = $2952 / 738

g ≈ $4

Now, substituting the value of 'g' back into Eugene's equation:

18h + 6($4) = $150

18h + $24 = $150

18h = $150 - $24

18h = $126

h = $126 / 18

h ≈ $7

Therefore, the cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

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Take note of the domain of possible solutions:

• √(2x + 1) is defined for 2x + 1 ≥ 0, or x ≥ -1/2

• √(x + 1) is defined for x + 1 ≥ 0, or x ≥ -1

So any solutions to this equation must fall in the interval x ≥ -1/2, or [-1/2, ∞).

To solve, move one of the root expressions to the right side, then square both sides:

√(2x + 1) = 2 + √(x + 1))

[√(2x + 1)]² = [2 + √(x + 1))]²

2x + 1 = 4 + 4 √(x + 1) + (x + 1)

Simplify this to

x - 4 = 4 √(x + 1)

and now square both sides again and solve for x :

[x - 4]² = [4 √(x + 1)]²

x ² - 8x + 16 = 16 (x + 1)

x ² - 8x + 16 = 16x + 16

x ² - 24x = 0

x (x - 24) = 0

x = 0   or   x - 24 = 0

x = 0   or   x = 24

Both of these solutions are greater than -1/2; however, if x = 0, we get

√(2×0 + 1) - √(0 + 1) = √1 - √1 = 1 - 1 = 0 ≠ 2

so the only solution is x = 24.

Answer:

• √(2x + 1) is defined for 2x + 1 ≥ 0, or x ≥ -1/2

• √(x + 1) is defined for x + 1 ≥ 0, or x ≥ -1

So any solutions to this equation must fall in the interval x ≥ -1/2, or [-1/2, ∞).

To solve, move one of the root expressions to the right side, then square both sides:

√(2x + 1) = 2 + √(x + 1))

[√(2x + 1)]² = [2 + √(x + 1))]²

2x + 1 = 4 + 4 √(x + 1) + (x + 1)

Simplify this to

x - 4 = 4 √(x + 1)

and now square both sides again and solve for x :

[x - 4]² = [4 √(x + 1)]²

x ² - 8x + 16 = 16 (x + 1)

x ² - 8x + 16 = 16x + 16

x ² - 24x = 0

x (x - 24) = 0

x = 0   or   x - 24 = 0

x = 0   or   x = 24

Both of these solutions are greater than -1/2; however, if x = 0, we get

√(2×0 + 1) - √(0 + 1) = √1 - √1 = 1 - 1 = 0 ≠ 2

so the only solution is x = 24.

Answer:

it is B

Step-by-step explanation:

=B

Using the Leading Coefficient Test the end behavior of the function  f(x) = 1234999x as the values of x increase towards infinity, ∞ is the functin also tends to infinity

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = 1234999x

The end behavior is determined by the leading Coefficient = 1234999, the problem has only one variable and hence the leading coefficient

x ⇒ ∞ f(x) ⇒ ∞

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