Mellisa is buying party favors to make gift bags

Equation of the line passing through the point of (-20, 4) and perpendicular to the line [(2x + 5y) = 10] will be [2y = (5x + 108)].

As per the question statement, a line passes through the point of (-20, 4) and is perpendicular to the line [(2x + 5y) = 10].

We are required to determine the equation of the above-mentioned line.

To solve this question, we need to know about the formula to express the point-slope form of a line, which goes as, [(y - y₁) = m(x - x₁)],

where (x₁, y₁) is a point through which the line passes, and "m" is the slope of the line.

Also, we need to know about the mathematical fact that, the product of the slopes of two perpendicular lines equate to (-1), i.e., if (m₁ and m₂) are the slopes of two perpendicular lines, then [(m₁ * m₂) = (-1)].

Converting [(2x + 5y) = 10] into the point-slope form of line, we get,

(2x + 5y) = 10

or, [5y = {(-2x) + 10}]

or, [y = {(-2/5)x + 2}]

Therefore, Slope of the line [(2x + 5y) = 10] is (-2/5).

Hence, slope of the line perpendicular to [(2x + 5y) = 10] is [-1/(-2/5)], i.e.,

Slope of the line perpendicular to [(2x + 5y) = 10] is (5/2).

Now, using [m = (5/2)] and (x₁, y₁) as (-20, 4), equation of the line will be

[(y - 4) = (5/2){x - (-20)}]

or, [(y - 4) = (5/2)(x + 20)]

or, [(y - 4) = (5/2x) + 50]

or, [2(y - 4) = 5x + 100]

or, [(2y - 8) = (5x + 100)]

or, [2y = (5x + 108)]

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The ratio is 1:8 and 1:64

Since each tile is one sixth of an inch in width and one fourth of an inch in length.

That is L1= 1/4  in addition to W1= 1/6 inches.

The real tiles are one sixth of a foot long and one tenth of a foot wide.

Since 1 foot equals 12 inches, that is in inches and inches. that is L2=2 and W2= 4/3

So, the length of the tile divided by its real length is equal to L1/L2

=(1/4)/2= 1/8

In addition, the relationship between the area of the tile in the model and the real area is given by:

(1/4 x 1/6)/ 2 x 4/3

= 1/64

Second method

Since there is a 1/8 ratio between the width of the model's tiles and their real width

As a result, there is dilatation with a scale factor of 1/8.

By virtue of dilatation, their area ratio = (1/8)^2 =1/64.

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Answer:

  100.32

Step-by-step explanation:

You want 88 increased by 14% using the multiplier method.

The multiplier used to increase an amount by some fraction (p) of that amount is (1 +p). Here, the fraction is 14%, or 0.14. That means the multiplier is ...

  multiplier = 1 +p

  multiplier = 1 +0.14 = 1.14

The increased amount is then ...

  88 × 1.14 = 100.32 . . . . . . . 88 increased by 14%

__

The actual work is done by a calculator, as shown in the attachment.

Given the point:

(-1, 4)

Let's find the equation of the line that passes through the point and is perpendicular to the line x = -4.

Here, the given line x = -4 is a vertical line that is always at x = -4.

The slope of a vertical line is undefined.

Since x = -4 is a vertical line it means the slope is undefined.

The slope of a line perpendicular to a vertical line is always zero.

Also, the line perpendicular to a vertical line must be a horizontal line.

Therefore, since the perpendincular line passes the point (-1, 4), it means the line will be:

y = 4

hereforem, the equation of the line that passes through the point (-1, 4) and is perpendicular to the line x = -4 is:

y = 4

ANSWER:

y = 4

By definite integrals, we find that the area of the region bounded by the functions f(x) and g(x) described in the statement is equal to 4.5 units.

In this problem we must determine the area between two functions, a quadratic equation f(x) and a linear equation g(x).

First, we need to determine the limits of the interval of x-values with the help of a graphing tool, represented by the points of intersection of the two functions.

The points of intersection of the two functions are (x₁, y₁) = (- 5, 4) and (x₂, y₂) = (- 2, 1), respectively. Then, the area is defined by the following definite integral:

[tex]I = \int\limits^{-2}_{-5} {[g(x) - f(x)]} \, dx[/tex]

[tex]I = \int\limits^{-2}_{- 5} {[(- x - 1) - (x + 3)^{2}]} \, dx[/tex]

[tex]I = - \frac{1}{2} \cdot [(- 2)^{2} - (- 5)^{2}] - [(- 2) - (- 5)] - (1 / 3) \cdot [(- 2 + 3)^{3} - (- 5 + 3)^{3}][/tex]

I = - (1 / 2) · (4 - 25) - 3 - (1 / 3) · (1 + 8)

I = - (1 / 2) · (- 21) - 3 - (1 / 3) · 9

I = 21 / 2 - 3 - 3

I = 21 / 2 - 6

I = 21 / 2 - 12 / 2

I = 9 / 2

I = 4.5

The area of the region represented by the definite integral introduced above is equal to 4.5 units.

The statement leads to a contradiction. Correct form is presented below:

Find the area of the region that is bounded above by the curve f(x) = (x + 3)² and the line g(x) = - x - 1 and bound above the x-axis.

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Solution

- The formula for finding the area of a triangle is given below:

- We have been given:

- Therefore, we can find the area as follows:

Final Answer

The area is 5.4cm²

The value of surface area will be equal to 450 cm square. Thus, option B is the correct answer.

A rectangular prism may be defined as a 3-dimensional solid figure containing 6 faces and its base are in form of rectangle. The surface area may be given as the sum of all individual side areas. The prism given is like a cube and has 6 sides. The sides given are top - bottom, left - right and front - back. In the case given in the question we have top and bottom given as 5×5 squares, and the other 4 sides are equal 5×20 rectangles. So, we find the area as following

From top - bottom: 2× 5×5 = 50 cm²

From left - right: 2× 20×5 = 200 cm²

From front - back: 2× 20×5 = 200 cm²

Thus, in total the surface area will be given as = 200 + 200 + 50 = 450 cm².

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Answer:

40

Step-by-step explanation:

2400 divided by 60 is 40

I hope this helps!

The total cost of purchasing the minimum quantities for the trip, including sales tax of 7% is $246.10, while you can buy 4 times more.

A sales tax is a use or consumption tax, indirectly levied by the government on buyers of certain taxable items.

The seller collects the sales tax on behalf of the government.

Total amount to spend on supplies = $1,000

Items         Cost Unit         Units       Total      Units       Total for more

Oxen:        $40 each           2            $80         8               $320

Food:        $0.20 per lb     500         100       2,000           400

Clothing:  $10 per set         5              50        20               200

Total cost before tax                      $230                        $920

7% sales tax                                     $16.10                         64.40

Total cost after tax                       $246.10                     $984.40

Change = $15.60

Thus, with $1,000, you can purchase 4 times the above quantities and still have some change after paying the required sales tax.

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Answer:

x = 6

Step-by-step explanation:

(6, -6), (6, -4)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁        -4 - (-6)      -4 + 6          2

m = ------------ = ------------ = ------------ = ------- = undefined

        x₂ - x₁         6 - 6              0            0

x = 6

I hope this helps!

Answer:

6 sweets

Step-by-step explanation:

add 30 until you are going over

X+1 depicts horizontal linear equation as x = -1 and slope = 0.

Given that the slope is 0, it shows a horizontal linear equation.

Every point on a horizontal line has the same y-coordinate.

If two points have the same y coordinate, b, then the line's equation is y=b.

The y-intercept of the horizontal line y=b is the point (0,b). The line y=0 is the only x-intercept for horizontal lines.

Horizontal lines have zero slope.

As a result, in the slope-intercept equation y = mx + b, m = 0. The equation is Y = b, where b is the y-coordinate of the y-intercept.

A line that is perpendicular to the x-axis is referred to as a horizontal line.

The graph of a relation of the form x = 5 is a line parallel to the origin since the value of x never changes.

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When the function f is transformed to g, the equation is -45.5x

The equation of function f is given as

f(x) = 6.5x

The transformation is given as

The above transformation rule can be represented as

(x, y) = (-x, 7y)

When the above rule is applied, we have the following equation

g(x) = -7f(-x)

So, we have

g(x) = -7 * 6.5x

Evaluate

g(x) = -45.5x

The above equation is a linear function

So, the domain and the range are the set of all real values and the y-intercept is 0

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An equation, in point-slope form, that represents Byron's distance from home, y, after hours is: B. y - 4 = 6(x - 1/2).

The point-slope form can be defined as an equation which is used when the slope of a line and one of the points on this line is known.

Mathematically, the point-slope form of a line is given by this equation:

y - y₁ = m(x - x₁)

Where:

Given the following data:

Average speed (slope), m = 6 mi/h.

Point, y = 4.

Point, x = 1/2

Substituting the given parameters into the formula, we have;

y - y₁ = m(x - x₁)

y - 4 = 6(x - 1/2)

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The level of ibuprofen in the patients bloodstream increased from 0 hours to 2 hours.

What is ibuprofen?

Ibuprofen is an example of an NSAID that is used to relieve pain, fever, and inflammation. This includes menstruation pain, migraines, and rheumatoid arthritis. Additionally, it can be applied to seal off a premature infant's patent ductus arteriosus. It can be given orally or intravenously. After an hour, it usually begins to function.

In the graph that is attached, the y-axis represents the concentration of ibuprofen in the patient's bloodstream, and the x-axis represents the number of hours since ibuprofen was last consumed.

As we can see from the graph, the curve increases from a time of 0 hours, which corresponds to 0 mg of ibuprofen, to a time of 2 hours, which corresponds to 400 mg of ibuprofen.

The curve starts to descend after that point. We will settle for the first assertion because increase is what we are interested in.

Thus, we may conclude that the increase in ibuprofen level occurred between 0 and 2 hours.

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The most appropriate choice for linear inequation will be given by-

The range of ages to which the squirrels live is 5 to 8 years

What is Linear Inequation?

Linear Inequation involves comparision between two values with the help of <,   >,   [tex]\leq , \geq[/tex]

   .

Here,

Let the range of ages (in years) to which the squirrels live be [tex]x[/tex] years

The lifespans of the squirrels may vary by as much as 1 year.

By the problem,

                        [tex]|x - 6.5|\leq 1.5\\-1.5 \leq x - 6.5 \leq 1.5\\x - 6.5\geq -1.5[/tex]and    [tex]x-6.5\leq 1.5[/tex]

                        [tex]x \geq 6.5-1.5[/tex] and [tex]x \leq 6.5 + 1.5\\[/tex]

                        [tex]x \geq 5[/tex] and [tex]x \leq 8[/tex]

The range of ages to which the squirrels live is 5 to 8 years

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Answer: a

Step-by-step explanation:

because 140 squared = 200x=48/4

From the given parameters to determine the cost of the airline ticket, we can interpret that that the maximum amount that each ticket costs is $295 while the maximum amount of bags is 5 bags.

We are given the linear equation that represents the cost of an airline ticket after adding a number of checked bags as;

y = 145 + 30x

where;

y is the cost (in dollars) of an airline ticket after adding a number of checked bags

x is the number of checked bags

Thus, if there is a maximum of 5 bags that can be checked, then we have;

y = 145 + 30(5)

y = $295

This means that the maximum amount that each ticket costs is $295 while the maximum amount of bags is 5 bags.

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The percent of the budget that is destined for sales is 19%, the percent for support is 28% and the percent for editorial is 3%. All together, they represent the 50% of the total budget. That 50% is equivalent to $62,500,000, to find the total annual budget divide this amount by the percent that it represents (in decimal form which is 0.5):

The total annual budget is $125,000,000.

The equation of the line that passes through the point (6,-5) and has a slope of -1/6 is y = (-1/6)x  - 4.

We know that, the slope intercept form of a line is given by:-

y = mx + c

Where,

m represents the slope of the line,

c represents the y -intercept and,

(x,y) represent the coordinates of each of the ordered pairs in the line

Hence, we can write,

m = -1/6

One of the ordered pairs, (x,y) is (6,-5).

Hence, we can write,

-5 = (-1/6)*6 + c

-5 = -1 + c

c = -5 + 1

c = - 4

Hence, the equation of the line is given by:-

y = (-1/6)x  - 4

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Step 1

Given; What is the precise definition of a limit in calculus?

The required definition is;

Answer;

Let f be a function defined on some open interval containing a (except possibly at a).

Then the limit as x approaches a of f is L written as;

if and only if

Answer

2

Step-by-step explanation:

1 + 1 =2

In mathematics, time is characterized as a continuing and continuous series of events that take place one after another, from the past through the present and into the future.

Yolanda watched videos for 1/2 minute in all.

Time can be viewed as an ongoing and continuous series of related events that take place one after another, from the past through the present and into the future, in mathematics.

Time is used to sequence events as well as to quantify, measure, and compare the length of occurrences or the gaps between them.

Given,

Yolanda watched a video for 3/8 minutes.

She watched another video for 1/8 minute.​

Solution:

Total video watch hour = 3/8 + 1/8

Total video watch hour = 4/8

On simplifying we get,

Total video watch hour = 1/2 minutes

Yolanda watched videos for 1/2 minute in all.

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Answer:

I think it is a function???

Step-by-step explanation:

Because a graph represents a function if it impossible to draw a vertical line that intersects the graph more than once.

I'm not sure if I'm correct, let me know please.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex] \displaystyle\qquad \tt \rightarrow \:1.) \: \: \: \frac{dy}{dx} = cot(x)[/tex]

[tex] \displaystyle\qquad \tt \rightarrow \:2.) \: \: \frac{dy}{dx} = 2x \sdot {3}^{ {x}^{2} } \sdot ln(3) [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

We need to find derivative of the following functions

[tex]\qquad \tt \rightarrow \:y = ln(sin(x))[/tex]

[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = \frac{d}{dx} (ln(sin(x)))[/tex]

[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{sin(x)} \sdot cos(x)[/tex]

[ by chain rule ]

[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = cot(x)[/tex]

[tex]\large{ 2.)\tt y = {3}^{{x}^{2}}} [/tex]

[tex]\qquad \tt \rightarrow \:y = {3}^{ {x}^{2} } [/tex]

[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = \frac{d}{dx} ( {3}^{ {x}^{2} } )[/tex]

[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = {3}^{ {x}^{2} } \sdot ln(3) \sdot(2x) \sdot(1)[/tex]

[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = 2x \sdot {3}^{ {x}^{2} } \sdot ln(3) [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The non real roots of the polynomial x³ – 7x² + 15x – 25 = 0 are; 1 + 2i, 1 – 2i

Non real roots are simply imaginary roots.

We are told that the real roots of the equation  x³ – 7x² + 15x – 25 = 0 is 5.

Now, it means that (x - 5) is a factor of the given polynomial. Thus, we can factorize the polynomial as;

(x - 5)(x² - 2x + 5) = 0

Now, to find the non - real roots, we will use quadratic formula on (x² - 2x + 5) to get;

x = [-(-2) ± √((-2)² - (4 * 1 * 5))]/2(1)

x = (2 ± √(-16))/2

x = 1 ± 2i

x = 1 + 2i, 1 – 2i

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Answer:

c

Step-by-step explanation:

The best estimate of the cost to ship 5 large packs is 94.75 and 3 small packages is 29.25.

What is the best estimate?

Best estimate means an income, expense, or circumstance prediction based on past amounts of income and expenses and known factual information concerning future circumstances which affect eligibility, expenses to be incurred; or income to be received in the benefit month.

Given that

Shipping company charges 18.95 for a large package.

Shipping company charges 9.75 for a small package.

For 5 large packs shipping company charges = 5 × 18.95 = 94.75

For 3 small packs shipping company charges = 3 × 9.75 = 29.25

Therefore,  the best estimate of the cost to ship 5 large packs is 94.75 and 3 small packages is 29.25.

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Using it's formula, it is found that the bond's yield with a face value of $5,000, yield of 7% and rate of 8%, is of 7.48%.

The bond's yield is given according to the following formula:

Yield = Annual Coupon Payment/Bond Price

These values are calculated considering the face value, the current yield and the coupon rate, all parameters which are given in this problem.

The Annual Coupon Payment is given by the multiplication of the face value and the Coupon Rate, hence:

Annual Coupon Payment = 5000 x 0.08 = $400.

The bond price is the given by the multiplication of the face value and 100% plus the yield, hence:

Bond Price = 5000 x 1.07 = $5350.

Then the bond's yield is given as follows, applying the formula:

Yield = 400/5350 = 0.0748 = 7.48%.

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