What is the slope of the line that passes through the points (9,1) and (10,−1)? Write your answer in simplest form.

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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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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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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With regards to the rigid transformations, Yes, it is true to state that ∠ABD is congruent to ∠EFM. This can be justified by translating ∠ABD by superimposing it on ∠EFM.

It is also true to state that ∠ ABD is congruent to ∠GFHG. To justify this, rotate ∠ABD by 180°

A rigid transformation in mathematics is a geometric transformation of a Euclidean space that retains the Euclidean distance between each pair of points. Rotations, translations, reflections, and any combination of these are examples of rigid transformations.

Hence, the above statements are true. Note that rigid transformations do not modify the distance angles, size or shape.

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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.

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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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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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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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

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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Line (0, 2), (-5, -3) ---> y = x + 2

Line (0, 5), (-5, -5) ---> y = 2x + 5

Point of intersection ---> we need to equate both equations:

If x = -3 ---> y = -3 + 2 ---> y = -1

The point of intersection in this case is (-3, -1) (the last one, from left to right).

Line (-2, 1), (-3, -1) ---> y = 2x + 5

Line (0, 2), (2, 0) ---> y = -x + 2

Equating both equations to find the intersection point:

If x = -1, then y = -(-1) + 2 ---> y = 1 + 2 ---> y = 3

The point of intersection is (-1, 3) (the second one, from left to right).

Line (4, -2), (1, 1) ---> y = -x +2

Line (4, 2), (0, -2) ---> y = x - 2

Then, we have ---> intersection point:

Using the second equation to find y ---> y = 2 -2 ---> y = 0

The point of intersection is (2, 0) (the first point, from left to right).

Line (2, -2) (0, 2) ---> y = -2x + 2

Line (2, 1), (3, 2) ---> y = x - 1

Then, we have:

Using the second equation to find y ---> y = 1 - 1 ---> y = 0

The point of intesection is (1, 0) ( the third point, from left to right).

m∠2 = m∠7

and

m∠4 = m∠8

Both are correct answers and should be ticked

Here, we want to select which of the statements must be correct based on the diagram given

a) m∠2 = m∠7

This is correct

m∠2 = m∠3 as they are vertically opposite angles

However, m∠3 = m∠7 as they are vertically opposite angles

b) m∠7 = m∠10

We cannot compare the relationship between b and c as the pair are not parallel lines

c) m∠8 = m∠9

This is not correct also as the pair of lines are not parallel

d) m∠4 = m∠8

These two are corresponding angles, so they are congruent and thus equal in value

Slope

[tex]\frac{-10-(-2)}{1-(-3)}=-2[/tex]

Equation

[tex]y+10=-2(x-1)[/tex]

x-intercept

The x-intercept is when y=0.

[tex]10=-2(x-1)\\\\-5=x-1\\\\x=-4[/tex]

So, the x-intercept is (-4, 0).

Answer:

Step-by-step explanation:

(i) Find the value of y when x = - 2

(ii) See the graph attached

(iii) The axis of symmetry is the vertical line passing through the vertex, which is x + 1 = 0 or x = - 1.

This is also reflected on the attached graph.

(iv) From the graph it is visible that in the given interval the function is decreasing, so the value at x = - 4 is the maximum and the value at x = - 2 is minimum:

These two points too are given on the same graph.

(v) There ate two x-intercepts, the one on the right is the larger one.

It is (0.732, 0), marked on the graph.

(vi) This function is the standard form of the given:

With the positive leading coefficient of 1, it has a minimum value but no maximum. The minimum of this function is at its vertex, which is (- 1, 3) as per graph.

(vii) The function y = x² + 2x is the translation of the given function up by two units.

So its minimum value is 2 units greater:

Answer: 57.14 km/hr

Step-by-step explanation:  if an hour is divided into quarters it will be in increments of 15 minutes, since  one hour is 60 minutes.  60 minutes divided by 5 is 15 minutes.  

So 1 hour and 38 minutes is rounded off to 1 hour and 45 minutes.

this is 1 hour + 3/4 hour = 1 3/4 hour.  This is same as 1.75 hour

3/4 is .75

speed divided by the time will give the average speed.

100km/1.75hours  = 57.14 km/per hour

Answer:

(a)  1 hour 45 min

(b)  57.1 km/h (nearest tenth)

Step-by-step explanation:

Given information:

[tex]\large\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]

[tex]\begin{aligned}\sf \dfrac{1}{4}\;hour &= \sf 1 \; hour \div 4 \\& = \sf 60 \;mins \div 4\\& = \sf 15 \; mins\end{aligned}[/tex]

Therefore, the nearest ¹/₄ hours either side of the given time is:

1 h 38 min 45 sec is 8 min 45 sec more than 1 hour 30 min.

1 h 38 min 45 sec is 6 min 15 sec less than 1 hour 45 min.

Therefore, the nearest ¹/₄ hour to the given time is:  

1 hour 45 min = 1.75 min (in decimal form)

Substitute the given distance and the rounded time (in decimal form) into the formula and solve for speed:

[tex]\begin{aligned} \implies \sf Speed & =\sf \dfrac{Distance}{Time}\\\\& = \sf \dfrac{100}{1.75}\\\\& = \sf 57.1\;km/h\;(nearest\;tenth)\end{aligned}[/tex]

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:

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!

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

[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 ❞

Answer:

6 sweets

Step-by-step explanation:

add 30 until you are going over

Here, use this to help you: https://www.map.mathshell.org/download.php?fileid=1676

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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Solving the circumference function, we have that:

The corresponding interval for diameters of the washers is 1.85 ≤ d ≤ 1.97.

The circumference of a circle of diameter d is given by:

C = 3.14d.

As stated in the problem.

The interval of circumference values is:

5.8 ≤ C ≤ 6.2.

Hence the lowest possible value for the diameter is given by:

3.14d = 5.8

d = 5.8/3.14

d = 1.85.

The highest possible value for the diameter is given by:

3.14d = 6.2

d = 6.2/3.14

d = 1.97.

Then the compound inequality that completes the given sentence is:

1.85 ≤ d ≤ 1.97.

The interval for the circumference values is given by:

5.8 ≤ C ≤ 6.2.

We have to complete the following sentence with the compound inequality:

The corresponding interval for diameters of the washers is

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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.

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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Answer:

Step-by-step explanation:

To find the value of x and y, isolate it on one side of the equation.

-3x+2y=4, 4x=13y=5

-3x+2y=4

[tex]\rightarrow \sf{x=-\dfrac{4-2y}{3}}[/tex]

Substitute.

[tex]\sf{4\left(-\dfrac{4-2y}{3}\right)-13y=5}[/tex]

Solve.

Use the distributive property.

A(B+C)=AB+AC

A(B-C)=AB-AC

[tex]\sf{=\dfrac{-16-31y}{3}=5}[/tex]

Isolate the term of y.

Multiply by 3 from both sides.

[tex]\sf{\dfrac{3\left(-16-31y\right)}{3}=5*3}[/tex]

Solve.

Multiply the numbers from left to right.

5*3=15

-16-31y=15

Add by 16 from both sides.

-16-31y+16=15+16

Solve.

15+16=31

-31y=31

Divide by -31 from both sides.

-31y/-31=31/-31

Solve.

y=-1

Substitute of y=-1.

[tex]\sf{x=-\dfrac{4-2\left(-1\right)}{3}}[/tex]

Solve.

Use the order of operations.

PEMDAS stands for:

4-2(-1)

Do parentheses by multiply first.

2(-1)=-2

4-(-2)

4+2=6

-6/3

Divide.

-6/3=-2

x=-2

[tex]\Rightarrow \boxed{\sf{x=-2, \quad y=-1}}[/tex]

Therefore, the correct answer is x=-2, and y=-1.

I hope this helps, let me know if you have any questions.

Given the following question:

Part A:

Your answer is option B, you can find this by checking the values. We are given 107, 128, 163, 212, 275 if you check the values on the graph, you can see that they are exact. So, your answer is option B.

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.