Each morning, Jon rides 1.5 miles to school and then rides to his aunt’s house after school. Later in the evening, he takes the same route to get back to his house. Over 5 days, he rides 44 miles.

Which equation can be used to find x, the distance from school to his aunt’s house?

[tex]\text{Given that,}\\\\\theta =\tan^{-1} \left(\dfrac y x \right)\\\\\\\dfrac{\partial \theta}{\partial x} = \dfrac{\partial }{\partial x} \tan^{-1} \left(\dfrac yx \right)\\ \\\\~~~~~~=\dfrac{1}{1 +\tfrac{y^2}{x^2}} \cdot y \dfrac{\partial }{\partial x} \left(\dfrac 1x \right)\\\\\\~~~~~~=\dfrac{yx^2}{x^2 +y^2} \cdot (-1)x^{-2}\\ \\\\~~~~~~=-\dfrac{yx^2}{x^2(x^2 +y^2)}\\\\\\~~~~~~=- \dfrac{y}{x^2 +y^2}\\\\\\[/tex]

[tex]\dfrac{\partial^2\theta}{ \partial x^2} = -\dfrac{\partial }{ \partial x} \left( \dfrac{y}{x^2+y^2} \right)\\\\\\~~~~~~=-y\dfrac{\partial}{\partial x} \left(\dfrac 1{x^2 +y^2} \right)\\\\\\~~~~~~=y (-1)(-1) (x^2 +y^2)^{-2} \dfrac{\partial }{\partial x}(x^2 +y^2)\\\\\\~~~~~~=\dfrac{y}{(x^2 +y^2)^2} \cdot (2x+0)\\\\\\~~~~~~=\dfrac{2xy}{(x^2 +y^2)^2}[/tex]

[tex]\text{Similarly,}~~\\ \\\dfrac{\partial \theta}{\partial y }= \dfrac{x}{x^2 +y^2}\\\\\\\dfrac{\partial^2 \theta}{\partial y^2 } = -\dfrac{2xy}{(x^2 +y^2)^2}\\\\\\\text{Now,}\\\\\dfrac{\partial^2 \theta}{\partial x^2 }+\dfrac{\partial^2 \theta}{\partial y^2 }\\\\\\=\dfrac{2xy}{(x^2 +y^2)^2} -\dfrac{2xy}{(x^2 +y^2)^2}\\\\\\=0[/tex]

Answer:

135 mile difference

Step-by-step explanation:

The nile is 4132 miles long according to Gogle and The amazon is 3997 miles long according to gogle

The answer is

for parallel : x-4=0

for perpendicular: y+4=0

The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y=mx+b.

Given line: x=-7

The slope of line x=7 is infinite

The equation of line passing through point (4,-4) and having slope infinite is

0.y+x=-7

So, 0.y= 4

hence, x=4

slope intercept form

x-4=0

Now, for perpendicular lines:

swap the coefficients on x and y with negative sign of x in x=-7

This is a vertical line, so the perpendicular line will be a horizontal line of the form y=b.

Since we are given that the line should pass through the point (4,−4), then the equation of the line is y=−4.

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Answer:

1. False

2. True

3. True

4. True

Step-by-step explanation:

A rational number is a number that can be written as a fraction of two integers. An irrational number can not be written as a fraction of two integers.

(Remember that an integer and a whole number are the same).

This means that...

All whole numbers/integers are rational.

3 is true for reasons mentioned above.

4 is just asking the same as 3.

By taking the product between the rate and the time, we will see that he does not finish the book.

We know that he can read 5 pages in 15 minutes. Then in one hour he can read 4 times that: 4*5 pages = 20 pages.

We conclude that Carter reads 20 pages per day, then, if he reads for 14 hours, then he reads a total of:

20*14 = 280

So he will read 280 pages in these 14 hours, which means that he will not finish the book.

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If the length of UP = 7, then the length of UQ will also be = 7 units.

A perpendicular bisector is a line that cuts a straight line into two both anteriorly and posteriorly.

From the given information:

If the length of UP = 7 units, then the length of UQ will also be = 7 units.

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Answer:

160 m

Step-by-step explanation:

Length of running track = Total Length of straight sections + Total length of curved sections

Solving :

⇒ 400 m = 2 x 120 m + Total Length of curved sections

⇒ Total Length of curved sections = 400 m - 240 m

⇒ Total Length of curved sections = 160 m

Answer:

4522mm³

Step-by-step explanation:

7×50×9 + 28×7×7 = 4522

Answer:

4522 mm^3.4522 mm^3.

Step-by-step explanation:

Splitting this up into 2 prisms, one vertical and the other horizontal:

Volume of each prism = length * width * height:

Volume of the figure =

Horizontal + vertical prism

= 7 * 9 * 50 + 7* 7* 28

= 3150 + 1372

= 4522 mm^3

Answer:

1. Yes, all sides are congruent

2. Yes, the opposite sides are parallel

3. Yes, adjacent sides are perpendicular

Answer:

The factorisation of 405

405 = 5x3x3x3x3

Answer:

405 = 3 x 3 x 3 x 3 x 5 = 3⁴ x 5

Step-by-step explanation:

I'll factor 405 with the Factor Tree Method.

Step 1: Place the number 405 on top of the factor tree.

Step 2: Notice that 405 can be divided by 5 -> 405 = 5 x 81. The two branches from 405 become 5 and 81.

Step 3: Continue factorizing other numbers in the tree until you are left only with the prime factors, which you cannot further factorize.

Step 4: Write the number as the product of prime factors you got.

405 = 3 x 3 x 3 x 3 x 5 = 3⁴ x 5

The coordinating sine value for this angle of rotation will be 4.189.

From the complete information, in the unit circle, there's a point with -1/2 and the x value is 240°.

In this case, the coordinating sine value for this angle of rotation will be:

= (240 × π)/180

= (240 × 3.142) / 180

= 4.189

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Answer:

1.75

Step-by-step explanation:

Finding average rate of change :

The average rate of change for P between 1992 and 2000 is -1.025.

The average rate at which one quantity changes in relation to another is known as the average rate of change function.

It can be determined by dividing the amount of one quantity's change by the amount of another quantity's change.

Average rate of change for a function 'f' in the interval [a, b] is,

A = f(b) - f(a) / (b-a)

So, the Average rate of change

= P(2000) - P(1992) / (2000 - 1992)

= (34.5 - 42.7) /(2000 - 1992)

= -8.2 / 8

= -1.025

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Answer:

helloo!!!!

first up first.... i love your profile pic....

oh and the answer is 744..

please read the explanation... it always helps!!

Step-by-step explanation:

alrighty..

so the total budget is 1200, and we want to know how much is 62% of that

so you follow the percent formula as follows:

1200/100= 12 --> 12 x 62= 744 (which is the answer!)

Answer:

The other rectangle is 4 squares unit.

Step-by-step explanation:

Area Rectangle Formula: Area = Length * Width

Area R1 = 3 * 3 = 9

Area R2 = (7 - 3) * (3 - 2) = 4 * 1 = 4

Answer: Area of a rectangle that is 4 square units.

Step-by-step explanation:

     See attached for my work.

    The area of a rectangle can be found with A = L * W.

Answer:

the square root of 99

6pi-6

pi^3

Step-by-step explanation:

The square root of 99 is approximately 9.9.

6pi-6 is approximately 12.8

pi^3 is approximately 12.8

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's get it solved ~

We have been given length and width of a rectangle in terms of x ~

that is :

Area of the rectangle is given ~ i.e 24 unit²

Area of rectangle in terms of x is :

[tex]\qquad \sf  \dashrightarrow \:(x - 2) \sdot(x + 3) = 24[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 3x - 2x - 6= 24[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} +x - 6 - 24 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} +x -30= 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 6x - 5x - 30 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{}( x + 6) - 5(x + 6)= 0[/tex]

[tex]f(x) = \begin{cases}x = - 6 \: \textsf{ \: if \:x + 6 = 0 } \\ \\ x = 5 \: \: \: \: \: \: \textsf{if \: x - 5 = 0} \end{cases}[/tex]

but since side of a rectangle can't be negative, we have to take value of x as 5

now, Perimeter of rectangle is ~

[tex]\qquad \sf  \dashrightarrow \:2(width \: + \: length)[/tex]

[tex]\qquad \sf  \dashrightarrow \:2(x - 2 + x + 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \:2(2x + 1)[/tex]

plug In the value of x ~

[tex]\qquad \sf  \dashrightarrow \:2(2(5) + 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \:2(10 + 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \:2(11)[/tex]

[tex]\qquad \sf  \dashrightarrow \:22 \: \: units[/tex]

So, the correct choice is b~

Answer:

The answer is ≈ 6214.78

(could put the sign because it wouldnt let me)

Step-by-step explanation:

Formulas:

[tex]A= {2} \pi r h + 2\pi r^{2}[/tex]

[tex]V=\pi r^{2}h[/tex]

[tex]V= A \frac{r}{2} -\pi r^{2} =1890 *\frac{9}{2} -\pi *9^{3} = 6214.77896[/tex]

rounded= 6214.78

~rere

The roots of this equation equation are:

x1 = 4

x2 = 8

This sentence given in the statement of this question is: Equation of the Second Degree. There are a few ways to solve it, but let's calculate by the factorization method.

Equation given: x² - 12x + 36 = 4

x² - 12x + 36 = 4

12x ➯ 2x . x6

36 ➯ 6²

x² - 2x . x6 + 6²

( x - 6 )² = 4

( x - 6 )² = 4

x - 6 = ±√4

x - 6 = ±2

x - 6 = ±2

x - 6 = -2

x - 6 = +2

x - 6 = -2

x = -2 + 6

x = 4

x - 6 = +2

x = 2 + 6

x = 8

Therefore, the correct results of this equation, will be:

x1 = 4

x2 = 8

Answer: 1333.(3)

Step-by-step explanation:

Let her monthly income be x. Then,

(1/10)x + (1/8)x = 300

(4/40)x + (5/40)x = 300

(9/40)x = 300

x = 300 / (9/40)

x = 300*40/9

x = 12000/9

x = 1333 1/3 = 1333.(3)

Answer:

it would be 75% :))

Answer:

75% of 80 = 60

Step-by-step explanation:

60/80 x 100

= 6/8

= 3/4

=75% of 100!

And that's how you find out the percentage.

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

          what is the value of 7x-3y-1 for x = -2 and y = 4?

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

Replace x with -2 and y with 4:-

[tex]\sf{7(-2)-3(4)-1}[/tex]

On simplification,

[tex]\sf{-14-12-1}[/tex]

On further simplification,

[tex]\sf{-27}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

$100

Step-by-step explanation:

$300-$200=$100

or

$200+$100=$300

Answer:

50%

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

2+10+3*10 =42 because there are 2 boxes inside each there are 5 then inside each boxes are 3

Answer:

0.8

Step-by-step explanation:

I'm  just writing this

Answer:

y = 1/3 x + 4

Step-by-step explanation:

y = 1/3 x + 4

The y intercept is 4 (when x = 0 from the graph) and the slope is rise (1) and run (3).

The density of the material that this figurine was made from in pounds/inch³ is 0.183 lb/in³

To answer the question, we need to know what density is

Density is the mass per unit volume of a material.

It is given by ρ = m/v where

Now, given that the toy is dropped into a basin filled with water and found to displace 125.4 mL of water. It's volume is v = 125.4 mL

= 125.4 × 1 mL

= 125.4 × 0.0610237 in³

= 7.65237198 in³

Also, given that the figurine is then put on a scale and found to be 1.4 pounds in weight. It's mass is m = 1.4 lb

So, the density of the material ρ = m/v

ρ = 1.4 lb/7.65237198 in³

ρ =  0.183 lb/in³

So, the density of the material that this figurine was made from in pounds/inch³ is 0.183 lb/in³

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Answer:

Everything is in the picture

Answer:

B

Step-by-step explanation:

Median value = 14    ( the number in the middle of the ascending-order list)

2 quartile   25% are below 11

3 quartile    25% are above 18

min 9       max = 20

Answer:

i think it's b

Step-by-step explanation: