Nick walked 5 miles to reach his aunt's house. From there he traveled 8 miles to the shopping mall on a bicycle. He traveled 80% faster on the bicycle than on foot. Let r represent his rate of walking in miles per hour. Identify the expression that represents the number of hours Nick took to reach the shopping mall in terms of r. Then find the time taken by Nick to reach the shopping mall if he walked at an average speed of 3 miles per hour

Step-by-step explanation:

Hello there!

Here is the solution to our problem:

To begin with, we give our equations labels as below;

3m − n = 2 ...................eq.1

2m + n = − 7 ..................eq.2

Then, Let's manipulate eq.2

2m + n = − 7

n = -7 - 2m ...............eq3

And finally substitute the manipulated eq.3 into eq.1

3m − n = 2

3m − (-7 - 2m) = 2

3m + 7 + 2m = 2

5m = -5

m = -1

Substitute the value of m into eq.3

n = -7 - 2(-1)

= -5

In terms of x and y;

(x,y) : (m, n) => (-1, -5)

Therefore (m, n) = (-1, -5)

I hope this helps.

Have a nice studies.

============================================================

Reason:

For now we'll only focus on the x coordinates. They are 4 and -8. Plot them on a number line and find the midpoint. To do this, add those values up and divide by two

(4 + (-8))/2 = -4/2 = -2

The value -2 is right in the middle of 4 and -8; hence it's the midpoint.

Repeat those steps for the y coordinates

(-6+10)/2 = 4/2 = 2

These two midpoints help lead to (x,y) = (-2, 2) which is the midpoint the given endpoints. By extension, it is the center of the circle.

Visual confirmation is shown below. I used the midpoint command in GeoGebra. Desmos is another graphing tool you can use.

Step-by-step explanation:

in a management information system, the quality of information is determined by its usefulness to users, and its usefulness determines the success of the information system.

The equation that the clerk can use to calculate their total bill is t + g.

From the information given, Yasuda family bought a toy that cost t dollars and a game that cost g dollars.

The equation to calculate their total bills will be:

= t + g

where,

t = cost of toy

g = cost of game.

In this case, the equation that the clerk can use to calculate their total bill is t + g .

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Answer:

4pi + 8 km

Step-by-step explanation:

the circumference of teh circle is d*pi = 8pi. since this is a semicircle the circumference is 4pi. then the perimeter is 4pi + 8

Real life scenarios of acute angles are:

Acute angles are angles that have a measure less than 90 degrees.

To create a real life scenario to illustrate acute angles, the following must be put in place:

Real life scenarios that satisfy the above highlights are:

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The lower bound for the profit is $2425.

When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0

The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434  

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Answer:

3.31662479

Step-by-step explanation:

3.31662479

The solution of x in -6 + 3x - 9x^2 = -16 is [tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]

The equation is given as:

-6 + 3x - 9x^2 = -16

Add 16 to both sides

10 + 3x - 9x^2 = 0

Rewrite as:

9x^2 - 3x - 10 = 0

Solve for x using the quadratic formula

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

So, we have:

[tex]x = \frac{3 \pm \sqrt{(-3)^2 - 4 * 9 * -10}}{2 * 9}[/tex]

Evaluate

[tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]

Hence, the solution of x in -6 + 3x - 9x^2 = -16 is [tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]

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The triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.

ΔABC is similar to ΔDEF  only if the ratio of two sides of ΔABC and the corresponding two sides of ΔDEF is equal and the angle included on both sides are congruent.

Suppose the two sides of ΔABC are AB and BC, and that of DEF is DE and EF, then for SAS similarity, we need

and

∠ABC = ∠DEF

In triangles ΔAED and ΔCGF,

AE = CF

AD = CG

∠E = ∠G = 90°

Then the triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.

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Answer:

The percentage of people enjoy New years Eve only = 3%

Step-by-step explanation:

The data indicates, The percentage of people enjoy New years Eve = 28%

The percentage of people enjoy New years Eve and Memorial Day = 12%

The percentage of people enjoy New years Eve and Forth of July = 18%

The percentage of people enjoy Enjoy all the three = 5%

The percentage of people enjoy New years Eve only

= The percentage of people enjoy New years Eve

   - The percentage of people enjoy New years Eve and Memorial Day

   - The percentage of people enjoy New years Eve and Forth of July

   + The percentage of people enjoy Enjoy all the three

= 28% - 12% - 18% + 5%

= 3%

Answer:

[tex]k > 3~~~\text{or}~~ k < -5[/tex]

Step-by-step explanation:

[tex]~~~~~|3k+3| > 12\\\\\implies 3k+3 < -12~~~~~~\text{or}~~~~~~~~~~3k+3 > 12\\\\\implies 3k < -12-3~~~~~~\text{or}~~~~~~~~~~3k > 12-3\\\\\implies 3k < -15~~~~~~~~~~~\text{or}~~~~~~~~~~3k > 9\\\\\implies k < -\dfrac{15}3~~~~~~~~~~~~\text{or}~~~~~~~~~~k > \dfrac 93\\\\\implies k < -5~~~~~~~~~~~~~~\text{or}~~~~~~~~~~k > 3[/tex]

Answer:

f(3) = 6

Step-by-step explanation:

you substitute 3 for x.

So you have 2(3) which is 2 multiplied by 3 which is 6

Answer:

tiookvgvc. jbjvth kivtcth jjvf h. bkbgv

Answer:

The IQR of the given distribution is

Step-by-step explanation:

The given distribution has the five-number

28, 34, 43, 59, 62

Divide these numbers in two equal parts.

(28, 34), 43,( 59, 62)

Now divide each parenthesis in two equal parts.

(28), (34), 43,( 59), (62)

It means first quartile is the average of 28 and 34. Third quartile is the average of 59 and 62.

The interquartile range (IQR) of this distribution is

Therefore the IQR of the given distribution is 29.5.

a) The time taken by the rocket to reach the maximum height is 2.75 seconds.

b) The maximum height of the rocket will be 127 feet.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Given that:-

a) The time taken by the rocket will be calculated as:-

We have a function h(t)=−16t²+88t+6. Now by taking the derivative of the function with respect to time and equating it to zero we will get the maximum time in which the rocket will reach the maximum height.

h(t)  =  -16t² + 88t + 6

h'(t)    =     0

-32t   +   88   =  0

32t      =      88

t     =    88 / 32    =  2.75 seconds

So the maximum time is 2.75 seconds.

b) Maximum height will be calculated as:-

Put the value of maximum time in the function h(t)  =  -16t² + 88t + 6 we will get the maximum height.

h(t)  =  -16t² + 88t + 6

h(2.75) = -16(2.75)² + ( 88 x 2.75 ) + 6

h(2.75) = 127 feet

Therefore the time taken by the rocket to reach the maximum height is 2.75 seconds and the maximum height of the rocket will be 127 feet.

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Answer:

The correct answer is: "Option [D]".

Step-by-step explanation:

Hi student, let me help you out!

....................................................................................................................................

Let's use the acronym PEMDAS. With the help of this little acronym, we will not make mistakes in the Order of Operations!  :)

[tex]\dag\textsf{Acronym \: PEMDAS}[/tex]

P=Parentheses,

E=Exponents,

M=Multiplication,

D=Division,

A=Addition,

S=Subtraction.

Now let's start evaluating our expression, which is [tex]\mathsf{6-(\cfrac{2}{3})^2}[/tex]

According to PEMDAS, the operation that we should perform is "E-Exponents".

Notice that we have a fraction raised to a power. When this happens, we raise both the numerator (2 in this case) and the denominator (3 in this case) to that power, which is 2. After this we obtain  [tex]\mathsf{6-\cfrac{4}{9}}[/tex].

See, we raised both the numerator and the denominator to the power of 2.

Now what we should do is subtract fractions.

Note that 6 and -4/9 have unlike denominators. First, let's write 6 as a fraction: [tex]\mathrm{\cfrac{6}{1}-\cfrac{4}{9}}[/tex]. Now let's multiply the denominator and the numerator of the first fraction times 9: [tex]\mathrm{\cfrac{54}{9}-\cfrac{4}{9}}[/tex].

See, now the fractions have the same denominator. All we should do now is subtract the numerators: [tex]\mathrm{\cfrac{50}{9}}[/tex].

∴, the answer is Option D.

Hope this helped you out, ask in comments if any queries arise.

Best Wishes!

[tex]\star\bigstar\underline{\overline{\overline{\underline{\textsf{Reach \: far. Aim \: high. Dream \: big.}}}}}\bigstar\star[/tex]

[tex]\underline{\rule{300}{5}}[/tex]

Calculate 2/3, to the power of 3, therefore

[tex]\bf{\left(\dfrac{2}{3}\right)^{2}=\dfrac{2\times2}{3\times3}=\dfrac{4}{9} }[/tex]

[tex]\bf{6-\dfrac{4}{9} }[/tex]

Convert 6 to the fraction 54/9.

[tex]\bf{\dfrac{54}{9}-\dfrac{4}{9} }[/tex]

Since 54/9 and 4/9 have the same denominator, join their numerators to subtract them.

[tex]\bf{\dfrac{54-4}{9} \ \ \to \ \ \ Subtract }[/tex]

Subtract 4 from 54 to get 50.

[tex]\bf{\dfrac{50}{9} \ \ \to \ \ \ Answer }[/tex]

Therefore, the correct alternative is "D".

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

32

Step-by-step explanation:

64×1÷2

64is divided by 2 =32

and 32×1=32

Answer:

0.0369

Step-by-step explanation:

normalcdf (1220,1320,900,200) is 0.0369

Answer:

130x+3

Step-by-step explanation:

The area is (10x)*(13x+3). 10x*13x=130x squared. So, it is 130x+3.

Answer: C: 130x2 + 30x

Step-by-step explanation:

Answer:

83

Step-by-step explanation:

41 plus 36 plus 36 is 83 is the answer for me

Answer:

A ≈ 25.1 cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]

  = π × 6² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]

  = 36π × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]

  = 18 × [tex]\frac{4\pi }{9}[/tex]

  = 2 × 4π

  = 8π

  ≈ 25.1 cm² ( to the nearest tenth )

Answer:

Wxndy~~

Answer:

Point A:

(1, 3) ------> (3, -1)

Point B:

(3, 3) ------> (3, -3)

Point C:

(3, 2) ------> (2, -3)

Step-by-step explanation:

To find the coordinates of a 90° clockwise rotation, use the following:

[tex](x, y)[/tex] -----> [tex](y, -x)[/tex]

This means you will switch the x and y coordinates of the point and then take the opposite of the x coordinate (if it is positive make it negative and if it is negative make it positive).

Point A:

(1, 3) ------> (3, -1)

Point B:

(3, 3) ------> (3, -3)

Point C:

(3, 2) ------> (2, -3)

Answer:

4/27 ezzzzzzzzzzzzzzzzzzzz

Answer: Choice A

Domain = all real numbers

Range = real numbers greater than or equal to -4

=====================================================

Explanation:

The domain is the set of allowed x inputs of a function.

We can replace x with any number we want to get some output for y = f(x)

This tells us the domain is the set of all real numbers.

-----------

The range is the set of numbers y such that [tex]y \ge -4[/tex]

In other words, we can have y = -4 or y > -4

This is because y = -4 is the lowest output possible, as indicated by the vertex point.

Answer:

b

Step-by-step explanation:

The equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = (5x)³.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Here, Horizontal shift (also called phase shift):

Left shift by c units: y = f(x + c)

Right shift by c units: y = f(x - c)

For this case, we're specified that:

Original function: y = x³

Transformation: horizontal stretch by a factor of 1/5

Assuming the horizontal axis is having input variable x, and vertical axis having output variable y = x³, and the fact that a function y = f(x) if is horizontally stretched by a factor k, becomes y = f(x/k) , we have:

          y = f(x)

          y = x³

           y = f (5x)

           y = (5x)³

Thus, The equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = (5x)³.

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Answer: It's D

Step-by-step explanation:

y = [-1/5x]^3 on edge

The number of chickens and sheeps on the Old MacDonals farm is 39 and 16 respectively.

let

x + y = 55

2x + 4y = 142

Multiply (1) by 2

2x + 2y = 110

2x + 4y = 142

4y - 2y = 142 - 110

2y = 32

y = 32/2

y = 16

substitute y = 16 into (1)

x + y = 55

x + 16 = 55

x = 55 - 16

x = 39

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Answer:

40%

Step-by-step explanation:

your answer is *dun dun dun*

30 + 40% = 42

I need some more text apparently so that drumroll at the top and this will hopefully suffice

The original volume of the gas would be 4.00 liters

Boyle's law is a gas law that states that the pressure of a gas is inversely proportional to it's volume with temperature kept constant.

It is represented thus;

P1V1 = P2V2

Where P1 = Original pressure = 6 atmospheres

V1 = Original volume =?

P2 = Final pressure =4 atmospheres

V2 = Final volume= 6 liters

Make the original volume V1, subject of formula

V1 = P2× V2 ÷ P1

V1 = 4× 6 ÷ 6 = 24 ÷ 6 = 4. 00 liters

Hence, the original volume of the gas is 4.00 liters

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