TEXT ANSWER
Jason provided the following work when asked to convert 0.105 to its simplest fraction
form.
1. Why did Jason get the problem wrong?
2. Provide the work for properly writing the decimal in its simplest fraction form.
Jason's Work:
0.105=
105
21
1000 200

1.

The slope intercept form is y=mx+b

4x-3y=2

subtract 4x from both sides

3y=2+(-4x)

Divide by 3

y=2/3+(-4x/3)

simplify:

y=2/3-4x/3

reorder:

y=-4/3x+2/3

slope= -4/3, y intercept= 2/3

2.

In the same way,

3x+2y=-3

2y=-3-3x

y=-3/2 - 3x/2

y+3/2=-3x/2

y=-3x/2-3/2

y=-3/2x-3/2

slope=-3/2, y intercept= -3/2

I hope this helped you.

In the word problem, if mike has 40 coins consisting of dimes and quarters and if the dimes were quarters and the quarters dimes, he would have 90 cents more, he has 17 quarters.

A word problem refers to a mathematical exercise where significant information on the problem is given in ordinary language and not mathematical notation.  Let x be the number of dimes (10 cents) and y be the number of quarters (25 cents). Hence, the total number of coins is:

x + y = 40

The amount of the total coins would be 0.1x + 0.25y.

If the dimes were quarters and quarters were dimes, he would have 90 cents more than the amount he has now.

Hence,

0.25x + 0.10y = 0.1x + 0.25y + 0.9

Solving,

0.25x – 0.1x = 0.25y – 0.1y +0.9

0.15x = 0.15y + 0.9

As x + y = 40, x = 40 – y

Substituting,

0.15 (40 – y) = 0.15y + 0.9

6 - 0.15 y = 0.15y + 0.9

0.15y + 0.15y = 6 – 0.9

0.3y = 5.1

y = 5.1/0.3 = 17

Hence, the number of quarters are 17.

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Answer:

Bag a, by 85 grams!

Step-by-step explanation:

1) Work out the weight of bag a

1 banana is 140 grams so to find out 8 you have to multiply them

140 x 8 = 1120

Bag a = 1120 grams

2) Work out the weight of bag b

1 pineapple weight 345 grams so to find out 3 you have to multiply them just like above

345 x 3 = 1035

Bag b = 1035

3) Find the difference

Bag a is 1120 grams and bag b is 1035

To find out out by how much you just have to subtract them

1120 - 1035 = 85

Hope this helps, have a great day!

Answer: Width = 7 inches, Length = 14 inches

Step-by-step explanation:

Let the width be [tex]w[/tex]. Then, the length is [tex]2w[/tex].

Using the formula for the perimeter of a rectangle,

[tex]2(w+2w)=42\\\\w+2w=21\\\\3w=21\\\\w=7\\\\\implies 2w=14[/tex]

2x^2+6x

2(-5)^2+6(-5)

2(25)+6(-5)

50+6(-5)

50+(-30)

50-30

20

The total change in yards where the team started is 36 yards

The given parameters in the question are:

Yards per play = 4 yards

Number of plays = 9 consecutive plays

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = 4 * 9

Evaluate

Total change = 36

Hence, the total change is 36 yards

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Increase in volume is 802424.77 cubic mm/s when the diameter is 80 mm.

Let the radius of the sphere be R.

So, the volume of the sphere is given by,

V = [tex]\frac{4}{3}\pi r^3[/tex]

Differentiating the above relation with respect to time 't' we get,

dV/dt = 4[tex]\pi r^2[/tex]. dr/dt

Given that, the change of radius (dr/dt) = 4 mm/s

When the diameter is 80 mm, then the radius = 80/2 = 40 mm

So the volume change when the diameter is 80 mm is given by,

dV/dt [tex]=4\pi\times40^2\times4\approx 802424.77[/tex] cubic mm/s

Hence the volume increase in 802424.77 cubic mm/s.

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Answer:

  see the attachment

Step-by-step explanation:

You want a graph of the given figure reflected over the line y = 1/3x +1.

The given line of reflection can be written in general form as ...

  y = 1/3x +1

  3y = x +3 . . . . . . multiply by 3

  x -3y +3 = 0 . . . . subtract 3y

This is in the general form ...

  ax +by +c = 0

where a=1, b=-3, c=3.

The line of reflection is the perpendicular bisector of the segment joining a point (x, y) with its reflection (x', y').

Using the formula in the second attachment, we find the reflection

  (x1, y1) ⇒ (x, y)

satisfies ...

  (x -x1)/a = (y -y1)/b = -2(ax1 +by1 +c)/(a² +b²)

or ...

  x = -2a/(a²+b²)·(ax1 +by1 +c) +x1

  y = -2b/(a²+b²)·(ax1 +by1 +c) +y1

Using the known values for a, b, c, we have ...

  x = -2(1)/(1² +(-3)²)·(x1 -3y1 +3) +x1 = (1/5)(4x1 +3y1  -3)

  y = -2(-3)/10·(x1 -3y1 +3) +y1 = (1/5)(3x1 -4y1 +9)

Rewriting the mapping in more conventional terms, we have ...

  (x, y) ⇒ ((4x +3y -3)/5, (3x -4y +9)/5)

It is convenient to let a spreadsheet do the repetitive tedious math. The third attachment shows the application of this mapping to the coordinates of the figure's vertices (clockwise from bottom).

__

Additional comment

The figure showing the reflected polygon was created by a geometry program using its "reflect over a line" feature.

The measurements of the rectangle are 10 cm and 5cm.

What is rectangle?

A rectangle could be a quadrilateral with four right angles in geometer geometry. It may be outlined as an angulate quadrilateral as a result of all of its angles square measure equal; or a quadrangle with a right angle.

Main Body:

Let the width be x.

According to question :

width is 5 more than 1 times the length(l), so

length (l) = width -5

Area if rectangle = 50 cm²

Formula for area of rectangle = length * width

⇒50 = x*(x-5)

⇒50 = x² - 5x

⇒x² - 5x - 50 =0

splitting the middle term

⇒x²- 10x +5x -50 = 0

⇒x(x-10) +5(x-10)

⇒(x-10)(x+5)

Hence the value for x = 10 or -5 .

but length can never be -ve so x= 10.

Width = 10 cm

length = width -5

length = 10 -5

l = 5cm

Hence Measurements of rectangle are 10cm and 5cm.

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Answer:

6 cm

Step-by-step explanation:

The circular mirror Dominic should buy is the mirror with a side length of

8 cm.

Option A is the correct answer.

A Square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side².

We have,

Old mirror.

Side = 9 cm

Area = 9 x 9 = 81 cm²

New mirror.

Side = 8 cm

Area = 64 cm²

Side = 7 cm

Area = 7 x 7 = 49 cm²

Side = 6 cm

Area = 6 x 6 = 36 cm²

64 cm² is closer to 81 cm².

Thus,

A circular mirror with a side length of 8 cm should be bought.

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The length of the line segment with points (-5, 5) (3, -1) is 10 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-5, 5) and (3, -1) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-5 - 3)² + (5 - -1)²}

d =√{64 + 36}

d = √100

d = 10 units

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The relationship between the perimeter and the side length of the hexagons is proportional.

A proportional relationship is one that illustrates the constant between the data that are given.

In this case, when the side length is 2, the perimeter is 12. The constant is:

= Perimeter / Length

= 12 / 2

= 6

Also, when the length is 3, the perimeter is 18. The constant will be:

= 18 / 3

= 6

Since they have 6 as constant, it's a proportional relationship.

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Answer:

x_6x=21_15_3x/. x+6x=21+15+3x

Step-by-step explanation:

The geometric system has a length of f = 4 cm and a length of g = 6 cm.

Herein we find a geometric system formed by two rectangles, the rectangle ABCD has an area of 60 square centimeters and the rectangle APQD has an area of 24 square centimeters. The area of a rectangle is equal to the product of the lengths of its base (b) and its height (h), both in centimeters.

First, describe the area formulas for the rectangles ABCD and APQD, both in square centimeters:

Rectangle ABCD

(g + 9) · f = 60        (1)

Rectangle  APQD

g · f = 24                 (2)

Where:

Second, use distributive property in (1):

By (1):

g · f + 9 · f = 60

Third, use substitution by (2) on (1) and determine the value of f:

(2) in (1):

24 + 9 · f = 60

9 · f = 36

f = 4

Fourth, determine the value of g:

By (2):

g = 24 / f

g = 24 / 4

g = 6

The lengths of f and g are 4 and 6 centimeters, respectively.

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Answer:

1256.64

Step-by-step explanation:

The equation of the line that passes through the points  (9,2) and (3,4) is x + 3y = 15  and the graph  is shown below .

In the question ,

it is given that

the required line passes through the points (9,2) and (3,4)

in order to find the equation of  line we first need to find slope .

so , the slope(m) will be

m = (4-2)/(3-9)

m = 2/(-6)

m = -1/3

The equation of the line passing through the point (3,4) having slope -1/3 is

y - 4 = (-1/3)(x - 3)

3(y - 4) = -1(x - 3)

3y - 12 = -x + 3

x + 3y = 12 + 3

x + 3y = 15

the graph of the line is drawn below .

Therefore ,The equation of the line that passes through the points  (9,2) and (3,4) is x + 3y = 15  .

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The speed of the wind is 50 mile per hour  .

In the question ,

it is given that

the speed of the plane is [tex]=[/tex] 200 miles per hour .

let the speed of the wind is = "w"

So ,the speed of the plane with wind is [tex]=[/tex] 200 + w

and the speed of the plane against  wind is [tex]=[/tex] 200 - w

we know that , distance [tex]=[/tex] speed × time

the plane flew "500 miles" with wind ,

which means ,

500 [tex]=[/tex] (200 + w) × t      .....(1)

and the plane flew 300 miles against the wind ,

which means ,

300 [tex]=[/tex] (200 - w) × t       ......(2)

adding both the equations ,

we get

800 [tex]=[/tex] t ( 200 [tex]+[/tex] w [tex]+[/tex] 200 - w)

800 = t × 400

t = 2

Substituting  , t = 2 in 500 [tex]=[/tex] (200 + w) × t      

we get

500 = (200 + w) × 2

500/2 = 200 + w

250 = 200 + w

w = 250 - 200

w = 50

Therefore , The speed of the wind is 50 mile per hour  .

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The set of ordered pairs that is a function is (d) (0, 0), (1, 1), (4, 2), (9, 3)

The list of options represents the given parameter

As a general rule, for an ordered pair to be a function;

The y values on the ordered pair must point to different x values

In (a) the y values 4, 5, 6 and 7 have the same x value of 3

So, it is not a function

In (b) the y values 5 and 8 have the same x value of 2

So, it is not a function

In (c) the y values -1 and 1 have the same x value of 1

So, it is not a function

In (d) all the y values have different x values

So, it is a function

Hence, the ordered pair that is a function is  (d)

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There was 110%  percent increase in the number of visitors.

Percent:

Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.

Given,

p x 3,700=4,070

There was a % percent increase in the number of visitors.

Here we need to find the increase in the percentage.

While we looking into the given question we have identified that,

The Old population = 3700

And the new population  = 4070

So, the value of P is calculated as,

=> p = 4070/3700

=> p = 1.1

When we convert this into percent then we get 110% as increase.

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Answer:

I believe the unit price would be $2.97

Step-by-step explanation:

Hope this helps! :))
Please let me know if its incorrect.

Answer:

[tex]f(x)=-|2x|[/tex]

Step-by-step explanation:

First, find the slope of the right side of the graph. It is -2. But because an absolute value always makes the value inside positive, we put the negative sign outside the absolute value.

The rule of thumb for absolute value graphs is: if it opens upwards, the absolute value is positive; if it opens downwards, the absolute value is negative.

So, the equation we can construct from this information is:

[tex]f(x)=-|2x|[/tex]

Step-by-step explanation:

-(10x + 2) > 5x - 1 - 8x

combine x terms on right side:

-(10x + 2) > -3x - 1

remove ()'s from left side:

-10x - 2 > -3x - 1

add 10x to both sides:

-10x - 2 + 10x > -3x - 1 + 10x

-2 > 7x - 1

add 1 to both sides:

-2 + 1 > 7x - 1 + 1

-1 > 7x

divide both sides by 7:

-1/7 > 7x /7

-1/7 > x or x < -1/7

in interval notation: (-∞, -1/7)

Answer

12

Step-by-step explanation:

click on square root

click on 144

then your answer will pop out below your equation

maximum height = 32ft

Given function  h(t) = -16t^2+40t+7

known data:

[tex]h{0}[/tex] = 7 ft

[tex]v_{0}[/tex] = 40 ft/s

we equate the first derivation to zero

and solve for time.

h(t) = -16t^2 + 40t+7

[tex]\frac{dh}{dt} (t)[/tex] = -32t+40 = 0

t = [tex]\frac{40}{32}[/tex] = 1.25s

second derivative and evaluate:

[tex]\frac{d^{2}h}{dt^{2}}[/tex] [tex]\frac{}{}(t)[/tex] = -32

the maximum height of the rocket with the respect to

the ground can be obtained by evaluating the function

h(1.25) = - 16[tex](1.25)^{2}[/tex]+40(1.25)+7 = 32 ft

therefore the rocket reaches maximum height at  h = 32ft.

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We have : (a+b)^2 = a^2 + 2ab + b^2.

So, we can see here : the first term (3x) is a, the second term (a) is b.

For it to be expanded as such, the second term in the bracket must be equal to a^2 when it is squared.

Therefore, the missing term is a.

Recheck : (3x + a)^2 = (3x)^2 + 2.3x.a + a^2 = 9x^2 + 6ax + a^2.

The equation is,

→ 3y - 7(y + 5) = y - 35

Now the value of y will be,

→ 3y - 7(y + 5) = y - 35

→ 3y - 7y - 35 = y - 35

→ -4y - y = -35 + 35

→ -5y = 0

→ y = 0/-5

→ [ y = 0 ]

Hence, option (a) is correct.

When the number of people is multiplied by 4, the number of pizzas is multiplied by 4.

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a proportional relationship can be modeled by the following mathematical expression:

y = kx

Where:

If the x-value is multiplied by 4, we have:

x = 5 × 4

x = 20

From the corresponding y-value for 20 is equal to 8 and as such the number of pizzas needed should be multiplied by 4, in order to produce an equivalent ratio.

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