Find the least length of a rope which can be cut into whole number of pieces of lengths 45cm, 75cm and 81 cm

Given:

Mark started reading on Saturday , and he is reading 40 pages per day.

Allen didn't start until Sunday , but he is still reading 45 pages a day.

To find:

How many days will it take Allen to catch up to Mark, and how many pages will they each have read?

Solution:

Let [tex]x[/tex] represent the number of days Allen has been reading. Then the number of days Mark has been reading is [tex](x+1)[/tex].

Mark is reading 40 pages per day. So, he will read [tex]40(x+1)[/tex] pages.

Allen is reading 45 pages a day. So, he will read [tex]45x[/tex] pages.

Allen catch up to Mark when they read equal number of pages.

[tex]40(x+1)=45x[/tex]

[tex]40x+40=45x[/tex]

[tex]40=45x-40x[/tex]

[tex]40=5x[/tex]

Divide both sides by 5.

[tex]\dfrac{40}{5}=\dfrac{5x}{5}[/tex]

[tex]8=x[/tex]

In 8 days Allen will catch up to Mark.

[tex]45x=45(8)[/tex]

[tex]45x=360[/tex]

Therefore, they each have read 360 pages.

Answer:

uh the 2nd one

Step-by-step explanation:

cause im smart

Answer:

Step-by-step explanation:

For this, we kind of have to test points to solve it. First, we can test theh interval x<= -2. Plug in  -2 and we get a negative value which works. Next, let's try -2<x<0. Plug in -1 and get a positive value which doesn't work.

Next try 0<=x<=7. Plug in any number like 4 and get a negative value which works.

Finally, try x>7. Plug in 8 for example and you would get a positive value. So the solution is

x <= -2 OR 0 <= x <= 7

Hello,

Step-by-step explanation:

[tex]f(x)=6x^2+2x-7\\g(x)=4x-3\\(f+g)(x)=f(x)+g(x)=6x^2+2x-7+4x-3=6x^2+6x-10\\\\(f-g)(x)=f(x)-g(x)=6x^2+2x-7-(4x-3)=6x^2-2x-4\\[/tex]

Answer:

15

Step-by-step explanation:

32-19 = 13 that have both

70-57= 13 that have both again from that sample

total number of people that have both : 13 + 13 = 26

11 kids don't have either one, so :

26-11 = 15

Let k be Kaden's current age and s Sally's current age.

Right now, Kaden is 18 years older than Sally, so

k = s + 18

In 5 years, Kaden will be 3 times older than Sally, so that

k + 5 = 3 (s + 5)

Substitute the first equation into the second one to solve for s :

(s + 18) + 5 = 3 (s + 5)

s + 18 + 5 = 3s + 15

s + 23 = 3s + 15

3s - s = 23 - 15

2s = 8

s = 4

Answer:

100%_$40.80

? × _$38.76

Step-by-step explanation:

100%×$38.76÷$40.80=95%

Answer:

40.80

Step-by-step explanation:

Answer:

Total time taken by train = 8 hour 32 minutes

Step-by-step explanation:

Given:

Time train leave Zurich = 22:40 min

Time train arrives in Vienna = 07:32

Find:

Total time taken by train

Computation:

Total time taken by train = [23:60 - 22:40] + 7:32

Total time taken by train = 1:20 + 7:32

Total time taken by train = 8:52

Total time taken by train = 8 hour 32 minutes

Answer:

20% of 10% of 1000 = 20

Step-by-step explanation:

Now we have to,

→ find the 20% of 10% of 1000.

Let's find 10% of 1000,

→ (10/100) × 1000

→ 0.1 × 1000

→ 100

Then 20% of 10% of 1000 is,

→ (20/100) × 100

→ 0.2 × 100

→ 20

Hence, the answer is 20.

Answer:

158.5

Step-by-step explanation:

= 52 - 6 × 1 + 75 × 3 / 2

= 52 - 6 + 75 × 3 ÷ 2

= 52 - 6 + 112.5

= 46 + 112.5

= 158.5

Answer:

The solution is 158,5

Step-by-step explanation:

52-6×1+75×3÷2

= 52-6+75×3÷2

= 46+225÷2

= 46+112,5

= 46+112,5

= 158,5

Answer:

Step-by-step explanation:

The function [tex]f(x)=x^2+4[/tex] is a positive upwards opening parabola with the vertex at (0, 4), whereas

the function [tex]g(y)=y^2+4[/tex] is a positive rightwards opening parabola (sideways parabola) with the vertex at (4, 0). This means that answer to this is that g(y) is reflected over the x axis whereas f(x) is reflected over the y axis.

Answer:

190%

Step-by-step explanation:

$1.56 is close to nearly 2x the value of $0.87

You can start by multiplying $0.87 by 2 to get $1.74

Now put $1.56 / $1.74

This gets you 0.89655172

By rounding this, you can get to 0.90

Move the decimal places two spots over to get a percentage = 90%

Since the eggs didn't decrease in value, you can add the 100% from the beginning of the problem.

100+90=190%

Answer:

Let the inverse of f(x) be h(x):

[tex]{ \tt{h(x) = \frac{1}{4x} }}[/tex]

Answer:

9/10 or 90 %

Step-by-step explanation:

There are 54+27+5+4 total people = 90

The people with diploma is 54+27 = 81

P (diploma) = number with diploma / total

                  = 81/90

                  =9/10

                   90%

Answer:

x = 6 x 7 = 42

Step-by-step explanation:

hope this helps

Answer:

[tex] \frac{x}{6} = 7 \\ x = 6 \times 7 \\ x = 42[/tex]

Answer:

3/5

Step-by-step explanation:

cos A = adjacent side / hypotenuse in a right triangle

cos A = 24/40

Cos A = 6/10

cos A = 3/5

Given:

The expression is:

[tex]\left(\dfrac{1}{7}-4\sqrt{3}\right)^3+\left(\dfrac{1}{7}+4\sqrt{3}\right)^3 [/tex]

To find:

The simplified form of the given expression.

Solution:

Formulae used:

[tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex]

[tex](a-b)^3=a^3+3a^2b+3ab^2+b^3[/tex]

Adding this formulae, we get

[tex](a-b)^3+(a+b)^3=2a^3+6ab^2[/tex]            ...(i)

We have,

[tex]\left(\dfrac{1}{7}-4\sqrt{3}\right)^3+\left(\dfrac{1}{7}+4\sqrt{3}\right)^3 [/tex]

Using formula (i), the given expression can be written as:

[tex]=2\left(\dfrac{1}{7}\right)^3+6\left(\dfrac{1}{7}\right)\left(4\sqrt{3}\right)^2[/tex]

[tex]=2\times \dfrac{1}{343}+6\left(\dfrac{1}{7}\right)48[/tex]

[tex]=\dfrac{2}{343}+\dfrac{288}{7}[/tex]

[tex]=\dfrac{2+14112}{343}[/tex]

[tex]=\dfrac{14114}{343}[/tex]

Therefore, the simplified form of the given expression is [tex]\dfrac{14114}{343}[/tex].

Given:

The expression is:

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]

To find:

The correct form of the partial fraction decomposition for the given expression.

Solution:

We have,

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]

By partial fraction decomposition, it can be written as:

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{A}{x+1}+\dfrac{B}{(x+1)^2}+\dfrac{Cx+D}{x^2+7}[/tex]           ...(i)

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B}{(x+1)^2(x^2+7)}[/tex]

[tex]4x^3+3x^2=(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B[/tex]

[tex]4x^3+3x^2=x^3A+x^3C+x^2A+x^2B+2x^2C+x^2D+7xA+xC+2xD+7A+7B+D[/tex]

[tex]4x^3+3x^2=x^3(A+C)+x^2(A+B+2C+D)+x(7A+C+2D)+7A+7B+D[/tex]

On comparing both sides, we get

[tex]A+C=4[/tex]

[tex]A+B+2C+D=3[/tex]

[tex]7A+C+2D=0[/tex]

[tex]7A+7B+D=0[/tex]

On solving these equations, we get

[tex]A=\dfrac{23}{32},B=-\dfrac{1}{8},C=\dfrac{105}{32},D=-\dfrac{133}{32}[/tex]

Substituting these values in (i), we get

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]

Therefore, the required partial fraction decomposition is:

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]

Answer:

A on Edg

Step-by-step explanation:

got it right

Answer:

It drove 30.08 kilometers in an hour.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

In this question:

177 kilometers in 5*60 + 53 = 353 minutes.

How many kilometers in 1 hour = 60 minutes?

177 km - 353 min

x km - 60 min

[tex]353x = 60*177[/tex]

[tex]x = \frac{60*177}{353}[/tex]

[tex]x = 30.08[/tex]

It drove 30.08 kilometers in an hour.

Answer:

Second option

Step-by-step explanation:

Let's assume that x is 1 and y is 3

a) [tex]\frac{1}{2}[/tex] < [tex]\frac{3}{2}[/tex] = true

b) -1 < -3 = false

c) 1+2 < 3+2 = true

d) 2 x 1 < 2 x 3 = true

Answer:

8 apples

Step-by-step explanation:

costof 8 apples=48

cost of 4 peaches=12

Answer:

Answer A: g(x) = (x + 4)² - 3(x + 4) - 2

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units left

f(x - n) - shift the graph n units right

f(x) = x² - 3x - 2.

shift 4 units left, f(x + 4) = (x + 4)² - 3(x + 4) - 2

Answer A: g(x) = (x + 4)² - 3(x + 4) - 2

Answer:

[tex]3uq \\ 3 \times 2 \times 6 \\ = 36[/tex]

Answer:

[tex]36[/tex]

Step-by-step explanation:

[tex]3uq \\ = 3(2)(6) \\ = 36[/tex]

Answer:

Option (A)

Step-by-step explanation:

From the picture attached,

ΔABC and ΔDEF are the similar triangles.

Therefore, by the property of similar triangles, their corresponding sides will be proportional.

[tex]\frac{AB}{DE}= \frac{BC}{EF}= \frac{AC}{DF}[/tex]

[tex]\frac{5.75}{18}=\frac{BC}{12}[/tex]

BC = [tex]\frac{12\times 5.75}{18}[/tex]

BC = 3.83 ft

Option (A) will be the correct option.

Draw a plane, showing the three (non-linear) points that define it.[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

See this attachment

Answer:

3293/72

Step-by-step explanation:

change to improper fraction to times.

Answer:

70 x 47x = 3290

.

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

Answer: 6x^3-35x^2+47x-12

Step-by-step explanation:

(2x-3)(x-4)(3x-1)

=(2x^2-11x+12)(3x-1)

=6x^3-35x^2+47x-12