A driver can deliver his newspapers in 80 minutes. His friend can take care of the same route in 2 hours. How long would it take them to do the job together? ​

[tex]\rule{200}4[/tex]

Answer : The required ratio is (14m-6):(8m+23) .

[tex]\rule{200}4[/tex]

Here we are given that the ratio of sum of first n terms of two AP's is (7n + 1):(4n + 27) .

That is.

[tex]\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{7n +1}{4n +27} \\[/tex]

As , we know that the sum of n terms of an AP is given by ,

[tex]\small\sf\longrightarrow \pink{ S_n =\dfrac{n}{2}[2a +(n-1)d]} \\[/tex]

Assume that ,

Using this we have ,

[tex]\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{\dfrac{n}{2}[2a + (n-1)d]}{\dfrac{n}{2}[2a' +(n-1)d'] } \\[/tex]

[tex]\small\sf\longrightarrow \dfrac{7n+1}{4n+27}=\dfrac{2a + (n -1)d}{2a' + (n -1)d' } . . . . . (i) \\[/tex]

Now also we know that the nth term of an AP is given by ,

[tex]\longrightarrow\sf\small \pink{ T_n = a + (n-1)d}\\[/tex]

Therefore,

[tex]\longrightarrow\sf\small \dfrac{T_{m_1}}{T_{m_2}}= \dfrac{ a + (n-1)d }{a'+(n-1)d'}. . . . . (ii)\\[/tex]

[tex]\longrightarrow\sf\small \dfrac{T_1}{T_2}=\dfrac{2a + (2n-2)d}{2a'+(2n-2)d'} . . . . . (iii)\\[/tex]

From equation (i) and (iii) ,

[tex]\longrightarrow\sf\small n-1 = 2m-2\\[/tex]

[tex]\longrightarrow\sf\small n = 2m -2+1 \\[/tex]

[tex]\longrightarrow\sf\small n = 2m -1 \\[/tex]

Substitute this value in equation (i) ,

[tex]\longrightarrow \sf\small \dfrac{2a+ (2m-1-1)d}{2a' +(2m-1-1)d'}=\dfrac{7(2m-1)+1}{4(2m-1) +27}\\[/tex]

Simplify,

[tex]\longrightarrow\sf\small \dfrac{ 2a + (2m-2)d}{2a' +(2m-2)d'}=\dfrac{14m-7+1}{8m-4+27}\\[/tex]

[tex]\longrightarrow\sf\small \dfrac{2[a + (m-1)d]}{2[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\[/tex]

[tex]\longrightarrow\sf\small \dfrac{[a + (m-1)d]}{[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\[/tex]

From equation (ii) ,

[tex]\longrightarrow\sf\small \underline{\underline{\blue{ \dfrac{T_{m_1}}{T_{m_2}}=\dfrac{ 14m-6}{8m+23}}}}\\[/tex]

[tex]\rule{200}4[/tex]

Answer:

102in2

Step-by-step explanation:

The formula for surface area is 2(wl+hl+hw). So plug in the measurements of the prism into the formula to get 102.

Answer:

8

Step-by-step explanation:

→ Find width of first painting

48 ÷ 6 = 8

→ Find length of second painting

64 ÷ 8 = 8

Answer:

1/13

Step-by-step explanation:

Probability of Sarah drawing a letter in her name

= number of letters in her name: S, A, R and H / total number of letters

= 4/26

Probability of drawing an odd number

= odd numbers / total numbers

= 5/10

Combining the above, Probability of her drawing a letter in her name and an odd number = 4/26 * 5/10

= 1/13

Total Alphabetical cards Sarah has ⇢ 26

Total Letters Sarah's name has ⇢ 4

Probability of getting a card with one of the letter in her name ⇢ 4/26

Total numerical Cards Sarah has ⇢ 10

Total odd numbers in those cards⇢5

Probability of getting a card with an odd number⇢ 5/10

probability of her drawing a letter in her name and an odd number⇢ 4/26 x 5/10 = 1/13

Answer:

  800 cm³

Step-by-step explanation:

The volume is the product of the base area and the "height" of the prism. Here, the base can be considered to be a 10 cm × 12 cm rectangle with a 4 cm × 5 cm cutout. Its area will be ...

  A = (10 cm)(12 cm) -(4 cm)(5 cm) = 120 cm² -20 cm² = 100 cm²

The product of this base area and the 8 cm height of the prism is ...

  V = Bh = (100 cm²)(8 cm) = 800 cm³

The volume of the prism is 800 cm³.

Answer: 2nd option: 9-i

Step-by-step explanation:

We can add the numbers and the terms with i separately.

12 - 5i - 3 + 4i = (12 - 3) + (-5i + 4i)

= 9 + (-i)

*Adding a negative is essentially subtracting a positive*

= 9-i

Answer:

The answer is

→ 9

Step-by-step explanation:

[tex]3+5+7-6=9[/tex]

Therefore, 9 is your answer.

Answer:

26

Step-by-step explanation:

[tex]5^{2}[/tex] = 5 · 5 = 25

then add 1

Answer:

26

Step-by-step explanation:

(5 x 5) + 1

25 + 1

26

Have an amazing day!!!

PLEASE RATE AND MARK BRAINLIEST!!!

Answer:

8.94

Step-by-step explanation:

hypotenuse=h

h=4^2+8^2

h=16+64

h=80

h=√80

h=8.94

Answer:

Step-by-step explanation:

[tex]hypotenuse=\sqrt{4^2+8^2} =\sqrt{16+64} =\sqrt{80}\approx 8.94[/tex]

Answer/Step-by-step explanation:

Explain the role of the GCF in factoring a polynomial.

The role of the GCF in factoring a polynomial is the largest monomial that divides evenly into each term. GCF is a factor that is shared by all terms within a polynomial. For instance, if we have a polynomial of the form A*B + A*C, the GCF is A since both terms have A as a factor.

Where is the GCF placed after factoring the GCF?

After factoring out the GCF, it's placed outside the parentheses, in front of the rest of the polynomial. Like the sample we previous use A*B+A*C = A(B+C).

How do you verify factoring is correct?

To Verify factoring is correct distributing the GCF to the polynomial within the parentheses.

~Learn with Lenvy~

Answer:

E = 27.125

Step-by-step explanation:

Hope this helps you.

Answer:

e=56

Step-by-step explanation:

since the denominator is 8, what can you divide by 8 to get something that you can add to 23 and get 30.

30-23=7

56//8=7

Answer:

A.

1. x = -5

2. x = -1

3. x = -2

4. x = 25/9

5. x = 1

B.

1. x ≤ 2

2. - 3≤ x ≤ 6

3. x ≤ 2

4. x ≤ 33/2

5. x ≤ 17/3

Step-by-step explanation:

Brainliest me please I answer it!!

A.

1. 5x + 12=2x-3

2. 3x+6= -2x+1

3. (x/2-4x=7)x2

4. 1.4x - 0.4x=6.2+3.8

5. 5x-10+2x=7x+28-38

B.

1. 2x/2 ≤ 4/2

2. 2x+3 > -3

2x+3< 15

3. 5x-4 >6

4. (2x./3+1/2>x-5)x6

5. 0.8+0.6x ≥4.2

Step-by-step explanation:

yo question doesn't make sense.

Answer:

Step-by-step explanation:

its A :)

Answer= y=2x+6

The slope-intercept form of an equation of a line: y=mx+b

m - slope

b - y-intercept

We have the points (5, -4) and (-1, 8). Substitute:

m= [tex]\frac{8-(-4)}{-1-5}[/tex] =[tex]\frac{12}{-6}[/tex] =-2

Put the value of the slope and the coordinates of the point (5, -4) to the equation of a line,

-4=-2(5)+b

=-10+b

6=b

y=2x+6

Answer:

=5x5x5

Step-by-step explanation:

5x5^2

=5x(5x5)

=5x5x5

Answer:

625

Step-by-step explanation:

5×5 to the power of 2

25 to the power of 2

25×25 = 625

Answer:

Pythagoras's Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides. Actually a 30 , 40 , 50 triangle is just a scaled up 3 , 4 , 5 triangle, which is a well known right angled triangle

Step-by-step explanation:

please mark me as brainlist please

Answer:

[tex]-\frac{27(-\frac{20t}{10}+x)^{n} }{50} +2.56[/tex]

Step-by-step explanation:

Answer:

1: 23

2: 15/3 which reduces to 5

3:  12/4 which reduces to 3

Step-by-step explanation:

used a calculator

Answer:

40%

Step-by-step explanation:

assuming you actually mean 10^5 and 10^6, to find percentages you do

part/total x percent/100

you have (6x10^5/1.5x10^6) x (x/100)

cross multiply, and you have 6x10^7=1.5x10^6x

divide on both sides by 1.5x10^6

x=40

so the answer is 40%

Answer: (1,-2)

Step-by-step explanation:

Answer:

no idea

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

28x^2yz and 16xy^2

GCF of 28 and 16: 4

GCF of x^2yz and xy^2: xy

The GCF is 4xy.

5x^2y^4, 10x^3y^5, and 15xy^2

GCF of 5, 10, and 15: 5

GCF of x^2y^4, x^3y^5, and xy^2: xy^2

The GCF is 5xy^2.

-hope it helps

Hi! Hope you're enjoying your day!

First of all, the G.C.F. stands for

Greatest Common Factor

So we need to find the Greatest Common Factor of the polynomials.

And yea, polynomials have Greatest Common Factors as well.

So, let's find all the Greatest Common Factors. :)

First, we have

[tex]\bold{28x^2yz}[/tex] and [tex]\bold{16xy^2}[/tex]

What are the common factors of these polynomials?

Well, there are plenty of them, like 2, 2x, y...

What is the Greatest Common factor?

Is it Option A, 12xy?

No, because neither 28 nor 16 is divisible by 12.

So we cross out Option A.

Is it Option B, 8xy?

No, because 28 isn't divisible by 8, and remember, if a number is evenly divisible by another number, then that number is a factor.

Example: 8 is a factor of 16 (16÷8=2); 8 is not a factor of 28, because

28÷8=3.5 (a decimal, not a whole number)

Is it Option C, 4xy?

Yeah, it seems like Option C is the right option.

[tex]\huge\checkmark[/tex]Both 28 and 16 are divisible by 4

[tex]\huge\checkmark[/tex]Both polynomials have an x and a y in them

[tex]\rule{250}{2}[/tex]

Find the GCF:

[tex]\bold{5x^2y^4,\:10x^3y^5, \:and\:15xy^2}[/tex]

Once again, is it Option A, 5x^3y^5?

No, because

✘ 5 and 10 aren't divisible by 3

✘ None of the 3 polynomials has a 3y term

In other words, Option A is wrong.

How about Option B?

You should see right off the bat that 5 and 15 aren't divisible by 10.

So now we have 2 options left.

Is it Option C, 5xy²?

Well,

✓All 3 polynomials are divisible by 5

✓ All 3 polynomials have a y² term

✓ All 3 polynomials have an x term.

Hence, the answers are

[tex]\boxed{\boxed{\bold{1. \;Option\;C; 2.\;Option\;C.}}}[/tex]

Hope everything is clear.

If you have any questions, please comment.

#LearningIsFun

[tex]\rule{200}{2}[/tex]

Answer:

1/3

Step-by-step explanation:

The slope of a line represents the variation in height per variation in length.

In our case, for every square you move up, you have to move 3 horizontally. The slope is thus

m= (vertical change) / (horizontal change) = 1/3

Answer:

1/3

Step-by-step explanation:

Answer:

The quadratic function, f(x) has the greater value.

Step-by-step explanation:

The given function written to us is in standard form, meaning it is easy to graph this function.

Since this function is going to open down-ward, we start with negative numbers.

[tex]f(-1)=3\\[/tex]

Since 3 is a greater value than 2, which we can see is the maximum value of g(x) by viewing the graph, f(x) is greater.

Answer:

C

Step-by-step explanation:

100-31.99-19.89=48.12

Answer:

Sis 97,U is 30,Tis19,R is 21and m is 37

Answer :

3/4.

Explanation

Find the GCD (or HCF) of numerator and denominator

GCD of 45 and 60 is 15

Divide both the numerator and denominator by the GCD

45 ÷ 15

60 ÷ 15

Reduced fraction: 3/4

Therefore, 45/60 simplified to lowest terms is 3/4.

Hi! I hope you are enjoying your day!

In order to simplify this ratio (and 45:60 is a ratio), we should divide both sides of the ratio by 5 (because both 45 and 60 are evenly divisible by 5)

Divide:

9:12

Is the ratio in its simplest form? No.

Why?

Because 9 and 12 can be divided by 3:

3:4

Now the ratio IS in its simplest form.

Hence, the answer is

[tex]\boxed{\boxed{\bold{3:4}}}[/tex]

Hope everything is clear.

If you have any questions, please comment.

#LearningIsFun

Answer:

x should be eliminated

hope it helps