OperumONS UNTUI a) Find the greatest number that divides 36, 45 and 63 without leaving a remainder. b) c) Find the greatest number by which 90, 120 and 150 are exactly divisible. Three drums contain 501, 60 l and 70 l of oil. Find the greatest capacity of a bucket which can empty out each drum with the exact number of fillings. Three bags contain 80 kg of wheat flour, 120 kg of corn flour and 160 kg of rice. What is the greatest number of people to whom these items can be distributed equally? What is the share of each item among them? d) e) Find the greatest number of children to whom 48 oranges, 80 bananas and 144 apples can be divided equally. Also find the shares of each fruit among them. 22 There are 120 mangoes in a basket and 168 mangoes in another basket. Find the greatest number of mangoes which are to be taken out at a time from each basket so that both of them will be emptied simultaneously. A rectangular floor is 12 m long and 10 m broad. If it is to be paved with squared marbles of the same size, find the greatest length of each squared marble.​

Answer:

2 i think it is

Step-by-step explanation:

Answer:

5438.5

Step-by-step explanation:

To complete this equation, we must use the order of operations also known as PEMDAS.

For the case of this problem, we start by multiplying or dividing numbers before adding or subtracting numbers.

First let's start on the left:

100 x 54 + 77 ÷ 2

5,400 + 77 ÷ 2

5,400 + 38.5

5438.5

I hope this helps! Just remember to always add or subtract number last and start on the left, so that you don't get confused.

Answer:

So 2,738.5

Step-by-step explanation:

100×54 equals

— 5,400

5,400+77 equals

—5,477

5,477÷2 equals

—2,738.5

The answer is 2,738,5

Answer:

78

Step-by-step explanation:

Answer:

A. 5,425.92 m3

Step-by-step explanation:

Radius = 24m

Length = 12m

Volume = Area * Length

Area = π * (radius ^2)

Radius = Diameter / 2

Radius = 24m / 2 = 12m

Area = π * (12m^2)

Area = 3.14 * 144  = 452.16m

Volume = 452.16m * 12m

Volume = 5425.92m3

Answer:

z=4x

=14y10

Step-by-step explanation:

this is the answer

Answer:

5x^2+3x^2+(3x+1)^2+(2x-4)^2

Answer:

Step-by-step explanation:

6-digit palindrome is the number n the form of:

This is divisible by 11 by default as the sum of the digits in odd placed is same as sum of the number in even places (remember the divisibility rule by 11):

Now, in order to be divisible by 99, the number must be divisible by 11 and 9.

According to divisibility rule by 9 the sum of all digits must be divisible by 9. You can see In our case we need to have (the minimum):

The smallest number we could get is when x is minimum, y is minimum, so:

The number we get is:

Proof:

Hello,

Let's assume n the palindrome

[tex]n=\overline{abccba}\\\\Since\ 99=9*11:\\\\the \ smallest\ \Longrightarrow \ a=1\\\\a+b+c+c+b+a=9*k\ ,\ k\in \mathbb{N}\\2*(a+b+c)=9*k\ \Longrightarrow \ k\in 2\mathbb{N} , \ : k=2\\\\1+b+c=9 \Longrightarrow \ b=0\ and\ c=8\\\\n=108801\\\\Proof:\\108801=9*12089 =11*9891\\Nota\ bene:(a+c+b)-(b+c+a)=11*p \Longrightarrow \ 0=11*p \Longrightarrow \ p=0[/tex]

Answer:

The finishing point 4

Step-by-step explanation:

32/8=4

Given:

The quadratic function is:

[tex]f(x)=x^2+3x-4[/tex]

To find:

The zeros of the given quadratic function.

Solution:

We have,

[tex]f(x)=x^2+3x-4[/tex]

Splitting the middle term, we get

[tex]f(x)=x^2+4x-x-4[/tex]

[tex]f(x)=x(x+4)-1(x+4)[/tex]

[tex]f(x)=(x+4)(x-1)[/tex]

For zeros, [tex]f(x)=0[/tex].

[tex](x+4)(x-1)=0[/tex]

[tex]x=-4,1[/tex]

Therefore, the correct option is (b).

9514 1404 393

Answer:

  B.  log_b(a) - log_b(d)

Step-by-step explanation:

The applicable rule of logarithms is ...

  log(a/b) = log(a) -log(b)

All the logs need to have the same base.

__

Here, the base is 'b', but the rule still applies:

  [tex]\log_b{\dfrac{a}{d}}=\log_b{(a)}-\log_b{(d)}[/tex]

Answer:

∠ ADC = 145°

Step-by-step explanation:

The central angle is equal to the measure of the arc that subtends it, then

∠ ADE = 70°

∠ EDC = 75°

∠ ADC = ∠ ADE + ∠ EDC = 70° + 75° = 145°

Answer:

both lines have the same slope, hence they are parallel to each other

Step-by-step explanation:

The equation of a straight line is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Two lines are said to be parallel to each other if they have the same slope, whereas two lines are perpendicular to each other if the product of their slopes is -1.

Given a line with an equation:

y = (2/3)x - 17

From the equation of the line with can see that the slope of the line is 2/3 and the y intercept is -17.

Also the other line has an equation of 4x - 6y = -6

6y = 4x + 6

y = (2/3)x + 1

Hence this line has a slope of 2/3 and a slope of 1.

Since both lines have the same slope, hence they are parallel to each other

Answer:

m = 0

y intercept = 1

Step-by-step explanation:

The given equation of the line is ,

[tex]\implies y = 1[/tex]

We know that the Standard equation of Slope Intercept Form of the line is,

[tex]\implies y = mx + c[/tex]

Where ,

On comparing to the Standard form of the line we get ,

[tex]\implies Slope = 0 [/tex]

[tex]\implies y - intercept= 1[/tex]

Slope of the line is 0, since y=mx+c, if m = 0, then y = c, where the constant (c)=1

y intercept of the line is y = 1.

Answered by GAUTHMATH

Answer:

1866.10604

Step-by-step explanation:

V=3.14(r sqaured)1/3h

Answer: 118°

Step-by-step explanation:

Answer:

B. - 2a + 18

Step-by-step explanation:

- 4a + 2( a + 9 )

= - 4a + 2a + 18

= - 2a + 18

Answer:

B

Step-by-step explanation:

got it right on edge :))

Answer:

400 miles

Step-by-step explanation:

825 - 425 = 400

Answer:

Step-by-step explanation:

825 - 425= 400 which is what she is going to drive on the second day

Answer:

The answer is B

Answer:

Probability of the chosen T-shirt not being black will be equal to 9/10

Step-by-step explanation:

In order to solve this we need to understand that probaility is equal to the number of those outcomes that we want divided by the total number of outcomes. In our case the total number of outcomes is 20 (2 + 7 + 11) which is the total number of T-shirts, and the number of outcomes that are favorable to us is equal to 18 (outcomes without a black T-shirt). Therefor probability of the chosen T-shirt not being black will be equal to...

18/20 = 9/10

Multiply the rate per quarter hour by quarter hours: 250g. This then gets added to the starting temperature of 2300

The answer would be : A. T = 250g + 2300

Answer:

She could've factored further

Step-by-step explanation:

a^5 can be written as a^4*a

so the answer should've been 3a^3b*sqrt(6ab)

BRAINLIEST PLEASEEEEEEEEEEE

Answer:

She should have factored a^7 as a^6 * a. Then sqrt(a^6 * a) = a^3 * sqrt(a).

[tex] 3a^3b\sqrt{6ab} [/tex]

Step-by-step explanation:

She should have factored a^7 as a^6 * a. Then sqrt(a^6 * a) = a^3 * sqrt(a).

Correct answer:

[tex] 3a^3b\sqrt{6ab} [/tex]

Answer: 16,200 Seconds

Step-by-step explanation:

Data: 4.5 hours(h)=x seconds(s)

Step One, Convert Hours Into Minutes

4.5h=4h and 30 minutes(m)

1h=60mx4=240m+30=270m

Reason: Since to convert to seconds, minutes are needed, you have to convert everything to minutes. And with 60 minutes in an hour you have to multiply 60 by 4 to get 240 and add 30 minutes to it(since it's 4.5 hours) to find ourselves at 270 minutes.

Step two, Convert Minutes Into Seconds

1m=60s

270mx60=16,200s

Reason: Since we are ultimately trying to get 4.5 hours into seconds, we have to convert the minutes we have into seconds by multiplying 270 minutes by 60(since 60 seconds are in a minute) to get our final answer of 16,200 seconds.

I hope this helps!

Answer:

pretty sure it would be 90 degrees

Answer:

1/root(3)

Step-by-step explanation:

the steps are in the pic above.

The value of tan pi/6 is 0.5773502.

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Given that, what is the exact value of tan pi/6,

To find the value of tan π/6 using the unit circle:

Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.

The tan of pi/6 equals the y-coordinate(0.5) divided by the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence, the value of tan pi/6 = y/x = 0.5774 (approx)

Learn more about trigonometric functions click;

https://brainly.com/question/6904750

#SPJ7

Answer:

1.3

Step-by-step explanation:

The Rest Of Them Are Writen As Fractions

Answer:

[tex]\sqrt{10}[/tex]

NOTE: the other answer is WRONG...

irrational means can not be written as a fraction (with whole numbers)

4/3 = 1.33333333333

Step-by-step explanation:

Answer:

da

Step-by-step explanation:

Answer:

1/2×d1×d2

=1/2× (4+4)(6+3)

=36

Answer:

(a) [tex]x\³ - 6x - 6[/tex]

(b) Proved

Step-by-step explanation:

Given

[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root

Solving (a): The polynomial

A cubic function is represented as:

[tex]f = (a + b)^3[/tex]

Expand

[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]

Rewrite as:

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

The root is represented as:

[tex]r=a+b[/tex]

By comparison:

[tex]a = $\sqrt[3]{2}[/tex]

[tex]b = \sqrt[3]{4}$[/tex]

So, we have:

[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]

Expand

[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

Evaluate like terms

[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]

Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]

So, we have:

[tex]f = 6 + 6r[/tex]

Equate to 0

[tex]f - 6 - 6r = 0[/tex]

Rewrite as:

[tex]f - 6r - 6 = 0[/tex]

Express as a cubic function

[tex]x^3 - 6x - 6 = 0[/tex]

Hence, the cubic polynomial is:

[tex]f(x) = x^3 - 6x - 6[/tex]

Solving (b): Prove that r is irrational

The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6

The divisors of -6 are: -6,-3,-2,-1,1,2,3,6

Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values

[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]

[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]

[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]

[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]

[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]

[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]

[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]

[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]

For r to be rational;

The divisors of -6 must divide f(x) without remainder

i.e. Any of the above values  must equal 0

Since none equals 0, then r is irrational

Answer:

x = 41 degrees

Step-by-step explanation:

Since two of the sides are shown as being congruent, the base angles are the same. We are given the top angle, which is 98 degrees. All the angles of a triangle add up to 180. We can subtract 98 from 180, giving us 82, and divide that by two (since the base angles are congruent), giving us a measure of 41 degrees for each of the bottom angles of the isosceles triangle.