Question

the product of two consecutive positive integers is 17 more than 5 times the sum find the numbers​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

Step-by-step explanation:

Step-by-step explanation:

Step-by-step explanation:

Given :

Area of Trapezium is 384 cm² .

Parallel sides of trapezium are in the ratio 3:5 .

Perpendicular distance / Height is 12 cm .

To Find :

Length of each parallel sides .

Solution :

$\longmapsto\tt{Let\:one\:parallel\:side\:be=3x}$

$\longmapsto\tt{Let\:other\:parallel\:side\:be=5x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}$

Putting Values :

$\longmapsto\tt{384=\dfrac{1}{{\cancel{2}}}\times{(3x+5x)}\times{{\cancel{12}}}}$

$\longmapsto\tt{384=(3x+5x)\times{6}}$

$\longmapsto\tt{384=18x+30x}$

$\longmapsto\tt{384=48\:x}$

$\longmapsto\tt{x=\cancel\dfrac{384}{48}}$

$\longmapsto\tt\bf{x=8}$

Value of x is 8 .

Therefore :

$\longmapsto\tt{Length\:of\:one\:parallel\:side=3(8)}$

$\longmapsto\tt\bf{24\:cm}$

$\longmapsto\tt{Length\:of\:other\:parallel\:side=5(8)}$

$\longmapsto\tt\bf{40\:cm}$

So , The Parallel sides of Trapezium are 24 cm and 40 cm .

Answer 2

Step-by-step explanation:

$\huge{\green{\underline{\underline{\tt{Solution:}}}}}$

Given,

☞ x = -1

Let, P(x) = 5x-4x²+3

$→\;{\sf{P(-1) = 5(-1)-4(-1)²+3}}$

$→\;{\sf{P(-1) = -5-4(+1)+3}}$

$→\;{\sf{P(-1) = -5-4+3}}$

$→\;{\sf{P(-1) = -9+3}}$

$➝\;\red{\bf{P(-1) = -6}}$

Hope It Helps You ✌️

$\huge\underbrace{\green{\tt{\diamond\; Solution:}}}$

Let

Total Pocket Money be 'x'

Now, Savings = 30% of x

$→\;\Large{\frac{30}{100}×x}$

☞ $→\;\Large{\frac{30x}{100}}$

Given,

Amount Spend = Rs. 280.

$→\;\Large{\sf{x - \frac{30x}{100} = 280}}$

LCM is '100'

$→\;\Large{\sf{\frac{100x-30x}{100} = 280}}$

$→\;{\sf{70x = 280×100}}$

$→\;\Large{\sf{x = \cancel{\frac{28000}{70}}}}$

$→\;\boxed{\sf{x = 400}}$

.:. Total Pocket Money is $\fbox\red{Rs.400}$

Hope It Helps You ✌️

Refer The Attachment ⬆️

$\huge\underbrace{\green{\tt{\diamond\; SoluTion:}}}$

$→\;{\sf{2x² = 128}}$

$→\;{\sf{x² = \Large\frac{128}{2}}}$

$→\;{\sf{x = \sqrt{64}}}$

$→\;{\sf{x = \sqrt{8²}}}$

$☞\;\Large{\red{\bf{x = 8}}}$

$\purple{\bf{MrMonarque}}$

Hope It Helps You ✌️

Refer The Attachment ⬆️

$\red{\sf{MrMonarque}}$

Hope It Helps You ✌️$\huge{\green{\underline{\underline{\tt{Solution:}}}}}$

Given,

☞ x = -1

Let, P(x) = 5x-4x²+3

$→\;{\sf{P(-1) = 5(-1)-4(-1)²+3}}$

$→\;{\sf{P(-1) = -5-4(+1)+3}}$

$→\;{\sf{P(-1) = -5-4+3}}$

$→\;{\sf{P(-1) = -9+3}}$

$➝\;\red{\bf{P(-1) = -6}}$

Hope It Helps You ✌️

$\huge\underbrace{\green{\tt{\diamond\; Solution:}}}$

Let

Total Pocket Money be 'x'

Now, Savings = 30% of x

$→\;\Large{\frac{30}{100}×x}$

☞ $→\;\Large{\frac{30x}{100}}$

Given,

Amount Spend = Rs. 280.

$→\;\Large{\sf{x - \frac{30x}{100} = 280}}$

LCM is '100'

$→\;\Large{\sf{\frac{100x-30x}{100} = 280}}$

$→\;{\sf{70x = 280×100}}$

$→\;\Large{\sf{x = \cancel{\frac{28000}{70}}}}$

$→\;\boxed{\sf{x = 400}}$

.:. Total Pocket Money is $\fbox\red{Rs.400}$

Hope It Helps You ✌️

Refer The Attachment ⬆️

$\huge\underbrace{\green{\tt{\diamond\; SoluTion:}}}$

$→\;{\sf{2x² = 128}}$

$→\;{\sf{x² = \Large\frac{128}{2}}}$

$→\;{\sf{x = \sqrt{64}}}$

$→\;{\sf{x = \sqrt{8²}}}$

$☞\;\Large{\red{\bf{x = 8}}}$

$\purple{\bf{MrMonarque}}$

Hope It Helps You ✌️

Refer The Attachment ⬆️

$\red{\sf{MrMonarque}}$

Hope It Helps You ✌️

Let $\sf p \geq 5$ be a prime number.... Prove that there exists an integer $\sf a$ with $\sf 1 \leq a \leq p - 2$ such that neither $\sf {a}^{(p - 1)} - 1$ nor [tex

$\huge\star\underline\mathtt\green{Question:-}$(◍•ᴗ•◍)❤ $\tt\pink{✰\:Define}$ $\sf 1. \:Acid$ $\sf 2.... \:Base$ $\sf 3. \:Salt$ No Spam‼️