All categories

3 years ago

Please solve this (Rational numbers 8th grade)

Mathematics

1 answer:

pochemuha3 years ago

4 0

Question # 1

Answer:

$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}=-\frac{3}{20}$

Step-by-step explanation:

Given the expression

$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}$

$=-\frac{2}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}$ ∵ $\frac{-2}{3}\times \frac{3}{5}=-\frac{2}{5}$

$=-\frac{2}{5}+\frac{1}{4}$ ∵ $\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}=\frac{1}{4}$

$\mathrm{Least\:Common\:Multiplier\:of\:}5,\:4:\quad 20$

$=-\frac{8}{20}+\frac{5}{20}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{-8+5}{20}$

$\mathrm{Add/Subtract\:the\:numbers:}\:-8+5=-3$

$=\frac{-3}{20}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$=-\frac{3}{20}$

Therefore,

$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}=-\frac{3}{20}$

Question # 2

Answer:

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}=-\frac{5}{28}$

Step-by-step explanation:

Given

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}$

$=-\frac{6}{35}-\frac{1}{6}\times \frac{3}{2}\times \frac{2}{5}\times \frac{1}{14}$ ∵ $\frac{2}{5}\times \frac{-3}{7}=-\frac{6}{35}$

$=-\frac{6}{35}-\frac{1}{140}$ ∵ $\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}=\frac{1}{140}$

$\mathrm{Least\:Common\:Multiplier\:of\:}35,\:140:\quad 140$

$=-\frac{24}{140}-\frac{1}{140}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{-24-1}{140}$

$\mathrm{Subtract\:the\:numbers:}\:-24-1=-25$

$=\frac{-25}{140}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$=-\frac{25}{140}$

$\mathrm{Cancel\:the\:common\:factor:}\:5$

$=-\frac{5}{28}$

Therefore,

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}=-\frac{5}{28}$

You might be interested in

Write an equation in point-slope form for the line that has a slope of 4/5 and contains the point (−5, −3).

ankoles [38]

y = mx + b, where m = slope, and b = y-intercept.

Since you are not given the y-intercept, you have to solve for it through the equation, y = (4/5)x (which is the slope you are given) + b, and replace x and y with values given, which are (-5,-3)

y = (4/5)x + b

-3 = (4/5)(-5) + b

-3 = -4 + b

1 = b

Then replace b in the first equation to get the answer

y = (4/5)x + 1

5 0

3 years ago

A car travels 45 mph. How far will it go in 4 hours and 20 minutes?

ra1l [238]

(The Explanation): What we are given is that the car drives 45 miles each hour. Furthermore, you need to multiply the amount of hours desired to the miles to get a total mile.

(Step-By-Step Instructions):

45(4) and 45(20) Multiply

The Answers: 4 hours = 180 miles / 20 hours = 900 miles

3 0

2 years ago

Pemdas (-10 + 2²) + 12

schepotkina [342]

Answer:

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

I need help on this hhhhhhhh

Anon25 [30]

$\huge\text{Hey there!}$

$\mathsf{\dfrac{10^{15}}{10^4}}$

$\mathsf{10^{15}}\\\mathsf{=10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times 10\times10\times10\times10\times10}\\\mathsf{= \boxed{\bf 1,000,000,000,000,000}}$

$\mathsf{\dfrac{\bold{1,000,000,000,000,000}}{10^4}}$

$\mathsf{10^4}\\\mathsf{= 10\times10\times10\times10}\\\mathsf{10\times10=\bf 100}\\\mathsf{100\times100}\\\mathsf{= \boxed{\bf 10,000}}$

$\mathsf{\dfrac{1,000,000,000,000,000}{\bf 10,000}}$

$\mathsf{\dfrac{1,000,000,000,000,000}{10,000}}\\\\\mathsf{= 1,000,000,000,000,000\div 10,000}\\\\\mathsf{= \boxed{\bf 100,000,000,000}}$

$\mathsf{10^{11}}\\\mathsf{10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10}\\\mathsf{= \boxed{\bf 100,000,000,000}}$

$\mathsf{100,000,000,000= 100,000,000,000= 10^{11}}$

$\boxed{\boxed{\large\text{Answer: BASICALLY }\mathsf{\dfrac{10^1^5}{10^4}\large\text{ is EQUAL to or EQUIVALENT to}}}}\\\boxed{\boxed{\mathsf{10^{11}}\large\text{ because they both give you the result of \bf 100,000,000,000}}}\huge\checkmark$

$\large\textsf{Good luck on your assignment and enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

3 0

2 years ago

Could you please help with this question for domain, range, and end behavior? I started it, but I think I'm doing it wrong.

Tanzania [10]

It looks like you have the domain confused for the range! You can think of the domain as the set of all "inputs" for a function (all of the x values which are allowed). In the given function, we have no explicit restrictions on the domain, and no situations like division by 0 or taking the square root of a negative number that would otherwise put limits on it, so our domain would simply be the set of all real numbers, R. Inequality notation doesn't really use ∞, so you could just put an R to represent the set. In set notation, we'd write

$\{x\in\re\mathbb{R}\}$

and in interval notation,

$(-\infty,\infty)$

The range, on the other hand, is the set of all possible outputs of a function - here, it's the set of all values f(x) can be. In the case of quadratic equations (equations with an x² term), there will always be some minimum or maximum value limiting the range. Here, we see on the graph that the maximum value for f(x) is 3. The range of the function then includes all values less than or equal to 3. As in inequality, we can say that

$f(x)\leq3$ ,

in set notation:

$\{f(x)\in\mathbb{R}\ |\ f(x)\leq3\}$

(this just means "f(x) is a real number less than or equal to 3")

and in interval notation:

$(-\infty,3]$

8 0

2 years ago