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1 year ago

-6<5t-1<0solve inequality

Mathematics

1 answer:

blsea [12.9K]1 year ago

8 0

To solve the inequality:

$-6$

Add 1 to the sides of the inequality:

$-6+1$

Then

$-5$

Dividing all the inequality by 5, we have:

$\frac{-5}{5}$

Graphically:

Or, in the interval notation(-1, 1/5).

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12 girls in a class of 15 girls have short hair and the rest have long hair . What percent of the girls has long hair ?

kati45 [8]

Step-by-step explanation:

long hair

15 - 12 = 3

long hair percentage

= 3 ÷ 15 × 100

= 20%

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3 years ago

There are 110 students on a bus filled with 129 people. What is the ratio of students to teachers?

Sunny_sXe [5.5K]

Answer:

110 : 19

students : teachers

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7 0

2 years ago

Find the particular solution of the differential equation that satisfies the initial condition(s). f ''(x) = x−3/2, f '(4) = 1,

sweet [91]

Answer:

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

Step-by-step explanation:

This differential equation has separable variable and can be solved by integration. First derivative is now obtained:

$f'' = x - \frac{3}{2}$

$f' = \int {\left(x-\frac{3}{2}\right) } \, dx$

$f' = \int {x} \, dx -\frac{3}{2}\int \, dx$

$f' = \frac{1}{2}\cdot x^{2} - \frac{3}{2}\cdot x + C$ , where C is the integration constant.

The integration constant can be found by using the initial condition for the first derivative ( $f'(4) = 1$ ):

$1 = \frac{1}{2}\cdot 4^{2} - \frac{3}{2}\cdot (4) + C$

$C = 1 - \frac{1}{2}\cdot 4^{2} + \frac{3}{2}\cdot (4)$

$C = -1$

The first derivative is $y' = \frac{1}{2}\cdot x^{2}- \frac{3}{2}\cdot x - 1$ , and the particular solution is found by integrating one more time and using the initial condition ( $f(0) = 0$ ):

$y = \int {\left(\frac{1}{2}\cdot x^{2}-\frac{3}{2}\cdot x -1 \right)} \, dx$

$y = \frac{1}{2}\int {x^{2}} \, dx - \frac{3}{2}\int {x} \, dx - \int \, dx$

$y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x + C$

$C = 0 - \frac{1}{6}\cdot 0^{3} + \frac{3}{4}\cdot 0^{2} + 0$

$C = 0$

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

5 0

3 years ago

Which algebraic expression is a polynomial? 3m2n-2m/n+1/n

Lesechka [4]

Answer:

d) $7mn+\frac{3m}{2}+\frac{5n}{4}$

Step-by-step explanation:

Which algebraic expression is a polynomial?

$a)3m^2n-\frac{2m}{n}+\frac{1}{n} \\b)\frac{2mn}{5}-\frac{\sqrt{m} }{4} +4m^5\\c)\frac{4m^3}{n^2}-3mn^5+\sqrt{8}\\d)7mn+\frac{3m}{2}+\frac{5n}{4}$

Answer: A polynomial is an expression with variables and coefficients separated by addition and subtraction. The following are used when determining if an expression is a polynomial:

i) Variables of a polynomial must not have negative exponent.

ii) Variables of a polynomial must not have fractional exponent.

iii) Dividing by an exponent is not allowed

iv) Exponent radicals are not allowed.

a) $3m^2n-\frac{2m}{n}+\frac{1}{n}$ is not a polynomial because dividing by an exponent is not allowed.

b) $\frac{2mn}{5}-\frac{\sqrt{m} }{4} +4m^5$ , is not a polynomial because exponent radicals are not allowed (√m)

c) $\frac{4m^3}{n^2}-3mn^5+\sqrt{8}$ is not a polynomial because dividing by an exponent is not allowed.

d) $7mn+\frac{3m}{2}+\frac{5n}{4}$ is a polynomial

4 0

3 years ago

Solve the following equation for the unknown quantity: 12x-8=3x+10. a. x=4 b. =2 c =12 d. x=1/2

dezoksy [38]

Answer:

b. x=2

Step-by-step explanation:

Step 1- Move the variable to one side.

12x-8= 3x+10

-3x -3x

9x-8= 10

Step 2- Add 8 to both sides.

9x-8= 10

+8 +8

9x= 18

Step 3- Divide to both sides.

9 9

x= 2

5 0

3 years ago