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3 years ago

Solve inequalities for x : |5x -3|< 12.

Mathematics

1 answer:

goldenfox [79]3 years ago

6 0

Hello!

→ To answer the question we need to know about inequations, then...

$\huge {\text {$ \blue{ \sf \mid 5x - 3 \mid < 12 } $}}$

$\swarrow$

$\huge {\text {$ \red {\sf \mid 5x \mid < 12+3 }$}}$

$\searrow$

$\huge {\text {$ \purple { \sf \mid 5x \mid < 15} $}}$

$\swarrow$

$\huge {\text {$ \bf \mid x \mid < 15 \div 5 $}}$

$\large {\text {$ \downarrow $}}$

$\huge {\boxed { \bf \mid x \mid < 3 }}$

Good studies!

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Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a comma-separated list.)

Vladimir79 [104]

Hello,

y=(1+x)/(1-x)

y=-1
Asymptote horizontal $\lim_{n \to \infty} \frac{1+x}{1-x} =-1$

x=1
Asymptote vertical $\lim_{x \to 1} \frac{1+x}{1-x}=\infty$

3 0

3 years ago

A vehicle travels on a highway at a rate of 65 mi/h how long does it take the vehical to travel 25 mi?

katrin [286]

Use the velocity formula and solve for time.v=d/t
t=d/v

Substitute your variables and solve.
65 mi/hr = 65 / 3600 mi/second
25 mi / ( 65/3600) = 1384.6 seconds

4 0

3 years ago

Help me please solve the circled question show your work

Rasek [7]

Part 1) Use the fact that there are 12 inches in a foot

a) How many inches tall is a 7 foot basketball player?

we know that

1 foot=12 inches

so by proportion

$\frac{12}{1} \frac{inches}{foot} =\frac{x}{7} \frac{inches}{feet} \\ \\x=12*7\\ \\x=84\ inches$

therefore

the answer Part 1a) is

$84\ inches$

Part b) If a yard is a 3 feet long, how many inches are in a yard?

we know that

1 yard=3 feet

1 foot=12 inches

Convert 3 feet to inches

by proportion

$\frac{12}{1} \frac{inches}{foot} =\frac{x}{3} \frac{inches}{feet} \\ \\x=12*3\\ \\x=36\ inches$

therefore

the answer Part 1b) is

$36\ inches$

Part 2) At the farmer's market two pounds of peaches cost $4.20 How much will five pounds cost?

by proportion

$\frac{4.20}{2} \frac{\$}{pounds} =\frac{x}{5} \frac{\$}{pounds} \\ \\2*x=4.2*5\\ \\x=4.2*5/2=\$10.5$

therefore

the answer Part 2) is

$\$10.5$

Part 3) Janice mother gave her a ten dollars bill to buy five pounds each of bananas and apples at the grocery store. When she got there she found that bananas were 80 c per pound and apples were $1.40 per pound.

Did Janice's mother give her enough money? If so, should she receive any change? If not, how much more money does she need?

we know that

Find the cost of the bananas

$5\ pounds*0.80\frac{\$}{pounds}=\$4$

Find the cost of the apples

$5\ pounds*1.40\frac{\$}{pounds}=\$7$

Sum the cost of the bananas and the cost of the apples

$\$4+\$7=\$11$

$\$11 > \$10$ ------> Janice's mother didn't give her enough money

She needs more money

She needs-------> $\$11-\$10=\$1$

therefore

the answer part 3) is

She needs $\$1$ more

3 0

3 years ago

if you save three pennies on January 1, six pennies on January 2, nine pennies on January 3, and continue this pattern for one y

Katarina [22]

Answer:

2003.85

Step-by-step explanation:

I realize I'm a year late, but the math of the previous answer was so terrible I'm honestly too horrified to let this be.

You have save by an increasing amount of 3 pennies per day. You start with 3 and build from that, each day, for 365 days. First, you must figure out what amount of pennies you shoved into your account on the final 365th day.

An= a1+(n-1)d

An=term you want

a1= term you begin with

n= term you want

d= constant amount

A_365= 3 + (365-1)*3

A_365= 1095

Arithmetic Sum: Sn = N/2 (a1 + an)

365/2 * (3 + 1095) = 200385.

This means you've invested a total of 200385 PENNIES after 365 days.

The question asks for dollars, not your rusting lincoln's.

As (I hope) you know, 1 Dollar = 100 pennies

200385 pennies/100 = 2003.85.

This means you have $2003.85 in your account by the conclusion of the 365th day.

4 0

3 years ago

Find the specified vector or scalar. . u = -4i + 1j and v = 4i + 1j; Find |u+v|. a. square root of 34. b. 5. c. 2

ExtremeBDS [4]

U = - 4 i + 1 j
v = 4 i + 1 j
| u | = √ (-4)² + 1² = √ 17
| v | = √4² + 1² = √ 17
| u + v | = √(u + v)²=
= √( u² + 2 u v + v² )= ...
cos ( u, v ) = (-16+1) / (|u| |v|) = -15/17
...= √(17 + 2 · √17 · √17 · ( -15/17) +17) =
= √ 34 - 30 = √ 4 = 2
Answer: C ) 2

3 0

3 years ago