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3 years ago

Isabella earned $129.60 at her job when she worked for 6 hours. How much money

Mathematics

1 answer:

Aloiza [94]3 years ago

8 0

Answer:

21.6

Step-by-step explanation:

you divide 129.60 by 6 and you get 21.6.

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Solve: 2x+7/5 - x-3/10 = x+1/15<br>find the value of x and verify the result will RHS

choli [55]

Step-by-step explanation:

<h3><u>Given Question :- </u></h3>

Solve for x :-

$\dfrac{2x + 7}{5} - \dfrac{x - 3}{10} = \dfrac{x + 1}{15}$

$\red{\large\underline{\sf{Solution-}}}$

Given linear equation is

$\rm :\longmapsto\: \dfrac{2x + 7}{5} - \dfrac{x - 3}{10} = \dfrac{x + 1}{15}$

$\rm :\longmapsto\: \dfrac{2(2x + 7) - (x - 3)}{10} = \dfrac{x + 1}{15}$

$\rm :\longmapsto\: \dfrac{4x + 14 - x + 3}{10} = \dfrac{x + 1}{15}$

$\rm :\longmapsto\: \dfrac{(4x - x) + (14 + 3)}{10} = \dfrac{x + 1}{15}$

$\rm :\longmapsto\: \dfrac{3x + 17}{10} = \dfrac{x + 1}{15}$

On multiply by 5 on both sides,

$\rm :\longmapsto\: \dfrac{3x + 17}{2} = \dfrac{x + 1}{3}$

On cross multiplication, we get

$\rm :\longmapsto\:3(3x + 17) = 2(x + 1)$

$\rm :\longmapsto\:9x +51 = 2x + 2$

$\rm :\longmapsto\:9x - 2x = 2 - 51$

$\rm :\longmapsto\:7x = - 49$

$\bf\implies \:x = - 7$

<h3><u>VERIFICATION</u></h3>

Consider, LHS

$\red{\rm :\longmapsto\: \dfrac{2x + 7}{5} - \dfrac{x - 3}{10}}$

On substituting the value of x, we get

$\red{\rm \: = \: \dfrac{2( - 7) + 7}{5} - \dfrac{ - 7 - 3}{10}}$

$\red{\rm \: = \: \dfrac{ - 14 + 7}{5} - \dfrac{ - 10}{10}}$

$\red{\rm \: = \: \dfrac{ - 7}{5} + 1}$

$\red{\rm \: = \: \dfrac{ - 7 + 5}{5}}$

$\red{\rm \: = \: \dfrac{ - 2}{5}}$

Consider RHS

$\green{\rm :\longmapsto\:\dfrac{x + 1}{15}}$

On substituting the value of x, we get

$\green{\rm \: = \: \dfrac{ - 7 + 1}{15}}$

$\green{\rm \: = \: \dfrac{ - 6}{15}}$

$\green{\rm \: = \: \dfrac{ - 2}{5}}$

$\rm \implies\:LHS=RHS$

HENCE, VERIFIED

5 0

3 years ago

Read 2 more answers

What is 15.8 in expanded form And What is 1.058 in expanded form and last what is 0.158 in expanded form

xeze [42]

1) 10.0 + 5.0 + .8
2) 1.000 + 0.050 + 0.008
3) 0.000 + 0.100 + 0.050 + 0.008

5 0

3 years ago

Read 2 more answers

Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of vector PQ.

polet [3.4K]

We are asked to determine the lengths of the line segment drawn with these points as endpoints. The equation of the distance between points is,
d = sqrt ((y2 - y1)² + (x2 - x1)²)
Substituting the coordinates of the points,
d = sqrt ((14 - 9)² + (4 - 2)²)
The numerical value for d is approximately 5.39.

6 0

4 years ago

This is a two-step equation. Steps: first add or subtract, then divide or multiply. 1. 5x - 7 = 48 2. 7n - 2 = 54 3. -4y + 7 = -

Bumek [7]

1. 5x - 7 = 48

5x = 48 + 7 = 55

x = 55/5 = 11

2. 7n - 2 = 54

7n = 54 + 2 = 56

n = 56 / 7 = 8

3. -4y + 7 = -21

-4y = -21 - 7 = -28

y = -28 / -4 = 7

4. x/2 + 5 = 12

x/2 = 12 - 5 = 7

x = 7 * 2 = 14

5. x/3 - 7 = 13

x/3 = 13 + 7 = 20

x = 20 * 3 = 60

6. -7 - 2 = 33 <- did you type this wrong?

-7x - 2 = 33

-7x = 33 + 2

-7x = 35

x = 5

7. -3x - 8 = -41

-3x = -41 + 8 = -33

x = -33 / -3 = 11

8. 3n - 7 = 35

3n = 35 + 7 = 42

n = 42 / 3 = 14

9. 7y + 9 = -47

7y = -47 - 9 = -56

y = -56 / 7 = -8

10. -8x + 4 = 68

-8x = 68 - 4 = 64

x = 64 / -8 = -8

11. 4n - 7 = -43

4n = -43 + 7 = -36

n = -36 / 4 = -9

12. 5x - 7 = 108

5x = 108 + 7 = 115

x = 115 / 5 = 23

13. 8 - 5w = -37

-5w = -37 - 8 = -45

w = -45 / -5 = 9

14. 42 = 18 + 4n

4n = 42 - 18 = 24

n = 24 / 4 = 6

15. 70 - 6x = 40

-6x = 40 - 70 = -30

x = -30 / -6 = 5

5 0

4 years ago

Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for ______ minutes on Monday. Eve

mr Goodwill [35]

Let $a_n$ be the n'th term of a sequence,

for example $a_1$ is the first term, $a_2$ is the second term and so on.
----------------------------------------------------------------------------------------------------
a sequence is arithmetic if the difference between any 2 terms is equal:

so an arithmetic sequence, for the first term = t, and the common difference = d, has the following form:

$a_1=t$

$a_2=t+d$

$a_3=t+d+d$

$a_4=t+d+d+d$

so clearly $a_n=t+d*(n-1)$
---------------------------------------------------------------------------------------------------
A sequence is geometric, if the ratio between any 2 consecutive terms is the same, and it is called the common ratio.

a geometric ratio with first term = t, and common ratio = r is:

$a_1=t$

$a_2=t*r$

$a_3=t*r*r$

$a_4=t*r*r*r$

thus clearly $a_n=t* r^{n-1}$
--------------------------------------------------------------------------------------------------

Part 1:

"<span>Jasmine practices the piano for __30___ minutes on Monday. Every day she ____increases_______ her practice time by ____5 minutes_____. </span>"

let $a_n$ be the number of hours Jasmine practices the n'th day,

for n=7, t=30, d=5 we have

$a_7=30+5*(7-1)=30+5*6=30+30=60$ ,

minutes is the time Jasmine practices on the 7the day.

Part 2

"<span>Anthony goes to the gym for ___60___ minutes on Monday. Every day he ___increases______his gym time by ____1/10_of the previous day_____. </span>"

if $S_n$ represents the minutes that Anthony goes to gym on the n'th day,

then

$S_1=60$

$S_2=60+1/10*60=10/10*60+1/10*60=11/10*60=1.1*60$

$S_3=1.1*1.1*60$

$S_4=1.1*1.1*1.1*60$

$S_5=1.1*1.1*1.1*1.1*60= (1.1)^{4}*60= 1.4641*60=87.85$
(minutes)

Part 3: it is clear that the formula that can be derived in Part 2 is:

$S_n=60*(1.1)^{n-1}$

so assume we want to find how many hours does Anthony spend in the gym on the 10th day,

then we calculate $S_10=60*(1.1)^{9}=60*2.358=141.5$ (minutes)

6 0

3 years ago