Which equation represents a linear equation

Answer:

Jack needs 6 hours and Jill needs 3 hours.

Step-by-step explanation:

Let's define the variables:

X  = rate at which Jack can write a holiday card.

Y = rate at which Jill can write a holiday card.

Each of them will need a given time to write a card, such that:

X*T = 1 card

We know that Jack needs 3 more hours to write a card than Jill, then Jill needs 3 hours less than Jack, so if Jack needs T hours, Jill will need T - 3 hours

Then we have the equation:

Y*(T - 3 hr) = 1 card

And we also know that when they work together, they need 2 hours, then:

(X + Y)*2 hr = 1 card.

So we have 3 equations:

X*T = 1 card

Y*(T - 3 hr) = 1 card

(X + Y)*2 hr = 1 card.

Now let's ignore the card part just for the equations, then we get:

X*T = 1

Y*(T - 3 hr) = 1

(X + Y)*2 hr = 1

To solve it, we first need to isolate one variable in one of the equations, let's isolate T in the first equation, we get:

T = 1/X

Now we can replace this in the second equation to get:

Y*((1/X) - 3hr) = 1

So now we have two equations:

(X + Y)*2 hr = 1

Y*((1/X) - 3hr) = 1

We need to do the same, isolate one variable in one of the equations, let's isolate Y in the above one:

Y*2hr = 1 - X*2hr

Y = (1 - X*2hr)/2hr

Now we can replace this in the other equation to get:

((1 - X)/2hr)*((1/X) - 3hr) = 1

Now we can solve this for X:

((1 - X)/2hr)*((1/X) - 3hr) = 1

(1 - X)*((1/X) - 3hr) = 2 hr

1/X - 3hr - X*2hr/X + X*2hr*3hr = 2hr

1/X - 3hr - 2hr + X*6hr^2 = 2hr

1/X + X*6hr^2 = 2hr + 3 hr + 2 hr = 7hr

1/X + X*6hr^2 = 7hr

Now we can multiply all by X to get:

X/X + X*(X*6hr^2) = 7hr*X

Now we have the quadratic equation:

(6hr^2)*X^2 - (7hr)*X + 1 = 0

We can find the solutions of this equation if we use the Bhaskara's formula, the solutions are:

[tex]X = \frac{-(-7hr) +- \sqrt{(-7hr)^2 - 4*(6hr^2)*1} }{2*6hr^2} = \frac{7hr +- 5hr}{12 hr^2}[/tex]

Then we have two solutions:

X = (7hr + 5hr)/12hr = 1 hr^-1

And this is the rate at which Jack writes a card, so the actual units are:

X =  0.167 card/hr

Then Jill's rate will be:

Y = (1 - X*2hr)/2hr = (1 - 1card/hr*2hr)/2hr = -0.5 card/hr

So we have a negative rate, this makes no sense, so we can discard this option. The other solution for X is:

X = (7hr - 5hr)/12hr = 0.166... hr^-1

And this is the rate at which Jack writes a card, so the actual units are:

X =  0.166... card/hr

If we have this, then the rate for Jill will be:

Y = Y = (1 - X*2hr)/2hr = (1 - 0.167card/hr*2hr)/2hr = 0.333 card/hr

Then we have:

X = 0.167 card/hr

If we use the first equation, we get:

(0.166... card/hr)*T = 1 card

T = 1 card/((0.166... card/hr)) =  6 hours

Then Jack needs 6 hours to write a card.

And we know that Jill needs 3 hours less than that, then Jill needs 3 hours.

Answer:

254 R 6

Step-by-step explanation:

Answer:

256 7/16

Step-by-step explanation:

2308/9 = 256 7/16

Answer:

D) Perpendicular

Step-by-step explanation:

Red: 5y+4x=-30

Blue: y=5/4x-5

Answer:

1/4 of a can

Step-by-step explanation:

He had 1/3 of a can.

He used 3/4 of the 1/3 of the can.

He used 3/4 * 1/3 of a can.

3/4 * 1/3 = 3/12 = 1/4

Answer: 1/4 of a can

Answer:

9x3+5x2=37

8-(7-5)^2+8=12

10-3+5+5x4=32

ill solve rest in comments

9x3+5x2=37

8-(7-5)^2+8=12

10-3+5+5x4=32

Answer:

Radius, Diameter and Circumference

The Radius is the distance from the center outwards. The Diameter goes straight across the circle, through the center. The Circumference is the distance once around the circle.

:)

Answer:

Radius = 8.7 cm

Step-by-step explanation:

The height and hypotenuse of the triangle is provided, so all we have to do is use the Pythagorean Theorem. [tex]\sqrt{15^{2}-12.2^{2}}[/tex] and this yields the answer.

Answer:

<A = 30°

The steps are given in the pic. Hope it will help :)

Answer:

they retain 3/5 or 60% of their initial weight

Step-by-step explanation:

Answer:

$4.95

Step-by-step explanation:

Answer:

4.59

Step-by-step explanation:

0.59x5=$2.95

2.95+2=4.59

Answer:

a

Step-by-step explanation:

the answer is a because the rrow is pointing right so the symbol is > and the point starts at -5

Answer:

hasta no se pero nimodoa esta bien adiós baybau

Answer:

y = 18

Step-by-step explanation:

[tex] \frac{21 + 7}{21} = \frac{y + 6}{y} [/tex]

[tex] \frac{28}{21} = \frac{y + 6}{y} [/tex]

Cross multiply

28*y = 21(y + 6)

28y = 21y + 126

28y - 21y = 126

7y = 126

y = 126/7

y = 18

Answer:

They saw 15 customers per hour.

Step-by-step explanation:

Yes 5.3 is greater than 5

5.3 > 5

Answer:

yes, it is.

Step-by-step explanation:

its a solution because in the graph below, 5.3 is in the shaded region. hope this helped!!

Answer:

x = 18

Step-by-step explanation:

Answer: It neither

Step-by-step explanation:

because x part is linear while y part is neither linear or exponential.

They both are supposed to have the same relationship since They are not then it’s neither linear or exponential.

Hope it help.

Given:

The value of a house is 600,000 in 2005.

It increased by 25% in 2006 and 10% in 2007 but dropped by 15% in 2007.

To find:

The value of the house in 2008.

Solution:

We have,

Value of house in 2005 = 600,000

It increased by 25% in 2006.

Value of house in 2006 = [tex]600,000+\dfrac{25}{100}600,000[/tex]

                                        = [tex]600,000+150,000[/tex]

                                        = [tex]750,000[/tex]

It increased by 10% in 2007

Value of house in 2007 = [tex]750,000+\dfrac{10}{100}750,000[/tex]

                                        = [tex]750,000+75,000[/tex]

                                        = [tex]825,000[/tex]

But it dropped by 15% in 2007.

Value of house in 2008 = [tex]825,000-\dfrac{15}{100}825,000[/tex]

                                        = [tex]825,000-123,750[/tex]

                                        = [tex]701,250[/tex]

Therefore, the value of the house in 2008 is 701,250.

Answer:

The expected frequency for the cell E2,2 is = 33

Step-by-step explanation:

The given data is

Gender               | 0-30| 30-60| 60-90| 90+       Totals

Male                    | 23    |    35   |   76    |  46        180

Female               |   31   |    42   |   46    |  16         135    

Totals                    54         77        122    62          315  

The expected frequency for the cell E2,2 is :

Expected for the (30-60 box for females)   =  Total of (30-6)/ (total )* females

                                                                      = ( 77/315)135= 33

Here p= 77/315 and n= 135

therefor X= pn = 33

χ²=  (33-42)²/33= 2.455  ( for the single value of E2,2=33)

Expected for the (30-60 box for males)   =  Total of (30-6)/ (total )* males

                                                                      = ( 77/315)180= 44

χ²=  (44-42)²/44= 0.09

The critical region is  χ² (0.05) 3 ≥  χ²= 11.34

Let the null and alternate hypothesis be

H0:the number of minutes spent online per day is not related to gender

against

Ha: the number of minutes spent online per day is related to gender

The single value of χ² for E2,2 = 2.45 is less than the critical value of 11.34.  

Answer:

24 tiles (none of the options given is correct)

Step-by-step explanation:

Number of tiles required to floor the room = area of the room/area of 1 tile

Area of the room = 36m * 24m = 864 m²

Area of 1 tile = 6² = 36 m²

Number of times required = 864/36 = 24 tiles

Answer:

For s students, at least 6s liters of water will be needed. So, for 30 students, at least 6*30 = 180 liters of water will be needed.

Step-by-step explanation:

This question is solved by proportions, using rule of three.

I am going to say that:

s is the number of students.

l is the number of liters of water needed for s students.

I have found that with five students in the class at least 30 litres of water is needed.

This means that:

[tex]\frac{s}{l} = \frac{5}{30}[/tex]

[tex]5l = 30s[/tex]

[tex]l = \frac{30s}{5}[/tex]

[tex]l = 6s[/tex]

This means that for s students, at least 6s liters of water will be needed. So, for 30 students, at least 6*30 = 180 liters of water will be needed.

Answer:

6/8 or in simple terms, 3/4

Step-by-step explanation:

[tex] \frac{1}{2} + \frac{1}{4} \\ = ( \frac{1}{4} + \frac{1}{4} ) + \frac{1}{4} \\ = ( \frac{1}{8} + \frac{1}{8} ) + (\frac{1}{8} + \frac{1}{8} ) + (\frac{1}{8} + \frac{1}{8} ) \\ = ( \frac{2}{8} ) + ( \frac{2}{8} ) + ( \frac{2}{8} ) \\ = \frac{6}{8} \\ = \frac{2 \times 3}{2 \times 4} \\ = \frac{3}{4} [/tex]

The given operation of the two fractions can be found as 6/8. The correct option is (D).

A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.

The number a is called as the numerator and b is the denominator.

The given expression is 1/2 + 1/4.

It can be solved using the strip given as below,

The number of 1/8 sections under 1/2 in the strip is 4.

And, the number of 1/8 sections under 1/4 in the strip is 2.

Then, the addition of the two fractions is equivalent to the total number of 1/8 sections under both of them.

It can be written in mathematical form as,

⇒  1/2 + 1/4

⇒ 4 × 1/8 + 2 × 1/8

⇒ 6/8

Hence, the required sum of the given fractions can be evaluated as 6/8.

To know more about fraction click on,

https://brainly.com/question/10354322

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Answer:

y = 5x + 2

Step-by-step explanation:

in order to find if a line is steeper, you need to look at the slope

the greater the slope, the steeper the line will be

y = 2x + 4

y = -4x - 1

y = 1/2x + 10

y = 5x + 2

out of all of these options, y = 5x + 2 has the largest slope. this means that it is the steepest one.

Answer:

3.8374326e+21

Step-by-step explanation:

id.k goo.gle said this

Answer:   2/3

Step-by-step explanation:

Answer: w + 1.3 = 2.7

Step-by-step explanation: i did it in khan academy ∩(︶▽︶)∩ HOPE IT HELPS

Answer:

The answer is 12

Step-by-step explanation:

You have to divide 5 and 60 or you can multiply by 5 until you get to 60.

Answer:

12

Step-by-step explanation:

60/5=12