Devon wants to write an equation for a line that passes
through 2 of the data points he has collected. The points
are (8, 5) and (-12, -9). He writes the equation
7x-10y=3. Is this a
reasoning.
good model? Explain your reasoning.

Answer:  Equations (b) and (e) do not have solutions

Step-by-step explanation:  b)  The x cancels out (-10x + 35) = -10x + 318;  35 = 318???? NO.  e)  3(x + 2) + 1 = x + 2(4 + x)​;  3x + 7 = 3x + 8.  The x cancels out again.

The other s can be solved for x.

Hi! I'm happy to help!

To solve this, we need to simplify all of the equations. There are 3 ways equations like this can go, infinitely many solutions, 1 solution, or no solution. Infinitely many is something like 6=6, that could mean infinite solutions because 6 always equal 6, and would apply in infinitely many ways. (in the equation) One solution refers to something like x=6. This tells your exactly what x is, and that is your only solution. (for the equation) And no solution is something like 5=6, 5 will never equal 6, so that is no solution. (to the equation)

Now, let's start out with our first equation. To find if our equations have solutions or not, we need to simplify them. We do this by singling out x to see what the solution is (if there is one).

x-9=2(x-3)+12

We can multiply 2, by x and -3 inside of the parenthesis, to simplify:

x-9=2x-6+12

Since we have at least one x on both sides, we can subtract it to isolate it:

x-9=2x-6+12

-x    -x

-9=x-6+12

Combine -6 and twelve:

-9=x-6+12

-9=x+6

Now, we subtract 6 to fully isolate x:

-9=x+6

-6   -6

-15=x

We see we have 1 solution, so you should not pick option 1.

Second equation:

5(-2x + 7) + 3 = -10x + 38

We should first multiply the parenthesis:

-10x+35+3=-10x+38

Since we want to simplify, let's add 10x on both sides

-10x+35+3=-10x+38

+10            +10x

35+3=38

Add 35 and 3:

38=38

Since 38 will always equal 38, there are infinite solutions, and you should not pick option 2.

Third equation:

(6x - 4) = 3(x - 2)

Since there is nothing outside of the parenthesis (right side), we don't need them:

6x-4=3(x-2)

From here, multiply the parenthesis:

6x-4=3x-6

Subtract 3x from both sides:

6x-4=3x-6

-3x   -3x

3x-4=-6

Add 4 to both sides to isolate x:

3x=-2

Divide both sides by 3, to fully isolate x:

x=-[tex]\frac{2}{3}[/tex]

Since there is only 1 solution, you should not pick option 3.

Fourth equation: (not sure if the 100 is supposed to be there)

0.01x + 0.001 = (x + 10)

First, let's subtract 0.01x from both sides:

0.001=9.99x+10

Then, we subtract 10 from both sides to start isolating x:

-9.999=9.99x

Then, we divide both sides by 9.99:

        ______

1.000900900=x

Kind of a weird number, but regardless, you should not pick option 4, because it has 1 solution.

Fifth equation:

3(x + 2) + 1 = x + 2(4 + x)​

First, let's multiply the parenthesis on both sides:

3x+6+1=x+8+2x

Combine like terms:

3x+7=3x+8

Subtract 3x from both sides:

7=8

7 will never equal 8, there will be no solution, and you should pick option 5.

You should pick option e, because it has no solution.

I hope this was helpful, keep learning! :D

Answer:

There are 6 days between each pick up days.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Remember that for this kind of question, when f(x) is given as 3, then 3 is the y value of the point. So you must have a point whose value is (x,3)

There is only one point that does that. x = - 2

The answer is D

Answer:

Gradient: m = -3/4

Step-by-step explanation:

Please view the PDF attached for full step by step explanation

Answer:

9/10

Step-by-step explanation:

0.9 = 90/100 9/10

0.90 is the same as 90/100

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Step-by-step explanation:

M=189

N = 48

A = M*N

A = 189 * 48

A = 9072

Answer:

(I). 20.03:

[tex] = 2.003 \times {10}^{1} [/tex]

(ii). 200.03

[tex] = 2.0003 \times {10}^{2} [/tex]

(iii). 2.034

[tex] = 2.034 \times {10}^{0} [/tex]

Step-by-step explanation:

bracket first in simplify

Answer:

It'll take 144 minutes for 5 pipes.

Step-by-step explanation:

[tex]{ \sf{6 \: pipes = 120 \: mins}} \\ { \sf{5 \: pipes = ( \frac{6}{5} \times 120) \: mins}} \\ \\ = { \sf{144 \: mins}}[/tex]

but practically, it seems to be abnormal. if 6 pipes take 120 mins, 5 pipes must takes a time greater than 120 mins cause amount of water flowing to the tank is decreasing.

But there is a possibility that pressure of water was increased for the case of five pipes, that's why it takes a time less than 120 mins. (t < 120)

Answer:

144 minutes

Step-by-step explanation:

here we use inverse proportion because the more pipes there are the less time is needed

the formula for inverse proportion is y = k/x

first we need to find k which is the constant

if y is the number of minutes and x is the number of pipes we can substitute these into the formula like so: 120 = k/6

to find k rearrange the formula to get k = 6 * 120 = 720

now that we have k we can substitute 720 (k) and 5 (x) into y = k/x

y = 720 / 5

y = 144

(y is the number of minutes in this case so the answer is 144 minutes)

Answer:

-9/38/100=-9/19/50

hope it helps!!!!!

Answer:

157.5

Step-by-step explanation:

14×180/16

= 315/2

= 157.5

Answer:

Step-by-step explanation:

16 sides  

n-2=14

14x 180 = 2250

2250/16 =157.5 = 158

Answer:

6 ft

Step-by-step explanation:

Answer:

U forgot to add zero while dividing

The quotient of 14.127 divided by 5.1 is 2.77

14.127 ÷ 5.1

To make the calculation easier without the use of a calculator :

Multiply both sides such that bith the dividend and divisor are integer values :

Multiply both by 1000

14.127 × 1000 = 14127

14127 51 × 1000 = 5100

Hence,

14127 ÷ 5100 = 14127 / 5100 = 2.77

Hence, 14.127 ÷ 5.1 = 2.77

Learn more : https://brainly.com/question/21416852

Step-by-step explanation:

x=y

x+2y=6

y+2y=6

3y=6

y=2

Step-by-step explanation:

x=y

x+2y=6

y+2y=6

3y=6

y=2

(Please vote me Brainliest if this helps!):

Answer:

2000

Step-by-step explanation:

Answer:

none

Step-by-step explanation:

38×2=76

43×2=86

45×2=90

Answer:

Equation of line is y = x - 5

Step-by-step explanation:

general equation of a line:

[tex]y = mx + c[/tex]

m » slope

c » y-intercept

for the slope, m :

[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1} } [/tex]

substitute in accordance of the points:

[tex]slope = \frac{ - 5 - 4}{0 - 9} = \frac{ - 9}{ - 9} \\ \\ m= 1[/tex]

for y-intercept :

[ consider point (0, -5) ]

[tex]y = mx + c \\ - 5 = (0 \times 1) + c \\ c = - 5[/tex]

Therefore, equation of line is

[tex]{ \boxed{y = x - 5}}[/tex]

Answer:

X=65

Step-by-step explanation:

X/5=13

X=13×5

=65

hope it helps!!!

Answer:

Blank1=4   blank2=2\3

Step-by-step explanation:

2\3 for 1 recipe

For 7 recipe = 7 x 2\3

= 14\2 x 2\3 -> take out the 2

14\3 = 14 divided by 3 is 4 with remainder of 2

So, 4 2\3

Answer:

The line drawn has a length of 6.4 cm.

Also it is divided into 4 equal parts.

Hence let the measure of the each equal part be ' x '

So x * 4 parts = 6.4 cm

=> x = 6.4 cm / 4

=> x = 1.6 cm

Hence the measure of each equal part is 1.6 cm.

Hence solved !

Step-by-step explanation:

Answer:

they travel 115 km/h long

Answer:

$123,200

Step-by-step explanation:

0.06 x 2 = 0.12

140,000 x 0.12 = 16,800

140,000 - 16,800 = 123,200

The original buyer paid the amount of $123,200 for the property.

The percentage is defined as a ratio expressed as a fraction of 100.

The property appreciated by 6% per year, so in two years it would have appreciated by 6% × 2 years = 12%.

Once we know the total appreciation, we can subtract that value from 100% to find the original purchase price as a percentage of the final sale price.

If the property appreciated by 12%, then the original purchase price must have been 100% - 12% = 88% of the final sale price.

Now, multiply the final sale price by the original purchase price as a percentage to find the original purchase price.

So, the original buyer paid the amount = 88% × $140,000 = $123,200

Therefore, the original purchase price was $123,200.

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ2

Answer:

320

Step-by-step explanation:

Distance covered by falcon in 2 hours=300*2=600 km

Distance covered by goose in 2 hours=140*2=280 km.

Falcon flew 600-280=320 km more than goose

Answer:

2 cups

Step-by-step explanation:

3 + 3 = 6 (one cup)

4 + 2 = 6 (two cups)

Answer:

[tex]2 \frac{2}{15} - 1 \frac{2}{3}[/tex]

[tex] = \frac{32}{15} - \frac{5}{3} [/tex]

[tex] = \frac{32 \times 1 - 5 \times 5}{15} [/tex]

[tex] = \frac{32 - 25}{15} [/tex]

[tex] = \frac{7}{15} [/tex]

Step-by-step explanation:

having denominator 6,

X/6= 2/3

X= 4

so, 4/6= 2/3

having numerator 10,

10/X= 2/3

X= 15

so, 10/15= 2/3

Answer:

If the function is the Area, then Area = length*width = x*(12-x) = 12x - x^2Domain is x>0, since you can't have a rectangle with negative length.

0 < x<6, If x is 7 then width would be 5, but x must be shorter

Step-by-step explanation:

Step-by-step explanation:

since the bases are the same all you have to do is just get the powers of both bases which is 3x + 1 and 10

you're then going to equate 3 x + 1 to 10 and then you have to make +1 cross to the other side making it become -1

you then can subtract 1 from 10 leaving you with 9

and at the LHS we have 3x

we are gonna get rid of the three by dividing it into itself and the 9 at the RHS then X = 3