Darren graphs the linear equations y=-2/5x+3 and 2x+5y=15. The graph look identical so he believes that the equations represent the same line. What mathematical argument can he construct to show that the two forms are equivalent?

Answers

Answer 1
Darren can change the 2x+5y=15 into slope-intercept form and it would be the same equation therefore on a graph it would be the same line because the slope and y-intercepts are the same
Answer 2

The slope and the intercept of both lines are the same. Because of that, the lines are identical.

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

Given that Darren graphs the linear equations y=-2/5x+3 and 2x+5y=15. Write both equations in the slope-intercept form and compare.

The general form of the equation of the line is:-

y = mx + c

y=-2/5x+3

Solve the equation to form their general form.

2x+5y=15.

5y = 15 - 2x

y = ( 15 / 5 ) - 2 / 5x

On comparing the two lines it is observed that the lines are having the same slope and intercept.

Therefore, the slope and the intercept of both lines are the same. Because of that, the lines are identical.

To know more about an equation of the line follow

brainly.com/question/18831322

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Related Questions

Determine the coordinate of the point shown. It’s on a (3,-5) (1,-2) (1.5, -2.5) (-2.5, 1.5)

Answers

Answer:

its a function

slope form:y+5=-1.18·(x-3)

(-2.5,1.5)

Step-by-step explanation:

Slope, m = 3, y-intercept, b = 5

Answers

Answer:

I can't help if I don't have enough to answer sorry

Step-by-step explanation:

What are the missing angles?

Answers

1. 51
2. 34
3. 95
4. 38
5. 47
6. 74
7. 59

I hope this helps!!

How to find the radius of a cylinder with only knowing it's height and diagonal thing here

Answers

The radius times pie equals the circumference. keep that in mind

there are 8 dinner rolls in a package. how many packages will be needed to feed 88 people if each person has 2 dinner rolls

Answers

Answer:

22

Step-by-step explanation:

8 times 10= 80 +8=88. now thats 11 packages. 11 times 2=22

The vertices of ΔMNO are M (1, 3), N (4, 9), and O (7, 3). The vertices of ΔPQR are P (3, 0), Q (4, 2), and R (5, 0). Which conclusion is true about the triangles?
The ratio of their corresponding sides is 1:2. 
The ratio of their corresponding angles is 1:2. 
They are similar by the definition of similarity in terms of a dilation. 
They are congruent by the definition of congruence in terms of rigid motions.​

Answers

C. They are similar by the definition of similarity in terms of a dilation.

The conclusion about the triangles is (c) they are similar by the definition of similarity in terms of a dilation.  

The coordinates are given as:

[tex]M = (1,3)[/tex]

[tex]N = (4,9)[/tex]

[tex]O = (7,3)[/tex]

[tex]P =(3,0)[/tex]

[tex]Q = (4,2)[/tex]

[tex]R = (5,0)[/tex]

Start by calculating the lengths of the triangles using the following distance formula

[tex]d = \sqrt{(x_1-x_2)^2 + (y_1 -y_2)^2}[/tex]

So, we have:

[tex]MN = \sqrt{(1 -4)^2 + (3 - 9)^2}[/tex]

[tex]MN = \sqrt{45}[/tex]

[tex]MO = \sqrt{(1 -7)^2 + (3 - 3)^2}[/tex]

[tex]MO = 6[/tex]

[tex]NO = \sqrt{(4 -7)^2 + (9 - 3)^2}[/tex]

[tex]NO = \sqrt{45}[/tex]

[tex]PQ = \sqrt{(3 -4)^2 + (0 - 2)^2}[/tex]

[tex]PQ = \sqrt{5}[/tex]

[tex]PR = \sqrt{(3 -5)^2 + (0 - 0)^2}[/tex]

[tex]PR = 2[/tex]

[tex]QR = \sqrt{(4 -5)^2 + (2 - 0)^2}[/tex]

[tex]QR = \sqrt{5}[/tex]

So, we have:

[tex]MN = \sqrt{45}[/tex]                  [tex]PQ = \sqrt{5}[/tex]

[tex]MO = 6[/tex]                       [tex]PR = 2[/tex]

[tex]NO = \sqrt{45}[/tex]                   [tex]QR = \sqrt{5}[/tex]

The above means that the triangles are not congruent.

So, we determine if they are similar by dividing the corresponding sides

[tex]k = \frac{MN}{PQ} = \sqrt{\frac{45}{5}} = 3[/tex]

[tex]k = \frac{MO}{PR} = \frac{6}{2} = 3[/tex]

[tex]k = \frac{NO}{QR} = \sqrt{\frac{45}{5}} = 3[/tex]

The scale factor is 3.

Hence, the triangles are similar

Read more about similar triangles at:

https://brainly.com/question/14285697

solve each system by graphing.​

Answers

This is how I believe it would look like

I really need help please help me

Answers

Answer:

top right

Step-by-step explanation:

If you imagine yourself building with that model you can see its that one

are any of these equivalent to 3/8 ?
2/7
8/3
9/24
5/18

Answers

Answer:

9/24 is

Step-by-step explanation:

Yup

-BaconSoup the scientist LOL

Answer:

9/24

Step-by-step explanation:

[tex]\frac{2}{7}= 0.28571428571\\\\\frac{3}{8}= 0.375\\\\\frac{2}{7}\neq \frac{3}{8}\\\\ \frac{8}{3}= 2.666...\\\\\frac{8}{3} \neq \frac{3}{8}\\\\\frac{9}{24}=\frac{9/3}{24/3} =\boxed{\frac{3}{8}}\\\\ \boxed{\frac{9}{24}=\frac{3}{8}}\\\\\frac{5}{18}= 0.27777...\\\\\frac{5}{18} \neq \frac{3}{8}[/tex]

Hope this helps.

3. Which is equivalent to the expression below?
4.5m + 8 - 2.3m - 3.5
A.6.7m
B. 6.8m + 4.5
C 2.2m + 11.5
D. 2.2m + 4.5

Answers

Answer:

D. 2.2m + 4.5

Step-by-step explanation:

The ratio of employees who own a red car to employees who own a black car is
1:5. If there are 6 employees who own a red car, how many employees own a
black car? *

Answers

Answer:

There would be 30 black cars.

Since the ratio is 1:5

And we know that there are 6 red cars,

we basically just input it in our ratio

so it would look like 6:x

Now, we just have to plug in for x.

To do that, you have to multiply 6 by 5

To match the ratio.

So that would give us 6:30

And if we divide by 5 we should get our original ratio.

I know this seems confusing haha, but I hope you get it, it's not as hard as it looks !!

Which point is a solution to this system of inequalities?
y 6
A) (7,-8)
B) (2,-3)
C) (5,-2)
D) (4,1)

Answers

Answer:

h

Step-by-step explanation:

Answer:

the answer is  c

Step-by-step explanation:

Need answer quick small information

Answers

Answer:

B

Step-by-step explanation:

Factorise: x*x-4*4

(x+4)(x-4)

so the answer is B.

Hope this helps

Merry Christmas!

B-(x+4)(x-4)
I sure about this answer

What was the battery’s charging level when the charging began?

Answers

Answer:

40%

Step-by-step explanation:

The line starts on 40%

Answer:

40%

Step-by-step explanation:

th line stars by the 40

Are x and 1/x like terms?

Answers

Answer:

no

Step-by-step explanation:

we'll say x=5

5 does not equal 1/5

no, but x also means 1 and 1/x is different

Find the domain of the vector function. (Enter your answer in interval notation.) r(t) = t − 2 t + 2 i + sin(t)j + ln(36 − t2)k

Answers

Answer:

The domain of the vector function is :  ( -6, -2) ∪ ( -2, 6)

Step-by-step explanation:

The given vector function  can be correctly expressed as:

[tex]r(t) = \dfrac{t-2}{t+2}i + sin \ tj + In(36-t^2) k[/tex]

The domain of the given function can be determined by finding the domain of each respective component.

To start with [tex]\dfrac{t-2}{t+2}[/tex]

Not defined, t = -2

Thus, the domain of the first component of the vector = [tex]( - \infty , -2) \cup ( 2, \infty )[/tex]

The 2nd component = sin t

No restriction on t

The 3rd component of the function is ㏑(36 - t²)

Let recall that natural is defined for +ve numbers,

i.e.

36 - t² > 0

(6 + t) (6 - t) > 0

Thus, it satisfies the inequality  -6 < t < 6

The third domain = (-6,6)

Overall;

The domain of the vector function is :  ( -6, -2) ∪ ( -2, 6)

Domain of a function is the set all possible inputs for that function.The domain of the given vector function is,

[tex](-6, -2) \cap (-2,6)[/tex]

What is domain?

Domain of a function is the set all possible inputs for that function.

Given information-

The vector function given in the problem is,

[tex]r(t)=\dfrac{t-1}{t+2} \hat i++sin(t)\hat j+ln(49-t^2)\hat k[/tex]

To find the domain of the above vector function, we need to find the domain of each function of vector quantity.

Lets find the domain of [tex]\hat i[/tex] first which is given by,

[tex]\dfrac{t-2}{t+2}[/tex]

This function is defined at all values except, t equals to -2 as the function is not defined at,

[tex]t=-2[/tex]

Hence the domain of component [tex]\hat i[/tex] is,

[tex](-\infty, -2) \cap (\infty,2)\\[/tex]

Lets find the domain of [tex]\hat j[/tex] first which is given by,

[tex]\sin(t)[/tex]

Two trigonometry function sine and cosine defined for all real number.

This function is defined at all real numbers. Hence the domain of component [tex]\hat j[/tex] is

Lets find the domain of [tex]\hat k[/tex] first which is given by,

[tex]\ln(36-t^2)[/tex]

Set the above argument greater than zero to find where the expression is defined.Thus,

[tex](36-t^2)>0\\(6+t)(6-t)>0[/tex]

Therefore,

The domain of it should be [tex](-6,6)[/tex]

Hence the domain of the given vector function is,

[tex](-6, -2) \cap (-2,6)[/tex]

Learn more about the domain here;

https://brainly.com/question/10197594


The pottery store can make 176 coffee mugs in an 8 hour day. How many mugs can they make in one hour
Watch your units!

Answers

Answer:

22 per hour

Step-by-step explanation:

8 divided by 176 lol Hope I did it right tho ;-;

Answer:

they can make 22 in one hour.

Solve the system for X:
y=3x +4
у=х+8 x +10

Answers

Answer: The answers are x=y/3–4/3, and x=y/9–10/9.

Step-by-step explanation: You’ll need to isolate the variable by dividing each side by factors that don't contain the variable.

A pet store sells dog treats and the prices are represented
in the graph
X = number of treats
y = cost (in dollars)
Select the true statement.
Select one
Each treat costs $0.50
Each treat costs $3
Each treat costs $2
Each treat costs 51

Answers

Answer: 1$

Step-by-step explanation:

at the zoo,the ratio of monkeys to gorillas is 5:1​

Answers

Answer:

thats a statement

Step-by-step explanation:

What is the product of 3.4 x 10-14 and 1.8 x 10287
O6.12 x 1014
O9.4x 1014
O5.2 x 1042
O6.12 x 1042

Answers

The last one is the correct answer I got it right

Ronda has 34.27 in her checking account. She deposits $25.00 into her account and then writes a check for $59.99. What is Ronda's account balance now?

Answers

-0.72 because u can’t write a check and u don’t have the funds

Solve the system, enter ur answer as an ordered triple.

Answers

Answer:

x = 1, y = -1, z = 3

Step-by-step explanation:

x - 2y + 2z = 9

y + 2z = 5

z = 3

According to the last equation, z is equal to 3 so we can plug that in and our new 2 equations will be:

x - 2y + 6 = 9

y + 6 = 5

We can subtract 6 from both sides of the second equation to end up with:

y = -1

Now plugging this into the first equation, we have:

x + 2 + 6 = 9

x + 8 = 9

Subtract 8 from both sides

x = 1



What is |-8|?
-16
-8
08
16

Answers

Answer:

it's 8

Step-by-step explanation:

lol girl I did this in the first day of school in 6th and I got the same answer , -8 is a negative, your supposed to put it back to a non negative when something is negative change it back to positive it's 8!

Solve the formula for the indicated variable.
B=yv+y​, for v
The solution is v=?

Answers

Answer: v = B/y -1

B = yv + y = (v + 1)y

=> B/y = v + 1

⇔ [tex]v=\frac{B}{y}-1[/tex]

Step-by-step explanation:

A store orders 22 boxes of light bulbs. Each box has 148 bulbs.
Which is the best estimate of the total number of bulbs the store orders?


plzzz answer.

Answers

Answer:

estimate, 3000. exact answer 3256

Step-by-step explanation:

hope this helps

A tv is on sale for 24% off. If the original price was $800, find the sales price?

Answers

Answer:

0.03

Step-by-step explanation:

calculator calculator calculator

Answer:

$608

Step-by-step explanation:

Turn the percentage into a decimal

$800(0.24) = 1$92

So you need to subtract 192 of 800

800 - 192 = $608

Hope this helps dude

This is Amy's box of candies.
She has already eaten 6 of them.

What fraction of the candies has Amy eaten?

Answers

Answer:

[tex] \frac{6}{9} [/tex]

or

[tex] \frac{2}{3} [/tex]

Step-by-step explanation:

There are nine in total and she has eaten 6, so the fraction would be 6/9.

If you need to simplify it it would be 2/3.

What’s 41/12 I need some explanation

Answers

41/12 is 3.4 or 341%

My house is 20 miles from yours, but on the map it is only 4 mm away.
What is the scale of the map?
A. 1 mm = 5 mi
B. 1 mm = 20 mi
C. 1 mi= 20 mm
D. 20 mm = 4 mi
E. 5 mi = 4 mm

Answers

Answer:

A. 1mm = 5mi

Step-by-step explanation:

20 mi divided by 4 mm would simplify down to 5 mi per 1mm. If there is 4 mm then there is 5mi*4mm which equals out to 4 mm = 20 mi.

A scale of the map is the relationship between the distance on the map to the actual distance. The scale of the map is 1 mm: 5 miles (ml). Thus the option A is the correct option.

To find out the scale of the map, we have to know about scaling of map.

What is the scaling of map?

The scaling of map is the ratio or relationship between the distance of the map to the original distance.

Given information-

The distance of the two houses on the ground is 20 miles.

The distance of the two houses on the map is 4 mm.

Suppose the scale of the map is [tex]s[/tex].

As the 20 miles distance on the ground is same as the 4 mm distance on the map.

Thus the scale of the map can be given as,

[tex]s=\dfrac{4\rm mm}{20\rm miles} \\s=\dfrac{1\rm mm}{5\rm miles}[/tex]

Hence the scale of the map is 1 mm: 5 miles (ml). Thus the option A is the correct option.

Learn more about the scale of map here;

https://brainly.com/question/10283478

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