1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olga2289 [7]
2 years ago
7

Simone claims that the slope of the line through (-2, 7) and (3, 0) is the same as the slope of the line through (2, 1) and (12,

-13) is simone's claim true or false
Mathematics
1 answer:
JulijaS [17]2 years ago
3 0

Answer:

Simone is correct

Step-by-step explanation:

Given

Line 1:

(x_1,y_1) = (-2, 7)

(x_2,y_2) = (3, 0)

Line 2:

(x_1,y_1) = (2, 1)

(x_2,y_2) =(12, -13)

Required

Is Simone correct?

Slope (m) is calculated using:

m = \frac{y_2 - y_1}{x_2 - x_1}

For Line 1

m = \frac{0 - 7}{3 - (-2)}

m = \frac{0 - 7}{3 +2}

m = \frac{-7}{5}

m = -\frac{7}{5}

For Line 2:

m = \frac{-13 - 1}{12 -2}

m = \frac{-14}{10}

Divide by 2/2

m = \frac{-14/2}{10/2}

m = \frac{-7}{5}

m = -\frac{7}{5}

By comparison, both lines have the same slope.

Hence, Simone is correct

You might be interested in
PLS HELP The pair of triangles below have two corresponding parts marked as congruent. What additional information is needed for
bulgar [2K]
The correct answer is a because it is a
7 0
3 years ago
8.4×0.5 showing work​
Katen [24]
Can u add a picture?
8 0
2 years ago
3,6,11,18,27,38
MakcuM [25]

Answer:  The pattern is x^2+2

where x is the term number

Example: the 5th term is 27 because x = 5 leads to x^2+2 = 5^2+2 = 27

=================================================

Explanation:

  • The jump from 3 to 6 is +3
  • The jump from 6 to 11 is +5
  • The jump from 11 to 18 is +7
  • The jump from 18 to 27 is +9
  • The jump from 27 to 38 is +11

The pattern of jumps is: 3, 5, 7, 9, 11

Those increments are going up by 2 each time.

Since we have a consistent pattern of increments, this means that the sequence follows a quadratic model.

Quadratics are stuff like x^2+7x+10 or 3x^2-7. The leading term has an exponent of 2.

-----------

If x is the term number and y is the term itself, then we have these points

(1,3)

(2,6)

(3,11)

(4,18)

(5,27)

(6,38)

The x coordinates increase by 1 each time. The y coordinates are the terms given by your teacher.

Pick exactly 3 of those points. I'll pick the first 3.

Why 3? Because we'll have 3 unknowns to solve for, in which we'll need 3 equations.

  • Plug (x,y) = (1,3) into y = ax^2+bx+c, then simplify. You should get the equation a+b+c = 3
  • Repeat for (x,y) = (2,6) and you should get 4a+2b+c = 6
  • Repeat for (x,y) = (3,11) and you should get 9a+3b+c = 11

-----------

We have this system of equations

\begin{cases}a+b+c = 3\\ 4a+2b+c = 6\\9a+3b+c = 11\end{cases}

There are a number of methods to solve this system. Substitution is what I'll go for.

Solve the first equation for c

a+b+c = 3

c = 3-a-b

Then use substitution.

4a+2b+c = 6

4a+2b+(3-a-b) = 6

3a+b+3 = 6

3a+b = 6-3

3a+b = 3

and

9a+3b+c = 11

9a+3b+(3-a-b) = 11

8a+2b + 3 = 11

8a+2b = 11-3

8a+2b = 8

We now have this reduced system of equations.

\begin{cases}3a+b = 3\\8a+2b = 8\end{cases}

I'll skip the steps as this solution is getting very lengthy as it is. The basic idea is to use substitution again. You should find that a = 1 and b = 0 form the solution set here.

Use those values to find c

c = 3-a-b

c = 3-1-0

c = 2

-----------

To summarize the previous section, we have these solutions:

a = 1, b = 0, c = 2

Therefore the equation y = ax^2+bx+c becomes y = 1x^2+0x+2 aka y = x^2+2. This lets us find any term.

Let's test it out.

  • If x = 1, then y = x^2+2 = 1^2+2 = 3
  • If x = 2, then y = x^2+2 = 2^2+2 = 6
  • If x = 3, then y = x^2+2 = 3^2+2 = 11

And so on. I'll let you test the other x values (4 through 6).

Another way to confirm the answer is to subtract 2 from each item in the original set {3,6,11,18,27,38} and you'll end up with {1,4,9,16,25,36}. This is the list of perfect squares. It shows that term x is simply x^2 but add on 2 so things are adjusted accordingly.

Side note: you can use a tool like GeoGebra or WolframAlpha to quickly solve the system of equations. However, I recommend it only as a means to check your answer rather than do the work for you.

7 0
2 years ago
I need help figuring out how to do this.
MrRa [10]
The answer will be letter "B" you take 450 times it by 4.29
and u get 1,930.50
7 0
2 years ago
Read 2 more answers
Bella and Heather put some money into their money boxes every week. The amount of money (y), in dollars, in their money boxes af
Hatshy [7]

Answer:

\boxed{ \text{B. 10 weeks, \$310 }}\\

Step-by-step explanation:

We have two conditions:

\begin{array}{lrcll}(1) & y & = & 25x + 60 & \\(2) & y & = & 30x + 10 & \\ & 25x + 60 & = & 30 x + 10 & \text {Set (1) = (2)} \\ & 50 & = & 5x & \text{Subtracted 25x from each side} \\& x & = & 10 &\text{Divided each side by 5} \\\end{array}\\$ $\\\boxed{ \textbf{The number of weeks is }x = 10}\\

   

    Bella: y = 25x + 60 = 25(10) + 60 = 250 + 60 = 310  

Heather: y = 30x + 10  = 30(10) +  10 = 300 + 10  = 310

7 0
3 years ago
Other questions:
  • In a if P is equals to 3 cm BD is equal to 3.9 CM PQ is equals to 3.6 cm and q f is equals to 2.4 CM state PQ is parallel to EF​
    9·1 answer
  • Please answer this question now
    8·2 answers
  • What is the hypotenuse of an triangle with sides 6 and 8 and angles 30 and 60 degrees?
    7·1 answer
  • A circular gear turns 60 per hour. through how many radians does it turn in a 24-hour day?
    13·2 answers
  • Y=5x-4
    9·1 answer
  • Is "when it comes to pets, do you prefer cats" biased or not? explain.
    13·2 answers
  • What is the same as 6.93 divided by 0.4
    8·1 answer
  • What is the value of the expression? –13.7+(–5+2.7)
    11·2 answers
  • How many pints of blood does a person have for every 14 lbs of body weight?
    7·2 answers
  • The sum of the second and third terms of G.P is six times the fourth term. Find the two possible values of the common ratio​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!