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
quester [9]
3 years ago
9

Which of the following give an equation of a line that passes through the point (6/5,-19,5) and is parallel to the line that pas

ses through the organ and point (-2,-12)
A. y= 6x-11
B. y= 6x-19/5
C. y= 6x-6/5
D. y= 6x+1
Mathematics
1 answer:
Ilya [14]3 years ago
6 0
Parallel lines, have the same slope, so the slope of the line through 0,0 and -2,-12, is the same as for the line running through (6/5,-19.5) as well, so what is it anyway?

\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
&({{ 0}}\quad ,&{{ 0}})\quad 
%   (c,d)
&({{ -2}}\quad ,&{{ -12}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-12-0}{-2-0}\implies \cfrac{-12}{-2}\implies 6

so, we're looking for the equation of a line whose slope is 6, and goes through (6/5,-19/5)

\bf \begin{array}{lllll}
&x_1&y_1\\
%   (a,b)
&({{ \frac{6}{5}}}\quad ,&{{ -\frac{19}{5}}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 6
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-\left( -\frac{19}{5} \right)=6\left(x-\frac{6}{5}  \right)
\\\\\\
y+\cfrac{19}{5}=6x-\cfrac{36}{5}\implies y=6x-\cfrac{36}{5}-\cfrac{19}{5}\implies y=6x-\cfrac{55}{5}
\\\\\\
y=6x-11
You might be interested in
F(x) ≥ -(x+4)^2<br>axis of symmetry: <br>vertex:
BlackZzzverrR [31]

Answer:

so the vertex is (-4, 0) and the axis of symmetry is x=-4

Step-by-step explanation:

f(x) ≥ -(x+4)^2

f(x) ≥ -(x- -4)^2

this is in the form

f(x)> a(x-h)^2 +k

where (h,k) is the vertex and h is the axis of symmetry

so the vertex is (-4, 0) and the axis of symmetry is x=-4

6 0
3 years ago
Question 6(Multiple Choice Worth 1 points) (06.01 LC) Choose the correct classification of 5x + 2x2 − 8 by number of terms and b
Yakvenalex [24]

Question 7: Choose the correct simplification of the expression (3x − 6)(2x2 − 4x − 5)

Answer:

7. 6x³ - 12x² + 12x + 15

Step-by-step explanation:

(3x-6)(2x² - 4x - 5)

3x • 2x² = 6x³

3x • -4x = -12x²

3x • -5 = -15

-6 • 2x² = -12x²

-6 • -4x = 24x

-6 • -5 = 30

combine terms

6x³ - 12x² - 15 - 12x² + 24x + 30

combine like terms

6x³ - 24x² + 24x + 15

hope this helps :)

in the future, only ask one question per brainly submission. thanks!

7 0
3 years ago
From 126 ounces to 48 ounces nearest percent
lianna [129]
That is a decrease of 78 ounces
5 0
3 years ago
Park rangers tagged fish in a state park to track their population. The function f(x)=200(1.05)x can be used to find the populat
Sedbober [7]

The given exponential function can be used to determine the

population of the fish at different times.

Response:

1. 200

2. 0.05

3. Please find attached the graph of the exponential function and the table

\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}

4. Range; [0, ∞)

Domain: [200, ∞)

5. 346 fishes (approximate value)

<h3>How is the population of the fish obtained from the exponential function?</h3>

The given function is f(x) = 200·(1.05)ˣ

1. The initial population is given by the value of the function when x = 0,

which is given as follows;

At x = 0, f(0) = 200·(1.05)⁰ = 200

  • The initial population of the fish is <u>200</u>

2. The rate of growth of the fish from the exponential function is given as follows;

The growth factor = 1.05

  • The growth rate =<u> 0.05</u>

3. Please find attached the graph of the exponential function created

with MS Excel.

The asymptote of the exponential function is the line, <u>y = 0</u>

The table of values is presented as follows;

\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}

4. The domain is the possible x-values which is; 0 ≤ x < ∞

The range is the possible y-values which is; 200 ≤ f(x) < ∞

Which gives;

  • Domain; [0, ∞)
  • Range: [200, ∞)

5. The population of the fish after 11 years is f(11) = 200·(1.05)¹¹

f(11) = 200 × (1.05)¹¹ ≈ 342

  • The population of the fish after 11 years is <u>346 (fishes)</u>

Learn more about exponential function here:

brainly.com/question/15662160

3 0
3 years ago
A club is hosting a party split the kids into groups so there are equal number of children in each group
DerKrebs [107]
How many kids are in the club?

3 0
3 years ago
Other questions:
  • What two numbers does the square root of 85 fall between?
    11·1 answer
  • On a map, Nancy uses a ruler to find the approximate distance between her town and California. The distance on the map is 35 cen
    15·2 answers
  • Sonia has three bracelets. she wears them all at the same time but in a diffrient order each day how many diffrent bracelet comb
    6·1 answer
  • Compare the value of the 8 in 4,428.37 and 92.85
    7·2 answers
  • Which of the following inverse functions are defined for x=-1/2? Select all thst apply.
    14·2 answers
  • A spherical balloon has a ​-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the b
    6·1 answer
  • protocol for flushing a cooling water system at a nuclear reactor requires that a drain valve be opened while the fill pumps are
    13·1 answer
  • In the diagram, JKLM~EFGH. Find the scale factor of JKLM TO EFGH. Plz help
    12·1 answer
  • Pls help ASAP will mark Brainlyest!!
    13·2 answers
  • Please help me with this question
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!