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
Alex787 [66]
3 years ago
6

The mathematics department sponsors Math Family Fun Night every year. In year 1, there were 35 participants. In year 3, there we

re 57 participants. They determined that they could write an equation of a line using (1,35) and (3,57) as their two points. What equation of a line can the Math department use to predict the amount of participants, y, for any given year, x?
A. y=111x+24
B. y=11x−24
C. y=22x+35
D. y=11x+24
Mathematics
2 answers:
Gala2k [10]3 years ago
8 0

Simple Answer:

D.  y=11+24

Doss [256]3 years ago
4 0
The equation of a line:
y=mx+b

(1,35) \\
x_1=1 \\ y_1=35 \\ \\
(3,57) \\ x_2=3 \\ y_2=57 \\ \\ 
m=\frac{y_2-y_1}{x_2-x_1}=\frac{57-35}{3-1}=\frac{22}{2}=11 \\ \Downarrow \\ y=11x+b \\ \hbox{plug the values of } x_1 \hbox{ and } y_1 \hbox{ into the equation:} \\
35=11 \times 1 + b\\
35=11+b \\
35-11=b \\
b=24 \\ \\
\boxed{y=11x+24}

The answer is D.
You might be interested in
Square root of 2tanxcosx-tanx=0
kobusy [5.1K]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/3242555

——————————

Solve the trigonometric equation:

\mathsf{\sqrt{2\,tan\,x\,cos\,x}-tan\,x=0}\\\\ \mathsf{\sqrt{2\cdot \dfrac{sin\,x}{cos\,x}\cdot cos\,x}-tan\,x=0}\\\\\\ \mathsf{\sqrt{2\cdot sin\,x}=tan\,x\qquad\quad(i)}


Restriction for the solution:

\left\{ \begin{array}{l} \mathsf{sin\,x\ge 0}\\\\ \mathsf{tan\,x\ge 0} \end{array} \right.


Square both sides of  (i):

\mathsf{(\sqrt{2\cdot sin\,x})^2=(tan\,x)^2}\\\\ \mathsf{2\cdot sin\,x=tan^2\,x}\\\\ \mathsf{2\cdot sin\,x-tan^2\,x=0}\\\\ \mathsf{\dfrac{2\cdot sin\,x\cdot cos^2\,x}{cos^2\,x}-\dfrac{sin^2\,x}{cos^2\,x}=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left(2\,cos^2\,x-sin\,x \right )=0\qquad\quad but~~cos^2 x=1-sin^2 x}

\mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\cdot (1-sin^2\,x)-sin\,x \right]=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2-2\,sin^2\,x-sin\,x \right]=0}\\\\\\ \mathsf{-\,\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}\\\\\\ \mathsf{sin\,x\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}


Let

\mathsf{sin\,x=t\qquad (0\le t


So the equation becomes

\mathsf{t\cdot (2t^2+t-2)=0\qquad\quad (ii)}\\\\ \begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{2t^2+t-2=0} \end{array}


Solving the quadratic equation:

\mathsf{2t^2+t-2=0}\quad\longrightarrow\quad\left\{ \begin{array}{l} \mathsf{a=2}\\ \mathsf{b=1}\\ \mathsf{c=-2} \end{array} \right.


\mathsf{\Delta=b^2-4ac}\\\\ \mathsf{\Delta=1^2-4\cdot 2\cdot (-2)}\\\\ \mathsf{\Delta=1+16}\\\\ \mathsf{\Delta=17}


\mathsf{t=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{2\cdot 2}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{4}}\\\\\\ \begin{array}{rcl} \mathsf{t=\dfrac{-1+\sqrt{17}}{4}}&\textsf{ or }&\mathsf{t=\dfrac{-1-\sqrt{17}}{4}} \end{array}


You can discard the negative value for  t. So the solution for  (ii)  is

\begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{t=\dfrac{\sqrt{17}-1}{4}} \end{array}


Substitute back for  t = sin x.  Remember the restriction for  x:

\begin{array}{rcl} \mathsf{sin\,x=0}&\textsf{ or }&\mathsf{sin\,x=\dfrac{\sqrt{17}-1}{4}}\\\\ \mathsf{x=0+k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=arcsin\bigg(\dfrac{\sqrt{17}-1}{4}\bigg)+k\cdot 360^\circ}\\\\\\ \mathsf{x=k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=51.33^\circ +k\cdot 360^\circ}\quad\longleftarrow\quad\textsf{solution.} \end{array}

where  k  is an integer.


I hope this helps. =)

3 0
3 years ago
Help me with the question
Norma-Jean [14]

Answer:

B

Step-by-step explanation:

B is the only one that is actually a point on the graph

3 0
3 years ago
2. There are 42 persons in a mathematics class, and everyone of them drinks either coffee or grape milk at
Basile [38]

Answer:

1.  8

2.  24

Step-by-step explanation:

The number of persons that drink grape milk only :

18 - 10 = 8

The number of persons that drink coffee :

42 - 8 = 34

The number of persons that drink coffee only :

34 - 10 = 24

5 0
2 years ago
Please help me with this.
zheka24 [161]

The sin A is equal to 12/13 and the tan (A) is equal to 12/5.

<h3>RIGHT TRIANGLE</h3>

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: hypotenuse^2=(leg_1)^2+(leg_2)^2. And the main trigonometric ratios are:

sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg} \\ \\

The question gives cos (A)=5/13. If cos (A) is represented by the quotient between the adjacent leg and the hypotenuse, you have:

adjacent leg=5

hypotenuse=13

Therefore, you can find the opposite leg of A from Pythagorean Theorem, see below.

hypotenuse^2=(leg_1)^2+(leg_2)^2\\ \\ 13^2=5^2+(leg_2)^2\\ \\ 169=25+(leg_2)^2\\ \\ 144=(leg_2)^2\\ \\ leg_2=12

Thus, the opposite leg is equal to 12. Now, you can find sin (A) since:

sin(A)= \frac{opposite\;leg}{hypotenuse}=\frac{12}{13}

Finally, you can find the tan (A) since:

tan(a )= \frac{opposite\;leg}{adjacent\;leg}=\frac{12}{5}

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ1

7 0
2 years ago
What is the slope of the line through (-10, 1) and (0,-4)?
ANEK [815]

Answer:

m=-1/2

Step-by-step explanation:

m=-4-1/0- -10

m=-1/2

8 0
3 years ago
Other questions:
  • Your cell phone plan costs $39.99 per month plus $0.11 for each text message you send or receive. You have at most $45 to spend
    15·1 answer
  • Did I put the correct answer? Please let me know ASAP! See the attachment.
    9·1 answer
  • Simplify: -m(7m + 3) – 4m2<br>A. 12m+4<br>B. -11m2-3m<br>C. -11m2+6m<br>D.5 m + 4 ​
    5·1 answer
  • What is the difference 1/8-3/10. A. -7/40 B.-3/40 C. 7/40 D. 17/40
    7·1 answer
  • A solid piece of wood shaped as a cylinder with an 8 centimeter diameter is cut shown
    6·2 answers
  • Howard works 7 hours each day. He earns $8.00 per hour. Which number sentence shows the total amount of money he earns in one da
    10·1 answer
  • Why is it valid to say that both a function and its inverse describe the same relationship
    5·1 answer
  • What is the value of S5?<br> S5 = <br> RETRY
    8·1 answer
  • a plant normally sells $6.50. today all plants are discounted by 25%. What is the sale price of the plant ?
    5·2 answers
  • What is the mean deviation of 17,18,18,15,15,14,5,12,6,20
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!