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
77julia77 [94]
3 years ago
15

A candidate for class president received at least 4 times as many votes as his opponent did. If the winning candidate received a

t least 716 votes, which inequality could be used to find how many votes his opponent received?
Mathematics
1 answer:
Shtirlitz [24]3 years ago
7 0

Answer:

4x ≤ 716

Step-by-step explanation:

(say x = # of votes the opponent received)

Since the winning candidate got at least 716 votes, we can know that there will be <em>a greater than or equal to sign, and that the greater side will point to the 716</em>: <em>ₙ ≤ 716</em>.

Also, if the winning candidate got exactly 716 votes, then that equation will look like this: <em>4x = 716</em>. We can use that left side into our inequality: 4x ≤ 716.

You might be interested in
Brianna is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $3.75. Brianna spent $18.75 a
maxonik [38]

Answer:

6 games and 3 rides

Step-by-step explanation:

Let the number of games Brianna played be x,

and the number of rides she went on be y.

Total cost for games= 1.25x

Total cost for rides= 3.75y

Since number of games is twice the number of rides,

x= 2y -----(1)

Total costs= cost of games +cost of rides

18.75= 1.25x +3.75y

Multiply the whole equation by 4 to remove the decimals:

75= 5x +15y

Simplify by dividing the whole equation by 5:

15 = x + 3y

Label the equation:

x +3y= 15 -----(2)

Although we can solve these 2 equations by substitution, since the question requires us to graphically solve, we have to graph 2 linear lines.

I will choose 3 points to plot on the graph for each equation:

x= 2y -----(1)

\begin{tabular}{|c|c|c|c|} \cline{1-4}x & 2(1) = 2&2(2) = 4&2(3) = 6\\ \cline{1-4}y & 1 &2&3\\ \cline{1-4}\end{tabular}

x +3y= 15 -----(2)

x= -3y +15

\begin{tabular}{|c|c|c|c|} \cline{1-4}x &  -3(1)+15= 12& -3(2)+15= 9& -3(3)+15= 6\\ \cline{1-4}y & 1 &2&3\\ \cline{1-4}\end{tabular}

Let's plot these points on a graph paper. Then, join them with a straight line for each straight line graph. Please see the attached picture for the graph.

From (1): y= ½x

From (2): 3y= 15 -x

y= 5 -⅓x

From the graph, the solution of the equation is (6,3). The solution is the point on the graph in which the 2 lines intersect.

x- coordinate: 6

y- coordinate: 3

Thus, Brianna played 6 games and went on 3 rides.

8 0
3 years ago
Read 2 more answers
For what value of c is the function defined below continuous on (-\infty,\infty)?
kozerog [31]
f(x)= \left \{ {{x^2-c^2,x \ \textless \  4} \atop {cx+20},x \geq 4} \right&#10;

It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if 
</span><span>\lim_{x \rightarrow 4} \  f(x) = f(4)

</span><span>In notation we write respectively
</span>\lim_{x \rightarrow 4-} f(x) \ \ \ \text{ and } \ \ \ \lim_{x \rightarrow 4+} f(x)

Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence 
\lim_{x \rightarrow 4-} f(x) = \lim_{x \rightarrow 4-} (x^2 - c^2) = 16 - c^2

Thus these two limits, the one from above and below are equal if and only if
 4c + 20 = 16 - c²<span> 
 Or in other words, the limit as x --> 4 of f(x) exists if and only if
 4c + 20 = 16 - c</span>²

c^2+4c+4=0&#10;\\(c+2)^2=0&#10;\\c=-2

That is to say, if c = -2, f(x) is continuous at x = 4. 

Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers (-\infty, +\infty)

4 0
3 years ago
Rezolvati 1) -2x+1= -7 2) 6+3x= -54+x 3) 2x+9= 7 +x 4) 3-2x= -x -6 5) -3(x+1) = -6 6) -4 (x -2)=12 7) -7(x-3)= -14
Natalija [7]
<span>Răspunsurile sunt

1. x= 4
2. x = -30
3. x = -2
4. x = 9
5. x = 1
6. x = -1
7. x = 5
</span>
3 0
3 years ago
Find the area of the kite.
Black_prince [1.1K]
Your answer is 36. hope it helps!
6 0
2 years ago
Read 2 more answers
How to tell if a 15 year old boy likes me quiz for 13 year olds?
EleoNora [17]
Http://www.allthetests.com/quiz30/quiz/1379266484/Does-He-Like-you-Back-10-13-year-olds-ONLY
3 0
3 years ago
Other questions:
  • Solve each inequality.Graph the solution on a number line.
    12·1 answer
  • What is the distance between the points A(2, -1) and B(-4, 2)
    9·1 answer
  • Two similar rectangular prisms have a scale factor of 3.4 and
    15·1 answer
  • (5, 3) is the solution to the system of linear equations:<br><br> True<br> False
    13·2 answers
  • There are 23 boys and 35 girls on the school's track and field team. After q boy at random to represent the school for an event
    12·1 answer
  • A number,n,is multiplied by -5/8. The product is -0.4. What is the value of n?
    14·2 answers
  • Find the equation of the line.<br> Use exact numbers.<br> y =
    14·2 answers
  • A hot air balloon is released into the air. During its straight ascent, the angle of elevation was 15° and, 3 minutes later, the
    10·1 answer
  • Like for like ? follow for follow ?
    10·1 answer
  • Between which two numbers is Negative 1.5 located on a number line? A number line going from negative 5 to positive 3 in increme
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!