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
skelet666 [1.2K]
3 years ago
12

Over the last three evenings, Donna received a total of 129 phone calls at the call center. The third evening, she received 3 ti

mes as many calls as the first
evening. The second evening, she received 9 more calls than the first evening. How many phone calls did she receive each evening?​
Mathematics
1 answer:
lakkis [162]3 years ago
5 0

Answer:

Number of calls received in 1st evening = 24

Number of calls received in 2nd evening = 33

Number of calls received in 3rd evening = 72

Step-by-step explanation:

Let

number of calls received in first evening be "x"

number of calls received in 2nd evening be "y"

number of calls received in 3rd evening be "z"

Total, in 3 evenings, we have 129 phone calls, so we can write:

x + y + z = 129

3rd evening, 3 times as first evening. We can write:

z = 3x

2nd evening, 9 MORE THAN FIRST. So we can write:

y = 9 + x

Now we replace 2nd and 3rd equation in 1st equation to get:

x + y + z = 129

x + 9 + x + 3x = 129

Now, first, we solve for x:

x + 9 + x + 3x = 129\\5x+9=129\\5x=120\\x=24

Solving for y:

y = 9 + x

y = 9 + 24

y = 33

Solving for z:

z = 3x

z = 3(24)

z = 72

Thus,

Number of calls received in 1st evening = 24

Number of calls received in 2nd evening = 33

Number of calls received in 3rd evening = 72

You might be interested in
How many points need to be removed from this graph so it will be a function?​
finlep [7]

Answer:

3 points

Step-by-step explanation:

in a function, an x-value must have only one y-value correlated with it.

So, you would need to remove either (-3, 2) or (-3, 3)

And, you would need to remove either (2, -2) or (2, -4)

<em>And, </em>you would need to remove either (1, 4) or (1, -4)

So--you need to remove 3 points in total for this to be a function.

[a y-value can have multiple x-values. the two points at -4 are allowed, and do not need to be removed for both of them to be there]

8 0
1 year ago
part 3. Find the value of the trig function indicated, use Pythagorean theorem to find the third side if you need it.​
Nat2105 [25]

Answer:  \bold{9)\ \sin \theta=\dfrac{1}{3}\qquad 10)\ \sin \theta = \dfrac{4}{5}\qquad 11)\ \cos \theta = \dfrac{\sqrt{11}}{6}\qquad 12)\ \tan \theta = \dfrac{17\sqrt2}{26}}

<u>Step-by-step explanation:</u>

Pythagorean Theorem is: a² + b² = c²   , <em>where "c" is the hypotenuse</em>

<em />

9)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{12}\quad \rightarrow \large\boxed{\dfrac{1}{3}}

Note: 4² + (8√2)² = hypotenuse²   →   hypotenuse = 12

10)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{16}{20}\quad \rightarrow \large\boxed{\dfrac{4}{5}}

Note: 12² + opposite² = 20²   →   opposite = 16

11)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{\sqrt{11}}{6}\quad =\large\boxed{\dfrac{\sqrt{11}}{6}}

Note: adjacent² + 5² = 6²   →   adjacent = √11

12)\ \tan \theta=\dfrac{\text{side opposite of}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{17}{13\sqrt2}\quad =\large\boxed{\dfrac{17\sqrt2}{26}}

Note: adjacent² + 7² = (13√2)²   →   adjacent = 17

5 0
3 years ago
Compare the given dimensions of four triangles. Which triangle is possible to construct? side lengths of 5 ft, 12 ft, and 13 ft
kobusy [5.1K]
(5,12,13) is a right triangle and can be constructed.
All the others do not satisfy the triangle inequality, i.e. the sum of two short sides must exceed the long side in order for the triangle to be constructed.
Examples:
2+11<15, so no
3+7<11, so no
4+8<15, so no
but 5+12>13  so yes, it can be constructed.
7 0
3 years ago
Read 2 more answers
Solve for X. I need help
Nuetrik [128]

Answer:

im just tryna get points  

Step-by-step explanation:

5 0
3 years ago
Help please!!!!!!!!!!!!!
nydimaria [60]
1. statement: angles 1 and 2 are supplementary, reason: adjacent angles on a straight line are supplementary
2. reason: Vertical angles are congruent
3. reason: Parallel lines for supplementary interior angles on the same side as the transverse
4. statement:angles 1 and 5 are equal reason:If two angles are supplementary to the same angle, they are congruent
5 0
3 years ago
Other questions:
  • What are the domain and range of the function below?
    15·2 answers
  • A rectangle is made up of 3 squares, and the perimeter of the whole figure is 88cm. Find the area of the rectangle.
    8·1 answer
  • Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y=4x^2+5x-1
    10·1 answer
  • A gym charges a one-time fee of $75 to join, plus membership dues of $25 per month. Which equation represents the total cost, C,
    13·2 answers
  • What is the standard unit of measurement for mass?
    13·1 answer
  • Are the following rational or irrational?
    6·1 answer
  • (5/8 x - 10) - (1/8 x - 12)
    11·2 answers
  • 1/2 times 2/3 divided by 1/4 times 1/2
    5·1 answer
  • If you were dividing X6 + 4x3 + 2, how many O's would you
    9·1 answer
  • Which relationship describes angles 1 and 2?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!