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gulaghasi [49]
3 years ago
15

Caroline and Chase are working on math homework. They decide to race to see who can finish first. Caroline is on number 12 and c

an solve 1 math problem in 1.5 minutes. Chase is on number 16 and can solve 1 math problem in 2 minutes. How many minutes will it take before they are on the same problem?​
Mathematics
1 answer:
tiny-mole [99]3 years ago
6 0

Answer:

It will take 24 minutes before they are on the same problem.

Step-by-step explanation:

Caroline is on number 12 and can solve 1 math problem in 1.5 minutes.

Per minute, she solved \frac{1}{1.5} = \frac{2}{3} of a problem. So, after t minutes, she will be on the problem:

Ca(t) = 12 + \frac{2t}{3}

Chase is on number 16 and can solve 1 math problem in 2 minutes.

Per minute, he solved \frac{1}{2} of a problem. So, after t minutes, he will be on the problem:

Ch(t) = 16 + \frac{t}{2}

How many minutes will it take before they are on the same problem?​

This is t for which:

Ca(t) = Ch(t)

So

12 + \frac{2t}{3} = 16 + \frac{t}{2}

\frac{2t}{3} - \frac{t}{2} = 4

\frac{4t-3t}{6} = 4

\frac{t}{6} = 4

t = 24

It will take 24 minutes before they are on the same problem.

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Solve the triangle. Round your answers to the nearest tenth.
sweet-ann [11.9K]

Answer:

  B.  m∠B = 118°, a = 17, c = 18

Step-by-step explanation:

The answer choices all agree on the values of ∠B and c, so we only need to compute the value of side a.

We can verify angle B is ...

  ∠B = 180° -30° -32° = 118°

By the law of sines, ...

  a/sin(A) = b/sin(B)

Multiplying by sin(A), we get ...

  a = b·sin(A)/sin(B) = 30·sin(30°)/sin(118°) ≈ 16.98855

  a ≈ 17.0 . . . units . . . . . matches choice B

__

If you like, you can also verify side c:

  c = b·sin(C)/sin(B) = 30·sin(32°)/sin(118°) ≈ 18.00512

  c ≈ 18.0 . . . units

5 0
3 years ago
5-6n=2n+5 <br>Solve for n
olganol [36]
<span>5-6n=2n+5 , 5 cancels out
-6n -2n = 0
-8n = 0
   n =0</span>
7 0
3 years ago
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-8(2x +x )/-2y , if x=-5, y=2 and z=0
Masteriza [31]

Answer:

<h3>              -8(2x +x )/-2y  = - 30</h3>

Step-by-step explanation:

x=-5, y=2 and z=0

-8(2x +x )/-2y =(-8•3x)/-2y = [-8•3(-5)] / (-2•2) = 120/(-4) =-30

5 0
3 years ago
Find zeros and y intercept of each function algebraically f(x)=x^3-10x^2+24x
monitta

Answer:

The zeros are 0, 4, 6.

The y-intercept is 0.

Step-by-step explanation:

f(x) = x^3 - 10x^2 + 24x

x^3 - 10x^2 + 24x = 0

x(x^2 - 10x + 24) = 0

x(x - 4)(x - 6) = 0

x = 0 or x - 4 = 0 or x - 6 = 0

x = 0 or x = 4 or x = 6

y-intercept:

Since x = 0 is a root, that means that the point (0, 0) is part of the function. That makes the y-intercept 0.

You can also solve for the y-intercept by letting x = 0 in the function and solving for f(0).

Let x = 0.

f(0) = 0^3 - 10(0^2) + 24(0)

f(0) = 0

y-intercept: 0

5 0
3 years ago
3(x + 3) + 10
Sphinxa [80]

Answer:

b-3x+19

Step-by-step explanation:

you have to open the bracket so 3*x=3x

3*3=9

therefore;3x+9+10=3x+19

7 0
3 years ago
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