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mars1129 [50]
3 years ago
5

Help with all of the questions?

Mathematics
1 answer:
jasenka [17]3 years ago
4 0
1. x + 3y = 3 and x - 2y = 0
2. (2,1)
3. solution
4. true
5.  equation 1 :                        equation 2 :
     x + y = 3                                x - 2y = 0
     2 + 1 = 3                                2 - 2(1) = 0
     3 = 3 (correct)                        2 - 2 = 0
                                                   0 = 0 (correct)

both equations are true...so (2,1) is a solution set to this system of equations
      
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Mrs. Computer is 3 times older than her daughter, Mousy. The sum of their ages is 52. How old is Mousy?
grandymaker [24]
Mousy=m
Mrs. Computer=3m
m+3m=52
4m=52
m=52/4
m=13
mousy=13, Mrs. Computer=3*13=39 
8 0
3 years ago
Short sleeve t-shirts cost $10 and long sleeve t-shirts cost $15. If the t-shirt shop made $485 selling 38 total t-shirts, how m
BartSMP [9]

Answer:

The t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.

Step-by-step explanation:

To solve this problem, we should create a system of equations.  Let's let short sleeve t-shirts be represented by the variable s and long sleeve t-shirts be represented by the variable l.  

We know that the shop sold 38 total shirts, or in other words, the amount of long sleeve and short sleeve shirts combined is 38.  If we write this as an equation, we get: s + l = 38.

We can make another equation with the prices of the shirts.  If we take each type of shirt and multiply each price by the number sold and add them together, we should get the shop's total profits.  Represented as an equation, this is: 10s + 15l = 485.

Now that we have two equations, we should try to solve the system.  In this case, it is easiest to use substitution, so we are going to rewrite the first equation in terms of one variable.

s + l = 38

s = 38 - l

If we substitute this equivalent value for the variable s into the second equation, we get:

10s + 15l = 485

10(38 - l) + 15l = 485

Now we have an equation that only has one variable, so we can simplify both sides and then isolate the variable.

380 - 10l + 15l = 485

380 + 5l = 485

5l = 105

l = 21

Now, we can substitute this value for l back into the first equation to solve for the variable s.

s + l = 38

s + 21 = 38

s = 17

Therefore, the t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.

Hope this helps!

5 0
3 years ago
Simplify the fraction completely.
k0ka [10]

Answer:

5

Step-by-step explanation:

40% means 40 parts out of 100. If we have made the numerator of the fraction 2, we have divided 40 by 20. To make this fraction equal to 40/100, we have to divide 100 by 20 as well, giving us 5.

3 0
2 years ago
Read 2 more answers
Solve 1/2cot(x)>=1/2 over 0<=x<=2pi
RSB [31]

9514 1404 393

Answer:

  (0, π/4] ∪ (π, 5π/4]

Step-by-step explanation:

Multiplying by 2 gives ...

  cot(x) ≥ 1

The cotangent function decreases from ∞ to 1 in the domain (0, π/4], and again in the domain (π, 5π/4]. The solution is the union of these two intervals.

  x ∈ (0, π/4] ∪ (π, 5π/4]

_____

(a, b] is interval notation for a < x ≤ b

3 0
3 years ago
A rectangular prism is 4 inches long, 3 inches wide and 8 inches tall . Eli packs the prism with unit cubes to find the volume.
bulgar [2K]

Answer:

V=96\ inch^2

Step-by-step explanation:

Given that,

A rectangular prism is 4 inches long, 3 inches wide and 8 inches tall.

We need to find the volume of the rectangular prism. The formula for the volume of prism is given by :

V=lbh\\\\V=4\times 3\times 8\\\\V=96\ inch^2

So, the volume of the prism is equal to 96\ inch^2.

6 0
3 years ago
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