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Andrei [34K]
3 years ago
13

Use substitution to solve the system of equations. y + x = 3 y = 1.5x + 1

Mathematics
1 answer:
jeyben [28]3 years ago
5 0

Answer:

x=0.8, y=2.2 (0.8, 2.2).

Step-by-step explanation:

y+x=3

y=1.5x+1

-------------

1.5x+1+x=3

2.5x=3-1

2.5x=2

x=2/2.5

x=0.8

y+0.8=3

y=3-0.8

y=2.2

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Marysya12 [62]

BC is 10 units and AC is 5+5\sqrt{3} units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

  • \frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}
  • AB is opposite to ∠C
  • BC is opposite to ∠A
  • AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ \frac{AB}{sin(C)}=\frac{BC}{sin(A)}

∵ AB = 5\sqrt{2}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}

- By using cross multiplication

∴ (BC) × sin(30) = 5\sqrt{2} × sin(45)

∵ sin(30) = 0.5 and sin(45) = \frac{1}{\sqrt{2}}

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ \frac{AB}{sin(C)}=\frac{AC}{sin(B)}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}

- By using cross multiplication

∴ (AC) × sin(30) = 5\sqrt{2} × sin(105)

∵ sin(105) = \frac{\sqrt{6}+\sqrt{2}}{4}

∴ 0.5 (AC) = \frac{5+5\sqrt{3}}{2}

- Divide both sides by 0.5

∴ AC = 5+5\sqrt{3} units

BC is 10 units and AC is 5+5\sqrt{3} units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0
3 years ago
A craft store buys 50 yards of satin ribon for $12.50. The store sells the ribbon by the foot. A customer can purchase 5 feet of
amm1812

Answer:

$8.1

Step-by-step explanation:

Convert 45 yards of ribbon to feet through proper conversion factor.  

  (45 yards)(3 ft / 1 yard) = 135 feet

Divide this number by 5 to determine the number of 5-ft ribbon that customers can purchased.

    n = 135 ft / 5 ft = 27

Then, multiply by $0.80.

   R = (27)($0.80) = $21.6

The profit is equal to $21.6 and $13.50,

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What is the solution to x ? <br><br> 7/3x + 1/3x = 3x + 6/3 + 5/3x
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How much is 5tenths-2tenths?
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3 0
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Roman55 [17]

Answer:

Proved

Step-by-step explanation:

From the given parameters, we have:

n = 9 i.e. the length of each security numbers

r = 2 i.e. 2 security numbers

Required

In 513 security numbers, 2 must have matching zeros

To do this, we make use of Pigeonhole principle.

First, we calculate the number of all security numbers not having matching zeros.

Each of the 9 digits can be selected in 2 ways.

2 ways implies that each digit is either 0 or not

So, total selection is:

Total = 2^9

Total = 512

Apply Pigeonhole principle

The principle states that: suppose there are n items in m containers, where n>m, then there is at least one container that contains more than 1 item.

This means that if there are 512 security number without matching zeros, then there is 1 (i.e. 512 + 1) with matching zeros.

512 + 1 = 513

8 0
3 years ago
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