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Cloud [144]
2 years ago
5

If two sweaters and four shirts cost $150, and four sweaters and three shirts cost $200, find the price of each shirt and each s

weater.
Mathematics
2 answers:
Tpy6a [65]2 years ago
5 0

Answer:

What the other guy said

Step-by-step explanation:

STALIN [3.7K]2 years ago
4 0

Answer:

shirt = $20

sweater = $35

Step-by-step explanation:

This question would be solved using simultaneous equation

Let the price of sweater be represented by a

Let the price of shirt be represented by b

The following equations can be derived from the question

2a + 4b = 150   equation 1

4a + 3b = 200   equation 2

Multiply equation 1 by 2

4a + 8b = 300    equation 3

Subtract equation 2 from 3

5b = 100

divide both sides of the equation by 5

b = 20

substitute for b in equation 1

2a + 4(20) = 150

2a + 80 = 150

collect like terms

2a = 150 - 80

2a = 70

divide both sides by 2

a = 35

Price of sweater = $35

Price of shirt = $20

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The area of the conference table in Mr. Nathan’s office must be no more that 175 ft^2. If the length of the table is 18 ft more
hodyreva [135]

Answer:

(0, 7]

Step-by-step explanation:

Let's call the width W and the length L.  The length is 18 feet more than the width, so:

L = W + 18

The area can be no more than 175, so:

A ≤ 175

LW ≤ 175

Since L = W + 18:

(W + 18) W ≤ 175

W² + 18W ≤ 175

W² + 18W - 175 ≤ 0

(W - 7) (W + 25) ≤ 0

-25 ≤ W ≤ 7

However, the width of the table can't be nonpositive, so:

0 < W ≤ 7

Or in interval notation, (0, 7].

6 0
3 years ago
Study the expression<br> x-y+ z(x + y)<br> Evaluate the expression if x = 10, y = -1, and z=0
vovangra [49]

Answer:

<em>The value of the expression is 11</em>

Step-by-step explanation:

<u>Evaluate Expressions</u>

An algebraic expression consists of a set of variables and constants related by algebraic operations like addition, subtraction, multiplication, etc.

To evaluate an algebraic expression, we replace the variables for the constant value they are assigned.

Let's consider the expression:

x-y+ z(x + y)

for x=10, y=-1, z=0

Substituting the variables for their values:

10-(-1)+ (0)(10 -1)

=10+1+ (0)(9)

=11+0=11

The value of the expression is 11

4 0
3 years ago
50
ozzi

Answer:

90 km, N 46° E

Step-by-step explanation:

<em>A jet flies due North for a distance of 50 km and then on a bearing of N 70° E for a further 60 km. Find the distance and bearing of the jet from its starting point.</em>

Look at the diagram I drew of this scenario. You can see the jet flies North for 50 km, and then turns at a 70° angle to fly another 60 km. We want to find the distance from the starting point, SP, to angle C (labeled).

This will be the jet's distance from its starting point.

In order to find the bearing of the jet from its starting point, we will need to find the angle formed between distances b and c, labeled angle A.

The <u>Law of Cosines</u> will allow us to use two known sides and one known angle to solve for the sides opposite of the known angle.

In this case, the known angle is 110° (angle B) so we will use the <u>Law of Cosines</u> respective to B.

  • b² = a² + c² - 2ac cosB

Substitute the known values into the equation and solve for b, the distance from the starting point (A) to the endpoint (C).

  • b² = (60)² + (50)² - 2(60)(50) cos(110°)
  • b² = 6100 -(-2052.12086)
  • b² = 8152.12086
  • b = 90.28909602
  • b ≈ 90 km

The distance of the jet from its starting point is 90 km. Now we can use this b value in order to calculate angle A, the bearing of the jet.

The <u>Law of Cosines</u> with respect to A:

  • a² = b² + c² - 2bc cosA

Substitute the known values into the equation and solve for A, the bearing from the starting point (clockwise of North).

  • (60)² = (90.28909602)² + (50)² - 2(90.28909602)(50) cosA
  • 3600 = 8152.12086 - 6528.909602 cosA
  • -4552.12086 = -6528.909602 cosA
  • 0.6972252853 = cosA
  • A = cos⁻¹(0.6972252853)
  • A = 45.79519
  • A ≈ 46°

The bearing of the jet from its starting point is N 46° E. This means that it is facing northeast at an angle of 46° clockwise from the North.

7 0
2 years ago
7x²+3y²-28x-12y=-19
grigory [225]
Complete the square for x and y.

7x^2 + 3y^2 - 28x - 12y = -19

7x^2 - 28x + 3y^2 - 12y = -19

7(x^2 - 4x) + 3(y^2 - 4y) = -19

7(x^2 - 4x + 4) + 3(y^2 - 4y + 4) = -19 + 28 + 12

7(x - 2)^2 + 3(y - 2)^2 = 21

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4 0
3 years ago
What is 1/5m - 20 = to
belka [17]

Answer:

math duh

Step-by-step explanation:

math duh :]

4 0
3 years ago
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