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Kitty [74]
2 years ago
15

Consider the following system of equations.

Mathematics
2 answers:
soldier1979 [14.2K]2 years ago
8 0

Answer:

  • A. Since 11 ≠ 9, there is no solution

Step-by-step explanation:

<u>Given system:</u>

  • 1.75x + 1.25y = 2.75
  • 7x + 5y = 9

<u>Multiply the first equation by 4:</u>

  • 4(1.75)x + 4(1.25)y = 4(2.75)
  • 7x + 5y = 11

We get same equation as the second one with the difference that the right side equals to 11.

Since left sides are same and right sides are different, the system has no solution.

Correct choice is A

Anit [1.1K]2 years ago
4 0

Step-by-step explanation:

1.75x + 1.25y = 2.75 (1)

7x + 5y = 9 (2)

On multiplying EQ. 1 by 4

4(1.75x + 1.25y) = 4(2.75)

7x + 5y = 11 (3)

We get the same LHS as equation 2 but not same RHS as equation 2

Option A is correct

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Jorge is asked to build a box in the shape of a rectangular prism. The maximum girth of the box is 20 cm. What is the width of t
MariettaO [177]

Answer:

The width of the box is 6.7 cm

The maximum volume is 148.1 cm³

Step-by-step explanation:

The given parameters of the box Jorge is asked to build are;

The maximum girth of the box = 20 cm

The nature of the sides of the box = 2 square sides and 4 rectangular sides

The side length of square side of the box = w

The length of the rectangular side of the box = l

Therefore, we have;

The girth = 2·w + 2·l = 20 cm

∴ w + l = 20/2 = 10

w + l = 10

l = 10 - w

The volume of the box, V = Area of square side × Length of rectangular side

∴ V = w × w × l = w × w × (10 - w)

V = 10·w² - w³

At the maximum volume, we have;

dV/dw = d(10·w² - w³)/dw = 0

∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0

2×10·w - 3·w² = 20·w - 3·w² = 0

20·w - 3·w² = 0 at the maximum volume

w·(20 - 3·w) = 0

∴ w = 0 or w = 20/3 = 6.\overline 6

Given that 6.\overline 6 > 0, we have;

At the maximum volume, the width of the block, w = 6.\overline 6 cm ≈ 6.7 cm

The maximum volume, V_{max}, is therefore given when w = 6.\overline 6 cm = 20/3 cm  as follows;

V = 10·w² - w³

V_{max} = 10·(20/3)² - (20/3)³ = 4000/27 = 148.\overline {148}

The maximum volume, V_{max} = 148.\overline {148} cm³ ≈ 148.1 cm³

Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)

The width of the box is;

6.7 cm

The maximum volume is;

148.1 cm³

5 0
3 years ago
How to solve this question
Viefleur [7K]

Answer:

7x+21 = 7x + 21

Step-by-step explanation:

7(x+3)=6-(-7x - 15)

L.H.S

=7(x+3)

=7x+21 (multiply 7 by (x+3))

R.H.S:

=6-(-7x - 15)

= 6+7x+15 (multiply the -ive sign in the bracket)

= 7x + 21 ( adding 15 and 6)

now compare the two sides

7x+21 = 7x + 21 hence we prove that L.H.S= R.H.S

4 0
3 years ago
Determine the probability of a negative result for a batch of size 10 if the positivity rate
Vlad1618 [11]

The probability of a negative result for a batch will be "0.3487".

Given values are:

Positivity rate,

  • p = 10% or, 0.1

Batch size,

  • n = 10

Now,

The probability of negative result will be:

→ P (batch \ negative) = (1-p)^n

By substituting the values, we get

→                               =(1-0.1)^{10}

→                               = (0.9)^{10}

→                               = 0.3487

Thus the answer above is right.

Learn more about the probability here:

brainly.com/question/17927863

8 0
2 years ago
If you go out to eat with friends and your meal was $ 72.50 , there is 6.75 % sales tax and you should tip the waiter 15 % . How
Ugo [173]

Answer:

divide this amount ($88.26875) by the number of people

Step-by-step explanation:

6.75% of $72.50 is 4.89375

15% of $72.50 is 10.875

72.50 + 4.89375 + 10.875 = 88.26875

divide this amount (88.26875) by the number of people

7 0
3 years ago
Evaluate the polynomial 6x - y for x= -3 and Y=2.<br> A.15 <br> B. -20<br> C.4<br> D.-16
ra1l [238]
I think the answer is B.
6(-3)=-18, and y=2
so 6x-y=-18-2=-20
6 0
3 years ago
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