All categories

3 years ago

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

Mathematics

2 answers:

liraira [26]3 years ago

5 0

Answer:12

Step-by-step explanation:

Oduvanchick [21]3 years ago

4 0

Answer:

The value is 12

Step-by-step explanation:

we have

$y=-2x+4$

Convert to standard form

$2x+y=4$ ----> equation A

Let

a ----> the missing value

$6x+3y=a$ ----> equation B

we know that

If the system of equations A and B has infinitely solutions, then equation A and equation B are identical

Multiply equation A by 3 both sides

$3(2x+y)=3(4)$

$6x+3y=12$ ----> new equation A

Equate new equation A and equation B

$a=12$

therefore

The value is 12

You might be interested in

The average time taken to complete a test follows normal probability distribution with a mean of 70 minutes and a standard devia

Dimas [21]

Under 45 mins is roughly 16%. This is because 68% of the curve exists within 1 SD of the mean. So 16% must be outside and smaller and 16% outside and larger (on average).

It is impossible to determine how likely you are to find someone with exactly the second amount. However, if you are looking for that or less, you would get 84%

3 0

3 years ago

Please Help Me! It’s Math! Please!

nadezda [96]

Answer:

D. About 800 years

Step-by-step explanation:

Use the half-life equation:

A = A₀ (½)ⁿ

where A is the final amount,

A₀ is the initial amount,

and n is the number of half-lives.

0.90A₀ = A₀ (½)ⁿ

0.90 = (½)ⁿ

To solve for n, take log of both sides:

log 0.9 = n log 0.5

n = (log 0.9) / (log 0.5)

n = 0.152

It takes 0.152 half-lives. The half-life of carbon-14 is 5730 years.

0.152 × 5730 years = 871 years

The closest answer is D.

8 0

3 years ago

In the equation x^2+10x+24=(x+a)(x+b), b is an integer. Find algebraically all possible values of b

Vinil7 [7]

(x+4)(x+6)
(x+6)(x+4)

8 0

3 years ago

Is Circumference of a circle same as area?

Klio2033 [76]

Answer:

The circumference of a circle is not the same as the area of the circle because the circumference represents the distance around the circle while the area represents the amount of space within the circle. Hope this helps.

5 0

3 years ago

Read 2 more answers

A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square

kondaur [170]

This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

V = length x width x height

That is:

$V = xxy = x^{2}y$

We also know that the <span>bin is constructed from 48 square feet of sheet metal, s</span>o:

Surface area of the square base = $x^{2}$

Surface area of the rectangular sides = $4xy$

Therefore, the total area of the cube is:

$A = 48 ft^{2} = x^{2} + 4xy$

Isolating the variable y in terms of x:

$y = \frac{48- x^{2} }{4x}$

Substituting this value in V:

$V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3}$

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

$\frac{dv}{dx} = 48-3x^{2} =0$

Solving for x:

$x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4$

Solving for y:

$y = \frac{48- 4^{2} }{(4)(4)} = 2$

Then, <span>the dimensions of the largest volume of such a bin is:
</span>
Length = 4 ft
Width = 4 ft
Height = 2 ft

And its volume is:

$V = (4^{2} )(2) = 32 ft^{3}$

8 0

3 years ago