All categories

3 years ago

What is the value of y in the solution to the system of equations?

Mathematics

1 answer:

AnnZ [28]3 years ago

7 0

Answer:

The correct answer is D. 8

Step-by-step explanation:

In order to find this, solve by multiplying the top equation by -6. Then add the equations together to get the x values to cancel. Then you may solve for y.

-2x - 3/2y = -6

2x - 3y = -30

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

9/2y = -36

y = 8

You might be interested in

At the park, there is a triangular sandbox with base = 12ft and height = 4ft. A drawing of the sandbox is shown above. Brie want

sammy [17]

Your question is not clear, but it looks as though you want to know how Brie can make a similar sandbox with base = 8ft.

Answer:

For Brie to make a similar sandbox, he must use a base = 8ft, and height = (8/3)ft

Step-by-step explanation:

It is possible for Brie to make a similar triangular sandbox with base = 12ft and height = 4ft.

All he must ensure is that the ratio of base to height of the original sandbox is the same ratio of base to height of the one he is trying to make.

The original sandbox is 12:4

Because he wants to use a base = 8ft, the sandbox he is trying to make is 8:x

Where x is the height of the sandbox he is trying to make.

Then for these sandboxes to be similar, the ratio 12:4 = 8:x

=> 12/4 = 8/x

12x = 8 × 4

12x = 32

x = 8/3

The height must be (8/3)ft

3 0

3 years ago

One number exceeds another by 1. the sum of the numbers is 21. what are the numbers

Cerrena [4.2K]

Try this solution:
1. if 1st number is 'x', the 2d number is 'y', then it is possible to make up the system of two equation according to the condition:
$\left \{ {{x-y=1} \atop {x+y=21}} \right. \ =\ \textgreater \ \ \left \{ {{x=11} \atop {y=10}} \right.$
2. one number is 11, another number is 10.

3 0

3 years ago

A bag of potatoes has a mass of 4 kilograms.Some potatoes are taken out.The mass is now 2305 grams.What is the mass of the potat

Colt1911 [192]

First, convert the kilograms to grams. One kilogram is 1000 grams. So multiply it by 1000. Then subtract 2305 from 4000. 4000-2305=1695. So 1695 grams were taken out.

5 0

3 years ago

Differentiate with respect to X <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20

Mice21 [21]

Power and chain rule (where the power rule kicks in because $\sqrt x=x^{1/2}$ ):

$\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'$

Simplify the leading term as

$\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}$

Quotient rule:

$\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}$

Chain rule:

$(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)$

$(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)$

Put everything together and simplify:

$\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}$

$=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}$

$=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}$

5 0

3 years ago

Need help Asap thank you in advance

julia-pushkina [17]

Answer:

$12x^4-20x^2+32x=4x(3x^3-5x+8)$

Step-by-step explanation:

<u>Common Factors</u>

An algebraic expression that is formed by sums or subtractions of terms can be factored provided there are numeric or variable common factors in all the terms.

The following expression

$Z=12x^4-20x^2+32x$

Can be factored in the constants and in the variable x.

1. To find the common factor of the variable, we must locate if the variable is present in all terms. If so, we take the common factor as the variable with an exponent which is the lowest of all the exponents found throughout the different terms. In this case, the lowest exponent is x (exponent 1).

2. To find the common factors of the constants, we take all the coefficients:

12 - 20 - 32

and find the greatest common divisor of them, i.e. the greatest number all the given numbers can be divided by. This number is 4, since 12/4=3, 20/4=5 and 32/4=8

3. The factored expression is

$Z=12x^4-20x^2+32x=4x(3x^3-5x+8)$

$\boxed{12x^4-20x^2+32x=4x(3x^3-5x+8)}$

3 0

3 years ago