Please help, and explain how to solve the problem.

A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 70% pure anti

andre [41]

Answer:

First brand of antifreeze: 21 gallons

Second brand of antifreeze: 9 gallons

Step-by-step explanation:

Let's call A the amount of first brand of antifreeze. 20% pure antifreeze

Let's call B the amount of second brand of antifreeze. 70% pure antifreeze

The resulting mixture should have 35% pure antifreeze, and 30 gallons.

Then we know that the total amount of mixture will be:

$A + B = 30$

Then the total amount of pure antifreeze in the mixture will be:

$0.2A + 0.7B = 0.35 * 30$

$0.2A + 0.7B = 10.5$

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:

$-0.7A -0.7B = -0.7*30$

$-0.7A -0.7B = -21$

+

$0.2A + 0.7B = 10.5$

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

$-0.5A = -10.5$

$A = \frac{-10.5}{-0.5}$

$A = 21\ gallons$

We substitute the value of A into one of the two equations and solve for B.

$21 + B = 30$

$B = 9\ gallons$

3 0

3 years ago

Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y 2x3y4 xy3?.

ki77a [65]

The degree of the sum and difference of the polynomials are 6 and 7 respectively.

given polynomials are:

$3x^5-2x^3y^4-7xy^3$

$-8x^5y+2x^3y^4+xy^3$

the sum of polynomials = $-5x^5y-6xy^3$

the difference of polynomials = $11x^5y-4x^3y^4-8xy^3$

<h3>what is the degree of a polynomial?</h3>

A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.

degree of sum = monomial with highest power = 5+1=6

degree of difference = monomial with highest power = 3+4 = 7

therefore, the degree of the sum and difference of the polynomials are 6 and 7 respectively.

to get more about polynomials refer to:

brainly.com/question/1600696

4 0

2 years ago

a tree casts a shadow 8 feet long. A 6-foot Man cast a shadow 4 feet long. The triangle formed by the tree and its shadow is sim

Elden [556K]

Answer:

12 feet

Step-by-step explanation:

Draw a diagram (see picture below). The tree and its shadow is one triangle, the man and its shadow is another triangle. We assume both are right triangles because people and trees stand vertical.

Create a proportion to solve. Put the missing value in a numerator.

Tree height / Tree shadow = Man height / Man shadow

$\frac{x}{8} =\frac{6}{4}$