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4 years ago

Ax + by = c To solve each literal equation for the given variable

Mathematics

1 answer:

vodka [1.7K]4 years ago

8 0

Answer:

Step-by-step explanation:

For a:

ax = c - by

a = (c - by)/x

For x:

ax = c - by

x = (c - by)/a

For b:

by = c - ax

b = (c - ax)/y

For y:

by = c - ax

y = (c - ax)/b

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9 times what equals 210

Ksenya-84 [330]

$9x = 210$

$x = \frac{210}{9} = \boxed{\frac{70}{3}}$

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4 years ago

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If two out of every three balls in a multi color package is pink how many balls in a package of 21 balls will be pink

LuckyWell [14K]

Answer:

14 balls will be pink out of 21 balls.

Step-by-step explanation:

Given that:

2 out of every 3 balls are pink in a multi color package.

Ratio of pink balls to balls drawn = 2:3

Number of balls in package = 21 balls

Number of pink balls = x

Ratio = x:21

This is a proportional relationship

2 : 3 :: x : 21

Product of mean = Product of extreme

3x = 21*2

3x = 42

Dividing both sides by 3

$\frac{3x}{3}=\frac{42}{3}\\x=14$

Hence,

14 balls will be pink out of 21 balls.

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3 years ago

A lake is 200 feet wide. Two boats start to move towards one another from opposite shores. In one minute, the first boat goes 40

NARA [144]

Answer:

I use faction

Step-by-step explanation:

The first boat.

$\frac{40 feet}{60 seconds}$ ÷ 10 = $\frac{4 feet}{6 seconds}$

$\frac{4 feet}{6 seconds}$ ÷ 2 = $\frac{2 feet}{3 seconds}$

The first boat move $\frac{2 feet}{3 seconds}$

The second one do the same

$\frac{30 feet}{60 seconds}$ ÷ 10 = $\frac{3 feet}{6 seconds}$

$\frac{3 feet}{6 seconds}$ ÷ 2 = $\frac{1.5 feet}{3 seconds}$

That is the speed of each boat.

The first boat need 50 minutes to get to the other side

2000 ÷ 2 =1000

1000 x 3 = 3000

3000 ÷ 60 = 50

The second boat need 66.6666666667 minutes to get to the other side

200 ÷1.5 = 1333.33333333

1333.33333333 x 3 = 4000

4000 ÷ 60 = 66.6666666667

8 0

3 years ago

1. A 35-pound mixture of metal includes 20 pounds of aluminum, 10 pounds of nickel,

Igoryamba

Answer:

7:1

Step-by-step explanation:

35mixture(:) means to5 copper

35: 5

35÷5:5÷5 = 7:1

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3 years ago

WILL MARK BRAINLIEST!!! Given p(x)=x3−4x2+15x+k and the remainder of the division of p(x) by (x+1) is equal to −8, what is the r

balandron [24]

Use the polynomial remainder theorem. If $p(x)$ is a polynomial of degree $n>1$ , then we can divide by a linear term $x-c$ to get a quotient $q(x)$ and remainder $r(x)$ of the form

$\dfrac{p(x)}{x-c}=q(x)+\dfrac{r(x)}{x-c}\iff p(x)=(x-c)q(x)+r(x)$

Then when $x=c$ , we get $p(c)=r(c)$ . In other words, the value of $p(x)$ at $x=c$ tells you the value of the remainder upon dividing $p(x)$ by $x-c$ .

So given that $p(x)=x^3-4x^2+15x+k$ , and the remainder upon dividing $p(x)$ by $x+1$ is -8, we know that $r(-1)=-8$ , so

$\dfrac{x^3-4x^2+15x+k}{x+1}=q(x)-\dfrac8{x+1}$
$\dfrac{x^3-4x^2+15x+k+8}{x+1}=q(x)$

Since $q(x)$ is a polynomial (not a rational expression), then we know that $x+1$ divides $x^3-4x^2+15x+k+8$ exactly. In particular, the remainder term of this quotient is 0. We can use long or synthetic division to determine $q(x)$ . I prefer typing out the work for synthetic division:

-1   |   1   -4   15    k + 8
.     |        -1     5       -20
- - - - - - - - - - - - - - - - - -
.     |   1   -5    20    k - 12

The remainder here has to be 0, so $k-12=0\implies k=12$ .

Finally, we can get the remainder upon dividing $p(x)$ by $x-1$ by evaluating $p(1)$ , which gives $p(1)=24$ .

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3 years ago

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