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2 years ago

Solve the following systems of equations without graphing 5x + 10y = 30 -5x +15y = 20

Mathematics

1 answer:

galben [10]2 years ago

8 0

Answer:

(2, 2)

Step-by-step explanation:

In this case, elimination would be the most efficient means of solving.

Simply, add the two equations, and you will be left with only one variable to solve for. (In this case y) You are then able to take your solution and plug it into an equation and solve for x, therefore giving you their intercept.\

5x + 10y = 30

-5x + 15y = 20

(x's cancel) 25y = 50

25y = 50

y = 2

5x + 10(2) = 30

5x + 20 = 30

5x = 10

x = 2

The solution to this equation is (2, 2)

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Margaret and Kevin both have to write an expression that is equivalent to 6 to the power of -4. Part A Who is correct? Part B Wh

AlekseyPX

Answer:

Margret is correct, Kevin is wrong.

Step-by-step explanation:

6^-4 can be written as (1/6)^4

By taking (1/6)^5 times you have (1/6)(1/6)(1/6)(1/6)(1/6), multiplying by 6 would cancel one of those (1/6ths) out. Meaning you would be left with (1/6)^4 or 6^-4

Kevin is wrong because taking 6^4 would not be the same as 6^-4, 6^4= 1296, multiplying that by 1/6 would not give you the same value as 6^-4. His mistake was that he did not take the reciprocal of 6^-4 and incorrectly removed a negative.

Hope this helps, for more assistance please check out: http://linktr.ee/x.squared/

8 0

3 years ago

A candle factory makes colored candles to sell in packages. Which of the following situations best represents a proportional rel

timurjin [86]

Answer:

D Each package has 8 yellow candle chips. A total of 18 packages will have 144 yellow candle chips.

Step-by-step explanation:

8/1 is proportional to 144/18

7 0

2 years ago

HELLPPPP ASAP

Vlada [557]

Answer:

The correct option is <u>(C) Exponential growth</u>.

Step-by-step explanation:

The simplest exponential function is: f(x) = $a^{x}$ , a>0, a≠1

If the x is positive then graph of exponential is increasing and if the x is negative then graph of exponential is decreasing.

In given function $f(x)=\frac{1}{2}\times(3)^x$

x is positive so, it is graph of exponential growth.

Hence, the correct option is <u>(C) Exponential growth</u>.

8 0

3 years ago

What is the quotient of 1.888\times 10^91.888×10 9 and 5.9 \times 10^65.9×10 6 expressed in scientific notation?

Jlenok [28]

Given:

The expressions are $1.888\times 10^9$ and $5.9\times 10^6$ .

To find:

The quotient of $1.888\times 10^9$ and $5.9\times 10^6$ expressed in scientific notation.

Solution:

Quotient of $1.888\times 10^9$ and $5.9\times 10^6$ is:

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=\dfrac{1.888}{5.9}\times \dfrac{10^9}{10^6}$

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=0.32\times 10^{9-6}$

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=0.32\times 10^{3}$

In the scientific notation, the first number is between 1 to 10. So, 0.32 can be written as $\dfrac{3.2}{10}$ .

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=\dfrac{3.2}{10}\times 10^{3}$

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=3.2\times 10^{3-1}$

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=3.2\times 10^{2}$

Therefore, the value of the quotient is $3.2\times 10^{2}$ .

8 0

3 years ago

A 5.5-foot-tall woman walks at 8 ft/s toward a street light that is 22 ft above the ground. What is the rate of change of the le

REY [17]

Answer: $\frac{8}{3}\ ft/s$

Step-by-step explanation:

Given

length of shadow =22 ft

height of woman =5.5 ft

speed of woman $\frac{dy}{dt}=8\ ft/s$

from the figure, we can write

$\frac{22}{x+y}=\frac{5.5}{x}$

at given instant

y=20 ft

so, using similar triangle properties

$\frac{22}{x+20}=\frac{5.5}{x}\\22x=5.5x+110\\16.5x=110\\x=6.67\ ft$

Again we can write

$\dfrac{22}{x+y}=\dfrac{5.5}{x}\\22x=5.5x+5.5y\\16.5x=5.5y\\3x=y\\\text{differentiate w.r.t time} \\3\frac{dx}{dt}=\frac{dy}{dt}\\\frac{dx}{dt}=\frac{1}{3}\times 8=\frac{8}{3}\ ft/s\ \text{away from the woman}$

5 0

3 years ago