MATHEMATICS HIGH SCHOOL

-6x-14y=16 and -2x+7y=17 solve by elimination show the work

Answers

Answer 1

Answer:

Answer:

(- 5, 1 )

Step-by-step explanation:

- 6x - 14y = 16 → (1)

- 2x + 7y = 17 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the x- term

6x - 21y = - 51 → (3)

Add (1) and (3) term by term to eliminate x

0 - 35y = - 35

- 35y = - 35 ( divide both sides by - 35 )

y = 1

Substitute y = 1 into either of the 2 equations and solve for x

Substituting into (1)

- 6x - 14(1) = 16

- 6x - 14 = 16 ( add 14 to both sides )

- 6x = 30 ( divide both sides by - 6 )

x = - 5

solution is (- 5, 1 )

Related Questions

A simple random sample of 50 adults was surveyed, and it was found that the mean amount of time that they spend surfing the Internet per day is 54.2 minutes, with a standard deviation of 14.0 minutes. What is the 99% confidence interval (z-score = 2.58) for the number of minutes that an adult spends surfing the Internet per day?Remember, the margin of error, ME, can be determined using the formula mc019-1.jpg. 49.1 minutes to 59.3 minutes 50.3 minutes to 58.1 minutes 54.2 minutes to 58.1 minutes 54.2 minutes to 59.3 minutes
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Prove that tan 225 cot 405 + cot 675 tan 765 = 0
How to solve this???
in a coordinate plane, if the y-coordinate of a point is positive, then the point is in the first quadrant.

Penny works at a localamusement park.
She earns $9.80 per hour.
She is also paid $7.00 for
meals and $3.00 for
transportation each day.
Last Friday, Penny earned
$88.40. Write and solve an
equation to determine how
many hours Penny worked
on Friday.

Answers

Answer:Penny worked 8 hours on Friday.

7 + 3 + 9.8h = 88.4

h = 8

Plz mark brainliest:)

If Mary deposits $275 in principal at an interest rate of 3.2 percent, how much interest will she earn in one year

Answers

I know 3.2% of $275 is $8.8
so i think $283.8

A foreman for an injection-molding firm admits that on 55% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 3% to 15%. The plant manager randomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off the machine the previous night?

Answers

Answer:

0.8594

Step-by-step explanation:

Let a denote the event of forgetting to shut off machine and b be the event of being defective.

-A foreman forgets to shut off machine 55% of the time.

-If he forgets, 15% of molds are defective.

-If he does not, 3% of molds are defective.

#The probability that he forgot to shut off the machine is calculated as:

$P(a \ and \ b)=0.55* 0.15\n\n=0.0825\n\n$

P(a and ~b)=0.55(1-0.15)=0.4675

P(~a and b) = (1-0.55)*0.03=0.0135

P(~a and ~b) = (1-0.55)*(1-0.03)=0.4365

#Conditional probability is defined as:

$P(a|b)=(P(a \ and\ b))/(P(a))\n\n=(P(a \ and \ b))/([(P(a \ and \ b)+P(\~a \ and \ b))\n\n\n=(0.0825)/(0.0825+0.0135)\n\n\n=0.8594$

Hence, the probability that the foreman forgot to shut off the machine the previous night is 0.8594

If a square has an area of 225 square feet what is the length of each side

Answers

The area of the square: $A=a^2$

where "a" is a length of side.

Therefore:
$A=225\ ft^2\ and\ A=a^2\Rightarrow a^2=225\Rightarrow a=√(225)\Rightarrow \boxed{a=15\ (ft)}$

PLEASE HELP. A playground is shaped like a rectangle with a width 5 times its length (l). What is a simplified expression for the distance between opposite corners of the playground?

Answers

Look at the picture.

Use the Pythagorean Teorem:
$l^2+(5l)^2=d^2\nl^2+5^2l^2=d^2\nd^2=l^2+25l^2\nd^2=26l^2\nd=√(26)^2\nd=√(26)\cdot√(l^2)\n\boxed{d=l√(26)}$

1) Find the inverse function of f(x)=1/2x+32)Use composition to verify that they are inverse relations?
3) f^ Domain : Range:
4) f^-1 Domain : Range:

Answers

y = 1/2x + 3
change x and y

x = 1/2y + 3
now find the value of y and that is inverse function

x - 3 =1/2 y
y = 2x- 6

f-(x) = 2x - 6

for both domain : ( - ∞ , + ∞ )

range f (x) : ( - ∞ , + ∞ ) - { 0 }
range f-(x) :( -∞ , +∞)

To find the inverse function you need to change $f(x)$ (call it $y$ ) and $x$ , then solve for $y$ :

$y = (1)/(2)x+3 \n x = (1)/(2)y + 3 \n x - 3 = (1)/(2)y \n 2x-6 = y$

So now you have $f^(-1)(x) = 2x-6$ .

Composition to prove inverse relation: $f \circ f^(-1) (x) = x$ :

$f(f^(-1)(x)) = (1)/(2)(2x-6)+3 = x - 3 + 3 = x \square$

Domain and Range of both functions is Real numbers since they are both linear equations.

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