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2 years ago

use the substitution method to solve the system of equations choose the correct ordered pair X+y=10 y=x-6

Mathematics

1 answer:

dimaraw [331]2 years ago

3 0

Answer:

(8,2)

Step-by-step explanation:

Set up the equation like this: x+x-6=10. You filled in x-6 for y because the second equation says y=x-6. When you solve, you add 6 to both sides of the equation (this is the addition property of equality in geometry). You now have x+x=16. Now, you can combine like terms (this would be the proof combine like terms in geometry) and you would be able to combine like terms because each of those x's are truely 1x+1x because a variable without a coefficient (the number in front of the variable) is an understood 1. So, (1)x+(1)x=2x. So, you have 2x=16. Now, divide by 2 on each side to get that x alone. This is the division property of equality in geometry. You find x=8. You now have the point (8,y) Now to find the y, plug in the 8 for x in one of the equations. If you plug it into the equation x+y=10 you get 8+y=10. Now subtract 8 from both sides (Subtraction property of equality in geometry). y=2. You get the same answer if you plug in 8 for the other equation. y=8-6. 8-6 is 2. Hope this helps! :)

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Find the solution to the following system using substitution or elimination:

raketka [301]

Answer:

B) (3,1)

Step-by-step explanation:

y = -2x + 7

y = 3x - 8

3x - 8 = -2x + 7

combine like terms:

5x = 15

divide both sides of the equation by 5:

x = 3

y = 3(3) - 8 = 1

4 0

3 years ago

The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. (a) Determine the

maxonik [38]

Answer:

a) 0.5 = 50% of flanges exceed 1 millimeter.

b) A thickness of 0.96 millimeters is exceeded by 90% of the flanges

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:

$P(X > x) = \frac{b - x}{b - a}$

The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.

This means that $a = 0.95, b = 1.05$

(a) Determine the proportion of flanges that exceeds 1.00 millimeters.

$P(X > 1) = \frac{1.05 - 1}{1.05 - 0.95} = \frac{0.05}{0.1} = 0.5$

0.5 = 50% of flanges exceed 1 millimeter.

(b) What thickness is exceeded by 90% of the flanges?

This is x for which:

$P(X > x) = 0.9$

$\frac{1.05 - x}{1.05 - 0.95} = 0.9$

$1.05 - x = 0.9*0.1$

$x = 1.05 - 0.9*0.1$

$x = 0.96$

A thickness of 0.96 millimeters is exceeded by 90% of the flanges

4 0

2 years ago

I'm not sure how to do this! 50 points?

Rus_ich [418]

Answer:

MOP=33

Step-by-step explanation:

MOP + MON = NOP

Substitute what we know

MOP = 3x-3

MON = 4x+9

NOP = 90 right angle

3x-3+4x+9 = 90

Combine like terms

7x+6 =90

Subtract 6 from each side

7x+6-6=90-6

7x = 84

Divide each side by 7

7x/7 = 84/7

x =12

We need to find MOP

MOP = 3x-3

=3(12)-3

36-3

6 0

2 years ago

Read 2 more answers

Recall that two angles are complementary if the sum of their measures is 90degrees°. Find the measures of two complementary angl

Law Incorporation [45]

Answer:

90degrees

Step-by-step explanation:

The sum of complimentary angles will always be 90degrees

4 0

2 years ago

If<br> DX/DT= 2cm/s <br> x=-1 <br> y=x^2+1<br> DY/DT=??

kobusy [5.1K]

Answer:

$\frac{dy}{dt}$ = - 4 cm/s

Step-by-step explanation:

Let us revise the chain rule

If $\frac{dy}{dt}$ = a and $\frac{dx}{dt}$ = b, then

$\frac{dy}{dx}$ = $\frac{dy}{dt}$ ÷ $\frac{dx}{dt}$ = $\frac{a}{b}$

∵ y = x² + 1

- Use the differentiation to find $\frac{dy}{dx}$

∴ $\frac{dy}{dx}$ = 2x

∵ x = -1

- Substitute x by -1 in $\frac{dy}{dx}$

∴ $\frac{dy}{dx}$ = 2(-1)

∴ $\frac{dy}{dx}$ = -2

∵ $\frac{dy}{dt}$ = $\frac{dy}{dx}$ × $\frac{dx}{dt}$

∵ $\frac{dx}{dt}$ = 2 cm/s

∴ $\frac{dy}{dt}$ = (-2) × (2)

∴ $\frac{dy}{dt}$ = - 4 cm/s

8 0

3 years ago