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3 years ago

It’s late work and I’ve forgotten how to do it

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

4 0

You want to eliminate one of the terms (x or y) in one of the equations so you can solve for the other variable. You have to multiply by the opposite number of the coefficient to be able to eliminate the term in the other equation. If the x coefficient is 2, then you have to multiply the entire other equation by -2. If the y coefficient is -5, then you have to multiply the entire other equation by 5.

10)
-4x + 9y= 9
x - 3y= -6

STEP 1:
multiply the bottom equation by 4
4(x- 3y)= 4(-6)
4x - 12y= -24

STEP 2:
add the top equation and the equation from step 2

-4x + 9y= 9
4x - 12y= -24
the x term cancels out

-3y= 15
divide both sides by -3

y= -5

STEP 2:
substitute the y value in either original equation to solve for x

x - 3y= -6
x - 3(-5)= -6

x + 15= -6
subtract 15 from both sides

x= -21

ANSWER: x= -21; y= -5
____________________

12)
-7x + y= -19
-2x + 3y= -19

STEP 1:
multiply the top equation by -3 to eliminate the y term and to solve for x

-3(-7x + y)= -3(-19)
21x - 3y= 57

STEP 2:
add the bottom equation and the equation from step 2 to solve for x

-2x + 3y= -19
21x - 3y= 57
the y term cancels out

19x= 38
divide both sides by 19

x= 2

STEP 3:
substitute the x value in step 2 to solve for y; you can use either original equation

-7x + y= -19
-7(2) + y= -19

-14 + y= -19
add 14 to both sides

y= -5

ANSWER: x= 2; y=-5

Hope this helps! :)

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3 years ago

a travel agency charges $64 for each bus ticket and $82 for each train ticket. how much does it cost to buy 3 bus tickets and 4

jekas [21]

520 dollars for 4 train tickets and 3 bus tickets.

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3 years ago

If m<BEG = (19x + 3)° and m<EGC = (m<GCB + 4x)°, which of the following statements is true about quadrilateral BEGC? Se

viktelen [127]

Answer:

The sum of all exterior angles of BEGC is equal to 360° ⇒ answer F only

Step-by-step explanation:

* Lets revise some facts about the quadrilateral

- Quadrilateral is a polygon of 4 sides

- The sum of measures of the interior angles of any quadrilateral is 360°

- The sum of measures of the exterior angles of any quadrilateral is 360°

* Lets solve the problem

- DEGC is a quadrilateral

∵ m∠BEG = (19x + 3)°

∵ m∠EGC = (m∠GCB + 4x)°

∵ The sum of the measures of its interior angles is 360°

∴ m∠BEG + m∠EGC + m∠GCB + m∠CBE = 360

∴ (19x + 3) + (m∠GCB + 4x) + m∠GCB + m∠CBE = 360 ⇒ add the like terms

∴ (19x + 4x) + (m∠GCB + m∠GCB) + m∠CBE + 3 = 360 ⇒ -3 from both sides

∴ 23x + 2m∠GCB + m∠CBE = 375

∵ The sum of measures of the exterior angles of any quadrilateral is 360°

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3 0

3 years ago

What are the steps to solve for: 1/5(x+5)=1/4(x-3)+1

andrew11 [14]

Step 1. Simplify $\frac{1}{5} (x+5)$ to $\frac{x+5}{5}$

$\frac{x+5}{5} = \frac{1}{4} (x-3)+1$

Step 2. Simplify $\frac{x+5}{5}$ to $1+ \frac{x}{5}$

$1+ \frac{x}{5} = \frac{1}{4} (x-3)+1$

Step 3. Simplify $\frac{1}{4} (x-3)$ to $\frac{x-3}{4}$

$1+ \frac{x}{5} = \frac{x-3}{4} +1$

Step 4. Cancel $1$ on both sides

$\frac{x}{5} = \frac{x-3}{4}$

Step 5. Multiply both sides by $20$ (the LCM of $5,4$ )

$4x=5(x-3)$

Step 6. Expand

$4x=5x-15$

Step 7. Subtract $5x$ from both sides

$4x-5x=-15$

Step 8. Simplify $4x-5x$ to $-x$

$-x=-15$

Step 9. Multiply both sides by $-1$

$x=15$

Done! :) Hope this helps! :)

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3 years ago

The probability that a single radar station will detect an enemy plane is 0.65. (a) How many such stations are required to be 98

Inga [223]

Answer:

4 stations

Step-by-step explanation:

If we need to be at least 98% certain that an enemy plane flying over will be detected by at least one station, we must ensure that there is at most a 2% chance that no radar stations detect the plane.

The probability that a single radar station does not detect the plane is 0.35.

For n radar stations:

$P=0.02=0.35^n\\n=\frac{log(0.02)}{log(0.35)}\\n=3.73$

Rounding up to the next whole station, at least 4 stations are needed.

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3 years ago