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4 years ago

6x-4y=54 -9x+2y=-69 substitution

1 answer:

7 0

$6x-4y=54\qquad\text{subtract 6x from both sides}\\\\-4y=-6x+54\qquad\text{divide both sides by (-2)}\\\\2y=3x-27\\\\\text{Substitute it to the second equation}\ -9x+2y=-69:\\\\-9x+(3x-27)=-69\\\\-9x+3x-27=-69\qquad\text{add 27 to both sides}\\\\-6x=-42\qquad\text{divide both sides by (-6)}\\\\\boxed{x=7}\\\\\text{Put the value of x to the equation}\ 2y=3x-27:\\\\2y=3(7)-27\\\\2y=21-27\\\\2y=-6\qquad\text{divide both sides by 2}\\\\\boxed{y=-3}\\\\Answer:\ \boxed{x=7\ and\ y=-3\to(7,\ -3)}$

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Juanita begins to factor an expression as shown. x2+3x−18=(x+)(x−) What numbers should be placed in the boxes from left to right

stich3 [128]

Answer:

Option A is the correct answer.

Step-by-step explanation:

Here we need to factorize x²+3x−18

The coefficient of x is 3 and the constant is -18

Which means

The sum of factors is 3

The product of factors is -18

The factors satisfying are 6 and -3

Here the factors are given in the type (x+)(x−)

So the value after plus is 6 and value after - is 3

Option A is the correct answer.

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3 years ago

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Of the following sets, which numbers in {1, 2, 3, 4, 5} make the inequality 5x + 2 > 12 true?

kicyunya [14]

Answer:

3,4,5

Step-by-step explanation:

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4 years ago

In the number 2,145,857 how does the digit 5 in the thousands place compare to the digit 5 in the tens place

Sergeeva-Olga [200]

Hello from MrBillDoesMath!

Answer:

The 5 in the thousands place means 5 * 1000 or 5000. The 5 in the tens place means 5* 10 or 50.

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4 years ago

Solve x exponent 3 = 125/27

LiRa [457]

Answer:

x=5/3

Step-by-step explanation:

=>x^3=125/27

=>x^3=(5/3)^3

=>x=5/3

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3 years ago

Read 2 more answers

How can i find area of abd triangle. .............

Nataly [62]

Answer:

6 square units

Step-by-step explanation:

The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.

<h3>angles</h3>

Any right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.

Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.

<h3>segments</h3>

The fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.

The tangent ratio is ...

Tan = Opposite/Adjacent

Applying that to angle β, we have

tan(β) = OD/AD [eqn 1]

tan(β) = BC/AC [eqn 2]

These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.

Equation [eqn 1] tells us ...

AD = OD/tan(β)

Equation [eqn 2] tells us ...

BC = AC·tan(β)

The area of ΔADB is ...

Area = 1/2bh

Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))

Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel

The length of AC is given as 6, and we know OD = 2, so the area is ...

Area = 1/2(2)(6) = 6

The area of triangle ADB is 6 square units.

6 0

3 years ago