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3 years ago

Solve for x. 3(x - 4) = 2x + 6 Α. Ο B. 2 C. 3.6 D. 10 E. 18

Mathematics

2 answers:

Zigmanuir [339]3 years ago

8 0

E. X=18 you can also just use Photomath or something if you need more help :)

LekaFEV [45]3 years ago

4 0

3(x - 4) = 3x - 12 (expand the brackets)
3x - 12 = 2x + 6
3x = 2x + 6 + 12 (put all of the integers on one side)
3x = 2x + 18 (simplify - collect like terms)
3x - 2x = 18 (put all of the unknowns on one side)
x = 18 (simplify - collect like terms)

Therefore, we know that x is equal to 18, and so the answer is E.

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A 9.85 m ladder is placed against a wall. The height to the top of the ladder is 5 m more than the distance between the wall and

Dafna1 [17]

Given:

Length of the ladder = 9.85 m

The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.

To find:

The height to the top and the distance between the wall and the foot of the ladder.

Solution:

let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).

Pythagoras theorem: In a right angle triangle,

$Hypotenuse^2=Base^2+Perpendicular^2$

In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.

Using the Pythagoras theorem, we get

$(9.85)^2=x^2+(x+5)^2$

$97.0225=x^2+x^2+10x+25$

$0=2x^2+10x+25-97.0225$

$0=2x^2+10x-72.0225$

Here, $a=2, b=10,c=-72.0225$ . Using the quadratic formula, we get

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\dfrac{-10\pm \sqrt{(10)^2-4(2)(-72.0225)}}{2(2)}$

$x=\dfrac{-10\pm \sqrt{676.18}}{4}$

Approximating the value, we get

$x=\dfrac{-10\pm 26}{4}$

$x=\dfrac{-10+26}{4},\dfrac{-10-26}{4}$

$x=\dfrac{16}{4},\dfrac{-36}{4}$

$x=4,-9$

Distance cannot be negative so $x\neq -9.$

Now we have $x=4$

$x+5=4+5$

$x+5=9$

Therefore, the base is 4 m and the height is 9 m.

5 0

3 years ago

If a bus driver leaves her first stop by 7:00 a.m., her route will take less than 37 minutes. If she leaves after 7:00 a.m., she

mr Goodwill [35]

What we know about this situation that either she will take less than 37 minutes:

r<37

or she will take more than 42 minutes

r>42

so it means that she cannot take between 37 and 42 minutes.

The best way to write it is:
37>r v r>42

where "v" means "or" in mathematical notation

4 0

4 years ago

Read 2 more answers

Using the following equation,find the center and radius of the circle <br><br> x^2 + 2x + y^2 +4y=20

Amiraneli [1.4K]

Answer:

center of x²+2x+y²+4y=20:(-1,-2),r=5

Step-by-step explanation:

look at the attachment above ☝️