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Ilya [14]
3 years ago
12

Narne:

Mathematics
1 answer:
Dafna1 [17]3 years ago
5 0

Answer:

x < -20

Step-by-step explanation:

Given the following question:

x+8 < -12

In order to solve one step inequalities, we solve how we would normally solve a one-step equation and then graph the answer on a number line.

x+8 < -12
8-8=0
-12-8=-20
x < -20

<u>Now to graph the inequality on a number line, keep a few things in mind:</u>
. x is less than -20 which means the line would go the opposite way of the negative 20.
. < is a greater than sign, not a greater than or equal sign (≤) so the number line will have a open point.
. The number line will have a point on -20.

Hope this helps.

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Which are the solutions to the quadratic equation x^2=9x+6
AlekseyPX
I will use a quadratic formula:

x^2=9x+6\ \ \ \ |-9x-6\\\\x^2-9x-6=0\\\\a=1;\ b=-9;\ c=-6\\\\b^2-4ac=(-9)^2-4\cdot1\cdot(-6)=81+24=105\\\\\sqrt{b^2-4ac}=\sqrt{105}\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\x_1=\dfrac{-(-9)-\sqrt{105}}{2\cdot1}=\dfrac{9-\sqrt{105}}{2}\\\\x_2=\dfrac{-(-9)+\sqrt{105}}{2\cdot1}=\dfrac{9+\sqrt{105}}{2}
5 0
3 years ago
Item 11
marysya [2.9K]

Answer:

4 ft higher

Step-by-step explanation:

Since the ladder is 10 ft long and its top is 6 feet high(above the ground), we find the distance of its base from the wall since these three (the ladder, wall and ground) form a right angled triangle. Let d be the distance from the wall to the ladder.

So, by Pythagoras' theorem,

10² = 6² + d²  (the length of the ladder is the hypotenuse side)

d² = 10² - 6²

d² = 100 - 36

d² = 64

d = √64

d = 8 ft

Since the ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up.

Now, let x be the distance the top of the ladder is moved, the new height of top of the ladder is 6 + x. Since the base moves twice the distance the top of the ladder moves up, the new distance for our base is 8 - 2x(It reduces since it gets closer to the wall).

Now, applying Pythagoras' theorem to the ladder with these new lengths, we have

10² = (6 + x)² + (8 - 2x)²

Expanding the brackets, we have

100 = 36 + 12x + x² + 64 - 32x + 4x²

collecting like terms, we have

100 = 4x² + x² + 12x - 32x + 64 + 36

100 = 5x² - 20x + 100

Subtracting 100 from both sides, we have

100 - 100 = 5x² - 20x + 100 - 100

5x² - 20x = 0

Factorizing, we have

5x(x - 4) = 0

5x = 0 or x - 4 = 0

x = 0 or x = 4

The top of the ladder is thus 4 ft higher

7 0
3 years ago
1. In an AP, the ratio of the 2nd term to the 7th term is 1/3. If the 5th term is
grandymaker [24]

Answer:

T15 = 31

Step-by-step explanation:

Its in the picture

I hope it helps :)

6 0
4 years ago
I need help with number 5 please
bearhunter [10]
I believe the answer is b
8 0
3 years ago
Can someone help please
Serjik [45]
X=106 with working shown in the photo

3 0
3 years ago
Read 2 more answers
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