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3 years ago

Solve the inequality. -4x + 15 < -21

Mathematics

1 answer:

Dmitriy789 [7]3 years ago

6 0

Answer:

x>9

Step-by-step explanation:

-4x + 15 < -21

Subtract 15 from each side

-4x + 15-15 < -21-15

-4x < -36

Divide each side by -4, remembering to flip the inequality

-4x/-4> -36/-4

x >9

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Answer:

See explanation

Step-by-step explanation:

Theorem 1: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

Theorem 2: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

1. Start point: By the 1st theorem,

$x^2=25\cdot (49-25)=25\cdot 24=5^2\cdot 2^2\cdot 6\Rightarrow x=5\cdot 2\cdot \sqrt{6}=10\sqrt{6}.$

2. South-East point from the Start: By the 2nd theorem,

$x^2=40\cdot (40+5)=4\cdot 5\cdot 2\cdot 9\cdot 5\Rightarrow x=2\cdot 5\cdot 3\cdot \sqrt{2}=30\sqrt{2}.$

3. West point from the previous: By the 2nd theorem,

$x^2=(32-20)\cdot 32=4\cdot 3\cdot 16\cdot 2\Rightarrow x=2\cdot 4\cdot \sqrt{6}=8\sqrt{6}.$

4. West point from the previous: By the 1st theorem,

$9^2=x\cdot 15\Rightarrow x=\dfrac{81}{15}=\dfrac{27}{5}=5.4.$

5. West point from the previous: By the 2nd theorem,

$10^2=8\cdot (8+x)\Rightarrow 8+x=12.5,\ x=4.5.$

6. North point from the previous: By the 1st theorem,

$x^2=48\cdot 6=6\cdot 4\cdot 2\cdot 6\Rightarrow x=6\cdot 2\cdot \sqrt{2}=12\sqrt{2}.$

7. East point from the previous: By the 2nd theorem,

$x^2=22.5\cdot 30=225\cdot 3\Rightarrow x=15\sqrt{3}.$

8. North point from the previous: By the 1st theorem,

$x^2=7.5\cdot 36=270\Rightarrow x=3\sqrt{30}.$

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$x^2=12.5\cdot (12.5+13.5)=12.5\cdot 26=25\cdot 13\Rightarrow x=5\sqrt{13}.$

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$12^2=x\cdot 30\Rightarrow x=\dfrac{144}{30}=4.8.$

101. East point from the previous: By the 1st theorem,

$6^2=1.6\cdot (x-1.6)\Rightarrow x-1.6=22.5,\ x=24.1.$

11. East point from the previous: By the 2nd theorem,

$20^2=32\cdot (32-x)\Rightarrow 32-x=12.5,\ x=19.5.$

12. South-east point from the previous: By the 2nd theorem,

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13. North point=The end.

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3 years ago

What is the vertex form of y=-2x2+4x + 3?

sukhopar [10]

Answer:

$y=-2(x-1)^2+5$

Step-by-step explanation:

we have

$y=-2x^2+4x+3$

This is the equation of a vertical parabola open downward

The vertex represent a maximum

Convert the quadratic equation into vertex form

step 1

Factor -2

$y=-2(x^2-2x)+3$

step 2

Complete the square

$y=-2(x^2-2x+1)+3+2$

$y=-2(x^2-2x+1)+5$

step 3

Rewrite as perfect squares

$y=-2(x-1)^2+5$ ----> equation in vertex form

The vertex is the point (1,5)

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3 years ago

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11111nata11111 [884]

Answer:

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3 years ago

John is twice as old as Mary. The sum of their ages is 21. How old is Mary?

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Answer:

Mary is 7

Because 14+7 =21

So j+m=21

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3 years ago