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elena55 [62]
3 years ago
15

Solve for x -6 >_ 10 - 4x

Mathematics
1 answer:
Otrada [13]3 years ago
6 0

We are given this inequality,

-6\geq10-4x

We will follow these steps to solve it:

Step 1:

First let us bring 10 to the left side.

10 is in addition on right, so we apply opposite operation of addition that is subtracting 10 from left side, we get

-6-10\geq-4x

-16\geq-4x

Step 2:

Next we have to eliminate -4 which is in multiplication with x on the right side.

So applying opposite operation of multiplication that is dividing both sides by -4.

We have to consider here that when we divide or multiply with a negative the sign of inequality reverses, that is ≥ becomes ≤ and vice versa.

\frac{-16}{-4}\leq x

x≥4

Answer is last option x≥4.

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Point G is the centroid of the right △ABC with m∠C=90° and m∠B=30°. Find AG if CG=4 ft.
o-na [289]

Answer: \text{Length of AG=}\frac{2\sqrt{63}}{3}

Explanation:  

Please follow the diagram in attachment.  

As we know median from vertex C to hypotenuse is CM  

\therefore CM=\frac{1}{2}AB

We are given length of CG=4  

Median divide by centroid 2:1  

CG:GM=2:1  

Where, CG=4

\therefore GM=2 ft

Length of CM=4+2= 6 ft  

\therefore CM=\frac{1}{2}AB\Rightarrow AB=12

In \triangle ABC, \angle C=90^0

Using trigonometry ratio identities  

AC=AB\sin 30^0\Rightarrow AC=6 ft

BC=AB\cos 30^0\Rightarrow BC=6\sqrt{3} ft  

CN=\frac{1}{2}BC\Rightarrow CN=3\sqrt{3} ft

In \triangle CAN, \angle C=90^0  

Using pythagoreous theorem  

AN=\sqrt{6^2+(3\sqrt{3})^2\Rightarrow \sqrt{63}

Length of AG=2/3 AN

\text{Length of AG=}\frac{2\sqrt{63}}{3} ft


5 0
3 years ago
Samuel earned $18.90 working last weekend. He worked for 24 hours. Which equation and
Ket [755]

Answer:

Is there any options? or do we need to make one?

6 0
3 years ago
Select ALL the correct answers.
skelet666 [1.2K]

Answer:

The statements that are true are:

  • 1.575 was the coffee yield , in thousands of kilograms,before the honeybees were introduced.
  • 1.16 represents the growth factor that reveals the rate at which the coffee yield increases.
  • 2 is the number of times the coffee yield was compounded per year.

Step-by-step explanation:

We are given a function that models The coffee yield, in thousands of kilograms, t years after the introduction of the honeybees.

Also, the coffee yield increases according to a model where the exponential change is compounded semiannually .

The function is given by:

f(t)=1.575(1.16)^{2t}

Here when t=0, i.e. before the honeybees were introduced we have:

f(0)=1.575

Also, the rate of increase i.e. the growth rate is denoted by : 1.16

Also, 2 represents the number of times the coffee yield is compounded per year.

8 0
3 years ago
What is 3x^2 + 4x - 8 = 0
r-ruslan [8.4K]

Answer:

Here is your answer: (In the picture)

Step-by-step explanation:

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8 0
2 years ago
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Cody sold half of his comic books and then bought seventeen more. He now has 41. With how many did he begin?
abruzzese [7]

Answer:

He begun with 48.

Step-by-step explanation:

48/2 = 24

24+17 = 41

5 0
2 years ago
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