Ria is performing an experiment in chemistry class with a certain

HELP LOOK AT THE SCREENSHOT<br><br> Find the value of x. (SHOW WORK)

Vanyuwa [196]

Answer: x = 2

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Explanation:

Refer to the diagram below.

I've added points D,E,F,G. This helps with labeling the segments and angles, and identifying the proper triangles (to see which are congruent pairs).

Triangle GEA is congruent to triangle GFA. We can prove this using the AAS congruence theorem. We have AG = AG as the pair of congruent sides, and the congruent pairs of angles are marked in the diagram (specifically the blue pairs of angles and the gray right angle markers)

Since triangle GEA is congruent to triangle GFA, this means the corresponding pieces segment GF and GE are the same length.

The diagram shows GF = 3x-4, so this means GE = 3x-4 as well.

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Through similar steps, we can show that triangle GEC is congruent to triangle GDC. We also use AAS here as well.

The congruent triangles lead to GD = GE. So GD = 3x-4. The diagram shows that GD = 6x-10

Since GD is equal to both 3x-4 and 6x-10, this must mean the two expressions are equal.

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Now let's solve for x

6x-10 = 3x-4

6x-3x = -4+10

3x = 6

x = 6/3

x = 2

4 0

3 years ago

Find the difference

kati45 [8]

Answer:

$\frac{x}{x+1}$

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is 3 = r/2 !?!?! ANYONE

kipiarov [429]

Answer:

Step-by-step explanation:

3 = r/2

6 = r

7 0

2 years ago

Read 2 more answers

the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate i

nekit [7.7K]

Answer:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

$A = \frac{1}{2}\cdot b\cdot h$ (Eq. 1)

Where:

$A$ - Area of the triangle, measured in square centimeters.

$b$ - Base of the triangle, measured in centimeters.

$h$ - Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

$\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}$ (Eq. 2)

Where:

$\frac{dA}{dt}$ - Rate of change of area in time, measured in square centimeters per minute.

$\frac{db}{dt}$ - Rate of change of base in time, measured in centimeters per minute.

$\frac{dh}{dt}$ - Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

$\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}$

$\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}$ (Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

$b = \frac{2\cdot A}{h}$

If we know that $A = 130\,cm^{2}$ , $h = 15\,cm$ , $\frac{dh}{dt} = 2.5\,\frac{cm}{min}$ and $\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}$ , the rate of change of the base of the triangle in time is:

$b = \frac{2\cdot (130\,cm^{2})}{15\,cm}$

$b = 17.333\,cm$

$\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)$

$\frac{db}{dt} = -2.262\,\frac{cm}{min}$

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

6 0

3 years ago

13. In ADGE,DG = 8,GE = 17, and DE = 15. What is the length of DF? Round to the nearest hundredth.

Ronch [10]

Answer:

Step-by-step explanation:

The trick is not to get all caught up in Pythagoras. There is a much simpler way to do it. Find the area of the triangle two different ways. DG and DE are at right angles. That is one way to find area. The other is use the height (DF) and multiply that by the hypotenuse GE.

DG*DE/2 = GE * DF/2 Multiply both sides by 2

DG*DE = GE * DF

DG = 8

DE = 15

GE = 17

8*15 = 17* DF

120 = 17 * DF Divide by 17

120/17 = DF

DF = 7.06

7 0

3 years ago