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Alekssandra [29.7K]
3 years ago
13

Solve for x. The triangles in each pair are similar. ​

Mathematics
1 answer:
KatRina [158]3 years ago
3 0

Answer:

Step-by-step explanation:

You need to pay very close attention to the triangle similarity statement.  This says that triangle NML is similar to triangle NVU.  But if you look at the way that triangle NVU is oriented in its appearance, it's laying on its side.  We need to set it upright so that angle N is the vertex angle, angle V is the base angle on the left, and angle U is the base angle on the right.  When we do that we see that sides NV and NM are corresponding and exist in a ratio to one another; likewise with sides VU and ML.  Setting up the proportion:

\frac{NV}{NM}=\frac{VU}{ML}

Filling in:

\frac{12}{36} =\frac{9}{9x}

Cross multiply to get

324 = 108x

and x = 3

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Find the quotient and reduce to lowest terms: ((x²-4)/(3x)) ÷ ((x-2)/(2x)).
DENIUS [597]

Answer:   2/3 * (× + 2 )

Step-by-step explanation:

((x²-4)/(3x)) ÷ ((x-2)/(2x)).          ⇒   [ ( ײ - 4 ) * 2x ] ÷ [ ( × - 2 ) *3x ]

Simplifying by x   [ 2 * ( ײ - 4 ) ] ÷ [ ( × - 2 ) *3 ] ⇒ (2/3)*{ [ ( x-2 )*(×+2)]÷ (×-2) }

Simplifying by ( ×+2)     2/3 * (× + 2 )

3 0
3 years ago
Which table has a constant of proportionality between y and x of 12?
Nikolay [14]

Answer & Step-by-step explanation:

To find if they have a constant of proportionality of 12, use the following:

\frac{y}{x}=12

Divide y by the x value (x,y), and if the remaining equation is true, then that table has a constant of proportionality of 12.*

:Done

*Make sure you check all the values in a table. Sometimes only the first values will have k=12, while the others don't.

**The constant of proportionality is represented by <em>k</em>.

3 0
3 years ago
Read 2 more answers
help me find the volume and area of this figure step by step pleasefyi the answer key my teacher gave me says that the surface a
alisha [4.7K]

The volume of the shape

We have a cylinder that is cut into two. Its external radius is 5ft, while its internal radius is 4ft.

External radius = internal radius + thickness

\begin{gathered} \text{External radius = 4ft + 1ft } \\ =\text{  5ft} \end{gathered}

Internal radius = 4ft (given)

Recall that the volume(V) of a full cylinder is:

V\text{ = }\pi r^2h

Since the cylinder is cut into two, the volume(V) is:

V\text{ = }\frac{\pi r^2h}{2}

height (h) = 12ft (given)

The volume of the shape:

\begin{gathered} =\text{ Volume of cylinder with a radius of 5ft - Volume of cylinder with a radius of 4ft} \\ =\text{ }\frac{\pi\text{ }\times5^2\text{ }\times\text{ 12}}{2}\text{ - }\frac{\pi\text{ }\times4^2\text{ }\times\text{ 12}}{2} \\ =\text{ 471.239 - }301.593 \\ =169.65ft^3 \end{gathered}

5 0
10 months ago
Please help me im about to fail!!!! Express your answer in scientific notation.
Illusion [34]

Answer:

3.74 x 10^5

Step-by-step explanation:

First expand the term in scientific notation into normal notation.

3.3 x 10^5   -   Here the ^5 tells us to move the decimal five places to the right, so we go from

3.30000 to

330000.00

So 3.3 x 10^5 = 330,000

Now add that to 44,000 and you get 374,000.

Return this number to scientific notation.  Move the decimal back to its spot before the 3.  We go from

374,000.00 to

3.74000

Once again the decimal has moved five places, so that is the number in the exponent of the our scientific notation, and therefore our answer is

3.74 x 10^5

3 0
2 years ago
Someone please help me !!!
alexandr1967 [171]

Because this triangle is a right traingle and has one angel that is 45 degrees, the third angle must be 45 degrees to because 90+45+45=180. With that, km must be the same length as lm. we know lm is 5 so km is 5 too. No we can plug this into the Pythagorean Theorem too get

5^2+5^2=c^2

25+25=c^2

50=c^2

√50=√c^2

√25*2=c

5√2=c

Thats your answer to the length of lk.

3 0
3 years ago
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