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Mamont248 [21]
3 years ago
9

Which of the following statements about Triangle ABC are correct?

Mathematics
1 answer:
irina [24]3 years ago
7 0

Answer:

A

Step-by-step explanation:

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What is 1/4(x+16)-x equal too
schepotkina [342]
<span>1/4(x + 16) - x =

First, distribute the 1/4.

= 1/4x + 1/4 * 16 - x

= 1/4x + 4 - x

= 1/4x + 4 - 4/4x

= 1/4x - 4/4x + 4

= -3/4x + 4

= -\dfrac{3}{4}x + 4</span>
8 0
3 years ago
In an arithmetic sequence, t4 + t5 + t6 = 300, and t15 +t16+ t17 = 201. Find t18.
stiks02 [169]
In an arithmetic sequence:
Tn=t₁+(n-1)d

t₄=t₁+(4-1)d=t₁+3d
t₅=t₁+(5-1)d=t₁+4d
t₆=t₁+(6-1)d=t₁+5d

t₄+t₅+t₆=(t₁+3d) +(t₁+4d)+(t₁+5d)=3t₁+12d

Therefore:
3t₁+12d=300    (1)


t₁₅=t₁+(15-1)d=t₁+14d
t₁₆=t₁+(16-1)d=t₁+15d
t₁₇=t₁+(17-1)d=t₁+16d

t₁₅+t₁₆+t₁₇=(t₁+14d)+(t₁+15d)+(t₁+16d)=3t₁+45d

Therefore:
3t₁+45d=201    (2)

With the equations (1) and (2) we make an system of equations:

3t₁+12d=300
3t₁+45d=201

we can solve this system of equations by reduction method.

  3t₁+12d=300
-(3t₁+45d=201)
-----------------------------
       -33d=99      ⇒d=99/-33=-3

3t₁+12d=300
3t₁+12(-3)=300
3t₁-36=300
3t₁=300+36
3t₁=336
t₁=336/3
t₁=112

Threfore:

Tn=112+(n-1)(-3)
Tn=112-3n+3
Tn=115-3n

Now, we calculate T₁₈:

T₁₈=115-3(18)=115-54=61

Answer: T₁₈=61




5 0
3 years ago
Can anyone help me understand how to evaluate the limit of this complex fraction?
SSSSS [86.1K]

Answer:

-1/9

Step-by-step explanation:

\lim_{x \to 3} \frac{1/x-1/3}{x-3}

For simplicity, let's multiply top and bottom by 3x:

\lim_{x \to 3} \frac{3-x}{3x(x-3)}

Factor out a -1:

\lim_{x \to 3} \frac{-(x-3)}{3x(x-3)}

Divide top and bottom by x−3:

\lim_{x \to 3} \frac{-1}{3x}

Evaluate the limit:

\frac{-1}{3(3)}\\-\frac{1}{9}

It's important to note that the function doesn't exist at x = 3.  As x <em>approaches</em> 3, the function <em>approaches</em> -1/9.

5 0
3 years ago
HELP FAST!! What is the volume of a right rectangular prism with a base that measures 4 in by 6 in. and a height of 7 in? A) 17
fredd [130]
You times the height,length,and width together and get 168in.3.
3 0
3 years ago
Read 2 more answers
Please help, and show work if you can!! :))
dmitriy555 [2]

Answer:

Step-by-step explanation:

ΔABD ≅ ΔCBD .

So AD = DC

8x - 4 = 3x + 1       {add 4 to both sides}

     8x = 3x + 1 + 4

     8x = 3x + 5 {subtract 3s from both sides}

  8x - 3x= 5

        5x = 5 {divide both sides by 5}

        x = 5/5

x = 1

8 0
3 years ago
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