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Deffense [45]
3 years ago
13

B is the midpoint of ac. Ab = x+9 and bc = 3x-7 find x and ac

Mathematics
1 answer:
natali 33 [55]3 years ago
7 0

To solve this problem, we need to know 2 relationships:

<h2>1. AC = AB + BC</h2>

The distance of AC is the sum of AB and BC.

AC = AB + BC

We know this since the distance of going from A to C (AC) is the same as going from A to B (AB), then B to C (BC).

<h2>2. AB = BC</h2>

The distance of AB is the same as AC.

AB = BC

We know this since B is in the middle of AC, so the distance from B to A (BA) is the same as the distance from B to C (BC).

You can see the attached image (at the bottom) for a visualization of this.

<h2>Putting them together</h2>

Since we know the values of AB and BC...

AB = x+9\\BC = 3x-7

...we can put these values into our 2nd equation and solve for x:

AB = BC\\x + 9 = 3x -7

Add 7 to both sides:

x + 16 = 3x

Subtract x from both sides:

16 = 2x

Divide both sides by 2:

8 = x\\x = 8

Knowing x, we can find the distance of AC using our first equation.

AC = AB + BC

Let's put in the values of AB and BC:

AC = (x+9) + (3x-7)

Before we put in x = 8, we can simplify this:

AC = (x+9) + (3x-7)\\AC = x + 9 + 3x -7\\AC = x + 3x + 9 -7\\AC = 4x + 9 - 7\\AC = 4x+2

We group x and 3x and add those together. Then we subtract 7 from 9.

With this equation, we can put in x = 8:

AC = 4x +2\\AC = 4*8 + 2

Since 4 * 8 = 32:

AC = 4 * 8 + 2\\AC = 32 + 2\\AC = 34

Finally, we have found both x and AC.

<h2>Answer</h2>

x = 8

AC = 34

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In a recent year, a sample of grade 8 Washington State public school students taking a mathematics assessment test had a mean sc
Daniel [21]

Answer:

The  number is  N  =1147 students

Step-by-step explanation:

From the question we are told that

    The population mean is  \mu  =  281

     The standard deviation is  \sigma  =  34.4

    The sample size is  n = 2000

percentage of the would you expect to have a score between 250 and 305 is mathematically represented as

      P(250 <  X <  305 ) =  P(\frac{ 250 - 281}{34.4 }  <  \frac{X - \mu }{\sigma }  < \frac{ 305 - 281}{34.4 }   )

Generally  

             \frac{X - \mu }{\sigma }  =  Z  (Standardized \ value \  of  \  X )

So  

         P(250 <  X <  305 ) =  P(-0.9012<  Z

       P(250 <  X <  305 ) = P(z_2 < 0.698 ) -  P(z_1 <  -0.9012)

From the z table  the value of  P( z_2 < 0.698) =  0.75741

                                         and  P(z_1 < -0.9012) =  0.18374

     P(250 <  X <  305 ) = 0.75741 - 0.18374

      P(250 <  X <  305 ) =  0.57

The  percentage is  P(250 <  X <  305 ) =  57\%

The  number of students that will get this score is

           N  = 2000 * 0.57

           N  =1147

6 0
3 years ago
Approximate pi plus the square root of 70 to the nearest hundredth.
stich3 [128]

Answer:

  11.51

Step-by-step explanation:

In general, a calculator is required to evaluate the irrational sum ...

  π + √70

<h3>Calculator result</h3>

The result from a readily-available online calculator is shown in the attachment.

  π + √70 ≈ 11.51

__

<em>Additional comment</em>

You have probably memorized pi to several digits: 3.1416. To obtain the required estimate means you need to approximate √70 to about the same level of precision.

For a number n = a² +b, the square root can be approximated by the continued fraction ...

  √n ≈ a +b/(2a +b/(2a +...))

Effectively, the root (r) can be iterated from the recursive formula ...

  r' = a +b/(a +r)

For √70, we have 70 = 8² +6   ⇒   a=8, b=6

If the initial approximation of the root is r0≈a=8, then a couple of iterations gives ...

  r1 = 8 + 6/(8 +r0) = 8 + 6/(8 +8) = 8 3/8

  r2 = 8 + 6/(8 +r1) = 8 +6/(8 +8 3/8) = 8 48/131

This has sufficient accuracy for the purpose. The decimal equivalent of the sum then becomes ...

  3.1416 +8.3664 = 11.5080 ≈ 11.51

5 0
2 years ago
The perimeter of a rectangle is 1000m. if the length is given as x , find the width in terms of x
BabaBlast [244]

\text{Given that,}\\\\\text{Perimeter = 1000 m}\\\\\implies 2(\text{Length} + \text{Width}) = 1000~ \text m\\\\\implies (x+ \text{Width}) = \dfrac{1000}2 =500~ \text m\\\\\implies \text{Width} =(500 -x) ~\text{m}

4 0
2 years ago
Triangle ABC is translated according to the rule (x,y) arrow (x+2,y-8) if the coordinates of the pre image of point B are (4,-5)
kherson [118]
Answer: the coordinates of B' are (6, -13)

Justification:

1) Translating triangle ABC according to the rule (x,y) → (x + 2, y - 8) means that every single point of the triangle will be translated two units to the righ (x + 2) and 8 units downward (y - 8).

2) To find the coordinates of anay image you have to add up 2 to the x coordinate (x + 2) and subtract 8 from the y-coordinate (y - 8).

3) Peforming those simple operations to the coordinates of the point B (4, -5), you will obtain the point B':

* x' = x + 2 = 4 + 2 = 6
* y' = y  - 8 = -5 - 8 = - 13

Answer: the coordinates of B' are (6, -13)
5 0
3 years ago
Marianna average 84 on her first three history exams. The first score was 67 the second score was seven less than the third scor
wel
Let S=score on the second exam, then
(67+S+(S+7))/3=84
cross multiply
2S+74=252
2S=178
S=89
So second exam: 89
third exam=89+7=96
Check: (67+89+96)/3=84 ok.
7 0
3 years ago
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