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umka21 [38]
2 years ago
8

if BD is perpendicular to AC M angle DBE equals 2x - 1 + m angle CBE equals 5x - 42 find the value of x​

Mathematics
1 answer:
Paha777 [63]2 years ago
7 0
<h2>Answer:</h2>

<h2>Step-by-step explanation:</h2>

I've drawn a graph in order to a better understanding of this problem. We know that:

BC is perpendicular to AC

∠DBE = 2x - 1

∠CBE = 5x - 42

Let's call the intersection of line BC and AC the point P, so:

∠P=90°

And points B, P and C form the triangle ΔBPC. On the other hand, ∠CBE and ∠PCB are Alternate Interior Angles, so:

∠PCB = ∠CBE = 5x - 42

Moreover:

∠PBC = 2x - 1 - (5x - 42)

∠PBC = 2x - 1 - 5x + 42

∠PBC = -3x + 41

The internal angles of any triangle add up to 180°. Hence for ΔBPC:

90° + ∠PBC + ∠PCB  = 180°

90° - 3x + 41  + 5x - 42  = 180°

2x + 89 = 180

2x = 91

x = 45.5°

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10. A school is trying to schedule periods of Chemistry and Algebra II.
pochemuha

Answer:

~62%

Step-by-step explanation:

Let n(A) be the number of students signed up for Algebra II.

Given that n(A) = 298

Let n(B) be the number of students signed up for Chemistry.

Given that n(B) = 328

n(A \cup B) will be the number of students who have signed up for either one or both of two subjects.

n(A \cup B) = 386

<em></em>

<em>Formula for n(A </em>\cup<em> B):</em>

n(A \cup B) = n(A) + n(B) - n(A \cap B)

Where n(A \cap B) is the number of students signed up for both the courses.

Putting the values in the formula above:

386 = 298 + 328 - n(A \cap B)

n(A \cap B) = 240

Formula for Probability of an event E:

P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}

P(A \cap B) = \dfrac{n(A \cup B) }{n(A \cap B)}

\Rightarrow P(A \cap B) = \dfrac{240 }{386}\\\Rightarrow P(A \cap B) = 62.17\%

Hence, the required probability is ~62%

3 0
2 years ago
Math how many models of 100 do u need to to model 3,200 explain
Keith_Richards [23]
32 because 32 x 100 = 3,200
4 0
2 years ago
1/3(4+18)-2 to the second power
skad [1K]

Answer:

3.33333333333

or

10          

 —— = 3.33333

 3            

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  1          

 (— • 22) -  22

  3          

Step  2  :

           1

Simplify   —

           3

Equation at the end of step  2  :

  1          

 (— • 22) -  22

  3          

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         22     22 • 3

   22 =  ——  =  ——————

         1        3  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

22 - (22 • 3)     10

—————————————  =  ——

      3           3

Final result :

 10          

 —— = 3.33333

 3            

3 0
2 years ago
Solve for n in the follow equation 4n - p = 3r
lukranit [14]
3R+P
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Add the P to the other side and divide by 4
5 0
2 years ago
A consumer is considering two different purchasing options for the car of their choice. The first option, which is leasing, is d
AVprozaik [17]

Answer:

  • y=250x+4000
  • y=400x+400

Step-by-step explanation:

Given that:

  • x represents the number of months of ownership; and
  • y represents the total paid for the car after ‘x' months.

<u>First Option (Leasing)</u>

250x - y + 4000 = 0

Expressing the equation in the Slope-Intercept Form y=mx+b, we have:

y=250x+4000

<u>Second Option (Financing)</u>

$400 for 0 months of ownership, (0,400), and $4400 for 10 months of ownership, (10, 4400).

First, we determine the slope of the line joining (0,400) and (10,4400)

Slope, m= \dfrac{4400-400}{10-0}= \dfrac{4000}{10}=400

We have:

y=400x+b

When y=400, x=0

400=400(0)+b

b=400

Therefore, the Slope-Intercept Form of the second option is:

y=400x+400

<u>Significance</u>

  • In the first option, there is a down payment of $4000 and a monthly payment of $250.
  • In the second option, there is a down payment of $400 and a monthly payment of $400.

<u>Part B</u>

We notice from the graph that after 24 months, the cost for leasing and financing becomes the same ($10,000). Therefore, a consumer will be better off financing since the downpayment for leasing is higher.

<u>i.e </u>

  • When x=0, y=$4000 for leasing
  • When x=0, y=$400 for financing

4 0
2 years ago
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