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erastova [34]
4 years ago
15

What is the solution set of the equation j+4/j+2=2−1/j ? Note: j≠0, −2

Mathematics
1 answer:
Hunter-Best [27]4 years ago
6 0

Answer:

 values of j are: 2 , -1

Step-by-step explanation:

We have been given:

\frac{j+4}{j+2}={2}-\frac{1}{j}

We will cross multiply in the above equation we get:

\frac{j+4}{j+2}=\frac{2j-1}{j}

j^2+4j=2j^2+4j-j-2

2j^2-j^2+4j-4j-j-2

j^2-j-2

We will solve the quadratic equation by factorizing:

j^2-2j+j-2

j(j-2)+1(j-2)

(j+1)(j-2)

hence, the values of j are: 2 , -1

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In the trapezoid ABCD (AB∥CD) point M∈AD, so that AM:MD=3:5. Line L ∥AB and going through point M intersects diagonal AC and leg
siniylev [52]

Answer:

\dfrac{AP}{PC}=\dfrac{3}{5}

\dfrac{BN}{CN}=\dfrac{3}{5}

Step-by-step explanation:

Consider triangles AMP and ADC. In these triangles,

  • angle A is the common angle, so \angle MAP\cong \angle DAC by reflexive property;
  • angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.

Hence, triangles AMP and ADC are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

\dfrac{AM}{AD}=\dfrac{AP}{AC}\\ \\\dfrac{3x}{3x+5x}=\dfrac{AP}{AC}\\ \\\dfrac{AP}{AC}=\dfrac{3}{8}\Rightarrow AP=\dfrac{3}{8}AC\\ \\PC=AC-AP=AC-\dfrac{3}{8}AC=\dfrac{5}{8}AC,

so

\dfrac{AP}{PC}=\dfrac{\frac{3}{8}AC}{\frac{5}{8}AC}=\dfrac{3}{5}

Consider triangles ACB and PCN. In these triangles,

  • angle C is the common angle, so \angle ACB\cong \angle PCN by reflexive property;
  • angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.

Hence, triangles ACB and PCN are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

\dfrac{CP}{AP}=\dfrac{CN}{CB}\\ \\\dfrac{5x}{3x+5x}=\dfrac{CN}{CB}\\ \\\dfrac{CN}{CB}=\dfrac{5}{8}\Rightarrow CN=\dfrac{5}{8}CB\\ \\BN=BC-CN=BC-\dfrac{5}{8}BC=\dfrac{3}{8}BC,

so

\dfrac{BN}{CN}=\dfrac{\frac{3}{8}BC}{\frac{5}{8}BC}=\dfrac{3}{5}

4 0
3 years ago
Please help me there is a pic thankyou ​
shutvik [7]

Answer:

2

Step-by-step explanation:

y^m x y^n = y^m+n

so y^-4 x y⁶ = y^-4+6

-4+6=2

NOTE: ^ means to the power of

e.g: y^2 is y² :)

5 0
3 years ago
Read 2 more answers
Given g(x) = 2x + 1, solve for a when g(x) = 7.
Over [174]
You would evaluate by plugging in the given number of 7 to get your answer.

7 0
3 years ago
Which algebraic expression means "four less than three times a number"?
MrMuchimi

Answer: is 4-3

Step-by-step explanation:

4-3

4 0
3 years ago
Please when you answer be sure cuz do you know the question that will let you know if you Fail or get a good mark. this question
Len [333]

Answer:

C

Step-by-step explanation:

It is c

3 0
3 years ago
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