1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aleksandr-060686 [28]
3 years ago
10

Solve for X. Please!!

Mathematics
1 answer:
pychu [463]3 years ago
3 0

Answer:

x = 37.5

Step-by-step explanation:

By Basic Proportionality Theorem:

\frac{x}{20}  =  \frac{46 - 16}{16} \\  \\   \frac{x}{20}  =  \frac{30}{16} \\  \\  x =  \frac{20 \times 30}{16}  \\  \\ x =  \frac{600}{16}  \\  \\ x = 37.5

You might be interested in
List the four facter of 10 factor pairs
LenaWriter [7]
1,10 and 2,5, 
those are the pairs
4 0
3 years ago
Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficie
Dvinal [7]
For part (a), you have

\dfrac x{x^2+x-6}=\dfrac x{(x+3)(x-2)}=\dfrac a{x+3}+\dfrac b{x-2}
x=a(x-2)+b(x+3)

If x=2, then 2=b(2-3)\implies b=-2.

If x=-3, then -3=a(-3-2)\implies a=\dfrac35.

So,

\dfrac x{x^2+x-6}=\dfrac 3{5(x+3)}-\dfrac 2{x-2}

For part (b), since the degrees of the numerator and denominator are the same, you first need to find the quotient and remainder upon division.

\dfrac{x^2}{x^2+x+2}=\dfrac{x^2+x+2-x-2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}

In the remainder term, the denominator x^2+x+2 can't be factorized into linear components with real coefficients, since the discriminant is negative (1-4\times1\times2=-7). However, you can still factorized over the complex numbers, so a partial fraction decomposition in terms of complexes does exist.

x^2+x+2=0\implies x=-\dfrac12\pm\dfrac{\sqrt7}2i
\implies x^2+x+2=\left(x-\left(-\dfrac12+\dfrac{\sqrt7}2i\right)\right)\left(x-\left(-\dfrac12-\dfrac{\sqrt7}2i\right)\right)
\implies x^2+x+2=\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)

Then you have

\dfrac{x+2}{x^2+x+2}=\dfrac a{x+\dfrac12-\dfrac{\sqrt7}2i}+\dfrac b{x+\dfrac12+\dfrac{\sqrt7}2i}
x+2=a\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)+b\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)

When x=-\dfrac12-\dfrac{\sqrt7}2i, you have

-\dfrac12-\dfrac{\sqrt7}2i+2=b\left(-\dfrac12-\dfrac{\sqrt7}2i+\dfrac12-\dfrac{\sqrt7}2i\right)
\dfrac32-\dfrac{\sqrt7}2i=-\sqrt7ib
b=\dfrac12+\dfrac3{2\sqrt7}i=\dfrac1{14}(7+3\sqrt7i)

When x=-\dfrac12+\dfrac{\sqrt7}2i, you have

-\dfrac12+\dfrac{\sqrt7}2i+2=a\left(-\dfrac12+\dfrac{\sqrt7}2i+\dfrac12+\dfrac{\sqrt7}2i\right)
\dfrac32+\dfrac{\sqrt7}2i=\sqrt7ia
a=\dfrac12-\dfrac3{2\sqrt7}i=\dfrac1{14}(7-3\sqrt7i)

So, you could write

\dfrac{x^2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}=1-\dfrac {7-3\sqrt7i}{14\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)}-\dfrac {7+3\sqrt7i}{14\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)}

but that may or may not be considered acceptable by that webpage.
5 0
3 years ago
Read 2 more answers
a ladder 10 ft long leans against a wall. The foot of the ladder is 8ft from the base of the wall. How high up the wall does the
Alekssandra [29.7K]

Answer:

6 ft.

Step-by-step explanation:

a^2+8^2=10^2\\a^2+64=100\\a^2+64-64=100-64\\a^2=36\\\sqrt{a^2}=\sqrt{36}\\a=6

5 0
4 years ago
Assemble the proof by dragging tiles to the statements HELLPPPPPP PLEASEEEE
TEA [102]

Answer:

See explanation

Step-by-step explanation:

1. JK\cong LM - given

2.  JL\cong LN - definition of midpoint (the midpoint of the segment divides the segment into two congruent segments)

3. \angle LJK\cong \angle NLM - corresponding angles theorem (corresponding angles theorem states: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.)

4. \triangle JLK\cong \triangle LNM - SAS (SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent).

8 0
4 years ago
Read 2 more answers
Pls help me ill mark you brainliest and show your work please
dexar [7]

Answer:

Infinately many solutions.

Step-by-step explanation:

2x-4=2(x-2)

Distribute

2x-4=2*x-2*2

2x-4=2x-4

Since both sides are the same, there are infinately many solutions.

Hope this helps!

8 0
3 years ago
Other questions:
  • A company buys printer paper in a box which contains 8 packages. If each package of paper costs 3 dollar, how much does a box of
    11·2 answers
  • Zach invested $50 and was able to triple his money in two years. Kayla also began with $50 in investments, and was able to cube
    13·2 answers
  • Please help on this problem
    13·1 answer
  • What are the solution(s) to the quadratic equation x2 - 25 = 0?
    8·1 answer
  • The petronas towers in Kuala Lumpur, Malaysia, are 452 meters tall. A woman who is 1.75 meters tall stands 120 meters from the b
    7·1 answer
  • Alex is painting an 8 foot mural on the wall of the community center. If he has finished 1/4 of the mural, how many feet of the
    9·1 answer
  • Help please !!!!!!!!!​
    6·1 answer
  • What is the range of the function f(x) = -4|x + 1| − 5?
    15·2 answers
  • Which parallelograms have perpendicular diagonals
    11·1 answer
  • Give me one example of an item where you would need to find the area of a square. Also, Give me one example of an item where you
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!