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11Alexandr11 [23.1K]
4 years ago
11

How do you solve this?

Mathematics
1 answer:
Naddika [18.5K]4 years ago
5 0
\dfrac{3+4i}{2+i}=\dfrac{(3+4i)(2-i)}{(2+i)(2-i)^{(*)}}=\dfrac{3\cdot2-3\cdot i+4i\cdot2-4i\cdot i}{2^2-i^2^{(**)}}\\\\=\dfrac{6-3i+8i+4}{4-(-1)}}=\dfrac{10+5i}{4+1}=\dfrac{10+5i}{5}=\dfrac{10}{5}+\dfrac{5i}{5}=\boxed{2+i}\to \boxed{a=2}\\\\used:\\(*)\ (a+b)(a-b)=a^2-b^2\\(**)\ i^2=-1
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An equilateral triangle has an apothem of 5 cm. Find the perimeter of the triangle to the nearest centimeter.
san4es73 [151]
The apothem is the distance from the center to the midpoint of one of the sides of a regular polygon.  You can make a right triangle with the apothem, the line from the midpoint to the corner and the line from the center to the corner.  An equilateral triangle has 60 degree angles (180/3).  The right triangle has half of one of those angles so 30 degrees.  Now we have a 30-60-90 triangle where the short leg is 5cm.  The long leg, which is also half of one side of the triangle is thus 5\sqrt{3}.  A whole side of the triangle is 10\sqrt{3}.  Multiply that by 3 to get the perimeter of <span>30\sqrt{3}.</span>
4 0
3 years ago
Jackson runs a farm stand that sells bananas and grapes. Each pound of bananas sells for $1 and each pound of grapes sells for $
mars1129 [50]

Jackson sold 27 pounds of bananas and 12 pounds of grapes.

Given that Jackson runs a farm stand that sells bananas and grapes, and each pound of bananas sells for $ 1 and each pound of grapes sells for $ 2.25, and Jackson sold 15 more pounds of bananas than pounds of grapes and made $ 54 altogether, to determine the number of pounds of bananas sold and the number of pounds of grapes sold the following calculation must be performed:

  • 25 x 1 + 10 x 2.25 = 25 + 22.50 = 47.50
  • 26 x 1 + 11 x 2.25 = 26 + 24.75 = 50.75
  • 27 x 1 + 12 x 2.25 = 27 + 27 = 54

Therefore, Jackson sold 27 pounds of bananas and 12 pounds of grapes.

Learn more about quantities in brainly.com/question/25823155

3 0
3 years ago
Solve for x:  (x − 2) = 4x. (1 point)​
Georgia [21]

Steps:

(x-2)=4x

Pretend that there is a one in front of x-2

1(x-2)=4x

Multiply the bracket by 1

x-2=4x

Move x to the other side .Whenever you move a number or letter the sign changes.

x-x-2=4x-x

-2=3x

Divide by 3 for -2 and 3

-2/3=3/3 x

x=-2/3

Check answer by using substitution method

(-2/3-2)=4(-2/3)

(-2/3-6/3)=-8/3

-8/3=-8/3

Answer is -2/3

3 0
3 years ago
Cuál es la propiedad de - 53 + 53 = 0 ?​
tatyana61 [14]

Answer:

Cancellation property

Step-by-step explanation:

la propiedad es propiedad de cancelación.

8 0
3 years ago
Write 6x+2y=-12 in slope intercept form​
Elena L [17]

Answer:

y = -3x - 6

Step-by-step explanation:

Slope intercept form:

y = mx +b

6x + 2y = -12

       2y = -6x - 12

\frac{2y}{2}=\frac{-6x}{2} - \frac{12}{2}\\\\ y = -3x - 6

4 0
3 years ago
Read 2 more answers
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