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2 years ago

Please help with one of these

Mathematics

1 answer:

LekaFEV [45]2 years ago

3 0

Number 10 is Answer: y=2.5/2x+3.5

Step-by-step explanation:

The 3.5 is the y intercept because it is when x is 0. The slope is just the change in y over the change in x

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A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 96 yards, what are its

Pachacha [2.7K]

Width = x
length = 2x

96 = x + x + 2x + 2x
96 = 6x
x = 16

2x is simply 16 × 2.

8 0

2 years ago

Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps

Firdavs [7]

ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the

x²y = -4 ... (I)

Condition 2: Real parts are the same

x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

x²y = -4 ... (I)
x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

y = -3 - x² ... (II)

Substituting into equation (I)

x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i

x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i

They result in conjugates

4 0

3 years ago

Read 2 more answers

Write an equation for the line that passes through the points (0, -6) and (-3, 0).

Dmitry [639]

Answer:

$\displaystyle y = -2x -6$

Step-by-step explanation:

x-intercept → Plug in 0 for y to get −3 for x

y-intercept → When x is set equal to 0 [(0, −6)]

I am joyous to assist you anytime.

3 0

2 years ago

A bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 5%per year. If the interest received

marin [14]

Answer: $31000 was loaned at 13%.

Step-by-step explanation:

Let x represent the amount loaned out at 13% interest rate.

Let y represent the amount loaned out at 5% interest rate.

The bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 5%per year. It means that

x + y = 68000

The interest received made from $x in one year is

13/100 × x = 0.13x

The interest received made from $y in one year is

5/100 × x = 0.05y

If the interest received was $5880, it means that

0.13x + 0.05y = 5880- - - - - - - - - 1

Substituting x = 68000 - y into equation 1, it becomes

0.13(68000 - y) + 0.05y = 5880

8840 - 0.13y + 0.05y = 5880

- 0.13y + 0.05y = 5880 - 8840

- 0.08y = - 2960

y = - 2960/- 0.08

y = 37000

x = 68000 - y = 68000 - 37000

x = $31000

5 0

3 years ago

What is a common denominator for 1/4 and 5/6!?!? PLEASE HELP!!!!!!

UNO [17]

A common denominator for 1/4 and 5/6...
1/4 = 3/12
5/6 = 10/12
the common denominator (LCM) would be 12

5 0

3 years ago

Read 2 more answers