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aleksandrvk [35]
3 years ago
15

Contains the point (-1, 2) and is parallel to x – 2y = -3

Mathematics
1 answer:
ivanzaharov [21]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange x - 2y = - 3 into this form

Subtract x from both sides

- 2y = - x - 3 ( divide all terms by - 2 )

y = \frac{1}{2} x + \frac{3}{2} ← in slope- intercept form

with m = \frac{1}{2}

• Parallel lines have equal slopes, thus

y = \frac{1}{2} x + c ← is the partial equation

To find c substitute (- 1, 2) into the partial equation

2 = - \frac{1}{2} + c ⇒ c = 2 + \frac{1}{2} = \frac{5}{2}

y = \frac{1}{2} x + \frac{5}{2} ← in slope- intercept form

Multiply through by 2

2y = x + 5 ( subtract 2y from both sides )

0 = x - 2y + 5 ( subtract 5 from both sides )

- 5 = x - 2y, thus

x - 2y = - 5 ← in standard form

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A biologist tags 25 birds with a band on their foot and lets them go back into the wild. The next year 100 total birds are captu
mestny [16]

Answer:

We can estimate a population of 500 birds.

Step-by-step explanation:

We can estimate the total bird population using a rule of three with the information given:

If we find 5 birds with the foot band among 100 birds captured, how many birds there are in total if inicially we put foot bands in 25 birds?

5 birds with foot band -> 100 birds captured

25 birds with foot band -> X total birds

X * 5 = 25 * 100

X = 25 * 100 / 5 = 500 birds

We can estimate a population of 500 birds.

7 0
3 years ago
I need answers 1-4 please!
madreJ [45]
1. Horizontal asymptotes: None
Vertical asymptote: x=-2
RD: 2
Domain: First picture
Range: first pic

2.HA: y=1
VA: x= -5 negative
RD: x= 5 no negative
Domain: second pic
Range second pic

3.HA: y=0
VA: x=-4,4
RD: none
D: 3rd pic
R: 3rd pic

4.HA: none
VA: x=3
RD: x=-2
D: 4th
R: 4th


I hope this helps!!!!!!!

8 0
3 years ago
A plumbing supply company has fixed costs of $9,000 per month and average variable costs of $9.30 per unit manufactured. The com
nekit [7.7K]

Answer:

8710 units

Step-by-step explanation:

<em>Step 1: Write all the data</em>

Fixed cost: $9000

Average variable cost: 9.3 per unit

Total cost: 90,000

Total units: x

<em>Step 2: Find the total variable cost</em>

Average variable cost is per unit so it has to be multiplied by the number of units to find the total variable cost.

Total variable cost = average variable cost per unit x number of units

Total variable cost = 9.3x

<em>Step 3: Make the formula for finding x</em>

Total cost = total fixed cost + total variable cost

90,000 = 9000 + 9.3x

81000 = 9.3x

x = 8709.67

Rounded off to 8710 units

!!

3 0
3 years ago
What is the solution set of x2 + 5x + 1 = 0?
DerKrebs [107]

Answer:

\huge\boxed{\left\{-\dfrac{5+\sqrt{21}}{2};\ \dfrac{-5+\sqrt{21}}{2}\right\}}

Step-by-step explanation:

x^2+5x+1=0\\\\\text{Use the quadratic formula:}\\\\\text{For}\ ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\\text{if}\ \Delta < 0,\ \text{then the equation has no real solution}\\\text{if}\ \Delta=0,\ \text{then the equation has one real solution}\ x=\dfrac{-b}{2a}\\\text{if}\ \Delta>0,\ \text{then the equation has two real solution}\ x=\dfrac{-b\pm\sqrt{\Delta}}{2a}

\text{We have}\\\\a=1,\ b=5,\ c=1\\\\\Delta=5^2-4(1)(1)=25-4=21>0\\\\x=\dfrac{-5\pm\sqrt{21}}{2(1)}=\dfrac{-5\pm\sqrt{21}}{2}

3 0
3 years ago
What is the opposite of –|–1|
Marianna [84]
What is the opposite of -|-1| so what is the opposite of -1? It's 1!!! Hope this helped!
6 0
3 years ago
Read 2 more answers
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