What do variables and function have in common

Answer:

y = 1/2 x + 3

Step-by-step explanation:

mid point of line BC = (2, 4)

slope of the line containing median (m) = 1/2

y intercept (b)= 3

since y = mx + b

y = 1/2x + 3

The median of a triangle is the line segment joining the any of the vertex to the mid-point of the opposite side of that vertex. The equation of the median through point A is given by y = 1/2x + 3.

A median of a triangle is a line segment joining one of the vertex of the triangle to the mid-point of the opposite side.

The median of an equilateral triangle also an angular bisector.

Given that,

The coordinates of A = (-2, 2)

The coordinates of B = (4, 10)

The coordinates of C = (0,-2)

Thus the coordinate mid-point of BC is given by (4+0)/2,(10-2)/2 = (2,4).

Now, to find the equation of median through A there are two points (-2,2) and (2,4).

Thus the equation of median an be written as,

(y-2)/(x+2) = (4-2)/(2-(-2))

=> y - 2 = 1/2(x+2)

=> y = 1/2(x+2) + 2

=> y = 1/2 x + 3

Hence, the equation of the line is y = 1/2 x + 3.

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Step-by-step explanation:

Shortest way to solve this question is to find the factors of the given expression.

The given expression is (x² + 13).

Now we have to factorize it.

(x² + 13) = x² + (√13)²

            = x² + [-(i)²√(13)²]  [Since i = √(-1)]

            = x² - (i√13)²

            = (x - i√3)(x + i√3) [Since (a² - b²) = (a + b)(a - b)]-by-

Answer:

Bruno = 15 years

Mother = 8 + 2(15) = 38 years

Father = 38 + 3 = 41 years

Step-by-step explanation:

Given that :

Let

Bruno's age = x

Mothers age = 8 + 2x

Father's age = 8 + 2x + 3 = 2x + 11

x + 8 + 2x + 2x + 11 = 94

5x + 19 = 94

5x = 75

x = 75 /5

x = 15

Bruno = 15 years

Mother = 8 + 2(15) = 38 years

Father = 38 + 3 = 41 years

Answer:

p=-1/2

Step-by-step explanation:

4(4p+6)=16

4p+6=4

4p=4-6

4p=-2

P=-2/4

p=-1/2

Answer: it would be 100 plus 65 = 165 hope this helped

Step-by-step explanation:

Answer:

Axis is a vertical line at x = 2

Vertex is (2, -1)

y-intercept is (0, 3)

Solutions are x = 1 and x = 3

Step-by-step explanation:

To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y

Let us do that

Use x = -1, 0, 1, 2, 3, 4, 5

∵ y = x² - 4x + 3

∵ x = -1

∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8

→ Plot point (-1, 8)

∵ x = 0

∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3

→ Plot point (0, 3)

∵ x = 1

∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0

→ Plot point (1, 0)

∵ x = 2

∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1

→ Plot point (2, -1)

∵ x = 3

∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0

→ Plot point (3, 0)

∵ x = 4

∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3

→ Plot point (4, 3)

∵ x = 5

∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8

→ Plot point (5, 8)

→ Join all the points to form the parabola

From the graph

∵ The axis of symmetry is the vertical line passes through the vertex point

∵ x-coordinate of the vertex point is 2

∴ Axis is a vertical line at x = 2

∵ The coordinates of the vertex point of the parabola are (2, -1)

∴ Vertex is (2, -1)

∵ The parabola intersects the y-axis at point (0, 3)

∴ y-intercept is (0, 3)

∵ x² - 4x + 3 = 0

∵ The solutions of the equation are the values of x at y = 0

→ That means the intersection points of the parabola and the x-axis

∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)

∴ Solutions are x = 1 and x = 3

Answer:

4.0

Step-by-step explanation:

Answer:

4.1

Step-by-step explanation:

4.1231056 is [tex]\sqrt{17}[/tex]

When rounding to the nearest tenth, we get

4.1

Hope I helped,

PumpkinSpice1

Answer: 90 seconds or 1 min. and 30 sec.

Step-by-step explanation:

72/4=18

18x5=90

Step-by-step explanation and answer:

The 6 sides of the die are numbered 1,2,3,4,5,6

There are 3 odd and 3 even numbers

probability of an odd number on 1st roll is:

3/6=1/2

When you want A AND B probabilities, you multiply

the events A and B

The number less than 3 are 1,2, so the probability is:

2/6=1/3

so the probability of both events are going to be:

(1/2) *(1/3)=1/6

Answer: she will have to pay $500 and her insurances has to pay $40,000

Step-by-step explanation:

Answer: She will pay 9,000 dollars. Her insurance company will have to pay 7,000.

Answer:

1 = 3

2 = 1 ( I assumed the equation is y-4 = [(x+5)]

3 = -6

Step-by-step explanation:

Answer: She will earn 6 dollars in two years!

Step-by-step explanation: 10% of 60 is 6 because 10 sixes make up 60.

Hope this helps, if not, comment below please!!!

well, my calculator gave me 0.53x^2 - 0.6x^3 for standard form, so i hope this helps :)

Answer:

=(x-2)(x-3)

Step-by-step explanation:

This is what I got. I hope this can help you.

Answer:

11 cars

Step-by-step explanation:

If he earned 70 cars 7 that means he earned 10 dollars per car. So in order to make 110 dollars he must wash 11 cars.

Answer:

11 cars

Step-by-step explanation:

$70total/7 cars= $10 per car

$110 total/$10 per car= 11 cars

Answer: 11718.75 I think.

Answer:

$11,718.75

Step-by-step explanation:

If $1,875,000 is the median salary, it means that was the top salary for all the 160 games

So, the answer is simply given by:

$ (1,875,000/160)

= $11,718.75

Answer:

The new temperature is 13 degrees Fahrenheit

Step-by-step explanation:

Answer:

$9,724.05

Step-by-step explanation:

8000(1+.05)^4= 9724.05

sry if im wrong :)

The amount after 4 years will be equal to $9,724.05

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.

Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-

Given that Mr.Turner invested $8,000 in an account for his daughter’s college education. The account pays 5% interest, compounded yearly.

The amount after 4 years will be calculated as:-

[tex]A = P ( 1 + \dfrac{r}{100})^{nt}[/tex]

[tex]A = 8000 ( 1 + \dfrac{5}{100})^{4}[/tex]

A =  9724.05

Therefore, the amount after 4 years will be equal to $9,724.05.

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Answer:

23 dollars

Step-by-step explanation:

so to figure out how much more you grab 20 and multiply by .15 as percent and you will get 3 dollars more so 23

Answer:

Please check the graph below.

Step-by-step explanation:

Given the function

[tex]y\:=\:x^2\:+\:6x\:+\:5[/tex]

Axis interception points of the function

x-axis interception points can be computed by setting y=0

[tex]x^2+6x+5=0[/tex]

[tex]\left(x+1\right)\left(x+5\right)=0[/tex]

Using the zero factor principle

if  [tex]\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]x+1=0\quad \mathrm{or}\quad \:x+5=0[/tex]

[tex]x=-1,\:x=-5[/tex]

Hence,

x-axis interception points are: (-1, 0), (-5, 0)

y-axis interception points can be computed by setting x=0

[tex]x^2+6x+5=0[/tex]

[tex]y\:=\:\left(0\right)^2\:+\:6\left(0\right)\:+\:5[/tex]

[tex]y=0+0+5[/tex]

[tex]y=5[/tex]

Hence,

y-axis interception points are: (0, 5)

From the graph, it is clear that at (-3, -4) the parabola changes direction, hence (-3, -4) it the "vertex".

Also at the point x=-2, then y is = -3

So, all the points are labeled and the graph is attached below.

Answer:

W > -5

Step-by-step explanation:

5×(-1) < 5W + 20

-5 < 5W + 20

-25 < 5W

-5 < W

W > -5

The correct answer is $30.5 or $31 if rounded

Explanation:

To find the total Rosa spent on the manicure, it is necessary to calculate the money spent on taxes and the money she tipped to the technician. The process is shown below:

Taxes:

$25 represents 100% of the cost and 7% percent represents the total taxes.

1. Write the values using x as the value you want to know

25 = 100

x   = 7

2. Use cross multiplication

x 100 =  175

3. Solve this equation

x = 175 / 100

x = 1.75 (Total price for taxes)

Tip:

Repeat the process but in this case calculate the 15% of $25

25 = 100

x =  15

x 100 = 375

x = 375 / 100

x = 3.75

Total: Finally, add the three values

$25 (cost of the manicure) + $ 1.75 (taxes) + $3.75 (tip) = $30.5 or $31 if rounded

Answer:

Yes

Step-by-step explanation:

-2(9)+4= -14  and -14 is equal to -14.

Answer:

its 85 feet :)

Answer:

-146

Step-by-step explanation:

Step-by-step explanation:

putting the value f(-9) in expression

= -(-9)^2-7×(-9)-2

= 81+63-2

=142