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2 years ago

Find the equation of the line shown.

Mathematics

2 answers:

vladimir1956 [14]2 years ago

4 0

Answer:

y = - x + 9

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 )

calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (0, 9) and (x₂, y₂ ) = (9, 0) ← 2 points on the line

m = $\frac{0-9}{9-0}$ = $\frac{-9}{9}$ = - 1

the line crosses the y- axis at (0, 9 ) ⇒ c = 9

y = - x + 9 ← equation of line

I am Lyosha [343]2 years ago

3 0

Answer:

y = -x + 9

Step-by-step explanation:

<u>Slope</u>

m = rise / run
m = -1 / 1
m = -1

<u>Y-intercept</u>

(0, 9) = (0, b)
b = 9

<u>Equation</u>

y = mx + b
y = -x + 9

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Please help me in this questions....

Ivahew [28]

Part (i)

I'm going to use the notation T(n) instead of $T_n$

To find the first term, we plug in n = 1

T(n) = 2 - 3n

T(1) = 2 - 3(1)

T(1) = -1

The first term is -1

Repeat for n = 2 to find the second term

T(n) = 2 - 3n

T(2) = 2 - 3(2)

T(2) = -4

The second term is -4

<h3>Answers: -1, -4</h3>

==============================================

Part (ii)

Plug in T(n) = -61 and solve for n

T(n) = 2 - 3n

-61 = 2 - 3n

-61-2 = -3n

-63 = -3n

-3n = -63

n = -63/(-3)

n = 21

Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).

<h3>Answer: 21st term</h3>

===============================================

Part (iii)

We're given that T(n) = 2 - 3n

Let's compute T(2n). We do so by replacing every copy of n with 2n like so

T(n) = 2 - 3n

T(2n) = 2 - 3(2n)

T(2n) = 2 - 6n

Now subtract T(2n) from T(n)

T(n) - T(2n) = (2-3n) - (2-6n)

T(n) - T(2n) = 2-3n - 2+6n

T(n) - T(2n) = 3n

Then set this equal to 24 and solve for n

T(n) - T(2n) = 24

3n = 24

n = 24/3

n = 8

This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.

<h3>Answer: 8</h3>

4 0

3 years ago

Question 4 (1 point)

Nostrana [21]

Answer:

The ball will hit the ground at 10 seconds and its maximum height is 1024 feet.

Step-by-step explanation:

Height of a mountain, h = 90 feet

Upward velocity of a ball, u = 64 ft/s

Its height as a function of time can be written by using the second equation of motion as follows :

$f(x) = -16t^2 + 64t + 960$ .....(1)

When it will hit the ground, f(x) = 0

$-16t^2 + 64t + 960=0\\\\16(-t^2+4t+60)=0\\\\-t^2+4t+60=0$

It is quadratic equation.

t = -6 s and t = 10 s

Neglecting -6 seconds, the ball will hit the ground at 10 seconds.

For maximum height,

Put f'(x) = 0

$-32t+64=0\\\\\\t=\dfrac{64}{32}\\\\t=2\ s$

Put t = 2 in equation (1)

$f(2) = -16(2)^2 + 64(2) + 960\\\\=1024\ \text{feet}$

Hence, the ball will hit the ground at 10 seconds and its maximum height is 1024 feet.

5 0

3 years ago

The graph of the function y = x^2 - x -2

svp [43]

I hope this graph helps

8 0

3 years ago

Find the volume of the cylinder. Round to the nearest tenth.

Svetllana [295]

Answer:

V = 56.5 mi^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

V = pi ( 3)^2 (2)

V = 18 pi

Letting p = 3.14

V = 56.52 mi^3

Rounding to the nearest tenth

V = 56.5 mi^3

6 0

3 years ago

The product 2 x 3/6 is shown by the fraction

Neko [114]

Answer:

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

3/3 =1

Your answer is 1

3 0

3 years ago