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3 years ago

Write the equation of a line that contains the points 4,1 and -4,5

Mathematics

1 answer:

Bingel [31]3 years ago

6 0

Answer: y = -1/2x+3

Step-by-step explanation:

Since we are given two points on the graph, we are going to use these points to find the slope using the formula m = y2-y1 / x2-y1, where m is equal to the slope.

Since it doesn't matter which points are 1 and which are two, we are just going to make (-4,5) x2 and y2, and (4,1) x1 and y1. Plugging everything in we get 5-1/-4-4 = 4/-8 = -1/2. So, -1/2 is our slope.

Now we can plug in the slope and one of our previous points, again it doesn't matter which one, into y = mx + b to find b, the y-intercept. We are going to use the point (4,1) and when we plug it in we get 1 = -1/2(4) + b and b ends up being equal to 3.

So when we plug in 3 for the y - intercept and -1/2 for the slope, we get y = -1/2x+3

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What’s is the inverse function of a(m)=0.6735e^0.423m

natta225 [31]

Answer:

$a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}$

Step-by-step explanation:

The function is $a(m)=0.6735e^{0.423m}$

Changing functional notation of a(m) to y:

$y=0.6735e^{0.423m}$

Now, interchanging m and y:

$m=0.6735e^{0.423y}\\$

Now, solving for y:

$e^{0.423y}=\frac{m}{0.6735}\\ln[e^{0.423y}]=ln[\frac{m}{0.6735}]\\0.423y=ln(\frac{m}{0.6735})\\y=\frac{ln(\frac{m}{0.6735})}{0.423}$

Thus, the inverse function is:

$a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}$

5 0

3 years ago

A survey of 100 people in New York City, NY found that.

S_A_V [24]

Answer: 0.9

Step-by-step explanation:

$\mathrm{Total \ sample \ space \ $=100$} \\\mathrm{Event \ $A = \ taking \ subway \ each \ day}$$P(A)=0.85$$Event $B=$ taking taxi $\because P(B)=0.6$$$P(A \cap B)=0.55$$$

$\begin{aligned}P(A \cup B) & \Rightarrow \text { Person taking either taxi/subway } \\&=P(A)+P(B)-P(A \cap B) \\&=(0.85-0.555)+(0.6-0.55)-0.55 \\&=1.45-0.55\\&\bf{=0.9} \end{aligned}$

7 0

2 years ago

Tina brought $37.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 6 as much as the

Firlakuza [10]

Answer:

18.75=p

s=14.06

b=2.34

Step-by-step explanation:

37.75=b+s+p

-4

33.75=b+s+p

s=3/4p

b=1/6s

33.75=1/6(3/4p)+3/4p+p

33.75=3/20p+3/4p+p

(33.75=18/20p+p)20

675=18p+p)/18

37.50=2p)/2

18.75=p

s=3/4p

3/4(18.75)

s=14.06

b=1/6s

1/6(14.06)

b=2.34

37.75-4=18.75+14.06+2.34=35.15

im missing 50 cents somewhere its wrong but close i think sorry

7 0

3 years ago

Please HELPppppppppppppppp

aleksandr82 [10.1K]

Answer:

Point of intersections are (0, -7) and (5, -2).

Step-by-step explanation:

From the graph attached,

A straight line is intersecting the circle at the two points (0, 7) and (5, -2).

Now solve algebraically,

Equation of the line → y = x - 7 -------(1)

Equation of the circle → (x - 5)² + (y + 7)² = 25 -------(2)

By substituting the value of y from equation (1) to equation (2)

(x - 5)² + (x - 7 + 7)² = 25

(x - 5)² + x² = 25

x² - 10x + 25 + x² = 25

2x² - 10x = 0

x² - 5x = 0

x(x - 5) = 0

x = 0, 5

From equation (1),

y = 0 - 7 = -7

y = 5 - 7 = -2

Therefore, point of intersections are (0, -7) and (5, -2).

6 0

3 years ago

1/2x-9=-25 what is your answer

Elodia [21]

First, let's only the expression with x stay on the let side: let's add 9 to both sides of the equation.

$\frac{1}{2} x-9+9=-25+9$
which is
$\frac{1}{2}x=-16$

now, let's multiply everything by 2:

$\frac{2}{2} x=-16*2$
$x=-32$

so the answer is -32!

4 0

3 years ago