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3 years ago

What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)?

Mathematics

2 answers:

Delicious77 [7]3 years ago

7 0

Answer:a

Step-by-step explanation:

Valentin [98]3 years ago

4 0

Answer: a) y = - 3/2 x + 7/2

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = y intercept

m represents the slope of the line.

m = (y2 - y1)/(x2 - x1)

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (3, - 1) and (- 1, 5),

y2 = 5

y1 = -1

x2 = - 1

x1 = 3

Slope,m = (5 - - 1)/(- 1 - 3) = 6/- 4 =

- 3/2

To determine the y intercept, we would substitute x = 3, y = - 1 and m= - 3/2 into y = mx + c. It becomes

- 1 = - 3/2 × 3 + c

- 1 = - 9/2 + c

c = - 1 + 9/2

c = 7/2

The equation becomes

y = - 3x/2 + 7/2

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Wai Kit had $45 more than Cheryl and 0.25 of what Zheng Yi had. If they had $510 altogether, how much less money did Cheryl have

GenaCL600 [577]

Step-by-step explanation:

Wai 1unit+45

Cheryl 1unit

Zheng 4units+180

Altogether 6units+225=510

6units = 510-225

6units=285

1unit=285÷6

= $47.5

So Wai =47.5+45 = 92.5

Cheryl =47.5

Zheng =4×47.5+180 =370

370-47.5=$322.5

Answer $322.5

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2 years ago

mai has 36$ to spend on movie tickets each movie ticket cost 4.50$ how many ticket can she buy multiplication problem

-Dominant- [34]

Answer:

Step-by-step explanation:

Mai has $36 and each movie ticket is $4.50.

You wanna divide 36 by 4.50 to find out how much tickets she can purchase which is 8.

6 0

2 years ago

Find the value of x,y and z. The Diagram is not a scale!

joja [24]

Answer:

x= 76, y = 63 z, 104

Step-by-step explanation:

We can find x since the three angles of a triangle add to 180 degrees

46+58+x = 180

104+x =180

Subtract 104 from each side

x = 180-104

x = 76

x and z form a straight line

x+z =180

76+ z = 180

Subtract 76 from each side

z = 180-76

z = 104

Z, 13 and y make a triangle

z+ 13 +y = 180

104+13+y = 180

117+y=180

Subtract 117 from each side

y = 180-117

y = 63

4 0

3 years ago

Sandra is making the shape of a rhombus. The first three angles are 75°, 75°, and 105°. What is the measure of the fourth angle?

mrs_skeptik [129]

Its 105° because the rhombus is essentially a square or rectangle of sorts and at least 2 sides have to be alike

3 0

3 years ago

Read 2 more answers

Fred the owl is looking down at a 67° angle from the top of a tree that is 15 ft tall, when he spots a bird on the ground. How f

guapka [62]

Answer:

Fred C. 16.30 ft

Gary B. 169.67 m

Step-by-step explanation:

Fred the owl...

Always draw a diagram first (see diagram below). We assume trees are perpendicular (at 90°) to the ground. The situation forms a right-angle triangle.

We need to find "x", which is the direct distance between the owl and the bird. "x" is also the hypotenuse, which is the longest side in a right-angle triangle. Since we know a side and an angle, we can find the hypotenuse using primary trigonometry ratios.

∠B will be the angle of reference (the angle we are "talking" about). The side we know is opposite to ∠B (15ft). We know it's opposite because it's not touching the angle. The side we need to find is the hypotenuse.

Use the trig. ratio sine because it has opposite and hypotenuse in it. The general formula is:

sinθ = opp/hyp

θ means the angle, and we know it is 67°.

Replace all the information you know:

sinB = opp/hyp

sin67° = (15ft) / x Isolate "x". Rearrange the equation.

xsin67° = (15ft) Divide both sides by sin67°

x = (15ft) / sin67°

x = 16.295... ft Exact answer in decimals

x ≈ 16.30 ft Rounded to nearest hundredth

Therefore Fred the owl is 16.30 feet from the bird.

Gary spots a monkey...

Draw a diagram first (see below). G is Gary, M is the monkey, T is the bottom of the Sears Tower. We need to find "x", which is the distance between the monkey and the bottom of the tower.

The angle of reference is M, which is 69°. We need to find the adjacent side and we know the opposite side. The trig. ratio that has adjacent and opposite is tangent.

tanθ = opp/adj

Replace all the information you know:

tanM = opp/adj

tan69° = (442m) / x Rearrange the formula to isolate "x"

xtan69° = 442m Divide both sides by tan69°

x = 442m / tan69° Solve by dividing

x = 169.6679.... m Exact decimal answer

x ≈ 169.67m Rounded to the nearest hundredth

Therefore the monkey is 169.67 metres from the tower.

Remember all the trig. ratios using the acronym SohCahToa.

o = opposite side

a = adjacent side

h = hypotenuse side

S = sine, sin for short

C = cosine, cos for short

T = tangent, tan for short

The operation is always dividing the first side in the acronym by the second side.

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

4 0

3 years ago