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Andrei [34K]
3 years ago
7

Write the rule for the linear function. Remember a function rule is written using f(x)

Mathematics
1 answer:
Marina CMI [18]3 years ago
4 0

Answer:

The rule for the linear function will be:

f(x) = -2x+5

Step-by-step explanation:

We know that linear function can be represented using the slope-intercept formula

y = mx+b

where m is the slope and b is the y-intercept

Given the function is linear

Taking two points from the table to determine the slope

  • (1, 3)
  • (2, 1)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(1,\:3\right),\:\left(x_2,\:y_2\right)=\left(2,\:1\right)

m=\frac{1-3}{2-1}

m=-2

Using the point-slope form of the line equation

y-y_1=m\left(x-x_1\right)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (1, 3)

y-y_1=m\left(x-x_1\right)

y - 3 = -2 (x-1)

y-3 = -2x+2

adding 3 to both sides

y-3+3 = -2x+2+3

y = -2x+5

or

f(x) = -2x+5

Therefore, the rule for the linear function will be:

f(x) = -2x+5

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Given 2x – 4y= 4:<br> Transform this equation into slope-intercept form
jeka57 [31]

Answer:

y=1/2x-1

Step-by-step explanation:

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8 0
3 years ago
All of the following expressions are equivalent except.___ 2+m m+2 m-(-2) -2-m
Pachacha [2.7K]

Answer:

\Huge \boxed{-2-m}

Step-by-step explanation:

2 + m

Rewrite with variable first.

m + 2

m + 2

Can’t be simplified further.

m - (-2)

Distribute negative sign.

m + 2

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4 0
3 years ago
3. Each day, the furniture store sells x tables and y chairs.
gulaghasi [49]

Answer:

answer A and B are the same there just the opposite of each other. so A or B would work.

Step-by-step explanation:

95×(12) +225×(12)

3 0
3 years ago
B) T is due north of C, calculate the bearing of B from C
choli [55]

Answer:

(a) 52°

(b) 322°

Step-by-step explanation:

(a) The details of the circle are;

The diameter of the circle = AOC

The center of the circle = Point O

The point the line AT cuts the circle = Point B

The point the tangent PT touches the circle = Point C

Angle ∠COB = 76°

We have that angle AOB and angle COB are supplementary angles, therefore;

∠AOB + ∠COB = 180°

∠AOB = 180° - ∠COB

∴ ∠AOB = 180° - 76° = 104°

∠AOB = 104°

OA = OB = The radius of the circle

Therefore, ΔAOB  =  An isosceles triangle

∠OAB = ∠OBA by base angles of an isosceles triangle are equal

∠AOB + ∠OAB + ∠OBA = 180° by angle summation property

∴ ∠AOB + ∠OAB + ∠OBA = ∠AOB + ∠OAB + ∠OAB = ∠AOB + 2×∠OAB = 180°

∠OAB = (180° - ∠AOB)/2

∴ ∠OAB = (180° - 104°)/2 = 38°

∠TAC = ∠OAB = 38° by reflexive property

AOC is perpendicular to tangent PT at point C, by tangent to a circle property, therefore;

∠TCA = 90° and ΔTCA = A right triangle

∠TAC + ∠ATC + ∠TCA = 180° by angle sum property

∠ATC = 180° - (∠TAC + ∠TCA)

∴ ∠ATC = 180° - (38° + 90°) = 52°

Angle ATC = 52°

(b) In ΔABC, ∠ABC = Angle subtended by the diameter = 90°

∴ ΔABC = A right triangle

∠ABC and ∠TBC are supplementary angles, therefore;

∠ABC + ∠TBC = 180°

∠TBC = 180° - ∠ABC

∴ ∠TBC = 180° - 90° = 90°

∠TCB = 180° - (∠TBC + ∠ATC)

∴ ∠TCB = 180° - (90° + 52°) = 38°

The bearing of B from C = (360° - 38°) = 322°.

7 0
2 years ago
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