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3 years ago

Write a linear function f with f(-4) = 2 and f(6) =-3

Mathematics

1 answer:

Anastasy [175]3 years ago

6 0

Answer:

f(x) = - $\frac{1}{2}$ x

Step-by-step explanation:

The standard form for a linear function is

f(x) = ax + b

Using the given values f(- 4) = 2 and f(6) = 3 , then

- 4a + b = 2 → (1)

6a + b = - 3 → (2)

Subtract (2) from (1) term by term to eliminate b

- 10a = 5 ( divide both sides by - 10 )

a = - $\frac{1}{2}$

Substitute a = - $\frac{1}{2}$ into either of the 2 equations and solve for b

Substituting into (1)

2 + b = 2 ( subtract 2 from both sides )

b = 0

Thus the linear function is

f(x) = - $\frac{1}{2}$ x

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Match each equation with its solution set. Tiles a2 − 9a + 14 = 0 a2 + 9a + 14 = 0 a2 + 3a − 10 = 0 a2 + 5a − 14 = 0 a2 − 5a − 1

sattari [20]

We have that

N 1)
a² − 9a + 14 = 0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(a² − 9a)=-14

Complete the square Remember to balance the equation by adding the same constants to each side

(a² − 9a+20.25)=-14+20.25

Rewrite as perfect squares

(a-4.5)²=6.25--------> (a-4.5)=(+/-)√6.25

a1=4.5+√6.25-----> a1=7

a2=4.5-√6.25-----> a2=2

the solution problem N 1 is the pair {7, 2}

N 2)

a² + 9a + 14 = 0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(a² + 9a)=-14

Complete the square Remember to balance the equation by adding the same constants to each side

(a² +9a+20.25)=-14+20.25

Rewrite as perfect squares

(a+4.5)²=6.25--------> (a+4.5)=(+/-)√6.25

a1=-4.5+√6.25-----> a1=-2

a2=-4.5-√6.25-----> a2=-7

the solution problem N 2 is the pair {-2,-7}

N 3)

a² + 3a − 10 = 0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(a² + 3a)=10

Complete the square Remember to balance the equation by adding the same constants to each side

(a² + 3a+2.25)=10+2.25

Rewrite as perfect squares

(a+1.5)²=12.25------> (a+1.5)=(+/-)√12.25

a1=-1.5+√12.25-----> a1=2

a2=-1.5-√12.25-----> a2=-5

the solution problem N 3 is the pair {2, -5}

N 4)

a² + 5a − 14 = 0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(a² + 5a) =14

Complete the square Remember to balance the equation by adding the same constants to each side

(a² + 5a+6.25) =14+6.25

Rewrite as perfect squares

(a+2.5)² =20.25-------> (a+2.5)=(+/-)√20.25

a1=-2.5+√20.25-----> a1=2

a2=-2.5-√20.25-----> a2=-7

the solution problem N 4 is the pair {2, -7}

N 5)

a² − 5a − 14 = 0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(a² − 5a)=14

Complete the square Remember to balance the equation by adding the same constants to each side

(a² − 5a+6.25)=14+6.25

Rewrite as perfect squares

(a-2.5)²=2025--------> (a-2.5)=(+/-)√20.25

a1=2.5+√20.25-----> a1=7

a2=2.5-√20.25-----> a2=-2

the solution problem N 5 is the pair {7, -2}

3 0

3 years ago

Read 2 more answers

Based on the information given say whether or not △ABC∼△FED. Explain your reasoning.

GalinKa [24]

Answer:

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F = $x$

m∠D = $2x-20$ °.

Now, let m∠A = m∠B = $y$

So, m∠C = m∠A + 30° = $y+30$

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B + m∠C = 180

$y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50$

Therefore, m∠A = 50°, m∠B = 50° and m∠C = m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

$2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50$

Therefore, m∠F = 50°

m∠E = 50° and

m∠D = $2x-20=2(50)-20=100-20=80\°$

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.

5 0

3 years ago

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ivann1987 [24]

The median (half-above and half-below) could not have changed, because "corrected value was still lower than any other salary" does not change the position of that observation (still least) in the sorted list of salaries.

6 0

3 years ago

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An equation is shown below: 5(2x - 8) + 15 = -15 Write the steps you will use to solve the equation and explain each step. (5 po

uranmaximum [27]

Answer:

x=1

Step-by-step explanation:

To solve this question we will have to open the bracket first

So let's solve the question

5(2x-8)+15=-15

Bracket first

10x-40+15=-15

We will have to solve the question further

10x-25=-15

Add 25 to both sides

10x=10

Let's make x the subject of formula by dividing both sides by 10

x=1

Therefore x is 1

8 0

3 years ago

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X/5=-7 solve for x Worth 10 points

Yuri [45]

Answer:

x = -35

Step-by-step explanation:

multiply both sides by 5

5x/5 = 5(-7)

simplify

x = -35

6 0

3 years ago

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Write a linear function f with f(-4) = 2 and f(6) =-3​

Write a linear function f with f(-4) = 2 and f(6) =-3