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3 years ago

Match each function with the corresponding function formula when h(x)=5-3x and g(x)=-3+5

Mathematics

1 answer:

Grace [21]3 years ago

4 0

Answer:

k(x) = (3g + 5h)(x) ⇒ (1)

k(x) = (5h - 3g)(x) ⇒ (3)

k(x) = (h - g)(x) ⇒ (2)

k(x) = (g + h)(x) ⇒ (4)

k(x) = (5g + 3h)(x) ⇒ (5)

k(x) = (3h - 5g)(x) ⇒ (6)

Step-by-step explanation:

* To solve this problem we will substitute h(x) and g(x) in k(x) in the

right column to find the corresponding function formula in the

left column

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

- Lets start with the right column

# k(x) = (3g + 5h)(x)

∵ g(x) = -3^x + 5

∵ 3g(x) = 3[-3^x + 5] = [3 × -3^x + 3 × 5]

- Lets simplify 3 × -3^x

take the negative out -(3 × 3^x), and use the rule a^n × a^m = a^(n+m)

∴ -3(3 × 3^x) = -(3^x+1)

∴ 3g(x) = -3^x+1 + 15

∵ h(x) = 5 - 3x

∵ 5h(x) = 5[5 - 3x] = [5 × 5 - 5 × 3x] = 25 - 15x

- Now substitute 3g(x) and 5h(x) in k(x)

∵ k(x) = (3g + 5h)(x)

∴ k(x) = -3^x+1 + 15 + 25 - 15x ⇒ simplify

∴ k(x) = 40 - 3^x+1 - 15x

∴ k(x) = 40 - 3^x+1 - 15x ⇒ k(x) = (3g + 5h)(x)

* k(x) = (3g + 5h)(x) ⇒ (1)

# k(x) = (5h - 3g)(x)

∵ 5h(x) = 25 - 15x

∵ 3g(x) = -3^x+1 + 15

∵ k(x) = (5h - 3g)(x)

∴ k(x) = 25 - 15x - (-3^x+1 + 15) = 25 -15x + 3^x+1 - 15 ⇒ simplify

∴ k(x) = 10 + 3^x+1 - 15x

∴ k(x) = 10 + 3^x+1 - 15x ⇒ k(x) = (5h - 3g)(x)

* k(x) = (5h - 3g)(x) ⇒ (3)

# k(x) = (h - g)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (h - g)(x)

∴ k(x) = 5 - 3x - (-3^x + 5) = 5 - 3x + 3^x - 5 ⇒ simplify

∴ k(x) = 3^x - 3x

∴ k(x)= 3^x - 3x ⇒ k(x) = (h - g)(x)

* k(x) = (h - g)(x) ⇒ (2)

# k(x) = (g + h)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (g + h)(x)

∴ k(x) = -3^x + 5 + 5 - 3x ⇒ simplify

∴ k(x) = 10 - 3^x - 3x

∴ k(x)= 10 - 3^x - 3x ⇒ k(x) = (g + h)(x)

* k(x) = (g + h)(x) ⇒ (4)

# k(x) = (5g + 3h)(x)

∵ g(x) = -3^x + 5

∵ 5g(x) = 5[-3^x + 5] = [5 × -3^x + 5 × 5] = 5(-3^x) + 25

∴ 5g(x) = -5(3^x) + 25

∵ h(x) = 5 - 3x

∵ 3h(x) = 3[5 - 3x] = [3 × 5 - 3 × 3x] = 15 - 9x

- Now substitute 5g(x) and 3h(x) in k(x)

∵ k(x) = (5g + 3h)(x)

∴ k(x) = -5(3^x) + 25 + 15 - 9x ⇒ simplify

∴ k(x) = 40 - 5(3^x) - 9x

∴ k(x) = 40 - 5(3^x) - 9x ⇒ k(x) = (5g + 3h)(x)

* k(x) = (5g + 3h)(x) ⇒ (5)

# k(x) = (3h - 5g)(x)

∵ 3h(x) = 15 - 9x

∵ 5g(x) = -5(3^x) + 25

∵ k(x) = (3h - 5g)(x)

∴ k(x) = 15 - 9x - [-5(3^x) + 25] = 15 - 9x + 5(3^x) - 25 ⇒ simplify

∴ k(x) = 5(3^x) - 9x - 10

∴ k(x) = 5(3^x) - 9x - 10 ⇒ k(x) = (3h - 5g)(x)

* k(x) = (3h - 5g)(x) ⇒ (6)

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r-ruslan [8.4K]

Answer:

15 = 2x - 3y

Step-by-step explanation:

We have the two points P1(3,-3) and P2(9,1).

First, calculate the slope between those points:

slope $= \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-3)}{9 - 3} = \frac{4}{6} = \frac{2}{3}$

Now simply move 3 steps from (3,-3) towards the y-axis to get the intersection with the y-axis (each step reduces x by 1 and applies the slope to the y-value):

(3,-3)

---> (2, -3 - (2/3)) = (2,-3 2/3)

---> (1, (-3 2/3) - 2/3) = (1, -4 1/3)

---> (0, (-4 1/3) - 2/3) = (0,-5)

This tells us, that our line intersects the y-axis at (0,-5).

The general form of a line is f(x) = <SLOPE> * x + <Y-VALUEATXEQUALSZERO>.

In our case: f(x) = y = (2/3)x -5.

To get it into the correct form, we simply subtract y from both sides and get:

0 = (2/3)x - y - 5

To get only integers just multiply everything with 3 and add 15 and get:

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3 0

2 years ago

!!!*BRAINLIEST*!!!

Sedbober [7]

Not sure but probably it’s b or c

4 0

3 years ago

Read 2 more answers

Here, thankyou!!!!!!!

FromTheMoon [43]

Answer:

Perimeter of i - 22CM

Area of i - 13CM^2

Perimeter of ii -38CM

Area of ii -66CM^2

Perimeter of iii -30CM

Area of iii- 42CM^2

Perimeter of iv - 50CM

Area of iv- 126CM^2

Step-by-step explanation:

SHAPE I:

PERIMETER = S + S + S + S + S +S

= 7 + 1 + 5 +3 +4 +2

= 22CM

AREA = Part a - 4 * 2 = 8cm^2 part B - 5 *1 = 5cm^2

Total = 8 + 5 = 13cm^2

SHAPE II:

PERIMETER = S + S + S + S + S +S

= 4 + 4 +5 + 6 + 9 + 10

= 38 CM

AREA = Part a - 5 * 10 = 50 cm^2 part B - 4 *4 =16 cm^2

Total = 50+16 =66 cm^2

SHAPE III:

PERIMETER = S + S + S + S + S +S

= 9 + 2 + 3 + 4 + 6 + 6

= 30CM

AREA = Part a - 6 * 6 = 42cm^2 part B - 3 * 2= 6cm^2

Total = 36 + 6 =42 cm^2

SHAPE IV:

PERIMETER = S + S + S + S + S +S

= 9 + 10 + 4 + 6 + 6 + 15

= 50 CM

AREA = Part a -15 * 6 = 90 cm^2 part B - 9 *4 = 36cm^2

Total = 90 + 36 = 126cm^2

HOPE THIS HELPED

6 0

3 years ago

You measure 25 turtles' weights, and find they have a mean weight of 31 ounces. Assume the population standard deviation is 12.8

Firlakuza [10]

Answer:

Margin of error = 4.21 ounces

Step-by-step explanation:

According to the Question,

Given That, You measure 25 turtles' weights, and find they have a mean weight of 31 ounces. Assume the population standard deviation is 12.8 ounces

Therefore, Sample mean = 31 ounces , Sample size(n) = 25 , Alpha(α) = 0.10 & Population standard deviation(σ) = 12.8 ounces

Thus, Margin of error = $Z_{critical}$ × σ / √n ( $Z_{critical}$ at α=.010 is 1.645)

Putting The Values, We get

1.645 × (12.8 / √25 ) ⇒ 4.2112 ≈ 4.21

Thus, the maximum margin of error associated with a 90% confidence interval for the true population mean turtle weight is 4.21 ounces

8 0

3 years ago