Find the slope-intercept equation of the line that has the given characteristics.
Slope 8 and y-intercept (0,9)

The missing parts of the proof of supplementary angles are:

Supplementary; ∠2 and ∠3; substitution; 2.

Supplementary angles are defined as angles whose measures sum to 180°.  Thus this is the first answer.  

Since we are told that ∠2 and ∠3 are supplementary, their measures sum to 180° and they are the second answer.

We know that m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.  We can substitute "m∠2 + m∠3" for 180° in the first equation; this is the substitution property.

To isolate m∠1 on the right, we will subtract m∠2 from each side, and get that m∠1 = m∠3 and the angles are congruent.

Read more about Supplementary angles at: https://brainly.com/question/12919120

#SPJ1

Answer:

2.5

Step-by-step explanation:

We Know

You buy 4 5/8 blue fabric and 2 1/8 green fabric .

4 5/8 = 37/8 = 4.625 blue fabric

2 1/8 = 17/8 = 2.125 green fabric

How much blue than green did you buy?

We Take

4.625 - 2.125 = 2.5

So, you buy 2.5 blue more than green.

To calculate how much Naruto spends on ramen in 15 days, we need to determine the total cost of ramen per day and then multiply it by 15.

Since Naruto receives a 33.33% discount, he pays 100% - 33.33% = 66.67% of the original price.

66.67% of 45 cents is (66.67/100) * 45 = 30 cents.

So, Naruto spends 30 cents on ramen per day.

To find out how much he spends in 15 days, we multiply the daily cost by the number of days:

30 cents * 15 = 450 cents.

Therefore, Naruto spends 450 cents, which is equivalent to $4.50, on ramen in 15 days.

Answer: The sales tax rate is 14%.

To find the sales tax rate, we can use the formula:

Sales Tax Rate = (Sales Tax / Cost before Tax) * 100

Given that the item costs $350 before tax and the sales tax is 14%, we can substitute the values into the formula:

Sales Tax Rate = (14 / 350) * 100

Simplifying the expression inside the parentheses:

Sales Tax Rate = 0.04 * 100

Multiplying 0.04 by 100:

Sales Tax Rate = 4

Therefore, the sales tax rate is 4%, which means that the sales tax on the item is 4% of the cost before tax.

For more such questions on tax rate, click on:

https://brainly.com/question/29327002

#SPJ8

The three true statements are:

Only f(x) and h(x) have y-intercepts.

Only f(x) and h(x) have x-intercepts.

The minimum of h(x) is less than the other minimums.

From the given table, we can compare the characteristics of the functions f(x), g(x), and h(x) to determine which statements are true.

Statement 1: Only f(x) and h(x) have y-intercepts.

Looking at the table, we can see that f(x) and h(x) have y-intercepts since they have values for f(0) and h(0), while g(x) does not have a y-intercept. Therefore, statement 1 is true.

Statement 2: Only f(x) and h(x) have x-intercepts.

To find x-intercepts, we look for values of x where the functions f(x), g(x), and h(x) equal zero. From the table, we can see that only f(x) and h(x) have x-intercepts, as they have values for x where f(x) and h(x) are equal to zero. Therefore, statement 2 is true.

Statement 3: The minimum of h(x) is less than the other minimums.

By comparing the values in the table, we can see that the minimum value of h(x) is -28, which is indeed less than the minimums of f(x) (-2) and g(x) (-7). Therefore, statement 3 is true.

Statement 4: The range of h(x) has more values than the other ranges.

The range of a function represents the set of all possible output values. From the table, we can observe that the range of h(x) has more values (-28, 0, 7, 14, 49) compared to the ranges of f(x) and g(x) (only two distinct values each). Therefore, statement 4 is true.

Statement 5: The maximum of g(x) is greater than the other maximums.

Looking at the values in the table, we can see that the maximum value of g(x) is 7, which is indeed greater than the maximums of f(x) (-2) and h(x) (14). Therefore, statement 5 is true.

for such more question on functions

https://brainly.com/question/16332322

#SPJ8

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

Using angle rules, the values of angles 1 to 6 are 64, 53, 116, 89, 32 and 44 respectively.

Angle 1 + 69 + 47 = 180 (sum of angles on a straight line)

Angle 1 = 180 - (69+47)

Angle 1 = 64°

Angle 2 + 64 + 63 = 180 (sum of angles in a triangle)

Angle 2 = 180 - (64+63)

Angle 2 = 53°

Angle 1 + Angle 3 = 180 (sum of angles in a triangle)

Angle 3 = 180 - 64

Angle 3 = 116°

Angle 6 + 136 = 180 (sum of angles on a straight line)

Angle 6 = 180 - 136

Angle 6 = 44°

Angle 5 + Angle 3 + 32 = 180 (sum of angles in a triangle)

Angle 5 + 116 + 32 = 180

Angle 5 = 180 - (116 + 32)

Angle 5 = 32°

47 + Angle 6 + Angle 4 = 180

47 + 44 + Angle 4 = 180

Angle 4 = 180 - 91

Angle 4 = 89°

Therefore, the values of angles 1 to 6 are 64, 53, 116, 89, 32 and 44 respectively.

Learn more on angles :https://brainly.com/question/25716982

#SPJ1

By using the given functions, each output value are as follows;

a. f(-5) = -13.

b. g(3) = -18.

c. 3g(1) - 4 = -10.

d. 2f(3) + g(2) = 14.

e. x = ±√8i or ±2√2i.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) under the given mathematical operation and independent variable.

Part a.

When x = -5, the output value for f(-5) is given by;

f(x) = 3x + 2

f(-5) = 3(-5) + 2

f(-5) = -13.

Part b.

When x = 3, the output value for g(3) is given by;

g(x) = -2x²

g(3) = -2(3)²

g(3) = -18.

Part c.

3g(1) - 4

3[-2(1)²] - 4

-6 - 4 = -10

Part d.

2f(3) + g(2)

2[3(3) + 2] + [-2(2)²]

22 - 8 = 14

Part e.

g(x) = 16

-2x² = 16

x² = -8

x = ±√8i or ±2√2i.

Read more on function here: brainly.com/question/10687170

#SPJ1

Answer:

Step-by-step explanation:

First, we need to find the difference between the price that he sold the shares for and the price that he bought them at: (67.68-60.65) = 7.03

That means that there was a gain of $7.03 per share for Archie.

That being said, since Archie bought 100 shares, we can multiply that number by 100 to find the total gain from selling the shares:

(7.03x100)= 703

The answer then is:

Archie gained $703 from selling all of his shares.