Using mental math, the approximate tip to leave for a bill of $81.79, if you tip 15% would be _____..

Answer: The correct option is second.

Explanation:

The given function is,

[tex]f(x)=5(0.8)^x[/tex]

If we graph a function is f(x), then its coordinates is defined as (x,f(x)).

When the graph of f(x) is reflect across the x-axis, then the the x-coordinate remains the same and the sign of y-coordinate is changed. It means after reflecting across the x-axis,

[tex](x,y)\rightarrow(x,-y)[/tex]

The given given equation can be written as,

[tex]y=5(0.8)^x[/tex]

To find the equation of the graph after reflection across the x-axis multiply both sides by -1.

[tex]-y=-5(0.8)^x[/tex]

Because f(x)=y and g(x)=-y.

[tex]g(x)=-5(0.8)^x[/tex]

Therefore the second option is correct and the graph of both function is given below.

Answer:

B. g(x) = –5(0.8)^x

Step-by-step explanation:

We have the function, [tex]f(x) = 5(0.8)^x[/tex].

It is required to reflect the function about x-axis.

Now, as we know,

Reflection across x-axis will flip the graph of the function and the function [tex]f(x)[/tex] becomes [tex]-f(x)[/tex].

So, the reflection of [tex]f(x) = 5(0.8)^x[/tex] across x-axis will give the function [tex]f(x) = -5(0.8)^x[/tex]

So, we see that,

Option B i.e. [tex]g(x) = -5(0.8)^x[/tex] is correct.

1. Solve the given equation for y.

x - 5y = 15

-5y = -x + 15

y = (-x + 15)/-5

y = (x/5) - 3

y = (1/5)(x) - 3

The slope is 1/5. See it?

The equation we are looking for has a slope which is the negative inverse of the slope in the equation we just solved for y.

The slope for the equation we want is -5 which is the negative inverse of 1/5. Undetstand?

We have the slope of the new equation and one point is given.

Plot BOTH into the point-slope formula and solve for y. To solve for a variable means to isolate the variable ALONE on one side of the equation.

y - y_1 = m(x - x_1)...This is the point-slope formula. Our given point is (5,-2)

y - 5 = -5(x - (-2))

y - 5 = -5(x + 2)

We now solve for y and that's it.

y - 5 = -5x - 10

y = -5x - 10 + 5

The equation we want is y = -5x - 5.

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Answer: C

Step-by-step explanation:

Answer:

C. the image and pre-image are congruent.  

Step-by-step explanation:

a triangle is reflected across the line x=2

Check with each option

A. the image and pre-image have the same orientation.

The image will not be in same order

B. the image and pre-image have different sizes. the size will not change

C. the image and pre-image are congruent. the reflection will not change the size. so they are congruent

D. the image and pre-image are separated by a given angle.

The angles never change in reflection

Jordan has 260 basketball cards and divides them evenly into 4 groups, resulting in 65 cards per group.

Jordan has 260 basketball cards and wants to divide them into 4 equal groups. To find the number of cards in each group, we need to perform a simple division. By dividing 260 by 4, we get:

Divide 260 by 4.

260 \/ 4 = 65.

Each group will have 65 cards.

Therefore, Jordan will have 65 basketball cards in each of the four groups.

Answer:

-12

Step-by-step explanation: I Took K12 TEST

Given a line of one billion people extending for 346,439 miles, the average shoulder width of a person in the line is approximately 1.83 feet.

To find the average shoulder width of the people in the line, we need to convert the total miles into feet, since the result wanted is in feet. There are 5,280 feet in one mile. So the total length in feet would be 346,439 miles * 5,280 feet/mile = 1,829,029,920 feet. Now, if there are 1 billion people in this line, then the average width of a person's shoulders would be the total length divided by the total number of people. Hence, the average shoulder width = 1,829,029,920 feet / 1,000,000,000 people = approximately 1.83 feet.

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The service charges would be, $88

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

Colin took out a loan with a principal of $32,800.

And, After five years, the interest and principal totaled $48,872.

Now,

The value of principal amount is,

⇒ 816 × 5 × 12 = 48960

Now, We get;

Amount of Colin pay in service charges is,

48960 - 48872= 88

Hence, The service charges were $88

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Answer:

C) 65°

Step-by-step explanation:

G ∈ NE, so ∠TNG = ∠TNE. ∠ATE = 90° because a radius (AT) is always perpendicular to a tangent line (ET) at the tangent point (T). A ∈ TN, so ΔTNG is a right triangle, and angles NET and TNE are complementary. Then ...

... ∠NET = 90° - ∠TNG

... = 90° - 25°

... ∠NET = 65°

The answer is, indeed, $550.

80 percent of needed milligrams is 1360

so

1360/.80 = x/1  

1700 milligrams or 1,700 milligrams of potassium

The equation for the linear model in a scatter plot can be determined by selecting any two points closer to the line and utilizing them to find its slope and y-intercept. This information is then used to write the equation y = mx + b, where m is the slope and b is the y-intercept.

The question pertains to the equation of the linear model in a scatter plot which basically describes the best fit line passing through the points on the plot. In simple terms, in a scatter plot if you choose any two points closer to the line, we can use these to determine the equation of that line.

Suppose you have two points (x1, y1) and (x2, y2), where x represents the independent variable and y is the dependent variable. To find the slope (m) of the line, we use the formula: m = (y2 - y1) / (x2 - x1). Once the slope is determined, we proceed to find the y-intercept (b), which is the y-value where the line crosses the y-axis.

The general form of a linear equation is y = mx + b. Hence, using the values of slope and y-intecept obtained earlier, we can write the equation of our line. For example, in the equations given in the question, -1.5 and 1.5 are the slopes and 6 is the y-intercept.

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In 5 minutes, the car will travel 6 kilometers.

To convert the car's speed from kilometers per hour to kilometers per minute, we need to divide the given rate by the number of minutes in an hour, which is 60. So, for a car traveling at 72 kilometers per hour, the rate in kilometers per minute is:

72 km/hr / 60 = 1.2 kilometers per minute.

Now, to calculate how many kilometers the car will travel in 5 minutes, we simply multiply the rate in kilometers per minute by the number of minutes:

1.2 km/min * 5 min = 6 kilometers.

Therefore, the car will travel 6 kilometers in 5 minutes at the rate of 72 kilometers per hour.