A ladder is leaning up against a 17 foot Wall at an angle of elevation of 37°. How far is the foot of the latter from the wall? Round your answer to the nearest 10th of a foot

After setting up a system of equations based on the given age relationships and solving for both Grace and Joseph, we deduce that Grace is 20 years old and Joseph is 40 years old currently.

Let's denote Grace's current age as G and Joseph's current age as J. According to the problem, Grace is half of Joseph's age, so we have the first equation:

G = 0.5 * J

In 10 years, Grace will be three-fifths of Joseph's age, giving us the second equation:

G + 10 = (3/5) * (J + 10)

Ten years ago, Grace was one-third of Joseph's age, which gives us the third equation:

G - 10 = (1/3) * (J - 10)

We now have a system of three equations with two variables. We can solve this system to find the current ages of Grace and Joseph. After solving for G and J, we find that Grace is 20 years old and Joseph is 40 years old.

The standard notation 0.0002 cm becomes 2 × 10^-4 and 0.02 cm becomes 2 × 10^-2, both in scientific notation.

The standard notation for 0.0002 centimeters is 2 × 10^-4 in scientific notation. Meanwhile, the standard notation for 0.02 centimeters is 2 × 10^-2 in scientific notation.

You arrive at these translations by recognizing that the number 0.0002 means you've moved the decimal point four units to the right from 2 (thus raising 10, the base, to -4), and 0.02 represents moving the decimal point two units to the right from 2 (thus raising 10 to the -2).

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y < -2x +3

A. (1, 1) → x = 1, y = 1

substitute:

1 < -2(1) + 3

1 < 1 FALSE

B. (3, 0) → x = 3, y = 0

substitute

0 < -2(3) +3

0 < -3 FALSE

C. (-3, 10) → x = -3, y = 10

substitute

10 < -2(-3) +3

10 < 9 FALSE

D. (0, 0) → x = 0, y = 0

substitute

0 < -2(0) + 3

0 < 3 CORRECT

Answer: D. (0, 0)

Answer: The correct answer is "Test scores will increase because the graph shows a negative association."

Step-by-step explanation: Negative association is decreasing and positive is increasing but in this case we flip it to get our answer.

The impact of time spent surfing the internet on students' test scores depends on whether the association represented on the scatter plot is positive or negative. In a positive association, scores increase with increased internet time, while in a negative association, scores decrease.

Based on the question, it seems there is a relationship between the time spent surfing the Internet and students' test scores which is represented by a scatter plot. The association between these variables can be either positive, negative, or no association. A positive association means as the hours of surfing the internet increase, the test scores also increase. A negative association implies that as the hours of surfing the internet increase, the test scores decrease.

However, the question didn't provide the information about whether the scatter plot shows a positive or a negative association between these two variables, which is crucial to determine what happens to the test scores as internet surfing time increases.

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Answer: The answer is (D). the image is attached.

Step-by-step explanation: We are given four figures from which we are to select the one with AB = AC.

In figure (A), AB and AC are two chords of the circle with common point A. Since the lengths of two chords of a circle may not be equal, so AB may not be equal to AC. This option is not correct.

In figure (B), AB is a tangent at point B and AC is the extension of a chord which meets the tangent AB at point A. Since the lengths of AB and AC may not be equal, so this option is also incorrect.

In figure (C), AB and AC are extensions of two chords which meets at point A outside the circle, so they may not be congruent. So, this option will also not work.

In figure (D), AB and AC are two tangents from a common point A to the circle at B and C respectively.

We have the Two-Tangent Theorem which states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.

So, we have AB ≅ AC.

Thus, (D) is the correct option.

There are a lot of ways to write an expression using only 3 to get an answer of 100. Some examples are:

1st example:

3 / 3 + 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3

= 1 + 99

= 100

2nd example:

3 / 3 + 3 * 3 * 3 * 3 + 3 * 3 * 3 – 3 * 3

1 + 81 + 27 – 9 = 100

The correct option is a. 625.

The total number of outcomes in 4 spins of the spinner can be found by multiplying the number of outcomes in one spin by itself 4 times, resulting in 625 outcomes.

The sample space for 4 spins of the spinner can be calculated by raising the number of outcomes in one spin to the power of the number of spins.

In this case, as there are 5 outcomes on the spinner, the total number of outcomes in 4 spins would be 5^4 = 625.

Therefore, the correct option is a. 625.

Segment AB has slope 0. Segment DE, with midpoints of AC and BC, also has slope 0. Thus, DE is parallel to AB.

To prove that segment DE is parallel to segment AB, we need to show that the slopes of both segments are equal.

The slope of segment AB, denoted as [tex]\( m_{AB} \)[/tex], can be calculated using the coordinates of points A and B:

[tex]\[ m_{AB} = \frac{{y_B - y_A}}{{x_B - x_A}} \][/tex]

Given that point A is at (0, 0) and point B is at [tex]\((x_2, 0)\)[/tex], the slope [tex]\( m_{AB} \)[/tex] is:

[tex]\[ m_{AB} = \frac{{0 - 0}}{{x_2 - 0}} = 0 \][/tex]

Now, let's find the coordinates of points D and E.

Point D lies on segment AC, so it is at the midpoint of segment AC. Therefore, the coordinates of point D, denoted as [tex]\((x_{D}, y_{D})\)[/tex], are the average of the coordinates of points A and C:

[tex]\[ x_{D} = \frac{{x_1 + 0}}{2} = \frac{{x_1}}{2} \][/tex]

[tex]\[ y_{D} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]

Similarly, point E lies on segment BC, so it is at the midpoint of segment BC. Therefore, the coordinates of point E, denoted as [tex]\((x_{E}, y_{E})\)[/tex], are the average of the coordinates of points B and C:

[tex]\[ x_{E} = \frac{{x_1 + x_2}}{2} \][/tex]

[tex]\[ y_{E} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]

Now, let's calculate the slope of segment DE, denoted as [tex]\( m_{DE} \)[/tex]:

[tex]\[ m_{DE} = \frac{{y_{E} - y_{D}}}{{x_{E} - x_{D}}} \][/tex]

Substituting the coordinates of points D and E:

[tex]\[ m_{DE} = \frac{{\frac{{y_1}}{2} - \frac{{y_1}}{2}}}{{\frac{{x_1 + x_2}}{2} - \frac{{x_1}}{2}}} \][/tex]

[tex]\[ m_{DE} = \frac{0}{{\frac{{x_1 + x_2 - x_1}}{2}}} \][/tex]

[tex]\[ m_{DE} = 0 \][/tex]

Since the slopes of segments AB and DE are both equal to 0, we can conclude that segment DE is parallel to segment AB.

Answer:0.6

Step-by-step explanation:

Answer:

[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]

Step-by-step explanation:

Hello

thanks for asking this question, I think I can help you with this

if you have the point-slope form of the equation of a line, just isolate "y" to find the slope-intercept form

Step 1

[tex]y-3=\frac{1}{2} (x-1)\\\\y-3=\frac{x}{2}-\frac{1}{2} \\Add\ 3\ in\ both sides\\\\y-3+3=\frac{x}{2}-\frac{1}{2} +3\\y=\frac{x}{2}-\frac{1}{2}+3\\y=\frac{x}{2}+\frac{5}{2}[/tex]

so the answer is

[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]

where 1/2 is the slope, and 5/2 is the intercept with y-axis

I really hope it helps , Have a great day.

The probability of independent events Q and R both occurring is calculated by multiplying the individual probabilities of each event. Thus in this case, P(Q and R) = (1/8) * (2/5) = 1/20.

The question posed asks for the probability of events Q and R both occurring. Given that Q and R are independent events, the likelihood of both happening is calculated by multiplying the probabilities of each event.

That is, P(Q and R) = P(Q)P(R). From the question, we know that P(Q) is 1/8 and P(R) is 2/5.

Therefore, the probability of both Q and R occurring would be (1/8) * (2/5) = 1/20.

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Answer:

C. < 1,6 > (x)

Step-by-step explanation:

We know that,

Translation is the transformation that shifts the image in any direction.

The general form of horizontal translation of f(x) to f(x±k) and vertical translation of f(x) to f(x)±k where k is any constant.

Now, as the given function 'X' is translated 1 unit to the left i.e. translated horizontally by 1 unit i.e. X+1.

Also, the function is translated 6 units up i.e. translated vertically by 6 units i.e. X+6.

Hence, the solution is < 1,6 >(x).

Answer:

1/7

Step-by-step explanation:

sqrt(32) = 5.66

 so it is in section B

Answer:

section B.

YOUR WELCOME

Answer:

The number of hours needed for the company to break even happens when  

, rearranging to make the equation 'zero' on LHS

, divide each term by 5

, factorise

, equate each factor to zero

and  

We choose the positive value of  

Hence, the number of hours needed to break even is

Step-by-step explanation:

Answer:

The value of function at x = -2 is [tex]\frac{4}{3}[/tex].

Step-by-step explanation:

Given : Function [tex]Y=12\times 3^x[/tex]

We have to evaluate the given function at x = - 2

Consider the given function [tex]Y=12\times 3^x[/tex]

Since, y is a function in terms of x.

So, put x = - 2 in given function.

We get,

[tex]Y=12\times 3^{-2}[/tex]

Since, [tex]3^{-2}=\frac{1}{3^2}=\frac{1}{9}[/tex]

[tex]Y=12\times \frac{1}{9}[/tex]

Simplify, we have,

[tex]Y=\frac{4}{3}[/tex]

Thus, The value of function at x = 2 is [tex]\frac{4}{3}[/tex].