Consider this scenario and then answer the next three questions: A land owner wants a good approximation of the width of his stream from point D to point C. At high point B, he lays a carpenter’s square (used to make right angles) so that he can sight along BC and BA. AD = 9.3 ft and BD = 15.7 ft.1) State the corresponding proportional sides between similar triangles ABC and ADB. 2) Calculate the length of segment AB. Round the answer to the nearest tenth. (Hint: Use Pythagorean Theorem)3) Answer the following questions about the previous scenario: (a) Write an algebraic expression to represent the length from A to C. (b) Write a proportion to find the distance across the stream. (c) What is the length across the stream?
Answers
1) Let's consider both triangles ABC and ADB:
Then the proportional sides between similar triangles is:
[tex]\frac{AB}{AD}=\frac{BC}{BD}=\frac{AC}{AB}[/tex]2)Since we have that AD=9.3 and BD=15.7, using the pythagorean theorem we get the following:
[tex]\begin{gathered} AB^2=AD^2+DB^2 \\ \Rightarrow AB^2=(9.3)^2+(15.7)^2=86.5+246.5=333 \\ \Rightarrow AB=\sqrt[]{333}=18.2 \\ AB=18.2 \end{gathered}[/tex]Therefore, AB=18.2 ft
3)a)the best way to represent the length from A to C is with the pythagorean theorem:
[tex]AC=\sqrt[]{AB^2+BC^2}[/tex]b)The proportion to find the distance across the stream is the segment DC, then:
[tex]\frac{AD}{BD}=\frac{DB}{DC}[/tex]c)We can find the length by using the values for AD, BD and DB that we previously got:
[tex]\begin{gathered} AD=9.3 \\ BD=15.7 \\ \Rightarrow\frac{9.3}{15.7}=\frac{15.7}{DC} \\ \Rightarrow DC\cdot(\frac{9.3}{15.7})=15.7 \\ \Rightarrow DC=\frac{15.7}{(\frac{9.3}{15.7})}=26.5 \\ DC=26.5 \end{gathered}[/tex]Finally, we have that the length across the stream is 26.5 ft
Related Questions
The dimensions of portable kennel can be expressed as width x, height x-0.2 and length x+0.4.What are dimensions of portable kennel with a volume of 7.4 ft^3?Use a graphing calculator to solve.
Answers
Assuming the portable kennel is a box (rectangular prism), the volume is:
[tex]V=WHL[/tex]Where W is the width, H is the height, and L is the length.
We are given the values:
W = x
L = x + 0.4
H = x - 0.2
The volume is:
[tex]V=x(x+0.4)(x-0.2)[/tex]The volume is known to be 7.4, thus:
[tex]x(x+0.4)(x-0.2)=7.4[/tex]We cannot directly solve the equation by algebraic methods, so we use a graph. Define the function:
[tex]y=x(x+0.4)(x-0.2)-7.4[/tex]We need to find the value of x that makes the value of y equal to 0.
The graph of the function is shown below:
We can see the solution for x is a value near x = 1.8. Zooming the graph around the solution:
Now we have a more accurate solution at x = 1.9.
The dimensions of the kennel are:
W = 1.9
L = 1.9 + 0.4 = 2.3
H = 1.9 - 0.2 = 1.7
Checking: 1.9 × 2.3 × 1.7 = 7.43
The volume is approximately equal to 7.4
A manager chooses 2 months of the year during which to have training. What is the size of the sample space in this experiment?
Answers
The sample space refers to all possible ways of choosing two months. Since we have 12 months to choose from, the number of ways would be
12C2
We are applying combination because the order of the months doesn't matter. From our calculator,
12C2 = 66
the size of the sample space in this experiment is 66
A group of students are making a flag to represent their team on game day. The students are going to sew together pieces of fabric to make a design and glue it to the center of the flag. The design is made up of a rectangle, triangle, and semicircle. The dimensions of the design are shown in the diagram.
Answers
Explanation:
First we have to find the areas of each piece and then add them up.
The area of a triangle is the length of the base multiplied by its height and divided by 2:
[tex]A_{\text{triangle}}=\frac{12in\times6in}{2}=36in^2[/tex]The area of a rectangle is the product of the lengths of the sides:
[tex]A_{\text{rectangle}}=10in\times12in=120in^2[/tex]The area of a circle is pi times the radius squared. For a semicircle it's half the area of the circle:
[tex]A_{\text{semicircle}}=\frac{\pi r^2}{2}=\frac{\pi\cdot5^2}{2}=\frac{25}{2}\pi\approx40in^2[/tex]The total area of the flag is:
[tex]\begin{gathered} A=A_{\text{triangle}}+A_{\text{rectangle}}+A_{\text{semicircle}} \\ A=36in^2+120in^2+40in^2 \\ A=196in^2 \end{gathered}[/tex]Answer:
B. 196 in²
Two tables are placed side by side. One table is 5 feet 4 inches wide, and the other is 5 feet 9 Inches wide. Together, how wide are they?Write your answer in feet and inches. Use a number less than 12 for inches.
Answers
The widths of the tables are 5 feet 4 inches wide and 5 feet 9 Inches wide.
The first step is to add the dimensions in feet. We have
5 + 5 = 10 feet
The next step is to ad the dimensions in inches. We have
4 + 9 = 13 inches
Recall,
1 foot = 12 inches
Thus means that 13 inches = 1 foot and 1 inch. Adding 1 foot and 1 inch to 10 feet, the total width would be
11 feet 1 inch
i need help asap with these questions please worth 100 of my grades
Answers
Find what X equals [tex]2(x + 7) = - 4x + 14[/tex]
Answers
To solve the expression: 2(x + 7) = - 4x + 14, just follow these steps:
1. Distribute the product on the left side of the equation:
2(x + 7) = - 4x + 14
2*x + 2*7 = - 4x + 14
2x + 14 = -4x + 14
2. subtract 14 on both sides:
2x + 14 - 14 = -4x + 14 - 14
2x = - 4x
3. Add 4x on both sides:
2x + 4x = -4x + 4x
6x = 0
4. Divide both sides by 6:
6x/6 = 0
x*6/6 = 0
x*1 = 0
x=0
Then x equals 0
10. Dice A has six sides and dice B has ten sides. What is the probability of NOT rolling a 1 with both dice A and dice B?
Answers
Answer:
66.7 percent hope this helps
Step-by-step explanation:
Carmen drove 240 miles using 9 gallons of gas. At this rate, how many gallons of gas would she need to drive 216 miles? gallons
Answers
We are given that 240 miles are driven using 9 gallons of gas. To determine the gallons of gas needed to drive 216 miles we use a rule of three like this:
[tex]\begin{gathered} 240mi\rightarrow9gal \\ 216mi\rightarrow x \end{gathered}[/tex]Now, we cross multiply:
[tex](240mi)x=(216mi)(9gal)[/tex]Now, we divide both sides by 240 mi:
[tex]x=\frac{(216mi)(9gal)}{240mi}[/tex]Now, we solve the operations:
[tex]x=8.1gal[/tex]Therefore, 8.1 gallons are needed.
PLS HELP ASAP POINTS WILL BE GIVEN AND BRAINY
make y the subject of this formula
W = [tex]\frac{5y -t}{r}[/tex]
Answers
Variable y as the subject of the formula of the equation W = ( 5y - t )/r is y = (Wr + t)/5
How to solve for y as a subject formula?The subject of a formula is simply a specific variable that is being worked out.
Given the formula in the question;
W = ( 5y - t )/r
To solve for y, first multiply both sides by r
W × r = ( 5y - t )/r × r
In the right side of the equation, r cancels out r.
W × r = ( 5y - t )
Wr = 5y - t
To isolate the term with y, add t to both sides
Wr + t = 5y - t + t
In the right side of the equation, t cancels out t.
Wr + t = 5y
Reorder equation
5y = Wr + t
Divide both sides by the coefficient of y
5y/5 = (Wr + t)/5
y = (Wr + t)/5
Therefore, solving for y as subject of the formula is y = (Wr + t)/5.
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the grades on the second statistics test for Mr. Montgomery’s class are in the following list. complete the frequency distribution table for the grades. A,A,D,D,A,B,A,D,D,D,F,F,C,C,A,C,B,A,C,F,F
Answers
The frequency table can be filled by counting the number of each grades in the list.
The grade A is 6 times, grade B is 2 times, grade C is 4 times, grade D is 5 times, grade F is 4 times.
Answer:
Grade Frequency
A 6
B 2
C 4
D 5
F 4
Hello I am quite confused by this question may you please help me solve and explain this? thank you:)
Answers
Given the mean score of a group of people in a quiz, the standard deviation of the scores of the people, and the score of a person, we can easily determine the z-score like this:
[tex]z=\frac{x-μ}{σ}[/tex]Where σ is the standard deviation, μ is the mean score and x is the score. By replacing 78 for μ, 4.2 for σ and 80 for x, we get:
[tex]z=\frac{80-78}{4.2}=0.4762[/tex]Then the z-score equals 0.4762. In this case, the score of 80 is a usual value since it is within one standard deviation of the mean.
Determine whether A ABC is similar to ADEF. If so state how do you know.E
Answers
Given data:
In triangle DEF ,
DF = 25
DE = 41
EF = 40
In triangle ABC,
AB = 96
AC = 61
BC = 96
From above it is clear that , corresponding sides of triangle are not similar
Therefore, the triangle are not similar.
x+6=4x+1-3xsolve for x
Answers
we place the x's on the same side and the number on the other side
[tex]\begin{gathered} x-4x+3x=1-6 \\ (1-4+3)x=-5 \\ 0x=-5 \\ 0=-5 \end{gathered}[/tex]x is removed, and equality is meaningless, so x has no solution
Suppose that x and y vary inversely and that y= 1/6 when x = 3. Write a function that models the inverse variation and find y when x = 10.
Answers
The function that models the inverse variation is: y = 1/2x.
When x = 10, y = 1/20.
What is a Function that Models an Inverse Variation?The function that models an inverse variation between two variables, x and y, can be expressed as:
y = k/x.
Given that y = 1/6 when x = 3, find the value of the constant, k, by substituting the values of x and y into y = k/x:
1/6 = k/3
Multiply both sides by 3
1/6(3) = k/3(3)
1/2 = k
k = 1/2.
The function for the inverse variation would be, y = 1/2/x
y = 1/2x
To find y when x = 10, substitute the value of x = 10 into the equation y = 1/2x:
y = 1/2(10)
y = 1/20
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Use the picture to fill in the green box Inequalities in two triangles
Answers
Step 1
Given;
Step 2
The size of the angle facing any side of a triangle determine how size or length of that side. The bigger the angle, the longer the side.
In a triangle, the largest side is opposite the largest angle and vice versa and the shortest side is opposite the smallest angle and vice versa
[tex]\begin{gathered} The\text{ angle facing x=63}^{\circ} \\ The\text{ angle facing y=62}^{\circ} \end{gathered}[/tex]Thus, 63 is bigger than 62. So we conclude that;
[tex]x>y[/tex]Answer;
help me please
thank you
Answers
Answer:
is a functiondomain: [-6, 2]range: [-4, 0]Step-by-step explanation:
You want to know if the graph of the semicircle centered at (-2, 0) with radius 4 extending below the x-axis is a function. You also want to know its domain and range.
FunctionThe graph passes the vertical line test. That is, no vertical line intersects the graph in more than one place. That means the relation is a function.
DomainThe domain of the function is the horizontal extent of the graph. The solid dots at the extreme points of (-6, 0) and (2, 0) indicate those points are part of the domain. The domain also includes all x-values between them. In interval notation, the domain -6 ≤ x ≤ 2 is written as ...
[-6, 2]
RangeThe range is the vertical extent of the graph. The semicircle extends from a low point of (-2, -4) to high points on the x-axis. Thus its range is -4 ≤ y ≤ 0, written in interval notation as ...
[-4, 0]
__
Additional comment
The brackets used in interval notation are square brackets if the end points are included in the interval. Otherwise, they are round brackets (parentheses).
Which of the following is the coordinate of the minimum?O (-9,-4)O (4,-6)0 (0,2)O (9,5)O (1,3)
Answers
In this case the answer is very simple.
The minimums are represented by the valleys.
Analyzing the graph we can say that the minimum would be:
(4 , -6)
That is the solution.
Put these numbersmin order from least to greatest 3/103/89/100.63
Answers
Please solve with explanation so I can use as reference in the future thank you!
Answers
Answer:
x=24
Step-by-step explanation:
y = x*c
x=2, y=7
2*c=7 => c=7/2
x*7/2 = 84
x = 84*2/7
x = 12*2
x = 24
I hope this helps TwT
Name the quadrant in which each of the points lies -1, -8
Answers
Given the point ( -1, -8 )
The x-coordinate of the point = -1
The y-coordinate of the point = -8
So, x < 0, y < 0
So, the point lies in the third quadrant
So, the answer will be Quadrant 3
please help i dont have as much time
Answers
Answer:
f(2) = -7
Step-by-step explanation:
f(x) = -2x-3
f(2) = -2(2)-3
f(2) = -4-3
f(2) = -7
help me please
thank you
Answers
In interval notation, the interval notation has [tex](-\infty, -4)[/tex].
Simplify the expression. 5+8(37)
Answers
Answer:
301
step by step explanation:
5+(8)(37)
=5+296
=301
Answer:
301
Step-by-step explanation:
using pemdas:
5+(8)(37)
=5+296
=301
the table show how many points eduardo scored during each game use mental math to find how many points he scored
Answers
The total points scored by Eduardo in the first three games is 97.
We are given a table that shows the points scored by Eduardo during three games.
In game 1, he scored 52 points.
In game 2, he scored 19 points.
In game 3, he scored 26 points.
In game 4, he scored 10 points.
We need to find the sum of the total points scored by him in the first three games.
A summation, also known as a sum, is the outcome of adding numbers or quantities arithmetically. A summation always has an even number of terms.
The points are 52 + 19 + 26 = 97.
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is 0.49 a rational or irrational number? Explain how you know.
Answers
The decimal 0.49 is a rational number.
What is a rational number?Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers, can be used to represent a rational number.
A rational number is a number that can be expressed as a fraction where the numerator is a whole number and the denominator is a whole number .
In this case, 0.49 is the same as 0.49 over 1. In other words, it can be seen that 0.49 can be written with a numerator and denominator like 49/100.
Therefore, it's a rational number.
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I NEED THIS ANSWER SOON!
Rewrite the expression 6a + 21 to demonstrate the distributive property. Describe how the rewritten expression can be verified to be equivalent to 6a + 21.
Answers
Answer:
it can be verified as 2a + 7
A hall has square tables that can seat 4 people each, When there are more than 4 people in a group, the tables are moved together. what is the greatest number of people who can sit at 7 tables lines up in a row?
Answers
28 people can sit on 7 tables in a row
Explanations:Number of people that can sit on a square table = 4
The greatest number of people that can sit on 7 tables = 7 x ( Number of people that can sit on a table)
The greatest number of people that can sit on 7 tables in a row = 7 x 4
The greatest number of people that can sit on 7 tables in a row = 28
combining functions to write a new function that models a real world solution please help!!!
Answers
SOLUTION
The standard charge is
[tex]S=0.60M+18.95[/tex]And the insurance charge is
[tex]I=0.15M+4.80[/tex]The total cost will be given as:
[tex]C=S+I[/tex]Substitute for S and I into the equation
[tex]C=0.60M+18.95+0.15M+4.80[/tex]Simplify the equation:
[tex]C=0.75M+23.75[/tex]Therefore the required answer is:
[tex]C=0.75M+23.75[/tex]help meeeeeeeeee pleaseee
Answers
The domain of the relation represented in the graph as given in the task content is; [2, infinity).
The range of the relation is; (-infinity, infinity).
What is the domain and range of the relation?It follows from the task content that the domain and range of the relation are to be determined from the graph given.
Since the range is the set of all possible output, y-values, it follows from the arrows in the graph that the range is the set of all real numbers and hence can be represented using interval notation as; (-infinity, infinity).
Also, the domain is the set of all possible input, x-values and can be determined from the graph as numbers greater or equal to 2 as 2 is the minimum of the curve.
Domain = [2, infinity).
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Determine whether the statement is always, sometimes, or never true. Complete the explanation.If line m is parallel to linen and the slope of line m is greater than 1, then the slope of linen is greaterthan 1.This statement is (select) true. If line m is parallel to line n, then the lines have (select)slope. Therefore, if the slope of line m is greater than 1, the slope of line m (select) greater than 1.
Answers
The given statement is
If line m is parallel to linen and the slope of line m is greater than 1, then the slope of linen is greater
than 1.
This statement is always true because parallel lines have the same exact slope, otherwise they wouldn't be parallel.
Therefore, the complete statement would be
This statement is always true. If line m is parallel to line n, then the lines have an equal slope. Therefore, if the slope of m is greater than 1, the slope of n is always greater than 1.
