To find the distance across a river, a forester sets up stakes at A, B,C and D so that
stakes D and B are in line with a larger tree T, on the opposite bank. Calculate the
width of the river using the measurements given. (Upload a Picture of your solution)
Answers
Answer:
75m
Step-by-step explanation:
They are similar triangles: they have two corresponding angles: in a triangle with an angle of 90°, the other two will be of 45°.
Now that we know they are similar, we can calculate the ratio of the sides, by doing 10/2=5
We want to know the side AT, so we can do that by multiplying DC for 5:
DC = 15 × 5 = 75m
You can also check this by applying Pythagoras' Theorem:
DB =
[tex] \sqrt{15^{2} + 2^{2} } [/tex]
Which equals 15.1 m
The hypotenuse of the other triangle is 15.1 × 5 = 75.5 m
Finally, we can apply for the last time the Pythagoras' Theorem to find AT:
[tex] \sqrt{75.5^{2} - 10 {}^{2} } [/tex]
Which equals 74.8 = 75 m
Related Questions
A. Joshua puts $8,765 in a
10-year 5.28% savings
certificate in which interest is
compounded quarterly. How
much total interest has he
earned at the end of the ...
a) second year?
b) fourth year?
c) seventh year?
d) tenth year?
Answers
The amount at the end of the second year is $9,734.49.
The amount at the end of the fourth year is $10,811.22.
The amount at the end of the seventh year is $12,653.68.
The amount at the end of the tenth year is $14,810.14.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $8765
r = 5.28%
n = 4 (quarterly)
Amount after 2 years.
A = 8765 [tex](1 + 0.0131)^2[/tex]
A = $9,734.49
Amount after 4 years.
A = 8765 [tex](1 + 0.0131)^4[/tex]
A = $10,811.22
Amount after 7 years.
A = 8765 [tex](1 + 0.0131)^7[/tex]
A = $12,653.68
Amount after 10 years.
A = 8765 [tex](1 + 0.0131)^{10}[/tex]
A = $14,810.14
Thus,
The amount at the end of the second, fourth, seventh, and tenth year is given above.
Learn more about compound interest here:
https://brainly.com/question/13155407
#SPJ2
Prove that 4x-1 =11,in which the value of x=3
Answers
Answer:
3
Step-by-step explanation:
substitute where x=3 into the equation
so 4*3-1=11
4×3-1=11
12-2=11
11=11
proved..
Solve for r.
√2/3r + 1 = 23
Answers
Answer:
2nd option
Step-by-step explanation:
[tex]\frac{\sqrt{2} }{3}[/tex] r + 1 = 23 ( subtract 1 from both sides )
[tex]\frac{\sqrt{2} }{3}[/tex] r = 22 ( multiply both sides by 3 to clear the fraction )
[tex]\sqrt{2}[/tex] r = 66 ( divide both sides by [tex]\sqrt{2}[/tex] )
r = [tex]\frac{66}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] ( rationalising the denominator )
r = [tex]\frac{66\sqrt{2} }{2}[/tex] = 33[tex]\sqrt{2}[/tex]
Answer:
B) r=33*sqrt(2)
Step-by-step explanation:
sqrt(2)/3r+1=23
sqrt(2)/3r=23-1
sqrt(2)/3r=22
sqrt(2)r=22*3
sqrt(2)r=66
r=66/sqrt(2)
r=66*sqrt(2)/(sqrt(2)*sqrt(2))
r=(66*sqrt(2)/2
r=33*sqrt(2)
Need help please if anyone one can help me now I will like that
Answers
Answer:
.
Step-by-step explanation:
question 5. Write an equation of the line that passes through the points (-2, -6) and (4, 6).
Answer in slope-intercept form
Answers
Answer:
y=2x-2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-(-6))/(4-(-2))
m=(6+6)/(4+2)
m=12/6
m=2
y-y1=m(x-x1)
y-(-6)=2(x-(-2))
y+6=2(x+2)
y=2x+4-6
y=2x-2
Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.
Graph y= 0.5x^2 - 4x +6 on the coordinate plane.
Vertex:
Is this considered a minimum or maximum point?
Axis of symmetry: x=
Roots: x= and x=
Answers
Answer:
V: (4, -2), min, Axis: x = 4, Roots 2 and 6
Step-by-step explanation:
Multiply everything x 2 to get rid of the decimal in front of x^2
2y = x^2 - 8x + 12
Factor
2y = (x - 6)(x - 2)
The roots are at 2 and 6.
The axis of symmetry is in the center between the roots, so it is x = 4.
Put 4 into the original equation to find y
y = 0.5(4*2) - 4(4) + 6
y = 8 - 16 + 6, y = -2
Vertex is at (4, -2). It is a minimum because the graph opens up since x*2 is positive.
What is the velocity of a car that traveled total of 75 km north in 1.5 hours?
Answers
Answer:
hope this helped!
Step-by-step explanation:
75 km = 75000 m
1.5 hours = 5400 sec
Applying the formula
Velocity
=
75000 m
5400 s
=
13.89 m/s
Please help question in pic
Answers
Answer:
7,3
Step-by-step explanation:
for every 5 it goes right it goes 4 up. 2,1+5,4=7,3
please help meeeeeeeeeeeeeeeeeeee
ty
Answers
Answer:
A
Step-by-step explanation:
hope this helped
Answer:
4y = -3x - 8
Step-by-step explanation:
What value of x satisfies the equation 3x – 2 = 2x + 4?
Answers
Answer:
x = 6
Step-by-step explanation:
3x - 2 = 2x + 4
First, we need only 1 set of x, so I'll subtract the smallest x from the other.
-2x both sides.
x - 2 = 4
Next, add +2 to both sides. (In these types of questions always do the inverse!)
And so your answer is:
x = 6
Answer:
x = 6
Step-by-step explanation:
1. Add 2 to both sides of the equation
3x - 2 = 2x + 4
3x - 2 + 2 = 2x + 4 + 2
2. Simplify
3x = 2x + 6
3. Subtract 2x from both sides of the Equation
3x - 2x = 2x + 6 - 2x
4. Simplify
x = 6
Two numbers are in a ratio 11:7. If the smaller number is 700, what is the larger number? Pls tell with steps
Answers
Answer:
The larger number is [tex]1100[/tex]
Step-by-step explanation:
Let larger number be [tex]x[/tex]
We have
[tex]\frac{x}{700} =\frac{11}{7} \\\\x=100\times11\\\\=1100[/tex]
Answer:
The larger number is 1100.
Step-by-step explanation:
Solution :
Let the,
>> Larger number be 11x. >> Smaller number be 7x.Now, According to the question :
[tex]\begin{gathered} \dashrightarrow\sf{Smaller \: number} = \tt{700} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{7x}= \tt{700} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{x}= \tt{700 \div 7} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{x}= \tt{ \dfrac{700}{7} } \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{x}= \tt{\cancel{\dfrac{700}{7}}} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow \sf{x}= \tt{100} \end{gathered}[/tex]
Hence, the value of x is 100.
Now, calculating the larger number :
[tex]\begin{gathered} \dashrightarrow\sf{Larger \: number} = \tt{11x} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{Larger \: number} = \tt{11 \times 100} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{Larger \: number} = \tt{1100} \end{gathered}[/tex]
Hence, the larger number is 1100
[tex]\rule{300}{1.5}[/tex]
Let a and b be real numbers where ab+0. Which of the following functions could represent the graph below?
O f(x) = x(x – a)3(x – b) 3
O f(x) = (x – a)2(x – 614
O f(x) = x(x – a) (x – 5)2
O f(x) = (x – a)5(x – b)
Answers
The following functions could represent the graph below then the correct option is B; y = (x - a)^2 (x - b)^4.
What is graph ?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
we have given that a and b are real numbers different than zero.
From the graph, we can see that the line touches the x-axis in two values.
Now, if we would have an equation such as:
y = x(x - a)^3 (x - b)^3
then when x = 0
y = 0(0-a)^3 (0-b)^3
y = 0
But in the graph, we can see that when x = 0, the value of y is different than zero,
(For example, if x > a and x < b we would have a negative value for y)
Then the correct option is B ;y = (x - a)^2 (x - b)^4
Learn more about graphing functions here:
https://brainly.com/question/14455421
#SPJ1
6. Find the value of y.
5
16
Answers
or 3.6
hopefully this helps you!
Giving brainliestttyttttt
Answers
Answer:
C
Step-by-step explanation:
Because its right
guys do you know 9 divided by 0.954 because when i calculate it , it shows this big number so can you put it in an short way?
Answers
Answer:
9.43
Step-by-step explanation:
You simply use the first couple digits of the solution your calculator gave you. (How many depends on the question you were asked)
Answer:
9 23/53
Step-by-step explanation:
The fraction is not particularly nice. It can be written as ...
9/0.954 = 9000/954 = 500/53 = 9 23/53
As a decimal, the fraction has a 13-digit repeat:
[tex]9.\overline{4339622641509}[/tex]
please help me if you can
Answers
B) 45 degrees (congruent angle)
C) 90 degrees (right angle)
D) 99 degrees (congruent angle)
E) 30 degrees (congruent angle)
F) 30 degrees (180-150=30, that is to find the other angle that is congruent to f)
5 2/12 x 10/11
Simplify the answer completely and change to a mixed number
Answers
Answer:
[tex]4\frac{23}{33}[/tex]
Step-by-step explanation:
[tex]5 \frac{2}{12}[/tex] × [tex]\frac{10}{11}[/tex]
[tex]\frac{62}{12}[/tex] × [tex]\frac{10}{11}[/tex]
[tex]\frac{62*10}{12*11}[/tex]
[tex]\frac{620}{132}[/tex]
Divide both sides by 4
[tex]\frac{155}{33}[/tex]
Now let us write it as a mixed number
[tex]4\frac{23}{33}[/tex]
Hope this helps you :-)
Answer:
Question :[tex] \dashrightarrow{5 \dfrac{2}{12} \times \dfrac{10}{11}}[/tex]
Solution :[tex] \dashrightarrow{5 \dfrac{2}{12} \times \dfrac{10}{11}}[/tex]
Coverting 5-1/2 into improper fraction :
[tex] \dashrightarrow{\dfrac{(5 \times 12) + (2)}{12} \times \dfrac{10}{11}}[/tex]
[tex] \dashrightarrow{\dfrac{(60) + (2)}{12} \times \dfrac{10}{11}}[/tex]
[tex] \dashrightarrow{\dfrac{60 + 2}{12} \times \dfrac{10}{11}}[/tex]
[tex] \dashrightarrow{\dfrac{62}{12} \times \dfrac{10}{11}}[/tex]
Performing multiplication :
[tex] \dashrightarrow{\dfrac{62 \times 10}{12 \times 11}}[/tex]
[tex] \dashrightarrow{\dfrac{620}{132}}[/tex]
Cutting the fraction into simplest form :
[tex] \dashrightarrow{ \cancel{\dfrac{620}{132}}}[/tex]
[tex] \dashrightarrow{ \dfrac{155}{33}}[/tex]
Coverting the improper fraction into mixed fraction :
[tex]{\dashrightarrow{\sf{\underline{\underline{\red{4 \dfrac{22}{33}}}}}}}[/tex]
Hence, the answer is [tex]\bf{4 \dfrac{22}{33}}[/tex].
find the value of x if p ll q
Answers
Answer:
maybe you can attach the screenshot of the task?
What is the equation for the line perpendicular to y=3/2x + 2 that contains (3, -5)?
Answers
Answer:
B?
COREEC IF WRONG
Answer:
y=-2/3x-3
Step-by-step explanation:
let the slope of the given line =m1
let the slope of the perpendicular line,=m2
m2=-1/m1
m2=-1/3/2
m2=-2/3
Now the equation of the perpendicular line
y--5=-2/3(x-3)
y+5=-2/3(x-3)
3y+15=-2x+6
3y=-2x+6-15
3y=-2x-9
y=-2/3x-3
Please help asap! I will mark brainliest for correct answer!!
a softball player hits a pitched ball when it is 4 feet above the ground. the initial velocity is 75 feet per second. Use the formula: h=-16t^2+vt+s. How long will it take for the ball to hit the ground?
Answers
Answer: Do the math, the positive solution
t = 5.0495 seconds (If it's wrong sorry, I havent done a problem like this one in awhile!)
Step-by-step explanation:
Maggie's brother is 5 years younger than three times her
age. The sum of their ages IS 43.
How old is Maggie?
Answers
Answer:
Step-by-step explanation:
Let Maggie's age = x
The brother's age = 3x - 5
x + 3x - 5 = 43
4x - 5 = 43 Add 5 to both sides
4x - 5 + 5 = 43+5
4x = 48 Divide by 4
4x/4 = 48/4
x = 12
Maggie = 12
Brother = 3*12 - 5
Brother = 36 - 5
Brother = 31
Compare 4:10 and 12:20 using fractions. Which ratio is smaller? How do you know?
Answers
times the whole ratio by two to get: 8:20 now we can compare it to 12:20 and so 8 < 12 so the first one is smaller
You have 4/3 chocolate bars. You want to give 1/2 of the chocolate bars you have to your friend. What fraction of the chocolate bars would each of you get
Answers
The fraction 8/3 of the chocolate bars would each of you get.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
You have 4/3 chocolate bars.
You want to give 1/2 of the chocolate bars to your friend.
To find the fraction of the chocolate bars would each of you get:
Use division operation,
4/3 ÷ 1/2
Rearranging to multiplication term,
4/3 x 2/1
= 8/3
Therefore, 8/3 fraction of the chocolate bars would each of you get.
To learn more about the division;
https://brainly.com/question/13263114
#SPJ2
Is 29/49 an interger
Answers
No, integers cannot be fractions or decimals.
What is the answer to this?
Answers
Answer:
option b.)y=1/4x-7/2.....
Work out the difference between 38.3 and 1.72
Answers
Answer:
36.58
Step-by-step explanation:
38.3-1.72=36.58
The value of the expression 38.3 - 1.72 will be 36.58.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The numbers are given below.
38.3 and 1.72
Then the difference between the numbers 6 and 1/3 will be given by putting a minus sign between them. Then we have
⇒ 38.3 - 1.72
⇒ 36.58
The value of the expression 38.3 - 1.72 will be 36.58.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
A triangle has side lengths of 2 feet, 5.4 feet, and 5 feet. The angle measures are 90 degrees, 73 degrees, 17 degrees. Another triangle has side lengths of 3 feet, 8.1 feet, 7.5 feet. The angle measures are 90 degrees, 73 degrees, 17 degrees. Are the triangles similar? If so, what is the scale factor going from the top triangle to the bottom triangle?
Answers
Answer:
Yes. The factor is 3/2 (=1,5)
Step-by-step explanation:
They have all the 3 angles congruent, so they are similar. You calculate the scale factor by dividing the hypotenuse (for example) of the second triangle by the hypotenuse of the first one.
Answer:
1) yes 2) 1.5
Step-by-step explanation:
have a nice day! <:
PLEASE HELP I NEED TO HAVE THIS DONE IN 30 MINUTES
Answers
Answer:
Yes it does. Because it's a linear graph, what Mena's it's a linear relationship, and linear relationships are proportional
Idrissa collected pennies in a fundraiser. He measured the mass of all the pennies he collected to be2,400 grams. Two pennies put together have a mass of 5 grams. How much money did Idrissa raise in
this fundraiser?
Answers
The total amount of pennies Idrissa raised in this fundraiser is = 960 pennies
The total mass of all the pennies = 2,400g
But two (2) pennies = 5g
Therefore, to calculate the total amount of pennies Idrissa raised you cross multiply.
That is: 2 pennies = 5g
x pennies = 2,400g
Making x the subject of formula,
[tex] x = \frac{2 \times 2400}{5} [/tex]
[tex]x = \frac{4800}{5} [/tex]
[tex]x = 960[/tex]
Therefore the total amount of pennies Idrissa raised in this fundraiser is = 960 pennies.
Learn more here:
https://brainly.com/question/294036
PLS SHOW ME HOW U GET THE ANSWER AND WILL GIVE BRAINLYEST
Answers
Answer:
38 degrees
Step-by-step explanation:
all triangles length added up are 180 degrees.
add 52 and 90 to get 142. Subtract to get 38 degrees.