To indirectly measure the distance across a river, Khalil stands on one side of the river
and uses sight-lines to a landmark on the opposite bank. Khalil draws the diagram
below to show the lengths and angles that he measured. Find PR, the distance across
the river. Round your answer to the nearest foot.
N
RI
185 ft
150 ft
0
275 ft
(Diagram is not to scale.)
ft
Submit Answer
Answer:
Answers
Khalil uses the method of similar triangles to find the distance across the river, [tex]\overline{PR}[/tex]
The distance across the river is [tex]\underline{308.\overline 3 \ feet}[/tex]Reasons:
The distances between the formed the sight-lines are;
[tex]\overline{RB}[/tex] = 185 feet
[tex]\overline{OC}[/tex] = 275 feet
The distance between the point close to the river and the next point further from the river [tex]\overline{RO}[/tex] = 150 feet
In triangles ΔPRB and ΔPOC, we have;
∠PRE = ∠POC = 90° Given
∠PER ≅ ∠PCO By corresponding angle formed between two parallel lines and a common transversal.
∴ ΔPRE is similar to ΔPOC by Angle-Angle, AA, similarity theorem
Which gives;
[tex]\displaystyle \frac{\overline {PR}}{\overline {PO}} = \mathbf{\frac{\overline {RE}}{\overline {OC}}}[/tex]
Let x represent the distance across the river, we have;
[tex]\overline{PR}[/tex] = x
[tex]\overline{PO}[/tex] = 150 + x
Which gives;
[tex]\displaystyle \frac{x}{150 + x} = \frac{185}{275}[/tex]
275·x = 185 × (150 + x) = 27,750 + 185·x
275·x - 185·x = 27,750
90·x = 27,750
[tex]\displaystyle x = \frac{27,750}{90} = \mathbf{308.\overline 3}[/tex]
Therefore, the distance across the river, x = [tex]\mathbf{\overline{PR}}[/tex] = [tex]\underline{308.\overline 3 \ feet}[/tex]
Learn more about similar triangles here
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Related Questions
The − and −axes, the ordinate = 3 and the curve =
2 + 1
Answers
Tyrone works in a grocery store and he puts boxes on shelves. There are 4 shelves in the cereal section of the store. All shelves hold the same number of boxes of cereal. If there are 80 boxes of cereal on the shelves, how many boxes are on each shelf? In complete sentence
Answers
Answer:
Each shelf can hold 20 boxes of cereal.
Step-by-step explanation:
Start with 80 boxes of cereal: (80)
There are 4 shelves for each box of cereal: (x/4)
Thus, we get the expression: 80/4=
(You may want to simplify this; giving you the answer of 20.)
HELP!? ✋
What strategies help prevent cancer?
Select all that apply.
Question 8 options:
using sunscreen
avoiding tobacco
getting enough sleep
eating a healthy diet
Answers
The radius of a circle is 2.5 centimeters (cm).
What is the circumference of the circle?
Answers
Answer:
15.7 cm to nearest 10th
Step-by-step explanation:
Circumference = 2 pi r = 2 pi 2.5
= 5 * pi
= 15.708 cm.
more help... please... I'm very stuck
Answers
A) 5percent of 40=2 ( 0.05*40)
Since it’s increase add 2 to 40=42
F) 40percent of 25= 10 (0.4* 25)
25-10=15
Question 8 of 25
An English teacher has equal numbers of fiction, literature,
and poetry books. Each day, she randomly selects one book
to read from. She designs a simulation to estimate the
probability that the next three books she selects are all
literature.
Which simulation design could she use to estimate the
probability?
Answers
The simulation design could she use to estimate the probability is
Number cube
Let 1, 6 = literature
Let 2, 5 = fiction
Let 3, 4 = poetry
Roll the cube three times. Repeat.
What is simulation?Simulation is the process of creating a model or representation of a real-world system or process and conducting experiments with the model to observe how it behaves or performs under different conditions.
We have,
This simulation design assigns each book in the teacher's collection a unique number from 1 to 6, with literature books assigned the numbers 1 and 6, fiction books assigned the numbers 2 and 5, and poetry books assigned the numbers 3 and 4.
Rolling a number cube simulates the teacher randomly selecting a book each day, and repeating this process three times allows for the estimation of the probability that three consecutive selections will be literature books.
This simulation design is appropriate because it accurately represents the probabilities of selecting literature, fiction, and poetry books from the teacher's collection and allows for repetition to simulate multiple days of book selections.
Thus,
The simulation design could she use to estimate the probability is
Number cube
Let 1, 6 = literature
Let 2, 5 = fiction
Let 3, 4 = poetry
Roll the cube three times. Repeat.
Learn more about simulations here:
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LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
Answers
Answer:
See below
Step-by-step explanation:
Dilation of 4
Z (0, -1) Z' (0, -4)
X (1, -1) X' (4, -4)
Which equation best matches the scenario below?
The total cost t is proportional to the number n of items purchased at a constant price of $4.
A) 4t = n
B) t = 4n
C) t = n ÷ 4
D) 4t = 4n
Answers
Answer:
Definetly t = 4n
answer pls having problem in this
Answers
[tex]\dfrac{\sqrt[3]{343}}{\sqrt[3]{-343}}=\dfrac{\sqrt[3]{343}}{-\sqrt[3]{343}}=-1[/tex]
What is the range of the relation below?
Answers
Answer:
D is correct
Step-by-step explanation:
PrOblem 1: Find the slope of the line containing the points: (3,-5) and (-1, -2)
Problem 2: Find the x and y intercepts of the line: 2x – 3y = 12
Problem 3: Graph the line x-4y=8
Answers
Answer:
1) -3/4
2) (6, 0), (0, -4)
3) connect (0,-2) and (8,0) together
Step-by-step explanation:
1) (-2) - (-5) / (-1) - 3 = -3/4
2) x = 0 -3y=12 y = -4, y= 0 2x = 12 x = 6, x intercept = (6, 0) y intercept = (0, -4)
3) x - 4y = 8 this could be written as y = x/4 - 2 and y intercept is (0, -2) and x intercept is (8, 0) so connect these points together and make a line
#1
m=y2-y1/x2-x1m=-2+5/-1-3m=3/-4#2
Inetercept form x/a+y/b=1
2x-3y=122/12x-3/12y=12/12x/6-y/4=1x inetercept at 6 and y intercect at -4
#3
Graph attached
3* what =1 because I'm genuinely unsure
Answers
Answer:
0.3 recurring so 0.33333333333333333333333333333333333333
and....
__________________________________________________________
How to Overcome Insecurity
Step 1
The first step of Voice Therapy involves vocalizing your self-critical thoughts in the second person.You can also write down these thoughts.
Step 2
In the second step, you can start to think and talk about the insights and reactions you have to exposing these mean thoughts.
Step 3
People often struggle with the third step of this process, because it involves standing up to long-held beliefs and insecurities about oneself. You will answer back to your voice attacks, expressing your real point of view.
Step 4
In step five of Voice Therapy, you start to make a connection between how the voice attacks are influencing your present-day behaviors.
Step 5
The final step involves making a plan to change these behaviors. If insecurity is keeping you from asking someone on a date or going after a promotion, it’s time to do the actions anyway. If you’re indulging in self-hating thoughts that encourage you to engage in self-destructive behaviors, it’s time to interrupt these behaviors and unleash the real you.
Hope it help and if it did please give brainliest
Stay safe and healthy
Thank You
Suppose that the market price for a bottle of vitamins is $1.61 and that at that price the total market quantity demanded is
255,340,000 bottles. How many firms will there be in this industry?
firm(s)
Answers
Answer:
255,340,000(1.61)= $411097400
Step-by-step explanation:
multiply the total amount of bottles by $1.61, since it costs $1.61 per bottle.
Which inequality below is true?
a. -2>4
b. -4< 2
C. -4> 4
d. -4> -2
Answers
Because 2 is greater than -4
Hope this helps!
Brainliest is much appreciated!
What percent of 111 is 94?
Answers
Answer:
I’d say 84.68%
comparing freezers
Maria compares two freezers.
Freezer A is 8 feet long, 4 feet wide, and 2 feet high.
Freezer B is 6 feet long, 4 feet wide, and 3 feet high.
correctly complete the statement : Freezer _ has _ more cubic feet than Freezer _ .
Answers
Answer:
Freezer B has 8 more cubic feet than Freezer A.
Step-by-step explanation:
Volume of Freezer A = 8 * 4 * 2 = 64 ft^3.
Volume of Freezer B = 6 * 4 * 3 = 72 ft^3.
72 - 64 = 8 ft^3.
Answer:
Freezer B has 8 more cubic feet than Freezer A.
Step-by-step explanation:
Hassan made a vegetable salad with 2 3/8 pounds of tomatoes, 1 1/4 pounds of asparagus, and 2 7/8 pounds of potatoes. How many pounds of vegetables did he use altogether?
Btw please show work.
Answers
Step-by-step explanation:
OK so
Tomatoes = 2 3/8 = 19/8 (turned into improper fraction)
Asparagus = 1 1/4 =5/4
Potatoes = 2 7/8 = 23/8
Total vegetables used =
19/8 + 5/4 + 23/8 = 42/8 + 5/4 = 42+10/8 =52/8
Answer is 52/8 = 6.5
Answer : 52/8 pounds were used altogether
See picture for solution.
The PTA was doing a fundraiser and bought 500 megaphones to sell for a pep rally. The profit, p, from the sale of megaphones can be represented by p(m) = 3.5m-875. Which inequalities represents the constraints of the range?
A. m>= - 875
B. 0<=p(m) <- 500
C. 0<=m<=500
D. p(m) >= -875
Answers
The inequality which represents the constraints of the range is D. p(m) ≥ -875
Since the PTA was doing fundraiser and bought 500 megaphones to sell for the pep rally, and the profit, p, from the sale of megaphones can be represented by p(m) = 3.5m - 875 where m = number of megaphones sold.
To find the inequalities represents the constraints of the range of p(m), we need to know the domain of m.
Since we have 500 megaphones and we can sell from 0 to 500 inclusive. So, the domain of m is 0 ≤ m ≤ 500.
To determine the range of p(m), we insert the values of m at its extreme points into p(m).
So, when m = 0
p(m) = 3.5m - 875
p(0) = 3.5(0) - 875
p(0) = 0 - 875
p(0) = -875
when m = 500
p(m) = 3.5m - 875
p(500) = 3.5(500) - 875
p(500) = 1750 - 875
p(500) = 875
Since for a profit, m ≥ 0. So, p(m) ≥ p(0) = -875
So, p(m) ≥ -875
So, the inequality which represents the constraints of the range is D. p(m) ≥ -875
Learn more about inequalities here:
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if a + b equal to pi by 4 then prove that 1 + cot a into 1 + cot B equal to 2 into cot a into cot b
Answers
Answer:
(cotA − 1) (cotB − 1) = 2
Step-by-step explanation:
A+B= π/4 = 180°/4 = 45°
A+B=45°
∴ cot(A+B)=cot45°
∴ cotBcotA−1 / (cotB+cotA) = 1
⇒cotB + cotA = cotBcotA = 1
⇒cotB + cotA − cotBcotA + 1 = 0
⇒cotBcotA − cotB − cotA − 1 = 0
⇒cotBcotA − cotB − cotA − 1 + 2 = 0+2
⇒cotBcotA − cotB − cotA + 1 = 2
⇒cotB(cotA − 1) (cotA − 1) = 2
⇒(cotA − 1) (cotB − 1) = 2
Proved
x+3x+3y+3z=21
Find the value of X.
Answers
Answer:
[tex] x = \frac{21 - 3y - 3z}{4} [/tex]Step-by-step explanation:
Question:-To find value of xEquation:-x + 3x + 3y + 3z = 21Solution:-=> x + 3x + 3y + 3z = 21
[On adding like terms x and 3x]=> 4x + 3y + 3z = 21
[On subtracting both sides with 3y]=> 4x + 3y + 3z - 3y = 21 - 3y
[On Simplification]=> 4x + 3z = 21 - 3y
[On subtracting both sides with 3z]=> 4x + 3z - 3z = 21 - 3y - 3z
[On Simplification]=> 4x = 21 - 3y - 3z
[On dividing both sides with 4][tex] = > \frac{4x}{4} = \frac{21 - 3y - 3z}{4} [/tex]
[On Simplification][tex] = > x = \frac{21 - 3y - 3z}{4} (ans)[/tex]
Given :
x + 3x + 3y + 3z = 21To Find :
The value of xSolution :
[tex]\qquad { \dashrightarrow \: { \sf{x + 3x + 3y + 3z = 21}}}[/tex]
Adding the like terms :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3y + 3z = 21}}}[/tex]
Transposing 3y to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3z = 21 - 3y}}}[/tex]
Now, Transposing 3z to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x = 21 - 3y - 3z}}}[/tex]
Dividing both sides by 4 :
[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{4x}{4} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{{x} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
Therefore, the value of x = 21 – 3y – 3z/4
The age melat five times older than the age of hana.In ten years time the ratio of the age of hana to melat is 5:9. find the present age of hana and melat?
Answers
Answer:
carbon take x(1)+4(-2)=0
x(1)-8=0
x(1)=8
x=8
really need help with this
Answers
Answer:
Step-by-step explanation:
You have 2 sides given in a right triangle. You can make an equation that will solve for x. In fact the tangent will do. There's no need to solve for the third side.
Tan(x) = opposite / adjacent
opposite = 39
adjacent = 76
Tan(x) = 39/76
Tan(x) = 0.5132
When finding an angle, you need to use the inverse tan.
x = tan-1(0.5132) Use 2nd function tan(x)
x = 27.16 degrees.
Step-by-step explanation:
first we need the length of the Hypotenuse (UW).
Pythagoras :
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90 degree angle).
UW² = 76² + 39² = 5,776 + 1,521 = 7,297
UW = sqrt(7297) = 85.42247948...
now we get x from the law of sine :
sinA/a = sinB/b = sinC/c
with the angles always being opposite of the sides.
so, we have
sin(x)/39 = sin(90)/sqrt(7297) = 1/sqrt(7297)
sin(x) = 39/sqrt(7297) = 0.456554296...
x = 27.16498506...° ≈ 27.2°
we could have done it without the Hypotenuse first.
as the angle W is 90-x
sin(x)/39 = sin(90-x)/76 = cos(x)/76
sin(x)/cos(x) = 39/76 = tan(x) = 0.513157895...
x = 27.16498506...° ≈ 27.2°
as expected, it is precisely the same result.
please help
meeeeeeeeeeeeeeee
Answers
Answer:
C 43
Step-by-step explanation:
happy holidays
Answer:
Since the two triangles are similar, the two medians AC and FH are in proportion. The proportionality rate is [tex]k=\frac{48}8=6[/tex]. That is the same ratio of the sides., so AD is k times the corresponding side FG, or [tex]\overline {AD} = k\overline{FG} = 6\times 9 = 63[/tex]
How to determine if Triangles are Congruent?
If they are, how do you know if they are SSS or ASA or SAS or AAS?
Essentially, how do I apply the different congruent thermos to the questions attached?
Answers
So basically what you have to do is first identify all of the sides or angles that equal eachother then you can see if you did a side side and side in a row etc, like 44 would be SAS because the vertical angles would be inbetween the two sides. 46 would be SSS because after you make the line in the middle for reflexive property you can see that there are three sides in a row. If this didnt help i recommend looking on Khan Academy
Can someone please help with this?
Solve the equation p2 + 14p = 32 by completing the square method (and need to show work)
Answers
Answer:
p=2,-16
Step-by-step explanation:
move all terms to left side and set equal to zero. then set each factor equal to zero
Help me plzzzzzzzzzzzzz
Answers
Answer: It is D
Step-by-step explanation:
please help tysm ill mark brainliest
Answers
Answer:
use pemdas(order of the operations)and you'll get the answer 27!!
Step-by-step explanation:
Jake has $120 to spend for a party. Juice costs $8. Pizza costs $12. Write the standard equ.
how much juice and pizza Jake can buy?
Answers
Answer:
$8x + $12y = $120
Step-by-step explanation:
x = amount of juice
y = amount of pizza
$120 = his total money
Find the area and perimeter of a square whose side length is
2x+3
Answers
Answer:
Area = 4x^2 + 12x + 9
Perimeter = 8x + 12
Step-by-step explanation:
50 POINTS FOR EACH PERSON PLSSSSS HELP!!!!!
∫[tex]x^{\frac{3}{2} }[/tex]㏑(x) dx
Answers
Answer:
Look at images below ^^
Step-by-step explanation:
I'm not sure if they are correct, since I'm not there yet. But I hope it's correct.