Answer:
For the first question [tex]x = 4\\ y = -1[/tex] and
For the second question [tex]x = 0.5\\ y = -1[/tex]
Step-by-step explanation:
Given:
1.
x - 3y = 7
3x + 3y = 9
2.
8x+ 3y = 1
4x + 2y = 0
Elimination method :
In the elimination method we need to make the coefficient of x or the coefficient of y same in both the equation so by adding or subtracting we can eliminate the x term or the y term.
Then substitute that values which you will get on eliminating in any equation you will get the corresponding value.
For the first question, the y coefficient is same hence by adding both the equation we can eliminate 3y term. so on solving we get
[tex](x - 3y) + (3x + 3y) = 7 + 9\\4x = 16\\x = \frac{16}{4}\\x = 4[/tex]
Now substitute X equal to 4 in equation x -3y = 7 we get
[tex]4 - 3y = 7\\-3y = 7 - 4\\-3y = 3\\y = \frac{3}{-3}\\ y = -1\\[/tex]
This way we have x is equal to 4 and y is equal to -1 for question number 1.
For the second question, we will make X coefficient same in the second equation that is multiplying by 2 to the equation 4x + 2y = 0 then we get
[tex]8x + 4y = 0\\[/tex]
Now the coefficient of x term become same now we will subtract the two equations that is 8x + 3y = 1 and 8x + 4y =0 we get
[tex](8x + 3y) - (8x + 4y) = 1 - 0\\3y - 4y = 1\\ -y = 1\\y = -1[/tex]
Now substitute y equal to -1 in equation 8x +3y = 1 we get
[tex]8x + 3\times -1 = 1\\8x - 3 = 1\\8x = 1 + 3\\8x = 4\\x = \frac{4}{8}\\ x = 0.5\\[/tex]
This way we have x is equal to 0.5 and y is equal to -1 for question number 2.
3. (First picture answer options are the 4 graphs after it.)
Answer:
The correct graph is attached below.
Step-by-step explanation:
Given:
Initial temperature is 0°.
Decrease in temperature per hour is 12°.
Since, the initial temperature is 0°, the line must pass through the origin as temperature is plotted along the y-axis.
Also, decrease in temperature per hour is 12°. So, this represents the slope of the line. So, the slope should be -12 as there is decrease in temperature with increasing time.
So, the correct graph will be a line passing through origin and the slope of the line must be -12. Also, the temperatures will be along the negative y-axis as the values are decreasing with time.
Hence, the third graph is the correct one and is shown below.
A jar contains a mixture of 10 black balls, 8 red balls, and 2 white balls all the same size. What is the probability of
drawing either a red, black, or white ball in one draw?
Answer:
black balls: 10/20 or 1/2
red balls :8/20 or 2/5
white balls: 2/20 or 1/10
Step-by-step explanation:
Answer:
The answer is 1
Step-by-step explanation:
8/20 or 0.4- probability of red ball in one draw
2/20 or 0.1 - probability of white ball in one draw
10/20 or 0.5 - probability of black ball in one draw
0.4 + 0.5 + 0.1 = 1
Sorry I'm late just wanted to put the right answer!
Can anyone help solve this equation?
Answer:
13
Step-by-step explanation:
3 x 3 = 9
7 + 3 = 10
7 + ? = 3 + 7 + 3 + 7
7 + ? = 20
? = 13
Answer:
13Step-by-step explanation:
[tex]p\times p=9\\\\p^2=9\to p=\sqrt9\to \boxed{p=3}\\\\c+p=10\qquad\text{put the value of}\ p\\\\c+3=10\qquad\text{subtract 3 from both sides}\\\\\boxed{c=7}\\\\c+s=p+c+p+c\qquad\text{put the values of}\ p\ \text{and}\ c\\\\7+s=3+7+3+7\\\\7+s=20\qquad\text{subtract 7 from both sides}\\\\\boxed{s=13}[/tex]
To perform car maintenance, a mechanic
charges for parts and $45 an hour for
labor. The total cost that Terri spent for
2 hour of car maintenance is $125.
Assume the relationship is linear. Find
and interpret the rate of change and the
initial value
Answer:
C = 35 + 45h
In the equation above $35 is the initial value which interprets the cost for motor parts and $45/hour is the rate of charge of the mechanic per hour.
Step-by-step explanation:
Charges for parts and $45 per hour for labor that takes a mechanic for maintenance of a car.
It costs $125 as Terri spent 2 hours for car maintenance.
Since the function is linear, so we can write
125 = 45 × 2 + x {Where x is the charges for parts}
⇒ x = 35
Therefore, the equation that models the situation is given by
C = 35 + 45h ......... (1)
where C is the total cost and h is the number of hours.
Here, in equation (1) $35 is the initial value that interprets the cost for parts and $45/hour is the rate of charge of the mechanic per hour. (Answer)
A 12 cm x 2 cm rectangle sits inside a circle with radius of 8 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
Diagram was not given.
Still I had drawn it, hope may it will helpful to you. So as per my diagram I had solved the sum.
The area of the shaded region is 176.96 ≈ 178 cm²
Step-by-step explanation:
Given:
radius of the circle = r = 8 cm
length of the rectangle = L = 12 cm
breadth of the rectangle = B = 2 cm
To Find:
Area of shaded region = ?
Solution:
[tex]\textrm{Area of rectangle} = Length\times Breadth\\= L\times B\\= 12\times 2\\= 24\ cm^{2}[/tex]
[tex]\textrm{Area of Circle} = \pi \times (radius)^{2} \\=\pi \times r^{2}\\=3.14\times 8^{2}\\=200.96\ cm^{2}[/tex]
Now, The Area of Shaded region will be
[tex]\textrm{Area of Shaded region}=\textrm{Area of Circle}-\textrm{Area of Rectangle}\\=200.96 - 24\\=176.96\ cm^{2} \\=178\ cm^{2}\........... \textrm{Rounded to tenth}[/tex]
The area of the shaded region is 176.96 ≈ 178 cm²
Answer:
177.06
Step-by-step explanation:
i got it wrong on khan academy
The solution to the given system of linear equations lies in which quadrant?
Ex-3y = 6
1 x+y=2
Quadrant III
Quadrant !
- 5
4
-3 -2
1
2
3
4
5
X
Quadrant III
| Quadrant IV
? 17
Answer:
The solution to the given systems of linear equation is {3, -1} lies in IV Quadrant.
Step-by-step explanation:
Given:
x-3y = 6 ........( 1 )
x+y=2 ........( 2 )
To find :
x = ?
y = ?
Solution:
Let solve the above equation to get the solutions.
Eliminate X by subtracting the two equations equation 1 minus equation 2
[tex](x-3y) - (x+y) = 6 - 2\\-4y = 4\\\therefore y=-1[/tex]
Now substitute for y = -1 in equation 2 we get
[tex]x+(-1)=2\\\therefore x = 2+1\\\therefore x = 3[/tex]
Therefore, solution set is {3, -1}
In
I Quadrant {x,y} = {+,+}......both the coordinates are positive.
II Quadrant {x,y} = {-,+}.....X coordinate is negative and Y coordinate is positive.
III Quadrant {x,y} = {-,-}......both the coordinates are negative.
IV Quadrant {x,y} = {+,-}.....X coordinate is positive and Y coordinate is negative. {3,-1}
Point A on the graph is the solution.
Answer:
For those who want a quick answer. Its D on edge
Step-by-step explanation:
7/8 of a rectangle is colored red. Damien cuts this red part into a number of pieces so that each piece is 1/24 of the whole rectangle. Find the number of red pieces Damien has.
Answer: Damien has 21 red pieces
Step-by-step explanation:
First, 7/8 of the rectangle is coloured red.
Then, the 7/8 was cut into a size 1/24 of the rectangle each.
That consequently means that 24 of those pieces will form the whole shape.
Since red covers 7/8 of the rectangle, the number of red pieces invariably becomes
⅞ × 24 pieces, which is equal to 21 pieces
Therefore, Damien has cut the red part of the rectangle into 21 pieces
Final answer:
Damien has 21 red pieces after dividing the red part of the rectangle, which is 7/8, into pieces that are each 1/24 of the whole rectangle.
Explanation:
To find the number of red pieces Damien has, we first determine the fraction of the rectangle that is colored red, which is 7/8. Then, we find the size of each piece that Damien cuts, which is 1/24 of the whole rectangle.
Since each piece is 1/24, and Damien is cutting up only the red part which is 7/8 of the whole, we calculate the number of pieces by dividing the red part by the size of each piece: number of red pieces = (7/8) / (1/24).
To do this division, we multiply by the reciprocal of the divisor: (7/8) * (24/1) = 21. Therefore, Damien has 21 red pieces.
The length of a rectangle is 7 yd more than double the width, and the area of the rectangle is 99 yd^2. find the dimensions of the rectangle.
Answer:
w(2w+7) = 99
2w^2 + 7w - 99 = 0
( 2w - 11 )(w + 9 ) = 0
w+9=0 results in negative measures
2w-11 = 0
2w = 11
w = 11/2 = 5.5
L = 2w + 7 = 18
What are ordered pairs for 4x - 2y = 10
Answer:
(0,−5),(1,−3),(2,−1)
Step-by-step explanation:
Boxes of different sizes are stacked to create a small sculpture. The openings of the boxes are all similar rectangles. The bottom edge of the smallest rectangular opening 3 centimeters, while the bottom edge of the largest rectangular opening is 9 centimeters. The perimeter of the smallest rectangular opening is 15 centimeters What is the perimeter of the largest rectangular opening?
I’ll put you as brainliest
A) 90 cm
B)42cm
C) 45 cm
Answer:
I believe C)45cm but I know for sure its not B)42cm
Step-by-step explanation:
The sum of 4 times a number and 2 equals 8
Answer:
1.5 or 3/2
Step-by-step explanation:
4x+2=8
4x=6
x=6/4
x=3/2
Isosceles JAM has convex angle M. JM=35,MA=4n+3, angle J=14w-1, and angle m=98 Find n. Find w. Find the perimeter of JAM
Answer:
n = 8, w = 3 and perimeter = 122.83 units.
Step-by-step explanation:
Let the angle M is the angle between the equal sides of isosceles JAM.
So, JM = MA
⇒ 35 = 4n + 3
⇒ 4n = 32
⇒ n = 8 (Answer)
Now, if ∠ J = 14w - 1 and ∠ M = 98°, then
2(14w - 1) + 98 = 180
⇒ 2(14w - 1) = 82
⇒ 14w - 1 = 41
⇒ w = 3 (Answer)
Now, draw a perpendicular bisector on JA from vertex M and it meets JA at P say.
So, Δ MPJ will be a right triangle with ∠ J = (14w - 1) = 41° {Since w = 3}
Hence, [tex]\cos 41 = \frac{JP}{JM} = \frac{JP}{35}[/tex]
⇒ JP = 35 cos 41 = 26.415
So, JA = 2 × JP = 52.83
So, the perimeter of Δ JAM is = 35 × 2 + 52.83 = 122.83 units (Answer)
Which equation has NO solution? A) 10x + 5 2 = 3x + 6 B) 8 − 6x 4 = 4 + 2x C) 12x − 11 4 = 3x − 2 D) 18x − 10 2 = 9x − 5
Answer:
B) 16x+11/4 =4x+5-2
Step-by-step explanation:
the equation that has no solution is B)[tex]\( \frac{16x + 11}{4} = 4x + 5 \).[/tex]
The correct option is (B).
To find out which equation has no solution, let's solve each equation and see if any leads to a contradiction.
A)[tex]\( \frac{10x + 5}{2} = 3x + 6 \)[/tex]
Multiply both sides by 2 to eliminate the fraction:
[tex]\( 10x + 5 = 6x + 12 \)[/tex]
Subtract (6x) from both sides:
[tex]\( 4x + 5 = 12 \)[/tex]
Subtract 5 from both sides:
( 4x = 7 )
Divide both sides by 4:
[tex]\( x = \frac{7}{4} \)[/tex]
B) [tex]\( \frac{16x + 11}{4} = 4x + 5 \)[/tex]
Multiply both sides by 4:
[tex]\( 16x + 11 = 16x + 20 \)[/tex]
Subtract (16x) from both sides:
( 11 = 20 ) - Contradiction
C) [tex]\( \frac{8 - 6x}{4} = 4 + 2x \)[/tex]
Multiply both sides by 4:
[tex]\( 8 - 6x = 16 + 8x \)[/tex]
Subtract 8 from both sides:
[tex]\( -6x = 8x + 8 \)[/tex]
[tex]\( -6x = 8x + 8 \)[/tex]
[tex]\( 0 = 14x + 8 \)[/tex] - Contradiction
D)[tex]\( \frac{18x - 10}{2} = 9x - 5 \)[/tex]
Multiply both sides by 2:
[tex]\( 18x - 10 = 18x - 10 \)[/tex] - No contradiction, the equation holds true for all ( x ).
So, the equation that has no solution is B)[tex]\( \frac{16x + 11}{4} = 4x + 5 \).[/tex]
complete question given below:
Which equation has NO solution?
A) (10x+5)/2 =3x+6
B) (16x+11)/4 =4x+5
C) (8-6x)/4 =4+2x
D) (18x-10)/2 =9x-5
Which of the following charts showing angle measures implies that quadrilateral ABCD and quadrilateral EFGH are not congruent
Answer:
D
Step-by-step explanation:
One or more corresponding angles are not congruent.
ABC is not congruent to EFG
BCD is not congruent to FGH
CDA is not congruent to GHE
DAB is congruent to HEF
Answer: D
Step-by-step explanation:
Stephanie knows that don has a bunch of nickels and dimes in his pocket and that the total amount is $3.25
Answer:
The quantity of currency in the pockets does Stephanie has is 45 nickles and 10 dims .
Step-by-step explanation:
Given as :
The total amount of money does Stephanie have = $ 3.25
The total money is in the form of nickels and dimes
Let the number of nickels = n
And The number of dims = d
∵ we know that 20 nickles makes 1 dollar
And 10 dimes makes 1 dollar
So , in total of 3.25 dollar the number of dime and nickles be
∵ 20 nickles makes 1 dollar
∴ 45 nickles will makes [tex]\frac{1}{20}[/tex] × 45 dollar
I.e 45 nickles will makes 2.25 dollar
Now, ∵ 10 dimes will make 1 dollar
So, The total number of nickles and dimes satisfying equation
45 nickles + 10 dimes = 2.25 dollar + 1 dollar = 3.25 dollar
Hence The quantity of currency in the pockets does Stephanie has is 45 nickles and 10 dims . Answer
Answer:
4.40
Step-by-step explanation:
The amount of money Ivan has in his pocket is n.
Meg has $3.25 more than Ivan. Meg has $7.65.
Complete the equation that models the situation. Then, give the value of n.
$3.25
÷
+
$7.65
×
$10.90
$4.40
Please need help on this
Answer:
Culinary school because it is shorter schooling and costs less
Step-by-step explanation:
can someone please help with this problem? what is 6- 5/6
Answer:
5 1/6
Step-by-step explanation:
6 = 36/6, because 6*6 = 6
36/6 - 5/6 = 31/6
31/6 = 5 1/6
Answer:5 1/6
Step-by-step explanation:
A runner finished the hundred meter race in 20 seconds. What was his speed in meters per second?
Answer:
5 meters/second
Step-by-step explanation:
100meters/20 seconds gives the average of 5 m/s
Final answer:
The runner's speed in the hundred meter race completed in 20 seconds is 5 meters per second. To calculate this, divide the total distance (100 meters) by the total time (20 seconds).
Explanation:
To calculate the speed of the runner in meters per second, we divide the distance travelled by the time it took to complete that distance. In this case, the runner completed a 100 meter race in 20 seconds. Using the formula speed = distance/time, we find that the speed is 100 meters / 20 seconds = 5 meters per second.
If the sprinter accelerates for the first 20 meters and then maintains that speed for the remainder of the 100-meter dash, we must first calculate the acceleration period's average speed. As it takes 20 seconds to run 100 meters, the speed over those 20 meters is also 5 meters per second. Once the sprinter reaches this speed at 20 meters, he will continue at this constant speed for the remaining 80 meters. Thus, the time to complete the race is the time taken to accelerate for 20 meters plus the time taken to run the remaining 80 meters at 5 m/s.
if 11 oranges cost $2.35, what is the cost of 18
Answer:
$3.8
Step-by-step explanation:
2.35/11=0.2136
0.2136*18=3.8448
A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) = -5t^2 + 20t + 4 gives the height h, in meters, of the ball t seconds after it is launched.
A. What equation can be used to tell whether the ball reaches a height of 12 m ?
B. Does the ball reach a height of 12m? (yes or no)
The maximum height reached is greater than 12m, hence the ball reach a height of 12m
The height of the toy cannon all launched is expressed as [tex]h(t) = -5t^2 + 20t + 4[/tex]
h is the height reached by the ball
t is the time taken by the ball to reach its maximum height
A) In order to determine whether the ball reached the height of 12m, we will have to substitute h = 12 into the formula as shown:
[tex]12= -5t^2 + 20t + 4\\ -5t^2 + 20t + 4 -12=0\\ 5t^2 - 20t +8=0\\[/tex]
Hence the equation that can be used to tell whether the ball reaches a height of 12 is [tex]5t^2-20t+8=0[/tex]
B) At the maximum height
dh/dt = 0
-10t + 20 = 0
-10t = -20
t = 20/10
t = 2
Get the maximum height reached
h(2) = -5(2)^2 + 20t + 4
h(2) = -5(4) + 20t + 4
h(2) = -20 + 20(2) + 4
h(2) = -20+40+4
h(2) = 24 m
Since the maximum height reached is greater than 12m, hence the ball reach a height of 12m
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To determine whether the ball reaches a height of 12 meters, we set the height equation equal to 12 and solve the quadratic equation. Upon solving, we find that the ball reaches 12 meters, hence the answer to whether the ball reaches 12 meters is yes.
Explanation:To determine whether the toy cannon ball reaches a height of 12 meters, we can set the height equation h(t) equal to 12 meters:
12 = -5t^2 + 20t + 4.
To solve for t, we need to rearrange the equation and solve the resulting quadratic equation:
0 = -5t^2 + 20t + 4 - 12
0 = -5t^2 + 20t - 8
This is the equation that can be used to tell whether the ball reaches a height of 12 meters. To determine if the ball does reach 12 meters, we solve for the roots of the equation:
-5t^2 + 20t - 8 = 0
Using the quadratic formula, we find the possible values for t. If there are real, positive solutions, it means the ball does reach 12 meters at those times.
Upon solving, we find that the ball indeed reaches a height of 12 meters because there are real, positive solutions for t.
Therefore, the answer to Part B is yes; the ball does reach a height of 12 meters.
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two families bought tickets for a game. one family paid $71 for 6 adults and 2 children. another family paid $56.50 for 4 children and 3 adults. how much do the tickets cost.
Answer:
Adult Ticket cost $9.50 and Children Ticket cost $7.00
Step-by-step explanation:
Let single adult tickets cost "a" and single children ticket cost "c"
6 adult and 2 children ticket is $71, we can write:
6a + 2c = 71
Also,
3 adult and 4 children tickets cost $56.50, so we can write:
3a + 4c = 56.5
We multiply 2nd equation by "-2", to get:
-2 * (3a + 4c = 56.5) = -6a -8c = -113
Now we add this equation with 1st and eliminate a and solve for c:
6a + 2c = 71
-6a -8c = -113
-------------------
-6c = -42
c = -42/-6
c = 7
To find a, we can plug this into 1st equation and then get our answer.
6a + 2c = 71
6a + 2(7) = 71
6a + 14 = 71
6a = 57
a = 57/6
a = 9.5
Hence,
Adult Ticket cost $9.50 and Children Ticket cost $7.00
Bryan wants to purchase a skateboard. He has $50 to spend. he finds one that regularly sells for $70.00 and is on sale for 40% off. Sales tax is 7%. Bryan says he has enough money to buy the skateboard. is he correct?
Bryan has enough to buy skateboard as it will cost $44.94
Step-by-step explanation:
Original price = $70.00
Discount = 40%
Amount of discount = 40% of original price
Amount of discount = [tex]\frac{40}{100}*70[/tex]
Amount of discount = [tex]\frac{2800}{100}[/tex]
Amount of discount = $28
Price after discount = Original price - amount of discount
[tex]Price\ after\ discount=70-28 = $42\\[/tex]
Sales tax = 7% = [tex]\frac{7}{100} = 0.07[/tex]
Sales tax amount = Price after discount (0.07)
[tex]Sales\ tax\ amount= 42(0.07) = $2.94\\[/tex]
Price of skateboard = Price after discount + sales tax
Price of skateboard = 42+2.94 = $44.94
Bryan has enough to buy skateboard as it will cost $44.94
Keywords: sales tax, subtraction
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6 Which expression is equivalent to 2x2 + 7x +4?
F
(2x - 1)(x + 4)
G
(2x + 1)(x - 4)
H
(2x + 1)(x+4)
J None of these
Answer: F. (2x – 1)(x + 4)
Step-by-step explanation:
https://socratic.org/questions/how-do-you-factor-2x-2-7x-4-1
The expression that should be equivalent to given equation is (2x – 1)(x + 4)
Given information:The equation is [tex]2x^2 + 7x +4[/tex]
Calculation of expression:[tex]2x^2 + 7x +4[/tex]
[tex]2x^2 +8x - x + 4\\\\2x (x + 4) - 1(x + 4)[/tex]
(2x -1 ) (x + 4)
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In a psychological experiment, a person is able to memorize M words in t minutes, where M= -0.001t^3 + 0.1t^2. Find the average rate of change in the number of words a person can memorize between 10 minutes and 20 minutes
the ratio of berries to Oranges is 10:1 if there are 25 oranges how many berries would there be
Answer:
250 berries
Step-by-step explanation:
10 to 1 means 10 times as many berries as oranges
25x10=250
If there are 25 oranges then the number of berries would be 250 and this can be determined by using the arithmetic operations.
Given :
The ratio of berries to Oranges is 10:1.
The following steps can be used to determine the number of berries if there are 25 oranges:
Step 1 - Let the total number of berries be 'a' and the total number of oranges be 'b'.
Step 2 - As per the given data:
[tex]\dfrac{a}{b}=\dfrac{10}{1}[/tex]
Step 3 - If there are 25 oranges then the number of berries would be:
[tex]\dfrac{a}{25}=\dfrac{10}{1}[/tex]
[tex]a = 25\times 10[/tex]
a = 250
So, if there are 25 oranges then the number of berries would be 250.
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The table below shows the numbers of tickets sold at a movie theater on Friday.
NUMBER OF TICKETS SOLD
Day
Adult Tickets
Children's
Tickets
1,678
976
Friday
Saturday
The number of each type of ticket sold on Saturday is described below.
• Adult tickets—2 times as many as the number of adult tickets sold
on Friday
• Children's tickets-3 times as many as the number of children's
tickets sold on Friday
Complete the table above to show the numbers of tickets sold on Saturday.
What is the total number of tickets sold over these two days?
The complete table:
NUMBER OF TICKETS SOLD ON FRIDAY AND SATURDAY
Day → Adult → ChildrenFriday → 1,678 → 976 Saturday → 3,356 → 2,928The total number of tickets sold over these two days is 8,938
Step-by-step explanation:
The table below shows the numbers of tickets sold at a movie theater on Friday.
NUMBER OF TICKETS SOLD
Day → Adult → ChildrenFriday → 1,678 → 976The number of each type of ticket sold on Saturday is described below
Adult tickets—2 times as many as the number of adult tickets sold on FridayChildren's tickets-3 times as many as the number of children's tickets sold on FridayWe need to complete the table above to show the numbers of tickets sold on Saturday and find the total number of tickets sold over these two days
∵ The number of adult tickets on Saturday is 2 times as many as
the number of adult tickets sold on Friday
∵ The number of adult tickets on Friday = 1,678
∴ The number of adult tickets on Saturday = 2 × 1,678 = 3,356
∵ The number of children's tickets on Saturday is 3 times as many
as the number of children's tickets sold on Friday
∵ The number of children's tickets on Friday = 976
∴ The number of children's tickets on Saturday = 3 × 976 = 2,928
The complete table:
NUMBER OF TICKETS SOLD ON FRIDAY AND SATURDAY
Day → Adult → ChildrenFriday → 1,678 → 976 Saturday → 3,356 → 2,928∵ Adult tickets sold over the 2 days = 1,678 + 3,356 = 5,034
∵ Children's tickets sold over the 2 days = 976 + 2,928 = 3,904
∴ The total tickets sold over the 2 days = 5,034 + 3,904 = 8,938
The total number of tickets sold over these two days is 8,938
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Is x÷9=-4 an expression or equation
From a plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35 degrees and 25 degrees. How far apart are the two ships?
Answer:
189.8 m
Step-by-step explanation:
See the diagram attached.
Now, the plane is at B and the two ships are at C and at D.
So, angle of depression of C from B is ∠ OBC = ∠ ACB = 35°
Again, the angle of depression of D from B is ∠ OBD = ∠ ADB = 25° ,
Now, from the right triangle Δ ACB,
[tex]\tan 35 = \frac{AB}{AC} = \frac{265}{AC}[/tex]
⇒ [tex]AC = \frac{265}{\tan 35} = 378.5[/tex] m.
Similarly, from the right triangle Δ ADB,
[tex]\tan 25 = \frac{AB}{AD} = \frac{265}{AD}[/tex]
⇒ [tex]AD = \frac{265}{\tan 25} = 568.3[/tex] m.
Hence, the distance between the ships = CD = AD - AC = 568.3 - 378.5 = 189.8 m (Approx.) (Answer)
The distance apart is the two ships is 189.8 meters.
Given
A plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35 degrees and 25 degrees.
What is the angle of depression?The angle of elevation, the angle of depression is the angle at which you would draw a line from a point on a horizontal line to intersect another point that falls below the line.
The plane is at B and the two ships are at C and at D.
Then,
The angle of depression of C from B is ∠ OBC = ∠ ACB = 35°.
And the angle of depression of D from B is ∠ OBD = ∠ ADB = 25°.
From the right triangle Δ ACB,
[tex]\rm Tan35= \dfrac{AB}{AC}\\\\ AC= \dfrac{265}{Tan35}\\\\AC = \dfrac{265}{0.70}\\\\AC =378.57[/tex]
Again in the right triangle Δ ADB,
[tex]\rm Tan 25=\dfrac{AB}{AD}\\\\AD =\dfrac{265}{Tan25}\\\\ AD = \dfrac{265}{0.46}\\\\AD =569.30[/tex]
Therefore,
The distance apart are the two ships is;
= 568.3 - 378.5 = 189.8 m
Hence, the distance apart is the two ships is 189.8 meters.
To know more about Angle of Depression click the link given below.
https://brainly.com/question/4790507
What operation must be done to both sides of the equation to solve for p- -3 7/9 = 5/6?
A) add 5/6. B) subtract 3 7/9. C) subtract 5/6. D) add 3 7/9
Given equation: p - -3 7/9 = 5/6
When you subtract a negative number you automatically change it to adding a positive number.
p - -3 7/9 = 5/6 → p + 3 7/9 = 5/6
To isolate p in this equation we need to subtract 3 7/9 to both sides.
p + 3 7/9 - 3 7/9 = 5/6 - 3 7/9
p = -161/18
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what is the value of this expression C to the 3rd power / 2 when c=4
Answer:
32
Step-by-step explanation:
c^3/2 when c=4
4^3/2
4^3=4*4*4=16*4=64
64/2=32