Answer:the correct answer is b
Step-by-step explanation:
A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 feet from the dock, the length of the rope form the boat to the dock is 3 feet longer than twice the height of the dock above the water. Find the height of the dock.
Given :
A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 feet from the dock, the length of the rope form the boat to the dock is 3 feet longer than twice the height of the dock above the water.
To Find :
The height of the dock.
Solution :
This will make a right angle triangle as given in link below .
Now , applying Pythagoras theorem :
[tex](2h+3)^2=h^2+12^2\\\\4h^2+9h+9=h^2+144\\\\h^2+4h-45=0\\\\(h-5)(h+9)=0[/tex]
Now , h = 5 or h = -9 .
Now , height cannot be negative .
So , height of the dock is 5 ft .
Hence , this is the required solution .
Leticia invests $200 at 5% interest. If y represents the amount of money after x time periods, which describes the graph of the exponential function relating time and money? The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time. The initial value of the graph is 200. The graph increases by a factor of 5 per 1 unit increase in time. The initial value of the graph is 500. The graph increases by a factor of 2 per 1 unit increase in time. The initial value of the graph is 500. The graph increases by a factor of 1.02 per 1 unit increase in time.
Answer:
A. The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time.
Hope this helps!
Step-by-step explanation:
The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time the graph of the exponential function relate to time and money.
Given that,
Leticia invests $200 at 5% interest.
If y represents the amount of money after x time periods.
We have to determine,
Which describes the graph of the exponential function relating time and money?
According to the question,
The graph represents the exponential function relating time and money.
Where y represents the amount of money after x time periods.
After 1 period the amount of money is,
[tex]\rm f(x) = 200 + 200\left(\dfrac{5}{100}\right)\\\\f(x) = 200(1+0.5)\\\\f(x)= 200(1.5)\\\\[/tex]
After 2 periods the amount is,
[tex]\rm f(x) = 200(1.5) \times (1.5)\\\\f(x) = 200. (1.5)^2[/tex]
After 3 periods the amount is,
[tex]\rm f(x) = 200(1.5)^2 \times (1.5)\\\\f(x) = 200. (1.5)^3[/tex]
Therefore,
The amount after x period is,
[tex]\rm f(x) = 200(1.5)^x[/tex]
The initial value is when x = 0,
[tex]\rm y = 200 (1.05)^0 \\\\y = 200\times 1\\\\y = 200[/tex]
And the increasing factor is 1.05 because any value is the previous one times 1.05.
Hence, The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time the graph of the exponential function relate to time and money.
For more details refer to the link given below.
https://brainly.com/question/17407467
tell if is: < or >
Answer:
-9 < -1
21/5 < 17/4
Answer:
-9 < -1
21/5 < 17/4
Step-by-step explanation:
A) when a number isnegitv ethe "smaller" number has more value. You would rather loose one doller than 9, right?
B) 21/5 = 4.20
17/4 = 4.25
and .25 os bigger than .20
Point O is on line segment NP. Given N P = 4x + 10, NO = 4x, and
OP = x + 5, determine the numerical length of NP.
Answer:
30
Step-by-step explanation:
Hope this will help:)
The numerical length of line segment NP will be 30 units.
What is a line segment?A line segment in mathematics has two different points on it that define its boundaries.
A line segment is sometimes referred to as a section of a path that joins two places.
Point O is on line segment NP.
Given NP = 4x + 10, NO = 4x, and OP = x + 5.
We know that for a line segment.
PN = PO + ON
4x + 10 = 4x + x + 5
x = 5
Then the numerical length of line segment NP will be
NP = 4x + 10
NP = 4(5) + 10
NP = 20 + 10
NP = 30
Then the numerical length of line segment NP will be 30 units.
More about the line segment link is given below.
https://brainly.com/question/25727583
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Which statements are true based on the diagram?
Select three options.
1. Points N and K are on plane A and plane S.
2. Points P and M are on plane B and plane S.
3. Point P is the intersection of line n and line g.
4. Points M, P, and Q are noncollinear.
5. Line d intersects plane A at point N.
Answer:
Points N and K are on plane A and plane S.
Point P is the intersection of line n and line g.
Points M, P, and Q are noncollinear.
e2020
Step-by-step explanation:
According to the given diagram of Intersecting planes, Option (1), Option (3), Option (4) are True.
What are planes?A plane is a two-dimensional, flat surface that stretches indefinitely.
When does a point lie on a plane?A point is said to lie on a plane when it satisfies the equation of plane which is ax^3 + bx^2 + cx+ d = 0 and sometimes it is just visible in the figure whether a point is lying on a plane or not.
In Option(1) : Points N and K are lying on the line of intersection of plane A and S and will satisfy the equation of both planes.
In Option(2) : Point P is lying on both planes B and S, but the point M is lying only on plane B, hence this option is wrong.
In Option(3) : It is clearly visible the Point P is the point of intersection of lines n and g.
In Option(4) : It is clearly visible that Points M,P,Q are not lying on the same line, hence they are non-collinear.
In Option(5) : Line d intersects the plane A at point L and not point N, hence this is also wrong.
Hence the correct options are 1,3,4.
Learn more about planes:
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Find the distance between A(2,5) and B(-2,9)
Answer:
The answer is
[tex]4 \sqrt{2} \: \: or \: \: 5.656 \: \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
A(2,5) and B(-2,9)
The distance between them is
[tex] |AB| = \sqrt{ ({2 + 2})^{2} + ({5 - 9})^{2} } \\ = \sqrt{ {4}^{2} + ({ - 4})^{2} } \\ = \sqrt{16 + 16} \\ = \sqrt{32} \\ [/tex]We have the final answer as
[tex]4 \sqrt{2} \: \: or \: \: 5.656 \: \: \: units[/tex]Hope this helps you
Seela rented a raft from River Rafter's Inc. She paid $100
to rent the raft and $25 for each hour. Martin rented a
raft from Oscar's Outdoor Shop. He paid $50 to rent the
raft and $35 per hour. For what number of hours will
both rafting companies charge the same amount?
Answer:
she paid $125 while he paid $85
Step-by-step explanation:
Consider the function represented by the graph. What is the domain of this function?
Two rays that intersect at a right angle are best described as which of the
following?
A. Parallel rays
B. Perpendicular rays
C. Skew rays
D. Intersecting rays
Answer:
B. Perpendicular rays
Step-by-step explanation:
Definition Perpendicular: Perpendicular lines, rays, or segments intersect at right angles. If lines, rays, or segments are perpendicular, then they are right angles. If lines, rays, or segments intersect. at right angles, then they are. perpendicular.
Hope this Helps
The rays that intersect at a right angle are perpendicular rays option (B) is correct.
What is a perpendicular line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
As we know,
From the definition, the perpendicular lines are the lines that intersect at right-angle or 90 degrees.
Two rays that intersect at a right angle are perpendicular rays.
Thus, the rays that intersect at a right angle are perpendicular rays option (B) is correct.
Learn more about the perpendicular line here:
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Which expression is equivalent to 3x + 14 + 3x + 10?
Answer:
6x+24
Step-by-step explanation:
The expression 6x+24 is equivalent to 3x+14+3x+10
3x+14+3x+10
3x+3x+14+10
6x+24
Hope this helps ;) ❤❤❤
Answer:
6x + 24
Step-by-step explanation:
Step 1:
3x + 14 + 3x + 10
Step 2:
6x + 14 + 10
Answer:
6x + 24
Hope This Helps :)
What is this? k/8-5≥-6
Answer:
k≥-8
Step-by-step explanation:
The Zoo charges $14 per visit for non-members. To become a member of the Zoo you will be charged a $36 one-time fee $2 per visit. At what number of visits will a member and non-member pay the same amount?
Answer:
7
Step-by-step explanation:
You divide the number of visits and the price. 14÷2=7
A container holds 2/3 gallon of apple juice. If four people from the cross-country track team share the juice equally, how much juice will each team member get?
Answer:
You would DIVIDE to solve this problem.
each runner will
get 1/6 gallon of apple juice
Step-by-step explanation:
dilations PLEASE HELP ME PLEASE
Answer:
D' (6, - 6 )
Step-by-step explanation:
Assuming the dilatation is centred at the origin then multiply the coordinates of D by 3, that is
D (2, - 2 ) → D'(3 × 2, 3 × - 2 ) → D' (6, - 6 )
HELP HELP HELP HELP HELPPPP!!
Answer:
1. whole number 2. rational number 3. integer
Step-by-step explanation:
Answer:
6 = natural and whole
1/64 = rational
-2 = integer
Step-by-step explanation:
Solve for x 5x - 5 = 5
Polynomial equation solver
5x - 5 = 5
Standard form:
5x − 10 = 0
Factorization:
5(x − 2) = 0
Solutions:
x = 10
5
= 2
hey please help, thank you!
write .48 as a fraction in simplest form
Answer:
12/25
Step-by-step explanation:
0.48 is read as "forty-eight hundredths," so we can write it as a fraction as
48/100.
Since both 48 and 100 have a common factor, we can reduce the fraction.
48 and 100 are both divisible by 4.
48/100 = 12/25
There are no common factors of 12 and 25, so 12/25 is the answer.
Answer:
12/25
Step-by-step explanation:
48/100 Divide by 2
24/50 Divide by 2 again
12/25 Can not be further simplified.
I hoped this helped you
find the additive inverse of 1/2 + 1/6 + 1/12
Answer:
3/4
Step-by-step explanation:
0.75 into a fraction
Answer:
the answer is 75/100 simplify into 3/4
Step-by-step explanation:
the answer is seventy five out of a hundred then simplify getting your answer as 3/4
AYUDAA es para hoyyy Un avión volaba a 14.800 metros de altura . Primero , bajo a 23.000 decímetros y luego 54 hectometros más a qué altura en kilómetros vuela ahora ? EN ESPAÑOL LA RESPUESTA POR FAVOR Gracias
Answer:
7.1 km or 7.1 kilometer
Step-by-step explanation:
Esta pregunta se resuelve mediante la conversión de unidades SI. Nuestra respuesta final será en kilómetros, por lo tanto, estamos convirtiendo todos los valores dados a kilómetros.
De la pregunta, tenemos la siguiente información:
Altura de vuelo actual del avión = 14.800 metros
1 metro = 0.001 kilómetro
14,800 metros =
14,800 × 0.001
= 14.8 kilómetros
Avión que descendió primero = 23.000 decímetros
1 decímetro = 0.0001 kilómetro
23,000 decímetros =
23,000 × 0.0001 kilómetro
= 2.3 kilómetros
Descendió la segunda vez = 54 hectómetros más
1 hectómetro = 0.1 kilómetro
54 hectómetros =
54 × 0.1 kilómetro
= 5.4 kilómetros
Por lo tanto, la altura en kilómetros que vuela el avión ahora se calcula como
14.8 km - 2.3 km - 5.4 km
= 14.8 km - (2.3 km + 5.4 km)
= 14.8 kilometros - 7.7 kilometros
= 7.1 kilometros
Por lo tanto, el avión vuela actualmente a 7.1 km o 7.1 kilómetros.
if 12 people can finish a job by 5 days how many days will be required finish the same job by 10 people
Answer:
4
Step-by-step explanation:
12p=5d
1p=5/12
10p=4.1666
≈4 days
Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
Answer:
C. {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
Step-by-step explanation:
I just did the quiz. Basically all you do is switch the x and y values for each coordinate pair in order to see if it would pass the line test. If it has double X values, it is not a function with an inverse function.
A(-7,3) B(4,5) the distance
Answer:
d= 5√5
Step-by-step explanation:
[tex]d =:\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\(-7,3)=(x_1,y_1)\\(4,5)=(x_2,y_2)\\\\d = \sqrt{(4-(-7))^2+(5-3)^2}\\\\d = \sqrt{(4+7)^2+(5-3)^2}\\\\d = \sqrt{(11)^2+(2)^2}\\\\d = \sqrt{121+4}\\\\d = \sqrt{125}\\\\d =5 \sqrt{5}[/tex]
tell me the integers between this:
Answer:
[tex]\huge\boxed{-2,-1,0,1}[/tex]
Step-by-step explanation:
The order of integers from -3 to 2 is:
-3 ⇒ -2 ⇒ -1 ⇒ 0 ⇒ 1 ⇒ 2
So, the integers between -3 and 2 are:
=> -2,-1,0 and 1
3 Hundreds = ____ Tens
Which equation models this relationship? Help plz
Answer:
Hey there!
t=5d.
This means that for every hour she walks, she will walk five miles.
Let me know if this helps :)
Scott made $169 for 13 hours of work at the same rate how much would he make for five hours of work
Answer:
$65
Step-by-step explanation:
169 ÷ 13 = 13
13 × 5 = 65
what divided by 3 is -2
Answer:
-1.5
Step-by-step explanation:easy
. A cylinder has a radius of 7 cm and a height of 12 cm. Calculate the total surface area. (Take π = 22/7)
Answer:
154cm^2
Step-by-step explanation:
Area of circle= pi×r^2
= 22/7 × (7cm)^2
= 22/7 × 49cm^2
= 154cm^2