An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. The executive then boarded the helicopter and flew to the corporate offices at an average speed of 78 mph. The entire distance from his home to the office was 169.5 if the executive spent the same amount of time in the car as he did the helicopter how long did it take the executive to get to work
Answers
Answer:
3 hours
Step-by-step explanation:
Speed is the ratio of distance traveled to time taken, it is given as:
Speed = distance / time
An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. He then took the helicopter and flew to the corporate offices at an average speed of 78 mph. Given that the executive spent the same amount of time in the car as he did the helicopter how long did it take the executive to get to work.
Let the amount of time the executive spent in the car be t hours, therefore the amount of time spent in the helicopter = t hours.
For car:
Speed = distance / time
35 = distance ([tex]d_1[/tex]) / t
[tex]d_1=35t[/tex]
For helicopter:
Speed = distance / time
78 = distance ([tex]d_2[/tex]) / t
[tex]d_2=78t[/tex]
The total distance traveled = 169.5 miles
[tex]d_1+d_2=169.5\\35t+78t=169.5\\113t=169.5\\t=169.5/113\\t=1.5\ hours[/tex]
The time taken for the executive to get to work = time spent on car + time spent on helicopter = 1.5 + 1.5 = 3 hours
Related Questions
John ran 1 2 mile in 5 minutes, and Al ran 1 3 mile in 4 minutes. Which runner ran at a faster rate?
Answers
Answer:
John ran at a faster rate
Step-by-step explanation:
If john runs 1/2 mile in 5 minutes, then for him to run 1 mile it would take 10 minutes because it takes john 5 minutes for every half of a mile. Now Al runs 1/3 mile in 4 minutes. If he would run 1 mile, it would take him 12 minutes because it takes him four minutes every third mile.
1/3 : 4 = 3/3 : 12 Al
1/2 : 5 = 2/2 : 10 John
From both of the rations John ran faster
If h(x) = x2-5x + 7
find: h(2)
Answers
Answer:
h(2)= 1
Step-by-step explanation:
h(x) = x^2-5x+7
h(2) = 2^2-5*2+7
h(2)= 1
Answer:
1
Step-by-step explanation:
you have to substitute 2 were there's x in the function
h(2)=x^2-5x+7
=2^2-5(2)+7
=4-10+7
=1
I hope this helps
Raj and Carlos are reading. Carlos reads a chapter in 444 minutes, which is 333 minutes less time than it takes Raj.
How long does it take Raj to read a chapter?
Answers
Answer:
777 minutes
Step-by-step explanation:
Take the amount it takes carlos add the difference between carlos and raj to get the amount it takes raj
444+ 333 = 777
In trapezoid ABCD, AB ∥ CD , m∠A=90°, AD=8 in, DC=9 in, CB=10 in, and ∠B is acute. Find DB.
Answers
Answer:
the length of DB is 17 in
Step-by-step explanation:
Consider the sketch attached.
We will draw an imaginary line from point C to met line AB at point E.
A right-angled triangle will now be formed between points CBE.
The dimensions of the right-angled triangle will be:
CB = 10 in
CE= 8 in
EB = unknown
We will now proceed to find out the length of side EB using the Pythagoras' theorem.
[tex]EB =\sqrt{CB^2 -CE^2} \\EB =\sqrt{10^2 -8^2} \\EB = 6 in[/tex]
From the shape, we can find out that another right-angled triangle is made between points DAB.
The dimensions of the triangle are:
DA= 8in
AB = 9 in + 6 in = 15 in
DB = unknown.
We will now proceed to find out the length of side DB using the Pythagoras' theorem.
[tex]DB =\sqrt{AD^2 +AB^2} \\DB =\sqrt{8^2 +15^2} \\DB = 17 in[/tex]
Therefore, the length of DB is 17 in
1% social security tax is charged up to the annual income of Rs 3,50,000 to an unmarried individual. If the monthly salary of an individual is Rs 16,400, how much social security tax should he pay in a year?
Answers
Answer:
Rs. 1968
Step-by-step explanation:
Tax rate = 1%
Monthly income of the person = rs. 16400
Now,
Yearly income of individual = rs. 16400×12=rs196800
Tax = tax rate × yearly income
= 1% × rs. 196800
= Rs.1968
Was the question this simple
Or I misunderstood the question :-(
Simplify
-
12 – 81 – 9
5.12
- 451
Answers
Answer:
-615.12
Step-by-step explanation:
hope this helps
plz mark as brainliest!!
Can check using a calculator
If g(x) = 1 - ¾ x
find: -5g(4) - 1
Answers
Answer:
-5g(4) - 1 is 9
Step-by-step explanation:
[tex]g(x) = 1 - \frac{3}{4} x[/tex]
when x is 4:
[tex]g(4) = 1 - \frac{3}{4} \times 4 \\ = 1 - 3 \\ = - 2[/tex]
therefore:
[tex] - 5g(4) - 1 = - 5( - 2) - 1 \\ = 10 - 1 \\ = 9[/tex]
Answer:
9
Step-by-step explanation:
g(x) = 1 - ¾ x
-5g(4) - 1
First find g(4) = 1 - 3/4(4) = 1 - 3 = -2
Then -5(-2) -1 = 10 -1 = 9
PLEASE HELP ME!!!!!!!!!!
Answers
Answer:
5:
x = 9 y = 34
x = 2 y = 6
x = -6 y = -26
x = 3 y = 10
x = 4 y = 14
6.
x = 8 y = 19
x = 5 y = 35
x = -2 y = -21
x = 1 y = 3
x = 4 y = 27
1.
x = 2 y = -5
x = 5 y = -2
x = -1 y = -8
x = 7 y = 0
x = 3 y = -4
2.
x = 8 y = 5
x = 2 y = -1
x = -2 y = -5
x = 9 y = 6
x = 1 y = -2
3.
x = 3 y = -1
x = 6 y = 2
x = -7 y = -11
x = 4 y = 0
x = 2 y = -2
4.
x = 6 y = 39
x = 5 y = 32
x = -9 y = -60
x = 1 y = 4
x = 2 y = 11
5. 6. 1. 2. 3. 4.
x | y | x | y x | y x | y x | y x | y
9 | 11 | 3 | 19 2 | -5 8 | 5 3 | -1 6 | 39
2 | 6 | 5 | 35 5 | -2 2 | -1 6 | 2 5 | 32
-6| -26 | -2 | -21 -1 | -8 -2 | -5 -7 | -11 -9 | -66
3 | 10 | 1 | 3 7 | 0 9 | 6 4 | 0 1 | 4
4 | 14 | 4 | 27 3 | -4 1 | -2 2 | -2 2 | 11
Hope this helps!
50 points pls help. question down below explaination is option but with if u want brainlist u know
Answers
Answer:
10/13, 2/3, 7/11, 3/5, 5/9
Step-by-step explanation:
5/9 , 7/11, 3/5, 2/3, 10/13
Changing to decimal form
.5555(repeating), .636363(repeating), .6 , .666(repeating) ,.769230769
The largest is 10/13
Then 2/3
Then 7/11
Then 3/5
The smallest is 5/9
Answer:
111
Step-by-step explanation:
111
Sala earns 12 dollars each hour working part-time at a bookstore. She earns one additional dollar for each book that she sells. Let A be the amount (in dollars) that Salma earns in an hour if she sells B books. Write an equation relating A to B. Then graph your equation using the axes below.
Answers
Answer:
y=12a+b
Step-by-step explanation:
A. ASA
B. CPCTC
C. AAS
D. SAS
Answers
Answer:
It is ASA congruence rule as the 2 angles and the included side of the triangle are equal
Explanation:
There are one side and 2 angles in the proof.
sin0+sin0+2sin0+3sin0
step by step
Answers
Answer:
0
Step-by-step explanation:
the value of sin 0 degree is always equal to 0.
=0+0+2x0+3x0
=0
Sinx0+sinx0+2sinx0+3sinx0
Any expression multiplied by 0
equals 0
0+sinx0+2sinx0+3sinx0
0+0+2sinx0+3sinx0
0+0+0+3sinx0
0+0+0+0
0+0+0
0+0
0
This did take me a lot of effort to write but hope it helps
Which expression can be used to convert 100 USD to Japanese yen?
wo competing gyms each offer childcare while parents work out. Gym A charges $9.00 per hour of childcare. Gym B charges $0.75 per 5 minutes of childcare. Which comparison of the childcare costs is accurate?
Answers
Usd>Yen~1->.009
Gym B costs 50%less
If the question is trying to compare hours to usd then Gym A is the most accurate representation of USD to Yen
On the number line below, P represents a number. What is the value of the opposite of that number? A number line from negative 4 to positive 4 in increments of 1 over 4, with all whole numbers alone labeled is shown. Put point P at the fifth tick mark to the right of 0. negative 2 and 2 over 4 negative 1 and 1 over 4 1 and 1 over 4 2 and 2 over 4
Answers
Answer:
[tex]-1\frac{1}{4}[/tex]
option 2
Step-by-step explanation:
In this number line, each interval equals 1/4.
P represents 1 1/4
So, opposite of number P is ( [tex]-1\frac{1}{4}[/tex] )
If $a+b = 8$, $b+c = -3$, and $a+c = -5$, what is the value of the product $abc$?
Answers
Answer:
a=3
b=5
c=-8
3+5+-8=0
Step-by-step explanation:
3+5=8
5+-8=-3
3+-8=-5
i think thia is correct you can double check
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. x 2 + 13x + 36
Answers
Step-by-step explanation:
of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. x 2 + 13x + 36
Answer:
you change your mind, drag the item to the trashcan. Click the trashiecan to clear all your answers. Factor completely and then place the factors in the proper location on the grid.
Step-by-step explanation:
Thanks!
A pantry contains 6 shelves each 42 inches long.
The shelves are to be relined with fresh paper.
The paper is sold in 1-yard rolls. The number
of 1-yard rolls needed is:
Answers
Answer:
7 1-yard rolls
Step-by-step explanation:
1 yard = 36 inches.
6(42 in) = 252 inches.
252 in/36 in = 7
Therefore, 7 1-yard rolls are needed.
The number of 1-yard rolls needed to sell 6 shelves each of 42 inches is 7.
Given,
A pantry contains 6 shelves.
Each shelves = 42 inches long.
The shelves are to be relined with fresh paper.
The paper is sold in 1-yard rolls.
We need to find the number of 1-yards rolls needed to sell 6 shelves.
How many inches is 1yards?1 yard = 36 inches.
We have,
6 shelves and each shelves is 42 inches.
1 shelves = 42 inches.
6 shelves = 6 x 42 inches
6 shelves = 252 inches.
And since,
36 inches = 1 yard
252 inches = (252/36) yard
252 inches = 7 yard
Thus the number of 1-yard rolls needed to sell 6 shelves each of 42 inches is 7 1-yard rolls.
Learn more about unit conversion here:
https://brainly.com/question/16209700
#SPJ2
$12,800 at 12% for 3 years find the total amount ?
Answers
Answer:
so first you do
12800*.12 which is 1536
so $1536 for 1 year
for 3 years multiply it by 3
1536*3=
$4608
so 4608+12800 =
17408 is totall
Mark brainliest
Does the graph represent a function?
Answers
Hey there!
No, the graph is not a function because it has two of the same inputs, (7, -6) and (7, -7).
It also can't be a linear function because the graphs are not pointed to form a straight line.
Hope this helps!
Have a great day!
Answer: No
Step-by-step explanation: Since we can draw a vertical line that passes through two points on the graph, the relation is not a function.
What is the determinant of k= 6 8 0 3
Answers
Answer:
18
Step-by-step explanation:
If it was helpful and what u were looking for
Then pls mark as brainliest
Choose a number line to model the following situation:
After a gain of 25 yards, the football team lost 25 yards on the next play. (4 points)
a
A horizontal number line is shown with labels at 0 and 25. A purple arrow (labeled gain 25 yds) begins at 0 and ends at 25. A red arrow (labeled lose 25 yds) begins at 25 and ends at 0.
b
A horizontal number line is shown with labels at negative 25, 0, and 25. A purple arrow (labeled gain 25 yds )begins at 0 and ends at 25. A red arrow (labeled lose 25 yds) begins at 0 and ends at negative 25.
c
A horizontal number line is shown with labels at 0, 25, and 50. A purple arrow (labeled gain 25 yds) begins at 0 and ends at 25. A red arrow (labeled lose 25 yds) begins at 50 and ends at 25.
d
A horizontal number line is shown with labels at 0, 25, and 50. A purple arrow (labeled gain 25 yds) begins at 0 and ends at 25. A red arrow (labeled lose 25 yds) begins at 25 and ends at 50.
Answers
Answer: A
Step-by-step explanation: because the number line shows a gain of 25 then a loss of 25, it represents the question showing +25 then -25. so the answer is A
Hope this helps
what is (8*8*8) * (8*8*8*8) in exponential form?
Answers
The exponent 7 tells us how many copies of "8" are being multiplied together.
The expression 8*8*8 is equal to 8^3, while 8*8*8*8 = 8^4
Multiplying 8^3 and 8^4 will have us add the exponents to get 8^7. The base stays at 8 the entire time.
The rule is a^b*a^c = a^(b+c) where the base is 'a' the entire time.
Answer:
8^ 7
Step-by-step explanation:
(8*8*8) * (8*8*8*8)
There are 3 8's times 4 8's
8^3 * 8^4
We know that a^b * a^c = a^ (b+c)
8 ^ ( 3+4)
8^ 7
Determine what type of model best fits the given situation: The height of a tree twenty feet tall increases by 2 feet per year.
Answers
Answer:
linear model
Step-by-step explanation:
This is a linear function. The initial value is 20 ft, and the yearly growth is 2ft/yr. Thus, the function is
height(t) = (20 ft) + (2 ft/yr)t, where t is the number of years.
Plz help I’ll mark brainliest
Answers
Answer:
[tex]\large \boxed{\mathrm{2 \ meters}}[/tex]
Step-by-step explanation:
The triangle formed is a right triangle.
We can use trig functions to solve.
The maximum length of the seesaw is the length of the hypotenuse of the triangle.
sin θ = opp/hyp
Let x be the hypotenuse length.
sin 30 = 1/x
x = 1/sin30
x = 2
The maximum length of the seesaw is 2 meters.
Answer:
2
Step-by-step explanation:
Take the right triangle formed by the seesaw.
Let x be the maximum heigth that we are looking for
● sin 30° = 1/x
Switch x and sin 30°
● x = 1 /(1/2)
● x = 1 ×(2/1)
● x= 1×2
● x = 2
Joseph said that a rhombus with side lengths of 6 meters and a height of 4 meters has the same area as a parallelogram with a base of 12 meters and a height of 2 meters. Is he correct? Critique Joseph's reasoning. help plzz
Answers
Answer:
Area(s) of both rhombus and parallelogram are equal at 24 meters squared. Therefore Joseph had the correct reasoning in regards to area(s) of both rhombus and parallelogram are equal at 24 meters squared.
Step-by-step explanation:
To equate area of the rhombus, multiply the side length and height of rhombus in meters. (6 meters×4 meters=Area of 24 m°2). Area of parallelogram = (12meters ×2 meters= 24 m°2. Area(s) of both rhombus and parallelogram are equal at 24 meters squared. therefore
f(x)2x/x+3,x≠-3 can somebody please explain.
Answers
Answer:
x cannot equal -3 because if -3 is plugged in for x, there will be a zero in the denominator and you cannot divide by 0
Please answer and show steps. Will mark brainliest.
Answers
Answer:
13.4 meters
Step-by-step explanation:
About the diagram
Attached is a diagram of the problem. The directions North and East are shown so that the usual clockwise from +x measurement of angles will correspond to the bearing angles given in the problem. That is, the bearing of 120° is an angle of 120° measured from North toward East. (The mirroring across the line y=x can be a little mind-bending, but it is isomorphic, so all angles and lengths remain unchanged.)
The other feature of this diagram is the projection of the 3-D problem into two dimensions. Effectively, the center angle rabbit-O-coyote represents a plan view (in the plane of the ground), and the triangles coyote-O-C1 and rabbit-O-R1 represent side views (views in the vertical plane).
The side views let us work out the ground distances O-rabbit and O-coyote, so that we can find the ground distance rabbit-coyote as the problem requests.
__
Problem solution
The distance from the tree (O) to the rabbit is the "adjacent" leg of the 30° angle of elevation from the rabbit to the tree top. The 10 m tree height is the "opposite" leg of that rabbit-O-R1 right triangle. We know the ratio of opposite to adjacent sides gives the tangent of the angle, so we have ...
tan(30°) = 10/(rabbit distance from tree)
Solving for the rabbit distance, we get
rabbit distance = 10/tan(30°) ≈ 17.3205 m
Similarly, the coyote distance from the tree will be ...
coyote distance = 10/tan(20°) ≈ 27.4748 m
__
These are two legs of the rabbit-O-coyote triangle. The angle at O between the rabbit and coyote is 120° -97° = 23°. These values are sufficient to let us use the Law of Cosines to find the distance d from rabbit to coyote:
d² = r² +c² -2rc·cos(23°)
d² = 17.3205² +27.4748² -2·17.3205·27.4748·cos(23°) ≈ 178.769
d ≈ √178.769 ≈ 13.37 . . . . meters
The distance from the rabbit to the coyote is about 13.4 meters.
_____
Additional comment
Note that the angle of depression to the rabbit from the horizontal is the same as the angle of elevation from the rabbit. This lets us draw the diagram without a bunch of extra lines.
-5+2(10b-2)=31 need help thanks!
Answers
Answer:
[tex]\Large \boxed{b=2}[/tex]
Step-by-step explanation:
-5+2(10b-2)=31
Expand brackets.
-5+20b-4=31
-9+20b=31
Add 9 on both sides.
20b=40
Divide both sides by 20
b=2
Answer:
b = 2Step-by-step explanation:
-5+2(10b-2)=31
Multiply the terms in the bracket
That's
- 5 + 20b - 4 = 31
Group like terms
Send the constants to the right side of the equation
That's
20b = 31 + 4 + 5
Simplify
20b = 40
Divide both sides by 20
We have the final answer as
b = 2Hope this helps you
5. A recent school survey found that 8 out of 10 students plan to go to college after graduating high school. At
that rate, how many of the 2540 students at the local high school plan to go to college?
318 students
2032 students
2000 students
3175 students
Answers
Answer:2032
Step-by-step explanation:
Since 80% of the students plan to go to college, 80% of 2540 is 2032. 2540x0.8
because
2540/10 x 8 =
ILL MARK BRAINLIEST TO FIRST CORRECT ANSWER
Dave solved a quadratic equation. His work is shown below, with Step 111 missing.
What could Dave have written as the result from Step 111?
\begin{aligned} \dfrac{1}{3}(x+4)^2&=48 \\\\ &&\text{Step }1 \\\\ x+4&=\pm 12&\text{Step }2 \\\\ x=-16&\text{ or }x=8&\text{Step }3 \end{aligned}
3
1
(x+4)
2
x+4
x=−16
=48
=±12
or x=8
Step 1
Step 2
Step 3
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
\left(\dfrac{1}{3}x+\dfrac{4}{3}\right)^2=48(
3
1
x+
3
4
)
2
=48left parenthesis, start fraction, 1, divided by, 3, end fraction, x, plus, start fraction, 4, divided by, 3, end fraction, right parenthesis, squared, equals, 48
(Choice B)
B
\left(\dfrac{1}{3}x\right)^2+\left(\dfrac{4}{3}\right)^2=48(
3
1
x)
2
+(
3
4
)
2
=48left parenthesis, start fraction, 1, divided by, 3, end fraction, x, right parenthesis, squared, plus, left parenthesis, start fraction, 4, divided by, 3, end fraction, right parenthesis, squared, equals, 48
(Choice C)
C
(x+4)^2=144(x+4)
2
=144left parenthesis, x, plus, 4, right parenthesis, squared, equals, 144
(Choice D)
D
(x+4)^2=16(x+4)
2
=16
Answers
Answer:
C is the correct answer
Step-by-step explanation: