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
PLEASE HELP ASAP WILL GIVE BRAINLY!!!!!!Some of the steps in the derivation of the quadratic formula are shown:
Step 3: –c + StartFraction b squared Over 4 a EndFraction = a(x squared + StartFraction b Over a EndFraction x + StartFraction b squared Over 4 a squared EndFraction)
Step 4a: –c + StartFraction b squared Over 4 a EndFraction = a(x + StartFraction b Over 2 a EndFraction) squared
Step 4b: negative StartFraction 4 a c Over 4 a EndFraction + StartFraction b squared Over 4 a EndFraction = a(x + StartFraction b Over 2 a EndFraction) squared
Which best explains or justifies Step 4b?
factoring a polynomial
multiplication property of equality
converting to a common denominator
addition property of equality
.
Answers
Answer:
i think it is the third one but dont know just an educational geuss
Step-by-step explanation:
The given steps from the derivation of the quadratic formula are:
Step 3: [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]
Step 4a: [tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
Step 4b: [tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
The property "converting to a common denominator" justifies step 4b. So, option C: "converting to a common denominator" is correct.
What is the quadratic formula?The quadratic formula is as follows:
x = [-b ± (√b²+4ac)]/2a
This formula is derived from the quadratic equation [tex]ax^2+bx+c=0[/tex].
What are the steps to derive the quadratic formula?The standard quadratic equation is [tex]ax^2+bx+c=0[/tex]
Step 1: [tex]ax^2+bx=-c[/tex]
Step 2: Taking 'a' as common
[tex]a(x^2+\frac{b}{a}x)=-c[/tex]
Step 3: Adding [tex]\frac{b^2}{4a}[/tex] on both sides
[tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x)+\frac{b^2}{4a}[/tex]
⇒ [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]
Step 4a: Factoring the polynomial
[tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
Step 4b: Converting to a common denominator
[tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
⇒ [tex]\frac{(-4ac+b^2)}{4a}=a(x+\frac{b}{2a})^2[/tex]
Step 5: Applying square root (on one side there is a square, so, on the other side it gets ±)
⇒ [tex]\frac{(-4ac+b^2)}{4a^2}=(x+\frac{b}{2a})^2[/tex]
⇒ ±[tex]\sqrt{\frac{(-4ac+b^2)}{4a^2}} =(x+\frac{b}{2a})[/tex]
⇒ [tex]x+\frac{b}{2a}[/tex] = ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
step 6: Subtacting [tex]\frac{b}{2a}[/tex] from both the sides
⇒ [tex]x=-\frac{b}{2a}[/tex] ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
⇒ x = [-b ± (√b²+4ac)]/2a
Thus, step 4b best explains or justifies the property "Converting to a common denominator".
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you move up 7 units and left 6 units. you end at (-1,5). where did you start?
Answers
Answer:I beleive it is (5,-2)
Step-by-step explanation:
A pet store specializes in exotic fish. The graph shows a proportional relationship between the number of fish and the number of fish tanks at
the store.
y
65
52
39
Fish
Fish
26
13
0
5
6
Fish Tanks
Answers
35m is the answer to the problom
Answer:
the correct answer is 13
Step-by-step explanation:
i got it correct on the test, hope this helps:)) !
2. Solvex2 - 6x = -5 by completing the square , Show all work for the steps below . ( a ) Forx ? - 6x + = -5+ , what value of c is used to complete the square ? ( b ) Substitute the value for c in Part 2 ( a ) . Then complete the square to rewrite the equation as the square of a binomial . ( c ) Solve for x
Answers
Answer:
see explanation
Step-by-step explanation:
Given
x² - 6x = - 5
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = - 5 + 9 [ part a, c = 9 ]
(x - 3)² = 4 [ part b ]
Take the square root of both sides
x - 3 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 3 to both sides )
x = 3 ± 2
Thus part c is
x = 3 - 2 = 1
x = 3 + 2 = 5
Help plz and explain if possible
Answers
Answer:
d
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLY!!!!!!!!!What is the vertex of the graph of the function f(x) = x2 + 8x − 2 ?
(−4, 18)
(0, -2)
(-8, -2)
(−4, −18)
Answers
===================================================
Explanation:
A graph is a nice addition (and it will likely help us see the vertex directly), but it isn't necessary because we can use the equation given to us. Though I recommend using a graphing calculator to confirm the answer.
The original function is the same as y = 1x^2+8x + (-2). We see that it is in the form y = ax^2+bx+c where
a = 1
b = 8
c = -2
Use the values of 'a' and b to get the value of h, which is the x coordinate of the vertex.
h = -b/(2a)
h = -8/(2*1)
h = -4
The x coordinate of the vertex is x = -4. Plug this into the original equation to get
f(x) = x^2+8x-2
f(-4) = (-4)^2 + 8(-4) - 2
f(-4) = -18
Plugging x = -4 into f(x) leads to y = -18. The point (-4, -18) is on the parabola. Furthermore, this is the vertex (h,k)
------------
Alternatively, you can complete the square as shown below
y = x^2 + 8x - 2
y = (x^2 + 8x) - 2
y = (x^2 + 8x + 0) - 2
y = (x^2 + 8x + 16 - 16) - 2
y = (x^2 + 8x + 16) - 16 - 2
y = (x+4)^2 - 18
y = 1(x+4)^2 - 18
y = 1(x-(-4))^2 - 18
The last equation is in the form y = a(x-h)^2 + k with (h,k) = (-4,-18) being the vertex. The 16 is the result of taking half of 8 and squaring that result. We have 16-16 = 0 to make sure that we don't change the equation and keep things balanced. This is the same as adding 16 to both sides. All of this is done so we can end up with the (x+4)^2 perfect square portion.You can expand out (x+4)^2 - 18 and you should get x^2+8x-2 again.
Because you need to rewrite in vertex form and use this form to find the vertex (h,k)
Which should get you to
(-4,-18)
What is the slope of the line through (2,-2) and (9, 3)
Answers
Answer:it is 5/7
Step-by-step explanation: the formula for slope is rise/run divide and you get 5/7
Answer:
slope = [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (9, 3)
m = [tex]\frac{3+2}{9-2}[/tex] = [tex]\frac{5}{7}[/tex]
Question: 4 x 1 2/5 Answer with a mixed number in simplest form!
Answers
Answer:
[tex]5\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]4*1\frac{2}{5} = 4 * \frac{7}{5} = \frac{28}{5} = 5\frac{3}{5}[/tex]
Answer:
[tex]\boxed{ 5\frac{3}{5}}[/tex]
Step-by-step explanation:
[tex]\displaystyle 4 \times 1\frac{2}{5}[/tex]
[tex]\sf Convert \ mixed \ fraction \ into \ improper \ fraction.[/tex]
[tex]\displaystyle 4 \times \frac{7}{5}[/tex]
[tex]\sf Multiply.[/tex]
[tex]\displaystyle \frac{28}{5}[/tex]
[tex]\sf Convert \ improper \ fraction \ into \ mixed \ fraction.[/tex]
[tex]\displaystyle 5\frac{3}{5}[/tex]
Describe the transformations that will map triangle A to triangle B and illustrate the similarity between the two triangles.
A) reflect triangle a across the y-axis and then translate triangle a 5 units down. B) reflect triangle A across the x-axis and then reflect triangle a across the y-axis.
C) translate triangle a 4 units down and then rotate triangle A 180° counterclockwise about the origin.
D) reflect triangle a across the x-axis and then rotate triangle A 90° counterclockwise about the origin
Answers
The triangle is shifted 4 units downwards and then is rotated about the origin.
What is image rotation?A rotation is a type of transformation which is a turn.A figure can be turned clockwise or counterclockwise on the coordinate plane.In both transformations the size 3 shape of the figure stays exactly the same.Given are triangles A and B.
Transformation 1 : The triangle is shifted 4 units downwards.
Transformation 2 : The figure is rotated about the origin.
Therefore, the triangle is shifted 4 units downwards and then is rotated about the origin.
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Two joggers start from different locations and simultaneously begin heading toward each other. One of the joggers jogs 19mph, while the other jogs 17mph. If the two joggers are 324 miles apart how many hours will it take before they meet?
Answers
Answer:
errror
Step-by-step explanation:
7. Assume two people, Swanson and Suzie, are standing 35 feet apart and are watching a boat
race. At a given moment, Swanson approximates the angle formed by the lead boat, himself, and
Suzie to be 30°. Suzie approximates the angle formed by the lead boat, herself, and Swanson to be
130. How far is the boat from Swanson?
130°
30"
35 feet
Swanson
Suzie
Part I: What is the missing angle in this triangle? (1 point)
Part II: Use the law of sines to find the distance from Swanson to the boat. (2 points)
Answers
Answer:
78.4 ft
Step-by-step explanation:
Part I:
Missing angle = 180° - (130 + 30) (sum of angles in a triangle)
= 180° - 160°
Missing angle = 20°
Part II: distance (d) from Swanson to the boat
Law of Sines is given as:
[tex] \frac{a}{sin(A)} = \frac{b}{sin(B)} [/tex]
Where,
a = d
A = 130°
b = 35 ft
B = 20°
Plug in the values and solve for d
[tex] \frac{d}{sin(130)} = \frac{35}{sin(20)} [/tex]
Multiply both sides by sin(130) to make d the subject of the formula
[tex] \frac{d}{sin(130)}*sin(130) = \frac{35}{sin(20)}*sin(130) [/tex]
[tex] d = \frac{35*sin(130)}{sin(20)} [/tex]
[tex] d = 78.4 ft [/tex]
On a certain map, 3 inches represents 15 miles. Briarwood and Middletown are 5 inches apart on the map. What is the actual distance between Briarwood and Middletown? A. 25 mi B. 30 mi C. 50 mi D. 75 mi
Answers
Answer:
i think the answer is a. 25
There are 6 flowers in vases in your kitchen. You want to put 3 of them on the dining room table for dinner tonight. Order isn’t important. How many ways can you display the flowers for dinner?
Answers
The required ways of the combination to display the flowers on the dinner is 20.
There are 6 flowers in vases in your kitchen. You want to put 3 of them on the dining room table for dinner tonight. Order isn’t important. How many ways can you display the flowers for dinner to determiined.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Examples of permutation and combination, Managing people, numbers, numerals, alphabets, letters , and colors are examples of permutations. Choosing of menu, foodstuffs, dresses, matters, and the group are examples of combinations.
Since, the total number of flower in vases is 6
3 of them to be selected for the dinner table tonight.
The combination is given as.
= C( 6 , 3)
= 6!/3!(6 - 3)!
= 6!/3!3!
= 20
Thus, the required ways of combination to display the flowers on dinner is 20.
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I NEED THE ANSWER ASAP
The number of students who smoke cigarettes at Broxton College is decreasing at a rate of one smoker every 6.31 days. At what rate in smokers per year is the number of smokers declining? Assume 365 days in a year and round to the nearest tenth of a smoker per year
Answers
Answer:
57.8
Step-by-step explanation:
We can set up a proportion for this, assuming x is the smokers lost in 365 days.
[tex]\frac{1}{6.31} = \frac{x}{365}[/tex]
Using the cross products property, we know that x will be equal to:
[tex](365\cdot1) \div 6.31\\365\div6.31\\\\\approx 57.8[/tex]
Hope this helped!
Translate the following into an algebraic expression: The number that is 40% more than five more than a number a.
Answers
Answer:
1.4a > 5+a
Step-by-step explanation:
If the number is increased by 40% of that number, then it multiplies by 1.4. So, the left side of the equation is 1.4a.
On the right side of the equation, if the number is increased by 5, then the equation is a + 5.
Since the left side of the equation is more than the right side of the equation, we add a greater than sign. So the expression is 1.4a > 5+a
Someone pls help me . Thank you sm
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
X = 24
m = 13/7 or about 1.86
▹ Step-by-Step Explanation
X/3 + 7 = 15
X + 3 * 7/3 = 15
X + 21/3 = 15
X = 24
3.5m - 1.5 = 5
35/10m - 15/10 = 5
5 * 7/2 * 5m - 3 * 5/2 * 5 = 5
m = 13/7 or about 1.86
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
explanation:
7/13 + 1/5 (its in fractions)
Answers
Answer:
48 ÷ 65
Step-by-step explanation:
hope it helps you
Answer:
[tex]\frac{48}{65}[/tex]
Step-by-step explanation:
Step 1: Find LCM for denominators
13(5) = 65
So we need to convert our fractions to add them
Step 2: Convert [tex]\frac{7}{13}[/tex] by multiplying both top-bottom by 5
[tex]\frac{7}{13} (\frac{5}{5} ) = \frac{35}{65}[/tex]
Step 3: Convert [tex]\frac{1}{5}[/tex] by multiplying both top-bottom by 13
[tex]\frac{1}{5} (\frac{13}{13} ) = \frac{13}{65}[/tex]
Step 4: Add the converted fractions
[tex]\frac{13}{65} +\frac{35}{65} =\frac{48}{65}[/tex]
And we have our answer!
Solve the equation using the multiplication property of equality and the reciprocal of 1 4 . 1 4 ( r − 5 2 ) = 1 8
Answers
Answer: I dont know if this is right but the is 8 Ive never done this before.
Step-by-step explanation:
1 =
4 =
1 =
4 =
r− 5 ⋅ 2 = 1 = r = 11
8 = r = 11
Please help ASAP!!!!!!!
Answers
Answer:
$86.81
Step-by-step explanation:
Using the given formula, we want to compute A for ...
P = 4750
r = 0.2279
n = 365 . . . . . assuming "exact" interest
t = 1 or 30
For 1 day late:
A = 4750(1 +0.2279/365)^(365·(1/365)) = 4752.97
For 30 days late:
A = 4750(1 +0.2279/365)^(365·(30/365)) = 4839.78
The difference in these payment amounts is ...
$4839.78 -4752.97 = $86.81
You would save $86.81 in interest charges by paying only 1 day late.
_____
Comment on the question
It would be a poor choice of credit card to use one that compounds interest daily. Most do so on a monthly basis.
Explanation : copied other person if you don’t mind
Find the total cost, to the nearest cent, for a sweater that costs $22.95 with an additional 5.5% sales tax. Show your work.
Answers
Answer:
22.95×1.055≈$24.21
22.95* 1.055= 24.21
Which of the following represents continuous data? A. Amount of coins in your pocket B. Time it takes to count the coins in your pocket C. Number of collector coins you own D. Value of the coins in your pocket
Answers
Answer:
Time it takes to count the coins in your pocket
Step-by-step explanation:
Find the slope of the line.
4/3
-4/3
-3/4
3/4
Answers
Answer:
-3/4
Step-by-step explanation:
slope is rise over run so you go down 3 first is is -3, and then right 4 times which means the slope is -3/4
What are all of the real roots of the following polynomial? f(x) = x^4 - x^3 - 13x^2 + x + 12
a) -1 and 1
b) -3, -1, 1, and 3
c) -3 and 3
d) -3, -1, 1, and 4
Answers
Answer:
1,-1,4,-3 so D
Step-by-step explanation:
0 = x^4 - x^3 -13x^2 + x + 12
x = 1,-1,4,-3
The final answer is -3,-1,1 and 4
What is the relation between roots and the biquadratic equation?The biquadratic equation is of the form ax⁴+bx³+cx²+dx+e and hence
The sum of roots is -b/a, the sum of the product of two roots is c/a, the sum of the product of three roots is -d/a, and the product of all four roots is e/a.
Solving the given problemThere is no specific method of solving a biquadratic equation, hence we use the trial and error method and also some form of the root.
So finding f(1) = 1-1-13+1+12 = 0 hence 1 is a root.
finding f(-1) = 1-(-1)-13-1+12 = 0 hence -1 is also a root.
So let other roots be p,q
Now we can use sum of roots formula which is p+q+1-1= 1, hence p+q=1
product of roots p*q*1*-1=12, pq= -12 substituting p = -12/q
-12/q+q = 1, multiplying q on both sides
q²-12=q, q²-q-12=0, q²-4q+3q-12 = 0, q(q-4q)+3(q-4)=0
(q-4)(q+3) = 0 hence the roots are 4,-3 also
Hence 1,-1,4, and -3 are the roots of the equation.
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find the value of a answers: a:15 b:14 c:19 d:16
Answers
Answer:
6a+10= 3a+55
6a-3a= 55-10
3a= 45
a= 45/3
a= 15
The answer is (A) 15
Hope this helps^°^
Answer:
A. 15
Step-by-step explanation:
The angles are vertical angles, therefore they are congruent. We can set the two measures equal to each other.
[tex]6a+10=3a+55[/tex]
Now, solve for a. We must get a by itself on one side of the equation.
First, subtract 3a from both sides of the equation.
[tex]6a-3a+10=3a-3a+55[/tex]
[tex](6a-3a)+10=55[/tex]
[tex]3a+10=55[/tex]
Next, subtraction 10 to both sides of the equation. We subtract because 10 is being added to 3a. The inverse of addition is subtraction.
[tex]3a+10-10=55-10[/tex]
[tex]3a=55-10[/tex]
[tex]3a=45[/tex]
3 and a are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 3
[tex]3a/3=45/3[/tex]
[tex]a=45/3[/tex]
[tex]a=15[/tex]
The value of a is 15 and choice A is correct.
A store pays $10 for each shirt it buys. The store sells each shirt for 60%
more. What is the price of a shirt at the store?
Answers
Answer:
16$ per shirt
Step-by-step explanation:
60% of 10 is 6
10 + 6 = 16
16% of 10 is 6
10+6=16
6.21(3.1) answer for number 6
Answers
What will I get for this 16 + x = 12
Answers
Second step: simplify to x= -4
Third step: fill it back into the equation to check, 16 + -4 = 12, and 12=12 this is a true statement
Answer:
x = -4
Step-by-step explanation:
16 + x = 12
16 - 16 + x = 12 - 16
x = -4
Find the value of y and x.
Answers
Answer:
x = 130°y = 65°Step-by-step explanation:
All inscribed angles intercepting the same arc have the same measure.
If you slide the vertex of angle y clockwise around the circle until it coincides with the vertex of the angle marked 65°, you see that those two inscribed angles (y and 65°) intercept the same arc, so have the same measure:
y = 65°.
The measure of an inscribed angle is half the measure of the intercepted arc, so the arc marked x is double the angle 65°.
x = 130°.
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] )
Michael just drank a cup of coffee to help him stay awake. The coffee had 110 milligrams of caffeine in it. If his body processes 5% of the caffeine every hour, how much will be left in 8 hours? A.74 B.72 C.56 D.73
Answers
Answer:C
Step-by-step explanation:
%5 of 110 is 5.5, 5.5 • 8= 54, 110-54= 56!
