Answer:
The correct answers are:
A) 60 miles; and B) 3.375 hours.
Explanation:
We will use the equation d = rt for this.
For the first leg of the trip, the bird travels 20 miles per hour for x hours. This gives us the equation
d = 20x
For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour. He also travels 6 miles less than the return distance, for x hours:
d-6 = 16x
To isolate d, we will add 6 to each side:
d-6+6 = 16x+6
d = 16x+6
We will set the two equations equal to one another, since they both equal d:
20x = 16x+6
Subtract 16x from each side:
20x-16x = 16x+6-16x
4x = 6
Divide both sides by 4:
4x/4 = 6/4
x = 1.5
He travels for 1.5 hours both times.
The first time, 1.5 hours at 20 miles per hour is:
d = 1.5(20) = 30 miles
The original trip is 30 miles. This makes the entire trip 30(2) = 60 miles.
On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:
24 = 16x
Divide both sides by 16:
24/16 = 16x/16
1.5 = x
If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:
24/1.5 = 30/x
Cross multiplying,
24*x = 1.5(30)
24x = 45
24x/24 = 45/24
x = 1.875
This gives him a total time of 1.5+1.875 = 3.375 hours
Step-by-step explanation:
PLEASE HELP MEEEEE!!!!
An electrician charges $40 to come to your house. She also charges $55 for each hour that she works. The electrician charges you a total of $190. How many hours does the electrician work at your house? Use h for the number of hours.
Answer: 2 hours and 40 minutes
Step-by-step explanation:
40 + 55h = 190 ( equation )-40 -4055h = 150/55 /55h = 2 hours and 40 min ( answer )The area of a triangle is 40 square inches.
The base of the triangle is x + 1,
and the height is x - 1.
Find the value of x, and the dimensions of the triangle.
A = 1/2bh
Answer:
+9 and -9
Step-by-step explanation:
Given that Sine theta = StartFraction 21 Over 29 EndFraction, what is the value of cosine theta, for 0 degrees less-than theta less-than 90 degrees? Negative StartRoot StartFraction 20 Over 29 EndFraction EndRoot Negative StartFraction 20 Over 29 EndFraction StartFraction 20 Over 29 EndFraction StartRoot StartFraction 20 Over 29 EndFraction EndRoot.
Answer:
[tex]cos\theta=\frac{20}{29}[/tex]
Step-by-step explanation:
Problem:
[tex]sin\theta=\frac{21}{29},cos\theta=?,0^\circ<\theta<90^\circ[/tex]
Given:
[tex]sin\theta=\frac{opposite}{hypotenuse}=\frac{21}{29}[/tex]
[tex]cos\theta=\frac{adjacent}{hypotenuse}=\frac{x}{29}[/tex]
Solve for adjacent side:
[tex]a^2+b^2=c^2[/tex]
[tex]x^2+21^2=29^2[/tex]
[tex]x^2+441=841[/tex]
[tex]x^2=400[/tex]
[tex]x=20[/tex]
Final answer:
[tex]cos\theta=\frac{20}{29}[/tex]
The value [tex]\rm Cos\theta[/tex] is 20/29 and it can be determined by using the Pythagoras theorem.
Given that,
The value [tex]\rm Sin\theta[/tex] is 21/29,
Where [tex]0^{\circ}< \theta<90 ^{\circ}[/tex].We have to determine,
The value of [tex]\rm Cos\theta[/tex]?
According to the question,
To determine the value of [tex]\rm Cos\theta[/tex] following all the steps given below.
The formula of [tex]\rm Sin\theta[/tex] is,
[tex]\rm Sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\\[/tex]
On comparing to the given value of [tex]\rm Sin\theta[/tex] is,
[tex]\rm Sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\\\rm Sin\theta =\dfrac{21}{29}\\\\[/tex]
Here, Hypotenuse = 29, and Perpendicular = 21
Then,
The formula of [tex]\rm Cos\theta[/tex] is,
[tex]\rm Cos\theta =\dfrac{Base}{Hypotenuse}\\\\[/tex]
Let, the base be x,
The value of base finding by using Pythagoras theorem,
[tex]\rm {(Hypotenuse)}2 = (Perpendicular)^2+ (Base)^2\\\\ (29)^2 = (21)^2 + (x)^2\\\\841= 441 +x^2\\\\x^2 = 841-441\\\\x^2 = 400\\\\x = 20[/tex]
The value of the base is 20.
Therefore,
[tex]\rm Cos\theta =\dfrac{Base}{Hypotenuse}\\\\\rm Cos\theta =\dfrac{20}{29}\\\\[/tex]
Hence, The value [tex]\rm Cos\theta[/tex] is 20/29.
For more details about Pythagoras theorem refer to the link given below.
https://brainly.com/question/13710437
Write an equation of a line which has a slope of -2 and goes through the point (-4,11)
Answer:
See answers below
Step-by-step explanation:
slope-intercept form- y=-2x+3
point slope form- y-11=-2(x+4)
Use the given slope and point to substitute into the point-slope formula
then you can solve for y=mx+b
Jacob says that (12 + 31) × 5 is
equivalent to 12 + 31 x 5 because of the
associative property.
Describe the associative property
in words.
Determine if Jacob is correct. Justify
your answer.
Answer:
Step-by-step explanation:
the associative property means that when you are adding OR multiplying you can group the numbers however you want
Jacob is wrong because (12 + 31) x 5 = 215 and 12 + 31 x 5 = 167
Find the equation of the line that goes through ( 2, 4 ) and ( 4, 6 ).
Answer:
y=x+2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-4)/(4-2)
m=2/2
m=1
y-y1=m(x-x1)
y-4=1(x-2)
y=x-2+4
y=x+2
in a class of 33 student 18 play football 1"basketball and 7 play both games how many students play non of the games
Answer:
20
Step-by-step explanation:
I'm pretty sure its 20 but I could be wrong but 20 is my best guess.
Answer:
16 of the 33 plays none.
Step-by-step explanation:
From the list, we get that 18 students play football, 1 basketball, and 7 both.
What we need to do here is add up 18 and 1
then we subtract 19 by 7 to cancel out the people who play both
and then subtract the total number of 33 by 17,
which gives you 16.
-
If f(9) = - 3, write a corresponding ordered-pair solution.
Answer:
(9,-3)
Step-by-step explanation:
u just have to plug it up
Write equations for the horizontal and vertical lines passing through the point (4-1)
Answer:
y = - 1 , x = 4
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (4, - 1 ) with y- coordinate - 1 , then
y = - 1 ← equation of horizontal line
The equation of a vertical line parallel to the y- axis is
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (4, - 1 ) with x- coordinate 4 , then
x = 4 ← equation of vertical line
if one rents a car from Airport Rent-a-Car, the charge is $79 plus 7 cents a kilometer. Savings Rent-A-Car charges $59 plus 9 cents a kilometer. If one will drive d kilometers, when is it cheaper to use Savings Rent-A-Car?
It will be cheaper to use Savings Rent-A-Car up to 1000 kilometers, from then on it will be cheaper to use Airport Rent-a-Car.
Given that if one rents a car from Airport Rent-a-Car, the charge is $ 79 plus 7 cents a kilometer, while Savings Rent-A-Car charges $ 59 plus 9 cents a kilometer, to determine, if one will drive D kilometers , when it is cheaper to use Savings Rent-A-Car, the following calculation must be performed:
79 + 0.07 x 30 = 79 + 2.1 = 81.1 59 + 0.09 x 30 = 59 + 2.7 = 61.7 79 + 0.07 x 300 = 100 59 + 0.09 x 300 = 86 79 + 0.07 x 600 = 121 59 + 0.09 x 600 = 113 79 + 0.07 x 900 = 142 59 + 0.09 x 900 = 140 79 + 0.07 x 1000 = 149 59 + 0.09 x 1000 = 149
Therefore, it will be cheaper to use Savings Rent-A-Car up to 1000 kilometers, from then on it will be cheaper to use Airport Rent-a-Car.
Learn more about maths in https://brainly.com/question/26027910
The ordered pairs (−4,−3)
, (−2,−2), (4,1), (6,2), and (8,3) represent a function. What is a rule that represents this function?
Write an inequality for the following statement:
The difference between twice a number and 6 is at least 35.
6−2n≥35
2n−6≥35
2n−6≤35
6−2n<35
The formula below represents the standard form of a quadratic equation.
ax2+bx+c=0
Solve for b.
b=−ax2−cx
x=−ax2−c
x=−ax2−cb
b=x−ax2−c
The tables below each follow a different pattern
Which table follows the input-output rule: “Each output is one less than double the input”
table 2
table 4
table 1
table 3
Which inequality accurately represents the graph shown below?
Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400 iPhone. Write an inequality you could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone.
55w+75≥400
75w+55≤400
55w+75≤400
75w+55≥400
The equations and inequality expresses the relationship between the variables.
The correct responses are;
First part; The rule that represent the function is; y = 0.5·x - 1Second part; the correct option is the inequality; 2·n - 6 ≥ 35Third part; [tex]\displaystyle \underline{b = \frac{- a\cdot x^2 - c}{x}}[/tex]Fourth part; Table 4Fifth part; [tex]\displaystyle \underline{y < -\frac{1}{2} \cdot x - 4}[/tex]Sixth part; 75·w + 55 ≤ 400Reasons:
First part;
The difference between y-values following a change in 2 units of the x-value is a constant, and is equal to 1;
The rate of change of the function, m, is therefore;
[tex]\displaystyle m = \frac{2 - 1}{6 - 4} = \frac{1}{2} = 0.5[/tex]
The slope and intercept form of the equation of the function is therefore;
y - 3 = 0.5·(x - 8) = 0.5·x - 4
y = 0.5·x - 4 + 3 = 0.5·x - 1
The rule that represent the function is; y = 0.5·x - 1
Second part;
2·n represent twice the number
The difference between twice the number and 6 = 2·n - 6
At least 35 = ≥ 35
Therefore, the inequality is; 2·n - 6 ≥ 35
Third part;
The given quadratic equation is; a·x² + b·x + c = 0
Therefore;
[tex]\displaystyle \underline{b = \frac{-c - a\cdot x^2}{x}}[/tex]
Fourth part;
The best correct option is table 4, given that the table is as follows;
[tex]\begin{tabular}{|c|cc|}In&&Out\\Not clear&&\\9&&17\\10&&19\end{array}\right][/tex]
Fifth part;
The y-intercept of the graph is -0.5
The slope is -4 ÷ 8 = -0.5
Therefore, the equation is; y = -0.5·x - 4
The shaded area is the area lower than the y-values, with broken lines (indicating < relationship) which gives, the correct inequality as follows;
[tex]\displaystyle \underline{y < -\frac{1}{2} \cdot x - 4}[/tex]
Sixth part;
The amount Jordan part-time job pays = $75
The amount he has already saved = $55
The cost of the iPhone = $400
Let w represent the number of weeks Jordan works, at his part-time job to purchase the iPhone, we have;
75·w + 55 ≤ 400
Learn more about writing equations and inequalities here:
https://brainly.com/question/14321394
Evaluate the expression wx when x = -15 and w = 5. wx = _________.
-3 75 -75 3
Answer:
-75
Step-by-step explanation:
i had the exam so it is write
Plz help with this question
Answer:
the area of the tile is 190 cm2
Jake earns $9.85 per hour working at a software company. He wants to earn at least $300 a week. How many full hours must he work to earn the money?
Answer:
30.4 hours
Step-by-step explanation:
300 divided by 9.85
This gives you 30.4
at noon, a tank contained 8 in. of water. after several hours, it contained 6 in. of water. what is the percent decrease of water in the tank?
Answer: 25%
Step-by-step explanation:
To find percent decrease, you take your final number minus your initial number, over your initial number, so you start with 6-8/8, and get 2/8 or 1/4, then you multiply that by 100, so you get 25. That's your percent decrease.
Is -4/-19 equivalent to -4/19
Answer:
No
Step-by-step explanation: The first one is positive and the second one is negative
Need help Now please
on High School geometry a is altitude, if it doesn’t show on the picture
Answer:
1. Altitude
2. Median
3. Angle bisector
4. Perpendicular bisector
how to find the legs of a right triangle with only the hypotenuse calculator
Answer:
The triangle must be an isosceles triangle so as to only get one measurement
Step-by-step explanation:
The Pythagorean theorem states that the square of the hight and base is added then square rooted to get the hypotenuse
THE FORMULA: A square+b square=c square
Brinda has come to her aunt's place and wants to play a game on the computer. The computer is shown in the figure. She presses the button marked A and is surprised to find that the computer starts immediately and there is already a file open. Which of the following is the best explanation of what happened?
Answer:
she clicks the file
Step-by-step explanation:
(This is easy, but confusing) What is 1+ 2+ 3+ 4+ 5 -6 divided by 7 times 8 - 9???
Answer:
=-0.8
Step-by-step explanation:
1+2+3+4+5-6÷7×8-9
15-6÷7×8-9
15-0.85×8- 9
15-6.8-9
=-0.8
geometry PLEASE HELP and explain how???
Answer:
x means times
Step-by-step explanation:
what is the quotient of 4/5 divided by 1/3
Answer:
2 2/5
Step-by-step explanation:
What is the value of the expression shown below, when p= 1 and q= 4
Answer:
The correct answer is 5.
Step-by-step explanation:
I got 100% on the assignment
2y-7.4y=141.36
solve for y
Sketch the graph of each linear inequality
Answer:
hope you can see these, the red graph is problem 3 and the blue graph is problem 5 :)
how to graph equations using x and y intercepts
Answer:
uhhh maybe ( x + 2 ) = y
Step-by-step explanation:
i dont know im on break and I don forgot how to do this
the perimeter of a square is 52cm
We know that:
Perimeter: 52cm4(side) = 52cmTo find the side, we will need to divide 52 by 4.
=> 4(side) = 52cm=> Side = 52 ÷ 4=> Side = 13cmTherefore, the side of the square with 52 cm of perimeter is 13 cm.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Please help me solve this! Very urgent :(
Answer:
last one
Step-by-step explanation:
Find two numbers that round to 387.4 when rounded to the nearest tenth.
Victoria is 30 years old. She has $700 in a checking account, $9000 in a savings account $16,000 in a retirement account, and owns a car worth $6000. What is the total value of her liquid assets?
A. $31,700
B. $9700
C. $15,700
D. $16,000
Answer:
B
Step-by-step explanation:
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