let's recall that d = rt, distance = rate * time.
a = speed of the airplane in still air.
w = speed of the wind
the distance travelled with the wind is 960 miles, so the return trip is pretty much just that, 960 miles.
when the airplane is going with with wind, the airplane is really not going as fast as "a" mph, is really going faster due to the wind, so the speed of the plane is "a + w", because the wind is adding its speed to it.
when the airplane is going against the wind is not really going "a" mph fast either, is really going slower at "a - w" mph, because the wind is subtracting speed from it, so
[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{with the wind}&960&a+w&5\\ \textit{against the wind}&960&a-w&6 \end{array}~\hfill \begin{cases} 960=(a+w)(5)\\\\ 960=(a-w)(6) \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{960=(a+w)(5)}\implies \cfrac{960}{5}= a + w\implies 192=a+w\implies \boxed{192-w=a}[/tex]
[tex]\stackrel{\textit{substituting on the 2nd equation}}{960=(\underline{192-w}~~ - ~~w)(6)}\implies \cfrac{960}{6}=192-w-w\implies 160=192-2w \\\\\\ 2w+160=192\implies 2w=32\implies w=\cfrac{32}{2}\implies \blacktriangleright w=16 \blacktriangleleft ~\hfill \blacktriangleright \stackrel{192 - 16}{176=a} \blacktriangleleft[/tex]
Question
The sum of four times a number and two is 14. Find the number.
Answer:3
Step-by-step explanation:let the number be x
4x+2=14
4x=14-2
4x=12
divide both sides by 4
4x/4=12/4
x=3
Jameson wants to construct a ladder that has 8 rungs. Each rung is
3.2 feet wide. The two sides measure 10.6 feet each. The wood is
sold for $2.25 per linear foot. Find how much the wood to construct
this ladder will cost Jameson. 5.NBT.7
Answer:
$23.85
Step-by-step explanation:
Linear foot- sold by the lenght.
Therefore you dont worry about the 3.2 feet wide
So now we multiply 10.6 * 2.25
which is...
$23.85
consider the equation 2 x +9 y = -18 A line parallel to the above line would have a slope of_________
A line perpendicular to the above line would have a slope of ________________
cos(theta)+1 / tan^2(theta) = cos(theta) / sec(theta) - 1
I had to only use a pic because no one would be able to understand, worth 100 points IF you get it correct.
Total left
2-1/4+2/4+1-3/49/4+2/4+7/49+2+7/418/44-2/4Answer:
[tex]4\:\dfrac{2}{4}[/tex]
Step-by-step explanation:
Add the amounts of each pie left :
[tex]2 \frac{1}{4}+\dfrac{2}{4}+1 \frac{3}{4}[/tex]
Separate the whole numbers and the fractions:
[tex]\implies 2+ \dfrac{1}{4}+\dfrac{2}{4}+1+\dfrac{3}{4}[/tex]
Add the whole numbers and fractions separately:
[tex]\implies 2+1+\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}[/tex]
[tex]\implies 3+\dfrac{6}{4}[/tex]
Convert 6/4 into a mixed number:
[tex]\implies 3+1\frac{2}{4}[/tex]
Add the whole numbers:
[tex]\implies 4\frac{2}{4}[/tex]
helphelphelphelphelphelphelphelphelphelphelphelphelphelphelp
Answer:
Its mass or size.
The amount possessed by an object directly upon the square of the speed. It increases the kinetic energy.
Solve: |2x+3|=2 CAN SOMEONE PLEASE EXPLAIN THIS TO ME!!!
Answer:
-1/2 or -5/2
Step-by-step explanation:
| | means the absolute value (distance from 0), so there is going to be a positive case and a negative case (distance from the negatives and distance from the positives).
POSITIVE CASE
[tex]2x+3=2\\2x=-1\\x=-\frac{1}{2}[/tex]
NEGATIVE CASE
[tex]-(2x+3)=2\\-2x-3=2\\-2x=5\\x=-\frac{5}{2}[/tex]
So, your answer would be -1/2 or -5/2.
Step-by-step explanation:
after 4x^2+12x+5
do sum and product but I solved it directly through calculator
hope it helps
find the total area of cardboard used in making a matchbox, complete with the sliding portion, 4cm long, 2.5cm wide, and 1.2cm deep (ignore the thickness of the cardboard)
Answer: 55.2 cm^2
Step-by-step explanation:
2(4x2.5 + 2.5x1.2 + 1.2x4) = 35.6 cm^2
(2x1.2x4 + 4x2.5) = 19.6 cm^2
(35.6 + 19.6) = 55.2 cm^2
What is the area?
2 yd
8 yd
5 yd
Answer:
28
Step-by-step explanation:
I assume the polygon is a trapezoid with parallel bases of 2 yd and 5 yd, and an altitude of 8 yd.
area of trapezoid = (base1 + base2)h/2
area = (2 yd + 5 yd)(8 yd)/2
area = 28 yd²
Q13
A man has a flight at 19:15 on Thursday. He must arrive at the airport 2 hours before this time to
check in.
He needs to know what time he should leave home.
He will park his car at the airport car park and it will take 15 minutes to get to the check in counter.
The distance from his house to the airport is 90 miles.
He will drive at an average of 60miles per hour.
Answer: around 6 or 5 o clock
Step-by-step explanation: hope this helps
100 PTS/// If you have a 2.5% chance of getting something every 3 minutes how long will it take until that's guaranteed?
Answer:
120 min
Step-by-step explanation:
step 1. divide 100% by 2.5 (=40)
step 2. 40 time 3 minutes = 120!
so by the time it gets to 120 minutes it 100% and guaranteed
Answer:
120 mn
Step-by-step explanation:
100 PTS/// If you have a 2.5% chance of getting something every 3 minutes how long will it take until that's guaranteed?
The measure of an angle is 74.4°. What is the measure of its complementary angle?
Answer:
15.6
Step-by-step explanation:
complementary angles sum up to 90
90-74.4=15.6
therefore the measure of it's complementary angle is 15.6
Given that V=1,3,4,2 and W= 6,4,7,2 then VW is
Select one:
of
O 4
0 1,3,6,7
O 2
0 2,4
Answer:
2,4 possibly
Step-by-step explanation:
if its V (intersection) W
then its 2,4
if it has something to do with patterns then i dont know
Alma reads 2 books each week Which number line best represents the number of weeks it
will take her to read at least 28 books?
Answer:
[C]
Step-by-step explanation:
To Find:
which number line represents the number of weeks it will take Alma to read at least 28 books.
Solve:
Create an inequality from the given information :
( 2x ≥ 28, where x represents the number of weeks)
Then divided both sides of the inequality by 2, resulting in x ≥ 14, or all values greater than or equal to 14.
Now, chosen the number line that shows all numbers greater than or equal to 14 (all the numbers to the right of 14 and including 14, which is indicated by a shaded circle).
Hence, [C} is the correct answer.
~Lenvy
The fuel gauge shows how much fuel is left in a 10 gallon tank. How far can you drive if the car's average fuel consumption is 40 miles per gallon?
Answer:
ok so we have 10 gallons left and we get 40 miles per gallon so this is just multiplycaiton
10*40=400
so you can get 400 more miles
Hope This Helps!!!
Find the equation that passes through the points (8,10) and (4,5). Give your results using function notation
Answer:
f(x) = 5/4x
Step-by-step explanation:
The equation of the line can be found using the 2-point form of the equation of a line:
y -y1 = (y2 -y1)/(x2 -x1)(x -x1)
This can be rearranged to the desired funtional form.
__
Using the given points (x1, y1) = (8, 10) and (x2, y2) = (4, 5), we have ...
y -10 = (5 -10)/(4 -8)(x -8)
y = (-5/-4)(x -8) +10 = (5/4)x . . . . . add 10 and simplify
The equation can be written ...
f(x) = 5/4x
How are genetic engineering and artificial selection different? (in your own words)
Artificial selection picks previously existing qualities by breeding individuals with favourable traits, whereas genetic engineering affects the genetic composition of plants or animals by adding new genes or silencing genes.
Solve the inequality 46 > y + 11
Answer:
Inequality Form:
y<35
Interval Notation:
(−∞,35)
Answer:
y is smaller than 34 or less
Step-by-step explanation:
put the 11 to the other side and make it a negative then you get 46-11=35 than it says 35>y
Help help help help
Step-by-step explanation:
can you tell me what you don't understand about this ?
because it is really simple, once you understand the transformations of equations.
remember, whatever we do to one side. we have to do also to the other side, so that the information in general stays the same.
(7 - 3x)/2 = 8 multiply both sides by 2
7 - 3x = 16 subtract 7 from both sides
-3x = 9 divide both sides by 3
-x = 3 multiply both sides by -1
x = -3
and that's the whole "secret" about solving an equation.
Answer:
x = -3Step-by-step explanation:
In the question we are given with an equation that is ( 7 - 3x ) / 2 = 8 . And we have asked to find the value of x .
Solution : -
[tex] \longrightarrow \qquad \: \dfrac{7 - 3x}{2} = 8[/tex]
Step 1 : Multiplying both sides by 2 :
[tex] \longrightarrow \qquad \: \dfrac{7 - 3x}{ \cancel{2} }\times \cancel{2 }= 8 \times 2 [/tex]
On further calculations, We get :
[tex] \longrightarrow \qquad \: 7 - 3x = 16[/tex]
Step 2 : Subtracting with 7 on both sides :
[tex] \longrightarrow \qquad \: \cancel{ 7 }- 3x - \cancel{ 7 }= 16 - 7[/tex]
On calculating further, We get :
[tex] \longrightarrow \qquad \: - 3x = 9[/tex]
Step 3 : Dividing with -3 on both sides :
[tex] \longrightarrow \qquad \: \dfrac{ \cancel{ - 3}x}{ \cancel{-3}} = \cancel{\dfrac{9}{ - 3} }[/tex]
On calculating further, We get :
[tex] \longrightarrow \qquad \: \red{\underline{\boxed{\frak{x = - 3}}}}[/tex]
Therefore, value of x is -3 .Verifying : -
Now , we are verifying our answer by substituting value of x in given equation . So ,
( 7 - 3x ) / 2 = 8[ 7 - 3 ( -3 ) ] / 2 = 8( 7 + 9 ) / 2 = 816 / 2 = 88 = 8L.H.S = R.H.SHence, Verified .Therefore , our answer is valid .
#Keep LearningWrite the linear inequality shown in the graph. The gray area represents the shaded region.
x > –3
y ≥ –3
y > –3
x ≥ –3
Answer:
y > –3
Step-by-step explanation:
by looking at the graph we notice that the (shaded/gray) area which we are focusing on covers all the values of x ,on the other hand it only covers the values of y which they are Greater than -3
Remark : y > -3 not y ≥ -3 because the line that separates the shaded region and the other one is a broken line.
Answer:
y > –3
Step-by-step explanation:
Lee watches TV for 4 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (10 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
Step-by-step explanation:
1 kilowatt=1000 watt
tv watch time=4*30=120
the watt tv consume=120*150=18000
the kilowatt tv consume=18000/1000=18
electricity cost =10*18
180 cents
Kim is 15 years old. Her father is 4 times as old as her now. In how many years time their total age be 115 years.
Answer:
100 later kim will be 115
Lily is $90\text{ cm}$ tall. If Anika is $\frac{4}{3}$ of the height of Lily, and Sadaf is $\frac{5}{4}$ of the height of Anika, how tall is Sadaf?
Answer:
your mom
u.w.u
lol
haha
study well
Tony saw 6 birds in a tree. 1/6 of them flew away. How many were left?
Answer:
5 birds flew away
Step-by-step explanation:
1/6x6=1
( 1 bird flew away)
so, 6-1=5
Answer:
[tex]\huge\boxed{\bf\:5\:\:birds}[/tex]
Step-by-step explanation:
Number of birds Tony saw = 6Fraction that flew away = ⅙Number of birds that flew away = ?
Number of birds that flew away = Number of birds × Fraction that leftNumber of birds that flew away = 6 × ⅙Number of birds that flew away = 1Number of birds remaining = ?
Number of birds remaining = Total number of birds - Number of birds that flew awayNumber of birds remaining = 6 - 1Number of birds remaining = 5[tex]\rule{150pt}{2pt}[/tex]
Help help help help help
Answer:
(-9, -6)
Step-by-step explanation:
100 Points and Brainly.
Graph The equation: y=(-x)-6
Gibberish for points WILL NOT be tolerated.
Please, if you can, try to make the mark ON the picture I have provided, in red.
function : y = (-x) - 6
Find x-intercept :
(-x) - 6 = 0(-x) = 6x = -6Find y-intercept :
y = (-0) - 6 y = -6mark these two points on both the axis and draw a straight linear graph.
passes coordinates : (0, -6), (-6, 0)
[tex]\\ \rm\rightarrowtail y=-x-6[/tex]
Take some point s
(1,-7)(2,-8)(3,-9)Graph it
the legnth of a rectangle is three times its width. if the length of the perimeter is 64 in, find the length and width
Answer:
Length and width of rectangle is 24 and 8 inchesStep-by-step explanation:
Given:
Length of rectangle is three times the widthPerimeter of rectangle is 64 InchesTo Find:
Length and WidthSolution:
Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:
Perimeter of rectangle = 2(L + B)
→ 64 = 2(3x + x)
→ 64 = 2(4x)
→ 64/2 = 4x
→ 32 = 4x
→ 32/4 = x
→ 8 = x
Hence,
Length of the rectangle = 3x = 3(8) = 24 inchesWidth of the rectangle = x = 8 inchesAnswer:
Length = 24 inchesWidth = 8 inches⠀
Step-by-step explanation :
⠀
As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in and we are to find the length and width of the rectangle. So,
⠀
Let us assume the width of the rectangle as w inches and therefore, the length will be 3w inches .
⠀
Now, According to the Question :
⠀
[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (3 x + x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{8x= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{64}{8} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar[/tex]
⠀
Therefore,
The width of the rectangle is 8 inches .⠀
Now, We are to find the length of the rectangle:
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 \times 8 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed{ \frak{\pmb{Length = 24}}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The length of the rectangle is 24 inches .⠀
What is the area of a triangle whose sides have length $\sqrt{70},$ $\sqrt{70},$ and $\sqrt{28}$?
Answer:
980
Step-by-step explanation:
[tex]A = \frac{H.B}{2} = \frac{28.70}{2} = 980[/tex]
Hope it helps!!!Brainliest pls!!!Answer:
21
Step-by-step explanation:
Help ASAP.
i need you to please break it down ive tried and just don't understand
Answer:
A) -4
Step-by-step explanation:
Question
[tex]\sf evaluate \ \dfrac{-4+(m+2)}{n} \ \sf when \ m=\dfrac23 \ and \ \sf n=\dfrac13[/tex]
Solution
Substitute the given values of m and n into the original expression:
[tex]\sf \implies \dfrac{-4+(\frac23+2)}{\frac13}[/tex]
Carry out the operation in the brackets first [tex]\sf (\frac23+3)=\frac83[/tex]
[tex]\sf \implies \dfrac{-4+\frac83}{\frac13}[/tex]
Now carry out the operation in the numerator [tex]-4+\frac83=-\frac43[/tex]
[tex]\sf \implies \dfrac{-\frac43}{\frac13}[/tex]
Dividing by a fraction is the same as multiplying by the flipped version of the fraction (flipped = swap the numerator and denominator of the fraction we are dividing by):
[tex]\sf \implies -\dfrac43 \div \dfrac13=-\dfrac43 \times \dfrac31[/tex]
To multiply a fraction, simply multiply the numerators and multiply the denominators:
[tex]\sf \implies -\dfrac43 \times \dfrac31=\dfrac{-4 \times 3}{3 \times 1}=-\dfrac{12}{3}[/tex]
Finally simplify:
[tex]\sf \implies -\dfrac{12}{3}=-4[/tex]
If EF || DG, and S and T are midpoints, then DG= ? Ef=13 ST=19
Answer: 25
Step-by-step explanation: