Two planes, which are 2940 miles apart, fly toward each other. Their speeds differ by 35mph. If they pass each other in 4 hours, what is the speed of each?
Answer:
385 mph350 mphStep-by-step explanation:
You want the individual speeds of airplanes that close the 2940 mile distance between them in 4 hours, and have a speed difference of 35 mph.
SetupThe closing speed is found using the relation ...
speed = distance/time
It is ...
(2940 mi)/(4 h) = 735 mi/h
If x represents the speed of the slower plane, then (x+35) is the speed of the faster one. The sum of their speeds is the closing speed:
x +(x +35) = 735
SolutionSimplifying, we have ...
2x +35 = 735
2x = 700 . . . . . . subtract 35
x = 350 . . . . . . . divide by 2
x+35 = 385 . . . . speed of the faster plane
The speeds of the planes are 350 mph and 385 mph.
The area of a certain desert (Desert 1) is eight times the area of another desert (Desert 2). If the sum of their areas is
27,000,000 square miles, find the area of each desert.
What is the area of Desert 1?
Answer:
1687500
Step-by-step explanation:
If their sum is 27,000,000 then their are millions of ways to find this answer. like one can be 13500000. But that answer is obviously incorrect. If you divide that by 8, your answer will be 1687500.
I NEED HELP ASAP WITH THESE QUESTIONS
1. The sum of twice a number and 5
2. Twice the sum of a number and 5
3. The square of five more than a number
Answer:1.2x+5 2.2(x+5) 3.(x+5)^2
Step-by-step explanation:
A baby American bison weighs 20kg. A baby blue whale weighs 100 times as great as a baby American bison. how much does a baby blue whale weigh
a baby blue whale weigh= 2000 kg
Simple equation :
A linear equation that involves only one variable is known as a simple equation or a linear equation in one variable. For example, \(3x + 2 = 23,x = 7,2x + 6 = 3x – 4,\)etc., are simple equations.Let us assume a situation, in which you go to the market to buy mangoes in a supermarket. Your mother gave you Rs.100 and said that you can keep Rs.40 for buying chocolates and for the remaining amount, you need to buy mangoes. When you went to the market, you found out that the price of one kg of mangoes was Rs.12. So, the final question is how many mangoes you should buy, so that everyone is satisfied. Recall the concept of simple equations from previous classes and proceed. Let us assume that you have to purchase kg of mangoes, so the total amount of money that you will be spent on buying mangoes will be Rs.12x. Now, you have Rs.40 for yourself, so you have an equation:
12 x + 40 = 100
12x = 100 – 40
12x = 60
x = 60/12 = 5, This is the same equation as above. Now when you will solve this, you will get to know the value of 5kg of mangoes. It means that you can buy 5 kg mangoes and spend Rs.40 on buying chocolates
weigh: to measure how heavy something is, especially by using a machine (scales)
given :
A baby American bison weighs=20kg
The solution according to Question =
Let the weight of baby blue whale = b
the baby blue whale weighs =100(a baby American bison)
b=100(20)
b=2000 weigh
a baby blue whale weigh= 2000 kg
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Translate this phrase into an algebraic expression.
The sum of 17 and twice Matt's score
Use the variable m to represent Matt's score.
Answer:
17 + 2 x m
Step-by-step explanation:
sum is to add and twice is to multiply by 2
IV. Are these ratios equivalent? 12 birds to 60 animals 17 birds to 85 animals Yes No
Answer:
True
Step-by-step explanation:
Both fractions simplify to 1/5 and thus are equivalent
I need help with math ngl
Answer:
Oldest to newest:
10^-35, 10 ^-10, 0
Step-by-step explanation:
Scientific notation
To figure out the power of 10 think "how many places do I move the decimal point?"
When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.
When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.
Find the slope of the line shown on the graph to the right.
Question content area bottom left
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
The slope would be [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Answer:
-4/-5
Step-by-step explanation:
Remember the formula to slope:
(y2 - y1)/(x2-x1) given two points on the line that are (x1, y1) and (x2, y2).
The two points given on this line are: (2,2) from the top left and (-3,-2) from the bottom left. Let's say (2,2) = (x1, y1) and (-3,-2) = (x2, y2). Plug the points into the formula:
(-2 - 2)/(-3-2) = -4/-5
FINAL ANSWER: -4/-5
The length of a rectangle is 3m less than double the witch, and the area of the rectangle is 27m^2. Find the dimensions of the rectangle.
Answer:
the area of the rectangle is A=L•W
The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m
A=L-W
27m²=(2W-3m)-W
27m2=2w2-3m-W
2w2-3wm-27m2=0
....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)
W=
2-2
w=(3m± √9m²+216m²)
w=(3m+ √225m²)
W=(3m± 15m...you need only positive root because width cannot be negative
W= 3m+15m
4
W=. 4
18m
W=4.5m ......now find the L
L=2.4.5m-3m
L=9m-3m
L=6m
Answer:
W = 4.5cm
L = 6cm
Step-by-step explanation:
You invested $27,000 in two accounts paying 4% and 7% annual interest, respectively. If the total interest earned for the year was $1440 how much was invested at each rate?
a = amount invested at 4%.
b = amount invested at 7%.
we know that whatever "a" and "b" may be, they total 27000, so we can say that a + b = 27000, likewise we can say that b = 27000 - a.
how much will it be for 4% of "a"? well, that's just (4/100) * a, or 0.04a.
how much will it be for 7% of "b"? well, that's just (7/100) * a, or 0.07b.
we also know that the earned interest by those two interest amounts is 1440, so
[tex]\begin{cases} a + b = 27000\\ b = 27000 - a \end{cases}\hspace{5em}0.04a~~ + ~~0.07b~~ = ~~1440 \\\\\\ \stackrel{\textit{substituting "b"}}{0.04a~~ + ~~0.07(27000-a)~~ = ~~1440}\implies 0.04a+1890-0.07a=1440 \\\\\\ 1890-0.03a=1440\implies -0.03a=-450\implies a=\cfrac{-450}{-0.03} \\\\\\ 15000=\textit{\LARGE a}\hspace{15em}\stackrel{27000~~ - ~~15000}{\textit{\LARGE b}=12000}[/tex]
could someone please help answer this.
Answer:
+ 12 yards
Step-by-step explanation:
8-3 = 5
5 + 12 - 5 = 12
Find the mystery number. It is a common multiple of 2,5 and 7. It has 3 digits. The sum of the digits is 10. The number is less than 500
The number is 280
In mathematics, Least Common Multiple is referred to by its entire name, whereas Highest Common Factor is its complete name. The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the H.C.F. describes the biggest factor existing between any given pair of two or more numbers. LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).
Two key techniques—the division method and the prime factorization approach—can be used to determine H.C.F. and L.C.M.
So we need to find the LCM of 2,5 and 7. Furthermore, we need to find multiply the LCM with a number which can make its sum of digits equal to 10.
LCM of 2,5 and 7 is 70
70 x 4 = 280
Sum of digits of 280 is 10, which is also less than 500
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How can you recognize when two integers are opposite numbers? Opposite numbers are always to the right of zero on the number line. Opposite numbers are always to the right of zero on the number line. Opposite numbers are the same distance from zero on both sides of the number line. Opposite numbers are the same distance from zero on both sides of the number line. Opposite numbers have one even number and one odd number. Opposite numbers have one even number and one odd number. Opposite numbers are always negative.
One can recognize when two integers are opposite numbers as C. Opposite numbers are the same distance from zero on both sides of the number line.
How to illustrate the information?It should be noted that opposite numbers are given as being 0 when added.
For example, the addition of 3 and -3 will be equal to 0.
Therefore, one can recognize when two integers are opposite numbers as Opposite numbers are the same distance from zero on both sides of the number line.
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Sandra bought 4 bars of chocolate and a packet of nuts for $11.50. If a bar of chocolate costs $0.50 less than a packet of nuts, find the cost of a packet of nuts
Answer:
A packet of nuts costs $2.70
Step-by-step explanation:
Let C represent the cost of a bar of chocolate and P represent the cost of a packet of nuts
4 bars of chocolate will cost $4C
1 packet of nuts costs $P
Total price Sandra paid is $11.50
This can be represented using
4C + P = 11.50 (1)
A bar of chocolate costs $0.50 less than a packet of nuts. So
P - C =0.50
-C + P = 0.50 (2)
Multiply eq (2) by 4 to get
-4C + 4P = 4 x 0.50
-4C + 4P = 2 (3)
Add equations (1) and (3) to eliminate the 4C term
4C + P - 4C + 4P = 11.50 + 2
P+4P = 13.50
5P = 13.50
Dividing by 5 on both sides
5P/5 = 13.50/5
P = 2.70
So a packet of nuts costs $2.70 (Answer)
To verify this is correct,
Use equation (2) to get
-C + P = 0.50
-C + 2.70 = 0.50
Add C to both sides
-C + 2.70 + C = 0.50 + C
2.70 = 0.50 + C
Subtract 0.50 from both sides
2.70-0.50 = 0.50 + C - 0.50
2.20 = C which is C= 2.20
Plug this value into equation (1)
4(2.20) + 2.70 = 8.80 + 2.70 = 11.50
So verified that answers are correct
shonda went for a drive in her new car. She drove for 147.5 miles at a speed of 59 miles per hour. For how many hours did she drive?
Answer:
2.5
Step-by-step explanation:
By Using s = d/ t
So t = d / s
t = 147.5 / 59= 2.51 fluid oz = ______
please answer asap
Graph the line with slope -1 passing through the point (-1, -2).
Step-by-step explanation:
find point (-1,-2)
go down one
go to the right one
repeat
draw line with arrows at each end
done!
Find the slope of (8,9) and (23,9)
Step-by-step explanation:
you mean the slope of the line between (8, 9) and (23, 9).
we can see that right away, as the y value does not change. it means it is a flat line, and that means the slope is 0.
now, formally :
the slope of a line is (y coordinate change / x coordinate change) when going from one point on the line to another.
the direction does not matter, but once we pick one for the comparison of one coordinate, we have to use the same direction also for the other.
I prefer to go from left to right.
so, from (8, 9) to (23, 9).
x changes by +15 (from 8 to 23).
y changes by 0 (from 9 to 9).
the slope is therefore 0/+15 = 0.
solve for x. 2/2+x=1/x+5
Answer:
Step-by-step explanation:
its 8 duh jk its your mom XD
Part 2 of 2
You invested $15,000 in two accounts paying 4% and 7% annual interest, respectively. If the total interest earned for
the year was $960, how much was invested at each rate?
$3000 and $12000
If you know the principal amount, the rate of interest, and the time periods, you can use the simple interest formula to calculate the interest.
The following is a simple interest formula:
SI = P *R * T /100
Where SI = simple interest
Principal (P)
interest rate, or R (in percentage)
T is the time period (in years)
The following formula is used to determine the overall sum:
Sum (A) = Principal (P) + Interest (I)
Where,
The entire amount repaid at the conclusion of the borrowing period is indicated by the letter (A).
You can also write the total amount formula for simple interest as follows:
A = P(1 + RT)
X+Y = $15000
0.04x + 0.07y = 960
0.04x + 0.07 ( 15000 - x) = 960
0.04x + 1050 - 0.07x = 960
0.03x = 90
x = $3000
y= $12000
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please help with this question the question is in the attached image
The coefficient matrix for the given system of equations is as follows:
[tex]\left[\begin{array}{ccc}2&-6&-1\\-10&9&5\\3&0&5\end{array}\right][/tex]
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The augmented matrix of a system is composed as follows:
The first column has the coefficients of x.The second column has the coefficients of y.The last column has the results, that is, the values of the other side of the equality.In standard notation, this system is given as follows:
2x - 6y = -1.-10x + 9y = 5.3x + 0y = 5.Hence the augmented matrix is given by:
[tex]\left[\begin{array}{ccc}2&-6&-1\\-10&9&5\\3&0&5\end{array}\right][/tex]
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If an individual makes $4,000 in salary per month and has a side job making $20 per hour for 10 hours a week for 4 weeks in a
month, and they receive $1,000 per month in rent from a roommate, what is their gross income?
O $4,000
O $4,800
O $5,800
O Cannot be determined, because taxes and deductions are not provided
The gross income will be $5,800.
It is given that per month salary of an individual is $4000 and from a side job he makes $20 per hour for 10 hours a week for 4 weeks and rent he got is $1000.
We have to calculate the gross income.
What do you mean by gross income ?
Gross income refers to the total income of a person or business from all resources.
As per the question ;
Per month salary = $4000
Earning from side job is given $20 per hour for 10 hours a week for 4 weeks.
i.e.,
= 20 × 10 × 4
= $800 for 4 week
and
the rent they receive = $1000
So ;
The gross income will be ;
= 4000 + 800 + 1000
= $5,800
Thus , the gross income will be $5,800.
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Four thousand five hundred eleven ten-thousandths in standard decimal form?
Oscar buys a bag of cookies that contains 7 chocolate chip cookies, 8 peanut butter cookies, 9 sugar cookies and 7 oatmeal cookies.
What is the probability that Oscar reaches in the bag and randomly selects a peanut butter cookie from in the bag and randomly selects a peanut butter cookie from
the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie?
Give your answer as a fraction, or accurate to at least 4 decimal places.
The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how probable an event is to do, or how likely it's that a proposition is true. The probability of an event is a number between 0(zero)(zero) and 1(one), where, roughly speaking, 0(zero) indicates the impossibility of the event and 1(one) indicates certainty.The more advanced the probability of an event, the more likely it's that the event will do.These generalities have been given a self-evident fine formalization in probability proposition, which is used extensively in areas of study similar to statistics, mathematics, wisdom, finance, gambling, artificial intelligence, etc.
P(sugar | oatmeal) = (7/25)(6/24) = 0.07
The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.
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If f(x) = 2ax + b/x-1, lim x→0 f(x) = -3, lim x→∞ f(x)=4, prove that: f(2)= 11.
If
[tex]f(x) = \dfrac{2ax+b}{x-1}[/tex]
Note that
[tex]f(2) = \dfrac{4a+b}{2-1} = 4a+b[/tex]
From the given information we have
[tex]\displaystyle \lim_{x\to0} f(x) = \lim_{x\to0} \frac{2ax+b}{x-1} = \frac{0+b}{0-1} = -b = -3 \\\\ ~~~~ \implies b=3[/tex]
and
[tex]\displaystyle \lim_{x\to\infty} f(x) = \lim_{x\to\infty} \frac{2ax+b}{x-1} = \lim_{x\to\infty} \frac{2a+\frac bx}{1-\frac1x} = \frac{2a+0}{1-0} = 2a = 4 \\\\ ~~~~ \implies a=2[/tex]
It follows that
[tex]f(2) = 4\cdot2+3 = 11[/tex]
as required.
Consider the following linear program.
Min 3A + 4B
s.t.
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0
Answer:
Minimum z =22 at A =6, B=1
See the graph below variable A is on the horizontal axis and variable B on the vertical axis
Step-by-step explanation:
We can solve using the graphical method
Min z = 3A + 4B
s.t.
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0
Draw two lines using the constraint equations
1A + 3B = 9
1A + 1B = 7
The feasible region for the inequality constraints is the region that satisfies all 4 constraints below
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0
This is the heavily shaded region in the graph. The minimum will be at one of the corner points
There are three corner points on the graph
(0,7), (6,1) and (9,0)
Plug in these coordinate values with A being the first and B being second in the parentheses and see which set of values makes the objective function the minimum
Point (7,0) ==> z = 3(0) + 4(7) = 28
Point (6,1) ==> z = 3(6) + 4(1) = 22
Point (9,0) ==> z = 3(9)+4(0) = 27
One person earns $58,000 per year. Another person earns $3450 per month.
How much more does the first person earn in a year than the second?
The first person earns $ more than the second person in one year.
Answer:
There are 12 months per year so:
58000 - 12(3450) = $________ more
Just plug into calculator or otherwise
work the arithmetic.
Hope this helps.
fx(7)(87x+7y)(5)⁴is equal to the root of?
R,S,Q and P are midpoints of OC, Cb, BA and OA OR=a CS=b and OP=c show that RS is parallel to PQ PLS HELP
a 3 gallon bottle of bleach costs 15.84. what is the price per cup?
Answer: $0.33 per cup
Step-by-step explanation:
15.84/3 to find the price per 1 gallon.
15.84/3 = 5.28 per gallon
There are 16 cups in a gallon, so divide the price of a single gallon by 16.
5.28/16 = price per cup
5.28/16 = .33
The price for each cup of bleach is $0.33.