The aircraft's average speed for the entire trip, both against and with the wind, is 200 miles per hour. This is calculated by dividing the total distance travelled (600 miles) by the total time taken (3 hours).
Explanation:To solve this problem, we'll use the formula for average speed: Total Distance/Total Time. In this case, the aircraft flies 300 miles against the wind and 300 miles with the wind, so the total distance is 600 miles (300+300).
The total time is the time it takes to fly against the wind plus the time it takes to fly with the wind, which is 3 hours (2+1).
So, the average speed for the entire trip is 600 miles/3 hours = 200 miles per hour.
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Which of the following is a rational equation?
A. 4-2(x-1)=x+3
B. 1/2x-1/3=4-x
C. 0.7x-3=0.09(x-5)
D. 6/x - 1 = 4/(x-2)
Answer:
B and D
Step-by-step explanation:
Since they're the fractions
Option B and Option D represent rational equation.
A rational equation is defined as any equation that can write in p/q form where q not equal to zero.
From given option it is observed that,
Option B, [tex]\frac{1}{2}x-\frac{1}{3} =4-x [/tex]
option D, [tex]\frac{6}{x}-1=\frac{4}{x-2} [/tex]
Both option have fraction term.
Hence, Option B and Represent rational equation.
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Find X and Y for both.
Answer:
Second picture: y=4 and x=7
First picture: x=70 degrees y=20 degrees
Step-by-step explanation:
Second picture:
One of the given triangles is an equilateral and the other is an isosceles.
Equilateral triangle has all congruent sides and it's angles are all congruent.
Isosceles triangle has two congruent angles and the opposite sides of those congruent angles are also congruent.
This implies all the side algebraic expression-measurements given are all equal.
5y-4=y+12
Add 4 on both sides:
5y=y+16
Subtract y on both sides:
4y=16
Divide both sides by 4:
y=4
So what is the side measurement for each of the sides given in terms of algebraic expressions?
y+12
4+12
16
Each side given in terms of an algebraic explanation is 16 units.
So we have also the following equation to solve:
3x-5=16
Add 5 on both sides:
3x=21
Divide both sides by 3:
x=7
So x=7 and y=4.
There is only one side in the picture that is possibly not 16. It is the one of the sides in the isosceles, not opposite the base angles.
------------------------------------------
First picture:
We are given x+y=90.
Since that one triangle is an isosceles we know that x+x+(180-40)=180
So let's solve the second equation for x then go back and solve for y in the first equation.
2x+140=180
Subtract 140 on both sides:
2x=40
Divide both sides by 2:
x=20
First equation:
x+y=90
So y=90-x=90-20=70.
Miguel says that to create rectangle F' he reflected rectangle F across the y-axis, dilated the reflection by a scale factor of 3, and translated the dilated figure to the right 2 units.
What mistake did Miguel make in describing the steps of his transformation?
A. He gave the incorrect scale factor.
B. He named the incorrect axis of reflection.
C. He gave the incorrect direction of translation.
D. He gave the incorrect number of units of translation.
Answer:
A. He gave the incorrect scale factor.
Step-by-step explanation:
The scale factor is the Multiplicative Inverse of 3, which is ⅓:
F → 12 × 6
F' → 4 × 2
This is a genuine statement because according to the graph, each block is worth 2, and ⅓ of 6 is 2, and ⅓ of 12 is 4.
I am delighted to assist you anytime my friend.
Answer:
the answer is A
Step-by-step explanation:
Miguel gave an incorrect scale factor. The shape decreased in size meaning it would have a scale factor under 1 but he put 3 meaning the shape got larger when really it shrunk. This means A is the correct answer
What is the area of the trapezoid?
13 m
16 m
19 m
232 m2
256 m2
328 m2
352 m2
Answer:
256m2.
Step-by-step explanation:
Answer:
256m^2
Step-by-step explanation:
How do you round 949999 to the nearest ten thousand
Answer:
950000
Step-by-step explanation:
the rule with rounding is if the number to the direct left is under 5, it stays the same but if it is 5 or above, you round up and everything behind becomes zeroes.
10x−8/3−4x=6x
whats the value of x?
(20 points!!!)
There is no solution of expression.
We have to given that,
An expression to solve,
⇒ 10x - 8/3 - 4x = 6x
Now, We can simplify as,
⇒ 10x - 8/3 - 4x = 6x
Combine like terms,
⇒ 6x - 8/3 = 6x
⇒ 6x - 6x = 8/3
⇒ 0 ≠ 8/3
Which is not possible.
Thus, There is no solution of expression.
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I need help!!! Please help me
Answer:
5 ≥ 0
Step-by-step explanation:
9w - 4w +6 ≥ 1 + 5w.
Subtract 9w - 4w = 5w.
5w + 6 ≥ 1 + 5w.
Subtract 1 from each side.
5w + 6 - 1 ≥ 1 - 1 + 5w
5w + 5 ≥ 5w
Subtract 5w from each side
5w - 5w + 5 ≥ 5w -5w
5 ≥ 0
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The school is taking students on a field trip. Each bus holds 32 students. If 140 students have RSVP'd, what is the fewest number of buses that can be used?
a) 5
b) 6
c) 7
Answer:
5
Step-by-step explanation:
because in 5 buses there could fit 160 students which is more than have rsvpd
Answer:
(a)
Step-by-step explanation:
Basically we're trying to figure out how many groups of 32 students are needed to have more than 140.
To do this, we take 140/32 (*BIG NOTE!! No matter what our answer is, we round up. If we rounded down, we'd be leaving some students behind, and we don't want that.)
140/32 = 4.375 (but remember, we round up no matter what)
so the answer is 5, which is A.
During the first year it is in business, another candy company sells
100 times as many boxes as the Cricket Candy Company. How
many boxes are sold by both companies during that first year?
The equation y-5=6(x+1) is written in point-slope form. What is the equation written in slope-intercept form?
A)y = 6x + 11
B)y = 6x – 1
C)y = 6x – 4
D)y = 6x + 6
Answer:
a. y = 6x + 11
Step-by-step explanation:
distribute and rearrange into slope-intercept form.
y - 5 = 6x + 6
add 5 to both sides
y = 6x + 6 + 5 ⇒ y = 6x + 11
Answer: Hello mate!
our equation is y - 5 = 6(x + 1), and we want to rewrite it in the slope-intercept form.
First lets distribute the parenthesis.
y - 5 = 6(x+1) = 6x + 6
now let's add 5 in both sides.
y-5 + 5 = 6x + 6 + 5
y = 6x + 11
Then the correct answer is the option A.
John made 12 dollars per delivery plus a base pay of 30 dollars.
If he made 150 dollars, how many deliveries did John make
Answer:
10
Step-by-step explanation:
$150 minus the base pay of $30 is $120. Divide this by the $12 he makes each delivery. 120/12=10
-1/4 in decimal form
Answer:
-0.25
Step-by-step explanation:
y
=
–x + 4
x + 2y
=
–8
How many solutions does this linear system have?
one solution: (8, 0)
one solution: (0, 8)
no solution
infinite number of solutions
Answer:
one solution
Step-by-step explanation:
Given two equation
y = -x+4 ... (1)
x+2y = -8 ...(2)
Substituting equation (1) into (2), we will have;
x+2(-x+4) = -8
Opening the bracket up
x-2x+8 = -8
-x = -8-8
-x = -16
x = 16
Substituting x = 16 back into equation 1:
y = -16+4
y = -12
This shows that the linear equation has one solution (16,-12)
Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $114, or she is able to buy 2 shirts and 4 sweaters for $164. How much does a shirt cost? How much does a sweater cost ?
Answer:
The cost of a shirt is $16 and the cost of a sweater is $33
Step-by-step explanation:
Let
x -----> the cost of a shirt
y -----> the cost of a sweater
we know that
[tex]3x+2y=114[/tex] -----> equation A
[tex]2x+4y=164[/tex]----> equation B
Solve the system by graphing
Remember that the solution of the system is the intersection point both graphs
The solution is the point (16,33)
see the attached figure
therefore
The cost of a shirt is $16 and the cost of a sweater is $33
Answer:
The cost of each shirt is 16$ and the cost of each sweater is 33$
Solution:
Let us consider “x” as the cost of each shirt and “y” as the cost of each sweater.
From question, Andrea has bought 3 shirts and 2 sweaters for 114$. Hence we form equation as,
3x + 2y = 114 ------ eqn 1
Similarly, Andrea has bought 2 shirts and 4 sweaters for $164. Hence we form equation as,
2x + 4y = 164 ----- eqn 2
By solving equation 1 and equation 2, we get the value of “x” and “y”.
On multiplying equation 1 by 2,we get
6x + 4y = 228 -------- eqn 3
Now solving eqn 2 and eqn 3
6x + 4y = 228
-2x - 4y = -164
4x + 0y = 64
4x = 64
[tex]x = \frac{64}{4}[/tex]
x = 16
Substituting the value of x in eqn 1, we get
3(16) + 2y = 114
48 + 2y = 114
2y = 114 - 48
2y = 66
[tex]y = \frac{66}{2}[/tex]
y = 33
Thus the values of x and y are 16 and 33. So the cost of each shirt is 16$ and the cost of each sweater is 33$
Write an equation for the description.
Ten times the sum of half a number x and 5 is 8.
10(1/2X + 5) = 8
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The statement 'Ten times the sum of half a number x and 5 is 8' can be translated into a mathematical equation as: 10 * (0.5x+5) = 8.
Explanation:To write the equation for the given description, we first need to translate the statement into mathematical terms.
The description is 'Ten times the sum of half a number x and 5 is 8'. In mathematics:
'The sum of' is represented by a plus '
So, translating the statement into an equation we get:
10 * (0.5x+5) = 8
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For 32 hours of work, you are paid $244.80. How much would you receive for 37 hours?
You would receive $
. (Round to the nearest cent as needed.)
Answer:
$283.05
Step-by-step explanation:
first divide $244.80 by 32, to find out how much you are making hourly. in this case you are making $7.65 an hour
next, multiply $7.65 by 5, to add the 5 hours, in this case you get $38.25.
next, add $38.25 to $244.80 and you get your answer!
Final answer:
To find out how much you would receive for 37 hours of work, set up a proportion using the given information and solve for x. The result is approximately $283.98.
Explanation:
To find out how much you would receive for 37 hours of work, we can set up a proportion using the information given. Since 32 hours of work pays $244.80, we can set up the proportion: 32/244.80 = 37/x. Cross-multiplying, we get: 32x = 244.80 * 37. Simplifying, we find that x = (244.80 * 37) / 32. Calculating the result, we find that you would receive approximately $283.98 for 37 hours of work.
Sketch and prove the following for the two congruent triangles ∆ABC and ∆DEF.
The medians drawn from vertex A and D are congruent.
Label medians MA and ND ; then △ABM≅△
by reason
Answer:
See explanation
Step-by-step explanation:
Given: ΔABC ≅ ΔDEF
AM, DN - medians
Prove: AM ≅ DN
Proof:
1. Congruent triangles ABC and DEF have congruent corresponding parts:
AB ≅ DE;BC ≅ EF;∠ABC ≅ ∠DEF.2. BM ≅ MC - definition of the median AM;
3. EN ≅ NF - definition of the median DN;
4. AB ≅ 2BM, EF ≅ 2EN
BM ≅ 1/2 AB,
EN ≅ 1/2 EF,
thus, BM ≅ EN
5. Consider two triangles ABM and DEN. In these triangles \:
AB ≅ DE (see 1));BM ≅ EN (see 4));∠ABM ≅ ∠DEN (see 1).So, ΔABM ≅ ΔDEN by SAS postulate.
6. Congruent triangles ABM and DEN have congruent corresponding sides BM and DN.
Round the following numbers to the nearest 10. 13-21-29
Answer:
13 --> 10
21 --> 20
29 --> 30
Answer:
The correct answer is: 10-20-30
Step-by-step explanation:
13 is between 10 and 20. The closest 10 for 13 is 10, because it's only 3 away (13 the other option would be 20 but it's 7 away, so way more.)
21 is between 20 and 30. The closest 10 for 21 is 20 ( it's only 1 away from 20, the other option would be 30 but it's 9 away, so way more.)
29 is between 20 and 30. The closest 10 for 29 is 30 (it's only 1 away from 30, the other option would be 20 but it's 9 away, so way more.)
What is the solution to the following equation?
|3x - 6| = 10
Answer:
B
Step-by-step explanation:
1) Set up the following two equations, because of the absolute value:
3x-6=10
3x-6=-10
2) Solve both equations:
3x=16
3x=-4
3) Divide both sides by 3:
x=16/3
x=-4/3
4) Make fractions proper:
x=5 1/3
x=-1 1/3
write down the coordinates of the point 5 units to the left of the y axis and 3 units above the x axis
The coordinates of the point is (-5,3)
How to determine the coordinates?Let the initial coordinate be:
Initial = (0,0)
5 units to the left of the x-axis represents a horizontal translation left by 5 units.
So, we have:
New = (0 - 5,0)
3 units above the y-axis represents a vertical translation up by 3 units.
So, we have:
New = (0 - 5, 0 + 3)
Evaluate
New = (-5, 3)
Hence, the coordinates is (-5,3)
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Kaleb had 136 songs on his mp3 player. if he deleted 56 songs, what is the ratio of songs he kept to songs he deleted
Answer:
80/56 = 1.42
Step-by-step explanation:
Total songs = 136
Number deleted = 56
Number kept = 136-56 = 80
The ratio of songs kept to songs deleted = 80/56 = 1.42
The proportions or ratio are used to compare quantities with each other, and are usually written with a colon (:) intermediate.
8 5/8 + 8 7/8 ????????
Answer:
17 1/2
Step-by-step explanation:
8 5/8 + 8 7/8
=17 1/2
Answer:
17 1/2
Step-by-step explanation:
8 5/8+8 7/8=...
So, let's take away the fractions for now.
What's 8+8?
Well, 8+8=16.
Now, let's take a look at the fractions.
5/8+7/8=...
Well, when we are adding fractions, the denominator will stay the same. So let's pretend that we are adding 5+7.
5+7= 12. So our answer is 16 12/8 Right?
wrong.
you will simplify the 12/8. Since the numerator is more than eight, we will subtract 8 from 12.
12-8=4
we will make the 8/8 a 1 and add it to the 16 to make it 17 4/8. We can still simplify this. The 4/8 becomes 1/2 making the answer: 17 1/2
Hope this helps!!!
Is the number 4.333..... rational or irrational?
Answer:
Irrational number
The number 4.333.... is a rational number because it can be expressed as the fraction 13/3. An irrational number, like Pi, cannot be expressed as a fraction of two integers.
Explanation:The number 4.333..... is an example of a rational number. Rational numbers can be expressed as a fraction of two integers, and in this case, 4.333.... can be expressed as 13/3. In contrast, an irrational number cannot be expressed as a fraction of two integers. For example, the number Pi is an irrational number because it can not be accurately expressed as a fraction.
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What is a multi step problem?
Answer:
In multi-step problems, one or more problems have to be solved in order to get the information needed to solve the question being asked.
the 9s in 9,905,482
Answer:
the 9s are in the millions and hundred thousands
Step-by-step explanation:
A car used 1/64 of a gallon of gas to drive 1/4 of a mile. at this rate, how many miles can the car travel using 1 gallon of gas?
HELP ! SHOW WORK AND I WILL MAKE YOU THE BRAINIEST ANSWER .
Answer: 4/64
Step-by-step explanation:
Since 1/4 * 4 = 1
We just have to multiply 1/64 times 4 to get the answer
1/64 * 4 = 4/64
Answer:
Car will cover 16 miles in 1 gallon of the gas.
Step-by-step explanation:
We can solve this question by unitary method.
∵ A car used [tex]\frac{1}{64}[/tex] gallons of gas to drive the distance = [tex]\frac{1}{4}[/tex] miles
∴ Car used 1 gallons to drive the distance = [tex]\frac{\frac{1}{4} }{\frac{1}{64} }[/tex]
= [tex]\frac{64}{1}\times \frac{1}{4}[/tex]
= [tex]\frac{64}{4}[/tex]
= 16 miles
Therefore, car will cover 16 miles in 1 gallon of the gas.
17) Given f(x) = 2x + 4, if the output is 12, what is the input? (Solve for x)
_ as an ordered pair:(, )
Answer:
the answer is 8 because when you set the equation equal to 12 and solve it you get 12
Step-by-step explanation:
Final answer:
To find the input for f(x) = 2x + 4 when the output is 12, solve the equation 12 = 2x + 4 for x, resulting in the input-value x being 4, with the ordered pair being (4, 12).
Explanation:
The question concerns finding the input for a given function when the output is known. The function provided is f(x) = 2x + 4, and we want to find the input value, or x, that produces an output, or f(x), of 12. To do this, we set up an equation where 12 = 2x + 4 and solve for x.
We first subtract 4 from both sides of the equation to get 8 = 2x. Then, we divide both sides by 2 to isolate x, resulting in x = 4.
The ordered pair representing the input-output relationship for the function when the output is 12 is (4, 12).
-15= z/-2 answer please?
Answer:
30
Step-by-step explanation:
[tex]-15=\frac{z}{-2}\\\\(-15)(-2)=z\\\\30=z[/tex]
Please need help urgent
the product of a number and 3 is 6 more than the number which equation models this sentence
Answer:
3x = 6 + x
Step-by-step explanation:
We can express the product of a number and 3 as:
3x
Where x is the number that we don't know.
Now it says that that product is 6 more than the number (x) so we can write it down:
3x (The product of a number and 3) = (is) 6 + x (6 more than the number)
3x = 6 + x
The sentence 'the product of a number and 3 is 6 more than the number' can be translated into the algebraic equation 3x = x + 6.
Explanation:The given statement can be translated into a mathematical equation in the following way: If we let x be the number in question, the first part of the sentence tells us that the product of the number and 3 can be modeled as 3x. The second part of the sentence tells us that this is 6 more than the number itself. This can be translated into the equation as x + 6. Thus, putting the two parts together, we get the algebraic equation 3x = x + 6.
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