To work this problem, you must assume that Juan's pedaling speed adds to the wind speed when going downwind, and that the wind speed subtracts from Juan's pedaling speed going upwind. (In other words, Juan's pedaling speed is relative to the air, not the ground.)
Let w represent the wind speed in miles per hour.
... distance = speed × time
Juan's total distance is 40 miles, so we have ...
... 40 = (11.5 +w)×1.75 + (11.5 -w)×2.50
... 40 = 48.875 - 0.75w . . . . . simplify
... -8.875/-0.75 = w . . . . . . . . subtract 48.875, divide by -0.75
... w = 11.833... = 11 5/6
The wind was blowing 11 5/6 miles per hour.
_____
Compared with real-life experience, and working through the details, this problem makes no sense whatever. Pedaling a bicycle is not like rowing a boat, where the current of the medium directly affects speed.
If you work through the segments of the problem, you find that Juan traveled 40.833 miles with the wind in the first 1.75 hours, so actually finished the race and then some. He spent the next 2.5 hours being blown backward by the wind, even though he was pedaling forward at 11.5 mph. (How much sense does that make?)
Which of the graphs below would result if you made the leading term of the following function negative?
We are given function F(x) = x^3 +3x^2.
Leading term is the term that has highest power of a variable.
For the given function we have highest power 3 of x.
Therefore, leading term is x^3. We don't have any sign in front of x^3. Therefore, it's a positive leading term.
And degree of the is highest power, that is 3.
Therefore, degree is an odd number.
According to problem, we need to make the leading term as a negative number.
So, we need to find a rule for end behaviour of the graph with:
Leading coefficent = Negative.
Degree : Odd.
Please note the rule, when leading coefficent a negative number and degree is odd.
x--> + ∞ f(x) ---> - ∞
x--> - ∞ f(x) ---> + ∞
We can see option D has f(x) ---> - ∞ for x--> + ∞ and f(x) ---> + ∞ for x--> - ∞.
Therefore, correct option is D.Answer: graph D
Step-by-step explanation: just took the test
Choose the equations that are not linear equations. - x - y = 2, x^2 + y = 4, x/2 - y^3 = 1, x = 5
Answer:
x^2 + y = 4x/2 - y^3 = 1Step-by-step explanation:
Any equation with a product of variables, or with a variable in an exponent or denominator, is not a linear equation. Here, "product of variables" includes powers and roots—any expression with an exponent other than 1, or a total of exponents other than 1.
The equations x^2 + y = 4 and x/2 - y^3 = 1 are not linear equations because they contain terms with variables raised to powers other than one, whereas - x - y = 2 and x = 5 are linear.
The question involves identifying which equations from the given list are not linear equations. Linear equations are of the form y = mx + b, where m and b are constants. Non-linear equations can include terms with variables raised to powers other than one, variables in the denominator, or variables under a radical.
The given equations are - x - y = 2, x^2 + y = 4, x/2 - y^3 = 1, and x = 5. The second equation, x^2 + y = 4, is not linear because it has a term x squared. The third equation, x/2 - y^3 = 1, is also not linear due to the term y cubed. Both of these equations contain expressions that disqualify them from being linear, as linear equations cannot have variables with exponents other than one. Therefore, these two are examples of a non-linear system of equations.
On the other hand, the first equation - x-y = 2 and the fourth equation, x = 5 are both linear. The first is in the standard linear form after being rearranged, and the fourth represents a vertical line in the xy-plane, which is a special case of a linear equation.
Please help me on this!
How does the $100 gift card affect the measure of center of the data?
It increases the mean value of the prizes.
It decreases the mean value of the prizes.
It increases the median value of the prizes.
It decreases the median value of the prizes.
Help asap! Will mark brainlyst
1 and a half is the correct answer (1 1/2) for the first one, for the second one it is D, and for the third one it is A.
Let's add both of the fractions together. They at 2 slices of pumpkin pie, and 3 slices of pecan pie. The fractions of these is 2/8 and 3/8. Added together, this is 5/8, so I believe this is your answer.
For this one, we can simply multiply the total acres by the cost per acre. 1240*52 is 64,480, so your land is worth a total of $64,480.
For this question, all we need to do is multiply the number of gallons Shelly's car can hold by the price per gallon. 14*3.56 is 49.84, so she'll be spending $49.84 to fill up her tank.
given the function f(x)=3^x, find the value of f^-1(27)
This is asking you to solve the equation ...
... 27 = 3^x
You can use logarithms to find
... log(27) = x·log(3)
... log(27)/log(3) = x = 1.43136376.../0.47712125...
... x = 3
Or, you can use your knowledge of small cubes and match exponents.
... 3^3 = 3^x
... 3 = x
The table below shows the number of shoppers at Jacob's store over a period of five months:
Month 1 2 3 4 5
Shoppers 50 250 1,250 6,250 31,250
Did the number of people at Jacob's store increase linearly or exponentially? A.Linearly, because the table shows an equal increase in number of shoppers for an equal increase in months
B. Exponentially, because the table shows an equal increase in number of shoppers for an equal increase in months
C.Linearly, because the table shows the number of shoppers increases by an equal factor for an equal increase in months
D.Exponentially, because the table shows the number of shoppers increases by an equal factor for an equal increase in months
We are given table
Month : 1 2 3 4 5
Shoppers: 50 250 1250 6250 3250
so, we have
first term =50
[tex]a_1=50[/tex]
Second term =250
[tex]a_2=250[/tex]
Third term =1250
[tex]a_3=1250[/tex]
[tex]a_4=6250[/tex]
[tex]a_5=31250[/tex]
now, we can find ratios
[tex]\frac{a_2}{a_1} =\frac{a_3}{a_2}=\frac{a_4}{a_3}=\frac{a_5}{a_4}=5[/tex]
we can see that all ratios are same and 5
so, this is exponential
so, option-D..........Answer
The table below shows the number of shoppers at Jacob's store over a period of five months:
Month 1 2 3 4 5
Shoppers 50 250 1,250 6,250 31,250
Did the number of people at Jacob's store increase linearly or exponentially?
Answer:
D.Exponentially, because the table shows the number of shoppers increases by an equal factor for an equal increase in months
A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?
because the leading coefficient is positive and the highest degree is odd (9) the function is negative for (-inf, -6). Then it crosses the -6 root to become positive until it crosses again the root -2. (it crosses because both roots have an odd multiplicity). then it touches on root 0 (does not cross due to an even multiplicity there), so function remains negative from -2 till root 4 where it crosses into the positive.
Given the above, only the first choice is a correct statement.
The true statement about the graph is: (a) the graph of the function is positive on [tex]\mathbf{(-6,-2)}[/tex]
The given parameters are:
[tex]\mathbf{Root = -6, Multiplicity = 1}[/tex]
[tex]\mathbf{Root = -2, Multiplicity = 3}[/tex]
[tex]\mathbf{Root = 0, Multiplicity = 2}[/tex]
[tex]\mathbf{Root = 4, Multiplicity = 3}[/tex]
Add up the multiplicities, to calculate the degree of the polynomial function
[tex]\mathbf{Degree = 1 + 3 + 2 + 3}[/tex]
[tex]\mathbf{Degree = 9}[/tex] --- odd number
The interval of the first root is:
[tex]\mathbf{Interval = (-\infty,-6)}[/tex]
The interval of the second root is:
[tex]\mathbf{Interval = (-6,-2)}[/tex]
A polynomial function with an odd degree, and a positive leading coefficient will start with negative values, until it reaches the smallest root, before it switched to positive values.
This means that, the function increases at: [tex]\mathbf{Interval = (-6,-2)}[/tex]
Hence, option (a) is correct.
Read more about polynomial functions at:
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How does sin 30degrees compare to sin -30degrees?
The sine function is an odd function, so the sine of -30° is the opposite of the sine of 30°.
sin(30°) = 1/2
sin(-30°) = -1/2
The sine of 30° is greater than the sine of -30°.
[Precalculus] Find the value of sin(x/2):
Put your number into the half-angle formula and simplify.
[tex]\displaystyle\sin{\frac{\theta}{2}}=\pm\sqrt{\frac{1-\cos{\theta}}{2}}=\sqrt{\frac{1-\frac{1}{3}}{2}}\\\\=\sqrt{\frac{1}{3}}=\sqrt{\frac{3}{9}}\\\\=\frac{\sqrt{3}}{3}[/tex]
The appropriate selection is ...
[tex]A)\quad\dfrac{\sqrt{3}}{3}[/tex]
Tom is putting cartons of ice-cream in one of the freezers. There are 13 boxes and each box contains 24 cartons. How many cartons of ice-cream are there in total?
There are a total of 312 cartons or ice cream in total.
I need geometry help
I don't know what is the correct classification for ∠BEC?
I can't tell if it's straight, acute, obtuse, or a right angle.
Angle BEC is the unmarked angle in the middle of the figure. Its value is the difference between straight angle AED (180°) and the two marked angles, 57° and 33°. That difference is ...
... 180° - 57° -33° = 90°
∠BEC is a right angle.
Answer:
Right angle
Step-by-step explanation:
We are given that
Angle AEB=[tex]57^{\circ}[/tex]
Angle CED=[tex]33^{\circ}[/tex]
We have to find the classification of angle BEC
We know linear sum =[tex]180^{\circ][/tex]
Angle AEB +Angle BEC+Angle CED=180
Substitute the values then we get
[tex]57+33+\angle BEC=180^{\circ}[/tex]
[tex]90+\angle BEC=180[/tex]
[tex]\angle BEC=180-90[/tex]
[tex]\angle BEC=90^{\circ}[/tex]
Hence, the angle BEC is right angle
Point C ∈ AB, AB = 30m. Point C is 1.5 times farther from point A than from point B. Find AC and CB.
We are given that
point C lies on AB
Let's assume AC=x
we know that
CB=AB-AC
[tex]CB=30-x[/tex]
Point C is 1.5 times farther from point A than from point B
so, we get
[tex]\frac{AC}{CB} =1.5[/tex]
now, we can plug values
[tex]\frac{x}{30-x} =1.5[/tex]
now, we can solve for x
[tex]x=1.5\left(30-x\right)[/tex]
[tex]x=18[/tex]
so, we get
[tex]AC=18[/tex]
now, we can find CB
[tex]CB=30-18[/tex]
[tex]CB=12[/tex]
so, we get
[tex]AC=18[/tex]
[tex]CB=12[/tex]...............Answer
Which ordered pairs are on the line 2x−3y=8 ? Select each correct answer. (12,−73) (−2,4) (2,−43) (−5,−6)
The answer is (-5,-6)
Answer:
Option D is correct.
(-5, -6)
Step-by-step explanation:
Ordered pair states that a pair of number that is locate a point on a coordinate plane i.,e (x, y)
Given the line: [tex]2x-3y = 8[/tex] .....[1]
Option A:
(12, -73)
Substitute the value of x = 12 and y = -73 in [1] we have;
2(12) - 3(-73) = 8
24 + 219 = 8
243 = 8 False.
Similarly for;
Option B
(-2, 4)
2(-2) - 3(4) = 8
-4 -12 = 8
-20 = 8 False.
Option C
(2, 43)
2(2) - 3(43) = 8
4-129= 8
-125= 8 False.
Option D
(-5, -6)
2(-5) - 3(-6) = 8
-10 +18 = 8
8 = 8 True.
Therefore, only (-5, -6) ordered pair is on the line 2x-3y = 8
Jon Ericson bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan.
At the end of 2 years he owes the bank $50,000. Now that interest rates have gone up to 13%, the bank will renew the mortgage at this rate or Jon can pay $50,000.
Jon decides to renew and will now pay $11.72 monthly per thousand on his loan. You can ignore the small amount of principal that has been paid.
What is the amount of the old monthly payment? $ ____
What is the amount of the new monthly payment? $ ____
What is the percent of increase in his new monthly payment? ____ %
You are told to ignore the amount of principal paid, so you are apparently to assume the loan amount was for $50 thousand.
a) The old monthly payment was $10.67×50 = $533.50
b) The new monthly payment is $11.72×50 = $586.00
c) The increase in monthly payment is figured in the usual way:
... (new/old -1)×100% = (1.0984-1)×100% = 9.84%
_____
In reality, about 3% of the loan will have been paid at the end of 2 years. Thus, the original loan amount may have been near $51,500. This problem is telling you to ignore the difference.
Remark
The first fact you need to know is that the bank has taken money from you and nothing has been reduced from the principle. Crafty people those bankers; you are going to pay off the interest before touching the principle. They're like you to refinance for the rest of your life at the rates you currently have.
Point. You started out with a 50k debt. You still have that same debt.
Solution
Givens
number of thousands (n) = 50000/1000 = 50
Amount paid per thousand (A) = 10.67
Total monthly payments (T) = ?
Part A
T = n * A
T = 50 * 10.67
T = 533.50 is the old monthly payment
Part B
T = n * A
T = 50 * 11.72
T = 586.00 new monthly payment.
Part C
This is a notes question. What have you been told in your notes on this question. You can find the raw amount just by subtracting 586 - 533.50 = 52.50
But how do you find the % increase. Which one of the payments do you use as your base?
In point of fact, you should be using the first number 533.5
What % will you get when you multiply that by 533.5 and get 52.50?
You are not trying to find 586. You are trying to find the number that you add to 533.5 to get to 586
The answer is (52.50 / 533.5)*100% = 9.84% is the % increase.
More Literal Expressions, please include the way you worked out.
A=h/2(a+b) solver for h
2A=h(a+b)
2A/(a+b)=h (Solution)
Solve the inequality |x| < 5. {x|-5 < x < 5} {x|x < -5 ∪ x > 5} {x|x -5 ∪ x < 5}
ANSWER
The correct answer is A
{[tex]x|-5<\:x<\:5[/tex]}
EXPLANATION
[tex]|x|<5[/tex]
This implies that
[tex]x<5\:or\:-x<5[/tex]
We solve the compound inequality to obtain,
[tex]x<5\:or\:x>-5[/tex]
Remember that, dividing through by negative 1 reverses the inequality sign
The solution set is
{[tex]x|-5<\:x<\:5[/tex]}
I just need help on number 14. Thank you very much.
I believe you only need to know one angle.
For example, if you know angle 1, you can calculate angle 3. Angle 2 = angle 3 and angle 4 = angle 1.
Also, Angle 5= angle 1 and so on...
A ferryboat makes four trips to an island each day.The ferry can hold 88 people.If the ferry is full on each trip,how many passengers are carried by the ferry each day?
That would be four times 88 passengers: 352 passengers per day.
Answer: 352
Step-by-step explanation:
88x4
HURRYYY!!! 20 POINTS AND BRAINLIEST IF CORRECT.
Which represents where f(x) = g(x)?
f(2) = g(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Its A i did the test
what is the answer for 300/2 by changing the number from mixed to improper and simplify at the end if needed
Simplify. Divide the number
300/2 = 150
150 is your answer (it is a whole number, no need to change to improper, unless you want 150/1)
hope this helps
will give brainliest plz hep!!!!!
Which line is a graph of the equation: 2x + 5y = 10?
Number graph ranging from negative five to five on the x axis and negative six to two on the y axis. Four lines are drawn in blue on the graph. Lines a and c have a positive slope and are parallel to each other. Lines b and d have a negative slope and are parallel to each other. Lines a and b intersect at (zero, two), and lines c and d intersect at (zero, negative two).
A. line a B. line b C. line c D. line d
Answer: The equation is of line "b"
Step-by-step explanation:
First we find the slope of the given line by using slope intercept form.
Converting the equation into slope intercept form
[tex] 5y=-2x+10 [/tex]
Divide both side by 5 we get
[tex] y= \frac{-2}{5} x+ 2 [/tex]
On comparing with
[tex] y =mx+c [/tex]
We get slope [tex] m=\frac{-2}{5} [/tex]
as the slope of line is negative therefore the line will be either line "b" or line "d"
As line "b" pass from (0,2)
On putting point [tex] x=0 &y=2[/tex] in given equation we get
[tex] 2(0)+5(2)=0+10=10 [/tex]
Which is equal to RHS of the line
Therefore the given equation is of line "b"
Now putting point (0,-2)
We get [tex] 2(0)+5(-2)=-10 [/tex]
Which is not equal to RHS and therefore line "d" is not the required line
Therefore the given equation is of line "b"
which is the slope of the like represented by the equation 2x+3y=-12
slope = - [tex]\frac{2}{3}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 2x + 3y = - 12 into this form
subtract 2x from both sides
3y = - 2x - 12 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x - 4 ← in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
[tex]\text{The slope-intercept form:}\ y=mx+b\\m-slope,\ b-y-intercept\\\\2x+3y=-12\qquad|\text{subtract 2x from both sides}\\\\3y=-2x-12\qquad|\text{divide both sides by 3}\\\\y=-\dfrac{2}{3}x-4\\\\Answer:\ \boxed{m=-\dfrac{2}{3}}[/tex]
what is the equation of the line
y = 1/2x - 4
y = 2x - 4
y = 2x + 2
y = 1/2x + 2
y = [tex]\frac{1}{2}[/tex] x + 2
the equation of a line in slope-intercept form is
y = mx + c (m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 4, 0 ) ← points from graph
m = [tex]\frac{0-2}{-4-0}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]
from the graph the y-intercept = (0, 2 ) → c = 2
y = [tex]\frac{1}{2}[/tex] x + 2 ← is the equation
The equation of the line is [tex]y = \frac{1}{2}x + 2[/tex]
The calculation is as follows:The equation of a line in slope-intercept form is
y = mx + c
Here m is the slope and c is the y-intercept
Now
[tex]m = ( y_2 - y_1 ) \div (x_2 - x_1 )[/tex]
Here
[tex](x_1, y_1 )[/tex]= (0, 2 ) and [tex](x_2, y_2 )[/tex] = (- 4, 0 )
Now
[tex]m = (0-2) \div (-4-0)\\\\= -2\div -4\\\\= \frac{1}{2}[/tex]
From the graph the y-intercept = (0, 2 ) i.e. c = 2
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If (c) were f(k) = -3/k+2, what value of k would be excluded from the domain?
k = - 2 is excluded from the domain
the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that k cannot be
solve k + 2 = 0 ⇒ k = - 2 ← excluded value
Jo flips a coin {H, T}; then rolls a 6-sided die {1, 2, 3, 4, 5, 6}.
How many possible outcomes are in the sample space of this experiment?
A. 4
B. 8
C. 12
D. 36
Answer:
Option C
Step-by-step explanation:
A coin has two outcomes Head (H) and tail (T).
So, the number of outcomes when a coin is tossed = 2
A coin has six outcomes [tex]\left \{ 1,2,3,4,5,6 \right \}[/tex]
So, the number of outcomes when a coin is tossed = 6
Therefore, possible outcomes when Jo flips a coin and then rolls a 6-sided die are [tex]\left \{ H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6 \right \}[/tex]
So, the number of possible outcomes = 12
Option C. is correct.
Using the concept of sample space, it is found that the number of possible outcomes in the experiment is given by:
C. 12
The sample space of an experiment is the set that contains all possible outcomes.
In this problem:
For the coin, there are 2 outcomes.For the dice, there are 6 outcomes.The coin and the dice are independent, thus, there are 2 x 6 = 12 possible outcomes, which means that the correct option is:
C. 12
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The price of a round trip ticket to San Francisco increases from $525.00 to $650.00. To the nearest whole percent, what is the percent of increase?
A) 18%
B) 24%
C) 28%
D) 30%
E) 34%
B
to calculate percent increase use
[tex]\frac{increase}{original}[/tex] × 100%
increase = $650 - $525 = $125
percent increase = [tex]\frac{125}{525}[/tex] × 100% = 24% → B
Answer:
The answer is B) 24%
Step-by-step explanation:
The formula for percentage increase is given as:-
Percentage Increase = ( New Price - Old Price ) /old price * 100
old price = $525
New Price = $650
Percentage Increase = 24%
Hence the price increases by 24%
Explain how (13 + 10) + 5 is solved differently from 13 + (10 + 5). A) For (13 + 10) + 5, you add 13 + 5 first, then add 10. For 13 + (10 + 5), you add the 10 + 13 first, then add 5. Eliminate B) For (13 + 10) + 5, you add 13 + 10 first, then add 5. For 13 + (10 + 5), you add the 10 + 5 first, then add 13. C) For (13 + 10) + 5, you add 13 - 10 first, then add 5. For 13 + (10 + 5), you add the 10 - 5 first, then add 13. D) For (13 + 10) + 5, you add 13 + 10 first, then subtract 5. For 13 + (10 + 5), you add the 10 + 5 first, then subtract 13.
Answer:
The answer is B
Step-by-step explanation:
Simple use P.E.M.D.A.S
Parentheses are always first, you add 13+10 then evaluate everything else.
Have a great day.
__________ are pairs of angles formed when a third line (transversal) intersects two other lines. These angles are on the opposite sides of the transversal and are between the other two lines.
"Opposite sides of the transversal..." Alternate
"Between the other two lines." Interior
Alternate Interior angles.
If they were outside the two lines they would be alternate exterior angles and if they were on the same side of the transversal then they would be corresponding angles.
find the sum (2x−6)+4(x−3)
The sum of the given expressions will be 6x-18.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression is (2x−6)+4(x−3). The summation will be calculated as
Sum = (2x-6)+4(x-3)
Sum = (2x-6)+4x-12
Then we combine like terms.
Sum = (2x-6)+4x-12
Sum = 6x-6-12
Sum = 6x-18
Therefore, the sum of the given expressions will be 6x-18.
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A number and its absolute value are equal. If you subtract two from the number, the new number and its absolute value are not equal. What do you know about the number?
A number and its absolute value are not equal when the number is less than zero. Since subtracting 2 makes the number less than zero, we know ...
... the number is a non-negative number less than 2. (0 ≤ n < 2)