Answer:
(a) 1825 = 2.25x + (2.25-1)(x -108)
(b) 560 mi/h
Step-by-step explanation:
(a) distance = speed·time
The first plane's speed is x. The distance it travels in 2.25 hours is 2.25x.
The second plane's speed is x-108. It travels only 1.25 hours (since it started an hour later). The distance it travels is then (2.25 -1)(x -108).
The problem statement tells us the total of the distances traveled by the two planes is 1825 miles, so we can write the equation ...
... 1825 = 2.25x + (2.25 -1)(x -108)
(b) Simplifying the equation gives ...
... 1825 = 3.50x -135
To solve this 2-step equation, we add 135, then divide by 3.50.
.. 1960 = 3.50x
... 1960/3.50 = x = 560
The first airplane's speed is 560 mph.
Check
In 2.25 hours, the first plane travels (560 mi/h)·(2.25 h) = 1260 mi.
In 1.25 hours, the second plane travels (452 mi/h)·(1.25 h) = 565 mi.
Then 2.25 hours after the first plane leaves, the planes are 1260 +565 = 1825 miles apart, as given in the problem statement.
The first plane's average rate is 560 mph. The equation that can be used to solve this problem is 2.25x + 1.25(x - 108) = 1825
To solve this problem, we need to set up an equation based on the information given.
First, let x represent the first plane's average rate in miles per hour (mph).The first plane left at 9:00 a.m. and traveled for 2.25 hours at x mph.The second plane left at 10:00 a.m., which is 1.25 hours before the distance was measured. Its speed is x - 108 mph (108 mph slower than the first plane).Using the distance formula (Distance = Speed x Time), we can write the distances covered by both planes.The first plane covered a distance of 2.25x miles.The second plane covered a distance of 1.25(x - 108) miles.The total distance between the two planes is the sum of their traveled distances: 2.25x + 1.25(x - 108) = 1825 miles.Simplifying the equation gives us:
2.25x + 1.25x - 135 = 1825
3.5x - 135 = 1825
Adding 135 to both sides:
3.5x = 1960
Dividing by 3.5:
x = 560
Therefore, the first plane's average rate was 560 mph.
I organized an ocean cleanup and we collected a total of 25 pounds of garbage 16 pounds of the garbage consisted of plastic what percent of the garbage was plastic
64%. You would divide 16 from 25 because you're trying to find the amount of garbage that was plastic.
Hope this helped! :)
Line segments JK and JL in the xy-coordinate plane both have a common endpoint J(-4,11) and midpoints at M, (2, 16) and M2 (-3,5), respectively. What is the distance between M, and M2? Round to the nearest tenth.
Answer:
12.1
Step-by-step explanation:
We use the formula for the distance between two arbitrary points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the xy-coordinate plane, that is:
[tex]d=\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}[/tex]
So, replacing the points [tex]M=(2,16)[/tex] and [tex]M_2=(-3,5)[/tex], we obtain:
[tex]d=\sqrt{(2-(-3))^2 + (16-5)^2}\\d=\sqrt{(2+3)^2 + (16-5)^2}\\d=\sqrt{5^2 + 11^2}\\d=\sqrt{146 }=12.083045... \simeq 12.1[/tex]
that is the answer.
note: observe that we only use the coordinates between the two midpoints and not the point J.
Simplify the expression where possible. (-4x 2) 2
Answer: 16x^4
Step-by-step explanation:
Find an equation for the plane which passes through the point p(1,3,3) and contains the line: l:x(t)=3t,y(t)=2t,z(t)=4+3t
Answer:
Step-by-step explanation:
Given that the plane passes through (1,3,3)
Also the plane contains the line x(t)=3t,y(t)=2t,z(t)=4+3t.
This means all points lying in this line will also lie in the plane.
Find out two points on this line.
First point: Let t =0. Point is (0,0,4)
Next point : Let t = 1: Point is (3,2,7)
Now we have 3 non collinear points (0,0,4) (3,2,7) and (1,3,3) lying on the plane.
Equation of the plane is
[tex]\left[\begin{array}{ccc}x-0&y-0&z-4\\3&2&3\\1&3&-1\end{array}\right] =0[/tex]
Simplify to get
x(-2-9)-y(-3-3)+(z-4)(9-2)=0
i.e -11x+6y+7z-28 =0
11x-6y-7z+28 =0 is the equation of the plane.
I got this one wrong please help I don't understand must so work...
If each item Kathy puts in the box weighs 2 kg, then the weight of p items will be 2p kilograms. Since the box weighs 1 kg, the total weight in kilograms will be ...
... 2p + 1
Kathy wants that value to be less than or equal to 10 kg, so her inequality will be
... 2p + 1 ≤ 10 . . . . . corresponds to selection D
i need help with this!
Answer:
bc
Step-by-step explanation:
The multiplication property of equality tells you that you can multiply both sides of the equation by the same amount. Choose that amount to be bd, the product of the denominators.
[tex]\dfrac{a}{b}=\dfrac{c}{d}\\\\\dfrac{a\cdot bd}{b}=\dfrac{c\cdot bd}{d}\\\\ad\dfrac{b}{b}=bc\dfrac{d}{d}\\\\ad=bc[/tex]
help please!!!!!!!!!!!!!!
1. You can make use of the Pythagorean theorem considering "a" to be the longer leg of the largest right triangle. Then the value of "a" can be calculated from
(16+9)² = 15² +a²
625 -225 = a²
√400 = a = 20
2. You can find the altitude of the largest triangle (the length of the unmarked vertical line), then find "a" as the hypotenuse of the medium-sized right triangle.
That altitude is ...
√(15² -9²) = √144 = 12
so the length "a" is ...
a² = 12² +16² = 144 +256 = 400
a = √400 = 20
3. Based on the 15 and 9 dimensions of the smallest right triangle, you can realize that these triangles are multiples of the 3-4-5 right triangle. Then you can use relevant ratios of the side lengths of any of the triangles of which "a" is a part.
a = 4/3×15 = 4/5×(9+16) = 5/4×16 = 20
One number is 11 more than twice another number. If the sum of the numbers is twice their difference, find the numbers.
Answer: 33 and 11
Step-by-step explanation: Both 11 and 33 would be the answr because 11 by the 2wice would be 33, and also 11 it's self would be the answer.
The numbers are x = 33 and y = 11 respectively.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is that one number is 11 more than twice another number and the sum of the numbers is twice their difference
Assume that the numbers are (x) and (y). Then, we can the model the equation as follows -
x = 2y + 11
x + y = 2(x - y)
Simplifying the equations, we can write -
x + y = 2(x - y)
x + y = 2x - 2y
2x - x - 2y - y = 0
x - 3y = 0
y = x/3
Put y = x/3 in x = 2y + 11, we get -
x = 2x/3 + 11
x - 2x/3 = 11
x/3 = 11
x = 33
then y = 33/3 = 11
Therefore, the numbers are x = 33 and y = 11 respectively.
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what is 15/1/20 as a improper fraction
I need help on this one please and thank you
The fair market rental rate for Fort Wayne was $611 in 2011 and $567 in 2005. Find the unit rate of change for rent in Fort Wayne during this period
If you assume the rental cost changes in a linear fashion, the change over 6 years was $44. The "unit rate of change" is then $44/(6 years) ≈ $7.33/year.
When attempting to do his/her homework, a student uses the addition property of equality to solve for a below. Which statement BEST applies to the sample below? a + 3 = 9 a + 3 – 3 = 9 – 9 a = 0 A. The student failed to keep both sides of the equation balanced. B. The student’s final answer does not have the variable a isolated. C. The use of the addition property of equality is sound, and the answer is correct. D. The student should have added 3 to the left side of the equation rather than subtracting.
The appropriate choice is ...
.... A. The student failed to keep both sides of the equation balanced
_____
The one rule I learned in my study of Algebra that makes it all make sense is "keep the equal sign sacred." That is, whatever you do to one side of the equation must also be done to the other side of the equation. (Various teachers show various shortcuts that make it look like you're doing different things to the different sides of the equation. Don't be confused. If the operation can't be put in terms of doing the same thing to both sides, it doesn't work.)
Of course, you can always add 0 or multiply by 1 whenever and wherever you want.
_____
For the above equation, the appropriate solution is
... a + 3 = 9
... a + 3 - 3 = 9 - 3 . . . . . . addition property of equality
... a + 0 = 6 . . . . . . . . . . . .rules of arithmetic
... a = 6 . . . . . . . . . . . . . . . additive identity property of 0
x/2 + 3 = -5 please help me
Hey there!!
Given equation :
... [tex]\frac{x}{2} + 3 = -5[/tex]
Subtracting 3 on both sides :
... [tex]\frac{x}{2} = -8[/tex]
Multiplying 2 on both sides :
... [tex]x = -16[/tex]
Hope my answer helps!!
the answer for x would be -16
Plz help will mark brainliest.
For the graph shown, the slope is changed to 1/5, but the y-intercept remains the same What is the resulting question equation for the new graph?
A. y=x+1/5
B. y=x-1/5
C. y= 1/5*+1
D. y= 1/5*-1
The answer is c since it has a slope of 1/5 and a y-intercept of 1
Remark
So far what you have is the y intercept which according the graph, is (0,1)
The general equation is y = mx + b
If you put the following point (0,1) into the general line formula, you will get b
Givens
y = 1
x = 0
Solve
Substitute the givens into the general line
1 = m*0 + b The m is no longer there.
b = 1 The y intercept is 1
So far what you have is
y = mx + 1
The problem tells you that the slope (m) = 1/5
The equation is y = (1/5)x + 1
None of the answers are correct. There is no x anywhere that is right. If x was present, the answer would be C.
I need help with this one please d÷12=1/6
Answer
d = 2
Step-by-step explanation:
d divided by 12 is the same as d/12?
d/12 = 1/6
cross multiply and get 12 = 6d.
6(2) = 12.
Divide 12 by 2 and you get 2/12 which simplifies to 1/6.
Hope I helped. ^-^
d = 2
given [tex]\frac{d}{12}[/tex] = [tex]\frac{1}{6}[/tex]
multiply both sides by 12
d = 12 × [tex]\frac{1}{6}[/tex] = 2
Lena is making two dishes for an event. Each batch of her and cheese recipe calls for 6 ounces of cheese and 2 tablespoons of basil. For every two pizzas she needs 16 ounces of cheese and 5 tablespoons of basil. Lena buys 32 oz package of cheese. Does she have enough to make 2 batches of Mac and cheese and 3 pizzas
Answer: No, it is not enough to make 2 batches of Mac and cheese and 3 pizzas.
Step-by-step explanation:
Since we have given that
She needed 6 ounces of cheese and 2 tablespoons of basil for each batch of her Mac and cheese.
Now,
For every two pizzas she needed 16 ounces of cheese and 5 tablespoons of basil.
So, for 2 batches of Mac and cheese she needed = 12 ounces of cheese
and if for 2 pizzas she needed = 16 ounces of cheese
For 1 pizza she needed = 8 ounces of cheese
For 3 pizza she needed = 8× 3=24 ounces of cheese
Total requirement of cheese = 24+ 12=36 ounces
But she only buys 32 ounces package of cheese .
So, it is not enough to make 2 batches of Mac and cheese and 3 pizzas and 4 ounces is still needed i.e.
36-32 =4 ounces .
Lena bought a 32 oz package of cheese, and since 60 ounces is greater than 32 ounces, she does not have enough cheese to make 2 batches of Mac and cheese and 3 pizzas with her current supply.
What is the cheese recipeIf Lena has enough cheese to make 2 batches of Mac and cheese and 3 pizzas.
Each batch of Mac and cheese requires 6 ounces of cheese, and she wants to make 2 batches,
so that's 6 ounces * 2
= 12
Each pizza requires 16 ounces of cheese, and she wants to make 3 pizzas,
so that's 16 ounces * 3
= 48
In total, for the Mac and cheese and the pizzas,
Lena needs 12 ounces + 48 ounces
= 60 ounces of cheese.
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Consider the trigonometric function f(x)=4cos(2x pi/2) +9
How do you determine the minimum and maximum values of this function?
Answer:
Make use of your knowledge of the maximum and minimum of the cosine function. Then scale and translate according to the way that function is scaled and translated to make f(x).
Step-by-step explanation:
f(x) is the cosine function, multplied by 4 and with 9 added to the result.
The minimum of the cosine function is -1. Multiplying that by 4 gives -4, and adding 9 gives 5.
The maximum of the cosine function is +1. Multiplying that by 4 gives +4, and adding 9 gives 13.
The minimum and maximum of f(x) are 5 and 13, respectively.
Max and Min:
Max = 13
Min = 5
COS Standard Period
[tex]2\pi[/tex]
COS Period with a multiplier of 2 on x
[tex]\pi[/tex]
COS Period with a multiplier of 2 on x and a Phase Shift
Answer to period
[tex]\frac{5}{4}\pi[/tex]
Step-By-Step Explanation:
Please view the image I have provided.
A car is traveling at a constant speed of 46 miles per hour. the formula for the distance traveled at the end of t hours is d=46t. Represent the distance at the end of 7,12, and 18 hours as ordered pairs in the form (t,d).
d = 46t
First, let's find "d" for 7 hours.d = 46(7)
d = 322 miles (7, 322)
Next, let's find "d" for 12 hours.d = 46(12)
d = 552 miles (12, 552)
Finally, let's find "d" for 18 hours.d = 46(18)
d = 828 miles (18, 828)
NEED HELP NOW!
The values in the table define the function f(x) . The value of f ^-1(3) is , and the value of f^-1(8) is .
f^-1 is found by reading the table from right to left, so find the f(x) number in the right hand column and f^-1 would be the number in the left hand column.
When f(x) = 3, x = 2
f^-1(3) would be 2
When f(x) = 8, x = 7
f^-1(8) = 7
As per the given value of the function , value of [tex]f^{-1}(3) = 2[/tex] and [tex]f^{-1}(8) = 7[/tex].
What is function?" Function is defined as the for each input value there is one and only one output."
According to the question,
From the given table value of function [tex]f(x)[/tex]defined for [tex]x[/tex]
Consider,
[tex]f(x) = y\\\\\implies x = f^{-1}(y)[/tex]
Value of required function we get,
[tex]y= 3\\\\\implies f^{-1}(3)= 2[/tex]
[tex]y= 8\\\\\implies f^{-1}(8)= 7[/tex]
Hence, as per the given value of the function , value of [tex]f^{-1}(3) = 2[/tex] and [tex]f^{-1}(8) = 7[/tex].
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please help! square root
Helpppppppppppppppp pleaseeeeeeeeeeeee
Factor. 9x^2+27x+45
9x^2 + 27x + 18 . hope i helped
The factors of the quadratic equation are (-3 - √11i) and (-3 + √11i).
What is a quadratic equation?A quadratic equation is an algebraic equation of degree 2.
Given a quadratic equation 9x² + 27x + 45 = 0.
We know simplifying a quadratic equation doesn't change the roots of the equation.
∴ We can divide each of the terms by 9 which makes the quadratic equation x² + 3x + 5 = 0.
Now two numbers which multiplied to 5 and add to 3 are not possible for real numbers, therefore, the roots must be imaginary.
We know Sridhar Acharya's formula which is [tex]\frac{ - b \pm\sqrt{b^2 - 4ac}}{2a}[/tex].
[tex]= \frac{ - 3 \pm\sqrt{3^2 - 4.1.5}}{2.1}[/tex].
[tex]= \frac{ - 3 \pm\sqrt{9 - 20}}{2}[/tex].
[tex]= \frac{ - 3 \pm\sqrt{-11}}{2}[/tex].
[tex]= \frac{ - 3 \pm\sqrt{11}i}{2}[/tex].
Therefore the factors of the quadratic equation are
(-3 - √11i) and (-3 + √11i).
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simplify 35x^3y^5/7x^2y^4 show work mark brainliest only answer if you know how to do laws of exponents
When you write expressions like this, you need to pay attention to the Order of Operations. As this is written, the only factor in the denominator is the one immediately after the division symbol: 7. This simplifies to
... (35/7)·x^(3+2)·y^(5+4) = 5x^5y^9
_____
We suspect you might intend ...
... (35x^3y^5)/(7x^2y^4) = (35/7)x^(3-2)y^(5-4) = 5xy
What is the definition where of additive inverse?
758x93= What is the answer and how to solve it
The answer is 70494.
Mr. Marquis had a metal pipe that was 1,000 cm in length. He cut the pipe into 16 shorter pieces of equal length. How long was each piece?
To answer this, divide 1000 cm by 16:
1000 cm
------------------ = 66 2/3 cm per piece
16 pieces
Q # 3 The scatter plot shows the number of mistakes a piano student makes during a recital versus the amount of time the student practiced for the recital .How many mistakes do you expect the student to make at the recital a free 6 hours of practicing?
Answer: Fourth option. 55 mistakes
Solution:
Please, see the attached graph.
Thanks.
Determine the solution to the following system of linear equations.
5x - 5y = 20
-2x + 2y = -4
no solution
infinitely many solutions
(5, 1)
(2, -2)
Answer:
no solution
Step-by-step explanation:
To put the first equation into standard form, with the coefficients mutually prime, divide it by 5:
... x - y = 4
To put the second equation into standard form, with the coefficients mutually prime and the leading coefficient positive, divide by -2:
... x - y = 2
These are inconsistent equations, hence have no solution.
Answer:
a
Step-by-step explanation:
given sin theta = 2/5 and 0 theta 90 find sin 2 theta
Given: sin theta = 2/5. This tells us that the lengths of the opp side and the hyp are 2 and 5 respectively. The adj side is found using the Pyth. Thm.: 5^2-2^2= 25-4 = 21, so that the adj side is sqrt(21).
The double angle formula for the sine is sin 2theta = 2 sin theta *cos theta.
In this particular problem, the sine of 2theta is 2*(2/5)*[sqrt(21) / 5], or:
(4/25)*sqrt(21).
Answer:
The value of [tex]\sin^2 \theta=\frac{4}{25}[/tex]
Step-by-step explanation:
Given : [tex]\sin \thet=\frac{2}{5}[/tex] and [tex]0<\theta<90[/tex]
To find : The value of [tex]\sin^2\theta[/tex] ?
Solution :
We have given the value of [tex]\sin \thet=\frac{2}{5}[/tex] and [tex]0<\theta<90[/tex]
To find [tex]\sin^2\theta[/tex] we just have to square [tex]\sin\theta[/tex]
[tex]\sin \theta=\frac{2}{5}[/tex]
Squaring both sides,
[tex](\sin \theta)^2=(\frac{2}{5})^2[/tex]
[tex]\sin^2 \theta=\frac{4}{25}[/tex]
Therefore, The value of [tex]\sin^2 \theta=\frac{4}{25}[/tex]
Please Help ASAP 20 points Find the slope of the line through the given points. (−1, 2) and (−5,10) (1,3) and (0,−9) (18, 6) and (−7, 7) (−7, 10 ) and (1, 10)
The slope we can get from using this y1-y2/x1-x2
so
10-3/-5-1=7/-6=-1 1/6
There's your slope
Find the coordinates of the points of intersection of the graphs with coordinate axes: y=−2x+4
You must get two equation to find point of intersections
Answer:
x = (2,0)
y = (0,4)
Step-by-step explanation:
Solve For x:
Lets take y as 0 so the equation is 0 = -2x + 4, and if we simplify the expression we get x = 4/2 which s x = 2 so the answer for x is (2,0)
Solve for y:
Lets take x as 0 so the equation is y = -2 · 0 + 4 which simplyfied to y = 4, so the answer for y is (0,4)