(18 1/5 * (-22 2/5)) - (-40 1/5) = -367.48
(-t^3+5t^2-6t)+(8t^2-8t)
Answer:
-t^3+13t^2-14t
Step-by-step explanation:
(-t^3+5t^2-6t)+(8t^2-8t)
Combine like terms
-t^3+5t^2+8t^2-6t-8t
-t^3+13t^2-14t
writie any assay about challenges of teaching mathematics on 21st century
A 10-ft ladder, whose base is sitting on level ground, is leaning at an angle against a vertical wall when its base starts to slide away from the vertical wall. When the base of the ladder is 6 ft away from the bottom of the vertical wall, the base is sliding away at a rate of 4 ft/sec. At what rate is the vertical distance from the top of the ladder to the ground changing at this moment?
Answer:
2.5/ft per sec
Step-by-step explanation:
its vertica.
The height of the ladder is decreasing at a rate of 24 ft/sec.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Let's denote the distance between the base of the ladder and the wall by x.
The length of the ladder = L.
Now,
L = 10 ft
dx/dt = 4 ft/sec
x = 6 ft.
The rate of change of the height of the ladder with respect to time.
Using the Pythagorean theorem, we have:
L² = x² + y²
Differentiating both sides with respect to time t, we get:
2L (dL/dt) = 2x(dx/dt) + 2y(dy/dt)
Substituting L = 10 ft, x = 6 ft, and dx/dt = 4 ft/sec.
20(dL/dt) = 12(4) + 2y(dy/dt)
Simplifying and solving for dy/dt.
dy/dt = (20/2y)(dL/dt) - 24
Now,
The height of the ladder.
Using the Pythagorean theorem again, we have:
y² = L² - x²
= 100 - 36
= 64
y = 8
Now,
Substituting y = 8 ft, dL/dt = 0
(since the length of the ladder is constant), and dx/dt = 4 ft/sec.
dy/dt
= (20/2(8))(0) - 24
= -24 ft/sec
Therefore,
The height of the ladder is decreasing at a rate of 24 ft/sec.
Learn more about the Pythagorean theorem here:
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Find the length of DM
Answer:
67
Step-by-step explanation:
DM=JM-JD=84-17=67
Answer:
Step-by-step explanation:
Solve each system by graphing.
9514 1404 393
Answer:
(x, y) = (4, -3)
Step-by-step explanation:
The solution is the point on the graph where the lines intersect:
(x, y) = (4, -3)
HURRY PLEASE!!
2 •(3(5+2)-1)
Answer:
hopei help you
Step-by-step explanation:
mark i brainliest answer
Answer: 40
Concept:
When encountering questions that ask for simplifying expressions, the easiest way is to follow the PEMDAS method:
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionSolve:
Given
2 · (3 (5 + 2) - 1)
Simplify parentheses by addition
=2 · (3 × 7 - 1)
Simpify multiplication first, then subraction
= 2 · (21 - 1)
= 2 · 20
Simplify multiplication
= 40
Hope this helps!! :)
Please let me know if you have any questions
Cheyenne's bi-weekly gross pay is $529.81. She sees that $18.54 was deducted for Medicare tax. What percent of Cheyenne's gross pay has been withheld for Medicare tax? Round to the nearest tenth. (2 points)
0.35%
2.2%
3.5%
Answer:
I got 3.5%
Step-by-step explanation:
Hope this helps
Which phrase describes the linear relationship between the x and y values shown in the table?
x l y
8 l 2
9 l 3
10 l 4
A. y is 6 times x
B. x is 6 times y
C. y is 6 less than x
D. y is 6 more than x
9514 1404 393
Answer:
C. y is 6 less than x
Step-by-step explanation:
It is not hard to check.
A. 6 times x is 6×8 = 48, not 2
B. 6 times y is 6×2 = 12, not 8
C. 6 less than 8 is 2; 6 less than 9 is 3
D. 6 more than 8 is 14, not 2
__
The relation described in C matches the table.
Solve this inequality:
-12a +7<31
Answer:
a > -2
Step-by-step explanation:
-12a +7<31
Subtract 7 from each side
-12a +7-7<31-7
-12a <24
Divide by -12, remembering to flip the inequality
-12a/-12 >24/-12
a > -2
Answer:
a>-2
Step-by-step explanation:
[tex]\sf{}[/tex]
=> -12a +7 <31
=> -12a+7-7<31-7
=> -12a<24
=> a>-2
Because the sum of angle measures in each triangle is 180°, the
sum of interior angle measures in a quadrilateral is
2 x 180°=
Answer:
It's 360
Step-by-step explanation:
2 x 180 = 360
Graph the line.
Y=-1/4x+4
Select the correct answers in the table.
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?
I need help plz!!
8.57396817...•5/8 is rational or irrational?
Answer:
Irrational
Step-by-step explanation:
Any non-zero rational number multiplied by an irrational number will be irrational. We can rewrite this as (8.57... * 5) / 8, but we have no idea how to make 8.57... * 5 rational, or expressed as the quotient of two integers.
It used to take 20 hours to get to Los Angeles, now it takes 12 hours, how much shorter was it?
Step-by-step explanation:
It takes 20 Hours to get to Los Angeles
Now it takes 12 hours....
Therefore we subtract 20 from 12
which becomes
20 - 12= 8.
So it's 8 hours shorter
In a geometric sequence, t4 = 8 and t7 = 216. Find the value of t2
Question 14 plz show ALL STEPS ASAP
Answer:
8/9
Step-by-step explanation:
Let the geometric series have the first term=a and common ratio=r. ATQ, ar^3=8 and ar^6=216. r^3=27. r=3. a=8/3^3=8/27. t2=ar=8/9
I need help with this please
Answer:
26. 35
27. 65
28. 13
Step-by-step explanation:
26. The big angle POR is given as 59 and the smaller angle inside it (POQ) is given as 24. Since the angles POQ and QOR add up to the angle POR,
QOR = POR - POQ | 59-24 = 35
27. We are given the angles of all the smaller angles in the large angle POS. POQ, QOR and ROS are 19, 31 and 15 respectively. Since all of them add up to create the angle POS, POS = 19+31+15 = 65
28. We can use the second and third given angles (POR and POQ) to find the QOR which we can then use to find ROS. This first step is very similar to 26. We are given POR as 61 and POQ as 28, therefore QOR = 61-28 = 33
Since we now know QOR and QOS, we can repeat the process and deduct that because the two smaller angles add up to the bigger one (QOS), we can find ROS by subtracting QOR (from above) from the given QOS (46):
46 - 33 = 13
Hope this helped!
Find the greatest common factor of these two expressions.
14w5y8x2 and 7w6x2
Answer:
[tex]7w^{5}x^{2}[/tex]
Step-by-step explanation:
We can start by looking at each variable and and constant separately. In the first one, the constant part is 14 and in the second its 7. We can notice that the GCF of these two is 7. Next we have the part with w. The first one is w^5 while the second is w^6. We can notice that we can factor w^5 out of both, so it is the GCF. We can notice that only the first one has a y, so we can ignore it since it is not in common with both expressions. Lastly, we have x: the first has x^2 and the second has x^2 as well. They are the same, so the GCF would just be x^2.
Now, we can multiply the results together to get the GCF of the whole expressions:
7 * w^5 * x^2 = [tex]7w^{5}x^{2}[/tex]
Mandy has $25 and she plans to save $2 each week. Her brother
Thomas has no money now, but he plans to save $3 each week.
Make a table that shows the amount of money Mandy and
Thomas have every week for 10 weeks. Let m be the
amount of money Mandy has and let y be the amount of
money Thomas has.
Write two different algebraic expressions to describe each
person's savings.
Tyler and Gabe went to the arcade and played the same two games, Tyler played five rounds of each game for 30$. Write two equations for the amounts the two boys spent. Then find the cost for one round each game.
Equations:
1. (30)(5)= 150
2. 30 + 30 + 30 + 30 + 30 = 150
I round:
30 dollars divided by 5 rounds = 6 dollars per round.
The total amount spent by the two boys is $300.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that Tyler and Gabe went to the arcade and played the same two games. Tyler played five rounds of each game for 30$.
We can write the total amount spent by the two boys as -
total amount = 2 x cost of each game x total number of games played
total amount = 2 x 30 x 5
total amount = 10 x 30
total amount = 300
Therefore, the total amount spent by the two boys is $300.
To solve more questions on equivalent expression, visit the link-
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Ginny writes down a secret number on her palm. She says that it is a three-digit even number. The units digit is 1 more than the hundreds digit. The tens digit is twice the sum of the units digit and the hundreds digit.
Answer:
Hello,
Answer 162
Step-by-step explanation:
Let say n the searched number.
[tex]n=\overline{abc}\\a>0\\c=a+1\\b=2*(a+c)\\\\.T.\ means\ True.\\\\\\\begin{array}{c|c|c|c}a&c&b&ok\\1&2&6&.T.\\3&4&14&.F.\\5&6&22&.F.\\7&8&30&.F.\end{array}\\\\\\\boxed{Answer\ n=162}\\[/tex]
Solve each equation.
1)-9 + x = 4
What is the GCF of the expression 5x2y + 10xy2?
Answer:
[tex]5xy[/tex]
Step-by-step explanation:
[tex]\mathrm{Factor\:}:5x^2y[/tex]
[tex]5\cdot \:x\cdot \:x\cdot \:y[/tex]
[tex]\mathrm{Factor\:}:10xy^2[/tex]
[tex]2\cdot \:5\cdot \:x\cdot \:y\cdot \:y[/tex]
Common factor:-
[tex]5\cdot \:x\cdot \:y[/tex]
OAmalOHopeO
Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))
Probably a simple answer, but I'm completely lost at what I'm being asked here.
Answer:
[tex]\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}[/tex]
Step-by-step explanation:
We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:
[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]
So, we can let j be the inverse function of h.
Function h is given by:
[tex]\displaystyle h(x) = y = 3x-2[/tex]
Find its inverse. Flip variables:
[tex]x = 3y - 2[/tex]
Solve for y. Add:
[tex]\displaystyle x + 2 = 3y[/tex]
Hence:
[tex]\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}[/tex]
Therefore, a = 1/3 and b = 2/3.
We can verify our solution:
[tex]\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}[/tex]
15 points PLEASE ANSWER
Answer:
D. (25π - 50) sq m
Step-by-step explanation:
Since ABCD is a square with the area of 100, we know that the dimensions are 10 by 10. With that, we can find that triangle ABC = 50 sq m because of (h*l)/2. Since A is the center of the circle that contains arc BD, we know that 10 is the radius of the quarter-circle ABC. Using (πr^2)/4 to get the area of the quarter-circle, we get that the quarter-circle ABC = 25π sq m. But the original triangle ABC in the quarter-circle is not shaded. Therefore, we subtract 50 from 25π, which leads to (25π - 50) sq m.
I hope this helped! :D
If x + 1 =3, then x=
Answer:
x = 2
Step-by-step explanation:
x + 1 = 3
transpose
x = 3-1
x= 2
You have 3 quarts of brown stock. you need 3 cups to make one serving of braised short ribs How many can you make
Answer:
4
Step-by-step explanation:
there are 3 cups in a quart
since there are 3 quarts i.e 4*3=12
since you need 3 cups to make a serving
12/3 =4 servings can be made
Mark earns $47,800 a year working for a delivery service. He is single and pays $2,152.60 in state income tax each year. He claims no dependents. What is the tax rate of Mark’s state he lives in?
Answer:
4.5%
Step-by-step explanation:
The tax rate=(2152.6/47800)*100=4.5%
I want to know the distance
here's the answer to your question
rmined that her father’s age is four less than three times her age. If a represents Marcy’s age, which expression represents her fathers age?
Answer:
3x - 4 is the expression that will represent her father's age
solve for x ! please help . (show work)
Answer:
x = -3
Step-by-step explanation:
12 - 4x-5x = 39
Combine like terms
12 - 9x = 39
subtract 12 from each side
12 -9x-12 = 39-12
-9x = 27
Divide by -9
-9x/-9 = 27/-9
x = -3
