The perimeter of a rectangle is 138
meters and the area is 1080 square
meters. Find the length and the width of
the rectangle.
Answers
Related Questions
One base of a trapezoid is decreasing at a rate of 888 kilometers per second and the height of the trapezoid is increasing at a rate of 555 kilometers per second. The other base of the trapezoid is fixed at 444 kilometers. At a certain instant, the decreasing base is 121212 kilometers and the height is 222 kilometers. What is the rate of change of the area of the trapezoid at that instant (in square kilometers per second)
Answers
The rate of change of the area of the trapezoid at that instant is 5 square kilometers per second and this can be determined by differentiating the area of the trapezoid with respect to time 't'.
Given :
One base of a trapezoid is decreasing at a rate of 8 kilometers per second and the height of the trapezoid is increasing at a rate of 5 kilometers per second. The other base of the trapezoid is fixed at 4 kilometers. At a certain instant, the decreasing base is 12 kilometers and the height is 2 kilometers.First, determine the area of a trapezoid, that is:
[tex]\rm A = \dfrac{b_1+b_2}{2}\times h[/tex]
[tex]\rm \dfrac{2A}{h}=b_1+b_2[/tex]
[tex]\rm b_2 = \dfrac{2A}{h}-b_1[/tex]
Now, differentiate the above expression with respect to 't'.
[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2A}{h^2}\dfrac{dh}{dt}-\dfrac{db_1}{dt}[/tex]
Now. substitute the values of the known terms in the above formula.
[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2\times (16)}{2^2}\times (5)-(-8)[/tex]
[tex]\rm \dfrac{db_2}{dt} = -32\;km/sec[/tex]
So, the area is decreasing at the rate of 5.
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Hurry help me pls
1/2 (6a + 8)=14
Answers
Answer:
a= 10/3
Step-by-step explanation:
multiply both sides by 2
get 6a +8 =28
subtract 8 from both sides
you get 6a=20
divide 6 both sides and 10/3.
Tell whether the other pair (8,2) is a solution of the system of linear equations.
x - y = 6
2x - 10y = 4
The ordered pair ______ a solution.
Answers
Is
Is not
The answer is not a solution
Answers
8 - 2 = 6
Yes the ordered pair is a solution
2(8) - 10(2) = 4
16 - 20 = 4
No the ordered pair is not a solution
By direct evaluation, we will see that the pair (8,2) is not a solution of the system of equations.
Evaluating a system of equations.
A given point is a solution of a system of equations if and only if it is a solution for both equations, then to see if (8, 2) is a solution of the given system, we need to replace the values in both equations and see if it is a solution of each one.
For the first one we have:
x - y = 6
8 - 2 = 6
6 = 6
So (8, 2) is a solution of the first equation.
For the second one we have:
2x - 10y = 4
2*8 - 10*2 = 4
16 - 20 = 4
-4 = 4
Note that this equation is false, then the point (8, 2) is not a solution for the second equation, then the point is not a solution for the system of equations.
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A sporting goods store is having a 15% off sale on all items. Which functions can be used to find the sale price of an
item that has an original price of X? You may choose more than one correct answer.
y=.85 x
Of(x) = 1.15
Sale = Original - 15
Of(x) = x - 15
Sale = Original - 15(Original)
Answers
Answer:
The function is:
[tex]f(x) = x - 0.15x[/tex]
Can also be written as:
[tex]Sale = Original - 0.15(Original)[/tex]
Step-by-step explanation:
Given that the sale percentage is 15%
In general, the sale price is calculated by finding the discount according to discount percentage and then subtracting the discount from original price.
Given that x is the original price
Then the discount will be:
[tex]Discount = Original Price * 0.15\\Discount = 0.15x[/tex]
The sale price will be:
[tex]Sale Price = Original\ Price - 0.15(Original\ Price)\\[/tex]
As x is the original price
[tex]f(x) = x - 0.15x[/tex]
Can also be written as:
[tex]Sale = Original - 0.15(Original)[/tex]
60 POINTS PLEASE HELP! If the parent function f (x) =log (x+1) were replaced by g (x)= -log(x-1) , how would the graph be affected? SEE PHOTO FOR ANSWER OPTIONS
Answers
Answer:
C is the correct awnser
Step-by-step explanation:
The current of a river is 2 miles per hour. A boat travels to a point 3 miles upstream and back in 2 hours. What is the speed of the boat in still water? The speed of the boat in still water is.
Answers
Answer:
1.5 miles per hour
Step-by-step explanation:
3 miles divided by 2 hours
A music store sold 10 to the third power CDs and 10 to the second power cd players if each CD cost $12 in each CD player cost 35 what was the stores total earnings
Answers
Answer:
$15500
Step-by-step explanation:
10^3 x 12 = 12,000
10^2 x 35 = 3,500
12,000 + 3,500 = 15,500
Suppose a constellation of stars is plotted on a coordinate plane. The coordinates of one star are (0,-8). The
point representing the star is then translated left 3 units. What are its new coordinates?
1. (0,-5)
2. (-3,-8)
3. (3.-8)
4. (0.-11)
Answers
Answer:
4
Step-by-step explanation:
You deposit $2000 in an account earning 7% interest compounded continuously. How much will you have in
the account in 15 years?
Answers
Answer:
$3,715.30
Step-by-step explanation:
Total P+I (A): $3,715.30
Principal (P): $2,000
Compound (n): Continuously
Time (t in years): 15 years
By plugging this into an interest rate calculator, the amount settles to be approximently $3,715.30
Hope this helps!
if cade shoots 359 free throws shoot in 4 hours, how many can he shoot in 6 hours
Answers
Explanation
You divide 359 by 4 and then you multiply the answer by 6
Kim made $5.35 on the first day
she set up her lemonade stand. If
she makes the same amount each
day for 6 days, how much money
will she have? (6-5)
A $42.80
B $37.30
C $32.10
D $28.70
Answers
Answer:
$32.10
Step-by-step explanation:
do 5.35 but six times and then add that all up then it will be 32.10
Answer:
C
Step-by-step explanation:
its c because 5.35 times 6 is C
Given f(x) = - 3x + 1 , solve for a when f(x) = - 5 .
Answers
Answer:
x=2
Step-by-step explanation:
-5=-3x+1
-1 -1
-6=-3x
divide both sides by -3
x=2
The value of x when f(x) = - 5, In the function f(x) = - 3x + 1 is 2.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f(x) = - 3x + 1.
Now, when f(x) = - 5 the equation would be,
- 5 = - 3x + 1.
- 5 - 1 = - 3x.
- 6 = - 3x.
3x = 6.
x = 2.
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Consider an ANOVA procedure to compare five population means. In this case, the total number of pairs to be considered in multiple comparisons is ten. If the probability that the null hypothesis is falsely rejected at least once in all six pairs needs to be 0.05, the probability that the null hypothesis is falsely rejected in each pair should be:________. (Give your answer to 4 decimal places.)
Answers
Answer:
The right response is "0.0085". A further explanation is given below.
Step-by-step explanation:
Let,
P (across each pair, this same null hypothesis would be wrongly rejected) be "a".
Therefore,
⇒ [tex]P=1-P(no \ time \ rejected)[/tex]
⇒ [tex]1-(1-a)^6 =0.05[/tex]
⇒ [tex]1-a=0.95^{(\frac{1}{6} )}[/tex]
⇒ [tex]a=1-0.95^{(\frac{1}{6} )}[/tex]
⇒ [tex]0.0085[/tex]
Which equation is y = –6x2 + 3x + 2 rewritten in vertex form
Answers
Answer:
14 + 3x
Step-by-step explanation:
6x2= 12
12 + 3x + 2
=14 + 3x
Answer:
y =-6(x-1/4)^2+19/8
Step-by-step explanation:
I hope this helps I don't have an explanation I just got it right on EDG 2021
God Bless You!!!!!
Arianna runs up 4 flights of stairs and then runs down 4 flights of stairs.
Does this situation represent additive inverses? Explain.
A
Yes; The numbers combine to eight.
B
Yes; The numbers combine to zero.
No; The numbers are both represented by the same integer.
D
No; The numbers cannot be added together.
Answers
Answer:
Yes this represents additive inverse,
Step-by-step explanation:
Since you are subtracting the same number 4 to get to zero.
Leslie invests $2500 in a savings account for 10 years. The account accrues interest at a rate
of 6% compounded semi-annually. How much money will be in the account at the end of the
10 years?
Answers
Answer:
You make $32,000 a year and want to save 10% of your income every year. How much should you put into savings every month?
$32$,000 x 0.10 = 3,200
You want to save $3200 a year.
You should be saving $266.67 a month or $133.33 a paycheck if you are paid
Step-by-step explanation:
The table shows how much money a grocery store receives for selling different amounts of asparagus.
ASPARAGUS SALES
NUMBER OF POUNDS
TOTAL SALES
4 lb=
$10
6 lb=
$15
8 lb=
$20
10 lb=
?
12 lb=
?
If the unit rate is constant what are the total sales for 12 pounds of asparagus?
A. $32.50
B. $25.00
C. $22.50
Answers
Answer:
The answer is 32.50
Step-by-step explanation:
You would just keep counting up by fives and then you would also have to add tax because it is food -- I am happy to help! :)
Carl bought an airline ticket. Two weeks ago, the cost of this
flight was $900. What is the percent increase?
HELPP
Answers
Answer:
hey can you give us the buying price of the ticket so we can find the increase? thanks :)
Step-by-step explanation:
Find the unit rate in decimal representation $150 for 22 ft.²
Answers
Answer:
$6.82 per foot
Step-by-step explanation:
To find the unit rate, divide.
150 / 22 ≈ 6.82
Best of Luck!
Andre is writing a paper for science class. He can type 30 words per minute.
What is the ratio of words to minutes? Write the ratio three ways.
Answers
Answer:
30/1, 30:1, 30 to 1
Step-by-step explanation:
Describe a situation that could be modeled with the ratio 3: 1.
Answers
Answer:
three boys to 1 girl
Step-by-step explanation:
a
Word problem: Jen wants to rent a car. There is a one-time fee of 50 dollars plus 40 dollars per day. Write an algebraic expression for the total cost for “d” days.
A. 90d
B. 50d + 40
C. 50 + 40d
D. 50d + 40d
Please help me!
Answers
Answer:
50+40d C
Step-by-step explanation:
Fine the distance between (-8, 4) and (-8, -2)
Answers
Answer:
The distance between the two points is six units.
Step-by-step explanation:
We are given two coordinate pairs:
(-8, 4)(-8, -2)With these, we can find the distance between the two using the distance formula. The distance formula is:
[tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, \ \text{where d is the distance.}[/tex]
Additionally, we need to label our coordinates. In math, coordinates are labeled as (x₁, y₁) and (x₂, y₂).
Therefore, our coordinate pairs can be labeled in this format.
(-8, 4)
x₁ = -8y₁ = 4(-8, -2)
x₂ = -8y₂ = -2Now, we can substitute these values into the formula and solve for d.
[tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d = \sqrt{(-8 - -8)^2 + (-2 - 4)^2}\\\\d = \sqrt{(0)^2+(-6)^2}\\\\d = \sqrt{0 + 36}\\\\d = \sqrt{36}\\\\d = 6[/tex]
Therefore, the distance between the two points is six units.
13, 11, 9, 7 what is the recursive rule
Answers
Answer:
it is -2
Step-by-step explanation:
because 13-2=11-2=9-2=7-2=5-2=3-2=1
A recipe for whole wheat pizza crust calls for 1 1/2 cups of all purpose flour. Jeremy has 5 7/4 cups of all purpose flour. If he makes the recipe, how much flour will he have left?
Answers
Answer:
Jeremy has 5 1/4 cups of all purpose flour after preparing his recipe.
Step-by-step explanation:
Since the recipe for whole wheat pizza crust calls for 1 1/2 cups of all purpose flour, 1.5 cups of that product is required to create the meal in question.
Now, since Jeremy has 5 7/4 of all purpose flour, it can be stated that he has 6.75 cups of it (7/4 = 1.75).
Therefore, to determine the amount of flour that Jeremy will have left over after preparing the recipe, it is necessary to perform the following calculation:
6.75 - 1.5 = X
5.25 = X
So since 0.25 is equal to 1/4, Jeremy has 5 1/4 cups of all purpose flour after preparing his recipe.
Determine the two z-scores that divide the area under the standard normal curve into a middle 0.874 area and two outside 0.063 areas.a. -1.45, 1.45
b. -1.39, 1.39
c. -1.53, 1.53
d. -1.46, 1.46
Answers
Simplify:w^30/(w^3)^2
Answers
Answer:
Step-by-step explanation:
[tex](a^{m})^{n} = a^{m*n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}\\\\\\\frac{w^{30}}{(w^{3})^{2}} = \frac{w^{30}}{w^{3*2}}[/tex]
[tex]= \frac{w^{30}}{w^{6}}\\\\=w^{30-6}\\\\= w^{24}[/tex]
Answer:
w^24
You would simplify the expression by first finding the product of (w^3)^2 which is w^6. Next you would divide w^30 and w^6 which would get you your answer which is w^24. Hope this helps!
3. The difference of the squares of two positive consecutive odd integers is 32. Find the
integers.
Answers
Answer:
7,9
Step-by-step explanation:
Let two consecutive odd integer=X and (X+1)
The difference of the squares of two positive consecutive odd integers is 32.
So(X+2)^2-x^2=32
(x^2+4+4x)-x^2=32
x^2+4+4x-x^2=32
4x=32-4
4x=28
X=28/4
X=7
So first integer=7
Second integer=7+2
=9.
What is the cost of a $40 after a 15% mark-up?
Answers
Answer:
Revenue: $46
Profit: $6
4) Gas mileage is the number of miles you can drive on a a gallon of gasoline.
A test of a new car results in 450 miles on 20 gallons of gas. How far could
you drive on 40 gallons of gas? What is the car's gas mileage?
Answers
Answer:
900 miles
Step-by-step explanation:
Simply multiply 450 by 2.
40 ÷ 20 = 2
450 x 2 = 900
OR
Based on Proportion:
[tex]\frac{450}{20}[/tex] x [tex]\frac{x}{40}[/tex]
Cross multiply:
450 x 40 = 18,000
20 x X = 20x
20x = 18,000
Divide by 20:
x = 18,000 ÷ 20
Solve:
x = 900