A rectangle has perimeter 68 meters, and its area is 280 sq-meters. find the dimensions of this rectangle. (for purposes of this problem only, the width is shorter than the length.)
Final answer:
The rectangle's length to be 20 meters and the width to be 14 meters.
Explanation:
We are given that a rectangle has a perimeter of 68 meters and an area of 280 square meters, and we need to find its dimensions. Let's call the length of the rectangle L and the width W.
The perimeter (P) of a rectangle is given by the formula P = 2L + 2W. We know the perimeter is 68 meters, so we can write the equation:
1. 68 = 2L + 2W
The area (A) of a rectangle is given by the formula A = L × W. We know the area is 280 square meters, so we can write the equation:
2. 280 = L × W
To find L and W, we solve these two equations simultaneously.
Divide the perimeter equation by 2 to simplify:
34 = L + W
We can then express W in terms of L using this equation:
W = 34 - L
Substitute this into the area equation:
280 = L × (34 - L)
This gives us a quadratic equation:
L2 - 34L + 280 = 0
Solving this quadratic equation, we find that L = 20 and W = 14 or L = 14 and W = 20. Since the width is shorter than the length, the dimensions of the rectangle are length 20 meters and width 14 meters.
HELP ASAP PLZ
what values of a, b, and c would you use in the quadratic formula for the following equation? 5x^2+9x=4
1. a=-4,b=9,c=5
2.a=5,b=9,c=-4
3.a=5,b=-4,c=9
4.a=5,b=9,c=4
The standard form is given by :
[tex] ax^{2} +bx +c=0 [/tex]
So we have to convert given equation in this form by bringing all terms to one side and making 0 on the other side.
[tex] 5x^{2} +9x=4 [/tex]
Now we have to bring 4 to the left side,
subtracting 4 on the left,
[tex] 5x^{2} +9x-4=0 [/tex]
Comparing our equation with standard form,
Answer : a=5, b=9 and c=-4 ( second option is right )
You can find the distance between two points on a number line by using the Pythagorean theorem.
Answer:
It is false
Read the following statement.
At least one angle is acute.
What is the first step of indirectly proving this statement?
Assume none of the angles are acute.
Assume at least one angle is obtuse.
Assume at least one angle is not acute.
Assume none of the angles are obtuse.
Answer:
Assume at least one angle is not acute.
Step-by-step explanation:
With an indirect proof, instead of proving that something must be true, you prove it indirectly by showing that it cannot be false.
An indirect prove starts assuming that the statement is false and then your goal is to arrive at a contradiction. Then, in this case, the first step of indirectly proving at least one angle is acute is assume at least one angle is not acute.
how much would 600 invested at 8% interest compounded continuously be worth after 3 years? round your answer to the nearest cent.
Triangle ABC has vertices of A(–6, 7), B(4, –1), and C(–2, –9). Find the length of the median from
A) 4
b) square Root of 18
C) 8
D) Square root of 68
PLEASE HELP FAST!!!!
As a pendulum swings , the angle (theta) that it makes with the vertical changes through its swing. The force of gravity pulling on the bob is given by F=mg sin (theta), where g is equal to 9.8m/s^2. If the mass of the pendulum is 0.01 kg, what is the force pulling on the pendulum when it makes a 22.5 degree angle with the vertical?
Answer:
Answer B
Step-by-step explanation:
The already given answer is correct, but if you need to know what answer it is without getting your calculator out, its B, or
0.049 (square)2 -(square) 2 N
0.049√2-√2 N
Choose as many answers as apply.
Which of the following are normal payroll deductions?
taxes
pension fund contributions
group health insurance premiums
Book of the Month Club
The payroll deductions among the given choices are Taxes, health insurance premiums and pension fund contributions.
Step-by-step explanation:Payroll deductions are those amounts which are deducted from an employee's payroll amount. These amounts are usually withheld by the employer where the employee works. Payroll deductions include insurance pension contributions, wage assignments, child support payments, taxes, and union and uniform dues.
The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of the area when r = 5 inches and r = 21 inches. (a) r = 5 inches
Final answer:
The rate of change of the area of a circle with a radius increasing at a constant rate can be calculated using the derivative of the area formula. For r = 5 inches, the rate is 30π square inches per minute and for r = 21 inches, the rate is 126π square inches per minute.
Explanation:
The student is asking about the rate of change of the area of a circle when its radius is increasing at a constant rate. This is a calculus problem that involves derivatives and can be solved using the formula for the area of a circle, A = πr² where A is the area and r is the radius. The rate of change of the radius, ℓr/ℓt, is given as 3 inches per minute.
To find the rate of change of the area, denoted as ℓA/ℓt, we take the derivative of A with respect to t, using the chain rule, which gives us ℓA/ℓt = 2πr(ℓr/ℓt). When r = 5 inches, substituting the values, we obtain ℓA/ℓt = 2π(5)(3) = 30π square inches per minute. Similarly, when r = 21 inches, ℓA/ℓt = 2π(21)(3) = 126π square inches per minute.
Plzzz help will give the brainliest for correct answer
the fortaleza telescope in brazil is a radio telescope. its shape can approximated with the equation y=0.013x2 is the relationship between x and y linear? is it proportional? explain
we have that
the given equation is
[tex]y=0.013x^{2}[/tex]
we know that
The general linear equation is equal to
[tex]y=mx+b[/tex]
where
m and b are real numbers
Every equation in this form is a linear equation. The linear equations represent linear functions. Equations than cannot be written in this form are not linear equations, and therefore are not linear functions
The given equation is not a line, is a quadratic equation, therefore is not a linear equation, is a non linear function.
Only a linear relationship can be proportional,
so
the relationship is not proportional
therefore
the answer is
the relationship between x and y is a non linear function and is not proportional
Find the complement of an angle whose measure is 74 degrees. Show all work.
Answer:
16⁰
Step-by-step explanation:
Angle = 74⁰
Complement = 90 - 74 = 16⁰
Bill had saved $825 from his last 8 paychecks. He saved either 75$ or 150$ a paycheck.for the 8 paychecks,how many times did bill save $75 from his paycheck
Let us assume the number of times Bill saved $75 from his paycheck = x
Let us assume he number of times Bill saved $150 from his paycheck = y
Since he saved 75$ or 150$ for the 8 paychecks.
So, x+y=8
y=8-x (Equation 1)
Since Bill saved $825 from his last 8 paychecks using $75 or $150.
So, 75x+150y=825 (Equation 2)
Substituting the value of 'y' from equation 1 in equation 2,
[tex] 75x+150(8-x)=825 [/tex]
[tex] 75x+1200-150x=825 [/tex]
[tex] 75x-150x=825-1200 [/tex]
[tex] -75x=-375 [/tex]
x = 5
Therefore, Bill saved $75, 5 times from his paycheck.
Answer:
5
Step-by-step explanation:
Math) The school principal wants to know whether the students in the entire school prefer football or basketball. The principal draws a random sample from the following groups: All school teachers All girls in each grade All students in each grade All students on the basketball team Which of the following groups best represents the population she should take a random sample from to get the best results for her survey? All school teachers All girls in each grade All students in each grade All students
I Will make you the BRAINLIEST!!!!pls answer:a movie Angelo brought a medium popcorn for $4 and a small drink for $3 and a box of fruit snacks for $5 write and solve a subtraction equation to find how much money Angela gave the cashier if you received $3 in change.
Find the length of the hypotenuse of a right triangle to the nearest tenth of a foot if the lengths of the legs are 13 and 15 feet.
2. Rhianna is buying a car for $14,390. She has a $1000 trade-in allowance and will make a $1500 down payment. She will finance the rest with a 4-year auto loan at 2.6% APR.
Answer:
$261.08
Step-by-step explanation:
Worth of Car=$14,390
Trade-in allowance=$1000
Down Payment= $1500
Value of Loan=14390-(1000+1500)
=$11890
The Monthly Payment for a loan P, taken at a Monthly interest rate, r for a number of m months, is gotten using the formula:
[TeX] Monthly\:Payment=\frac{rP}{1-(1+r)^{-m}} [/TeX]
P=$11890
Monthly Interest Rate,r=0.026/12=0.002167
Number of Months, m=4*12=48 Months
[TeX] Monthly\:Payment=\frac{0.002167*11890}{1-(1+0.002167)^{-48}} [/TeX]
=$261.08
The Monthly Payment on the car loan is $261.08.
how many triangles can you make with 3cm, 4cm and 11cm
plz help will mark BRAINLIEST algebra 2
mittens are marked down 25% the sale price is 3.15 a pair what was the original price of a pair of mittens
What is the period of the sinusoid given by y=-3cos(2pi/5 x)?
Sue can sew a precut dress in 3 hours. helen can sew the same dress in 2 hours. if they work together, how long will it take them to complete sewing that dress? round to one decimal place.
Final answer:
Sue and Helen can sew a dress in 1.2 hours when working together.
Explanation:
Calculating Time to Sew a Dress Together
Sue and Helen are working together to sew a dress and we need to calculate the total time it will take them to complete the sewing when working simultaneously. Sue can sew a precut dress in 3 hours, which means Sue's rate is 1 dress per 3 hours, or
1/3 dress per hour. Helen can sew the same dress in 2 hours, which means Helen's rate is 1 dress per 2 hours, or
1/2 dress per hour. Working together, their combined rate is the sum of their individual rates:
Total rate = 1/3 + 1/2
This results in a combined rate of 5/6 dresses per hour when we find a common denominator and add the fractions. To find the time it takes them to sew one dress together, we take the reciprocal of their combined rate:
Time = 1 / (5/6) hours
This simplifies to 6/5 hours.
Therefore, Sue and Helen will take 1.2 hours to complete the dress when working together.
Solve for j
j/-2 + 7 =-12
The required value of j is 38.
What are linear equation?A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.
Now the given expression is
j/-2 + 7 =-12
Substracting 7 both the side. We get,
j/-2 + 7 -7 = -12 - 7
Solving both sides,
j/-2 = -19
Now multiplying whole equation with -2,so the equation becomes
j = 38
which is the required value of j.
Hence,the required value of j is 38.
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lemon squash 2 parts concentrate to 5 parts of water. if you put 90ml of concentrate in a glass, how much water should be added?
It is given in the question that in the lemon squash 2 parts concentrate is added to 5 parts of water. Thus it makes the concentrate to water ratio as 2:5 or [tex] \frac{2}{5} [/tex]. Now, if this ratio is maintained then the amount of water to be added to 90 ml concentrate in a glass can be calculated as:
[tex] \frac{2}{5}=\frac{90}{x} [/tex]
Where x is the amount of water to be added, in ml (milliliters).
Cross multiplication of the above equation will give us:
[tex] 2x=90\times 5=450 [/tex]
Dividing both sides by 2 we will get:
[tex] x=\frac{450}{2}=225 [/tex]
Thus, if we put 90ml of concentrate in a glass, the water that should be added must be 225 ml.
The amount of water should be added is 225 ml if the lemon squash is 2 parts concentrated to 5 parts of water. if you put 90ml of concentrate in a glass
What is the ratio?It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign: between the numbers.
We have:
Lemon squash 2 parts concentrate to 5 parts of water.
Let's suppose the amount of water is x ml
Then according to the problems the ratios:
[tex]\frac{2}{5} =\frac{90}{x}[/tex]
2x = 90×5
2x = 450
x = 225 ml
Thus, the amount of water should be added is 225 ml if the lemon squash is 2 parts concentrated to 5 parts of water. if you put 90ml of concentrate in a glass
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A brand new filled jar of salsa is 11 cm tall and a has a radius of 6 cm. Kelly eats some of the salsa and the salsa in the jar is now 6 cm high.
Approximately how much salsa did Kelly eat?
Round your final answer to the nearest whole number.
188 cm³
565 cm³
679 cm³
1244 cm³
Before we begin please note that a jar is always cylindrical in shape if not mentioned otherwise. Thus, we will take a cylindrical jar in this case.
Since Kelly eats some of the salsa and the salsa in the jar is now 6 cm high, we know that Kelly ate the amount of Salsa whose volume is missing from the jar.
To find the missing volume on the Salsa jar all that we need to do is to find the height of the missing volume which is given to us as h= 6 cm. We already know that the radius of the jar, r=6 cm. Thus, the amount of Salsa Kelly has eaten is:
[tex] V=\pi(6)^2\times 6\approx678.6\approx679 [/tex] [tex] cm^3 [/tex]
Thus, the third option is the correct answer
Twenty-four students took a test. Fourteen students earned an A and 10 students earned a
b.A student will be randomly chosen.What is the probability that the student earned an A on the last test? Enter your answer as a fraction , in simplest form , in the box .
A trapezoid has bases that measure 10 centimeters and 14 centimeters and a height that measures 8 centimeters. What is the area?
Mr. Foley wants to randomly select 3 students for a committee. He used 3 coins to conduct a simulation to predict the probability that the committee will have at least 2 girls. The results of 16 trials of the simulation are shown below. Let H represent a girl and T represent a boy.
TTH HTH THH HHH
HTT THT THT HHT
HHT THH TTT HTT
HHH HTH TTH HHT
Based on the results of the simulation, what is the probability that the committee Mr. Foley selects will have at LEAST 2 girls?
A rectangular piece of plastic has an area of 10 square millimeters and a perimeter of 22 millimeters. What are the dimensions of the piece of plastic? millimeters by millimeters
The dimensions of the rectangular piece of plastic are either 2mm by 5mm or 5mm by 2mm, based on the given area and perimeter.
Explanation:We'll use the formula for the perimeter of a rectangle: 2(length + width) = perimeter and the formula for area: length x width = area. Given we have area of 10mm2 and perimeter of 22mm, we can set up two equations. Let's denote the length as 'L' and the width as 'W'.
Formula of perimeter of a rectangle: 2(L + W) = 22
Formula of area of a rectangle: L * W = 10.
We solve these two equations simultaneously. We get two possible solutions: Dimensions could be either {2mm, 5mm} or {5mm, 2mm}. Either the length is 5mm and the width is 2mm, or the length is 2mm and the width is 5mm.
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The first term in a geometric sequence is 1/9 and the common ratio is −3. Find the 7th term in the sequence.
The 7th term of the sequence is 81
The nth term of a geometric sequence is expressed as:
[tex]T_n=ar^{n-1}[/tex]
a is the first term = 1/9r is the common ratio = -3n is the number of terms = 7Substitute the given parameters into the formula to have:
[tex]T_7=1/9(-3)^{7-1}\\T_7=1/9(-3)^6\\T_7=1/9(729)\\T_7=81[/tex]
Hence the 7th term of the sequence is 81
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