The dimensions of the rectangle are length = 22 meters and width = 13 meters
What is area of rectangle?[tex]A=l\times w[/tex], where 'l' is the length and 'w' is the width of the rectangle.
For given question,
Suppose 'l' is the length and 'w' is the width of the rectangle.
The length of a rectangle is 4 meters less than twice the width.
So, we get an equation,
⇒ l = 2w - 4
The area of the rectangle is 286 square meters.
⇒ A = 286 sq. m.
Using the formula for the area of the rectangle,
[tex]\Rightarrow A=l\times w\\\\\Rightarrow 286=(2w-4)\times w\\\\\Rightarrow 286=2w^2-4w\\\\\Rightarrow 2w^2-4w-286=0[/tex]
Now, we solve the quadratic equation [tex]2w^2-4w-286=0[/tex]
[tex]\Rightarrow 2w^2-4w-286=0\\\\\Rightarrow w^2-2w-143=0\\\\\Rightarrow (w-13)(w+11)=0\\\\\Rightarrow w-13=0~~~or~~~w+11=0\\\\\Rightarrow w=13~~~or~~~w=-11[/tex]
w = -11 is not possible.
So, the width of the rectangle is 13 meters.
And the length of the rectangle would be,
[tex]\Rightarrow l \\= 2w - 4\\=(2\times 13)-4\\=22[/tex]
Therefore, the dimensions of the rectangle are length = 22 meters and width = 13 meters
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write an algebraic expression that models the word phrase.
the product of 8 and the sum of a number x and 3
You drove to your cousin's house, which is 460 miles away. After two hours, you had go e 100 miles. After 8 hours, you reached your destination. Write an equation that gives the number of miles you had driven, y, in germs of the number of hours you had driven, t.
To express the number of miles driven, y, in terms of the number of hours driven, t, we first find the speed and then use it to formulate the equation of the line as y = 60t. However, to accurately represent the entire trip, we must include the initial 100 miles driven in 2 hours, leading to y = 60t - 20 as the final equation.
To write an equation that gives the number of miles driven, y, in terms of the number of hours driven, t, we can use the relationship between distance and travel time. Given that after two hours you had gone 100 miles and after 8 hours, you reached your destination, which is 460 miles away, we establish two points on our distance-time graph: (2, 100) and (8, 460).
Using the two points, we can find the slope of the line, which represents the speed:
Slope (speed) = (change in distance) / (change in time) = (460 - 100) miles / (8 - 2) hours = 360 miles / 6 hours = 60 miles/hour.
We can now express the equation of the line as y = mx + b, where m is the slope and b is the y-intercept. The y-intercept represents the distance at time zero, which for most driving scenarios we assume to be 0 miles. Thus, the equation becomes y = 60t. However, this equation would not accurately represent the entire trip since it doesn't account for the initial 100 miles driven in the first 2 hours.
To adjust for that, we'll introduce an offset for the initial 100 miles traveled in the first 2 hours. The y-intercept would be 100 miles less than if we had started from 0 miles at 0 hours. The corrected equation for the entire trip would be of the form y = 60t + b, where b = y - 60t and y are the miles covered in the initial 2 hours, which is 100 miles. Substituting the values, we get b = 100 - 60 x 2 which equals -20.
The final equation, accounting for the first 2 hours of travel, would therefore be: y = 60t - 20.
what is the circumference of a circle p PB=29m
Answer:
The circumference of the given circle = 182.12 meters
Step-by-step explanation:
The circle P is given to us in which length of PB = 29 meter
Now, Since P is the center of the circle so PB will be the radius of the circle
So, Radius of the circle = 29 meter
We need to find the circumference of this circle with radius 29 meter
So, Circumference of the circle = 2π × radius of the circle
⇒ Circumference of the circle = 2 × 3.14 × 29
= 182.12 meter
Hence, The circumference of the given circle = 182.12 meters
A submarine hovers at 240 meters below sea level.if it descends 160 meters and then ascends 390 meters,what is the new position
12<3b or 2b+14<4 please help
If I spoke with 800 customers in 40 hours how many customers did I speak to every 30 minutes
Answer:
10 customers were spoken to in every 30 minutes
Step-by-step explanation:
First, we convert 40 hours into minutes by multiplying it with 60 [as 1 hour = 60 minutes]
So, 40 hours = 40*60 minutes
= 2400 minutes
In 2400 minutes, number of customers served = 800
In 1 minute, number of customers served = [tex]\frac{800}{2400}[/tex]
In 30 minutes, number of customers served = [tex]\frac{800}{2400}*30[/tex]
= [tex]\frac{800}{2400} * \frac{30}{1}[/tex]
= [tex]\frac{800*30}{2400*1}[/tex]
= [tex]\frac{24000}{2400}[/tex]
= 10
So,
10 customers were spoken to in every 30 minutes
Final answer:
You spoke with 10 customers every 30 minutes.
Explanation:
To find out how many customers you spoke to every 30 minutes, we can set up a proportion. We know that you spoke with 800 customers in 40 hours, which is equivalent to 2400 minutes. So, the proportion is:
800 customers / 2400 minutes = x customers / 30 minutes
Now, we can cross-multiply and solve for x:
800 * 30 = 2400 * x
x = 800 * 30 / 2400
x = 10
Therefore, you spoke with 10 customers every 30 minutes.
If i is raised to an even power, then it can not simplify to be
a. -1
b. 1
c. i
How many 1/4 cup portions can be served from 12 quarts of potato salad?
Which is another way to check the sum of 104 + 34 + 228 + 877? A. 877 – 104 + 34 + 228 B. 34 – 104 + 228 + 877 C. 877 + 228 + 34 + 104 D. 877 – 228 – 34 – 104
by adding the numbers in a different order would be a way to check so the answer is:
C. 877 + 228 + 34 + 104
Anyone know the answers for #8 and #9?
24=6−2(2n+3) What value on n makes the equation true?
what percentage is 699 of 4736
PLEASE HELP!!!!! I DONT UNDERSTAND!!!! :(
A city's population is represented by the function P=25,000(1.0095)t , where t is time in years.
How could the function be rewritten to identify the daily growth rate of the population?
What is the approximate daily growth rate?
I need to know the three points of inflection
A web server hosting company advertises 99.999 percent guaranteed network uptime. (a) how many independent network servers would be needed if each has 98 percent reliability? (round your answer up to the nearest whole number.) network servers (b) how many independent network servers would be needed if each has 89 percent reliability? (round your answer up to the nearest whole number.) network servers
a. The 50 independent network servers would be needed if each has 98% reliability.
b. Approximately 9 independent network servers would be needed if each has 89% reliability.
To calculate the number of independent network servers needed for a given level of reliability, we can use the following formula:
[tex][ \text{Number of servers} = \frac{1}{1 - \text{Reliability}} ][/tex]
a) For servers with 98% reliability:
[tex][ \text{Number of servers} = \frac{1}{1 - 0.98} = \frac{1}{0.02} = 50 ][/tex]
Therefore, 50 independent network servers would be needed if each has 98% reliability.
b) For servers with 89% reliability:
[tex][ \text{Number of servers} = \frac{1}{1 - 0.89} = \frac{1}{0.11} \approx 9 ][/tex]
Therefore, approximately 9 independent network servers would be needed if each has 89% reliability.
what is the unit rate of 1/5 and 1/4
what values make the inequality x+6/6-x<0 true?
It's C if you're taking the test
Fill in each blank with the correct word to complete the sentence. The rules of the order of operations tells you to multiply and divide in order from _________ to ______
The rules of the order of operations tells you to multiply and divide in order from left to right.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The order of operations can be remembered by the acronym PEMDAS, which stands for: parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right. There are no parentheses in this problem, so start with exponents. Then, multiply and divide from left to right.
Hence, the rules of the order of operations tells you to multiply and divide in order from left to right.
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Write the equation of the line containing the point (3, –2) and having a slope of 2 in slope-intercept form.
The equation of a line containing the point (3, –2) and having a slope of 2, is y = 2x-8
What is an equation of a line?The general equation of a line in two variables of the first degree is represented as Ax + By +C = 0, A, B ≠ 0 where A, B and C are constants which belong to real numbers. When we represent the equation geometrically, we always get a straight line.
Given that a line containing the point (3, –2) and having a slope of 2, we need to find the equation of the line,
So, the general equation of a line is y = mx+c
Where, m is the slope and c is the y-intercept.
Therefore,
y = 2x+c
Now, put x = 3 and y = -2 in the equation to find the value of c,
-2 = 3(2)+c
-2 = 6+c
c = -8
Put the value of c in the equation,
y = 2x-8
Hence, the equation of a line containing the point (3, –2) and having a slope of 2, is y = 2x-8
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The graph below represents the price of sending video messages using the services of a phone company. What is the constant of proportionality?
How do you take the limit of this
The limit of the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) is DNE
To take the limit of the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6), we proceed as follows
Since we have the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) and we want to take the limit, we proceed thus,.
First, we divide both the numerator and denominator by x⁴. So,
lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) = lim x → ∞(x⁴ - 9x² + x)/x⁴ ÷ (x³ - x + 6)/x⁴
= lim x → ∞(x⁴/x⁴ - 9x²/x⁴ + x/x⁴ ÷ (x³/x⁴ - x/x⁴ + 6/x⁴)
= lim x → ∞(1 - 9/x² + 1/x³ ÷ (1/x - 1/x³ + 6/x⁴)
Now, taking the limit as x tends to infinity, we have that
= lim x → ∞1 - lim x → ∞9/x² + lim x → ∞1/x³ ÷ lim x → ∞1/x - lim x → ∞1/x³ + lim x → ∞6/x⁴
= (0 - 9/∞² + 1/∞³)/(1/∞ - 1/∞³ + 6/∞⁴)
= (0 - 9/∞ + 1/∞)/(1/∞ - 1/∞ + 6/∞)
= (∞ - 0 + 0)/(0 - 0 + 0)
= (∞)/(0)
= DNE
Lane's arm span is 61 inches. If his height is 1⁄4 foot longer than his arm span, how tall is he?
1 foot = 12 inches
1/4 foot = 12/4 = 3 inches
61 +3 = 64 inches tall ( 5 ft 4 inches)
Assign point_dist with the distance between point (x1, y1) and point (x2, y2). the calculation is: distance = squarerootof( (x2 - x1)2 + (y2 - y1)2 ). sample output for the given program:
The program is an illustration of functions
Functions are collections of defined program statements, that are executed when evoked
The program in Python, where comments are used to explain each line is as follows:
#This imports the math module
import math
#This defines the function
def calculateDistance(x1,y1,x2,y2):
#This calculates the distance between the points
dist = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
#This returns the calculated distance
return dist distance
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A summer camp has divided its campers into 8 groups of 9 campers.How many campers are at the summer camp?
What is the probability of rolling a sum of 8 on a standard pair of six-sided dice? express your answer as a fraction or a decimal number rounded to three decimal places, if necessary?
The probability of rolling a sum of 8 on a pair of standard six-sided dice is 5 out of 36, or 0.139 rounded to three decimal places.
Explanation:The subject of your question is
probability
, a topic in Mathematics. To solve this, we want to know the total number of outcomes when two dice are rolled; which is 6*6 = 36. Then we determine how many of these outcomes result in a sum of 8. Upon careful examination, we find that there are 5 (2,6), (3,5), (4,4), (5,3), and (6,2). Therefore, the
probability of rolling a sum of 8
on a standard pair of six-sided dice is 5 out of 36, which can be expressed as
5/36 or 0.139
rounded to three decimal places.
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Which expression represents the distance between 4.7 and −11.2 on the number line? Drag and drop the correct expression into the box.
Answer:
15.9Step-by-step explanation:
[tex]\text{The formula of a distance between two points on a number line:}\\\\d=|a-b|\\\\\text{for}\ a\geq b:\ d=a-b\\=========================\\\\\text{We have}\ 4.7\ \text{and}\ -11.2.\ \text{Substitute:}\\\\d=4.7-(-11.2)=4.7+11.2=15.9[/tex]
The distance between 4.7 and -11.2 on the number line is 15.9.
Explanation:The distance between two points on a number line can be found by taking the positive difference between their coordinates. In this case, the distance between 4.7 and -11.2 is found by subtracting the smaller number from the larger number and taking the absolute value.
Distance = |-11.2 - 4.7| = |-15.9| = 15.9
Therefore, the correct expression is Distance = 15.9.
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Suppose the graph of a line has a negative slope and a positive y-intercept. Through which quadrants does the line pass?
William Right broke his leg in an accidental fall. He has a deductible of $150 and a coinsurance payment equal to 20% percent of the cost less the deductible. The entire bill for medical services was $750.00.
How much did William pay? $
How much did the insurance company pay? $
We know that William
paid his deductible that amount is the $150.
Then William paid 20 percent of everything else. That's 20 percent of (750
minus 150), it is equal to 150.
Then the insurance company paid 80 percent of (750 minus 250), it is equal to
480.
Answer:
its is he payed 270 and insurance payed 480
Step-by-step explanation:
just simply add up the numbers to 750 and the only ones that go together are 270 + 480 = 750 hope it helps :)
Simplify or compute : a times a times a divided by 3a
jase farm has 9 chickens each laid 3 eggs, he also has 4 horses. ednas farm has chickens which laid a total of 23 eggs, jase wonders whose chickens laid more eggs. What is a good plan to find whose chickens laid more eggs?
Jase's chickens laid more eggs.
From the information given, Jase farm has 9 chickens and each laid 3 eggs, therefore the total eggs laid will be:
= 9 × 3
= 27 eggs.
On the other hand, Ednas farm has chickens which lay a total of 23 eggs. Therefore, since 27 eggs are more than 23 eggs, Jase's chickens laid more eggs.
In conclusion, Jase's chickens laid more eggs.
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