Final answer:
The area of a rectangular field that is 400 meters long and 350 meters wide is calculated by multiplying the length and width in meters to get square meters and then converting to square kilometers. The field's area is 0.14 square kilometers.
Explanation:
To calculate the area of a rectangular field, you multiply the length by the width. The area is usually given in square units.
In this case, the field is 400 meters long and 350 meters wide. To find the area in square meters, we do the following calculation:
Area = Length × Width
Area = 400 m × 350 m
Area = 140,000 m2
To convert square meters to square kilometers, you need to remember that 1 square kilometer equals 1,000,000 square meters. Therefore, you divide the area in square meters by 1,000,000 to get the area in square kilometers:
Area in square kilometers = Area in square meters / 1,000,000
Area in square kilometers = 140,000 m2 / 1,000,000
Area in square kilometers = 0.14 km2
The area of the field is 0.14 square kilometers.
To find the area of the rectangular field in square kilometers, the measurements of 400 meters and 350 meters must first be converted to kilometers, resulting in an area of 0.14 square kilometers.
Explanation:To calculate the area of a rectangular field in square kilometers, we can use the formula for the area of a rectangle which is length × width. First, we need to convert the measurements into the same unit, so we will convert meters to kilometers. We know that 1 kilometer is equivalent to 1000 meters. Therefore, a field that is 400 meters long is 0.4 kilometers long (400 ÷ 1000 = 0.4 km), and a field that is 350 meters wide is 0.35 kilometers wide (350 ÷ 1000 = 0.35 km).
Now, with both measurements in kilometers, we can find the area:
To find the area of a rectangular field, you need to multiply its length by its width. In this case, the length is 400 meters and the width is 350 meters. So, the area of the field is 400 * 350 = 140,000 square meters.To convert this to square kilometers, we need to divide the area by 1,000,000 (since there are 1,000,000 square meters in a square kilometer). So, the area of the field in square kilometers is 140,000 / 1,000,000 = 0.14 square kilometers.Therefore, the area of the rectangular field is 0.14 square kilometers.In parallelogram LMNO, MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, and
OP = (2x – 1) m.
Parallelogram L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P.
What are the values of x and y?
Answer:
x = 11 m
y = 2 m
Step-by-step explanation:
The given figure is parallelogram, with MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, and OP = (2x – 1) m
It is property of parallelogram that, the diagonals bisect each other.
Thus, from above,
MP = OP and LP = PN
Thus,
[tex]2x-1 = 21[/tex]
[tex]2x = 22[/tex]
[tex]x = 11[/tex]
and,
[tex]y+3 = 3y-1[/tex]
[tex]2y = 4[/tex]
[tex]y = 2[/tex]
Thus, x = 11 m and y = 2 m
Answer:
D. x = 11 m, y = 2 m
Step-by-step explanation:
Identify the equation of the linear function through the points (- 2,- 7) and (1,2). Then state the rate of change of the function. What is the equation of the linear function?
A. y = 3x - 1
B. y = - 3x - 1
C. y = 3x + 1
D. y = -3x + 1
The rate of change is ( ? ).
Answer:
The equation of line is y = 3 x - 1 , i.e option A .
The rate of change = m = 3
Step-by-step explanation:
Given as :
The points are
([tex]x_1[/tex],[tex]y_1[/tex] ) = (- 2, -7)
([tex]x_2[/tex],[tex]y_2[/tex] ) = (1 , 2)
Let The slope = m
Now, The slope is calculated in points form
So, Slope = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
I.e m = [tex]\dfrac{2-(-7)}{1-(-2)}[/tex]
or, m = [tex]\dfrac{9}{3}[/tex]
I.e m = 3
So, The slope of points = m = 3
I,e Rate of change = m = 3
Now, the equation of line in slope - point form can be written as
y -[tex]y_1[/tex] = m ( x - [tex]x_1[/tex])
where m is the slope of line
i.e y - (-7) = ( 3 ) × ( x - (-2) )
or, y + 7 = 3 × (x + 2)
∴ y + 7 = 3 x + 6
Or, y = 3 x + 6 - 7
Or, y = 3 x - 1
So, The equation of line is y = 3 x - 1
Hence, The equation of line is y = 3 x - 1 , i.e option A .
And The rate of change = m = 3 Answer
Is the product of square root of 16 and 4/7 rational or irrational
The square root of 16 is rational 4.
The ratio of 4 and 7 is rational 0.5714285714285
The product is hence rational.
The product of the square root of 16 and 4/7 (which equals 16/7) is rational.
What are rational and irrational numbers?Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.
The square root of 16 is 4, and 4/7 is a rational number. When you multiply a rational number (4/7) by an integer (4), the result remains rational.
Calculation: √16 * 4/7 = 4 * 4/7
= 16/7
16/7 is the product which is a rational number.
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Which expression can be used to check the answer to 56 divided by negative 14=n
Answer:
n=-4
Step-by-step explanation:
56/-14=n
n=-4
What is 2 5/10 x 3/4
Answer: 1.87500 or 15/8 simplified 1 7/8
Step-by-step explanation:
Answer:
1 7/8
Step-by-step explanation:
So you want to make 2 5/10 into a improper fraction which is 25/10. so 25/10*3/4 you need to do cross cancel but you can't cross cancel so the answer is just going to be 15/8 which is also 1 7/8 hope this helps ;))
A square on a coordinate plane has one vertex at (2.5,33) and a perimeter of 14 units. If all of the vertices are located in Quadrant I, what are the coordinates of the other 3 vertices? Please show how you solved this in a step-by-step order.
Answer:
A(2.5,36.5)
D(6,36.5)
and
C(6,33)
All of the following are equivalent except _____.
-5(x - 1)
-5x + 5
5 - 5x
(5 - 5)x
Please explain how you got your answer, thanks
(5 - 5)x because it equals -5x+5x which is 0
all the others equal -5x +5
Answer:
(5-5)x
when you distribute the x here it becomes 5x-5x which is 0 this is the only problem that equals 0
A dress that costs x dollars is on sale for 30% off. Write an expression to represent the sale price, in dollars, of the dress.
The expression to represent the sale price, in dollars, of the dress is x - 0.3x dollars
Solution:Given that dress that costs "x" dollars is on sale for 30% off
To find: expression to represent the sale price, in dollars, of the dress
Let the original price of dress is "x"
It is on sale for 30% offer. Which means 30 % of "x" is offer price
Sales price means the price of dress after offer
So the sales price is written as original price - offer price
Sales price = original price - offer price
Sales price = x - 30 % of x
On simplification we get,
[tex]\text {Sales price }=x-\frac{30}{100} \times x=x-0.3 x[/tex]
Thus the sales price of dress is x - 0.3x dollars
D/3+10=14 solve the equation
Answer: d = 12
Step-by-step explanation: First isolate d/3 by subtracting 10 from both sides of the equation. That gives you d/3 = 4.
From here, since d is being divided by 5, multiply both sides of the equation by 5 so d = 12.
If d , e, and f are midpoints of the sides of ABC, find the perimeter of ABC.
The perimeter of a triangle with midpoints d, e, and f on each side is twice the sum of segments d, e, and f. However, without specific numerical values for d, e, and f, the exact numerical measurement for the perimeter of triangle ABC cannot be determined.
Explanation:The question is referring to a specific characteristic of geometry known as the midpoint. The midpoints, in this case d, e, and f, divide each side of the triangle into two equal parts. The side length of ABC is equal to double the sum of segments d, e, and f since they represent the half lengths of the sides.
However, please note that without any additional information or numeric representation, we cannot compute the exact numerical measurement of the perimeter of triangle ABC.
To illustrate, if we were given that the lengths d, e, and f were respectively 5 units, 6 units, and 7 units, we would calculate the perimeter of triangle ABC by adding the lengths of d, e, and f and multiplying the sum by 2.
In such a scenario: Perimeter of ABC = 2 * (d + e + f) = 2 * (5 units + 6 units + 7 units) = 2 * 18 units = 36 units.
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a games room charges a $13 entrance fee, plus $2.35 per hour of play time. Annie Marie has $29.45. how long can she play in the games room? a) Choose a variable and write an inequality for this problem
Answer:
a) The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].
b) Annie Marie can play maximum of 7 hours.
Step-by-step explanation:
Given:
Entry fee charge of game room = $13
Cost of hourly playtime = $2.35 per hour
Total Money Annie Marie has = $29.45
We need to find number of hours she can play with this amount.
Let number of hours she will play be 'x'.
No we know that Total Money she has should be less than or equal to sum of Entry fee charge of game room and Cost of hourly playtime multiplied by number of hours she can play.
Framing in equation form we get;
[tex]13+2.35x\leq 29.45[/tex]
Hence The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].
On Solving this equation we get;
Subtracting both side by 13 we get;
[tex]13+2.35x-13\leq 29.45-13\\\\2.35x\leq 16.45[/tex]
Now dividing both side by 2.35 using division property of Inequality we get;
[tex]\frac{2.35x}{2.35}\leq \frac{16.45}{2.35}\\\\x\leq 7 \ hrs.[/tex]
Hence Annie Marie can play maximum of 7 hours.
. (6.03) Which of the following best describes the expression 6(y + 3)? (4 points) The product of two constant factors six and three plus a variable The sum of two constant factors six and three plus a variable The product of a constant factor of six and a factor with the sum of two terms The sum of a constant factor of three and a factor with the product of two terms
Answer:
B The sum of two constant factors six and three plus a variable
Step-by-step explanation:
Last Sunday, the average temperature was 8%, percent higher than the average temperature two Sundays ago. The average temperature two Sundays ago was T
degrees Celsius.
Which of the following expressions could represent the average temperature last Sunday?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
\left(1+\dfrac{8}{100}\right)T(1+
100
8
)Tleft parenthesis, 1, plus, start fraction, 8, divided by, 100, end fraction, right parenthesis, T
(Choice B)
B
T+8T+8T, plus, 8
(Choice C)
C
1.08T1.08T1, point, 08, T
(Choice D)
D
1.8T1.8T1, point, 8, T
(Choice E)
E
T+0.08T+0.08
Final answer:
The expressions that correctly represent an 8% increase from T are (1 + 8/100)T, which simplifies to 1.08T, and 1.08T directly. So, choices (A) 1.08T and (C) 1.08T are correct.
Explanation:
The student is asked to determine which expression represents the average temperature last Sunday when it was 8% higher than the temperature two Sundays ago, given as T degrees Celsius. To find 8% of T, the student would multiply T by 0.08. To calculate the total average temperature last Sunday, the student would then add this to T.
The correct expressions that represent this situation are:
(Choice A) A: [tex](1 + \dfrac{8}{100})T[/tex]or 1.08T. This is because multiplying T by the fraction 8/100 gives us 8% of T, and adding T to that gives the increased temperature.(Choice C) C: 1.08T. This is a direct calculation, as multiplying by 1.08 is the equivalent of increasing a number by 8%.Expressions (Choice B) B: T + 8 and (Choice D) D: 1.8T incorrectly represent an absolute increase of 8 degrees and an 80% increase, respectively, not an 8% increase. Expression (Choice E) E: T + 0.08T is equivalent to 1.08T and is also correct.
Therefore, the correct answers are (Choice A) and (Choice C).
The Chinstrap Penguin about 68.58 centimeters tall whilethe Emperor penguin is 1.143 meters tall. How many centimeters taller is theEmperor penguin than the chinstrap pengin
Answer:
45.72 cm
Step-by-step explanation:
Given: Height of the Chinstrap Penguin= 68.58 cm
Height of the Emperor penguin= 1.143 meter
Lets calculate the height of Emperor penguin in centimeter.
Remember, 1 meter = 100 centimeter
∴ Converting the unit of height of Emperor penguin.
[tex]1.143\times 100= 114.3\ cm[/tex]
∴ Height of Emperor penguin is 114.3 cm.
Now, comparing the height of Chinstrap penguin and Emperor penguin´s height.
[tex]114.3\ cm - 68.58\ cm= 45.72\ cm[/tex]
∴ The Emperor penguin is 45.72 cm taller than Chinstrap penguin.
Two step equations
-5n+8=-7
Find the minimum or maximum value off
x^2 + 6x +11
Answer:
The minimum is the point (-3,2)
Step-by-step explanation:
we have
[tex]x^{2} +6x+11[/tex]
This is a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
Convert the equation in vertex form
Complete the square
[tex]f(x)=(x^{2} +6x+3^2)+11-3^2[/tex]
[tex]f(x)=(x^{2} +6x+9)+11-9[/tex]
[tex]f(x)=(x^{2} +6x+9)+2[/tex]
Rewrite as perfect squares
[tex]f(x)=(x+3)^{2}+2[/tex] ----> equation in vertex form
The vertex is the point (-3,2)
therefore
The minimum is the point (-3,2)
Question: 3 of 20
Mark for Review
Instructions
Review Test
Stop Test
Sean ears $300 in a regular work week. A regular work week for Sean consists of 5 work days with 8 hours a day. How much money
does Sean eam each hour?
Answer:
Sean earns $7.5 in each hour.
Step-by-step explanation:
Given:
Money earned by Sean = $300
Number of hours worked in a day = 8 hrs
Number of days of work in a week = 5
We need to find Money earned in each hour.
First we will find Total hours work in a week.
Total hours work in a week is equal to Number of hours worked in a day multiplied by number of days work in a week.
Framing in equation form we get;
Total hours worked in a week = [tex]8\times5 = 40\ hrs[/tex]
Now we will find money earned for each hour.
Money earned each hour will be calculated by Dividing Total Money earned in a week by Total number of hours worked in a week.
Framing in equation form we get;
Money earned each hour = [tex]\frac{300}{40} = \$7.5[/tex]
Hence Sean earns $7.5 in each hour.
Write a two column proof.
Step-by-step explanation:
AC ≅ EF, given
AB ≅ ED, given
∠C ≅ ∠F, right angles are congruent
ΔABC ≅ ΔEDF, SSA congruence
BC ≅ DF, corresponding parts of congruent triangles are congruent
There are 4 red and 6 green marbles in a jar. What is the probability of drawing two green marbles, with replacement?
2/5
9/25
3/5
4/25
Select EACH correct answer
Answer:
[tex]\frac{9}{25}[/tex]
Step-by-step explanation:
Number of red balls = 4
Number of green balls = 6
Total number of balls = 6+4 =10
Probability of drawing a green marble is given as
⇒ [tex]\frac{Number\ of\ green\ balls}{Total\ number\ of\ balls}[/tex]
⇒ [tex]\frac{6}{10}[/tex]
The ball is replaced after drawing.
Probability of drawing a green ball a second time will be:
⇒ [tex]\frac{Number\ of\ green\ balls}{Total\ number\ of\ balls}[/tex]
⇒ [tex]\frac{6}{10}[/tex]
Thus, probability of drawing 2 green balls with replacement can be given as:
⇒ (Probability of drawing a green marble) [tex]\times[/tex] (Probability of drawing a green ball a second time)
⇒ [tex]\frac{6}{10}\times\frac{6}{10}[/tex]
⇒ [tex]\frac{36}{100}[/tex]
Simplifying fraction by dividing numerator and denominator by their GCF.
⇒ [tex]\frac{36\div 4}{100\div 4}[/tex]
⇒ [tex]\frac{9}{25}[/tex] (Answer)
Use the following figure to answer the question.
∠ 2 and ∠ 4 are adjacent angles.
True
False
Answer:
False, they are opposite angles
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
this is what i maked on my work
The difference between 2 times x and y is less than or equal to 1
Answer:
???
Step-by-step explanation:
Answer:
Step-by-step explanation:
2 times x -------> 2x
The difference between 2 times x and y is 2x - y
The difference between 2 times x and y is less than or equal to 1:
2x - y<= 1
What is the solution to the equation 5a^2 - 44 = 81
A. Plus minus 25
B. -5
C. Plus minus 5
D. Plus minus 125
Answer:
Step-by-step explanation:
5a^2 - 44 = 81
5a^2 = 81 + 44 {add 44 both the sides}
5a^2 = 125
a^2 = 125/5 {divide both sides by 5}
a^2 = 25
a^2 = 5*5
a = ±5
Answer:
Option c) is correct
ie, a=plus minus 5 or [tex]a=\pm 5[/tex]
Step-by-step explanation:
Given equation is [tex]5a^2-44=81[/tex]
To find the solution of the given equation we have to solve the equation
[tex]5a^2-44=81[/tex]
[tex]5a^2=81+44[/tex]
Now applying the algebraic sum to the terms on the right hand side of the equation
[tex]5a^2=125[/tex]
[tex]a^2=\frac{125}{5}[/tex]
Now applying the division rule
[tex]a^2=25[/tex]
Therefore [tex]a=\pm 5[/tex]
Therefore option c) is correct
ie, [tex]a=\pm 5[/tex].
HELP:Sarah, who is 19 feet away from Justin, has a ball in her hand. Sarah throws the ball away from Justin at a speed of 5 feet per second. It takes the ball 4 seconds to reach a third friend, Brandon. When the ball reaches Brandon, how far away is it from Justin?
Answer:
Justin is 1 feet far away from Brandon
Step-by-step explanation:
As shown in the diagram, we let the distance between Justin and Brandon be x
[tex]Speed = \frac{distance}{time} [/tex]
from the question
the total time taken by the ball to reach Brandson=4s
Also the total distance is travelled by the ball=19+x
while the average speed=5ft/s
By substitution we obtain
[tex]5 = \frac{19 + x}{4} [/tex]
[tex] \implies4 \times 5 = 19 + x[/tex]
[tex]\implies20=19 + x[/tex]
[tex]\implies20 - 19 = x[/tex]
x=1 feet
The ball is 39 feet away from Justin. The ball, thrown by Sarah at 5 feet per second away from Justin, reaches Brandon in 4 seconds at a distance of 39 feet from Justin.
We need to understand the direction and speed of Sarah's throw relative to the distance between Sarah, Justin, and Brandon.
Sarah throws the ball away from Justin at a speed of 5 feet per second for 4 seconds. The formula to calculate the distance covered by the ball is:
Distance = Speed × TimeSo, Distance = 5 feet/second × 4 seconds = 20 feetThe ball travels 20 feet away from Sarah. Since Sarah is already 19 feet away from Justin, we need to add this distance to determine how far the ball is from Justin:
Distance from Justin = Sarah's Distance from Justin + Distance Traveled by the BallDistance from Justin = 19 feet + 20 feet = 39 feetHence, the ball is 39 feet away from Justin when it reaches Brandon.
someone solve this equation much appreciated!
Answer:
[tex]\frac{2A}{h} = b[/tex]
Step-by-step explanation:
this can be done by simple manipulation .in the given equation, A is the subject.so, by the above statement you can understand the meaning of making something as a subject.given equation: A = 1/2 bhmultiply both the sides by 2,2A = bh
divide both the sides by h,[tex]\frac{2A}{h} = b[/tex]
so, the required form is : [tex]\frac{2A}{h} = b[/tex]
4x/2+11x-20=0
Solve for quadratic formula
Answer:
I think -4 and 1.25
Step-by-step explanation:
Times the sum of a number and two is less than seven times the number
Answer:
[tex]x >\frac{3}{2}[/tex]
Step-by-step explanation:
The complete question is
Three times the sum of a number and two is less than seven times the number. Find the number
Let
x -----> the number
we know that
The linear equation that represent this problem is
[tex]3(x+2) < 7x[/tex]
Solve for x
Apply distributive property left side
[tex]3x+6 < 7x[/tex]
Subtract 3x both sides
[tex]6 < 7x-3x[/tex]
[tex]6 < 4x[/tex]
Divide by 4 both sides
[tex]\frac{6}{4}< x[/tex]
Simplify
[tex]\frac{3}{2}< x[/tex]
Rewrite
[tex]x >\frac{3}{2}[/tex]
Arc are subtends a central angle measuring 3pi/5 radians . What fraction of the circumference is this arc?
Answer:
The arc is 3/10 of the circumference
Step-by-step explanation:
we know that
The complete circumference subtends a central angle of 2π radians
so
using proportion
Find out what fraction of the circumference represent an arc with a central angle of 3pi/5 radians
[tex]\frac{1}{2\pi}=\frac{x}{(3\pi/5)}\\\\x=\frac{(3\pi/5)}{2\pi}\\\\x=\frac{3}{10}[/tex]
Mathematics MH help ty
When multiplying (or dividing) both sides of an inequality by a negative number, the inequality symbol must be reversed/flipped, regardless of how many steps taken when solving the inequality.
If you were to multiply (or divide) by a positive number, then you would not have to reverse/flip the inequality symbol.
The question in the image is incomplete, so I cannot provide a true/false answer, but this information should be what you need to easily choose an answer.
Let me know if you need any clarifications and happy studying~
Answer:
False
Step-by-step explanation:
only flip symbol when dividing by a negative number
On a recent survey, 40% of those surveyed indicated that they preferred walking to running. If 540 people preferred walking, how many people were surveyed
Answer:
The Total number of people were surveyed is 1,350 people.
Step-by-step explanation:
Given as :
The total number of people who preferred walking = 540 people
The percentage of people who preferred walking to running = 40% of the total people
Let The Total number of people were surveyed = n people
Now, According to question
The total number of people who preferred walking = 40% of the total number of people were surveyed
Or, 40% of n = 540
Or, [tex]\dfrac{40}{100}[/tex] × n = 540
Or, n = [tex]\frac{540\times 100}{40}[/tex]
∴ n = 1350
So,Total number of people were surveyed = n = 1350 people
Hence,The Total number of people were surveyed is 1,350 people. Answer
The population of Bumpton increased by 10% from 1980 to 1990 and decreased by 10% from 1990 to 2000. What is the net percent change in the population of Bumpton from 1980 to 2000?
Answer:
10-10=10+10 its the same it will increase and decrease the increased level