The dimensions of the fenced-in area is given as
either length is 35 yards and width is 80 yards ,
or length is 40 yards and width is 70 yards .
In the question ,
given that the total length of the fence (perimeter) = 150 yards
let L be the length of the portion to be fenced
let B be the width of the house
Given that , one side of the portion is fenced using the back side of the house
So, the perimeter of the portion to be fenced is 2L+B
equating both the perimeter ,we get
2L+B=150
B=150-2L ....(i)
Also , given that the area of the fenced-in portion = 2800 yards
also the formula for area of fenced-in portion = L×B
hence
L*B=2800
Substituting the values of B from equation(i) , we get
L*(150-2L)=2800
150L - 2L² = 2800
2L² - 150L + 2800 = 0
simplifying further , we get
L² - 75L + 1400 = 0
L² -40L -35L +1400 = 0 .....using splitting the middle term
L(L-40) -35(L-40) = 0
(L-35)(L-40) = 0
So , L = 35 yards or L = 40 yards
Using L = 35 yards , we get B = 150-2(35) = 80 yards
and using L =40 yards , we get B = 150-2(40) = 70 yards .
Therefore , the dimensions of the fenced-in area is given as
either length is 35 yards and width is 80 yards ,
or length is 40 yards and width is 70 yards .
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help me I can't solve this question
The constant of proportionality of the given function of the graph would be 3 / 4.
What is the constant of proportionality?The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.
Let the equation below which is shown in the graph:
y = kx ....(i)
where k is the constant of proportionality.
As per the given graph, take a point x = 4, and y = 3
Substitute the values x = 4, and y = 3 in the equation (i)
3 = k × (4)
4k = 3
k = 3 / 4
Thus, the constant of proportionality of the given function of the graph would be 3 / 4.
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Lona received a stamp collection from her grandmother. The collection is in a leather book and currently has 120 stamps. Lona joined a stamp club, which sends her 12 new stamps each month. The stamp book holds a maximum of 500 stamps. a. Complete the table at right. b. How many stamps will Lona have in one year from now?zetb c. Write an equation using function notation to represent the total number of stamps that Lona has in her collection after n months. Let the total be represented by t(n). Month Stamps
0, 120
1 ,132
2
3
4
5
Using a linear function, it is found that:
a. The table is completed as follows: Month 2, Stamps 144; Month 3, Stamps 156; Month 4, Stamps 168; Month 5, Stamps 180.
b. She will have 264 stamps after one year.
c. The function is given by: t(n) = 120 + 12n.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the function in this problem, we have that:
The intercept is of 120, as the initial value is of 120 stamps.The slope is of 12, as 12 stamps are added each month to the collection.Hence the function is given by:
t(n) = 120 + 12n.
To complete the table, we find the numeric values are follows:
t = 2, t(2) = 120 + 12(2) = 144.t = 3, t(3) = 120 + 12(3) = 156.t = 4, t(4) = 120 + 12(4) = 168.t = 5, t(5) = 120 + 12(5) = 180.One year from now is 12 months, hence:
t(12) = 120 + 12(12) = 264.
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Refer to the figure below if m<2 = (a+15)
, and m<3=(a+35) find the value of a that :-P hi
The value of a that makes ∠2 and ∠3 perpendicular is 20.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
From the image, HL is perpendicular to HJ, hence:
m∠2 + m∠3 = 90° (Definition of perpendicular)
Substituting gives:
(a + 15) + (a + 35) = 90
2a + 50 = 90
a = 20
value of a = 20
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Mr. Jones jogs the same route each day. The amount of time he jogs is inversely proportional to his jogging rate.
What option gives possible rates and times for two of his jogs
5 mph for 2 hours and 4 mph for 3 hours
4 mph for 2.25 hours and 6 mph for 1.5 hours
gives possible rates and times for two of his jogs
1.Let's determine the relationship between the rate of jogging and the time f jog in each scenario.
First Rate = [tex]\frac{6}{1.5} =4[/tex] time = 1.5 hours
Second Rate = [tex]\frac{5}{1.25} = 4[/tex] time = 1.5 hours
As a result, in this instance, the duration of his runs does not appear to be inversely related to their intensity.
2.First Rate = [tex]\frac{5}{2} =2.25[/tex] time = 2 hours
Second Rate = [tex]\frac{4}{3} =1.33[/tex] time = 3 hours
Therefore, in this instance, the duration of his runs appears to be inversely related to his pace.
3.First Rate = [tex]\frac{4}{2.25}[/tex]=1.77 time = 2.25 hours
Second Rate = [tex]\frac{6.5}{1.5} =4[/tex] time = 1.5 hours
Therefore, in this instance, it appears that the duration of his runs is inversely related to his speed.
4.First Rate = [tex]\frac{4.5}{3}[/tex]=1.5 time = 3 hours
Second Rate =[tex]\frac{6}{4} =1.5[/tex] time = 4 hours
Therefore, in this instance, it does not appear that the length of time he runs is inversely related to the speed at which he runs.
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Write and solve an equation to solve the problem. lisa is 4 centimeters taller than her friend lan. lan is 8 centimeters taller than jim. every month, their heights increase by 2 centimeters. in 4 months, the sum of lan's and jim's heights will be 170 centimeters more than lisa's height. how tall is lan now? let h be lan's height today in centimeters.
After solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.
As given ,
Let h be Lan's height today in centimeters.
As per the relation between Lan, Lisa and Jim height we have,
Lan=h cm
Lisa=h + 4
Jim=h -8
After 4 months, every month their heights increase by 2 cm
Lan=h + 8
Lisa=h + 4 +8
Jim=h -8 +8
Required equation for given condition:
Lan + Jim=170 +Lisa
⇒h +8 + h -8 + 8=170 + h + 4+8
⇒2h+8=h+182
⇒h=174cm
Therefore, after solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.
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Andrea is buying some new shirts and sweaters. She is able to buy 5 shirts and 3
sweaters for $89 or she is able to buy 9 shirts and 8 sweaters for $207. How much
does a shirt cost? How much does a sweater cost?
Answer: Shirt = $7 and Sweater = $18
Step-by-step explanation:
5 Shirts, 3 sweaters = $89 (1)
9 Shirts, 8 sweaters = $207 (2)
1 Shirt = $?
1 Sweater = $?
Shirts = x
sweaters = y
(1) -> 5x + 3y = 89
(2) -> 9x + 8y = 207
(1) * 8 = 40x + 24y = $712
(2) * 3 = 27x + 24y = $621
(1) single out 24y -> 24y = $712 - 40x
put value of 24 y into (2)
(2) -> 27x + $712 - 40x = $621
Now solve
-13x = $-91
remove negative -> 13x = $91
x = $7
So a shirt is $7
And we can put $7 into (1) at the start -> 5(7) + 3(y) = $89
35 + 3y = $89
3y = $54
y = $18
Hence x = $7 and y = $18
So Shirt = $7 and Sweater = $18
Which two situations result in a solution of 0?
Responses
On Tuesday morning, the temperature outside is −5∘F. On Tuesday night, the temperature outside is 5∘F. How much does the temperature change from Tuesday morning to Tuesday night?
On Tuesday morning, the temperature outside is − − 5 ∘ ∘ F. On Tuesday night, the temperature outside is 5 ∘ ∘ F. How much does the temperature change from Tuesday morning to Tuesday night?
On Friday morning, a student earns $35 mowing lawns. On Friday night, the student spends the $35 while out with friends. How much of the money that the student earns from mowing lawns is left?
On Friday morning, a student earns $ 35 mowing lawns. On Friday night, the student spends the $ 35 while out with friends. How much of the money that the student earns from mowing lawns is left?
A vacationer goes scuba diving and is at a depth of −30 yards during the dive. Later in the day, the vacationer hikes up to a lookout 30 yards above the ocean. What is the vertical distance between the diving position and the lookout position?
A vacationer goes scuba diving and is at a depth of − − 30 yards during the dive. Later in the day, the vacationer hikes up to a lookout 30 yards above the ocean. What is the vertical distance between the diving position and the lookout position?
A student walks 5 blocks west to school then another 10 blocks west after school. How far is the student from the starting location?
A student walks 5 blocks west to school then another 10 blocks west after school. How far is the student from the starting location?
A student owes a friend $7.50. If the student pays the friend $7.50, how much does the student owe the friend?
A student owes a friend $ 7.50 . If the student pays the friend $ 7.50 , how much does the student owe the friend?
The two situations which would result in a solution of 0 include the following:
B. On Friday morning, a student earns $35 mowing lawns. On Friday night, the student spends the $35 while out with friends. How much of the money that the student earns from mowing lawns is left?
D. A student owes a friend $7.50. If the student pays the friend $7.50, how much does the student owe the friend?
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
For this exercise, the expression which represents the first situation is given by:
Amount of money left = $35 - $35
Amount of money left = 0
For this exercise, the expression which represents the second situation is given by:
Amount of money owed = $7.50 - $7.50
Amount of money owed = 0.
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4.) Johnny played a video four times in a row. Each time he played he lost 15 points. How
many points did he lose in all after playing the games?
1-19
2-60
3-(-60)
4- (-19)
A physics student walks 100 meters in 80 seconds. The student stops for 30 seconds, and then walks 200 meters farther in 90 seconds. What is the average speed of the entire walk?.
The average speed of the student for his entire walk is equal to 1.5 m/s. Therefore, option (b) is correct.
What is the average speed?
The average speed of a body is calculated as the total distance traveled in a fixed interval of time. The average speed can be determined by dividing the total distance traveled by a body by the total time.
The average velocity is a single value if the object moves uniformly. Speed is a scalar quantity, it has no specified direction. The average speed has the S.I. unit the same as velocity i.e. m/s.
Given the distance covered by a student in first 80 sec = 100m
After stooping for 30sec again cover a distance of 200m in 90sec.
The total distance traveled by the student = 100 + 200 = 300m
The time taken by student to cover distance = 80 + 30 +90 = 200 sec
The average speed of the student = total distance/ total time taken
= 300/200 = 1.5 m/s
Therefore, the average speed of the student is equal to 1.5m/s.
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what is the answer for D
Answer:
Where's a photo or sum??
While the flight some humming birds can flap Thor wings about 500 times in 10 seconds. At this speed how many times might a hummingbird flap it wings in 60 seconds complete the table
Answer:
I don't see a table :/
Step-by-step explanation:
if a humming bird flaps his/her wings 500 times in 10 seconds you just have to do 500 x 6
humming birds flap their wings about 3000 times per minute
answer: 3,000
"Don't have a good day, have a great day"
-Guy
Is the Ordered Pair (3. – 2) a solution to the following equation? 3x - 2y = 13
Yes, the Ordered Pair is a solution to the equation.
No, the Ordered Pair is NOT a solution to the equation.
Please help with the questions provided in the pictures below
Answer:
the answer is gonna be d
Step-by-step explanation:
Find the equation of the line that is parallel to the line y = -3x + 2 and passes through the point (-8 , 1). Write the equation in the point slope form.
Please help !!
(College Algebra)
Answer:
y - 1 = - 3(x + 8)
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 2 ← is in slope- intercept form
with slope m = - 3
• Parallel lines have equal slopes
the equation ofa line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - 3 and (a, b ) = (- 8, 1 ) , then
y - 1 = - 3( x - (- 8) ) , that is
y - 1 = - 3(x + 8)
help me please help help
According to the solving the following equation:
The standard form: x³ + 3x² - 6x - 8
degree: 3
constant term: 8
How are polynomials created?A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.
What are the polynomial's rules?No part of an algebraic expression should be - Variables' square roots. variable powers that are fractional. variable powers that are negative. variables in any fraction's denominator.
According to the given data:Given polynomial, (x + 4) (x - 2) (x + 1)
Keeping the third bracket constant while simplifying the first two results in,
= (x² - 2x + 4x - 8)(x +1 )
= (x² + 2x - 8)(x+1)
On further simplifying we get,
= x³ + 2x² +x² -8x +2x -8
= x³ + 3x² - 6x - 8
So, the standard form is x³ + 3x² - 6x - 8 , degree is 3, leading co-efficient is 1 and the constant term is -8
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The number m and 58 are additive inverses. Drag and drop 58 and m to their correct positions on the number line.
The value of m which is an additive inverse of 58 is -58.
What numbers are additive inverses?Additive inverse is what you add to a number to make the sum zero. When two numbers are added together to get 0, then we say both the numbers are additive inverses of each other.
Since m is the additive inverse of 58, hence:
m + 58 = 0m = -58
The additive inverse of 58 is -58.
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Determine the total surface area of the composite shape below
Answer:
118.558 cm^2
Step-by-step explanation:
Ok, a rectangular cube and a Cylinder.
Let's start with the rectangular cube.
SA= 2(lw + lh + wh)
total surface area = 94 cm^2
Now the Surface Area of the of the Cone.
A=2πrh+2πr^2
A=2πrh+2πr^2=2·π·1·5+2·π·1^2≈37.69911 cm^2
Since the cone is standing on top of the rectangular cube, we need to deduct just the area of the circle.
A=πr2=π·12≈3.14159 cm^2
So, 84 cm^2 + 37.69911 cm^2 - 3.14159 cm^2
Sum the quantities:
84 cm^2 + 37.6991 cm^2 - 3.14159 cm^2
Sum the numbers 84 + 37.7 - 3.142 = 118.558:
Answer: 118.558 cm^2
The slope of MN¯¯¯¯¯¯¯ is −3.
Which segments are parallel to MN¯¯¯¯¯¯¯?
The segments are parallel to TU and WX
So, The correct options are 2 and 3
Given,
The slope of MN is -3
To find the which segments are parallel to MN?
Now, According to the given options:
We know that,
The slope of parallel lines are always equal. Therefore the line which have slope -3 is parallel to MN.
The formula to find the slope is:
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
Now, Slope for PQ,
[tex]m_{1} = \frac{7-6}{8-3}[/tex] = 1/5
Slope for TU,
[tex]m_{2} = \frac{10-1}{5-8} =[/tex] -3
Slope for WX,
[tex]m_{3} = \frac{0-6}{4-2} = \frac{-6}{2} =[/tex] -3
Slope for RS,
[tex]m_{4} = \frac{2-3}{4-1} =[/tex] -1/3
Therefore, The segments are parallel to TU and WX
So, The correct options are 2 and 3
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Kareem caught a 4 3/4 pound fish. How much did it weigh in ounces?
Answer:
76 ounces as ( 1 lb = 16 oz ) 4 3/4 * 16 = 76
Step-by-step explanation:
4 3/4 pounds = 76 ounces or 4 3/4 pounds = 2.15456376 kilograms
16 Oz for $2,24 ounces for $3
Using Unitary Method 16 Oz for $2,24 ounces for $3 is a true statement.
As given in the question,
16 Oz for $2,24 ounces for $3 is solved by Unitary Method as follows:
16 Oz for $2
24 ounces for $3
Above statement is true.
If $2 fetches 16 Oz
then $1 will fetch 8 Oz
hence $3 will fetch 24 Oz (by Unitary Method)
Thus the given statement is true.
Alternately, the statement can be verified to be true or false as follows:
16 Oz for $2
1 Oz for $(2/16)
24 Oz for $ (24x2/16) = $3
Therefore, the given statement is valid and true. The Unitary Method has been applied either way to check the validity of the given statement and found to be valid (true). It is worthwhile to mention that Oz stands for ounces (abbreviation)
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Need help on question 5 please ASAP I’m going to really appreciate it
Answer:
x+7
Step-by-step explanation:
to shift the function up, you need to add -4x by 4
and to shift the function to the left you need to add 1 by 6
If f(x) = 1/x which equation describes the graphed function? Apex ...
The equation that describes the graphed function [tex]f(x) = \frac{1}{x}[/tex] is option A:[tex]y = (x + 2) - 1.[/tex] This is shown in the graph given below, and transformation is translation.
To mathematically derive this equation, start with the original function [tex]f(x) = \frac{1}{x}[/tex].
The given function [tex]f(x) = \frac{1}{x}[/tex] has a reciprocal relationship between x and y.
To perform a horizontal translation 2 units left, substitute (x + 2) for x. This gives:[tex]f(x + 2) = \frac{1}{x + 2}[/tex].
Next, to achieve a vertical translation 1 unit down, subtract 1 from the function.
Thus, [tex]f(x + 2) - 1 = \frac{1}{x + 2}- 1[/tex].
Simplifying further, combine the terms gives:
[tex]y = (x + 2) - 1.[/tex]
This equation represents the original function :
[tex]f(x) = \frac{1}{x}[/tex]
After a horizontal translation of 2 units left and a vertical translation of 1 unit down.
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greastest common factour and the distrabutive property 18+24
Answer:
6(3 + 4)
Step-by-step explanation:
GCF of 18 and 24 is 6
6 (3 + 4)
I hope this helps!
Triangle STU with vertices S(- 1, - 6); T(0, - 3) and U(3, - 4) in the line y = - x
Triangle STU have vertices S'(6,1); T'(3,0) and U'(4,-3) after reflection across y = -x.
The triangles is reflected across the line y = -x.
If any point A(a,b) is reflected across y = -x then the coordinates of x and y axes will be interchanged and the coordinates will become negative,
So the reflected point A' will be (-a,-b).
So, after reflection,
S(-1,-6) will become S'(6,1) after reflection across y = -x.
T(0,-3) will become T'(3,0) after reflection across y = -x.
U(3,-4) will become U'(4,-3) after reflection across y = -x.
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Which statement cannot be assumed based on the diagram?
A) <GBE and <DBC are adjacent
B) <DBC is vertical to <FDE
C) <EDF and <EDC are adjacent
D) <ABG and <GBD are adjacent.
The statement that cannot be assumed based on the figure is that
<DBC is vertical to <FDE. This makes option B the answer.
Why < DBC is vertical to < FDE cannot be assumed in the given figureThe given data consist of various intersections and line types however the line type used to vertical angles are not among.
The line type responsible for vertical angles or used for vertical angle theorem is the parallel lines and a transversal line. This two lines are used together to prove or get angles that are vertical
We can therefore conclude that <DBC is vertical to <FDE is the the correct option
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A ball is thrown into the air with an upward volocitt o 12ft/se. The equation for the ball’s heigh (h) at any time (t) is h (t) =-4t^2+12t+5 find the time(s) at which the ball reaches a height of 10ft. Express solutions as decimals rounded to tenths place. Separate solutions with a comma with leaving any space
The required time at which the ball reaches a height of 10 ft is 0.5 sec.
Given that,
A ball is thrown into the air with an upward velocity o 12ft/s. The equation for the ball’s height (h) at any time (t) is h (t) =-4t^2+12t+5 find the time(s) at which the ball reaches a height of 10ft.
Here,
Given equation,
h(t) =-4t²+12t+5
For height 10 ft time,
10 = -4t² + 12t + 5
4t² - 12t + 5 = 0
4t² -10t - 2t + 5 = 0
2t(2t - 5) - 1(2t - 5) = 0
(2t-1)(2t -5) = 0
t = 1/2, 5/2 (5/2 can be negelected)
Thus, the required time at which the ball reaches a height of 10 ft is 0.5 sec.
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Find measure of angle g rounded to the nearest degree
We need to know about trigonometry to solve this problem. The measure of angle G is 27.9°
Trigonometry is related to functions of angles and their applications. There are six main functions of an angle, sine, cosine, secant,cosecant,tangent and cotangent. Here in this question we know the measure of all the sides of the triangle, and the angle T is 90°. We will be using the function tangent(tan) to solve for angle G. The base of the triangle is RG and the height is TR.
RG=8 TR=15
tan G=base/height=RG/TR=8/15=0.533
G=[tex]tan^{-1}[/tex] 0.53=27.9°
Therefore the measure of the angle G is 27.9°.
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Use the four-step procedure for solving the following variation problem
The height that a ball bounces varies directly as the height from which it was dropped. A tennis ball dropped from 14 inches bounces 8.4 inches. From what height was the tennis ball dropped if it bounces
42 inches?
The tennis ball needs to be dropped from the height of
(Type an integer or a decimal)
so that it bounces 42 inches.
9
Height was the tennis ball dropped if it bounces 42 inches is 0.7 inch.
What do you understand by direct proportionality?
If two quantities are directly proportional, it means that when one quantity increases at a certain rate, the other quantity also increases at the same rate up to a constant value. It is represented by the proportional symbol ∝.
Let the height of the ball bounces be h
The height of the ball drobbed from be y
It is given that the height that a ball bounces varies directly as the height from which it was dropped.
⇒ h ∝ y
⇒ h = ky where k is the constant of proportionality.
It is given that a tennis ball dropped from 14 inches.
⇒ y = 14 inches
Tennis ball bounces back to 8.4 inches.
⇒ h = 8.4 inches
⇒ 8.4 = k × 14
⇒ k = 8.4/14 = 0.6
Now, tennis ball dropped from 42 inches
y = 42
⇒ h = 42 × 0.6 = 0.7
Therefore, height was the tennis ball dropped if it bounces
42 inches is 0.7 inch.
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ken and hamid run around a track it takes ken 80 seconds to complete a lap it takes hamid 60 seconds to complete a lap how many laps would they have won to both meet on the starting line
When Ken and Hamid race around a track, Ken completes a lap in 80 seconds while Hamid completes a lap in 60 seconds. ken will run 3 laps where as Hamid will run 4 laps.
Given that,
When Ken and Hamid race around a track, Ken completes a lap in 80 seconds while Hamid completes a lap in 60 seconds.
We have to find if they had faced off on the starting line, how many laps would they have won.
We have to find the LCM of the 80 and 60.
The prefix "LCM" stands for "Least Common Multiple." The smallest multiple that two or more numbers share is known as the least common multiple.
LCM of 80 and 60 is 240
240=80×3
ken will complete 3 laps.
240=60×4
Hamid will complete 4 laps.
Therefore, ken will complete 3 laps where as Hamid will complete 4 laps.
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Find hcf
a) x³-1, x^4 + x² + 1, x³ + 2x² + 2x + 1
Answer:
Hope the picture will help you