Answer:
2w^2.
Step-by-step explanation:
Let "w" be the width of the walkway. Then, the length of the garden is 6.5(6x + 6) - 2w and the width of the garden is 6.5(6x + 6) - 2w.
The area of the garden is 6(4.5x + 2.5) = 6 * 4.5 * x + 6 * 2.5 = 27x + 15
The area of the garden and walkway is (6.5(6x + 6) - 2w)^2 = 27x + 15 + 2w^2
Equating the two expressions for the area of the garden:
27x + 15 = 27x + 15 + 2w^2
Thus, the area of the walkway is:
Write the ratio in unit rate form. There are 25 runners on a cross country team. 5 of the runners are boys. Write the unit rate comparing all runners to boys.
The ratio the unit rate comparing all runners to boys is 5:1.
What is the unit rate formula?How to Calculate Unit Rate The denominator of a unit rate is always 1. Therefore, divide the denominator by the numerator so that the denominator equals one in order to determine the unit rate. The unit rate is 50km/5.5 hours = 9.09 km/hour, for instance, if 50km are travelled in 5.5 hours.
What does a typical unit rate mean?A unique form of ratio called a unit rate has a denominator (second number) of one. You are comparing a quantity to one when using a unit rate. Miles per gallon, price per pound, and pay rate per hour are a few examples of popular unit rates.
To know more about ratio visit:-
brainly.com/question/29467965
#SPJ1
Mayra's brother is driving back from college to visit. His college is 330 miles away. After an hour of
driving, he still has 275 miles to go. If the roads are clear, he'll be able to keep up that pace for the
whole drive. Write a linear function to model how much further he'll have to go over time.
The linear function to model how much further he'll have to go over time is h(t) = 330 - 55t
How to write a linear function?Total distance between home and college= 330 miles
Distance remaining to cover= 275 miles
Distance covered= Total distance between home and college - Distance remaining to cover
= 330 miles - 275 miles
= 55 miles
Time taken to cover 55 miles= 1 hour
h(t) = 330 - 55t
Where,
h = distance remaining to cover
t = time
Ultimately, h(t) = 330 - 55t is the linear function which represents how much further he'll have to go over time.
Read more on linear function:
https://brainly.com/question/4025726
#SPJ1
Originally, a department store bought a set of dishes at a cost of $57.68 and marked it up 125%. After a month, the set of dishes had not sold, so the store marked it down 50%. What was the discounted price?
$
The discounted price of the set of dishes would be = $63.89
How to calculate the discounted price?The original cost of the dishes = $57.68
The percentage increase of the cost of the dishes = 125%
That is,
= 125/100 × 57.68
= 7210/100 = $72.10+57.68 = $129.78
After one month, the store marked it down by 50%, therefore the discounted price;
= 50/100 × 129.78/1
= 6489/100
= $65.89
= 129.78-65.89 = $63.89
Learn more about discounts here:
https://brainly.com/question/28390698
#SPJ1
The discounted price is $64.89
What was the discounted price?From the question, we have the following parameters that can be used in our computation:
Cost = $57.68
Mark up = 125%
Mark down = 50%
The discounted price is then calculated as
price = cost * (1 + mark up) * (1 - mark down)
So, we have
price = 57.68 * (1 + 125%) * (1 - 50%)
Evaluate
price = 64.89
Hence, the price is 64.89
Read more aout discount at
https://brainly.com/question/5168855
#SPJ1
Two of the interior angles of a polygon are 140° and 160° , the remaining and 150°. Find the number of sides of the polygon
the number of sides of the polygon 12 sides
Which polygon has a space inside?An interior angle is a shape's internal angle. The closed shape with sides and vertices is a polygon. All of the inner angles of a regular polygon are equal to one another. For instance, a square has interior angles that are all exactly right angles, or 90 degrees.
In a regular polygon, all internal angles are equal. Interior angle of a polygon = sum of interior angles number of sides is the formula for determining the amount of an interior angle.
The n-sided polygon's inner angle total equals (n-2).
180°, thus as follows:
140°+160°+ (n-2)150 = (n-2)180°
or, 300° = (n-2)(180° - 150°).
or, 300° = (n-2) 30°
or, 10= n - 2.
alternately, n = 10 + 2 = 12 sides.
To know more about polygon visit:-
https://brainly.com/question/30108398
#SPJ1
|60| ___ |-60|
>
=
<
can you help me about that problem
Answer:
the correct answer to this equation would be: >
Cody purchased a bag of carrots costing $1.54. If Cody received $4.41 in change, how much money did he give to the cashier?
Answer: Cody gave the cashier $2.87.
Step-by-step explanation:
To determine the amount of money Cody gave to the cashier, you can subtract the amount of change he received from the cost of the carrots.
$4.41 (change) - $1.54 (cost of carrots) = $2.87
So, Cody gave the cashier $2.87.
To prove KLM = KLN, which triangle congruence postulate could you use? (last option is F. AAA)
The congruence postulate used to prove the congruence of triangles KLM and KLN is given as follows:
E. ASA.
What is the Angle-Side-Angle congruence theorem?The Angle-Side-Angle (ASA) congruence theorem states that if any of the two angles on a triangle are the same, along with the side between them, then the two triangles are congruent.
For this problem, we have that the two angles between segment LK are equal for each triangle, as LK is a bisection of these two angles, along with segment LK, hence the ASA congruence postulate was used and the correct option is given by option E.
More can be learned about congruence theorems at brainly.com/question/3168048
#SPJ1
Two different workers are producing a specialized part for a machine. The number of parts produced per hour by the workers are as follows:
Worker A: 5, 4, 4, 6, 7, 5, 6, 3
Worker B: 4, 8, 1, 9, 2, 9, 4, 3
Both workers averaged 5 parts per hour. Which worker has the higher variance and standard deviation?
The worker B has a higher variance of σ² = 9 and standard deviation of 3
What is Standard Deviation?The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Standard Deviation is calculated by
Each number's deviation from the mean must be determined, and then squared.
Next, add up all of these values.
Divide the result by the quantity of numbers.
Then calculate its square root.
Given data ,
Let the data of worker A = { 5, 4, 4, 6, 7, 5, 6, 3 }
Let the data of worker B = { 4, 8, 1, 9, 2, 9, 4, 3 }
Now , the mean of worker A = 5
The mean of worker B = 5
So , the standard deviation of worker A is calculated as
The sum of the difference of the data from mean is
SD = √ ( 5 - 5 )² + ( 5 - 4 )² + ( 5 - 4 )² + ( 5 - 6 )² + ( 5 - 7 )² + ( 5 - 5 )² + ( 5 - 6)² + ( 5 - 3 )² / 8
On simplifying the equation , we get
SD = √ ( 12/8 )
SD = √1.5
Standard deviation σ = 1.2247449
And , the variance of worker A is σ² = 1.5
Now ,
The standard deviation of worker B is calculated as
The sum of the difference of the data from mean is
SD = √ ( 5 - 4 )² + ( 5 - 8 )² + ( 5 - 1 )² + ( 5 - 9 )² + ( 5 - 2 )² + ( 5 - 9 )² + ( 5 - 4)² + ( 5 - 3 )² / 8
On simplifying the equation , we get
SD = √ ( 72/8 )
SD = √9
Standard deviation σ = 3
And , the variance of worker A is σ² = 9
Hence , the worker B has higher standard deviation
To learn more about standard deviation click :
https://brainly.com/question/28189061
#SPJ1
Determine the solution to the inequality.
1/4|x+1|>4
a. x ≥ -1 or x ≥ 17
b. x < -17 or x ≥ 15
c. x < -9 or x > 7
d. x < -2 or x > 0
Answer:
bbbbbbbbbbbbbb
see attched image for sol
PLS HELP !
solve the inequality 
3/4 |1/3 + 2| < 6
a. x > -8 and x < -4
b. x > -30 and x < 2
c. x < -30 and x < 18
d. x > -30 and x < 18
The solutions of the equation are x < 18 and x < - 30.
Solution on inequalities:Solutions of equations are the numerical values of the variables that will satisfy the condition in the given equation. Similarly, the solutions of inequalities are the values of variables that can satisfy the given inequality.
We can solve an inequality by adding or subtracting the same integer on both sides, or we can multiply or divide by the same number on both sides until we get the value of 'x'.
Here we have
3/4 |1/3x + 2| < 6
We can solve the above equation as follows
3/4 |1/3x + 2| < 6
Multiply by 4 on both sides
=> 4 [ 3/4 |1/3x + 2| ] < 4 × 6
=> 3 |1/3x + 2| < 24
=> | x + 6| < 24
=> x + 6 < ± 24
=> x + 6 < 24 and x + 6 < - 24
Subtract - 6 on both sides
=> x + 6 - 6 < 24 - 6 and x + 6 - 6 < - 24 - 6
=> x < 18 and x < - 30
Therefore,
The solutions of the equation are x < 18 and x < - 30.
Learn more about Inequalities at
https://brainly.com/question/30231190
#SPJ1
What is 70% of 90 as a number thank you
Answer:
70 percent of what number is 90?
90 is 70% of 128.57
Steps to solve "90 is 70 percent of what number?"
We have, 70% × x = 90
or,
70
100
× x = 90
Multiplying both sides by 100 and dividing both sides by 70,
we have x = 90 ×
100
70
x = 128.57
If you are using a calculator, simply enter 90×100÷70, which will give you the answer.
Answer: 70 % of 90 = 63
Step-by-step explanation:
70 % x 90.
= (70/100) x 90
= (70*90)/100
= 6300/100
= 63
Use Cramer's rule to solve the following system. Determine D, Dx, Dy and use these values to
solve x and y.
- 8x+4y=8
3x - 5y = 4
D=
(Type an integer)
Dx =
(Type an integer)
D₁ = 0
(Type an integer)
X =
(Type an integer or fraction. Do not simplify fraction.)
y =
(Type an integer or fraction. Do not simplify fraction.)
The values of D, Dx, Dy , x and y are
D=28
Dx= -56
Dy= -56
x=-2
y=-2
What are matrices ?
The word "matrix" can be used to refer to a rectangular array or table with numbers or other components arranged in rows and columns. Any number of columns and rows are allowed. Matrix operations include addition, multiplication, transposition, scalar multiplication, and many others.
Write the matrices by taking coefficients of x and y in different columns as:
[tex]\begin{bmatrix} -8 & 4 \\ 3 & -5 \end{bmatrix} =\begin{bmatrix} 8 \\ 4&\end{bmatrix}[/tex]
Determinant of LHS = D
[tex]D=\begin{vmatrix} -8 & 4 \\ 3 & -5 \end{vmatrix}[/tex]
D=28
Substitute the x-column with the RHS to find Dx
Substitute the y-column with the RHS to find Dy
[tex]Dx=\begin{vmatrix} 8 & 4 \\ 4 & -5 \end{vmatrix}[/tex]
Dx= -56
[tex]Dy=\begin{vmatrix} -8 & 8 \\ 3 & 4 \end{vmatrix}[/tex]
Dy= -56
x=Dx / D = -56/28 = -2
y=Dy / D = -56/28 = -2
The values of D, Dx, Dy , x and y are
D=28
Dx= -56
Dy= -56
x=-2
y=-2
To learn more about the matrices from the given link
https://brainly.com/question/27929071
#SPJ1
help me i need help whats the answer
Answer:
17
degree
jjaokaohshdh
Step-by-step explanation:
Joppa
also
aijsiwso
akoakwbd
Lily is working two summer jobs, making $11 per hour babysitting and $14 per hour clearing tables. Lily must earn a minimum of $180 this week. Write an inequality that would represent the possible values for the number of hours babysitting,
�
b, and the number of hours clearing tables,
�
c, that Lily can work in a given week.
If f(1) = 5 and f(n) = 5f(n-1) + 5 then find the value of f(3)
The value of function for f(5) is 3125.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given that, f(1) = 5 and f(n) = 5f(n − 1)
Now, for finding the the 5th term we have to find the remaining four term before the 5th term.
So, n=2
f(2) = 5f(1)
f(2)= 5(5)
f(2)= 25
Now, n=3
f(3) = 5f(2)
f(3)= 5(25)
f(3)= 125
Now, n=4
f(4) = 5f(3)
f(4)= 5(125)
f(4)= 625
Now, n=5
f(5) = 5f(4)
f(5)= 5(625)
f(5)= 3125
Hence, the value of function for f(5) is 3125.
Learn more about function here:
brainly.com/question/12431044
#SPJ1
Please help. I don’t know how to work it out and need somebody to show me
The distance of AB is 117.992 meters.
What is Law of Sines?Law of sines is a law in trigonometry which states that the ratios of the angle to the opposite side of a triangle are equal.
For triangle ABC,
sin A / a = sin B / b = sin C / c
where a, b and c are the sides opposite to the angles A, B and C respectively.
Here,
∠B = 112° 10' = 112° + 0.167° = 112.167°
∠C = 15° 20' = 15° + 0.333° = 15.333°
By the angle sum property of triangle,
∠A = 180° - (∠B + ∠C)
∠A = 180° - (112.167° + 15.333°)
= 52.5°
Using law of sines,
sin A / BC = sin C / AB
sin (52.5°) / 354 = sin (15.333°) / AB
AB = [354 × sin (15.333°)] / [sin (52.5°)]
AB = [354 × 0.264] / [0.793]
AB = 117.992 meters
Hence the distance across the river is 117.992 meters.
Learn more about Law of Sines here :
https://brainly.com/question/17289163
#SPJ1
determine whether or not the function f(x)= x^2 +2x if x<0 x^3-2x if x>0 is continuous at x=0
The given function f(x) = x² + 2x when x <0 and f(x) = x³ - 2x when x > 0 is continuous at x=0
What is continuity ?In mathematics, The function is called as continuous at the particular value of x, if right hand limit, left hand limit and the value of function at x all are equal.
RHL = LHL = F(x)
Limit exist and continuous
Given that,
F(x) = x² + 2x {x ≤ 0}
= x³ - 2x { x > 0}
To check whether it is continuous at x = 0
First taking LHL,
F(0) = 0² + 2x0
= 0
Now, taking RHL
F(0) = 0³ - 2x0
At x = 0
F(0) = 0² + 2x0
= 0
RHL = LHL = F(0)
Hence, the given function is continuous at x =0
To know more about limits and continuity check:
brainly.com/question/30328478
#SPJ1
what is the slope of the line passing through the points (-3, 4) and (2, -1)
Answer:
-1
Step-by-step explanation:
You want the slope of the line through the points (-3, 4) and (2, -1).
SlopeThe slope is given by the formula ...
m = (y2 -y1)/(x2 -x1)
Using the given points, we find the slope to be ...
m = (-1 -4)/(2 -(-3)) = -5/5 = -1
The slope of the line through the given points is -1.
If P is the circumcenter of ABC, AD = 7x - 6; DB = 5x + 8, and PC = 35, find DP.
If P is the circumcenter of ABC, the DP is 13.27 units.
What is the value of DP?
The value of DP is calculated by applying the following method as shown below.
Based on the given figure, D is the midpoint of AB
Line AD = BD, so line DP is perpendicular to line AB and the following equation can be formed to determine value of x.
7x - 6 = 5x + 8
2x = 14
x = 14/2
x = 7
DB = 7x - 6
DB = (7 x 7 ) - 6 = 43
Let PC = 45
PC = PB = 45
Apply Pythagoras theorem to determine DP;
DP² = PB² - DB²
DP² = 45² - 43²
DP² = 176
DP = √176
DP = 13.27 units
Learn more about circumcenter here: https://brainly.com/question/21299234
#SPJ1
I need a detailed explanation of how 0.667 as a fraction equals 2/3. this isn't making sense.
The reason 0.667 is equal to 2/3 is because when you divide:
2 ÷ 3 = 0.6666666667.
You can shorten 0.6666666667 to 0.667.
That is how 2/3 is equal to 0.667.
Mark me Brainliest. :D
Complete the description of the piecewise function graphed below.
The required description of the given piecewise function is graphed below.
f(x) = 3 if [-5, -2]; f(x) = -3 if (-2, 3]; and f(x) = 3 if (3, 4]
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
f(x) = 3 if [-5, -2]
This the sub-function define between the interval [-5, -2].
f(x) = -3 if (-2, 3]
This the sub-function define between the interval (-2, 3].
f(x) = 3 if (3, 4]
This the sub-function define between the interval (3, 4].
Learn more about the piecewise function here:
https://brainly.com/question/12700952
#SPJ1
I know this looks easy but to me is hard will mark u brainliest!!!
Answer:
14q/25
Step-by-step explanation:
14q/25
Reuben and Maria walk around a track. Reuben walks each lap in 9 minutes. Maria walks each lap in 6 minutes. The two of them begin at the starting line at the same time. They walk until they meet again at the starting line. how many laps does Reuben complete? how many laps does maria complete? and how much time does it take for them to meet again at the starting line?
1) The number of laps that Reuben completes is; 2 laps
2) The number of laps that Maria completes is; 3 laps
3. It will take 18 minutes for Reuben and Maria to meet again at the starting line.
How to solve Algebra Word problems?The parameters to solve the problem are;
Time for each lap by Reuben = 9 minutes
Time for each lap by Maria = 6 minutes
Let us find the L.C.M(Lowest common multiple) of 6 and 9;
Factors of 6 = 2 * 3
Factor of 9 = 3 * 3
Thus, L.C.M = 2 * 3 * 3 = 18 Minutes
This represents the time it will take for them to meet again at the starting line.
Read more about Algebra Word problems at; https://brainly.com/question/21405634
#SPJ1
The length of a string in yards is a function ƒ(n) of the length n in inches. Write a function rule for this situation.
The function rule for this situation is f(n) = 1/36n
How to write a function rule for this situation.From the question, we have the following parameters that can be used in our computation:
The length of a string in yards is a function ƒ(n) of the length n in inches.
The conversion of yards to inches is
Yard = 1/36 * Inches
When represeted as a function, we have
f(n) = 1/36n
Hence, the function is f(n) = 1/36n
Read more about function at
https://brainly.com/question/25638609
#SPJ1
Topic 21 Angles of Triangles
3.
88 1
180'
姐
5.
(8x-35)
For questions 3 and 4, find the measure of each missing angle.
11 180
ई
-64
(3x-1)
(6r-5)
6.5
642
•92⁰
m22 = 24
m21 =
m23-
m24 =
m25=
80
For questions 5 and 6, find the value of x.
6.
(i=11)
2x+20)
(11X-63)
mel-
m/2=
m23-
m24
m25-
m26-
m47 =
The value of x is 13 and the angles in the triangle are 38,69 and 73 respectively.
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
From the given figure,
In the given triangle ,
The triangles are 3x - 1 , 8x - 35 and 6x - 5
The sum of all angles is always is 180 degrees.
so,
we get,
3x - 1 + 8x - 35 + 6x - 5 = 180
17x - 41 = 180
17x = 180 + 41
17x = 221
x = 221 / 17
x = 13
so,
3x - 1 = 3*13 - 1 = 38
8x - 35 = 8* 13 - 35 = 104 - 35 = 69
6x - 5 = 6*13 - 5 = 78 - 5 = 73
Therefore, The value of x is 13 and the angles in the triangle are 38,69 and 73 respectively.
To learn more about Triangle from given link.
https://brainly.com/question/2773823
#SPJ1
The vertices of a right-angled triangle are A(1, 0), B(7, 0) and C(1,8). Plot the points A, B and C on a sheet of graph paper. Hence, find the area of triangle ABC. (05)
Answer:24 sq. units
Step-by-step explanation:
The length of the base is (7-1)= 6 units. The height is 8 units.
Area =1/2*l*b=24
If the car climbs 60 m vertically how far must the car have travelled horizontally?
The the gradient of the slope is 2/15
The horizontal distance is 150 meters
How to determine the horizontal distanceFrom the question, we have the following parameters that can be used in our computation:
Gradient = 2/15
Vertical distance = 60 meters
The gradient is calculaed as
Gradient = Vertical distance/Horizontal distance
So, we have
Horizontal distance = Vertical distance/Gradient
This gives
Horizontal distance = (60)/(2/5)
Evaluate
Horizontal distance = 150
Hence, the distance is 150 meters
Read more about slope at
https://brainly.com/question/16949303
#SPJ1
Someone help me with this math problem.
From the graph, she walked at a rate of [tex]\frac{25-10}{5-2}=5 \text{ ft/s}[/tex].
Therefore, she walked faster on her next three walks compared to her first two walks.
Consider the function shown on the graph. Which function does the graph represent? f(x) = (x + 3)(x + 7) f(x) = (x – 3)(x – 7) f(x) = 3(x – 3)(x – 7) f(x) = 11(x + 3)(x + 7)
The solution is Option C.
The value of the function is f ( x ) = 3 ( x - 3 ) ( x - 7 )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 3 ( x - 3 ) ( x - 7 ) be equation (1)
On simplifying the equation , we get
y = 3 ( x - 3 ) ( x - 7 )
And , the point ( 8 , 15 ) lies on the graph
Substituting the values in the equation , we get
when x = 8
y = 3 ( 8 - 3 ) ( 8 - 7 )
y = 3 ( 5 )
y = 15
Therefore , the point P ( 8 , 15 ) lies on the graph of the function
And , the graph has two zeros at (3,0) and (7,0)
Hence , the graph of the function is f ( x ) = 3 ( x - 3 ) ( x - 7 )
To learn more about graph of polynomials click :
https://brainly.com/question/16957172
#SPJ1
Answer:
c
Step-by-step explanation:
c
please explain how we measure the range and the domain in the following graphs, please
For the first function, the domain and the range are given as follows:
Domain: (-∞, ∞).Range: (-∞, -4].For the second function, the domain and the range are given as follows:
Domain: [-6, 0]Range: [3,6].How to obtain the domain and the range of a function?The domain of a function is the set that contains all the input values that can be assumed by the function, hence it is given by the set that contains all the values of x in the graph of the function.
The range of a function is the set that contains all the output values that can be assumed by the function, hence it is given by the set that contains all the values of y in the graph of the function.
More can be learned about the domain and the range of a function at brainly.com/question/30248800
#SPJ1