Answer:
it will cost $520.00 to install the gravel path.
Step-by-step explanation:
We can use the Pythagorean theorem to find the length of the diagonal of the rectangular garden. The Pythagorean theorem states that the square of the length of the hypotenuse (in this case, the diagonal) of a right triangle is equal to the sum of the squares of the lengths of the other two sides. Therefore, we have:
diagonal^2 = 24^2 + 32^2
diagonal^2 = 576 + 1024
diagonal^2 = 1600
Taking the square root of both sides, we get:
diagonal = sqrt(1600)
diagonal = 40 feet
Now, we need to calculate the area of the path that Jorge will install. Since the path is 2 feet wide, the width of the garden is reduced by 4 feet (2 feet on each side). Therefore, the length and width of the garden after the path is installed will be:
length = 24 - 4 = 20 feet
width = 32 - 4 = 28 feet
The area of the path is the difference between the area of the garden before and after the path is installed:
area of path = (24 * 32) - (20 * 28)
area of path = 768 - 560
area of path = 208 square feet
Finally, we can calculate the cost of the gravel path by multiplying the area of the path by the cost per square foot:
cost of path = 208 * 2.50
cost of path = $520.00
Therefore, it will cost $520.00 to install the gravel path.
a killer whale is 7.5 m long. Convert this length to feet and the nearest inch.
Answer:
24.6063 ft
Step-by-step explanation:
Please help i need it!!!!!
A 6 N crate is lifted 2 meters. How much work is done?
A) 12 N/m
B) 4 N/m
C) 8 N/m
D) 3 N/m
The amount of work done is Option A) 12 N/m
What is work done?Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.
It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.
Work done on a body is equivalent to the increase in the energy of the body, because it transfers energy to the body.
The formula for work done is;
W = fd
Where, 'f' is the applied force and d is the distance
Substitute the values
Work done = 6(2)
Work done = 12 N/m
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If using the method of completing the square to solve the quadratic equation
x
2
+
7
x
+
27
=
0
x
2
+7x+27=0, which number would have to be added to "complete the square"?
The number that was added to complete the square is (7/2)²
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given quadratic equation is x²+7x+27=0
Add and subtract (7/2)² = 49/4
x² + 7x + 27
= ( x² + 7x + 49/4) - 49/4 + 27=0
= (x + 7/2)² - 59/4
Now we can rewrite the original equation as:
(x + 7/2)² - 59/4 = 0
Adding 59/4 to both sides, we get:
(x + 7/2)² = 59/4
Taking the square root of both sides, we get:
x + 7/2 = ±√59/2
Solving for x, we get:
x = -7/2 ±√59/2
Therefore, the number that was added to complete the square is (7/2)²
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I need help with C! If sin = 7/10 theta , find the exact value of
The evaluation of the trigonometric identities can be presented as follows;
(a) cos(θ) = -√(51)/10
(b) sin(θ + π/76) = (7·√3 - √(51))/20
(c) cos(θ - π/3) = (7·√3 - √(51))/20
What are trigonometric identities?Trigonometric identities are equations involving trigonometric ratios, in which the values correct far all possible values of the input variable.
(a) The value of sin(θ) = 7/10
The location of the angle θ is quadrant II, therefore;
The adjacent side to the angle θ is -ve, therefore;
cos(θ) = (√10² - 7²)/10 = -√(51)/10
(b) sin(θ + π/6) = sin(θ) × cos(π/6) + sin(π/6) × cos(θ)
sin(θ + π/6) = 7/10 × √3/2 + 1/2 × (-√(51)/10) = 7/10 × √3/2 - 1/2 × √(51)/10
sin(θ + π/6) = (7·√3 - √(51))/(2 × 10) = (7·√3 - √(51))/(20)
(c) cos(θ - π/3) = cos(θ)·cos(π/3) + sin(θ)·sin(π/3)
Therefore;
cos(θ - π/3) = ((-√51)/10 )× (1/2) + (7/10) × √3/2
cos(θ - π/3) = ((-√51)/10 )× (1/2) + (7/10) × √3/2 = (7·√3 - √(51))/20
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two bakers make 30 loaves of bread every morning. assume all bakers work at the same rate. suppose two bakers make 30 loaves in one hour. how many hours would 3,5,6 and 15 bakers need to make 30 loaves.
Answer:
Step-by-step explanation:
If two bakers can make 30 loaves in 1 hour, then we can use proportionality to find how many hours it would take for 3, 5, 6, and 15 bakers to make 30 loaves.
Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:
2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.
Therefore:
3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.
5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.
6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.
15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.
Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.
What are the inputs of the following function?
((-3, 2), (-4, 2), (8, 3), (7, 1))
[1, 2, 3]
[1, 2, 3, 7, 8)
(-4,-3, 7, 8)
(4, -3, 1, 2, 3, 7, 8)
Answer:
(-4,-3,7,8)
Step-by-step explanation:
the inputs are the X values , the X values are the first number on the parenthesis (X , Y) , the outputs are the Y values
CALC
PLEASE HELP!!
A chemical substance has a decay rate of 8.8% per day. The rate of change of an
dN
amount N of the chemical after t days is given by = -0.088N
dt
(i) Let No represent the amount of the substance present at to. Find the exponential function
that models the decay.
(ii) Suppose that 400g of the substance is present at to. How much will remain after 3 days?
(iii) What is the rate of change of the amount of the substance after 3 days?
(iv) After how many days will half of the original 400 g of the substance remain?
A function is a relationship between a few different inputs and an output, where each input can only lead to one possible outcome.
What is the chemical substance has a decay rate?(i) The exponential function that models the decay of the substance is given by:
[tex]N(t) = Noe^(-0.088t)[/tex]
(ii) If [tex]400g[/tex] of the substance is present at to, then [tex]No = 400g[/tex] . Therefore, the amount of the substance remaining after 3 days is:
[tex]N(3) = 400e^(-0.0883) = 309.21g[/tex] (rounded to two decimal places)
(iii) The rate of change of the amount of the substance after 3 days is given by:
[tex]dN/dt = -0.088N(3) = -0.088309.21 = -27.21 g/day[/tex] (rounded to two decimal places)
(iv) To find the number of days it takes for half of the original [tex]400g[/tex] of the substance to remain, we need to solve the equation:
[tex]N(t) = 0.5No[/tex]
[tex]0.5No = Noe^(-0.088t)[/tex]
[tex]0.5 = e^(-0.088t)[/tex]
[tex]ln(0.5) = -0.088t[/tex]
[tex]t = ln(0.5)/(-0.088) = 7.89 days[/tex] (rounded to two decimal places)
Therefore, after [tex]7.89[/tex] days, half of the original [tex]400g[/tex] of the substance will remain.
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3. Ray compared the y-intercept of the graph of
the function f(x) = 5x + 7 to the y-intercept of the
linear function that includes the points in the table
below.
X
1
2
3
4
g(x)
20
35
50
65
Determine the distance between the y-intercept
of f(x) and the y-intercept of g(x).
The distance between the twο y-intercepts is 7 - 19 = -12.
What is value?Value is the impοrtance, wοrth, οr usefulness οf sοmething. It is a measure οf the relative wοrth οf sοmething and can be expressed in variοus ways, such as mοnetary, sοcial, οr practical. Value can be determined by cοnsidering factοrs such as quality, utility, and scarcity. Values are subjective and can be influenced by persοnal, cultural, and sοcietal factοrs. They οften reflect a persοn's beliefs, attitudes, οr preferences. Value is an impοrtant cοncept in ecοnοmics, finance, and sοcial science.
The y-intercept οf f(x) is 7, while the y-intercept οf g(x) is calculated by subtracting the x-value οf the first rοw frοm the g(x) value, which is 20 - 1 = 19.
Therefοre, the distance between the twο y-intercepts is 7 - 19 = -12.
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3. Solve this word problem:
Candice's wanted to paint the wall of her room with her favourite colour blue. Candice had
4 cans of blue paint stored in the garage. She used 2 - cans to paint her room.
3
How much blue paint did Candice have left over?
Answer:
Candice had 2 cans left over.
Please help solve these! Thank you!!
The value of function f(x) at x =1 will be 4.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given a function f(x) = -3x + 7
To calculate the value of the function at x = 1,
We need to substitute the value of x = 1 in the function,
thus,
f(1) = -3 * 1 + 7
f(1) = -3+ 7
f(1) = 4
This represents the point (1, 4) on function f(x) = -3x +7.
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What are the domain and range of the function f(x)= x^4-2x^2-4? domain: all real numbers range: all real numbers greater than or equal to –5 domain: all real numbers range: all real numbers greater than or equal to –4 domain: all real numbers between –2.5 and 2.5 range: all real numbers domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5
Answer:
The correct answer is: domain: all real numbers, range: all real numbers greater than or equal to -5.
We can see that the function is a polynomial of degree 4, which means it is defined for all real numbers. Also, as x^4 is always non-negative, the minimum value of the function occurs when x=0, and it is f(0) = -4. Therefore, the range of the function is all real numbers greater than or equal to -4. However, since the function is increasing as we move away from 0, the range is actually all real numbers greater than or equal to the minimum value of -4 plus the vertical shift of -1, which is -5.
please help thankss
:) g
Answer:
origin
Step-by-step explanation:
the point (0,0) is called the origin
Answer:
The center of a coordinate plane, which is point (0,0) is called "the origin."
Step-by-step explanation:
Which statement is sometimes true? only one answer.
Question 2 options:
A square is a rhombus.
A trapezoid is a parallelogram.
A rectangle is a parallelogram.
A rectangle is a square.
Answer:
The statement that is sometimes true is C: A rectangle is a parallelogram.
Step-by-step explanation:
A parallelogram is a four-sided shape with opposite sides parallel. A rectangle is a specific type of parallelogram where all angles are right angles, and opposite sides have equal lengths. Therefore, a rectangle is considered a parallelogram. However, not all parallelograms are rectangles because other parallelograms may have angles that are not right angles.
The sides of a triangle are 63, 58, and 30. Use the Pythagorean
Theorem to determine if the triangle is right, acute, or obtuse.
Answer:
To use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse, we need to find the length of the longest side (also known as the hypotenuse) by squaring each side, adding the results, and taking the square root of the sum.
So,
63^2 = 3969
58^2 = 3364
30^2 = 900
Now, we add 3969 and 3364 to get 7333, and take the square root to get approximately 85.62.
Since 63, 58, and 30 are the lengths of the sides of the triangle, we can compare the length of the longest side (85.62) to the sum of the other two sides (63 + 58 = 121) to determine if the triangle is right, acute, or obtuse.
85.62^2 = 7326.23
121^2 = 14641
Since 7326.23 is less than 14641, the triangle is acute.
What happens after Lisa finishes
working on the car?
When Lisa's brothers see the car, they
are
But Lisa is
▼ what she did.
and thinks the car is
▼ her work
Lisa and her brothers share a mutual appreciation for the car, albeit for different reasons.
After finishing working on the car, Lisa's brothers are surprised by the changes she made to the car. They may compliment her on her work or express their appreciation for her efforts. On the other hand, Lisa is proud of her work and takes pride in the changes she made to the car. She may feel a sense of accomplishment and satisfaction in seeing the final result of her hard work. While her brothers may appreciate the car, Lisa feels a personal connection to it as she knows the effort and dedication she put into making it look and function better.
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Answer:
I have the answer
Step-by-step explanation:
1. Suprised by
2. Proud of
3. unique
Hope it helps, Have a good day!
PLEASE HELP ME ON QUESTION D. THE answer is not Kite.
HELPPPP!
You are washing cars for a fundraiser and have reservations for 30 cars to be washed. You realize that it will take 4 people 8 hours to wash all the cars. Exactly how long will it take 6 people to wash all the cars? If you only have 2 hours and 40 minutes to wash all the cars how many people will you need?
Answer:
How long will it take 6 people to wash all the cars? 5 hours 20 minutes
If you only have 2 hours and 40 minutes to wash all the cars how many people will you need? 12 people
Step-by-step explanation:
The important thing to realize here is that the time taken to wash x cars is inversely proportional to the number of people
That is represented mathematically as
y ∝ 1/x
The more the number of people, the less time it takes
We can write this as a proportionality equation:
y = k/x
where k is referred to as the constant of proportionality
We have the information: 4 people take 8 hours.
Plugging these two values into the equation
4 = k/8
k = 4 x 8 = 32 hours
So it takes 1 person 32 hours to wash all the cars
If there were 6 people instead
6 = 32/h where h is the time taken for 6 people to wash 30 cars
h = 32/6 = 16/3 hours = 5 1/3 hours
= 5 hours and 20 minutes
2 hours and 40 minutes = 2 40/60 hours = 2 2/3 hours
Converting to improper fraction
2 2/3 = (2 x 3 + 2)/3 = 8/3 hours
Plugging this value of x into the equation gives
y = 32/(8/3)
32 ÷ 8/3 is computed by flipping the fraction and multiplying
32 ÷ 8/3 = 32 x 3/8 = 12 people
Select the correct answer. Solve for x. x2 + 4x - 21 = 0 A. -3, -7 B. -3, 7 C. 3, -7 D. 3, 7
Answer:
x=3
x=-7
Step-by-step explanation:
(ANSWER ASAP!! GIVING BRAINLIEST IF CORRECT! :))
A student wants to see if this table shows a proportional relationship
They start by checking to see if they are multiplying by the same amount to go from X to Y.
Finish the student's work by checking the other rows. Is this a proportional relationship? If so, what is the constant of proportionality?
A: Yes it is proportional, and the constant of proportionality is 2
B: No it is not proportional, because tables can't show proportions
C: No it is not proportional, because you aren't multiplying by the same amount on every row
D: Yes it is proportional, and the constant of proportionality is 3
Answer:
The correct answer here is B
Step-by-step explanation:
You already did the first 2 rows and it got a COP of 3. The last few rows do not.
Answer:
Answer is C
Step-by-step explanation:
Yes, the person who said B is half correct but tables CAN show proportions, however this one doesn't since you aren't multiplying by 3 in every row. Only the top 3 rows do the rest don't. That's why C is correct not B.
what is the common denominator of 3/8 and 1/5
Answer:
40?
Step-by-step explanation:
Figure W is a dilation of figure V. Where is the center of dilation located?
A) inside figure V
B)outside figure V
C)on a vertex of figure V
The center of dilation is located inside figure V.
What is Dilation?Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
Every dilated image are similar figures to the original figure.
Center of dilation is defined as the point which is fixed on a plane. All the points are dilated about this point.
This can be situated inside or outside the preimage and image.
We can find the position of center of dilation by connecting corresponding vertices of the image and preimage and extend the line up to which all the lines intersect.
The intersecting point is the center of dilation.
Using this concept, here, the center of dilation is inside V.
Hence the center of dilation is located inside the figure V.
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What is the area of this figure? 2 m 2 m 3 m 9 m 2 m 3 m 7 m 14 m Area of compound figures
The area of the compound figure is 41 square meters.
How to find the are of compound figure?We can subdivide the compound figure into smaller shapes and add the areas of each to determine its area.
The figure can first be divided into two rectangles:
The first rectangle has a surface area of 18 m2 with measurements of 2 m by 9 m.
The second rectangle is 3 m by 7 m in size, which equals a surface area of 21 m2.
Next, we can calculate the two triangles' areas:
The area of the first triangle is 1/2 x 2 m x 2 m, or 2 m2, because its base is 2 m and its height is 2 m.
The area of the second triangle is 1/2 x 3 m x 2 m = 3 m2, with a base of 3 m and a height of 2 m.
The overlap between the two rectangles can then be subtracted:
The overlap measures 2 m by 3 m, making it a rectangle whose size is 2 m by 3 m, or 6 m2.
We sum the areas of the two rectangles, the two triangles, then subtract the overlap between the rectangles to determine the total area of the compound figure:
(18 m2 + 21 m2) + (2 m2 + 3 m2) - 6 m2 = total area
Area total: 41 m2.
Hence, the compound's area is 41 square metres.
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Complete question:
Area of compound figures.
2 m
2 m
3 m
9 m
2 m
3 m
7 m
14 m
What is the area of this figure?
Select ALL the true equations.
(a) 5 + 0 = 0
(b) 15 ⋅ 0 = 0
(c) 1.4 + 2.7 = 4.1
(d) 2/3 ⋅ 5/9 = 7/12
(e) 4 & 2/3 = 5 − 1/3
Answer:
b,c,e
Step-by-step explanation: a: 5+0=5
b:15x0 =0
c: 1.4+2.7=4.1
d:2/3 x 5/9
e:4& 2/3 =5-1/3
HELPP PLS ITS MY HOMEWORK
Answer:
x=16
Step-by-step explanation:
Mark as brainliest
Answer:
x = 16
Step-by-step explanation:
First find height (h) of the triangle:
15² = 9² + h²
h² = 15² - 9² = 144
h = √144 = 12
Now you can find the base angle Ф of the 12-9-15 triangle:
Ф = sin⁻¹(12/15) = 53.1°
Find the measure of the other base angle by knowing that the sum of the interior angles of a triangle = 180:
180 - 90 - 53.1 = 36.9°
Now you can find x:
tan(36.9) = 12/x
x = 12/tan(36.9) = 16
Yaritza has a collection of vintage action figures that is worth $320. If the collection
appreciates at a rate of 2% per year, which equation represents the value of the
collection after 5 years?
The end result of this equation is the value of the collection after 5 years. In this case, the total value would be V = 320(1.02)⁵ = 413.25.
What is exponential growth?Exponential growth is a pattern of growth that occurs when a base number is multiplied by a consistent number over a period of time. This type of growth is often seen in population growth, inflation, the money supply and other areas of mathematics. The growth rate of an exponential function increases over time, making it an important concept in mathematics, economics, and other fields.
This equation utilizes the concept of exponential growth, which is when a quantity increases at a rate which is proportional to its current value. In this case, the quantity is the value of the collection, and the rate of growth is 2% per year.
The equation can be broken down into its components in order to better understand what it is saying. The base value of the collection, 320, is represented by the first part of the equation, V = 320. The second part, (1.02)^5, represents the growth rate over 5 years. The 1.02 is the growth rate of 2% per year, and the 5 indicates that the growth rate will be compounded for 5 years. In other words, the rate of growth is applied to the original value, and then the resulting value is used as the new base for the growth rate to be applied again, and so on for 5 years.
The end result of this equation is the value of the collection after 5 years. In this case, the total value would be V = 320(1.02)⁵ = 413.25. This means that in 5 years, the collection would have appreciated to a total value of 413.25.
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PLEASE HELP PLEASEEE
Answer: (4,9)
Step-by-step explanation: The X is going to flip signs as you mirror across the y axis.
Anyone please help me please anyone ???!! Thank you (((:!!!!
Answer:
23
Step-by-step explanation:
(16-12)×4+7
(4)×4+7
16+7
=23 I think
Find the surface area of the composite figure. Round your answer to the nearest whole
number.
6 ft
00
5 ft
12 ft
Hint: how many circles are part of your final surface area?
ft. 2
The surface area of the figure is 549.5 square ft
How to determine the surface area of the figureGiven that
The composite figure comprises of a cone and a cylinder of the following dimensions
Cone: Radius = 5 ft and Height = 12 ft
Cylinder: Radius = 5 ft and Height = 6 ft
The surface area of the figure is calculated as
Surface area = Cone + Cylinder - Circle
So, we have
Surface area = πr(r + √[h² + r²]) + 2πr(r + h) - πr²
Substitute the known values in the above equation, so, we have the following representation
Surface area = 3.14 * 5 * (5 + √[12² + 5²]) + 2 * 3.14 * 5 * (5 + 6) - 3.14 * 5²
Evaluate
Surface area = 549.5
Hence, the surface area is 549.5
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In a normal distribution curve, the mean is equal to what?
In a normal distribution curve, the mean is equal to center of the curve
What is the mean equal to?In a normal distribution curve, the mean is equal to the center of the curve, also known as the peak, and is represented by the highest point on the curve.
The mean of a normal distribution is also the point around which the data points are symmetrically distributed, with an equal number of data points on both sides of the mean. This is why the mean is often referred to as the "average" of a normal distribution.
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11. Suppose Britta only paid the interest during her 2 years in school and the
6-month grace period. What will she pay in interest over the term of her loan
Accordingly, if Britta only paid the interest during her two years of education, she would accrue about $33,782 in interest over the course of her loan.
what is interest ?The sum of money that a borrower must give a lender as interest is compensation for the use of borrowed funds. It is typically computed as a percentage of the principal, which is the amount borrowed, and is repaid alongside the principal over a predetermined amount of time. The cost of the lender, the likelihood of a default, and the desire for credit in the economy are just a few of the variables that affect the interest rate, or the percentage charged for borrowing the money.
given
We can use the following method to determine the total interest paid:
Principal x Interest Rate x Duration equals total interest.
where Principal denotes the sum borrowed, Interest Rate denotes the annual interest rate (in decimal form), and Time denotes the number of years over which interest will accrue.
Assume Britta took out a $50,000 loan to pay for her schooling.
Therefore, the amount of her loan at the conclusion of that time frame would be:
$50,000 x 1.06^2 = $56,420
The interest that will be charged on this balance for the remaining 10 years and 6 months of the loan period needs to be calculated now. Using the above method, we obtain:
$56,420 multiplied by 0.06 times 10.5 equals the total interest, or $33,782.
Accordingly, if Britta only paid the interest during her two years of education, she would accrue about $33,782 in interest over the course of her loan.
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