Using the Pythagorean Theorem, it is found that the lot has an area of about 35 acres.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Researching the problem on the internet, the lot has one leg of 800 feet and the hypotenuse is of 3900 feet, hence the other leg is found as follows:
[tex]800^2 + l^2 = 3900^2[/tex]
[tex]l = \sqrt{3900^2 - 800^2}[/tex]
l = 3817 feet.
What is the area of a right triangle?The area of a right triangle is given by half the multiplication of it's legs. Hence, the area of the lot, in square feet, is given by:
A = 0.5 x 800 x 3817 = 1,526,800 square feet.
Each square feet is equivalent to 0.000029568 acres, hence the area in acres is given by:
Aa = 0.000029568 x 1,526,800 = 35 acres.
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Which is the correct classification of StartRoot 18 EndRoot?
irrational number, non-repeating decimal
irrational number, terminating decimal
rational number, terminating decimal
rational number, non-repeating decimal
The correct classification for √18 is an irrational number, non-repeating decimal.
The correct classification of √18 is an irrational number.An irrational number is a number that cannot be expressed as a fraction (ratio) of two integers and cannot be written as a terminating or repeating decimal.
√18 cannot be simplified to a fraction, and when expressed as a decimal, it is a non-repeating decimal that continues indefinitely without a pattern.
Therefore, the correct classification for √18 is an irrational number, non-repeating decimal.The number √18 is the square root of 18. An irrational number is a number that cannot be expressed as a fraction of two integers (a/b) where a and b are integers and b is not equal to zero.
When we calculate the square root of 18, we find that it is approximately 4.24264. However, this decimal representation continues indefinitely without repeating or terminating. It does not settle into a pattern of digits that repeats infinitely like a rational number or terminate after a finite number of decimal places.
Since √18 cannot be expressed as a fraction and its decimal representation is non-repeating and non-terminating, it falls under the category of an irrational number.
Therefore, the correct classification of √18 is an irrational number, specifically a non-repeating decimal.
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Find the prime factorization of the composite number 10692
When decomposing into prime factors, it is when a number is taken out of its half, third, fifth and seventh, and it is also possible for the same number number.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{10692 }\\ \ 5346\\ \ 2673\\ \ \ \ 891\\ \ \ \ 297\\ \ \ \ \ 99\\ \ \ \ \ 33\\ \ \ \ \ 11\\ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 3\\ 3\\ 3\\ 3\\ 3\\ 11\\ \: \end{matrix} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 10692=2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot11=\bf{2^{2}\cdot3^{5}\cdot11 } \end{gathered}$}[/tex][tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
A quadrilateral has vertices E(–4, 2), F(4, 7), G(8, 1), and H(0, –4). Which statements are true? Check all that apply.
A) The slope of EH is -8/5
B) The slopes of EF and GH are both 5/8
C) FG is perpendicular to GH.
D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.
E) Quadrilateral EFGH is a rectangle because all angles are right angles.
Answer:
D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.
B) The slopes of EF and GH are both 5/8
Step-by-step explanation:
The following inference can be made about each answer choices:
For option A
A) The slope of EH is 3/2 and not -8/5
For EH, slope = (2--4)/(0--4) = 6/4 =3/2
For option B
B) The slopes of EF and GH are both 5/8
slope of a graph can be determined by change in y axis/ change in x axis
For EF, slope = (7-2)/(4--4) = 5/8
for GH, slope = (1--4)/(8-0) = 5/8
For option C
C) FG is perpendicular to GH, its can't be determined since it is concluded that the quadrilateral is a parallelogram, therefore this option is wrong.
For option D
D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.
Slope of a graph can be determined by rise divided by run change in y axis/ change in x axis
For EF, slope = (7-2)/(4--4) = 5/8
for GH, slope = (1--4)/(8-0) = 5/8
For EH, slope = (2--4)/(0--4) = 6/4 =3/2
for FG, slope = (7-1)/(8-4) = 6/4 =3/2
EF and GH give the same slope, likewise EH and FG and they are opposite to each other, this make them parallel. Therefore, EFGH is a parallelogram.
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Choose the equation that satisfies the data in the table.
[xy−100−41−8]
A. y=−4x−4
B. y=−14x+4
C. y=4x−4
D. y=14x+4
The linear equation that satisfy the data in the table is: A. y = −4x − 4.
How to Find the Linear Equation for a Data in a Table?Given the table attached below, find the slope (m) = change in y / change in x using two pairs of values, say, (-1, 0) and (0, -4):
Slope (m) = (-4 - 0)/(0 - (-1)) = -4/1 = -4
Find the y-intercept (b), which is the value of y when x = 0. From the table, when x = 0, y = -4.
b = -4.
Substitute m = -4 and b = -4 into y = mx + b
y = -4x + (-4)
y = -4x - 4
The equation that satisfy the data is: A. y = −4x − 4.
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Please answer the question down below!! <3
Answer:
4 inches
Step-by-step explanation:
In a regular pentagon, all sides are equal in length
Convert the number in scientific notation to standard notation.
[tex]1.8 * 10^6[/tex]
Cancel tickets for his church is carnival for a total of 2820 children’s tickets cost three dollars each an adult tickets cost five dollars each the number of children so is 30 more than three times the number of adult tickets sold how many children tickets and how many adult tickets did he sell
Taking into account the definition of a system of linear equations, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Amount of children tickets and adult tickets soldIn this case, a system of linear equations must be proposed taking into account that
"x" is the amount of children tickets sold."y" is the amount of adult tickets sold.Galen sold tickets of his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. The number of children’s tickets sold was 30 more than 3 times the number of adult tickets sold.
So, the system of equations to be solved is
[tex]\left \{ {{3x+5y=2820} \atop {x=3y+30}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first you get:
3×(3y+30)+5y=2820
Solving:
3×3y+3×30+5y=2820
9y+90+5y=2820
9y+5y=2820 - 90
14y= 2730
y= 2730÷ 14
y= 195
Remembering that x=3y +30, then:
x= 3×195 + 30
Solving
x=585 +30
x=615
Finally, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.
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The measure of an interior angle of a regular polygon is 120°. What is the measure of each exterior angle? The polygon has how many sides?
Answer:
60°, arms 6
Step-by-step explanation:
let the total arms = n
total generated angles in a regular polygon is = (n-2)×180
now,
(n-2)×180 = 120 n
or, 180n - 360 =120n
or, 60n = 360
or, n = 6
14 A ladder 10m long leans against a wall and make 45" with the ground. What is the height of the wall? 14 A ladder 10m long leans against a wall and make 45 " with the ground . What is the height of the wall ?
Answer:
A 10m ladder is leaning against a wall. The ladder makes an angle of 78o with the ground. How high up the wall does the ladder reach? Please include a diagram in the answer.
Th function you need is the sine function. The sine of 78° is about 0.978. That is the ratio of the opposite side (wall) over the hypotenuse (ladder) of the right triangle in this problem.
10 m · sin 78° = 10 m · 0.978 = 9.78 meters.
The ladder reaches 9.78 meters up on the wall.
Step-by-step explanation:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
A quadratic equation is an equation whose leading coefficient is of the second degree. The correct options are A, B, and E.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c. The Roots of the quadratic equation:
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The complete question is:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot
8(x2 + 2x + 1) = 3 + 1
8(x2 + 2x) = –3
If we simplify the given options, then the option that is correct is,
A.) 8(x² + 2x + 1) = –3 + 8
8x² + 16x + 3 = 0
B.) 8x² + 16x + 3 = 0
[tex]x = \dfrac{-16\pm\sqrt{16^2-4(8)(3)}}{2(8)}\\\\x = -1 \pm \dfrac{\sqrt{10}}{4}\\\\x = -1 \pm \sqrt{\dfrac{10}{16}}\\\\x= -1 \pm \sqrt{\dfrac{5}{8}}[/tex]
E.) 8(x² + 2x) = –3
8x² + 16x + 3 = 0
Hence, the correct options are A, B, and E.
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0000
O
1. Simplify 3 + 2 - 1
+6
2-5
03 A
О 25
Answer:
10
Step-by-step explanation:
3+2-1+6=5-1+6=4+6=10
consider the parabola given by the equation:
f(x)=2x^2+12-9
find the following for this parabola:
a) the vertex
b) the vertical intercept is the point
c) find the coordinates of the two x-intercept of the parabola and write them as a list, separated by commas
Answer:
First simply it as 2x²+3
(a) vertex (0,3)
(b)f(0)=3
(c) no x-intercept
The amount left from you net income after your fixed expenses have been paid.
The profit is the amount left from you net income after your fixed expenses have been paid.
The amount earned by an individual or corporation after costs, allowances, and taxes is referred to as net income. Net income in company is what remains after all costs, such as salaries and wages, the cost of goods or raw materials, and taxes, have been paid.
Profit is a financial gain, specifically the sum obtained over that which was used to acquire, maintain, or produce the good or service.
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
Hence the profit is the amount left from you net income after your fixed expenses have been paid.
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I need to know the answer
Answer: [tex]f(x)=-(x-5)^{2}(x+2)[/tex]
Step-by-step explanation:
There is a double root at x=5 and a single root at x=-2, so we know f(x) is of the form [tex]f(x)=a(x-5)^{2}(x+2)[/tex] for some constant a.
To find a, we can substitute the coordinates of the y-intercept, (0, -50).
[tex]-50=a(0-5)^{2}(0+2)\\\\-50=50a\\\\a=-1[/tex]
So, [tex]f(x)=-(x-5)^{2}(x+2)[/tex]
Complete this shape so that it is symmetrical about the reflection line
A balanced and proportionate likeness observed in two sides of an item is characterized as symmetry. The shape can be completed as shown below.
What is symmetry?A balanced and proportionate likeness observed in two sides of an item is characterized as symmetry. It signifies that one side is a mirror image of the other. The line of symmetry is the imaginary line or axis along which you can fold a figure to produce the symmetrical halves.
The shape can be completed as shown below, so that the complete shape is symmetrical about the given axis.
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Which relation below is NOT a function?
A. {(-2, 4), (1,3), (0,4)}
B. {(5,5), (4,4), (3,3) }
C. {(-4,0), (-7,0), (11, 0)}
D. {(1,4), (2,5) (1,7)}
The relation {(1,4), (2,5) (1,7)} is not a function because there is two mirror image of y for a single value of x option (D) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we know for every single value of x there should be only one image in y set.
If there are multiple images are there for a single value of x then the relation is not a function.
In a set of relations:
D. {(1,4), (2,5) (1,7)}
There is two mirror image of y for a single value of x:
Thus, the relation {(1,4), (2,5) (1,7)} is not a function because there is two mirror image of y for a single value of x option (D) is correct.
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3. The function represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period.
(a) During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
(b) Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
(c) When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.
Answer:
a
Step-by-step explanation:
Hakim, Edmund and Paul share a bag of guppies. There are 132 guppies in the bag. The ratio of Hakim's share to Edmund's share is 2:3. The ratio of Edmund's share to Paul's share is 1:2. How many guppies does each boy get? Hakim , Edmund and Paul share a bag of guppies . There are 132 guppies in the bag . The ratio of Hakim's share to Edmund's share is 2 : 3 . The ratio of Edmund's share to Paul's share is 1 : 2 . How many guppies does each boy get ?
Answer:
Hakim's share = 2 x 12 = 24 guppies
Edmund's share = 3 x 12 = 36 guppies
Paul's share = 6 x 12 = 72 guppies
Step-by-step explanation:
We will have Hakim's share as the base unit.
Hakim : Edmund = 2:3
Edmund : Paul = 1:2
Hakim : Edmund : Paul = 2:3:3x2 = 2:3:6
Total units = 2+3+6 = 11 units
11 units = 132 guppies
1 unit = 132/11 = 12 guppies
Hakim's share = 2 x 12 = 24 guppies
Edmund's share = 3 x 12 = 36 guppies
Paul's share = 6 x 12 = 72 guppies
Question
Of the food donated, 1 lb 6 oz of vegetables, 2 lb 3 oz of meat, and 8 oz of condiments were
weighed. What is the total weight of food donated?
Provide your answer below:
boz
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Of the food donated, 1 lb 6 oz of vegetables, 2 lb 3 oz of meat, and 8 oz of condiments were weighed, the total weight of food donated is 65 ounces.
What is unit?Units are used to measure and express quantities. In the context of the given problem, units are used to indicate the weight of the donated food items.
Pounds (lb) and ounces (oz) are units of weight commonly used in the United States. One pound is equal to 16 ounces.
To add these weights together, we need to make sure they are all in the same units. Let's convert everything to ounces:
- 1 lb 6 oz = 22 oz (since 1 lb = 16 oz, and 6 oz + 16 oz = 22 oz)
- 2 lb 3 oz = 35 oz (since 2 lb = 32 oz, and 3 oz + 32 oz = 35 oz)
- 8 oz = 8 oz
Now we can add the weights:
22 oz + 35 oz + 8 oz = 65 oz
Therefore, the total weight of food donated is 65 ounces.
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X^2=50 where x is a real number
The value of x in the given expression x² = 50 is 5√2
Data obtained from the questionx² = 50Value of x =?How to determine the value of xx² = 50
Thake the square root of both sides
x = √50
Recall
√50 = √(25 × 2) = 5√2
Thus,
x = √50
x = 5√2
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3y-12x=24 and goes through point (2,-6) . write your answer in y=mx+b
Answer:
y= 4x+8
Step-by-step explanation:
Add 12x to both sides.
3y=24+12x
The equation is in standard form.
3y=12x+24
Divide both sides by 3.
3
3y
=
3
12x+24
Dividing by 3 undoes the multiplication by 3.
y=
3
12x+24
Divide 24+12x by 3.
y=4x+8
The function g is related to one of the parent functions
g(x) = 2 √x
a.) Identify the parent function f.
b.) Use function notation to write g in terms of f.
If the function f(x) is shifted right upward by 2 units, then the function f(x) will be equal to the function g(x). Then the parent function is f(x) = √x .
What is an absolute function?The value of the absolute function is always positive.
The absolute function is given as
f(x) = a√x
The function g is related to one of the parent functions g(x) = 2 √x
Then the parent function f(x);
f(x) = √x
If the function f(x) is shifted right upward by 2 units, then the function f(x) will be equal to the function g(x).
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The quantity of a good demanded rises from 1000 to 1500 units when the price falls from $1.50 to $1.00 per unit. The price elasticity of demand for this product is approximately
The price elasticity of demand for this product is approximately will be 1.
What is the price elasticity?The price elasticity is given as
[tex]\rm PE = \dfrac{\dfrac{Q_f-Q_i}{Q_f+Q_i}}{\dfrac{P_f-P_i}{P_f+P_i}}\\\\\\[/tex]
The quantity of a good demanded rises from 1000 to 1500 units when the price falls from $1.50 to $1.00 per unit.
The price elasticity of demand for this product is approximately will be
[tex]\rm PE = \dfrac{\dfrac{1500-1000}{1500+100}}{\dfrac{1.5-1}{1.5+1}}\\[/tex]
On further solving, we have
PE = (500 / 2500) x (2.5 / 0.5)
PE = 1
The price elasticity of demand for this product is approximately will be 1.
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What is the value of x in the equation 1/5x - 2/3y=30 when y= 15
Substituting in y=15,
[tex]\frac{1}{5}x-\frac{2}[3}(15)=30\\\\\frac{1}{5}x-10=30\\\\\frac{1}{5}x=40\\\\x=\boxed{200}[/tex]
What is the value of 6¹?
6° = 1
6 = 6
6 = 36
6 = 216
Answer:
6=6
Step-by-step explanation:
This is because the exponent is multiplying it by one so technically you don't have to do anything but multiply 6*1
Hope this helps
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Fun fact: ANY number powered to the}\\\huge\textbf{1 it automatically that number(just }\\\huge\textbf{regular multiplication).}[/tex]
[tex]\mathsf{6^1}\\\\\\\mathsf{\approx 6\times1}\\\\\\\large\text{So, you're making it 6 ONE TIME}\\\\\mathsf{= \bf 6}\\\\\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ B.\ 6^1 = 6}}}\huge\checkmark[/tex]
[tex]\large\text{Random\ note\ for\ rest\ of\ equations:}\\\\\mathsf{6^0\rightarrow \bf 1}\\\\\mathsf{6^2\rightarrow 6\times 6 \rightarrow \bf 36}\\\\\mathsf{6^3\rightarrow 6\times6\times6\rightarrow 36\times6\rightarrow \bf 216}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
pls help me solve for x in this equation! + brainest
Answer:
x = -3
Explanation:
[tex]\rightarrow \sf \sqrt[3]{\sf 3x + 1} = -2[/tex]
[tex]\rightarrow \sf \sf 3x + 1 = (-2)^3[/tex]
[tex]\rightarrow \sf \sf 3x + 1 = -8[/tex]
[tex]\rightarrow \sf \sf 3x = -8-1[/tex]
[tex]\rightarrow \sf \sf 3x = -9[/tex]
[tex]\rightarrow \sf \sf x = -3[/tex]
Answer:
[tex]\sqrt[3]{3x+1} =-2\\(\sqrt[3]{3x+1})^{3} =(-2)^{3} \\3x+1=-8\\3x=-9\\x=-3[/tex]
Hope it helps!
Need help with this geometry question
Answer: C
Step-by-step explanation:
[tex]50 < 5x-10\\\\60 < 5x\\\\x < 12[/tex]
However, the angle has to have positive measure, so:
[tex]5x-10 > 0\\ \\ 5x > 10\\\\x > 2\\\\\therefore \boxed{2 < x < 12}[/tex]
Photo is attached, please help! Will give brainliest
Here you go! please make sure you read it all too understand it, and make sure you try work before asking for help :D Have a awesome day/night
Answer:735
Step-by-step explanation:I was hoping you’d have another. Dv/dt=d/dt((7+5t)^3)=3x5x((7+5t)^2)=15x49. Does this work?
A rectangular fence has a perimeter of 184 feet. The length is four feet less than three times the width. Find the length and the width. = 2+2
Answer:
lenth = 68 [ft]; width=24 [ft].
Step-by-step explanation:
1) if the length is 'l' and the width - 'w', then it is possible
2) to write the condition 'The length is four feet less than three times the width' as 3w-4=l;
3) to write the given perimeter as 2(w+l)=184.
4) then it is possible to make up the system:
[tex]\left \{ {{2(w+l)=184} \atop {3w-4=l}} \right. \ = > \ \left \{ {{w+l=92} \atop {3w-l=4}} \right. \ = > \ \left \{ {{w=24} \atop {l=68}} \right.[/tex]
HELP PLEAES ASAP!!!!!
Volume is a three-dimensional scalar quantity. As per the Cavaleri's principle the volume of both the figures will be the same.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
What is Cavaleri's principle?According to Cavalieri's principle, if two figures have the same height and cross-sectional area throughout each point along that height, they have the same volume.
The height of both the objects is 16 cm, also the base area of both the objects is 96 cm². As it can be observed that for both the object there base area is the same through out their height.
Hence, as per the Cavaleri's principle the volume of both the figures will be the same.
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