Answer:
area of land purchased =247
The area of the land Rachel purchased is approximately 10,055.64 square feet.
How to calculate the area?We can start by finding the area of one acre in square feet, which is given as 43,560 square feet.
To find the area of 1/5 acre, we can divide 43,560 by 5, which gives us 8,712 square feet.
Since Rachel's land is in the shape of an isosceles triangle, we need to find the base and height of the triangle in order to calculate its area. Let's call the length of the base "b" and the height "h".
We know that the area of a triangle is given by the formula:
Area = (1/2) x base x height
So, we can rearrange this formula to solve for the height:
height = 2 x Area / base
Now we can substitute in the values we know:
Area = 8,712 square feet
base = unknown
height = unknown
We also know that the triangle is isosceles, which means that two of the sides are equal in length. Let's call the length of one of these sides "s". Then the length of the base can be expressed in terms of s as:
base = 2s
We can use the Pythagorean theorem to find the height in terms of s:
s² + (h)² = (2s)²
s² + h² = 4s²
h² = 3s²
h = s x √(3)
Now we can substitute this expression for the height in terms of s into the formula we derived for the area:
Area = (1/2) x base x height
Area = (1/2) x 2s x s x √(3)
Area = s² x √(3)
We know that the area of the triangle is 1/5 of an acre or 8,712 square feet, so we can set this equal to the expression we just derived for the area and solve for s:
s² x √(3) = 8,712
s² = 8,712 / √(3)
s = √(8,712 / √(3))
Now that we know the length of one of the equal sides of the isosceles triangle, we can find the length of the base by multiplying by 2:
base = 2s
base = 2 x √(8,712 / √(3))
Finally, we can substitute in the values we just found for the base and height into the formula for the area of the triangle:
Area = (1/2) x base x height
Area = (1/2) x 2 x √(8,712 / √(3)) x √(3) x √(8,712 / √(3))
Area = 2 x 8,712 / √(3)
Area = 17,424 / √(3)
Therefore, the area of the land Rachel purchased is approximately 10,055.64 square feet.
To know more about an area follow
https://brainly.com/question/25292087
#SPJ2
Find the difference. 256,805 - 136,667 *
Answer: 120,138
Step-by-step explanation:
Answer: 120,138
Step-by-step explanation:
Subtract
Use the diagram of the cylinder to answer the question. Use 3.14 for π and round to the nearest tenth. SHOW PROOF PLEASE
803.84 square inches is the surface area of a cylinder with an 8-inch radius and 8-inch height.
What is the surface area of a solid?Any solid shape has a surface area equal to the total of the areas of its faces. For instance, to calculate the surface area of a cuboid, we add the areas of all the rectangles that make it up.
According to the given information:The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given values, we get:
Surface Area = 2 × 3.14 × 8² + 2 × 3.14 × 8 × 8
= 401.92 + 401.92
= 803.84 square inches
the surface area of the cylinder with radius 8 inches and height 8 inches is 803.84 square inches.
To learn more about the surface area of the cylinder visit:
brainly.com/question/27440983
#SPJ1
Which of the following is the product of (3x − 5) and (3x + 5)?
Answer:
\( {9x}^{2} - 30x + 25\)
\(\huge\underline\bold\blue{ƛƝƧƜЄƦ}\)
(3x + 5)(3x - 5)
By using identity
(a + b)(a - b) = a² - b²
3x² - 5²
9x² - 25
Micheal is saving money to buy a bike. So far, he has saved $15 which is 3/5 of the total cost of the bike. How much does the bike cost?
PLEASE HELP
Answer:
let t = total cost
3/5 x t = 15
3t = 75
t= 25
bike cost $25
A bullet is shot vertically upward with an initial velocity of 128 ft/s. The bullet height after t seconds is y(t) = 128t - 16t². What is the
velocity when the bullet hits the ground?
We have the position function, \(y(t)=128t-16t^2\), that represents the height of a bullet shot from a rifle, we are also told that the initial velocity of the bullet is \(v_{0} =128 ft/s\).
To start, we need to find the time the bullet hits the ground. The bullet will hit the ground when it's position is equal to zero. So let \(y(t)=0\) and solve for t using algebraic means.
\(\Longrightarrow \hspace 00=128t-16t^2 \Longrightarrow \hspace00=-16t(t-8)\)
So, \(t=0s\) or \(t=8s\).
Logically the value of 8s would make sense as the bullet has to travel upwards and downwards. So it takes the bullet 8 seconds to hit the ground.
The question ask to find the velocity of the bullet when it hits the ground, we know time, now we just need to find the velocity function. We know that the derivative of the position function is equal to the velocity function (\(y'(t)=v(t)\)). So take the derivative of \(y(t)\).
\(\Longrightarrow y'(t)=v(t)=128-32t\)
We need to know the velocity of the bullet as it hits the ground. We know the time at which the bullet hits the ground, so plug that value into our function for velocity.
\(\Longrightarrow v(8)=128-32(8)\Longrightarrow v(8)=128-256 \Longrightarrow v(t)=-128ft/s\)
Thus the velocity of the bullet right before it hits the ground is -128 ft/s.
find the 7th term of G.P :1/6,1/3,2/3
Answer:
10 2/3
Step-by-step explanation:
The common ratio is 2. Each term is being multiply by 2 to get to the next term.
To find the 7th term you take the first term and multiply that by the common ratio to the n-1 or 6th power.
\(1/6(2)^{6}\) = 10 2/3
At Stater Brothers there is a gallon of ice cream for $4.75 it is on sale for 15%
off. How much is the price of the ice cream after the sale?
How much was saved?
Answer:
Price after sale: $4.04
$0.71 saved
Step-by-step explanation:
Find the length of the rectangle whose area is 99 square inches and the width is 9 inches.
Answer:
the answer is 11
Step-by-step explanation:
??×9=99
9÷99=11
11×9=99
Answer: the answer is 11.
Step-by-step explanation:
because we know the width is 9, and the area is 99. but we don't know the length. so this is when you set up your equation: Lx9=99 (L= length) so the inverse operation of multiplication is division so divide 99 by 9 (99/9). and you get 11!
expressions or equations.
Select all the ways to name 14.09.
a. 1,409 hundredths
b. 1 ten + 409 hundredths
c. 1 ten + 4 ones + 9 tenths
d. 140 tenths +9 hundredths
e. 1,409 tenths
Snails travel at a rate of approximately 0.013 meters per second. Assuming this snail has an incredible sense of direction and stamina, how long will it take a snail to make the same journey? That is, change 1171.1 miles into hours of snail travel. USE DIMENSIONAL ANALYSIS TO MAKE YOUR CALCULATION! Include units at each step.
It will take the snail 40,271.33 hours (time) to travel 1,171.1 miles (distance) at 0.013 meters per second (speed).
How are the hours determined?The hours that it will take the snail to travel the distance is determined by first converting the miles into meters at 1 mile = 1,609.34 meters.
The speed per second is also converted into speed her hour.
The conversions use the mathematical operations of division and multiplication.
Time = distance/speed.
Data and Calculations:Total distance in miles = 1,171.1 miles
Total distance in meters = 1,884,698.07 meters (1,171.1 x 1609.34)
Speed = 0.013 meters per second
Speed in hours = 46.8 meters per hour (0.013 x 60 x 60)
The number of hours to cover the distance = Total Distance/Speed
= 40,271.33 hours (1,884,698.07/46.8)
Thus, it will take the snail 40,271.33 hours to cover a distance of 1,171.1 miles at a speed of 0.013 meters per second.
Learn more distance, time, and speed at https://brainly.com/question/26046491
#SPJ1
The cash register subtracts $2.00 from a $10 Coffee Cafe gift card for every medium coffee the customer buys. Use the graph to write an equation in slope-intercept form to represent this situation.
The equation of the line in the slope-intercept form is: y = -2.00 x + 10.
The slope and provided point are both in the equation for the straight line.
The generic point (x, y) must satisfy the equation if we have a non-vertical land in a that passes through any point(x1, y1) has gradient m.
y-y₁ = m(x-x₁)
It is the necessary equation for a line in the form of a point-slope.
That gift card to the Coffee Café has been provided. = $10
Medium coffee = $2.00
customers
The quantity of coffees a consumer can purchase can be represented using a linear equation.
Slope formula
m = (8 - 10)/(1 - 0)
m = -2
Now consider the line's point-slope shape.
y-y₁ = m(x-x₁)
( y - 10) = -2.00 ( x - 0)
y = -2.00 x + 10
The slope: m = - 2.00
The equation of the line: y = -2.00 x + 10
The y-intercept is 10
Learn more about slope-intercept here
https://brainly.com/question/1884491
#SPJ1
6 root 6 plus 5 root 6
The solution to the radical expression 6 root 6 plus 5 root 6 is 11√6
How to evaluate the expression?From the question, we have the following parameters that can be used in our computation:
6 root 6 plus 5 root 6
Rewrite the above expression using mathematical operators and mathematical symbols
So, we have the following representation
6√6 + 5√6
The terms of the above expression are radical expressions
The radicand in the terms is √6
Since both expression have the same radicand, then it means that we can add the terms
So, we have the following representation
6√6 + 5√6
Evaluate the sum
So, we have the following representation
6√6 + 5√6 = 11√6
Hence, the solution is 11√6
Read more about expression at
https://brainly.com/question/15775046
#SPJ1
2. Using transformations of a basic y = log(x) graph, find the domain, range,
vertical asymptote, and sketch the graph of the graph of R(x) = 2 log(-(x + 6)) + 1.
Use interval notation for the domain and range.
Domain:
Range:
Vertical Asymptote: x =
Graph →
Use the axes given, at right. Remember to sketch the
vertical asymptote.
Answer:
Step-by-step explanation:
range:34
domain14
range 12
how do you write 10^3 / 10^7 in standard form for properties of exponents
Answer:
1 / 10000
Step-by-step explanation:
10^3 / 10^7
apply exponent rule: x^a / x^b = x^(a-b)
10^3 / 10^7 where a = 3 and b = 7
10^(3 - 7) = 10^(-4)
apply exponent rule: a^-b = 1 / a^b
1 / 10^(4)
10^4 = 10000
1 / 10000
Let me know if you have any questions !
AND WELCOME TO BRAINLY :)
Answer:
10^-4
Step-by-step explanation:
In division of powers (when the numbers are the same), you subtract both the powers. In this case, it would be 3 - 7 = -4, resulting in a power of -4
How do you write equations in Point-slope form?
For a line with a slope a and a known point (h, k), the point-slope form is:
y = a*(x - h) + k
How to write an equation in point slope form?A general linear equation can be written in slope-intercept form as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that a line passes through a point (h, k), then the point-slope form of that line is:
y = a*(x - h) + k
Notice that particularly, the y-intercept can be written as (0, b), then the slope-intercept form is also a point-slope:
y = a*(x - 0) + b
y = a*x + b
Learn more about linear equations by reading:
https://brainly.com/question/1884491
#SPJ1
36. What is true about this quadratic function?
F(x)=-x +4
O a) It will not factor into two binomials.
Ob) It has no real number solutions.
Oc) It is not a function.
d) Its vertex is a maximum.
WILL MARK BRAINLIEST
A desk drawer is shaped like a rectangular prism. The height of the drawer is 7 inches. The bottom of the drawer has an area of 210 square inches.
What is the volume of the desk drawer?
Enter your answer in the box.
Answer:
1470 inches cubed
Step-by-step explanation:
Vol=length × width × height
But ALSO,
length × width = Area,
So we find another Volume equation,
Vol = BaseArea × height
This is the information you are given in the question.
Vol = 210 × 7
Vol = 1470 inches cubed
Distribute a negative -(5.5q+7)
Hi there! :)
Answer:
\(\huge\boxed{-5.5q - 7}\)
-(5.5q + 7)
Distribute:
-(5.5q) -(7)
-5.5q - 7
Answer:
Z≥0 = {0, 1, 2, .
Step-by-step explanation:
Just took test
What type of triangle and are they congruent
Answer: AAS and both triangles are congruent
Step-by-step explanation: Hello! Since you are given two angles and one side that are congruent in both triangles, you know that they are either congruent by ASA (angle side angle congruence postulate) or AAS (angle angle side) congruence postulate. The way you tell the difference between the two is by how the congruent angles and the congruent side is shown. In ASA, the congruent side would be the included side between both congruent angles. Since the congruent side is not in between both angles and both angles do not share the congruent side to the other triangle, the triangles are congruent by AAS. The triangles two given shared angle and given congruent side is in the order of angle angle side, so the triangles are related by AAS. This means that the triangles are congruent.
Fun fact:
By CPCTC, you know that corresponding parts are congruent in congruent triangles. If you know two or more triangles are congruent, then each of their angles and sides are congruent as well.
I hope this helps you!
MARKING BRAINLEIST IF CORRECT AND QUICK
Answer:
Basically the first one
Step-by-step explanation:
In the equation it shows how it's all negative
So meaning the answer choices should also be all negative
There's also an addition sign which means we are gonna add it all up anyway
The 1st one shows the perfect definition for it
Use the definition of the derivative to differentiate v=4/2 pie r^3
I suspect 4/2 should actually be 4/3, since 4/2 = 2, while 4/3 would make V the volume of a sphere with radius r. But I'll stick with what's given:
\(\displaystyle \frac{dV}{dr} = \lim_{h\to0} \frac{2\pi(r+h)^3-2\pi r^3}{h}\)
\(\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{(r^3+3r^2h+3rh^2+h^3)- r^3}{h}\)
\(\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{3r^2h+3rh^2+h^3}{h}\)
\(\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} (3r^2+3rh+h^2)\)
\(\displaystyle \frac{dV}{dr} = 2\pi \cdot 3r^2 = \boxed{6\pi r^2}\)
In Mathematica, you can check this result via
D[4/2*Pi*r^3, r]
If a = (0,0) and b= (8,2) what is the length of ab
Step-by-step explanation:
on the coordinate grid you can imagine a right-angled triangle.
the direct distance between the 2 points is the Hypotenuse (the baseline opposite of the 90° angle).
and the x-coordinate difference and the y- coordinate difference of the 2 points are the 2 legs.
we can then use Pythagoras
c² = a² + b²
with c being the Hypotenuse, a and b being the legs.
so,
distance² = (8-0)² + (2-0)² = 64 + 4 = 68
distance (= length ab) = sqrt(68) = sqrt(4×17) = 2×sqrt(17) =
= 8.246211251...
Before the search and collection of evidence, there must be _______.
A. Informed consent by the owner
B. A crime
C. A chain of custody
D. A search warrant
I’m stuck between D and B because law enforcement can conduct a search without a search warrant if there is consent by the owner. It is not C because that would be either during or after the collection of evidence.
Answer:
D) A search warrant
Step-by-step explanation:
A search warrant is required before the search and collection of evidence to ensure legal authorization and protection of individuals' rights against unreasonable searches and seizures.
Option B, "A crime", is incorrect because the presence of a crime is not a prerequisite for conducting a search and collection of evidence. There are various situations where searches and evidence collection may occur without a crime being involved, such as regulatory inspections, consented searches, or investigations into potential threats or risks.
By your logic when you say law enforcement can conduct a search without a search warrant if there is consent by the owner, that would mean option A would be right, but of course, it's not.
The length of a rectangle is 3m less than double the witch, and the area of the rectangle is 27m^2. Find the dimensions of the rectangle.
Answer:
the area of the rectangle is A=L•W
The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m
A=L-W
27m²=(2W-3m)-W
27m2=2w2-3m-W
2w2-3wm-27m2=0
....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)
W=
2-2
w=(3m± √9m²+216m²)
w=(3m+ √225m²)
W=(3m± 15m...you need only positive root because width cannot be negative
W= 3m+15m
4
W=. 4
18m
W=4.5m ......now find the L
L=2.4.5m-3m
L=9m-3m
L=6m
Answer:
W = 4.5cm
L = 6cm
Step-by-step explanation:
How does one solve for the n+1st term with the nth term of a sequence
Answer:
The answer is option BStep-by-step explanation:
The nth term of the sequence is
A(n) = 5n + 7
To find the (n+1)st term substitute n+1 into the general equation
That's
For (n + 1)st term
A(n+1) = 5(n+ 1) + 7
A(n+1) = 5n + 5 + 7
A(n+1) = 5n + 12Hope this helps you
\( n^{\text{th}} \text{ term is } 5n+7 \)
forget n for a while.
let's call it t .
The \( t^{\text{th}} \text{ term is } 5t+7 \)
agreed? I don't think there should be a problem.
you're asked what's the \((t+1)^{\text{th}}\) term.
let's call it u . so just like we did before,
\( u^{\text{th}} \text{ term is } 5u+7 \)
but we know, \(u=t+1\)
So, \(5u+7=5(t+1)+7=5t+12\)
does that answer your question?
A carpet expert believes that 8% of Persian carpets are counterfeits. If the expert is accurate, what is the probability that the proportion of counterfeits in a sample of 827 Persian carpets would be greater than 7%
Answer:
\( z=\frac{0.07-0.08}{0.00943}= -1.06\)
And we can use the normal standard distribution table and the cmplement rule and we got:
\( P(z>-1.06) = 1- P(z<-1.06) = 1-0.1446= 0.8554\)
Step-by-step explanation:
For this case we know the following info given:
\(p=0.08\) represent the population proportion
\( n= 827\) represent the sample size selected
We want to find the following proportion:
\(P(\hat p>0.07)\)
For this case we can use the normal approximation since we have the following conditions:
i) np = 827*0.08 = 66.16>10
ii) n(1-p) = 827*(1-0.08) =760.84>10
The distribution for the sample proportion would be given by:
\( \hat p \sim N (p ,\sqrt{\frac{p(1-p)}{n}}) \)
The mean is given by:
\(\mu_{\hat p}= 0.08\)
And the deviation:
\(\sigma_{\hat p}= \sqrt{\frac{0.08*(1-0.08)}{827}}= 0.00943\)
We can use the z score formula given by:
\( z=\frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}\)
And replacing we got:
\( z=\frac{0.07-0.08}{0.00943}= -1.06\)
And we can use the normal standard distribution table and the cmplement rule and we got:
\( P(z>-1.06) = 1- P(z<-1.06) = 1-0.1446= 0.8554\)
Evelyn has a summer babysitting job that pays $12 per hour. She wants to know how many hours she has to babysit to afford a new bike. The bike she wants costs $120.
Answer:
10
Step-by-step explanation:
You just gotta do 120/12 which is 10
a salesman earns 25% commission he sells amount to 2450 shillings after giving a buyers 2% discount . calculate his commission. Suppose all the goods were sold at marked price , what would be is earnings?
Answer:
Step-by-step explanation:
A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings
Commission = 612.50 shillings
B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:
2,450.00 shillings = X - X * 2% = X - 0.02 X --->
------> 0.98 X = 2,450.00 shillings
------>X= 2,450.00 / 0.98
------> X = 2,500.00 shillings
NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings
NEW COMMISSION = 625 shillings
Which expression is equivalent to -3(2x - 8) + 4x?
Answer:
- 2x + 24
Step-by-step explanation:
- 3(2x - 8) + 4x ← distribute parenthesis by - 3
= - 6x + 24 + 4x ← collect like terms
= - 2x + 24 or 24 - 2x
Hey there!
-3(2x - 8) + 4x
DISTRIBUTE -3 within the parentheses
= -3(2x) - 3(-8) + 4x
= -6x + 24 + 4x
COMBINE the LIKE TERMS
= (-6x + 4x) + (24)
= -6x + 4x + 24
= -2x + 24
Therefore, your answer should be:
-2x + 24
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Three-fourths of the yard is covered with grass and one-fourth is used as a garden. The sprinkler could only water 1/5 of the yard, so the rest died. Use the model to find out how much of the grass died.
3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
Let's start by breaking down the information given:
- Three-fourths of the yard is covered with grass.
- One-fourth of the yard is used as a garden.
- The sprinkler could only water 1/5 of the yard.
To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.
Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.
The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.
To find the portion of the grass that died, we subtract the watered portion from the total grass area:
Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.
Simplifying, we get:
Portion of grass that died = 3/5.
Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
for more such question on grass visit
https://brainly.com/question/6204338
#SPJ8