Answer:
20 m
Step-by-step explanation:
You want to know the uniform width of a lawn around a 120 m by 80 m building such that the area of the lawn is equal to the area of the building.
SetupLet x represent the width of the lawn. Then the dimensions of the area that includes the lawn and building will be (120 +2x) meters by (80 +2x) meters. We want that area to be equal to twice the area of the building:
(120 +2x)(80 +2x) = 2(120·80)
SolutionDividing by 4 gives a slightly simpler equation.
(60 +x)(40 +x) = 60(80)
2400 +100x +x^2 = 4800 . . . . eliminate parentheses
x^2 +100x -2400 = 0 . . . . . . subtract 4800 and put in standard form
(x +120)(x -20) = 0 . . . . . . . factor
Values of x that make the factors zero are ...
x = -120, x = 20
Only the positive solution makes any sense in this context.
The width of the lawn must be 20 m.
__
Additional comment
The total area of the plot is ...
total area = (building area) + (lawn area)
When the lawn area is equal to the building area, then we have ...
total area = (building area) + (building area)
total area = 2·(building area)
This is the relation we used in the solution above.
Dan spent half of his weekly allowance. He then earned $8.90 by completing some chores. What is his weekly allowance if he currently has $14.70 (prior to getting his weekly allowance he had $0)?
The required allowance that Dan has prior is given as $11.6.
Given that,
Dan spent half of his weekly allowance. He then earned $8.90 by completing some chores. What is his weekly allowance if he currently has $14.70 (prior to getting his weekly allowance he had $0) is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the allowance Dan has be x,
According to the question,
x/2 + 8.90 = 14.70
x = 29.40 - 17.80
x = $11.6
Thus, the required allowance that Dan has prior is given as $11.6.
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Adam’s house is 12 miles from his house. It takes his older brother 20 minutes to drive him school. What is his brother’s driving speed
Step-by-step explanation:
I assume we want ca miles/hour answer as speed.
but just formally, any distance per time unit is speed.
in that sense
12 miles / 20 minutes = 3 miles / 5 minutes
is the speed.
but now to convert this to miles/hour.
we want to multiply 3/5 or 12/20 by f/f, so that the denominator is 1 hour.
by multiplying the numerator by the same value we make sure the speed ratio remains the same.
so, what "f" do we need to multiply 20 with to get 60 (1 hour = 60 minutes) ?
right, f = 3
therefore, we get
12/20 × 3/3 = (12×3)/(20×3) = 36/60 = 36 miles / 1 hour
his brother's driving speed was 36 miles/h or 36 mph.
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
This is
20, 10, 5, …
This is sequence and the is equal to .
The given series is a geometric sequence with a common ratio of 1/2 it is also written as 0.5.
What is geometric sequence?A geometric progression, also known as a geometric sequence, is a non-zero number sequence in which each term after the first is found by multiplying the previous one by a fixed, non-zero number known as the common ratio.
Number sequences are groups of numbers that adhere to a pattern or rule. A geometric sequence is one in which the rule is to multiply or divide by a specific number each time.
We have,
20, 10, 5, …
The distinction between consecutive terms is:
10 - 20 = -10
5 - 10 = -5
Since -10 ≠ -5, therefore the given series has no standard difference, which means the given sequence is not arithmetic.
The ratio between consecutive terms is:
10/20 = 1/2
5/10 = 1/2
The given series has a common ratio of 1/2, which means the given sequence is geometric. it is also written as 0.5.
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I need help ASAP 50% of my grade this term
Answer:
The first 4 terms are 3,9,15, and 21
Step-by-step explanation:
The first term in the recursive formula is 3 (it is important because that would be the number we substitute for the second term. This logic also applies to finding the next term with the answer to the previous term) The formula is an = a(n-1) + 6. Because of this formula the nth on the right side is the previous one plus 6. With that in mind let find the mext three terms To find a2 you would first substitute n for 2 making it a2 = a(2-1) +6 which is a2 = a1 + 6. We know that the first term is 3 so we substitute a1 for 3 to get a2 = 3 + 6 which is 9. The second term is 9 To find a3 we do the same steps for solving a2 only this time we use the second term to put in place of a2+ 6 which is 9 + 6 which equals to 15. The third term is 15 Again we are doing the same steps to find a4 but we use the third term to substitute for a3 + 6 which is 15 + 6 which equals to 21. The fourth term is 21.There's a image of all of the work above
of the following, which population is most dense? please choose the correct answer from the following choices, and then select the submit answer button. answer choices 100 individuals per 100 square meters 5000 individuals per 200 square meters 100,000 individuals per 20,000 square meters 15,000 individuals per 10,000 square meters
The population that is most dense is the one for 5000 individuals per 200 square meters
Given the following information:
100 individuals per 100m^2
5000 individuals per200m^2
100,000 individuals per 20,000m^2
15,000 individuals per 10,000m^2
We find the population that is most dense using the formula:
Population density=(No. of people/Land area)
For 100 individuals per 100m^2,
Population density=100/100=1
For 5000 individuals per200m^2
Population density=5000/200=25
For 100,000 individuals per 20,000m^2
Population density=100,000/20,000=5
For 15,000 individuals per 10,000m^2
Population density=15,000/10,000=1.5
Hence, highest population density is 25 for 5000 individuals per200m^2
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In the diagram below, the three lines intersect in the same point,
forming six numbered angles
Answer:
A , B, D, F
Step-by-step explanation:
A) ∠1 ≅ ∠ 4 {Vertically opposite angles are congruent}
B) m∠2 + ∠4 + ∠6 = 180° {Straight line angles}
∠6 ≅ ∠3
⇒ ∠2 + ∠4 + ∠3 = 180°
D) ∠2 + ∠3 + ∠4 = 180° {Straight line angles}
f) ∠2 + ∠3 = ∠5 + ∠6 {Vertically opposite angles}
The table shows a proportional relationship between the weight on a spring scale and the distance the spring has stretched.
a. Complete the table.
b. Describe the scales you could use on the x and y axes of a coordinate grid that would show all the distances and weights in the table.
distance (cm) weight (newtons)
20 28
55
140
1
a)Table is completed below.
b)The scale should take the coefficient 1.4 into account, therefore the x-axis scale will be 100 with 1-cm intervals and the y-axis scale will be 140 with 1.4-newton intervals.
What is proportional relationship?
Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
Given.
The proportion is: according to the first row of the proportional relationship
y = kx
28 = k*20
k = 28/20 = 1.4
the following is the function:
y = 1.4x
a) Fill in the following table:
Weight and distance (in centimeters) (newtons)
20 | 28
55 | 55*1.4 = 77
140/1.4 = 100 | 140
1 | 1*1.4 = 1.4
b) The scale should take the coefficient 1.4 into account, therefore the x-axis scale will be 100 with 1-cm intervals and the y-axis scale will be 140 with 1.4-newton intervals.
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Work out the area of this circle.
Take to be 3.142 and write down all the digits given by your calculator.
10 cm
please help !!
Answer:
Area is 314.2 cm²
Step-by-step explanation:
- Consider a circle whose radius is r, while calculating its area, the formula is derived from its circumference;
[tex]{ \rm{circumference = 2\pi r}}[/tex]
- but area is the integral of circumference;
[tex]{ \rm{area = \int circumference }} \\ \\ { \rm{area = \int2\pi r \: dr}}[/tex]
- Assume area is between the center to the edge from r = 0 to r = r
[tex] { \rm{area = 2\int^{r}_{0}\pi r \: dr}} \\ \\ { \rm{area = 2[\pi ( \frac{ {r}^{2} }{2} )]^{r} _{0} }} \\ \\ { \rm{area = \pi {(r)}^{2} - \pi {(0)}^{2} }} \\ \\ { \boxed{ \rm{area = \pi {r}^{2} }}}[/tex]
- From the question given, the circle has a radius of 10cm
[tex]{ \rm{area = 3.142 \times {10}^{2} }} \\ \\ { \bf{area = 314.2 \: {cm}^{2} }}[/tex]
[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]
4р+2=3р-7 what is the answer show work
Answer:
p = -9
Step-by-step explanation:
4p + 2 = 3p -7 subtract 3p to get p's on the same side
1p + 2 = -7 subtract 2 to get p alone
p = -9
Answer:
p = -9
Step-by-step explanation:
4p + 2 = 3p -7 subtract 3p to get p's on the same side
1p + 2 = -7 subtract 2 to get p alone
p = -9
Which of the following statements best describes a survey question?
A question you will ask the people in your sample.
A question designed to collect a single datum.
A multiple choice question.
A question designed to obtain customer feedback.
Answer:
A question you will ask the people in your sample.
What is the product of 54 and 2.2*10^6 expressed in scientific notation
The product of 54 and 2.2*10^6 expressed in scientific notation 1.188 x 10⁸
Formulate the following given the conditions: 54 × 2.2 × 106
Incorporate and multiply: (54 x 2.2) = 106
Determine the quotient or product:
118.8 × 106
Write the amount in scientific notation as follows: 1.188 108
1.188 108 written in scientific notation
Solution: 1.188 x 10⁸
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Amber wants to put a carpet on the floor of her bedroom. The floor is a square with an area of 7.29 square feet. How long should the piece of carpet on each side
The piece of carpet on each side of the floor will be 10.8 feet.
How to calculate the value?From the information, Amber wants to put a carpet on the floor of her bedroom and the floor is a square with an area of 7.29 square feet.
It should be noted that the side will be
= ✓7.29
= 2.7 feet.
Therefore, the perimeter will be found and this will be:
= 4 × side
= 4 × 2.7
= 10.8 feet
This illustrates the length.
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which counterexample can be used to show that the following conjecture is false?
The other conjecture from A to C is true the only false conjecture is the option D.
Adjacent angles
Якщо 1 <a<2 i 2<b<4,то:
Answer:
A
Step-by-step explanation:
a/b;
2/1=2;
5/4=1.25
that's why we can write it this way: 1.25 < a/b < 2
means the answer is A
Simplify: 10x-5y+2x-3y
Answer: 12x-8y
- Hope this helped.
Answer:
12x-8y
Step-by-step explanation:
combine 10x and 2x
the combine (-5y) and (-3y)
I have a lot more but I just need help!
Answer:
v = 8
Step-by-step explanation:
[tex]2(2v + 9) = 50[/tex]
[tex]2v + 9 = 25[/tex]
[tex]2v = 16[/tex]
[tex]v = 8[/tex]
If B = 2s + s² and A = 3 - 4s², find an expression that equals B + 3A in
standard form
Answer:
- 11s² + 2s + 9
Step-by-step explanation:
B = 2s + s²
A = 3 - 4s²
then
2s + s² + 3(3 - 4s²)
=2s + s²+ 9 - 12s²
= - 11s² + 2s + 9
Ming estimated that there would be 21 members in his bicycle club by the end of summer. There were actually 15 members at the end of summer. What is the percent error of Ming’s estimate?
The percent error of Ming’s estimate is 40%.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
here, it is given that :
Estimated number of members in his bicycle club by the end of summer = 21
Actual number of members in his bicycle club by the end of summer = 15
Now, the percent error of Ming’s estimate :
percent error = {(21-15)/15 } x 100
percent error = (6/15) x 100
percent error = 40%
Therefore, the percent error of Ming’s estimate is 40%.
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three congruent regular hexagons can be drawn in such a way that all of them overlap each other and create more than 6 distinct areas or compartments.
Yes
By drawing 36 little ones and 1 small one
May you guys/girls please help me I have to submit this before mid night and I do not fail because my parents will get me , so may y'all please help me out!?
Answer:
Answer down below!
Step-by-step explanation:
Let's start off by finding a point in the graph where we can start off on
This point that we can use it (0,-3)
From there, we use rise/run to find the slope
We go up 1 and over 1
Thus, our slope is 1!
HELP URGENT!!!
Find the common ratio of the geometric sequence 19.
38, 76, ...
The common ratio of the Geometric sequence 19, 38, 76 .... is 2.
What is common ratio of the Geometric sequence ?The distance between each number in a geometric series is known as the common ratio.
The reason it is common to all numbers and also the ratio between two consecutive numbers in the sequence is why it is known as the common ratio.
Divide the nth term by the (n-1)th term in a geometric series to find the common ratio.
The common ratio of the Geometric sequence 19, 38, 76 is
common ratio = (38/19) = 2
or common ratio = 76/38 = 2
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use the graph to determine wither the function is even, oddPlease check photo
EXPLANATION:
Given;
We are given a graph of a function.
Required;
We are required to determine from the graph if the function is even, odd or neither even nor odd.
Solution:
To determine this from a graph, we should note that a function which is symmetrical with the y-axis is an even function. The graph which is symmetrical with the origin after a 180 degree rotation is an odd function.
Observe that if this graph is flipped from left to right (across the y-axis), it would not retain its original shape.
However, if the graph is rotated 180 degrees about the origin, it would retain its original shape.
Therefore, the graph depicted is an odd function
ANSWER:
The function is an ODD function
Help I tried solving this a billion times!!!!!!!!!!
3(5-x)-2(5+x)=3(x+1) solve for x
Primarily use the Distributive Property to solve this equation.
3(5 - x) - 2(5 + x) = 3(x + 1)
Distribute the outer terms.
3(5) + 3(-x) - 2(5) - 2(x) = 3(x) + 3(1)
15 - 3x - 10 - 2x = 3x + 3
-3x - 2x + 15 - 10 = 3x + 3
-5x + 5 = 3x + 3
Now, isolate all x terms.
-5x + 5x + 5 = 3x + 5x + 3
5 = 8x + 3
5 - 3 = 8x + 3 - 3
2 = 8x
2/8 = 8x/8
x = 1/4
researchers studying meditation contacted over 1{,}0001,0001, comma, 000 randomly selected adults in 101010 nations. the results showed that those who meditated on a regular basis were less likely to suffer from stress than adults who meditate less regularly or not at all. can we conclude that meditating caused the lower stress? why?
Not necessarily, because this was not an experiment.
In my opinion, Yet scientific evidence from case studies, surveys of meditator experiences, and historical studies is emerging to show that meditation can be associated with stress, negative effects, and mental health problems. Meditation can induce a state of deep relaxation and a calm mind. During meditation, you focus your attention and eliminate the stream of disorganized thoughts that can fill your mind and cause stress. This process can lead to increased physical and emotional well-being.
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At what position on the number line is the red dot located?
Answer:
The red dot is between -7 and -8 on the number line so it has a fractional or decimal value. The number of equal parts from one whole number to the next whole number is the number in the denominator. The number of equal parts from -7 to the red dot is the number in the numerator.
Step-by-step explanation:
Answer:
pi/2
Step-by-step explanation:
sqrt(2) is around 1.4
sqrt(pi) is around 1.75
sqrt(4) is 2
So only option left is pi/2 which is around 1.57
29 What is the length of a rectangle with width 10 in. and area 45 in.²?
Answer:
l=4.5
Step-by-step explanation:
The area of a rectangle is length times width.
Area = LW
L = length
W = width
L = Area / W
L = 45 / 10
L = 4.5
What is the x intercept of 5x + 4y = -40
O (0,-8)
O (-8,0)
O (-10,0)
O (0, -10)
Answer: the answer is (0,-8)
DONT IGNORE HELP PLEASE
Answer:
1500
Step-by-step explanation:
-10 < 2 + x <-1 please help solve and graph :,(
Answer:
See below
Step-by-step explanation:
Given g(x)=2x+3 solve for x when g(x)=3
Answer:
x=0
Step-by-step explanation:
3=2x+3
Subtract 3 on both sides
0=2x
x=0