The 38 square feet increase in the area of the patio following the increase in the length and width by 2 feet and the 2 square feet increase following the increase in the length by 2 feet and decrease in the width by 2 feet indicates that the area of the patio is 70 square feet.
What is the area of a plane shape?The area of a plane figure is the space occupied by the figure of a specified surface upon which it is placed.
Let L represent the length of the patio, and let W represent the width of the patio, we get;
Area of the patio = L × W
(L + 2) × (W + 2) = L·W + 2·L + 2·W + 4 = Area + 38
Therefore; (L + 2) × (W + 2) = L·W + 2·L + 2·W + 4 = L × W + 38
2·L + 2·W + 4 = 38 (subtraction property)
2·L + 2·W = 38 - 4 = 34
2·L + 2·W = 34...(1)
(L + 2) × (W - 2) = L·W - 2·L + 2·W - 4 = Area + 2 = L·W + 2
L·W - 2·L + 2·W - 4 - L·W = L·W + 2 - L·W (Subtraction property)
2·W - 2·L - 4 = 2
2·W - 2·L - 4 + 4 = 2 + 4 = 6 (Addition property)
2·W - 2·L = 6...(2)
The simultaneous equations (1) and (2) are solved as follows;
Adding equation (1) to equation (2), we get;
2·L + 2·W + 2·W - 2·L = 34 + 6 = 40
4·W = 40
W = 40 ÷ 4 = 10
W = 10
The width of the patio, W = 10 feet
2·W - 2·L = 6, therefore;
2 × 10 - 2·L = 6
2·L = 2 × 10 - 6 = 14
L = 14/2 = 7
The length of the patio, L = 7 feet
The area of the patio = L × W
L × W = 7 feet × 10 feet = 70 square feet
The area of the patio = 70 square feet
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Due to inflation, the price of an item increased by 45% and then dropped by 20% By what percent did the price increase?
Answer:
16%
Step-by-step explanation:
Let's assume the original price of the item was Rs. 100.
After the price increased by 45%, the new price became:
New price = Original price + (45% of Original price)
New price = 100 + (0.45 x 100)
New price = Rs. 145
Now, the price dropped by 20% from the increased price of Rs. 145:
Final price = New price - (20% of New price)
Final price = 145 - (0.2 x 145)
Final price = Rs. 116
We can calculate the overall change in price by finding the difference between the final price and the original price:
Overall change in price = Final price - Original price
Overall change in price = 116 - 100
Overall change in price = 16
So, the price increased by Rs. 16. To find the percentage increase, we can use the formula:
Percentage increase = (Overall change in price / Original price) x 100%
Plugging in the values, we get:
Percentage increase = (16 / 100) x 100%
Percentage increase = 16%
Therefore, the price of the item increased by 16%.
BRAINLIEST PLEASE
The percentage by which the price increased is; 16%
Percentage Increase
Let the price of an item be denoted as x
Now, we are told that the price of the item increased by 45%. Thus means that the price will be; 1.45x
Now, the price after inflation decreased by 20% or 0.2. Thus;
Final price is now; 1.45x(1 - 0.2)
⇒ 0.8(1.45x)
⇒ 1.16 x
Since the original price is x, then;
Difference in price = 1.16x - x
Difference in price = 0.16x
In percentage, this difference in price represents a 16% increase.
The complete question is;
Due to inflation, the price of an item increased by 45% and then dropped by 20%. By what percent did the price increase?
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what is the probability that a randomly selected college graduate has changed majors more than two times? a. 0.594 b. 0.323 c. 0.406 d. 0.271
Susie is going to rent an apartment in Smallville, where other monthly expenses will sum up to $2831. Susie makes $8609 each month.
Write the inequality for the possible amounts of money Susie can spend renting her apartment in Smallville in order for Susie to have some money left over each month.
Use x to represent the cost of the rent in Smallville and don't use the $ symbol in the inequality.
Answer:
x = $2351
Step-by-step explanation:
I need help please :)
By using normal distribution of probability, it can be calculated that-
a) When x = 142, z = 1.4
b) When x = 130, z = 0.6
c) When x = 103, z = -1.2
What is normal distribution of probability?
Normal distribution of probability is a continuous type probability distribution whose probability density function is given by
f(x) = [tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}}[/tex]
Where z = [tex]\frac{x - \mu}{\sigma}[/tex] , [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation
Here Systolic blood pressure is normally distributed
Mean = 121
Standard deviation = 15
a) x = 142
z = [tex]\frac{142 - 121}{15}[/tex] = 1.4
b) x = 130
z = [tex]\frac{130 - 121}{15}\\[/tex] = 0.6
c) x = 103
z = [tex]\frac{103 - 121}{15}[/tex] = -1.2
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a quadratic function can be used to model the height, in feet, of an object above the ground in terms of the time, in seconds, after the object was launched. according to the model, an object was launched into the air from a height of 0 feet and reached its maximum height of 3136 feet 14 seconds after it was launched. based on the model, what was the height, in feet, of the object 1 second after it was launched?
The height of the object 1 second after it was launched is equals to 243.1 feet.
Let the launching velocity /initial velocity = u ft./s
and final velocity = 0 feet/sec , because at the maximum height, the final velocity of launching is '0'.
Maximum height , s = 3136 feet
time, t = 14 sec
Using the Equation of motion,
v² - u² = -2gs
where, v --> final velocity
u --> initial velocity
g --> acceleration due to gravity and it is a constant with value 9.8 m/sec²
s --> distance ( max. height)
plugging all known values in above formula,
0 - u² = -2 (9.8)(3136) = - 61465.6
=> - u² = - 61465.6
=> u² = 61465.6
=> u = √61465.6 = 247.92 ~ 248
=> u = 248 feet/sec
Now, the height, in feet, of the object 1 second after it was launched is
s = ut + (1/2)(-g)t²
=> s = 248(1) + (1/2)(-9.8)(1)
=> s = 248 - 4.9 = 243.1 feet
So, the required height is 243.1 feet.
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Please help me respond this
Answer:i don't know thanks for the brainy money tho
Step-by-step explanation:
two buses leave towns miles apart at the same time and travel toward each other. one bus travels slower than the other. if they meet in hours, what is the rate of each bus?
two buses leave towns miles apart at the same time and travel toward each other. then the Rate of first bus = 72 mph and Rate of second bus = 62 mph
let first bust travels at x mph
then, 2nd but will travel at ( x - 10) mph
distance travelled by first bus in 2 hours = 2x
distance travelled by 2nd but in 2 hours = 2( x- 10) = 2x - 20
distance between the two is 268 miles
so we can write
2x + 2x - 20 = 268
4x = 288
x = 288 / 4 = 72 mph
rate of first bus = 72 mph
and second bus = 72 - 10 = 62 mph
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Find the inverse of the function.
y = 3x + 3
Write your answer in the form ax + b. Simplify any fractions.
y =
Submit
CAN YOU PLEASE HELP ME I AM IN GRADE 12 I NEED SOLVE THIS QUESTION
WHATS 1+1=
Answer:
2
Step-by-step explanation:
1 + 1 = 2
I hope my answer helps you :)
Answer:
2 or Window
Step-by-step explanation:
1 + 1 = 2
OR
1 + 1 = WINDOW!
What is the prime factorization of 168?
22 x 32 x 5
34 x 7
22 x 17
23 x 3 x 7
Answer:
[tex]2^3 * 3 * 7[/tex]
Step-by-step explanation:
Linked below.
Find two factors and break down individually. Circle prime numbers. If there are more than one of the same prime number, write as an exponent:
i.e. 6 x 6 = [tex]6^{2}[/tex]
Determine the distance between the points (−2, −8) and (−9, −3). square root of 148 units square root of 125 units square root of 74 units square root of 24 units
Answer: C - square root of 74
Step-by-step explanation: took the test and got it right. hope this helps.
have a good day :)
Answer:
[tex]\sqrt{74}[/tex]
Step-by-step explanation:
Which of the following is not a type of graph?EulerHamiltonianTreePath
Answer:
Step-by-step explanation:
Answer = D Explanation: If some closed walk in a graph contains all the edges then the walk is called Euler. 32) Which of the following is not a type of graph ? Answer = D Explanation:Path is a way from one node no another but not a graph.
12. Look at this shape:
Which image
shows a reflection and why?
Answer:
Answer is B.
Step-by-step explanation:
Option A seem to look like a rotation of 180°.
Option B is a reflection across the x-axis.
Option C is a translation shift.
Need Help!!!!!!!!! Solve for side similar triangle
Answer: root 70
Step-by-step explanation:
starting info:
KL = 2NM
KM = 20
NO = 7
Using the fact the ratio of similar sides must be equal:
KL/NO = KM/NM
Therefore sub in values…
KL/7 = 20/NM
As KL = 2NM
2NM/7 = 20/NM
Rearrange:
2(NM)^2 = 140
(NM)^2 = 70
NM = root(70)
(Obviously take positive as can’t have negative length)
The football team ha a total of 50 jerey. There are 20 medium jerey. What percent of the jerey are medium ize jerey?
the total number of medium jerseys (20) by the total number of jerseys (50). To express this as a percentage, we must multiply the result by 100. Which results as 40%
In order to calculate the percentage of medium jerseys, we must divide the total number of medium jerseys (20) by the total number of jerseys (50).
To express this as a percentage, we must multiply the result by 100. Therefore, 20 ÷ 50 = 0.4 and 0.4 x 100 = 40%. Thus, 40% of the jerseys are medium size. the total number of medium jerseys (20) by the total number of jerseys (50). To express this as a percentage, we must multiply the result by 100. Which results as 40%
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2 A bag contains three red counters, four green counters, two yellow counters and one white
counter. Two counters are drawn from the bag one after the other, without being replaced.
Calculate:
a P(two red counters)
b P(two green counters)
c P(two yellow counters)
d P(white and then red)
e P(white or yellow, in either order but not both)
f P(white or red, in either order but not both).
g What is the probability of drawing a white or yellow counter first and then any
colour second?
P (two red counters) = 1/15
P (two green counters) = 2/15
P (two yellow counters) = 1/145
P (white and then red) = 1/30
P (white or yellow, in either order but not both) = 3/10
P (white or red, in either order but not both) = 2/5
The probability of drawing a white or yellow counter first and then any
color second = 7/30
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of red counters = 3
Number of green counters = 4
Number of yellow counters = 2
Number of white counters = 1
Total number of counters = 3 + 4 + 2 + 1 = 10
The probability of drawing 2 red counters.
= [tex]^3C_2[/tex] / [tex]^{10}C_2[/tex]
= 3 / 5 x 9
= 1/ 15
The probability of drawing 2 green counters.
= [tex]^4C_2[/tex] / [tex]^{10}C_2[/tex]
= 2 x 3 / 5 x 9
= 2/15
The probability of drawing 2 yellow counters.
= [tex]^2C_2[/tex] / [tex]^{10}C_2[/tex]
= 1 / 45
The probability of drawing one white and then one red counter.
= 1/10 x [tex]^3C_1[/tex]/[tex]^{9}C_1[/tex]
= 1/10 x 3/9
= 1/10 x 1/3
= 1/30
The probability of drawing one white or one yellow counter.
= 1/10 + 2/10
= 3/10
The probability of drawing one white or one red counter.
= 1/10 + 3/10
= 4/10
= 2/5
The probability of drawing one white or one yellow counter and one any counter.
= 3/10 x 7/9
= 7/30
Thus,
The required probabilities are given above.
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Select the equation that is the inverse of the given function.
f(x) = x-3/5
O f¹(x) = 5x + 15
O
O f-¹(x) = 5x +3
O f-¹(x) = 3x - 5
○f-^1(x)= -5/3x
DONE ✔
Answer:
2. ......................
a bookcase is 5 feet high and 5 feet wide as shown. two braces are going to be built diagonally across the back of the case. how long is the piece of wood that is needed for each brace?
The piece of wood that is needed to build each brace 5√2 feet.
Let the piece of wood that be needed to build each brace x feet.
A bookcase is 5 feet high and 5 feet wide, so
By condition we can write (5^2)+(5^2)=x^2
⇒25+25=x^2
⇒ 50=x^2
x=√50
prime factors:
50=2 × 5 × 5
50 = 2 × 5^2
√50 = √(25 × 2) = 5√2
The piece of wood that is needed to build each brace 5√2 feet .
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What question does the equation 525=25(x-2) help answer
Answer: x=23
Step-by-step explanation:
1. First we need to find how much needs to be multiplied by 25, so 525/25=21.
2. Now that we know that x-2=21, we do 21+2.
3. 21+2=23, so x=23
Please give brainliest.
1. solve 2x-5/7 - 2x-1/2 = 3
2. solve x+1/2 + 2x-1/4 + x+2/3
3. A= 8/x+1 and B=2x+5/x
Given 5-A-B=0
Work out the possible values of x.
Give your solutions to two decimal places.
Answer:
1.
2(2x-5)-7(2x-1)=3
Multiply both sides of the equation by 14, the least common multiple of 7,2.
2(2x−5)−7(2x−1)=42
Use the distributive property to multiply 2 by 2x−5.
4x−10−7(2x−1)=42
Use the distributive property to multiply −7 by 2x−1.
4x−10−14x+7=42
Combine 4x and −14x to get −10x.
−10x−10+7=42
Add −10 and 7 to get −3.
−10x−3=42
Add 3 to both sides.
−10x=42+3
Add 42 and 3 to get 45.
−10x=45
Divide both sides by −10.
x= −10/45
Reduce the fraction to lowest terms by extracting and canceling out 5.
x=− 2/9
2. I don't know this one. Sorry.
3. is in the file
PLEASE HELP FAST ILL GIVE BRAINLIEST IF CORRECT!!!!
The two lines graphed below are not parallel. How many solutions are there to the system of equations?
A. One solution
B. Infinitely many solutions
C. Two solutions
D. No solutions
Answer: (A) One solution
Two companies are trying to sell laptops to a school district. The tables show to total cost for laptops purchased from each of the companies.
Company 1
1=$425
3=$475
5=$525
Company 2
1=$250
3=$350
5=$450
How many laptops would the school district have to purchase for the cost to be the same for both companies?
The school district have to purchase 8 laptops for the cost to be the same for both companies.
What is sequence?
A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is the number of elements.
Given that the company 1 offers:
The cost of 1 laptop is $425.
The cost of 3 laptop is $475.
The cost of 5 laptop is $525.
The difference of cost 1 laptop to cost 3 laptop = the difference of cost 3 laptop to cost 5 laptop = $50
The company 2 offers:
The cost of 1 laptop is $250.
The cost of 3 laptop is $350.
The cost of 5 laptop is $450.
The difference of cost 1 laptop to cost 3 laptop = the difference of cost 3 laptop to cost 5 laptop = $100
Take the cost as a sequence:
The common difference of first sequence is 50/2 = 25.
The common difference of second sequence is 100/2 = 50.
Assume that the school district needs to buy n computer.
The nth term of a sequence is a + (n - 1)d, where a is the first term, d is common difference.
The nth term of the first sequence is 425 + (n - 1) 25
The nth term of the second sequence is 250 + (n - 1) 50
According to question,
425 + (n - 1) 25 = 250 + (n - 1) 50
425 + 25n - 25 = 250 + 50n - 50
25n - 50n = 250 - 50 - 425 + 25
- 25n = -200
Divide both sides by 25
n = 8
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500 milliliters =
liters
Answer: 0.5 Liters
Step-by-step explanation:
1 Liter = 1000 milliliters
500 milliliters = 0.5 Liters
I just need to take 500 divided by 1000 = 0.5 Liters
Name the Special Segment that Matches the picture below.
The special segment that matches the picture is the Median.
What is the median segment?
A median is a line segment that connects any triangle vertex to the middle of the opposite side. It is also the path that connects an angle's opposite internal side to its midpoint. At the centroid, they coexist.
From the figure, the given triangle in which segment is concurrent at the centroid. It bisects each side of the triangle into two equal parts.
Hence, the special segment that matches the picture is the Median.
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Which of the following choices correctly names angles 2 and 3?
alternate interior angles corresponding angles
alternate exterior angles
vertical angles
The choice that correctly names angles 2 and 3 is called the: D. vertical angles.
What is the Definition of Vertical Angles?Two angles are named vertical angles if both angles form a pair of angles that share the same vertex both not the same side, and they are on the opposite sides of two straight lines that intersect each other.
Given the image above, it shows that angle 2 and angle 3 form a pair that shares the same vertex when two straight lines intersect, and both angles are non-adjacent angles, that is they do not share any common side with each other.
Therefore, according to the definition given above, the angles 2 and 3 can be correctly named as: D. vertical angles.
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Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof
The triangles JKL and XYZ are congruent by Side-Angle-Side Theorem as KL ≅ XV, JK ≅ VZ, ∠ K ≅ ∠V.
How to prove that two triangles are congruentHerein we find a case of two triangles that we must prove that they are congruent, this is a congruency problem. Two triangles are congruent if the two triangles share the same sides in the same order. In accordance to the figure, we find the given assumptions:
KL ≅ XV, JK ≅ VZ, ∠ K ≅ ∠V
This assumptions satisfies the Side-Angle-Side Theorem and according to it we conclude that the triangles JKL and XYZ.
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Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
(Please explain, thanks!!)
Answer:
y > -2/3x + 2, y [tex]\geq[/tex] x
[tex]\left \{ {{y > -2/3x + 2} \atop {y \geq x}} \right.[/tex]
Step-by-step explanation:
Knowledge Needed
A system of linear inequalities is graphing 2 lines.
If the line's y side is less than it's x-side (y </ [tex]\leq[/tex] x), shade below.
If the line's y side is greater than it's x-side (y </ [tex]\leq[/tex] x), shade above.
If the line is dotted, it is < or >.
If the line is filled in, it is [tex]\leq[/tex] or [tex]\geq[/tex].
Where both regions are shaded is the solution.
Question
Examine the dotted line.
1) We know it is < or > because it is dotted.
2) We know it is y > .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.
3) We know the y-intercept, when x=0, is 2.
4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is -2/3.
y > -2/3x + 2
Examine the solid line.
1) We know it is [tex]\geq[/tex] or [tex]\leq[/tex] because it is solid.
2) We know it is y [tex]\geq[/tex] .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.
3) We know the y-intercept, when x=0, is 0.
4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is 1.
y [tex]\geq[/tex] 1x + 0
y [tex]\geq[/tex] x
The solution to the linear inequality is when both lines are shaded in (true), which means both lines are the solution together.
y > -2/3x + 2, y [tex]\geq[/tex] x
Answer:
y ≥ x andy > - 2/3x + 2------------------------------
Find the lines first, then determine inequalities based on the shaded region and types of lines.
One line has positive slope and passes through the origin. Its x and y-coordinates are same, hence it is:
y = xThe shaded region is above this line and the line is solid, therefore the inequality is:
y ≥ xThe second line has a negative slope and it has y-intercept at (0, 2), x- intercept at (3, 0).
Its slope is m = (0 - 2)/(3 - 0) = - 2/3.
So the line is:
y = - 2/3x + 2Again, the shaded region is above the line, and the line is dashed, hence the inequality is:
y > - 2/3x + 2find the general solution of the given second-order differential equation. y'' − 10y' + 26y = 0
The general solution of the given second-order differential equation is
y = [tex]e^{5t}[/tex]([tex]c_{1}[/tex]cost + [tex]c_{2}[/tex]sint).
In the given question we have to find the general solution of the given second-order differential equation.
The given second-order differential equation is:
y'' − 10y' + 26y = 0
We can write this equation as
d^2(y)/dx^2 − 10dy/dx + 26 = 0
Let d/dx = D
then, d^2/dx^2 = D^2
Now the equation is:
(D^2 − 10D + 26)y = 0
Now solving the equation as a quadratic equation.
m^2 − 10m + 26 = 0
m = [tex]\frac{-(-10)\pm\sqrt{(-10)^2-4\times1\times26}}{2\times1}[/tex]
m = [tex]\frac{10\pm\sqrt{100-104}}{2}[/tex]
m = [tex]\frac{10\pm\sqrt{-4}}{2}[/tex]
m = [tex]\frac{10\pm2i}{2}[/tex]
m = 5±1
Now the general equation for quadratic equation is
y = [tex]e^{at}[/tex]([tex]c_{1}[/tex]cosbt + [tex]c_{2}[/tex]sinbt)
As a = 5 and b = 1
Now the general solution of the given second-order differential equation is y = [tex]e^{5t}[/tex]([tex]c_{1}[/tex]cost + [tex]c_{2}[/tex]sint).
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At Freddy's Eatery, three steak burgers and two orders of fries cost $18. Two steak
burgers and three orders of fries cost $15.75. What is the cost of one steak burger?
A) $5
B) $4.50
D) $6.50
C)
$2.25
To solve this problem, we can set up a system of equations to represent the given information. Let x represent the cost of one steak burger. Then we can set up the following system of equations:
3x + 2(f) = 18
2x + 3(f) = 15.75
Where f represents the cost of one order of fries.
Subtracting the second equation from the first equation gives us:
x = 18 - 2(f) - 15.75 + 3(f)
= 18 - 15.75
= 2.25
Therefore, the cost of one steak burger is $2.25, which is answer choice C.
Using the distance formula, what is the distance of C (-4, -2) and D (3, 5)?
15
45
9.8
22