On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q (10,30), R(-10, 30), S(-10, - 10), and T(10,- 10), and represents the floor plan of a room. Find the perimeter and area of the room.
Answers
Question:
On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q (10,30), R(-10, 30), S(-10, - 10), and T(10,- 10), and represents the floor plan of a room. Find the perimeter and area of the room.
Solution:
Notice that the polygon QRST is a rectangle. The perimeter of a rectangle is the sum of the lengths of its sides. Notice that the measures that each side is:
QR = ST = 20
RS = QT = 40
then the perimeter P is:
\(P\text{ = 2(20) + 2(40) = 40 + 80= 120}\)Then, we can conclude that the perimeter of the floor is :
\(P\text{ = 120}\)
now, the area of the rectangle is base times height, then in this case we have that the area of the given rectangle is:
\(A\text{ = 20 x 40 = 800}\)Then, we can conclude that the area of the floor is :
\(A\text{ = 800}\)
Related Questions
4x-2=18x+5
Show ur work
Answers
Step-by-step explanation:
\(4x - 2 = 18x + 5\)
Collect like terms and simplify
\( - 2 - 5 = 18x - 4x \\ - 7 = 14x\)
Divide both sides of the equation by 14
\( \frac{ - 7}{14} = \frac{14x}{14} \\ - \frac{1}{2} = x\)
Answer:
x = -1/2
Step-by-step explanation:
4x-2=18x+5
-2-5=18x-4x
-7=14x
-7/14=14/14x
-1/2=x
Do these ratios form a proportion?
3 parents to 10 children
6 parents to 15 children
yes
no
Answers
Answer:
nope
Step-by-step explanation:
Answer:
no they are not
f(x) = x² - 6x-7
g(x) = x + 1
Answers
Answer:
(-1, 0) and (8, 9)
Step-by-step explanation:
x² - 6x-7 = x + 1
x² - 7x - 8 = 0
(x - 8)(x + 1) = 0
x = -1, 8.
When x = - 1, y = 0
and x = 8, y = 9
i need help plz ok plz
Answers
Explanation: 0.48 x 3 = 1.44
0.73 x 4 = 2.92
1.44 + 2.92 = 4.36
suppose section 1 has 30 students and section 2 has 20. find the sd of the scores of all the students in the class
Answers
The standard deviation of the scores of all the students in the class to be:
σ = √[(Σ(x - 80)2) / 50] = 11.18
The standard deviation of the scores of all the students in the class is calculated using the formula
σ = √[(Σ(x - μ)2) / N]
where μ is the mean of the scores and N is the total number of students in the class.
In this case, the total number of students in the class is 50 (30 from section 1 and 20 from section 2). Let's assume that the mean of the scores for all students is 80.
Therefore, the standard deviation of the scores of all the students in the class is calculated as follows:
σ = √[(Σ(x - 80)2) / 50]
In this equation, Σ(x - 80)2 is the sum of the squared differences between each student's score and the mean. We can calculate this sum by first finding the squared difference for each student and then adding them up.
For example, if the scores of the 30 students in section 1 are 86, 95, 78, etc., the squared differences will be (86 - 80)2 = 36, (95 - 80)2 = 225, (78 - 80)2 = 4, and so on. Adding all these squared differences will give us the sum of the squared differences for all the students in the class.
Finally, substituting this sum and the value of N (50) in the formula, we get the standard deviation of the scores of all the students in the class to be:
σ = √[(Σ(x - 80)2) / 50] = 11.18
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Find the polar equation of the conic with focus at the pole, directrix y=3 and eccentricity of 2.
Answers
To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.
The general form of the polar equation for a conic with focus at the pole is given by:
r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)
Where:
- r is the distance from the origin (pole) to a point on the conic.
- e is the eccentricity.
- d is the distance from the pole to the directrix.
- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.
- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.
In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.
Substituting these values into the general equation, we get:
r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)
Simplifying further:
r =\(\frac{6}{1+2\cos(\theta)}\)
Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:
r =\(\frac{6}{1+2\cos(\theta)}.\)
This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.
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I dont get this question equation
y=0.5 (6) - 4
I know that 0.5 is equivalent to 1/2 but I just don’t get this question
Answers
To solve the equation, you first need to simplify 0.5(6) to get 3, since 0.5 is equivalent to 1/2 and multiplying 6 by 1/2 gives you 3. So the equation becomes:
y = 3 - 4
Next, you need to subtract 4 from 3 to get -1. So the solution to the equation is:
y = -1
Therefore, when the value of the independent variable is 6, the value of the dependent variable is -1.
Answer
\(\pink\sf{y=-1}\)
Step-by-step explanation
I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).
We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:
\(\sf{y=3-4}\)
And now we just simplify the last part:
\(\sf{y=-1}\)
∴ answer: y = -1
PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS RIGHT (NO LINKS)
Identify the surface area of the composite figure to the nearest tenth.
Answers
Answer:
D.
Step-by-step explanation:
6a² = surface area for cube
6(5)² = 150
2\(\pi\)(r)(h)+2\(\pi\)r² = surface area cylinder
2\(\pi\)(2)(3)+2\(\pi\)(4) = 20pi
150 + 20pi = 212.8318531
Which number can be placed in the blank to make this number sentence true? In other words, 316
times which number equals 1?
Answers
The number that can be placed in the blank to make the number sentence true is given as follows:
1/316.
How to solve the number sentence?The number sentence for this problem is given as follows:
"316 times which number equals 1".
The number is unknown, hence the variable that represents the number is given as follows:
x.
The times word means a multiplication operation, hence the expression is given as follows:
316x = 1.
Now we must simply solve the expression 316x = 1 for the variable x, applying the division, which is the inverse operation of the multiplication, hence:
x = 1/316.
Which is the number that satisfies the number sentence.
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Understand How far apart are two parallel lines ℓ and m such that
T〈4, 0〉 (△DEF) = (Rm ∘Rℓ)(△DEF)?
Answers
Answer:
2 units
Step-by-step explanation:
NO LINKS!!!
12. Find the inverse of the following functions using what you know about inverse operations. Some of these functions do not have a functional inverse. If it has no functional inverse, write "No inverse function"
Answers
Answer:
a) No inverse function
\(\textsf{b)} \quad c^{-1}(x)=5+\sqrt{x-2},\;\; c\geq2\)
\(\textsf{c)} \quad f^{-1}(x)=-\dfrac{2x}{3x-5}\)
Step-by-step explanation:
Part aGiven function:
\(a(x)=-4x^2+3\)
To find the inverse of the function, swap x and y:
\(\implies x=-4y^2+3\)
Rearrange the equation to isolate y:
\(\implies x-3=-4y^2\)
\(\implies y^2=-\dfrac{x-3}{4}\)
\(\implies y^2=\dfrac{3-x}{4}\)
As the domain and range of function a(x) are unrestricted, the inverse relation is a “sideways” parabola and therefore it is not a function, since it fails the vertical line test.
Part bGiven function:
\(c(x)=(x-5)^2+2,\;\;x\geq5\)
As the domain of function c(x) is restricted to x ≥ 5, the range is also restricted.
Range: c(x) ≥ 2To find the inverse of the function, swap x and y:
\(\implies x=(y-5)^2+2\)
Rearrange the equation to isolate y:
\(\implies x-2=(y-5)^2\)
\(\implies \pm\sqrt{x-2}=y-5\)
\(\implies y=5\pm\sqrt{x-2}\)
As the domain of function c(x) is restricted to x ≥ 5 then:
\(\implies y=5+\sqrt{x-2}\)
Replace y with c⁻¹(x):
\(\implies c^{-1}(x)=5+\sqrt{x-2}\)
The domain of the inverse of a function is the same as the range of the original function. Therefore, the domain of the inverse function is restricted to x ≥ 2.
Part cGiven function:
\(f(x)=\dfrac{5x}{3x+2}\)
To find the inverse of the function, swap x and y:
\(x=\dfrac{5y}{3y+2}\)
Rearrange the equation to isolate y:
\(\implies x(3y+2)=5y\)
\(\implies 3xy+2x=5y\)
\(\implies 3xy-5y=-2x\)
\(\implies y(3x-5)=-2x\)
\(\implies y=-\dfrac{2x}{3x-5}\)
Replace y with f⁻¹(x):
\(\implies f^{-1}(x)=-\dfrac{2x}{3x-5}\)
Susan works as a cleaner. She worked for 6 hours one day at a rate of $18 per hour and for 5 hours at another home at $20 per hour. Calculate her wage for the hours she worked.
Answers
Based on the given parameters, the value of Susan's wage is $208
How to determine Susan's wagesFrom the question, we have the following parameters that can be used in our computation:
6 hours one day at a rate of $18 per hour 5 hours at another home at $20 per hourTo find susans total wage, we find the amount worked in each place then add them together.
so, we have the following representation
Home 1 = 6hours at $18/hr= 6 x 18=$108Home 2 = 5hours at $20/hr= 5 x 20=$100Next, we add the values of the wages in each home as stated above
Using the above as a guide, we have the following:
Total wage = $108 + $100
Evaluate the sum
Total wage = $208
Hence, the total value of the wages is $208
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A person from Switzerland consumes about 9.1 kilograms of chocolate per
year. A person from the United States consumes about 4.7 kilograms of
chocolate per year. How many times as much chocolate will a Swiss
person consume in one year than someone from the United States? Round
your final answer to the nearest tenths
Answers
Answer:
switzerland was the leading country in chocolate consumption per capita in 2017, with citizens eating nearly nine kilos of the sweet stuff in that year. World renowned for the chocolate they produce, it seems the Swiss themselves can’t get enough of the candy. Germany, the country’s neighbor, is equally addicted, importing the largest share of Swiss chocolate of all countries in the world.
Step-by-step explanation:
Answer: a swede would consume 1.9 times as much chocolate as an American.
Step-by-step explanation: 9.1 / 4.7 = 1.93617021. round to the nearest tenth = 1.9.
1.93617021 times 4.7 equals 9.1
Write an equation that expresses the following relationship.
w varies directly with u and inversely with the square of d
In your equation, use k as the constant of proportionality.
Answers
Answer:
w = \(\frac{ku}{d^{2} }\)
Step-by-step explanation:
An equation that expresses the given relationship is ud²=1.
Given that, w varies directly with u and inversely with the square of d.
We need to write an equation that expresses the following relationship.
What is directly and inversely varies?Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant.
Now, w∝u⇒w=ku
and w∝1/d²⇒w=k/d²
⇒wd²=k
⇒w=wd²u
⇒ud²=1
Therefore, an equation that expresses the given relationship is ud²=1.
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Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
Answers
The total cost of the pita bread and hummus dips will be $305.00.
To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:
Cost of pita bread:
Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates
Cost of each crate = $15.00
Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00
Cost of hummus dips:
Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes
Cost of each box = $20.00
Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00
Therefore, the expressions Toula can use to determine the costs are:
Cost of pita bread = 3 crates × $15.00/crate
Cost of hummus dips = 13 boxes × $20.00/box
The total cost will be the sum of the costs of pita bread and hummus dips:
Total cost = Cost of pita bread + Cost of hummus dips
Total cost = $45.00 + $260.00
Total cost = $305.00
Therefore, the total cost of the pita bread and hummus dips will be $305.00.
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A.60
B.120
C.240
D.360
Answers
Answer:
b i think brainlest me plz
Step-by-step explanation:
Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours how far did Simon drive in all
Answers
Answer:
415 miles
Step-by-step explanation:
Start with the speed equation:
speed = distance/time
Now solve the speed equation for distance:
distance = speed × time
Apply the speed equation solved for distance to the two parts of the trip.
4 hours at 55 mph:
distance = 55 mph × 4 hours = 220 miles
3 hours at 65 mph:
distance = 65 mph × 3 hours = 195 miles
Add the two distances to find the total distance:
total distance = 220 miles + 195 miles = 415 miles
Answer: 415 miles
Answer:
415 miles
Step-by-step explanation:
Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.
How far did he drive?
d=rt
For the first part of the trip:
d = 55 * 4 = 220 miles
For the second part of the trip:
d = 65*3 =195 miles
Add the miles together
220+195 = 415 miles
I need help ASAP!!!!
Answers
Answer:
r=5
Step-by-step explanation:
25^3 = 15626
-5^3 = -125
5^3 = 125
15^3 = 3375
Answer:
R=5
Step-by-step explanation:
You first have to find the cube root
The cube root of 125 is 5
r=5
The mass of a cube, M (kg), is proportional to the cube of the length of its edge, L(m). The mass of the cube is 80 kg when the length of its edge is 35 cm. Work out M (to 2 DP) when L=0.3 m
Answers
Answer:
M=K*L
(K is the constant we use)
when L=35cm, M=80,
meaning K=80/0.35=228.571428571
so when L=0.3
we do 0.3*228.571428571=68.5714285713
rounded to 2dp= 68.57kg
9514 1404 393
Answer:
50.38 kg
Step-by-step explanation:
The mass is proportional to the cube of edge length, So, if the edge length is decreased by a factor of 30/35 = 6/7, the mass is decreased by a factor of (6/7)³. That is, the smaller cube will have a mass of ...
(80 kg)(6/7)³ ≈ 50.38 kg
__
If you want to write an equation, you can write the equation for the proportionality:
M = kL³
80 kg = k(0.35 m)³
k = 80/0.35³ kg/m³
Then for the shorter length, we have ...
M = k(0.3 m)³ = 80(0.3/0.35)³ kg = 80(6/7)³ kg ≈ 50.38 kg . . . . as above
what are coordinates of point j?
Answers
Answer:
(7,4)
Step-by-step explanation:
The x always goes first and the y goes second
Answer:
7,4
Step-by-step explanation:
x,y
Find x for brainiest
Answers
Ssss
A company's year-end data shows the following amounts. Current assets $65,000 Current liabilities $25,000 Net income $7,500 Net sales $125,000 Total assets $150,000 Based on this information, what is the company's current ratio?
Answers
The company's current ratio is 2.6.
What is the current ratio?
Current ratio is an example of a liquidity ratio. Liquidity ratios are financial ratios measure a firm's ability to honour its short terms obligations.
Current ratio = current asset /current liability
$65,000 / 25,000 = 2.6
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can you help me find this solution if you can explain it to me please also
Answers
100-48-14-2= 36%. Because the whole thing is 100% and I removed all the other animals to find the percentage of cats chosen.
Then we want to know the number of classmates:
Cat= 36% of 50 people = 0.36 x 50=18
Fish= 14% of 50 people = 0.14 x 50= 7
Now we see the difference between them :
18-7=11 people
The answer is D which is 11.
Kurt can ride his bike for 30 miles with the wind in the same amount of time that he go 21 miles against the wind. If the winds speed is 6 mph, what is Kurt’s speed on his bike
Answers
SOLUTION:
In this question, we are given the following:
Kurt can ride his bike for 30 miles with the wind in the same amount of time that he goes 21 miles against the wind. If the wind's speed is 6 mph, what is Kurt’s speed on his bike?
Step 2:
The details of the solution are as follows:
Let Kurt's speed on the bike be U,
Kurt can ride his bike for 30 miles with the wind in the same amount of time,
If the wind's speed is 6 mph, it means that:
\((\text{ U+ 6 \rparen t = 30 -- equation 1}\)
If he goes 21 miles against the wind and the wind's speed is 6 mph, it means that:
\((U-6)t\text{ = 21 --- equation 2}\)\(\begin{gathered} solving: \\ (U+6)t\text{ = 30 --equation 1} \\ (U-6)t\text{ = 21 --equation 2} \\ Divide\text{ equation 1 by equation 2, we have that:} \\ \end{gathered}\)\(\begin{gathered} \frac{(U+6)t\text{ }}{(U-6)t\text{ }}=\text{ }\frac{30}{21} \\ Then,\text{ we have that:} \\ 21\text{ \lparen U+6 \rparen = 30 \lparen U-6 \rparen} \\ 21U\text{ + 126 = 30 U -180} \\ collecting\text{ like terms, we have that:} \\ 126+\text{ 180 = 30 U -21 U} \\ 9U\text{ = 306} \\ Divide\text{ both sides by 9, we have that:} \\ U\text{ = }\frac{306}{9} \\ U\text{ = 34 miles per hour} \end{gathered}\)CONCLUSION:
Kurt's speed on his bike = 34 miles per hour
I GIVE BRAINLIST
Todd used 18 centimeters of tape to wrap 2 presents. How much tape will Todd need in all if he has to wrap 3 presents? Assume the relationship is directly proportional.
Answers
Answer:
27 centimeters
Step-by-step explanation:
2 presents = 18
Divide by 2 to find how much tape he needs for 1 present
1 present = 18/2 = 9
Multiply by 3 to find how much tape he needs for 3 presents
3 presents = 9 * 3 = 27
can you solve these please and show your work
Answers
Write how many tens. Then add.
60+ 10 =
Enter the correct numbers in the boxes.
Tens + tens = tens
Answers
Answer:
60 contain 6 tens
then
60+10
contain
7 tens
the
correct answer
is
7 tens
Answer:
6 tens + 1 ten = 7 tens
Step-by-step explanation:
6 tens = 60
1 ten = 10
7 tens = 70
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
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Question 1 of 14
Which of the equations or inequalities below are true?
A. -4 + 6 = 1
B. -4 + 6 7-2
C. -4 + 6 24
D. -4+6 s 2
Answers
question seems incomplete
there are no notations for inequalities
The admission fee at an amusement park is $3.50 for children and $5.40 for adults. On a certain day, 351 people entered the park, and the admission fees collected totaled $1523. How many children and how many adults were admitted?
Answers
Answer:
Adults=155, children = 196
Step-by-step explanation:
