Look at the rectangle and the square:
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 12 inches, and the width QR is labeled as 6 inches. The side LM of the square is labeled as 6 inches
Sam says that the length of diagonal SQ is two times the length of diagonal OM.
Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
(Sorry for the low quality image)
Answers
Answer:
Sam is incorrect
Step-by-step explanation:
We can calculate the lengths of the diagonals using Pythagoras' identity.
The diagonals divide the rectangle and square into 2 right triangles.
Consider Δ SRQ from the rectangle
SQ² = SR² + RQ² = 12² + 6² = 144 + 36 = 180 ( take square root of both sides )
SQ = [tex]\sqrt{180}[/tex] ≈ 13.4 in ( to 1 dec. place )
Consider Δ ONM from the square
OM² = ON² + NM² = 6² + 6² = 36 + 36 = 72 ( take square root of both sides )
OM = [tex]\sqrt{72}[/tex] ≈ 8.5 in ( to 1 dec. place )
Now 2 × OM = 2 × 8.5 = 17 ≠ 13.4
Then diagonal OM is not twice the length of diagonal SQ
Related Questions
Find the area of the shape.
Answers
Answer:
Step-by-step explanation:
The Naturally Made Bath and Body store pays $550 a month for rent and utilities. The average cost for its products to be manufactured is about $3.00 an item. If the average price for a product sold in the store is $5.50, what will the break-even point be?
Answers
Answer:
Break-even point is at quantity 220.
Step-by-step explanation:
Given the rent amount that is fixed cost for the store = $550
The average cost of the goods = $3
The average price of the goods = $5.50
Let the total number of break-even items = Q
Thus, total revenue = 5.50 x Q = 5.50Q
At break-even, TR = TC
5.50Q = FC + VC
5.50Q = 550 + 3Q
5.50Q - 3Q = 550
2.50Q = 550
Q = 550 / 2.50
Q = 220
Thus break-even point is at quantity 220.
The distance needed to stop a car, d, varies directly as the square of the speed, s, at which it is travelling. A car travelling at a speed of 70 km/h requires a distance of 40 m to make a stop. What distance is required to stop a car travelling at 80 km/h?
Answers
Answer:
52.24 km
Step-by-step explanation:
Given that,
The distance needed to stop a car, d, varies directly as the square of the speed, s, at which it is travelling.
d = ks²
Where
k is constant
When s₁ = 70 km/hr, d₁ = 40 m, s₂ = 80 km/hr, d₂ = ?
So,
[tex]\dfrac{d_1}{d_2}=\dfrac{s_1^2}{s_2^2}\\\\d_2=\dfrac{d_1s_2^2}{s_1^2}\\\\d_2=\dfrac{40\times 80^2}{70^2}\\\\d_2=52.24\ km[/tex]
So, the new distance is 52.24 km.
holaaandaaa cuanto es 22+22
Answers
Step-by-step explanation:
22+22=44
Es una pregunta fácil, incluso un niño pequeño puede responder a esto.
What is the completely factored form of this polynomial?
x^4- 8x^2 + 16
A. (X+2)^2(x-2)^2
B. (x^2-4)^2
C. (x^2+4)(x+2)(x-2)
D. (x+2)(x-2)
Answers
Answer:
A. (x + 2)²(x - 2)²
Step-by-step explanation:
x⁴ - 8x² + 16 =
(x² - 4)(x² - 4) =
(x - 2)(x + 2)(x - 2)(x + 2) =
(x - 2)²(x + 2)²
says hint: divide, i dunno
Answers
distance= rate * time
distance/rate=time
(2.4 *10^20)/ (1.2*10^5) = 2 * 10^15 seconds
I have to solve the equation:
[tex] |4 \sqrt{2} - 6 | + |2 \sqrt{10} - 6| [/tex]
The first thing I tried is simply removing the modules, it seemed like the most logical solution and this is the answer I got, but it wasn't any of the options:
[tex]4 \sqrt{2} + 2 \sqrt{10} + 12[/tex]
The second thing I tried is putting both equations in one module and sum the first one with the second one in parentheses like this:
[tex] |4 \sqrt{2} - 6 + (2 \sqrt{10} - 6 | = \\ = |4 \sqrt{2} - 6 + 2 \sqrt{10} + 6 | = \\ = 4 \sqrt{2} + 2 \sqrt{10}[/tex]
But this wasn't in the answers either.
After I checked, the correct answer was:
[tex]2 \sqrt{10} - 4 \sqrt{2} [/tex]
So I was wondering where does the minus come from?
It is in a module and between the modules, there's a plus and even if that plus somehow turns into a minus when it goes inside the modules, which I'm not aware of, it would still turn into a plus because it is in a module ;-; Or I'm just st*pid, I don't know.
Answers
Think back to the definition of absolute value:
• If x ≥ 0, then |x| = x.
• If x < 0, then |x| = -x.
In other words, the absolute value always returns a positive number. So if x is positive, leave it alone; but if it's negative, then you have to negate it to get a positive number back.
This means that you cannot simply reduce |x - y | to x - y because you need to consider the possibility that x - y may be negative, in which case |x - y | would reduce to -(x - y) = y - x.
In this case,
|4√2 - 6| = -(4√2 - 6) = 6 - 4√2
because 4√2 < 6, which you can determine by comparing both of these numbers as square roots:
4√2 = √16 √2 = √32
6 = √36
and √32 < √36 because 32 < 36.
Similarly,
|2√10 - 6| = 2√10 - 6
because
2√10 = √4 √10 = √40
6 = √36
So ultimately,
|4√2 - 6| + |2√10 - 6| = (6 - 4√2) + (2√10 - 6) = 2√10 - 4√2
does this graph show a function pic out of the multiple choice to explain how
Answers
Answer:
B
Step-by-step explanation:
The vertical line test means that if there can't be two y values on the same x point. For example, if you put a vertical line through the red line, it would hit two points, meaning that it isn't a function.
Need help on this!! Will give 20 points!!!
Answers
Answer:
80 mm
Step-by-step explanation:
1/p + 1/20 = 1/16
Subtract 1/20 from both sides
1/p = 1/16 - 1/20
Use 160 as common denominator
1/p = 10/160 - 8/160
1/p = 2/160
1/p = 1/80
Cross multiply
80 = p
80 mm
A girl runs 2 km in 1 hour . How long will she take to ran 500 m ?
Answers
Answer:
1/4 he
Step-by-step explanation:
Answer:
1/4 hour
Step-by-step explanation:
convert 2 km to m
1 km = 1000m
2 km = 2*1000 m
=2000 m
distance time taken
2000 m 1 hour
500 m let be x
2000/500 = 1/x
do cross multiplication
500*1 = 2000*x
500/2000 = x
1/4 = x
Which expression is equivalent
Answers
Answer:
[tex]\sqrt[6]{2\\}[/tex]
Step-by-step explanation:
Rewriting
2 ^1/2 ÷ 2 ^ 1/3
We know a^ b ÷ a^c = a^ (b-c)
2 ^ (1/2 -1/3)
Getting a common denominator
2^ ( 3/6 - 2/6)
2^ 1/6
[tex]\sqrt[6]{2\\}[/tex]
Answer:
[tex]\sqrt[6]{2}[/tex]
Step-by-step explanation:
We can start by writing the expression as one power of two, and then comparing it to the options. The square root of two is the same and [tex]2^{\frac{1}{2} }[/tex] and the cube root of two is the same as [tex]2^{\frac{1}{3} }[/tex]. Therefore, we can rewrite the expression:
[tex]\frac{2^{\frac{1}{2} }}{2^{\frac{1}{3} }}[/tex]
Now, to write them as one power of two, we can use the quotient rule which states, [tex]\frac{x^m}{x^n} = x^{m-n}[/tex]:
[tex]2^{\frac{1}{2} -\frac{1}{3}}[/tex]
We just need to subtract 1/3 from 1/2 to get:
[tex]2^{\frac{1}{6} }[/tex]
This is the same as the 6th root of 2, which is the second option.
how do i solve this
[tex] {x}^{6} [/tex]
Answers
Answer:
You did give anything to solve
Step-by-step explanation:
x⁶ is just a single term
If you had posted an equation like
x⁶ = 64
Take the cube root of both side
x² = 4
Take the square root of both sides
x = ± 2
PLZZ HELP ME ITD MEAN THE WORLD
Answers
Answer: 33/3
Step-by-step explanation:
I don't know the question is weird but it probably is 33/3
-7 2/3 + (-5 1/2) + 8 3/4
Answers
Answer:
the answer would be -1339/24
2 Points
(25x
0
The equation ya
represents Michelle's regular
130(x-38) +950 %> 38
hourly and overtime wage. Based on this equation, what is Michelle's
overtime hourly pay?
A. $30
B. $38
O C. $950
O D. $25
Answers
Answer:
The answer is "35.22".
Step-by-step explanation:
Let the given equation:
[tex]\to 130(x-38) +950 \% \times 38=0\\\\\to 130x- 4940+\frac{950}{100} \times 38=0\\\\\to 130x- 4940+9.5\times 38=0\\\\\to 130x- 4940+361=0\\\\\to 130x- 4579=0\\\\\to 130x= 4579\\\\\to x= \frac{4579}{130}\\\\\to x= 35.22[/tex]
Answer: $25
Step-by-step explanation: took the quiz
A monkey is trying to scale a tree That is 6O feet tall. Each minute, the monkey... -Goes up three feet -But, slips down two feet How long will it take the monkey to get to the top of the tree?
Answers
Answer:
58 Minute
Step-by-step explanation:
According to the Question,
Given, A monkey is trying to scale a tree That is 6O feet tall. Each minute, the monkey Goes up three feet But, slips down two feet.Therefore, he climbs (3-2)1 Foot in 1 minute. Now at 57minute, he scales 57feet.
Now, at the 58th minute, he climbs 3 feet MoreThus 57 feet + 3 feet = 60feet( Reached the Top of the tree Now he Never Fall again)
the monkey will take total 58 minutes to get to the top of the tree.Type the correct answer in each box.
Answers
HELP ASAPPPP!!!!!!!
Find the y-intercept of the line y-7x= -3
Answers
Answer:
y - intercept = - 3
Step-by-step explanation:
The equation of a line is typically written as y=mx + b where m is the slope and b is the y-intercept.
Given :
y - 7x = - 3
y = 7x - 3 [ convert to standard line equation form ]
Therefore , y - intercept = - 3
Answer:
-3
This is the y intercept because when you re-arrange the equation to form y=mx+c, the y-intercept( c) is -3.
(1) At the local nursery, 1/2 of the plants for sale are flowers and another 1/10 of them are
bushes. What fraction of the plants for sale are either flowers or bushes?
Answers
Answer:
6/10
Step-by-step explanation:
Look at is a whole. Half the plants are flowers, and just a few are bushes. That leaves other plants that are neither.
We can find a total amount of plants that are either flowers or bushes by combining the two.
Because 1/2 and 1/10 are not currently combinable, you must find a common denominator. This common denominator is 10. If you multiply 2 by 5, you'll get 10.
[tex]\frac{1}{2} +\frac{1}{10}[/tex]
[tex]\frac{5}{1} (\frac{1}{2} )+\frac{1}{10}[/tex]
[tex]\frac{5}{10} +\frac{1}{10}[/tex]
[tex]\frac{6}{10}[/tex]
This means that 6/10 of the whole number of plants are either flowers or bushes. You could also say it means that 4/10 of the plants are something other than flowers or bushes.
I hope this helped :)
Sum of cubes:
(a + b)(a2 – ab + b2) = a3 + b3
Difference of cubes:
(a – b)(a2 + ab + b2) = a3 – b3
Which products result in a sum or difference of cubes? Check all that apply.
(x – 4)(x2 + 4x – 16)
(x – 1)(x2 – x + 1)
(x – 1)(x2 + x + 1)
(x + 1)( + x – 1)
(x + 4)(x2 – 4x + 16)
(x + 4)(x2 + 4x + 16)
Answers
Answer:
C and E
Step-by-step explanation:
Answer:
3 and 5
Step-by-step explanation:
The solution of this problem is in this picture.
A and B are the subsets of a universal set U. If U = {1,2,3,4,5,6,7,8,9,10} A={1,2,3,5,7,9} and B ={1,2,3,6}, show that AUB complement=AΠB complement
Answers
Answer:
AUB= {1,2,3,5,6,7,9}
AnB={1,2,3}
If i= square root of -1, what is the value of i^3
Answers
Answer:
[tex] - i[/tex]
Step-by-step explanation:
Set up equation.
[tex]i {}^{3} = y[/tex]
[tex] {i}^{2 } \times i = y[/tex]
[tex] - 1 \times i = y[/tex]
[tex] - i = y[/tex]
The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean $400 and standard deviation $20. How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?
Answers
Answer:
$425.6 should be budgeted for weekly repairs and maintenance.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean $400 and standard deviation $20.
This means that [tex]\mu = 400, \sigma = 20[/tex]
How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?
This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 400}{20}[/tex]
[tex]X - 400 = 20*1.28[/tex]
[tex]X = 425.6[/tex]
$425.6 should be budgeted for weekly repairs and maintenance.
Two friends Vicky and Love start a business together. They decided to share their capitals depending upon the variable
expenditure. The capital of the two
partners together is given by polynomial 6x+10x -35, which is the product of
their individual share factors.
On the basis of the above information,
answer the following questions.
i) The total expenditure of Vicky and Love
when x = 10 is (in )
(a) 375 (b) 475
(c) 575 (d) 675
(ii) The shares of the Vicky and Love
individually is
(a) 2x +7, 3x -
5
(b) 3x -5, 2x +7
(c) Both (a) and (b)
(d) None of the above
(iii) The value of x, when their shares are
equal
(a) 12 (b) 10
(c) 8 (d) 6
(iv) The value of x, when their total share is
equal tob0
7
(a)- (b) 3
(c) Both (a) and (b) (d) None of these
(v) The sum of their expenditure is
(a) 5r -2 (b)5x+2 (c) 4x-2 (d) 4x+2
Answers
contruct triangle LMN with LM=6cm,MM=9cm and LN =5cm
Answers
Answer:
LNM are quations the answer
Step-by-step explanation:
L=5x3 5,8 M=9x8x3+40-9 N=23-90)+90
Please help me out for the question is it
A.275 centimeters
B.94 centimeters
C.144 centimeters
D.85 centimeters
You’ll be marked as brainliest
Answers
I think c because from what remember taking this test
PLS HELP ASAP!! THX
For questions 6-9 refer to the box plots (Assume their positions are on the same number line). Write your responses in complete sentences using content specific vocabulary.
Answers
Answer:
Did you find them ?
Step-by-step explanation:
Hannah lost four points on a test and earned four points on an extra credit question what does the sum of 0 mean in the description of this situation?
Answers
Answer:
Is that it's not about the answers and the questions
Help and explain pls and thankyouuuuuu
Answers
Answer:
shhsksbsvsvdbdhsbs. c
9514 1404 393
Answer:
(d) -3
Step-by-step explanation:
Put the number into the expression and do the arithmetic.
f(g(-2)) = f(-2-3) = f(-5) = 2(-5) +7 = -10 +7
f(g(-2)) = -3
si alguien me ayuda en esta doy coronita
Answers
Answer: yuh Step-by-step explanation: yuh
Answer:
11/8, 7/4, 8/2
someone reported me
