Question 2
Which statement best explains
why the sum of the areas of the
two white squares in Figure 2 is
the same as the area of the white
square in Figure 1?
The combined area of the four triangles is equal to the area of the large white
square.
In each triangle, the length of side a plus the length of side b equals the length
of side c. That means that a? + b2 = c?.
In each figure the total area is equal and the area of the 4 triangles is equal, so
the remaining white area in each figure must also be equal.
Answers
Answer:
the third option
Step-by-step explanation:
that is actually the proof for Pythagoras :
both squares have the total area of (a + b)².
each of the triangles (4 in figure 1, 4 in figure 2) has the same area as the others : a×b/2
so, for figure 1
(a + b)² = 4×a×b/2 + c² = 2×a×b + c²
and for figure 2
(a + b)² = 4×a×b/2 + a² + b² = 2×a×b + a² + b²
2×a×b + c² = 2×a×b + a² + b²
c² = a² + b²
Related Questions
A. What is the formula for exponential growth?
B. What does each variable mean?
Please someone help!!! It’s for my final pleaseee!!!
Answers
Answer:
A. exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. The equation can be written in the form f(x) = a(1 + r)x or f(x) = abx where b = 1 + r. ... r is the percent growth or decay rate, written as a decimal, b is the growth factor or growth multiplier.
Two integers are relatively prime if, and only if, their greatest common divisor is 1. For example, 2 and 3 are relatively prime, 1 and 1 are relatively prime, but 2 and 2 are not. You toss two dice, one blue and one gray. What is the probability that when the dice stop rolling that the pip count on the blue die is relatively prime to the pip count on the gray die and the gray die is showing six pips
Answers
Answer:
A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)
Step-by-step explanation:
A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)
Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides.
O polygon, hexagon
O polygon, dodecagon
polygon, decagon
O not a polygon
Answers
it is a polygon and it would be a decagon since there are 10 sides
Answer:
It is a polygon, hexagon.
Step-by-step explanation:
Types of polygons include: Triangle, quadrilateral, Pentagon, hexagon, heptagon, octagon, nonagon, and decagon. a hexagon has 6 sides this has 8 so it isn't a hexagon but it can be a decagon so it's the second answer.
There are 550 calories in 100 g of bacon. There are 196 calories in a fried egg. Philip has 60 g of bacon and two fried eggs for breakfast. Work out the total number of calories in this breakfast.
Answers
Answer:
509.6 calories
Step-by-step explanation:
196+196=392 calories
10g of bacon=19.6 calories
60g of bacon=19.6×6=117.6 calories
392+117.6=509.6 calories
determine the slope and y intercept and write the equation in slope intercept form
Answers
Answer: slope is 2 and the y-intercept is 1 intercept form is y=2x+1
Step-by-step explanation:
what is the intercepts of the line?
x-intercept and y-intercept
4x-1=3y+5
Answers
Answer: X (3/2,0) Y (0,-2)
Step-by-step explanation:
4 x ( 2 + 5 )^2 - 5^2
Answers
=4*49-25
=196-25
=171
A farmer had 21 goats all but 9 died how many survive ?
Answers
Answer:
9
Step-by-step explanation:
All but 9
Answer:
12
Step-by-step explanation:
I used a calculator I hhhhhhj
Question: Assume you have a balance of $1000 on a credit card with an APR of 12%, or 1% per month. You start making monthly payments
of $200, but at the same time you charge an additional $100 per month to the credit card. Assume that interest for a given month is based on
the balance for the previous month. The following table shows how you can calculate your monthly balance. Complete and extend the table to
show the balance at the end of each month until the debt is paid off. How long does it take to pay off the credit carddebt?
nts
Fill out the table row by row and continue until the last full payment. Round to the nearest cent as needed.
Month
Payment
Expenses
Interest
New Balance
a
urces
0
---
$1000
es
1
$200
$100
$10
$910
4/7
fing
2
$200
$100
ection
3
$200
$100
4
$200
$100
Answers
1. The extension of the table to show the month-end balances until full debt settlement is as follows:
Month Payment Expenses Interest New Balance
0 $0 $0 $0 $1,000
1 $200 $100 $10 $910 ($1,000 - $200 + $100 +$10)
2 $200 $100 $9.10 $819.10 ($910 - $200 + $100 + $9.10)
3 $200 $100 $8.19 $727.29 ($819.10-$200+$100+$8.19)
4 $200 $100 $7.27 $634.56 ($727.29-$200+$100+$7.27)
5 $200 $100 $6.35 $540.91 ($634.56-$200+$100+$6.35)
6 $200 $100 $5.41 $446.32 ($540.91-$200+$100+$5.41)
7 $200 $100 $4.46 $350.78 ($446.32-$200+$100+$4.46)
8 $200 $100 $3.51 $254.29 ($350.78-$200+$100+$3.51)
9 $200 $100 $2.54 $156.83 ($254.29-$200+$100+$2.54)
10 $200 $100 $1.57 $58.40 ($156.83-$200+$100+$1.57)
11 $200 $100 $0.58 ($41.02) ($58.40-$200+$100+$0.58)
Data and Calculations:
Credit card balance = $1,000
APR = 12%
Monthly APR = 1%
Monthly payments = $200
Monthly charge = $100
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Which of the following best describes a ratio?
Answers
Often time we want to relate one amount or quantity with another, from the given options the one that best describes a ratio is option
A. A comparison of two numbers
A ratio indicates how many times one number contains another. E.g, if there are five balls and nine lemons in a bowl of fruit, then the ratio of balls to lemons is five to nine. Similarly, the ratio of lemons to oranges is 5∶8
Learn more on ratios:
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Which of the following is the greatest common factor of 48 and 32?
Answers
Answer:
8
Step-by-step explanation:
cus...
Outliers have very little or no effect on which of the following check all that apply mean median mode range or standard deviation
Answers
Outliers are data elements that are far from the other elements of a dataset, and they have little or no effect on the median and the mode
Outliers are usually large or very low values, and they always affect the mean of the dataset.
Also, they affect the range of the dataset.
The standard deviation is dependent on the mean of the dataset.
This means that, outliers would also have effects on the standard deviation.
However, outliers are most likely not to have a considerable effect on the median and the mode of the dataset.
Hence, the true options are mode and median
Read more about outliers at:
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A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained the wishes the estimate to be within three percentage points
with 90% confidence, assuming that
(a) he uses the estimates of 21.3% male and 19.5% female from a previous year?
(b) he does not use any prior estimates?
(a)n (Round up to the nearest whole number)
(b) (Round up to the nearest whole number.)
Answers
Using the z-distribution and the formula for the margin of error, it is found that:
a) A sample size of 54 is needed.
b) A sample size of 752 is needed.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
Item a:
The estimate is [tex]\pi = 0.213 - 0.195 = 0.018[/tex].
The sample size is n for which M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2[/tex]
[tex]n = 53.1[/tex]
Rounding up, a sample size of 54 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.05[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
[tex]n = 751.7[/tex]
Rounding up, a sample of 752 should be taken.
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A jogger ran 13.5 miles in 3 hours.
What is the unit rate?
Answers
Answer:
Unit rate = 4.5 mph.
Step-by-step explanation:
Unit rate: 13.5/3
=> Unit rate: 4.5 mph.
Hoped this helped.
solve the inequality x-3 < 3x -7
Answers
Answer:
x > 2 or 2 < x
Step-by-step explanation:
x-3 < 3x-7
-3 < 2x-7
4 < 2x
2 < x
x > 2
Two sides of a triangle measure 10 feet and 14 feet. Which
inequality shows the possible lengths for the third side, x?
Answers options:
10 ≤ x ≤ 14
4 ≤ x ≤ 24
10 < x < 14
4 < x < 24
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The third side of the Triangle should be greater than the difference of other two sides, so
[tex]x > 14 - 10[/tex][tex]x > 4[/tex]And, The third side should be less than the sum of other two sides that is ~
[tex]x < 14 + 10[/tex][tex]x < 24[/tex]Considering these two inequalities, we get ~
[tex]4 < x < 24[/tex]please help i am stuck
Answers
Explanation:
All of these are done the same way.
1. Set your compass to a distance slightly longer than the distance from the point to the line you want the perpendicular to.
2. Using the point as a center, draw an arc that intersects the line in 2 places. Consider those points to be "P" and "Q".
3. You can leave the compass as is, or set it to any other distance longer than half the distance between P and Q. Using this radius, and using P and Q as centers, draw intersecting arcs on the other side of the line from the original point. Consider the intersection of those arcs to be point "R".
4. A line through the original point and point R will be perpendicular to the line, as you want.
_____
In problem 1, the point and line are obvious.
In problem 2, the point is the vertex opposite the line of interest. (There will be 3 similar constructions.)
Hi guys im stuck on this maths question
(2/5)^-3
Answers
Answer:
15.625
Step-by-step explanation:
Answer:
[tex] (\frac{2}{5} ) {}^{ - 3} \\ = (\frac{a}{b} ) {}^{ - x} = (\frac{b}{a} ) {}^{x} \\ so \: \: \: \: \: \: (\frac{2}{5} ) {}^{ - 3} \\ = (\frac{5}{2} ) {}^{3} \\ = \frac{5 {}^{3} }{2 {}^{3} } \\ \: = \: \frac{125}{8} [/tex]
QUICK! I NEED HELP ASAP
---------------------
w−(−1/3)=2.05
Enter your answer as a mixed number in simplest form in the box.
w =
Answers
Answer:
w=6
Step-by-step explanation: you should just look it up on line
Answer:
The correct answer is 1 43/60
Step-by-step explanation:
you convert 2.05 to a fraction and get 2 23/60 - (-1/3) = 1 43/60
i also took the test
Solve the inequalities from parts A and D for the variables b and n, respectively.
Part A:2b<56
Part D:n<56
Answers
Answer:
Part A: b < 28
Part D: n < 56
Step-by-step explanation:
part A: divide each term in and simplify.
Inequality Form: b < 28
part d: this is already solved but can be shown in multiple forms.
Inequality Form: n < 56
Interval Notation: ( -∞ , 56)
Round 61.373737842 to the nearest ten-millionth
Answers
Answer:
61.3737378
Step-by-step explanation:
First find the ten millionth digit, and the digit after it.
The digit "8", the seventh digit to the right of the decimal point is the ten millionth digit.
As the digit after "8" is 4, which is less than 5, so simply round the digit "4" down.
Thus the answer is 61.3737378
Mr. and Mrs. Bruce took a boat trip which left Cala for Friends’ Island at 11:45 in the morning. The trip lasted for 1 hour and 20 mins. When did they arrive at Friends’ Island?
Answers
-
What are the odds of winning a game, if the probability of winning the game is 4/10
Answers
Answer:
40%
Step-by-step explanation:
4/10 = 40/100
40/100 as a percentage is 40%
51 is 10% of what number
Answers
Answer:
10 percent of 51 is 5.1
Answer:
51=10
510=100
Step-by-step explanation:
51=10/100
x10
510
For homework, Tina is asked to write down the opposite value for each number listed. Which comparison did Tina write incorrectly?
Answers
Answer:
x
Step-by-step explanation:
It still would be a negative.
The comparison that Tina wrote incorrectly is X. Then the correct option is B.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The table is given below.
Comparison Number Opposite value
W -3 3
X -(-9) 9
Y 0 0
Z 4 - 4
The number -(-9) is also written as 9 and the opposite number of 9 is negative 9. Then the comparison that Tina wrote incorrectly is X. Then the correct option is B.
More about the Algebra link is given below.
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One x-intercept for a parabola is at the point (-0.4,0). Use the quadratic formula to find the other x-intercept for the parabola defined by this equation: y = 5x2 + 7x + 2 Separate the values with a comma. Round, if necessary, to the nearest hundredth.
Answers
Answer:
-1
Step-by-step explanation:
Set y=0.
[tex]5 {x}^{2} + 7x + 2 = 0 \\ x = \frac{ - 7± \sqrt{ {7}^{2} - 4(5)(2)} }{2(5)} \\ x = \frac{ - 7± \sqrt{ 9} }{10} \\ x = \frac{ - 7±3}{10} \\ x = - \frac{2}{5} \: \: \: \: or \: \: \: \: - 1[/tex]
The x-intercepts are - 0.4 and - 1.
The other x-intercept is - 1.
Answer: 1,0
Step-by-step explanation:
At State College last term, 63 of the students in a Physics course earned As, 85
earned Bs, 123 got Cs, 84 were issued Ds, and 64 failed the course. If this grade
distribution was graphed on a pie chart, how many degrees would be used to indicate
the B region?
Answers
Answer:
a
Step-by-step explanation:
The graph shows the distribution of the amount of time (in minutes) people spend watching TV shows on a popular streaming service. The distribution is approximately Normal, with a mean of 71 minutes and a standard deviation of 15 minutes.
A graph titled Streaming T V has time (minutes) on the x-axis, going from 11 to 131 in increments of 15. The highest point of the curve is at 71.
What percentage of people spend between 41 and 56 minutes watching TV shows on this streaming service?
a- 13.5%
b- 34%
c- 47.5%
d- 95%
answer:a 13.5
Answers
Using the normal distribution, it is found that the percentage of people spend between 41 and 56 minutes watching TV shows on this streaming service is:
a) 13.5%
In a normal distribution 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]
It 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, which is the percentile of X.In this problem:
The mean is of 71, hence [tex]\mu = 71[/tex]The standard deviation is of 15, hence [tex]\sigma = 15[/tex]The proportion between 41 and 56 minutes is the p-value of Z when X = 56 subtracted by the p-value of Z when X = 41, hence:
X = 56:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{56 - 71}{15}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.16
X = 41:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41 - 71}{15}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.025
0.16 - 0.025 = 0.135
0.135 x 100% = 13.5%
Hence option a is correct.
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What is one website you can visit in order to request free credit report from any of the three bureaus?
Answers
Answer: annualcreditreport.com
Step-by-step explanation: The only authorized website for free credit reports, or call 1-877-322-8228
Is 5.12 times 10n =512
Answers
Answer:
it is D
Step-by-step explanation:
I have to show you, but if I do it don't on the paper
