The hypotenuse of a right triangle is 5inches long. The shorter leg is 1 inch shorter than the longer leg. Find the side lengths of the triangle.
Length of the shorter leg:
Length of the longer leg:
Length of the hypotenuse:
Answers
Answer:
Hypotenuse = 5 in
Longer leg = 4 in
Shorter leg = 3 in
Step-by-step explanation
The longer leg = x
The shorter leg = x - 1
Now through Pythagoras theorem:
hyp^2 = leg1^2 + leg2^2
5^2 = x^2 + (x - 1)^2
25 = x^2 + x^2 - 2 x + 1^2
25 = 2 x^2 - 2 x + 1
2 x^2 - 2 x - 24 = 0
2 ( x^2 - x - 12) = 0
2 (x - 4) (x + 3) =0
then x = 4 or x = - 3
We use the positive answer since we are looking for a length
then longer leg is 4 inches long,
and therefore the shorter one is one inch shorter than 4 in . That is:
shorter leg = 3 inches
Related Questions
234 + 300 and scram. ok bio now go do homework no ples
Answers
Answer:
534
Step-by-step explanation:
Tickets to a concert a Lake Sumter Community College cost $5 for general admission or $4
with a student ID. If 184 people paid to see the concert and $812 was collected, how many
of each type of ticket were sold?
On the basis of total cost per day for business travel to New York City and Washington DC
Answers
The required number of general admissions is 76 and the number of admission with student id is 108.
Here,
let the number of general admissions be x and the number of the admission with student id be y
Using arithmetic operations
According to the question,
x + y = 184
x = 184 - y - - - -(1)
5x + 4y = 812 - - - - (2)
From equation (1)
5 (184 - y) + 4y = 812
920 - 5y + 4y = 812
-y = 812 - 920
-y = 108
y = 108
Put y in equation 1
x = 184 - 108
x = 76
Thus, the required number of general admission is 76, and the number of admission with student id is 108.
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The half-life of radon is 385 days. What fraction of a sample with no atoms remains at the end of 77 days?
Answers
Step-by-step explanation:
calculate the missing angle 'a'
9:57
Answer
Hence in 77 days 107. will decay Remain = 90%
Explanation
Given: half life = 385 half-life
To find: what fraction remains after 22 days
Solution.
Let total amount = 100%.
time taken for decaying Si%. = 385
In time of 72 days = 305 77
= 5
→ Remarwiny = 50 = 10%.
Hence in 72 days 1-7. will decay Remain = 90%.
In which of the following numbers does the value of the digit 5 have one tenth the value as it does in the number 45.82?
Answers
Answer:
The value of 5 digit is the ones place in 45.82 because point infront of it
Answer: The value of 5 digit is the ones place in 45.82 because point infront of it
Step-by-step explanation:
A particular fruit's weights are normally distributed, with a mean of 212 grams and a standard deviation of 20 grams.
If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?
Answers
Answer:
220 grams.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
\(\mu = 212, \sigma = 20, n = 22, s = \frac{20}{\sqrt{22}} = 4.264\)
If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?
We have to find the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(1.88 = \frac{X - 212}{4.264}\)
\(X - 212 = 1.88*4.264\)
\(X = 220\)
The answer is 220 grams.
look at pic 10 pts will mark brainilest
Answers
Answer:
A
Step-by-step explanation:
It’s a
Answer:
A
Step-by-step explanation:
this isa because the 2 rectangles on the net will make the sides and the triangles will finish the prism when u fold it it will be a rectangular prism plz mark me brnliest ill send u friend request
There are 80 people in a choir.
Half the people in the choir are women.
The number of men in the choir is one quarter of the number of women.
The rest of the people in the choir are children.
the number of children in the choir : the number of men in the choir = n : 1
Work out the value of n.
You must show how you get your answer.
n =
Answers
There are 30 children in the choir
Number of people in the choir = 80
Number of women = 1/2 × 80 = 40.
Number of men = 1/4 × 40 = 10
Therefore, the number if children will be:
Men + Women + Children = 80
10 + 40 + n = 80
n = 80 - 40 - 10
n = 50
There are 30 children in the choir.
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Answer:
N=3
Step-by-step explanation:
Number of people in the choir = 80
Number of women = 1/2 × 80 = 40.
Number of men = 1/4 × 40 = 10
Therefore, the number if children will be:
Men + Women + Children = 80
10 + 40 + n = 80
n = 80 - 40 - 10
n = 50
There are 30 children in the choir.
The average temperature at Paul's
school last week was 1°F. The actual
temperature varied by less than 2°.
Solve and graph the absolute value
inequality to represent the range
of possible temperatures.
Answers
Answer: 3>x
Step-by-step explanation:
2 > x - 1
+1 +1
3 > x
A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 10% of scores B: Scores below the top 10% and above the bottom 58% C: Scores below the top 42% and above the bottom 20% D: Scores below the top 80% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 67.3 and a standard deviation of 7.3. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
Answers
Answer:
The numerical limits for a D grade are 58(lower limit) and 61(upper limit).
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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.
Scores on the test are normally distributed with a mean of 67.3 and a standard deviation of 7.3.
This means that \(\mu = 67.3, \sigma = 7.3\)
D: Scores below the top 80% and above the bottom 9%
This means that lower bound is the 9th percentile and the upper bound is the 100 - 80 = 20th percentile.
9th percentile:
This is X when Z has a pvalue of 0.09. So X when Z = -1.34.
\(Z = \frac{X - \mu}{\sigma}\)
\(-1.34 = \frac{X - 67.3}{7.3}\)
\(X - 67.3 = -1.34*7.3\)
\(X = 57.52\)
Rounding to the nearest whole number, 58.
20th percentile:
This is X when Z has a pvalue of 0.2. So X when Z = -0.84
\(Z = \frac{X - \mu}{\sigma}\)
\(-0.84 = \frac{X - 67.3}{7.3}\)
\(X - 67.3 = -0.84*7.3\)
\(X = 61.17\)
Rounding to the nearest whole number, 61.
The numerical limits for a D grade are 58(lower limit) and 61(upper limit).
A solid figure is separated into 2 rectangular prisms. The volume of rectangular prism A is 75 cubic yards. Rectangular prism
B has a length of 7 yards and a width of 3 yards. The total volume of the solid figure is 180 cubic yards. What is the height of
rectangular prism B?
Answers
The height of rectangular prism B is 5 yards.
Let's first find the volume of rectangular prism B:
The volume of the solid figure = Volume of prism A + Volume of prism B
180 = 75 + length × width × height of prism B
105 = length × width × height of prism B
We know that the length of prism B is 7 yards and the width is 3 yards,
Substitute those values:
105 = 7 × 3 × height of prism B
105 = 21 × height of prism B
height of prism B = 105/21
height of prism B = 5
Therefore, the height of rectangular prism B is 5 yards.
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)) How many solutions does this equation have?
12 + 4t - 14t = -13t - 18
Answers
Answer:
t = -10
Step-by-step explanation:
Ok so,
12 - 10t = -13t -18
12 - 10t + 13t = -13t + 13t - 18
12 + 3t = -18
12 - 12 + 3t = -18 - 12
3t = -30
t = -10
hope this helps! have a good day!
Write an addition equation or a subtraction equation (your choice!) to describe the diagram.
Answers
The addition equation or a subtraction equation to describe the diagram is (-9)—(-4) = -13
We know that,
In a mathematical operation we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have a line graph shown in the picture.
The small arrow represents the length of 4 but as it is indicating negative direction, so we take -4
Similarly, the big arrow represents the length of 9 as it is indicating negative direction, so we take -9
The sum of the lengths:
(-9)—(-4) = -13
Thus, the addition equation or a subtraction equation to describe the diagram is (-9)—(-4) = -13
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a) angle of line of From a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three figure bearings? A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point. (b) How far is the boy now from the start- ing point? A boy runs 200 m on a bearing of 230°.
Answers
a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$
\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}
100 sin 35° = 80 sin 55°=57.73 mT
herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.
Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.
To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.
Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.
Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.
To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.
(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus
:$$c^2 = a^2 + b^2$$
where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$
c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$
Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.
Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$
Therefore, the bearing of the boy's current position from the starting point is N51°E.
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Craig is considering four loans. Loan L has a nominal rate of 8.254%, compounded daily. Loan M has a nominal rate
of 8.474%, compounded weekly. Loan N has a nominal rate of 8.533%, compounded monthly. Loan O has a nominal
rate of 8.604%, compounded yearly. Which of these loans will offer Craig the best effective interest rate?
a. loan L
b. loan M
c. loan N
d. loan O
Answers
The loan that will offer Craig the best effective interest rate is a) Loan L with a real percentage rate of 8.6%.
What is an effective interest rate?An effective interest rate is the real percentage rate on an interest-paying investment which removes the effects of compounding over time.
The formula for computing the effective interest rate is as follows:
Effective Interest Rate, r = (1 + i/n)^n - 1.
Nominal Interest Rates Compounding Periods
Loan L 8.25% 365 days
Loan M 8.47% 52 weeks
Loan N 8.533% 12 months
Loan O 8.604% Yearly
Effective Interest Rates:Loan L = (1 + 0.0825/365)^365 - 1
= 1.08598 - 1
= 0.086
= 8.6%
Loan M = (1 + 0.0847/52)^52 - 1
= 1.0883 - 1
= 0.0883
= 8.83%
Loan N = (1 + 0.08533/12)^12 - 1
= 1.0887 - 1
= 0.0887
= 8.87%
Loan O = (1 + 0.08604/1)^1 - 1
= 1.08604 - 1
= 0.08604
= 8.604%
Thus, we advise Craig to take Loan L because it offers the least-costly effective interest rate.
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What is the length of EF in the right triangle below?
D
26
10
E
F
Answers
The measure of side length EF in the right triangle is 24.
What is the measure of side length EF?The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c² = a² + b²
From the diagram:
Hypotenuse DE = c = 26
Leg DF = a = 10
Leg EF = b = ?
Plug in the values and solve for b:
c² = a² + b²
26² = 10² + b²
676 = 100 + b²
b² = 676 - 100
b² = 576
b = +√576 ( we take the positive value since we are dealing with dimensions)
b = 24
Therefore, the length EF is 24.
Option C)24 is the correct answer.
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I need help asap thank you..
Answers
Step-by-step explanation:
the angle TSW is the total angle and is 73°.
from that total angle, we have one part : angle 1 = 36°.
as angle TSW = angle 1 + angle 2
we have
73 = 36 + angle 2
angle 2 = 73 - 36 = 37°
Cho has 1/5 liter of water. he pours equal amounts of water intyo 3 cups. write an expression for the number of liters of water in each cup.
Answers
Answer:
\(\frac{1}{15}\) liters
Step-by-step explanation:
\(\frac{1}{5}\) ÷ 3=
\(\frac{1}{5} *\frac{1}{3} =\\\\\frac{1}{15}\)
There is 1/15 liters of water in each cup.
Answer:
1/15 liters
Step-by-step explanation:
1/5 ÷ 3= 1/15
RULES of Dividing fractions
Keep switch flip
keep 1/5 the same. Flip the division sign to multiplication.
Flip 3/1 into 1/3.
Which solid has a greater volume?
Answers
Answer: B
Step-by-step explanation:
Step-by-step explanation:
C - equation for a cylinder is as follows V=πr2h Wich equals the same as the equation for a cone which is V=πr2h/3 and totals 235.62
Solve for x in this equation
Answers
find the value of x. if necessary, round to the nearest tenth
a. 13.7 in
b. 11.7 in
c. 6.9 in
d. 9.7 in
Answers
Two men shared the cost of
business in the ratio 3 : 5. If the
smaller share is N450.00, find the
total cost of the business.
Answers
Answer:
if 3 is smallest and it ratio is 450 that means 450/3=150
5*50=750
3:5
450+750=1200
-5 1/4 -(-7 1/2) simplify
really fast pleas
Answers
Heyy I just need some help with question 13,17,19 if anyone could help me and show the work that would be amazing thank you!!
Answers
Answer:
13. Answer: 0
17. Answer: 3
19. Answer: 2
Step-by-step explanation:
13. f(g(3))
First find g(3) on the right graph.
We see that at x = 3, g(x) = 4
So g(3) = 4
Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer
17.f(f(5))
f(5) = 1
f(f(5)) = f(1) = 3 answer
19. g(g(2))
g(2) = 0
g(g(2)) = g(0) = 2 answer
The table represents a linear relationship
X—2 0 4
Y-4 3 1
Which equation represents the table
Y=1/2x+5
y=-1/2x+3
Y=2x-3
Y=-4x+2
Answers
The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.
To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.
Given the table:
X: 2 0 4
Y: -4 3 1
We can plot these points on a graph and see that they form a straight line.
Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.
Based on the given options, we can now evaluate each equation to see which one represents the line:
Y = 1/2x + 5
When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.
Y = -1/2x + 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.
Y = 2x - 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.
Y = -4x + 2
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.
In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.
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Which sequence of transformations produces an image that is not congruent to the original figure?
A. A reflection across the x axis followed by a rotation of 180 counterclockwise
B. A translation of 6 units to the left followed by a reflection across the x-axis
C. A rotation of 90° clockwise followed by a translation of 4 units to the left
D. A translation of 4 units to the left followed by a dilation of a factor of 3
Answers
Answer:
D. A translation of 4 units to the left followed by a dilation of a factor of 3
Step-by-step explanation:
Of the transformations, rotation, reflection, translation, dilation, the first three (rotation, reflection, translation) are known as "rigid" transformations. They do not change the shape or size of the object. Any result of a rigid transformation is congruent to the original.
Dilation, by its nature, changes the size of the object, so the result is NOT congruent to the original.
Choice D includes dilation, so the image is not congruent to the original.
Which polynomials are prime? Check all that apply.
2x²+ 7x + 1
0 5x²-10x + 5
O 3x² + 8
04x²-25
Ox²+36
Answers
The requried only prime polynomial among the given options are 2x²+ 7x + 1, 3x² + 8, and x²+36.
What is a polynomial function?A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.
Here,
The first polynomial 2x²+ 7x + 1 cannot be factored therefore it is a prime polynomial.
The second polynomial 5x²-10x + 5 can be factored as 5(x-1)² and is therefore not a prime polynomial.
The third polynomial 3x² + 8 cannot be factored over the integers and is therefore a prime polynomial.
The fourth polynomial 4x²-25 can be factored as (2x-5)(2x+5) and is therefore not a prime polynomial.
The fifth polynomial x²+36 cannot be factored therefore it is a prime polynomial.
Therefore, the only prime polynomial among the given options is 3x² + 8.
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There are three one day cricket matches between India and Australia in a week 6359 people watch with the first match 8531 people watch the second match and 10027 watch the 3rd match how many people in all watch the three matches
Answers
Match 2=8531
Match 3=10027
Add all of them together and u get 24,917 which is your answer
It rains a lot in Longview. On three days it rained 0.4 inches, 0.68 inches, and 1.6 inches. What was the total rainfall for those three days? Explain your answer.
Answers
Answer: 2.68
Step-by-step explanation: 0.4 + 0.68 + 1.6
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answers
The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.
Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.
To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.
Let's start with the first equation:
2 + x = 5
Subtract 2 from both sides:
x = 3
Now let's move on to the second equation:
x + 1 = 4
Subtract 1 from both sides:
x = 3
Notice that we got the same value of x for both equations, so they are equivalent.
Next, let's look at the third equation:
9 + x = 6
Subtract 9 from both sides:
x = -3
Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.
Now, let's move on to the fourth equation:
x + (-4) = 7
Add 4 to both sides:
x = 11
This value of x is also different from the first two equations, so it is not equivalent to them.
Finally, let's look at the fifth equation:
-5 + x = -2
Add 5 to both sides:
x = 3
Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.
So, correct options are A, B and E.
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Complete question is:
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
In a race, a bicyclist travels 2/3 of a mile in 1/3 hour. Determine the unit rate for the speed in miles per hour.
Question 10 options:
1/2 mile per hour
1 mile per hour
4/3 miles per hour
2 miles per hour
Answers
The unit rate for the speed in miles per hour will be 2 miles per hour.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
In a race, a bicyclist travels 2/3 of a mile in 1/3 hour.
Now,
Since, Distance cover by bicyclist = 2/3 miles
Time = 1/3 hour
We know that;
⇒ Speed = Distance / Time
Substitute all the values, we get;
⇒ Speed = 2/3 ÷ 1/3
= 2/3 × 3/1
= 2 miles per hour
Thus, The unit rate for the speed in miles per hour = 2
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