The triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
a) Given that, 3 in., 4 in. and 5 in.
By using Pythagoras theorem, we get
5²=3²+4²
25=9+16
25=25
So, the triangle is right triangle.
b) The given sides of triangle measures 5 in., 6 in. and 7 in.
To determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side.
7²<5²+6²
49<25+36
49<61
So, the triangle is acute angle triangle.
c) The given sides of triangle measures 8 in., 9 in. and 12 in.
12²>8²+9²
144>64+81
144>125
So, the triangle is obtuse angle triangle.
Therefore, the triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.
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A regular octagon has a radius of 6 ft and a side length of 4.6 ft. what is the approximate area of the octagon? 71 ft2 101 ft2 110 ft2 202 ft2
Answer:
Option B is correct.
The approximate area of regular octagon is, 101 square ft.
Step-by-step explanation:
Given: A regular octagon has a radius of 6 ft and a side length of 4.6 ft.
To find the area of a regular octagon(A) of side length a is given by :
[tex]A=2\cdot(1+\sqrt{2})a^2[/tex]
Given the length of side, a= 4.6 ft
Substitute the value of a=4.6 ft in the given formula of area:
[tex]A=2\cdot(1+\sqrt{2})\cdot(4.6)^2[/tex] or
[tex]A=(2+2\sqrt{2})\cdot (21.16)[/tex] or
[tex]A=(2+2.828)\cdot(21.16)[/tex]
Simplify:
[tex]A=4.828\cdot 21.16 =102.16048[/tex] square ft.
therefore, the approximate area of regular octagon is, 101 square ft
how many cups of grape punch containing 10% fruit juice and berry punch containing 20% fruit juice must be added together to create 12 cups of punch with 18% fruit juice?
A high-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.07 inches per second, and that r = 36 inches at time t = 0. Determine the equation that models the volume V of the balloon at time t, and find the volume when t = 400 seconds.
Find the sum of the first 100 terms in the series
[tex] \frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + . . . \frac{1}{n*(n+1)} [/tex]
Find the length of an arc that subtends a central angle of 135° in a circle of radius 2 mi
In the figure, if AB ≅ CD, then
A. AB ⊥ CD
B. CE ≅ BE
C. ∠CEA ≅ ∠CEB.
D. arc AB ≅ arc CD.
Answer:
D. arc AB ≅ arc CD.Step-by-step explanation:
To solve this problem, we need to use the Intersecting Chords Theorem which states "when two chords intersect each other inside a circle, the products of their segments are equal".
Applying this theorem, we have
[tex]AE \times EB = CE \times ED[/tex]
Where [tex]AB=AE+EB[/tex] and [tex]CD=CE+ED[/tex], also [tex]AB \cong CD[/tex], which means
[tex]AE+EB=CE+ED[/tex]
However, if both chords are equal, then their arcs are also equal, that's the easiest way to deduct it, that is
[tex]arc(AB) \cong arc(CD)[/tex]
Because an arc is defined by its chord basically, and in this case they are congruent.
Part A: Solve -vp + 30 < 45 for v .. show your work.
Part B: Solve 3w - 6r = 30 for r .. show your work.
determine the slope of y=3x^2-8 at (x,y)
Human iq scores are approximately normally distributed with mean 100 and standard deviation 15. determine the minimum iq scores for the top 5% of the population.
To solve this problem, we make use of the z statistic. A population of 5% means that we are looking for the population at >95%, P = 0.95. Using the standard distribution tables for z, a value of P = 0.95 indicates a value of z of z = 1.645
Now given the z and standard deviation s and the mean u, we can calculate for the value of IQ of the top 5% (x):
x = z s + u
x = 1.645 (15) + 100
x = 24.675 + 100
x = 124.675
Therefore the minimum iq score for the top 5% of the population is around 124.675
The minimum IQ score for the top 5% of the population, with a normal distribution mean of 100 and a standard deviation of 15, is approximately 124.7. This is found by using the z-score that corresponds to the 95th percentile, which is 1.645, and applying it to the formula for a score in a normal distribution.
To determine the minimum IQ score for the top 5% of the population, given that human IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution. Typically, the top 5% of values on a normal distribution lie above a certain z-score threshold. This z-score corresponds to the point on the distribution where the cumulative area to the left is 95% (100% - 5%), since we are looking for the score above which the top 5% of scores fall.
To find this z-score, we look up the value in a standard normal distribution table or use a statistical software or calculator. The z-score that corresponds to the 95th percentile is typically around 1.645. To find the actual IQ score, we can then apply the following formula:
IQ Score = Mean + (Z-score * Standard Deviation)
Plugging the values in:
IQ Score = 100 + (1.645 * 15)
IQ Score = 100 + 24.675
IQ Score = 124.675
Therefore, the minimum IQ score for the top 5% of the population is approximately 124.7 (since IQ scores are usually reported to the nearest whole number).
Write the standard form of the equation of the line passing through the point (2,5) and perpendicular to the line 4x - y = 2. The answer key says that the answer is x + 4y = 22, but I'm confused on how to get there
To find the perpendicular line's equation, first find the negative reciprocal of the original line's slope. Next, use the point-slope form with the given point. Lastly, rearrange the equation into standard form, resulting in x + 4y = 22.
To find the equation of a line that is perpendicular to another line and passes through a given point, you need to perform a series of steps. The first line's equation is given as 4x - y = 2. Firstly, solve for y to put it in slope-intercept form, y = mx + b. Here, the equation becomes y = 4x - 2, so the slope (m) is 4. The slope of the perpendicular line will be the negative reciprocal of this, which is -1/4.
The next step is to use the point-slope form of the line, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes. For the point (2,5), the equation of the line is y - 5 = -1/4(x - 2). Multiplying both sides by 4 to clear the fraction gives 4y - 20 = -x + 2.
Finally, rearrange the equation to get it into standard form, Ax + By = C, giving us x + 4y = 22. This is the standard form of the equation we were seeking.
Give the degree and classify the polynomial by the number of terms- 3
A)degree 1, monomial
B)degree 1, binomial
C)degree 0, monomial
D)degree 0, binomial
Answer:
Step-by-step explanation:
the answer is a
What is the length of the hypotenuse, x, if (12, 35, x) is a Pythagorean triple?
Answer:37
Step-by-step explanation:
12•12=144
35•35=1225
1225+144=1369
Square root 1369=37
How to find the volume of a parallelepiped with 8 vertices?
The volume of parallelepiped with 8 vertices is 75 units.
What is Volume of Parallelepiped?A parallelepiped's volume is determined by multiplying its surface area by its height.
The area of the parallelogram base is the cross product's magnitude, ∥a×b∥ , according to its geometric specification, and the vector a×b direction is perpendicular to the base.
Given:
let the 8 vertices are (0,0,0), (3,0,0), (0,5,1), (3,5,1), (2,0,5), (5,0,5), (2,5,6), and (5,5,6).
so, Volume = det [tex]|\left[\begin{array}{ccc}0&3&2\\5&0&0\\1&0&5\end{array}\right] |[/tex]
= |0( 0- 0) - 3(25- 0) + 2(0 - 0)|
= |0 - 75 + 0|
= |- 75|
= 75 units
Hence, the volume of parallelepiped with 8 vertices is 75 units.
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Simplify 6 to the fifth power over 7 cubed all raised to the second power. 6 to the seventh power over 7 to the tenth power 6 to the tenth power over 7 to the sixth power 6 cubed over 7 12 to the fifth power over 14 cubed
Answer:
6 to the tenth power over 7 to the sixth power
Step-by-step explanation:
Given phrase,
6 to the fifth power over 7 cubed all raised to the second power,
[tex]\implies (\frac{6^5}{7^3})^2[/tex]
By using [tex](a^m)^n=a^{mn}[/tex]
[tex]=\frac{6^{5\times 2}}{7^{3\times 2}}[/tex]
[tex]=\frac{6^{10}}{7^6}[/tex]
= 6 to the tenth power over 7 to the sixth power
Simplify the expressions
(6⁵/7³)² = 2143588816/117649
(6⁷/7¹⁰) = 279936/282475249
(6¹⁰/7⁶) = 60466176/117649
(6³/7) = 216/7
(12⁵/14³) = 90855/1001
To simplify the given expressions, we can calculate the numerical values and perform the necessary operations. Let's evaluate each expression:
(6⁵/7³)²:
First, calculate the numerator and denominator:
Numerator: 6⁵ = 6 × 6 × 6 × 6 × 6 = 7776
Denominator: 7³ = 7 × 7 × 7 = 343
Now, substitute the values into the expression and square the result:
(7776/343)² = (7776/343) × (7776/343) = 2143588816/117649
The simplified form is 2143588816/117649.
(6⁷/7¹⁰):
Calculate the numerator and denominator:
Numerator: 6⁷ = 6 × 6 × 6 × 6 × 6 × 6 × 6 = 279936
Denominator: 7¹⁰ = 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 = 282475249
Substitute the values into the expression:
279936/282475249
This expression cannot be simplified further.
(6¹⁰/7⁶):
Calculate the numerator and denominator:
Numerator: 6¹⁰ = 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 60466176
Denominator: 7⁶ = 7 × 7 × 7 × 7 × 7 × 7 = 117649
Substitute the values into the expression:
60466176/117649
This expression cannot be simplified further.
(6³/7):
Calculate the numerator and denominator:
Numerator: 6³ = 6 × 6 × 6 = 216
Denominator: 7
Substitute the values into the expression:
216/7
This expression cannot be simplified further.
(12⁵/14³):
Calculate the numerator and denominator:
Numerator: 12⁵ = 12 × 12 × 12 × 12 × 12 = 248832
Denominator: 14³ = 14 × 14 × 14 = 2744
Substitute the values into the expression:
248832/2744 = 90855/1001
The simplified form is 90855/1001.
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Simplify 6 to the fifth power over 7 cubed all raised to the second power. 6 to the seventh power over 7 to the tenth power 6 to the tenth power over 7 to the sixth power 6 cubed over 7 12 to the fifth power over 14 cubed
(6⁵/7³)²
(6⁷/7¹⁰)
(6¹⁰/7⁶)
(6³/7)
(12⁵/14³)
HELP! Will give Brainliest! Using dimensional analysis, convert 293 cm into m. (1 m= 100 cm)
(and this is also a Chemistry Question)
I get how to work out the other question, but I'm confused on this one
Do not use spaces in your answer. If f(x) = (-x)3, then f(-3) =
When constructing a circle circumscribed about a triangle, what is the purpose of constructing perpendicular bisectors?
A security fence encloses a rectangular area on one side of a park in a city. three sides of fencing are? used, since the fourth side of the area is formed by a building. the enclosed area measures 392392 square feet. exactly 5656 feet of fencing is used to fence in three sides of this rectangle. what are the possible dimensions that could have been used to construct this? area?
(02.03 LC)
Read the following statement:
Line segment AB is congruent to line segment CD.
Which of the following is an equivalent statement?
AB overbar similar to CD overbar
AB overbar congruent to CD overbar
AB overbar equal to CD overbar
AB overbar element to CD overbar
Answer:
AB overbar congruent to CD overbar
Explanation:
The question is asking whether Line segment AB is CONGRUENT to line segment CD.
The meaning of congruent is having the same shape and size.
Congruent ≅
Element ∈
Equal =
Similar ~
In conclusion, you could say:
AB ≅ CD
I cannot type the lines over the top AB and CD but they are there.
(I know this question is probably old, and i am also tying this so I remember as well, but the other answer didn't have a bit bigger explanation so if anyone comes across this i hope this helped. :)
If two or more objects are the same copy in length and shape then that will be said to be congruent thus AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent thus options (B) and (C) is correct.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
In other meaning, if you can copy a figure then that copy and the original figure will be congruent.
All line segments are in the same shape and have degrees as one in the equation therefore only one criterion which is length is needed to prove congruency.
So, congruent lines are lines whose lengths are the same.
The sign of congruency is ≅ so AB ≅ CD.
Hence " AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent to AB ≅ CD".
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The first term of a geometric sequence is –2 and the common -1/4. What are the next three terms of the sequence?
Please help me,I need help understand so I can do my own! Worth 20 points!!
Candis took out a payday loan with an effective interest rate of 15,400%. if she had 220 to invest for a year at this interest rate, how much would make in interest?
A. 3,388,000
B 338,800
C.. 3388
D 33,880
To find the interest Candis would make from a 15,400% interest rate on a $220 investment for one year, we calculate using the simple interest formula, resulting in $33,880.
Explanation:The question asks us to determine how much interest Candis would make from a payday loan with an effective interest rate of 15,400% if she invested $220 for a year. To calculate the interest earned, we can use the formula for simple interest which is I = Prt, where I is interest, P is principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.
Converting 15,400% to a decimal, we get 154. Then, apply the formula:
I = $220 × 154 × 1
This gives us:
I = $33,880
Therefore, Candis would make $33,880 in interest after one year, which corresponds to option D.
A rectangle is placed around a semicircle as shown below. the width of the rectangle is 6ft . find the area of the shaded region. use the value 3.14 for π , and do not round your answer. be sure to include the correct unit in your answer.
The shaded region is by assumption the region which is not covered by the semicircle in in given rectangles.
The area of the shaded region is given by 15.48 sq. ft.
What is a semicircle?
A semicircle is a circle cut in half. Thus, one circle produces two semicircle.
Firstly we will find the area of the rectangle and then subtract the area of the semicircle to find the are of the shaded region.
Since the radius of the semicircle is equal to width of the rectangle(6 ft), thus the length of the diameter of the circle( twice the radius which is 12 ft) serves as length of the considered rectangle.
Thus, we have:
[tex]\text{Area of the given rectangle\:} = 6 \times 12 = 72 \: \rm ft^2[/tex]
Since the semicircle is having radius of 6 ft, thus:
[tex]\text{Area of semicircle} = \dfrac{\pi r^2}{2} = \dfrac{3.14 \times 6^2}{2} = 56.52 \: \rm ft^2[/tex]
Thus, area of the shaded region will be equal to area of rectangle - area of semicircle = 72 - 56.52 = 15.48 sq. ft.
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If Matrix A has dimensions 1x4 and Matrix B has dimensions 3x4, can these be multiplied?
the old price for school lunches is $5. The new price is $5.25. What is the percent increase in the cost if school lunches? Write answer as percent. The formula is p=b-a/a. b =new price for lunch. a=old price for lunch. P=percent increase
p=(5.25-5.00)/5.00
p=0.25/5.00
p=0.05
p = 5% increase
please i need help....the question is.........
area = H/2*(b1+b2)
8.1 = 1.5/2*(6.7 +b2)
8.1=0.75*(6.7+b2)
10.8=6.7+b2
b2=10.8-6.7
b2=4.1m
Adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall. Approximately what percent of the adult male population is taller than the average basketball player? 0.135% 0.875% 49.875% 99.875%
Answer:
A. 0.135%
Step-by-step explanation:
We have been given that adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall.
We need to find the area of normal curve above the raw score 79.
First of all let us find the z-score corresponding to our given raw score.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{z-score}[/tex],
[tex]x=\text{Raw-score}[/tex],
[tex]\mu=\text{Mean}[/tex],
[tex]\sigma=\text{Standard deviation}[/tex].
Upon substituting our given values in z-score formula we will get,
[tex]z=\frac{79-70}{3}[/tex]
[tex]z=\frac{9}{3}[/tex]
[tex]z=3[/tex]
Now we will find the P(z>3) using formula:
[tex]P(z>a)=1-P(z<a)[/tex]
[tex]P(z>3)=1-P(z<3)[/tex]
Using normal distribution table we will get,
[tex]P(z>3)=1-0.99865 [/tex]
[tex]P(z>3)=0.00135[/tex]
Let us convert our answer into percentage by multiplying 0.00135 by 100.
[tex]0.00135\times 100=0.135%[/tex]
Therefore, approximately 0.135% of the adult male population is taller than the average basketball player and option A is the correct choice.
What is the probability of getting exactly 2 heads, given that the first toss is a head?
there is a 1/2 probability of getting heads on any one flip
since the first one landed on heads you have a 1/2 probability f getting a 2nd one
Probability = 1/2
Graph y < 1/3x + 1/2
What is the solution to the system of linear equations graphed below?
A. (3.5, -4)
B. (-4, 3.5)
C. (0,3)
D. (0,-4)
Look at the picture.
Answer: A. (3.5, -4)