Answer:
It is a right triangle.
Step-by-step explanation:
By the Inverse Pythagoras Theorem if 39^2 = 36^2 + 15^2 then it is a right triangle.
39^2 = 1521
36^2 + 15^2 = 1296 + 225 = 1521.
So it is a right triangle.
Based on the converse of the Pythagorean Theorem, the triangle with the following side lengths is a right triangle.
What is the Converse of the Pythagorean Theorem?
The converse of the Pythagorean Theorem states that a triangle is a right triangle if the sum of the squares of two of its legs are equal to the square of the length of the longest side (hypotenuse).
The longest side in the triangle is 39 in. Therefore:
39² = 36² + 15²
1,521 = 1,521
Based on this, we can conclude that the triangle given is a right triangle.
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(10Q) Determine the graph of the cosine curve with an amplitude of 2 and a period of 2.
ANSWER
See attachment.
EXPLANATION
The cosine function is symmetric with respect to the y-axis.
If the cosine function has an amplitude of 2 then, its range is
-2≤y≤2
If the period is 2 , then its must complete a full cycle on the interval, [-2,0],[0,2], [2,4], etc.
The graph that has all these features is shown in the attachment.
Identify the volume of the composite figure. HELP PLEASE!!
Answer:
Vol. of the composite figure is 189 m³
Step-by-step explanation:
Find the volume of the larger figure by mult. together its 3 dimensions:
V = (9 m)(8 m)(3 m) = 216 m³.
Next, find the volume of the "notch," which is (3 m)³, or 27 m³.
Finally, subtract the "notch" volume from the 216 m³ volume found earlier:
216 m³ - 27 m³ = 189 m³
Find the real number root
Answer:
There is no real number root
Step-by-step explanation:
There is no real number root because there is a negative number inside the root.
No real number root
MethodThere is no real number root because it is a negative numberWhat is the volume of the cylinder below?
The answer is D. 36pi units^3
Hope this helps!
The formula for cylinder volume is: pi*r^2*h
For this case we have that the volume of the cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
h: It is the height of the cylinder
A: It is the radius of the cylinder
We have to, according to the given data:[tex]h = 4\\r = 3[/tex]
Substituting:
[tex]V = \pi * (3) ^ 2 * 4\\V = \pi * 9 * 4\\V = 36 \ pi[/tex]
[tex]36 \pi \ units ^ 3[/tex]
ANswer:
Option D
[tex]36 \pi \ units ^ 3[/tex]
a private plane is traveling due east at a rate of 155 mph. a south wind is blowing 35 mph. what is the actual velocity of the plane?
Answer:
158.9 mph E 12.7° S
Step-by-step explanation:
Since the components of the motion are perpendicular to each other then magnitude of the resultant can be found using the Pythagorean theorem:
|v| = √(155^2 +35^2) ≈ 158.9 . . . . mph
The angle can be found using the tangent relationship:
tan = opposite/adjacent
The angle south of east will be
angle = arctan(35/155) ≈ 12.7°
The velocity vector can be described by ...
158.9 mph E 12.7° S
_____
As a bearing, the vector might be described as either of ...
• 158.9 mph at 102.7°
• 158.9 mph S 77.3° E
Solve for Y (please help me solve!)
Answer:
b = 10
Step-by-step explanation:
a) Solve by inspection. b=10 makes both fractions equal to 1.
Both the numerator and denominator of the fraction on the right are 2 greater than those of the fraction on the left. The fractions will be equal when numerator and denominator are equal.
__
b) Multiply by 60 and solve in the usual way.
6b = 5(b+2)
b = 10 . . . . . . . . . . subtract 5b
__
c) Expand the fraction on the right, subtract the variable term.
b/10 = b/12 + 2/12
b(1/10 - 1/12) = 1/6
b/60 = 1/6 . . . . simplify
b = 60/6 = 10 . . . . multiply by 60
_____
Comment on the question
There is no "y", so you cannot solve for y. This is another example of poor quality control (editing) of math curriculum materials. It is my sincere wish that you not have to put up with that. Math is tough enough without this added confusion.
Answer:
b=10
Step-by-step explanation:
Find the dimensions of a rectangle whose width is 6 miles less than its length and whose area is 112 square miles.
Answer:
Step-by-step explanation:
Be the sides x[tex]x, x+6[/tex] you know [tex]x(x+6) = 112[/tex] or [tex]x^2 +6x -112 = 0[/tex][tex]x= -3 \pm \sqrt{9+112} = -3\pm 11[/tex] the solution is [tex]x=8, x=-14[/tex] The negative answer is to be discarded, your rectangle has sides 8 and [tex]8+6=14[/tex] miles
The length of the rectangle is 14 miles and the width of the rectangle is 8 miles.
How to find the area and the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Area of the rectangle = (L × W) unit^2
Perimeter of the rectangle = 2(L + W) units
Let the width of the rectangle be represented by W, while the length is represented by L.
Given the width is 6 miles less than its length, therefore, the width can be written as,
W = (L - 6) miles
Now given the area of the rectangle is 112 sq. miles, therefore, the area of the rectangle can be written as,
Area of the rectangle = Length × Width
112 = L × W
112 = L × (L-6)
112 = L²-6L
L = 14, -8
Since the length, L can not be negative, the value of L is 14 miles, therefore, the width will be 8 miles.
Hence, the length of the rectangle is 14 miles and the width of the rectangle is 8 miles.
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EASY Brainliest. What is the parent graph?
Answer:
D
Step-by-step explanation:
The given function builds on the parent graphy = x^2.
The answer is D. y=x^2
Identify the sine function with the given attributes.
amplitude: 1; period: 2; phase shift: 3; vertical shift: 4
Answer:
Last option
[tex]f(t)=sin(\pi(t -3)) + 4[/tex]
Step-by-step explanation:
The general sine function has the following form
[tex]y = Asin(bt-\phi) + k[/tex]
Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.
[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.
k is the vertical displacement.
[tex]\phi[/tex] phase shift
We know that:
amplitude: 1; period: 2; phase shift: 3; vertical shift: 4
Thus:
[tex]A =1[/tex]
[tex]\frac{2\pi}{b}=2[/tex]
[tex]b=\pi[/tex]
[tex]\phi=3[/tex]
[tex]k=4[/tex]
Then the function is:
[tex]f(t)=sin(\pi(t -3)) + 4[/tex]
The answer is last option
What is m∠B?
Round the value to the nearest degree.
Answer:
46°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Cos = Adjacent/Hypotenuse
You are given the lengths of the hypotenuse of the triangle and the side adjacent to the angle you want to find. So, the cosine function describes the relationship:
cos(B) = AB/CB = (20 cm)/(29 cm)
B = arccos(20/29) ≈ 46.397°
B ≈ 46°
The student is looking for the value of an angle, m∠B, which requires solving an equation and rounding to the nearest integer. The provided information does not give a direct method or equation for calculating m∠B, thus an answer cannot be given confidently.
Explanation:The student is asking to calculate the value of an angle, denoted as m∠B, to the nearest degree. This is a mathematics problem likely involving geometry or trigonometry.
In the information provided, different equations and scenarios for calculating angles and magnitudes are given, but they seem to be disconnected, and the specific question regarding m∠B isn't directly addressed by the provided equations and examples.
Without a direct relationship or equation including m∠B, or a diagram to reference, it is not possible to confidently provide the value of m∠B. However, the excerpts suggest that if we had an equation and needed to find an angle such as m∠B, we would solve the equation and then round the result to the nearest integer, as angles are typically given in integers when degrees of freedom are considered.
The first row of a section in a stadium has 10 seats. The second row has 11 seats. The third row has 12 seats. This pattern continues and the section has 24 rows.
How many seats are in this section?
answers ?
is it 516?
Answer: I believe it is 33 seats
Step-by-step explanation:
Answer:
516
Step-by-step explanation:
is what is the first month of an year an example of a statistical question
No there is no variability cause the answers will always be the same
this would be a non-stat question
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
What is the best way to gather information for each of the scenarios?
Select Survey, Experiment, or Observational study for each scenario.
1.Observation study
2.Survey
3.Experiment
4.Survey
Hope thiz help:)
In choosing between a survey, experiment, or observational study, consider the requirements of your study and the nature of the data you hope to collect. Surveys are good for widespread data, experiments allow control of variables, and observational studies are good for observing natural behavior.
Explanation:The best way to gather information in research scenarios depends on the nature of the scenarios in question. However, here are brief descriptions for each method:
Survey: This involves collecting information by asking a series of questions. It is good for collecting a large amount of data or when the target population is widespread.Experiment: This involves manipulating one or more variables to determine the effect on another variable. It is generally used when the researcher has control over the variables.Observational Study: This involves observing subjects in their natural environment without interference. It is useful when ethical or practical considerations mean an experiment is not possible.Depending on the scenario, choose the method that fits best with the data needed and the practical considerations of conducting the study.
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Price of automobile= $3,000
Number of payments made in a year=12
Number of payments made = 36
Monthly payment amount = $93.33
True annual interest rate?
The true annual interest rate for this loan is approximately 1.44 or 144%.
The Breakdown
To calculate the true annual interest rate, we can use the formula for calculating the interest rate on a loan:
True Annual Interest Rate = [(Monthly Payment Amount × Number of Payments) / Loan Amount - 1] × 12
Given the information provided:
Loan Amount = $3,000
Number of Payments = 36
Monthly Payment Amount = $93.33
Substituting these values into the formula:
True Annual Interest Rate = [(93.33 × 36) / 3000 - 1] × 12
Calculating this expression:
True Annual Interest Rate = [(3360 / 3000) - 1] × 12
True Annual Interest Rate = (1.12 - 1) × 12
True Annual Interest Rate = 0.12 × 12
True Annual Interest Rate = 1.44
Therefore, the true annual interest rate for this loan is 1.44 or 144%.
Identify the volume of a cone with radius 6 m and height 11 m. HELP PLEASE!!
Answer: 414.48
Step-by-step explanation:
r: the radius of the base
h: height
The volume of a cone is given by:
V = π ∙ r2 ∙ h / 3,
where π ∙ r2 is the base area of the cone.
π defines the ratio of any circle's circumference to its diameter and is approximately equal to 3.141593, however the value 3.14 is often used.
Answer:
V = 414.7 m3
Step-by-step explanation:
Thats your answer :))
Write an equation in standard form for the circle shown.
Answer:
B
Step-by-step explanation:
The intercepted angle is given as "34x+4"
The arc is 196.
Any intercepted angle of an arc that falls in the opposite circumference, it will have a measure half that of the arc intercepted.
Hence,
34x+4 = (0.5)(196)
34x + 4 = 98
34x = 98 - 4
34x = 94
x = 94/34 = 2.76
Answer choice B is right.
What is the point of intersection when the system of equations below is graphed on the coordinate plane?
A) (0, 4)
B) (4, 0)
C) no intersection point
D) infinite intersection points
D. Infinite intersection points
Divide both sides of the second equation by 2 to find that it is equal to y = 4 - x, which is the same as the first equation.
Since they are the same equation, they are always touching each other since they are the exact same line, which means they are always intersecting, and there are infinite intersection points.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Cynthia decides she is going to purchase a used passenger car. Her grandparents agree to pay for 50% of the passenger car. To get an idea of prices Cynthia looks at listings in a local used automobile publication and on a local internet site.
Which answer best describes the sample and population?
Answer:
its going to have to be option c
Step-by-step explanation:
because it shows all the listings of cars next to her
Answer: D) sample: local listings and internet sites
population: all used passenger cars
Step-by-step explanation:
A sample is a subset of items from a larger population.
A population includes all of the elements from a set of data.
Cynthia wants to buy a used passenger car.
All available used cars is the POPULATION
Cynthia looks at local listings and on internet sites.
This is a subset of all available used cars so this is the SAMPLE
Furthermore, she may not find what she is looking for and may expand her subset to include used car lots, etc.
help help help someone
Answer:
B
Step-by-step explanation:
This is easier to follow if you write it out the long way.
g(x) = (x + 3)/x
g(f(x)) = (f(x) + 3)/f(x)
g(x^2 - 7) = (x^2 + 7 + 3)/(x^2 + 7)
g(x^2 - 7) = (x^2 +10 ) / (x^2 + 7)
g(-5) = ( (-5)^2 + 10) / ( (-5)^2 + 7)
g(-5) = ( 25 + 10) / (25 + 7)
g(-5) = 35/32
Find the distance..
Please help!!!
Answer:
d = 7.071068
Step-by-step explanation:
Evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y, z) = (x + y2) i + xz j + (y + z) k, r(t) = t2 i + t3 j − 2t k, 0 ≤ t ≤ 2 $$ correct: your answer is correct.
[tex]\vec r(t)=t^2\,\vec\imath+t^3\,\vec\jmath-2t\,\vec k[/tex]
[tex]\mathrm d\vec r=(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt[/tex]
[tex]\vec f(x,y,z)=(x+y^2)\,\vec\imath+xz\,\vec\jmath+(y+z)\,\vec k[/tex]
[tex]\vec f(x(t),y(t),z(t))=(t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k[/tex]
The line integral is
[tex]\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^2\bigg((t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k\bigg)\cdot(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2(2t^7-6t^5+4t)\,\mathrm dt=\boxed{8}[/tex]
Given:
[tex]\to \bold{\int_{c} \ F \cdot dx}[/tex]
Where
[tex]\to \bold{F(x,y,z)=(x+y^2)i+xzj+(y+z)K}[/tex] and C is given by the vector function [tex]\bold{r(t)}[/tex].
[tex]\to \bold{r(t)=t^2i+t^3j-2tk,\ \ 0\leq t\leq 2}\\\\\to \bold{dx=(2ti+3t^2j-2k)dt}\\\\[/tex]
therefore
[tex]\to \bold{x=t^2}\\\\ \to \bold{y=t^3}\\\\ \to \bold{z=2t}\\\\\to \bold{F(r)=(t^2+(t^3)^2)i+t^2(-2t)j+(t^3-2t)k}\\\\[/tex]
[tex]\bold{=(t^2+t^6)i-2t^3j+(t^3-2t)k}\\\\[/tex]
[tex]\bold{\therefore}\\\\\bold{F(r).dx=((t^2+t^6)i-2t^3j+(t^3-2t)k).(2ti+3t^2j-2k)}\\\\[/tex]
[tex]=\bold{((t^2+t^6)2t-2t^3(3t^2)+(t^3-2t)(-2)]dt}\\\\=\bold{(2t^3+2t^7-6t^5-2t^3+4t)dt}\\\\=\bold{(2t^7-6t^5+4t)dt}\\\\[/tex]
Calculating the line integral:
[tex]\bold{\int_{c}\ F .dx=\int^{2}_{t=0} (2t^7-6t^5+4t)dt}\\\\[/tex]
[tex]=\bold{[\frac{t^8}{4}-t^6+2t^2]^{2}_{0}}\\\\=\bold{\frac{2^8}{4}-2^6+2(2)^2}\\\\=\bold{\frac{256}{4}-64+2(4)}\\\\=\bold{64-64+8}\\\\=\bold{8}[/tex]
Therefore the final answer "8".
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Jennifer works part time making crafts. She is paid $12 for each plaque that she completes. One particular week, she made 30 plaques. Find her gross income for the week.
Answer:
360
Step-by-step explanation:
Jennifer earned a total of $360 by making 30 plaques in one week.
Explanation:The subject of this question is Mathematics. Your question is how much Jennifer earned for making 30 plaques in one week if she's paid $12 each. To find out, you simply multiply the number of plaques (30) by how much she earns for each one ($12). So, 30 plaques * $12/plaque = $360. Therefore, Jennifer's gross income for the week is $360.
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The pillars in front of Mr. Jefferson's home are shaped like cylinders with a height of 24 ft and a radius of 8 in. What is the lateral area of each pillar
Answer:
The lateral area is [tex]4,608\pi\ in^{2}[/tex] or [tex]32\pi\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of a cylinder (pillar) is equal to
[tex]LA=2\pi rh[/tex]
Remember that
1 ft=12 in
Find the lateral area in square inches
we have
[tex]r=8\ in[/tex]
[tex]h=24\ ft[/tex] ----> convert to inches
[tex]h=24*12=288\ in[/tex]
substitute the values
[tex]LA=2\pi (8)(288)[/tex]
[tex]LA=4,608\pi\ in^{2}[/tex]
Find the lateral area in square feet
we have
[tex]h=24\ ft[/tex]
[tex]r=8\ in[/tex] -----> convert to feet
[tex]r=8/12=(2/3)\ ft[/tex]
substitute the values
[tex]LA=2\pi (2/3)(24)[/tex]
[tex]LA=32\pi\ ft^{2}[/tex]
A person invests $1,150 in an account that earns 5% annual interest compounded continuously. Find when the value of the investment reaches $2,000. If necessary round to the nearest tenth.
The investment will reach a value of $2,000 in approximately_____years.
Answer:
11.1 years
Step-by-step explanation:
The formula for interest compounding continuously is:
[tex]A(t)=Pe^{rt}[/tex]
Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:
[tex]2000=1150e^{{.05t}[/tex]
We will simplify this first a bit by dividing 2000 by 1150 to get
[tex]1.739130435=e^{.05t}[/tex]
To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with
ln(1.739130435)=.05t
Taking the natural log of that decimal on our calculator gives us
.5533852383=.05t
Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.
WILL MARK BRAINLIEST PLEASE HELP ASAP. The value of n is a distance of 1.5 units from -2 on a number line.
Answer:
see explanation
Step-by-step explanation:
There are 2 possible positions for n, that is
- 2 - 1.5 = - 3.5
OR
- 2 + 1.5 = - 0.5
Both are 1.5 units distance from - 2
The possible values of n are -0.5 and -3.5
Step-by-step explanation:
Analyze two cases
1) n-(-2)=1.5
Solve for n
n+2=1.5
n=1.5-2
n=-0.5
2) -2-n=1.5
n=-2-1.5
n=-3.5
18, 19, 20, 20, 23, 26, 260
What is the better measure of center for these data? Mean or median? Why? Explain your answer.
Answer:
Median
Step-by-step explanation:
This set of data has an extreme outlier, which will throw off the mean. The median, on the other hand, does not change or changes minimally whether or not the outlier is there.
By default, the mean is always better, but if an outlier, such as this one, is too large, the median is better.
A wall with an area of (3x2 + 4x + 1) square units has a rectangular window that has a width of (x + 2) units and a length of (x + 1) units. The wall also has a built-in shelving unit that occupies an area of (x2 + 5x + 6) square units of wall space. If the wall is to be covered with wallpaper, how much wallpaper will be required?
Answer:
the total available area = (3x^2 + 4x + 1) - (2x^2 + 8x + 8) = x^2 - 4x - 7
Step-by-step explanation:
The question seems to ask available area and not how much wallpaper is required. Let's calculate the area of the rectangular window. Area of a rectangle = Length * Breath Area = (x + 2) * (x + 1) = x^2 + 3x + 2 The wall also has a built- in shelving unit that occupies an area of (x^2 + 5x + 6). So total area occupied by the rectangular wall and shelf is (x^2 + 3x + 2) + (x^2 + 5x + 6) = 2x^2 + 8x + 8. If the wall is to be covered with wallpaper
Sorry for the wait
what is the length of Y on this circle?
8 units
10 units
12 units
18 units
Check the picture below.
A _____ has two-fold rotational symmetry.
A. circle
B. equilateral triangle
C. square
D. line
A circle, square and a line has a two fold symmetry.
What is rotational symmetry?A figure is said to be rotationally symmetric if when it is rotated along its axis remains the same. F
Given is to find the quotient when 6 is divided by 444.
If an object appears identical after a rotation of 180 degrees, that is twice in a 360 degrees rotation, then it is said to have a 2-fold rotation axis. A circle, square and a line has a two fold symmetry.
Therefore, a circle, square and a line has a two fold symmetry.
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If the angle of elevation of the escalator is 10° 21’ 36° find th length of the escalator (picture provided)
Answer:
The length of the escalator ≈ 1088.8 ft ⇒ answer (b)
Step-by-step explanation:
* Lets explain the problem
- Consider the escalator and the vertical raise formed a right
angle triangle
- The length of the escalator is the hypotenuse
- The vertical rise is on leg of the right triangle
- The angle of elevation is the angle between the hypotenuse
and the horizontal
* Now lets solve the problem
∵ Angle of elevation = 10° 21' 36"
∵ Vertical distance = 195.8 feet
* The vertical is opposite to the angle of elevation
∴ sin angel of elevation= the vertical/the length of the escalator
∴ sin(10° 21' 36") = 195.8/the length of the escalator
- By using cross multiplication
∴ The length of the escalator = 195.8/sin(10° 21' 36") = 1088.8 feet
* The length of the escalator = 1088.8 ft