The right angle with in 3-4-5 triangle is naturally 90 degrees. Always opposite the fourth side, at 53.13 degrees, are the other two angles: 36.87 degrees (just opposite the 3rd side).
Explain the 3 4 5 triangle and its properties?Specialized triangles, such as 3-4-5 triangles, can be solved using the Pythagorean theorem.
Any triangle with a single right (90°) angle is referred to as a right triangle. Typically, a tiny square marker is placed within the right triangle to denote this. In every right triangle, these two sides closest to the right angle are shorter than the hypotenuse, the side directly across from the right angle. A right triangle with integers on each side is known as a Pythagorean triple.Thus, this 3-4-5 right triangle is one of the most well-known Pythagorean triples. The hypotenuse, its longest side opposite its right angle, is measured at 5, while the shorter sides measure at 3 and 4.
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Zachary is a waiter at a restaurant. Each day he works, Zachary will make a guaranteed wage of $40, however the additional amount that Zachary earns from tips depends on the number of tables he waits on that day. From past experience, Zachary noticed that he will get about $7 in tips for each table he waits on. How much would Zachary expect to earn in a day on which he waits on 11 tables? How much would Zachary expect to make in a day when waiting on tt tables?
Zachary expects to make $40 + $7 x tt (number of tables) in a day when waiting on tt tables
If Zachary waits on 11 tables, he can expect to make an additional $7 in tips for each table, for a total of 11 tables * $7/table = $77 in tips.
When added to his guaranteed wage, Zachary can expect to earn $40 (guaranteed wage) + $77 (tips) = $117 for that day.
To calculate how much Zachary would expect to make in a day when waiting on tt tables, we can use the equation:
Earnings = $40 (guaranteed wage) + $7 (tips/table) x tt (number of tables)
So if tt represents the number of tables Zachary waits on, then he can expect to earn:
Earnings = $40 + $7 x tt
For example, if Zachary waits on 15 tables, he can expect to earn $40 + $7 x 15 = $190.
Zachary can use this equation to calculate his expected earnings for any number of tables he waits on in a day.
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What number needs to be added to 5 and 3 so that the ratio of the first number to the second
becomes 4:3?
Answer:
3
Step-by-step explanation:
Choose a variable to represent the number to be added to 5 and 3.
[tex]\frac{5+x}{3+x}=\frac{4}{3}[/tex]
"Cross-multiply."
[tex]3(5+x)=4(3+x)\\\\15+3x=12+4x\\\\15=12+x\\\\3=x[/tex]
Check: The ratio of 5+3 to 3 + 3 is 8:6, equal to the ratio 4:3.
identify the vertical and horizontal asymptotes for f(x)=2x^2+4 over x^2-5x+6
The vertical asymptotes are 2 and 3 and horizontal asymptotes is 2
What are horizontal and vertical asymptote?An asymptote is a horizontal/vertical oblique line whose distance from the graph of a function keeps decreasing and approaches zero, but never gets there.
Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function.
Therefore, the denominator is x²-5x+6,
= x²-5x+6 = 0
using factorization method
x²-3x-2x+6 = 0
(x²-3x)(-2x+6) = 0
x(x-3) -2(x-3)
x-2 = 0 or
x-3 = 0
x = 2 or 3
The degree of the power of numerator and denominator are equal, there for the horizontal asymptote y = 2x²/x² = 2
therefore the vertical asymptote is x = 2and 3 and horizontal asymptote is y = 2
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Which number is greatest?
19/5
V15
3.88
Please hurry its timed
By algebra properties and trigonometric formulas, the roots x₁ = 30° + n · 360° and x₂ = 210° + n · 360° are solutions of trigonometric function tan x - √(1 - 2 · tan² x) = 0. (Correct choice: B)
How to determine the solutions of a trigonometric equation
In this problem we find a given trigonometric function, whose solution must be found by combining algebra properties and trigonometric formulas. First, write the entire expression:
tan x - √(1 - 2 · tan² x) = 0
Second, use algebra and root properties:
tan x = √(1 - 2 · tan² x)
tan² x = 1 - 2 · tan² x
3 · tan² x = 1
Third, clear x by algebra properties and inverse trigonometric properties:
tan² x = 1 / 3
tan x = √(1 / 3)
tan x = 1 / √3
tan x = √3 / 3
x = tan⁻¹ (√3 / 3)
x = 30° or x = 210°
Since tangent function has a period of 2π (360°), then the solutions of the trigonometric function is:
x₁ = 30° + n · 360°, x₂ = 210° + n · 360°.
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20. Below are massesof students taken in a medical centre. 37 60 35 38 59 34 56 42 55 48 39 33 36 35 43 52 39 64 41 35 20 31 29 45 32 54 66 44 47 45 27 24 48 28 55 (a) Starting with the class 20-29 and class size of 10, make a frequency distribution table for the data. (2 marks)
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Class} & \text{Frequency}\\\cline{1-2}20-29 & 5\\\cline{1-2}30-39 & 12\\\cline{1-2}40-49 & 9\\\cline{1-2}50-59 & 6\\\cline{1-2}60-69 & 3\\\cline{1-2}\end{array}[/tex]
=====================================================
Explanation:
The given data set is
{37, 60, 35, 38, 59, 34, 56, 42, 55, 48, 39, 33, 36, 35, 43, 52, 39, 64, 41, 35, 20, 31, 29, 45, 32, 54, 66, 44, 47, 45, 27, 24, 48, 28, 55}
It sorts to
{20, 24, 27, 28, 29, 31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39, 41, 42, 43, 44, 45, 45, 47, 48, 48, 52, 54, 55, 55, 56, 59, 60, 64, 66}
The five values 20,24,27,28,29 are between 20 and 29. This means the first class or bin will have a frequency of 5.
The next interval spans from 30 to 39. There are 12 items in this interval, and those 12 items are this subset {31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39}. This means we have a frequency of 12 for the interval from 30 to 39.
Keep this process going until you get to the end of the data set.
due tmr help plssssss‼️
Answer:
5π units
Step-by-step explanation:
The arc length of a semicircle is calculated as
length = [tex]\frac{1}{2}[/tex] πd ( d is the diameter ) , then
length = [tex]\frac{1}{2}[/tex] π × 10 = 5π units ← exact answer
what is the domain and range of f(x)=-7x^2-14x-9
Range is f(x) < -2
* The < should have a line under it*
**Sorry i couldn't find the domain**
In our class there are 40 boys. 22 students are girls write a ratio comparing girls to boys
Answer:
Its 22:40
Step-by-step explanation:
Answer: 22:40
Pretty simple
Step-by-step explanation:
Find the measure of the angle
Answer:
155°
Step-by-step explanation:
The angle between the x and y axes is 90°
The required angle = 90° + 65° = 155°
Answer:
Well, y is 90˚ and another angle is 65˚ that means that the unknown angle must be 25˚
Step-by-step explanation:
A cat, a dog, and a gerbil. What generalization can you make?
Answer:
They are fluffy, and are great pets. They eat food and generally have the same bodily functions. The only difference is pet food, mental action (actions) and size. Also their tails.
4.1 is ten times as much as____
9.2 is ten times as much as___
Answer:
4.1 is 10 x 0.41
9.2 is 10x .92
Can I have brainliest?
Step-by-step explanation:
4.1 is ten times as much as 0.41
9.2 is ten times as much as 0.92
what is the measure indicated in the parallelogram
Answer:
? = 74°
Step-by-step explanation:
• in a parallelogram, consecutive angles sum to 180° , that is
? + 106° = 180° ( subtract 106° from both sides )
? ( ∠ G ) = 74°
Hello good morning do anyone think they could help please
Answer:2
Step-by-step explanation:
Write down the gradient and y intercept of each of these lines y=2x
Answer:
[tex]gradient = 2 \\ y - intercept = 0[/tex]
The gradient of this line is 2 and the y-intercept is (0, 0)
Brianna is making fruit dip. The
recipe calls for 1/2 cup of yogurt
per serving. If the container has
3 cups of yogurt, how many
servings can she make?
Help hurry
one leg of a right triangle is 8 cm what could the other length be justify your answer
Answer:
6-L2
10-hypotenuse
Step-by-step explanation:
Pythagorean theorem
Answers to these please no links or files
I think the answer is 4. She my attached picture of my work! I hope this helps you,have a great day!
I WILL GIVE YOU 55 PTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. Name the point with the given coordinates (2, 4). (1 point)
H
J
G
K
Answer:
G
Step-by-step explanation:
Given: (2, 4)
2 is the x coordinate, 4 is the y coordinate.
At the end of a snowstorm, Peyton had 8 inches of snow on her lawn. The temperature then increased and the snow began to melt at a constant rate of 1 inch per hour. Assuming no more snow was falling, how much snow would Peyton have on her lawn 2 hours after the snow began to melt? How much snow would Peyton have on her lawn after t hours of snow melting?
The amount of snow on Peyton's lawn after 2 hours is 4 inches
amount of snow after t hours y = 8 - t
How to model the required equationA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable = amount of snow remaking
m = slope = 1 inch per hour
x = input variable = number of hours
c = y intercept = 8 inches of snow on Peyton's lawn
The equation as described in the problem is represented using linear function as as follows
y = 8 - x
in 2 hours x = 2
y =8 - 2 = 4 inches
The quantity of snow after t hours
x = t
y = 8 - t
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fFind the length of the arc on a circle with radius of 27 meters and intercepted by a central angle of 120 degrees
The length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.
We know that the length of the arc of a circle = Radius of the circle × angle subtended by the arc (in radians)
Here radius of the circle is 27 m
The angle subtended is 120°
Hence we will first convert the angle into radians
Angle in radians = Angle in degree X π/180
= 120 X π/180
= 2π/3
Therefore, the length of the arc = 27 X 2π/3
= 18π m
Therefore, the length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.
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Charlie reads quickly. He reads 1 3/7 pages every 2/3 minutes. Charlie reads at a constant rate: How many pages foes he read per minute?
In one min Charlie can read is [tex]2\frac{1}{7}[/tex] pages at a constant rate.
What is Unitary Method ?A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilize this technique for math computations.
In the unitary technique, the value of a unit or one quantity is always counted first, and the values of additional or less quantities are subsequently determined. This approach is known as the unitary method for this reason. Due to the fact that they generate two distinct sorts of variations, there are two different types of unitary approaches.
Direct VariationIndirect VariationIn [tex]\frac{2}{3}[/tex] min Charlie can read [tex]1\frac{3}{7} = \frac{10}{7}[/tex] pages
In one min Charlie can read is: [tex]\frac{10}{7}*\frac{3}{2} = \frac{30}{14} = 2\frac{2}{14} =2\frac{1}{7}[/tex]
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You earned ten dollars. You spent two-fifths of what you earned. How much
did you spend?
dollars
Answer:
2 dolalrs
Step-by-step explanation:
Is (1,-2) a solution to this system of equations?
20x+20y=-2
2x+5y=-8
YES OR NO
The point (1, -2) is not a solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, the correct option is NO, the solution is (2.5, -2.6)
What is a system of equations?A system of equations are two (or more) equations that have common variables.
The system of equation is presented as follows;
20·x + 20·y = -2
2·x + 5·y = -8
The specified possible solution of the equation is; (1, -2)
Making y the subject of each of the equations, and plugging in the value of x = 1, for the first equation, we get;
20·x + 20·y = -2
20·y = -2 - 20·x
y = (-2 - 20·x)/20
Therefore; y = (-2 - 20 × 1)/20 = -1.1
When x = 1, y = -1.1, therefore, the point (1, -2), is not a solution to the first equation, 20·x + 20·y = -2
Evaluating the second equation, we get;
2·x + 5·y = -8
5·y = -8 - 2·x
y = (-8 - 2·x)/5
Plugging in x = 1, we get;
y = (-8 - 2 × 1)/5 = -2
When x = 1, y = -2, therefore, the point (1, -2), is a point on the graph of the second equation, 2·x + 5·y = -8, but it is not a solution to the system of equation
The solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, can by found by equating both expressions for y as follows;
y = (-2 - 20·x)/20 and y = (-8 - 2·x)/5
Therefore; (-2 - 20·x)/20 = (-8 - 2·x)/5
-10 - 100·x = -160 - 40·x
60·x = 150
x = 150 ÷ 60 = 2.5
x = 2.5
y = (-2 - 20 × 2.5)/20 = -2.6
y = -2.6
The correct option is therefore, no, the solution to the system of equation is; (2.5, -2.6)Learn more about systems of linear equations here: https://brainly.com/question/11867840
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Find the cost of 1m 30cm at 80p per meter.
Answer:
120p
Step-by-step explanation:
if its 80 per meter then all you do is multiply 80 by 1.5 (1.5m = 1m 30cm) and you get 120p simple as that
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Mhanifa please help! You don't have to draw a diagram if you dont want to
Answer:
10.44 mStep-by-step explanation:
The ladder is the hypotenuse of the triangle with legs of 3 m and 10 m.
The length of the ladder is:
[tex]l = \sqrt{3^2+10^2} = \sqrt{109} = 10.44 m[/tex]Find the 19th term of the arithmetic sequence 8,17,26,..
Answer:
170
Step-by-step explanation:
use the formula An = A1 + d(n-1) to identify the arithmetic sequence. An = 9n - 1
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Work out the value of (6.31 x 10^5)+(2.6 x 10^4)
Give your answer in standard form
The answer in standard form is given by 65.7 ×10⁴
What is the Standard Form of a Number?A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.
Given here: (6.31 x 10⁵)+(2.6 x 10⁴)
Simplifying the equation further we get
(6.31 x 10⁵)+(2.6 x 10⁴)= 63.1×10⁴+2.6×10⁴
=65.7×10⁴
Hence, The answer in standard form is given by 65.7 ×10⁴
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Question Show that the binomial is a factor of the polynomial. Then factor the polynomial completely. f(x)=x4−6x3−8x+48; x−6
Answer:
(x-2)(x²+2x+4)(x-6)
Step-by-step explanation:
6 | 1 -6 0 -8 48
_____6_0_0_-48__
1 0 0 -8 | 0
As we can see, our remainder is 0, so x-6 is indeed a factor of the polynomial. Also, we can see that the factored polynomial is [tex]x^4-6x^3-8x+48=(x^3-8)(x-6)=(x-2)(x^2+2x+4)(x-6)[/tex]
help me please anyone
9514 1404 393
Answer:
(2x -1) by (x +5)
Step-by-step explanation:
We presume that the dimensions of the parking lot correspond to factors of the polynomial. The factorization is ...
2x^2 +9x -5
= 2x^2 +10x -x -5
= 2x(x +5) -1(x +5)
= (2x -1)(x +5)
Possible dimensions of the parking lot are (2x-1) and (x+5).