To find the length of the longest side of the triangle, use the Pythagorean theorem to solve for x and determine the side lengths of the triangle.
Explanation:To find the length of the longest side of the triangle, we need to determine which side is the hypotenuse. In a right triangle, the hypotenuse is the side opposite the right angle. Using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can find the length of the hypotenuse.
Let's denote the three sides of the triangle as A, B, and C. The left side is 2x + 12, the bottom side is 6x - 2, and the right side is 5x - 9. Since we can't determine which side is which based on the given information, we can use the variables.
By applying the Pythagorean theorem, we can set up the equation (2x + 12)^2 + (6x - 2)^2 = (5x - 9)^2. Expanding and simplifying this equation will allow us to solve for x and find the lengths of the sides of the triangle. Once we have the side lengths, we can determine which side is the longest.
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your primary jobs gross income is 3468.73/month deductions are fica (7.65%) federal tax witholding (11.5%) and state tax withholding (7.8%) how much are your ficed expenses if they are 36% of your relized income
Answer:
$912.21
Step-by-step explanation:
Your primary jobs gross income = $3468.73
All deductions 7.65% (fica) + 11.5% (federal) + 7.8% (state tax) = 26.95%
Income after deductions = 3468.73 - ( 26.95% × 3468.73 )
= 3468.73 - (0.2695 × 3468.73)
= 3468.73 - 934.82
= $2,533.91
Fixed expenses on your realized income = 36%
Fixed expenses = 36% × 2,533.91
= 0.36 × 2,533.91
= $912.2076 ≈ $912.21
Fixed expenses are $912.21
For which of the following displays of data is it not possible to find the mean?(Expert and Ace only please)
frequency table
line plot
stem-and-leaf plot
histogram
Answer:
The histogram
Step-by-step explanation:
It is difficult to find mean of a histogram
What is Histogram ?It is a chart that help in visualize the distribution of values in a dataset.
It is difficult to find mean just by looking at the data of the histogram
Hence , d) Histogram is the answer
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The cost of removing x percent of pollutants is expressed by the function , where C is in thousands of dollars. Which conclusion can be derived from this statement?
a)The cost of removing 40 percent of the pollutants is $120,000.
b)The cost of removing 80 percent of the pollutants is $960,000.
c)The vertical asymptote lies at x = 0.
d)The vertical asymptote lies at x = 240.
what is the range of y=3cosx-1?
a) -4 ≤ x ≤ 4
b) -4 ≤ x ≤ 2
c) -3 ≤ x ≤ 3
d) -2 ≤ x ≤ 0
Answer: The correct option is (b) [tex]-4\leq y\leq 2.[/tex]
Step-by-step explanation: We are given to select the correct range of the following function
[tex]y=3\cos x-1.[/tex]
We know that the range of the cosine function is from - 1 to 1.
That is,
[tex]-1\leq \cos x\leq 1\\\\\Rightarrow -(1)\times 3\leq 3\times \cos x\leq 3\times 1\\\\\Rightarrow -3\leq 3\cos x\leq 3\\\\\Rightarrow -3-1\leq 3\cos x-1\leq 3-1\\\\\Rightarrow -4\leq 3\cos x-1\leq 2\\\\\Rightarrow -4\leq y\leq 2.[/tex]
Thus, the range of the given function is [tex]-4\leq y\leq 2.[/tex]
Option (b) is CORRECT.
Which of the equations below shows the relationship in the table? [X] [15] [5] [3] [1] ------------------------------------------ [Y] [1] [3] [5] [15]] A. y = 15x B. y = x - 14 C. y = x + 2 D. y = 15 x
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
There are a total of 18 chairs. If the ratio of the red chairs tobrown chairs is 2 to 4, how many of them are red?
Answer:Of the 18 chairs, 6 are red
Step-by-step explanation:
Given total no of chairs =18
Ratio of red chairs to brown chairs =2:4=[tex]\frac{2}{4}[/tex]
So there are 6(2+4) parts chair out of which 2 are red and 4 are brown
∴ 6 part equals 18 chairs
1 part equals [tex]\frac{18}{6}[/tex]
=3 chairs
Now 2 part equals 2×3=6
i.e. there are 6 red chairs
Which two equations would be most appropriately solved by using the zero product property?
Select EACH correct answer.
Which two equations would be most appropriately solved by using the quadratic formula?
Select EACH correct answer.
Answer:
1 - B and C
2 - B and C
Step-by-step explanation:
Ques 1: We know that,
Zero Product Property states that 'If ab=0, then either a=0 or b=0 or both are zero'.
So, from the options, we see that,
The equation [tex](x-3)(x+4)=0[/tex] can be solved using this property.
Also, the equation [tex]2x^2+6x=0[/tex] can be simplified to [tex]2x(x+3)=0[/tex].
So, this [tex]2x(x+3)=0[/tex] can also be solved by the given property.
Since, the other options cannot be factorized.
Hence, the correct options are B and C.Ques 2: We know that,
The quadratic formula is used to solve find the solution of the quadratic equation of the form [tex]ax^2+bx+c=0[/tex].
So, from the options, we see that,
The equations [tex](x-3)^2=36[/tex] and [tex](x+8)(x+9)=0[/tex] can be solved directly by using the 'Zero Product Property'.
The other equations cannot be solved directly and would be solved using the quadratic formula.
Hence, the correct options are B and C.Choose an equation for the relationship between the measures of the segments, angles, and arcs.
The following polynomials can be factored using the techniques of this lesson. x^2-36
the correct answer to that question would be true
Answer:
true
Step-by-step explanation:
A P E X
Given an exponential function for compounding interest, A(x) = P(1.04)x, what is the rate of change?
A. 0.04%
B. 1.04%
C. 104%
D. 4%
The given expression is
[tex] A(x) = P(1.04)^x [/tex]
Which can also be written as
[tex] A(x) = P(1+0.04)^x [/tex]
And the formula of compound interest is
[tex] A(x) = P(1+r)^x [/tex]
On comparing, we will get rate of change equals to 0.04 or 4 %.
So the correct option is the last option .
Sally has completed 1/3 of her shift; Jerry has completed 5/6 of his shift; David has finished 1/2 of his shift; Mona has 7/8 of her shift remaining. Out of the four employees, Who has completed the most work time?
Jerry completed the most work time.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
Sally has completed 1/3 of her shift.
Jerry has completed 5/6 of his shift.
David has finished 1/2 of his shift.
Mona has 7/8 of her shift remaining.
Now,
Since, Mona has 7/8 of her shift remaining.
Hence, The time for Mona = 1 - 7/8
= 1/8
We make all the denominator equal by taking LCM of 3, 6, 2, 8.
Thus, LCM of [3, 6, 2, 8] = 24
Hence, Sally has completed 8/24 of her shift.
Jerry has completed 20/24 of his shift.
David has finished 12/24 of his shift.
Mona has completed 3/24 of his shift.
Clearly, Jerry completed the most work time.
Thus, Jerry completed the most work time.
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Find sec θ if θ is in Quadrant IV and sinθ=-1/5
Answer:
i got the answer 5(sqrt6)/12
8.
A particular sound wave can be graphed using the function y = –3 sin x. Find the period of the function.
period = 2pi
period = –3
period = 3
period = 1/2
1. The table shows the height, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds.
2. How many seconds are required for the pendulum to swing from its position furthest to the right to its position furthest to the left?
3. How many degrees is the painted spot turning in 0.75 s?
Enter your answer in the box.
4. What is the average daily maximum temperature in March?
Round to the nearest tenth of a degree if needed.
Use 3.14 for π .
Enter your answer in the box
5. What is the greatest temperature the substance reached during the experiment?
Round to the nearest tenth of a degree if needed.
Use 3.14 for π .
Enter your answer in the box.
NEED HELP ASAP!!!
What is the value of x?
/Users/mikaylee/Desktop/8104613-NG_IMC_SemB_09_UT_01.png
How to solve for the third side of an isosceles triangle?
Which inequality represents the following sentence?
Twelve fewer than a number is at least 18.
12 + x ≤ 18
x – 12 ≥ 18 (This one correct?)
12 – x ≥ 18
x – 12 < 18,
Answer:
B) x - 12 ≥ 18.
Step-by-step explanation:
Given : Twelve fewer than a number is at least 18.
To find : Which inequality represents the following sentence?.
Solution : We have given
Twelve fewer than a number is at least 18.
Let the number be x .
According to question :
Twelve is less than a number x .
x - 12 ( negative sign used for fewer).
x - 12 ≥ 18.
Here we used greater than equal to sign because x- 12 is at least 18 mean is must be 18 or greater than 18.
Then equation become x - 12 ≥ 18.
Therefore, B) x - 12 ≥ 18.
Solve 5x + 1 = 2x2 + 9x. Which are steps in the process of completing the square used to solve the equation?
ANSWER CHOICES
1 = 2(x2 + 2x)
1 = 2x2 + 4x
2 = 2(x2 + 2x + 1)
3 = 2(x + 1)2
2 = 2(x + 1)2
Answer:
Choices (1), (2) and (4)
Step-by-step explanation:
5x + 1 = 2x² + 9x
By subtracting 5x form both the sides of the equation.
(5x + 1) - 5x = 2x² + 9x - 5x
1 = 2x² + 4x
1 = 2(x² + 2x)
By adding 2 on both the sides
1 + 2 = 2(x² + 2x) + 2
1 + 2 = 2(x² + 2x + 1)
3 = 2(x² + 2x + 1)
3 = 2(x + 1)²
Therefore, choices (1), (2) and (4) are the steps that have been used to complete the square.
To solve the equation 5x + 1 = 2x^2 + 9x using the method of completing the square, follow these steps: move all terms to one side of the equation, combine like terms, divide all terms by the coefficient of x^2, take half of the coefficient of x, square it, and add it to both sides of the equation, factor the left side of the equation, take the square root of both sides, and solve for x.
Explanation:To solve the equation 5x + 1 = 2x2 + 9x using the method of completing the square, the following steps are used:
Move all terms to one side of the equation: 2x2 + 9x - 5x - 1 = 0Combine like terms: 2x2 + 4x - 1 = 0Divide all terms by the coefficient of x2: x2 + 2x - 1/2 = 0Take half of the coefficient of x, square it, and add it to both sides of the equation: x2 + 2x + 1 = 1/4Factor the left side of the equation: (x + 1)2 = 1/4Take the square root of both sides: x + 1 = ±1/2Solve for x: x = -1 ± 1/2Which operation is NOT closed for polynomials?
A) (x3 + 8x − 5) (x4 + 6x + 2)
B) (x2 + 4x − 5)(8x2 + 3x − 6)
C) (6x2 + 2x − 3) + (x2 − 5x + 4)
D) −(2x2 + 2x − 5) − (x2 + 2x + 9)
Answer:
A
Step-by-step explanation:
You had a typo with A, and I think that is the answer as well, seeing as you typed all of your other answers correct, and none of them were labeled open by the first answerer, despite the typo.
A garage contains a combination of 20 bikes and tricycles. In total, there are 44 wheels. How many bikes and how many tricycles are in the garage.
The solution explains how to find the number of bikes and tricycles in a garage based on the total number of wheels and the given combination.
Explanation:The question: A garage contains a combination of 20 bikes and tricycles. There are a total of 44 wheels.
Step-by-step solution:
Let's denote the number of bikes as B and the number of tricycles as T.
Each bike has 2 wheels, so the total number of wheels contributed by the bikes is 2B.
Each tricycle has 3 wheels, so the total number of wheels contributed by the tricycles is 3T.
Given that the total number of wheels is 44, we can form the equation: 2B + 3T = 44.
Since there are 20 bikes and tricycles in total, we have the equation: B + T = 20.
Solving the system of equations, we find that there are 12 bikes and 8 tricycles in the garage.
The bar graph shows the z-score results of four employees for two different work weeks.
Which employee had the least earnings for Week 1?
Usan
Percy
Oberto
Michael
Melinda goes blowing on Saturday afternoon. She bowls three games nand pays for shoe rental. Define a variable and write an expression to represent the total cost Melinda pays. Then find the total cost if one game cost 4$
How do you determine if two lines are perpendicular?
Which graph matches this situation
HELP PLEASE!!
Which is greater, the total volume of three spheres, each of which has a diameter 3 in., the volume of one sphere that has a diameter 8 in., or the volume of a hemisphere with a diameter of 9 in.?
a) The volume of three spheres, each with a diameter of 3 inches, is greater.
b) The volume of one sphere with a diameter of 8 inches is greater.
c) The volume of the hemisphere with a diameter of 9 in. is greater.
d) The two volumes are the same.,
Answer:
Step-by-step explanation:
Answer:
Here is my answers for the practice that I have come across. It may be the new one. I also shortened it.
1. find the SA of a grape fruit with a c of 14cm.
62 cm^2
2. a sphere has a volume of 900 ci. find SA
451
3. a solid metal cube with an edge length of 9 in is melted and reshaped into a sphere. which is SA of sphere
391.7
4. the sphere below fits snugly inside a cube with 6 in edges what is the v of the space between the sphere and the cube
102.9
5. find the v in terms of pi of a sphere with a SA of 9 pi square feet
9/2 pi ft^3
6. which of the following is the greatest the total v of 3 sphere each of which a diameter of 5 in the v of one sphere that has a diameter 8 in or the v of a hemisphere with a diameter of 10 in
the v of 1 sphere with a diameter of 8 in is greatest
7. a sphere has center 0 0 0 and a radius of 5
0 -3 4
8. find v of figure the diameter of the base is 4 cm
46/3 pi cm^3
9. a sphere with a radius of 5 cm fits inside a box every face is tangent to the sphere
6 pi
10. tennis balls are sold in packs of 3 and come packaged in a plastic cylindrical container there is no space between
69 square inches
Step-by-step explanation:
triangle abc is an isosceles right triangle. what is the measure of a base angle
Answer:
The measure of the base angle = 45°
Step-by-step explanation:
For better explanation of the solution see the attached figure of the diagram :
Given : An isosceles right triangle ABC
To find : Measure of the base angle
Solution :
Since, The triangle is right angle triangle.
⇒ m∠B = 90°
Also, ΔABC is an isosceles triangle
So, AB = BC
Now, Angles opposite to equal sides are equal
⇒ m∠A = m∠C
Now, Using Angles sum property of a triangle
⇒ m∠A + m∠B + m∠C = 180°
⇒ m∠C + 90° + m∠C = 180°
⇒ 2m∠C = 180° - 90°
⇒ 2m∠C = 90°
⇒ m∠C = 45°
Hence, The measure of the base angle = 45°
Can someone please help me with this question?! (geometry)
Answer:
see below
Step-by-step explanation:
The arc length (s) can be found in terms of angle (θ) and radius (r) as ...
s = rθ
Dividing by r gives ...
s/r = θ
Since the angles are the same for the two circles, the ratios of interest are ...
[tex]\dfrac{s_1}{r_1}=\dfrac{s_2}{r_2}=\theta [/tex]
Just need an answer
Which of the following are among the five basic postulates of Euclidean geometry?
Check all that apply.
A. All equilateral triangles are also equiangular.
B. A circle can be drawn with any center and radius.
C. Through a point not on a given line, there is exactly one line parallel to the given line.
D. All right angles are equal to one another.
Answer:
Choices B, C, and D are correct.
Step-by-step explanation:
Euclid's Five postulates are as follows:
1. A straight line segment may be drawn from any given point to any other.
2. A straight line may be extended to any finite length.
3. A circle can be drawn with any center and radius.
4. All right angles are congruent/equal to each other.
5. Through a point not on a given line, there is exactly one line parallel to the given line.
Now looking at these postulates and the choices we are given we see that only choice B, C, and D match with above.
From the options given, the statements that are among the five basic postulates of Euclidean Geometry are: B, C, and D.
The five basic postulates of Euclidean geometryThe five (5) basic postulates are:
Any straight line segment is drawn from any point to another.Any straight line can be drawn and extended to any finite length.Circles are drawn given a center and radius.Right angles are always congruent.If a given point is not on a given line, there exist a line that is parallel to the given line.Therefore, from the options given, the statements that are among the five basic postulates of Euclidean Geometry are: B, C, and D.
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