Answers
orthogonal = perpendicular.
an altitude in a triangle is the perpendicular distance stemming from a vertex.
where all these orthogonal segments meet is the ORTHOcenter.
The described point M is a Orthocenter.
What is an Orthocenter?"The orthocenter is the point where all the three altitudes of the triangle cut or intersect each other. Here, the altitude is the line drawn from the vertex of the triangle and is perpendicular to the opposite side. Since the triangle has three vertices and three sides, therefore there are three altitudes."
"The orthocenter will vary for different types of triangles such as Isosceles, Equilateral, Scalene, right-angled, etc. In the case of an equilateral triangle, the centroid will be the orthocenter. But in the case of other triangles, the position will be different. Orthocenter doesn’t need to lie inside the triangle only, in case of an obtuse triangle, it lies outside of the triangle."
In this figure, the altitudes of triangle JKL is given.
Since, these are altitudes they interest each other at orthocenter.
Hence, A is the correct answer.
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Related Questions
Determine whether the relation shown is a function. Explain how you know.
Answers
Answer:
It is not a function
Step-by-step explanation:
The plot shows (1, 1) and (1, 3) are both defined by the relation. It does not pass the "vertical line test", which requires the relation be single-valued everywhere.
Answer:
This is not a function
Step-by-step explanation:
To determine whether a relation is a function, we can use the vertical line test. If a vertical line touches the relation in more than one point, it is not a function.
Since a vertical line will touch the relation at two points at x=1
(1,1) and (1,3) this is not a function
Michael is making a deposit with a check and wants cash back. His deposit slip has his name, his account number, the date, the amount of the check, the amount of cash that he wants, his signature, and what else?
a.his date of birth
b.his social security number
*c.the net deposit amount*
d.the balance of money in the account
(edit) ANSWER: *C*
Answers
Answer:
The correct answer option is c. the net deposit amount.
Step-by-step explanation:
We know that Michael is making a deposit with a check and wants some cash back.
According to The Federal Reserve System and The Federal Deposit Insurance Corporation, the deposit slip must have the name his name, his account number, date, amount of the check, amount of cash that he want, his signature and the net deposit amount.
Answer:
C
Step-by-step explanation:
The function f(x) = 7 – 4x + x2 written in vertex form is f(x) = (x – 2)2 + 3. What is the axis of symmetry for the function? X = –3 x = –2 x = 2 x = 3
Answers
Answer:
x = 2
Step-by-step explanation:
The vertex form tells you the vertex is (x, y) = (2, 3). The vertical line through the vertex, x=2, is the axis of symmetry.
Answer:
x = 2
Step-by-step explanation:
took the test on edge
PLS HELP HOW DO U SLOVE THIS
Answers
Explanation:
There is nothing to "solve." This equation is a trig identity.
Often, it works well to express all trig functions in terms of sine and cosine. When you're trying to prove an identity, you usually pick one side to rearrange, and leave the other side alone. Here, we will rearrange the right side.
[tex]\csc\theta=\dfrac{\cot\theta+1}{\cos\theta+\sin\theta}\\\\\csc\theta=\dfrac{\dfrac{\cos\theta}{\sin\theta}+1}{\cos\theta+\sin\theta}=\dfrac{\left(\dfrac{\cos\theta+\sin\theta}{\sin\theta}\right)}{\cos\theta+\sin\theta}=\dfrac{1}{\sin\theta}\\\\\csc\theta=\csc\theta[/tex]
A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle θ. How should θ be chosen so that the gutter will carry the maximum amount of water?
Answers
Answer:
θ = 60°
Step-by-step explanation:
The cross sectional area of the trapezoid shape will be that of a trapezoid with bases of 10 cm and (10 cm + 2·(10 cm)·cos(θ)) and height (10 cm)·sin(θ).
That area in cm² is ...
A = (1/2)(b1 +b2)h = (1/2)(10 + (10 +20cos(θ))(10sin(θ)
A = 100sin(θ)(1 +cos(θ))
A graphing calculator shows this area to be maximized when ...
θ = π/3 radians = 60°
_____
A will be maximized when its derivative with respect to θ is zero. That derivative can be found to be 2cos(θ)² +cos(θ) -1, so the solution reduces to ...
cos(θ) = 1/2
θ = arccos(1/2) = π/3
How do you find the length of the legs of an isosceles triangle?
Answers
Answer:
Step-by-step explanation:
This is a rational expression because the denominator contains a variable. This is a polynomial with 3 terms. This is a rational expression because the denominator contains a variable. This is a polynomial with 4 terms. This is a rational expression because the denominator contains a variable. This is a polynomial with 4 terms. This is a rational expression because the denominator contains a variable. This is a polynomial with 3 terms. This is a rational expression because the denominator contains a variable. This is a polynomial with 5 terms.
Answers
Answer:
i agree
Step-by-step explanation:
Given the functions, f(x) = 2x^2 + 2 and g(x) = 3x + 1, perform the indicated operation. When applicable, state the domain restriction.
A)2x2 - 3x + 1
B)2x2 - 3x + 3
C)5x3 + 2x2 + 2
D)6x3 + 6x + 3
Answers
Answer:
the one that equals to 7
Step-by-step explanation:
Answer: The answer is B 2x2 - 3x+3
Step-by-step explanation:
Please help me find the area of two similar octagons
Answers
Answer:
3:5
Step-by-step explanation:
The areas of two similar octagons are 9m² and 25m²
The scale factor of their areas is [tex]\frac{25}{9}[/tex] or 9:25
The scale factor of their side lengths is [tex]\sqrt{25/9}[/tex] or 3:5
ANSWER
3:5
EXPLANATION
The given similar octagons have areas 9 m² and 25m² .
Let the scale factor of their side lengths be in the ratio:
m:n
[tex] {( \frac{m}{n}) }^{2} = \frac{9}{25} [/tex]
We take square root of both sides to get;
[tex] \frac{m}{n} = \sqrt{ \frac{9}{25} } [/tex]
We simplify the square root to get
[tex] \frac{m}{n} = \frac{3}{5} [/tex]
Therefore the scale factor of their side lengths is 3:5
I will give brainliest. please help! <3
Answers
Answer:
Given in the problem , as ΔBEC is an equilateral triangle , ∠GCD=90°,m∠ECD=30°
Step-by-step explanation:
Step1:
Statement 2:
as ΔBEC is an equilateral triangle
statement 3:
BG ≅ GC as FG is perpendicular bisector given in the problem.
Statement 4.
∠CFG =60° as as ΔBEC is an equilateral triangle
Staement 5 : Reason : All the angles of an equilateral triangle are 60°
step 2 :-
Statement 1.
as ΔBEC is an equilateral triangle is given in the fourth statement of the problem.
Statement 2.
m∠GCE = 60° as it is contained in ΔBEC which is an equilateral triangle. All the angles of an equilateral triangle are 60°.
Statement 3:
∠GCD =90° as ABCD is a square
Statement 4:
m∠ECD=∠GCD-m∠GCE
=90°-60°
=30°
Hence Proved
Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths. Base 3.5 feet, altitude 3/4 feet. 2 1/8 sq. Ft. 2 5/8 sq. Ft. 3 3/8 sq. Ft.
Answers
A = bh
A = (3.5)((0.75)
A = 2.625
A = 2_5/8 ft^2
Which of the following represents another way to write the function rule f (x) = 3x + 1?
A. x = 3y + 1
B. f ( 1 ) = 4
C. f (y) = 3x + 1
D. y = 3x + 1
Answers
Answer:
d
Step-by-step explanation:
y=mx+b
Answer:
D. y = 3x+1
Step-by-step explanation:
A -- this describes the inverse function rule (x and y are interchanged).
B -- this describes one point that is described by the function rule, but does not cover the remaining infinite number of points.
C -- there is no variable y in the right side of the rule, so this would give f(1) = 3x+1, f(2) = 3x+1, and so on. The value will always be "3x+1" for any function argument. This is not the same as the given function rule.
D -- y (or any other variable except x) can stand in for f(x), so this is the same as y = f(x). It is another way to write the function rule.
In order to unload clay easily, the body of a dump truck must be elevated to at least 50°. The body of a dump truck that is 15 feet long has been raised to 9 feet. Will the clay pour out easily? Show your work and draw a diagram to support your answer.
Please include the following:
• A diagram
• The trig equation you are solving and the steps you take to solve it.
• An answer in the context of the problem.
_________ (Yes or No), The clay ___________ (will or will not) pour out easily when the body of the dump truck is raised to 9 feet. I know this because ______________________________________.
Answers
Answer:
No; the angle of elevation of the front bottom of the dump truck body will be only 31°, much smaller an angle than the required 50°
Step-by-step explanation:
Let the body of the truck rest upon the x-axis with the rear body at (0, 0). The front of that body is located at (15, 0). The dump body is elevated to 9 ft.
We thus have a right triangle with base 15 ft and height 9 ft, and want to know what the angle is. The angle is at (0, 0). The front of the body is at (0, 15), and when elevated that point will be located at (15, 9).
The tangent function relates the angle to the opposite side (length 9 ft) and the adjacent side (length 15 ft):
tan Ф = opp / hyp = 9 / 15 = 31 degrees.
NO: the elevation of the front of the dump truck body is only 31° approx. The clay will not easily dump from the body.
what is the ratio for the surface areas of rectangle prisims shown below given that they are similar and that the ratio of their edge lengths is 7:3
Answers
Answer:
B. 49:9
Step-by-step explanation:
The ratio of surface areas is the square of the ratio of edge lengths:
7² : 3² = 49 : 9
The recyclables have been sorted into plastic and glass. The number of plastic items is 30 less than nine times the number of glass items. The recyclables are 85% plastic. How many glass items are there?
a. 6
b. 9
c. 15
d. 18
Answers
Answer:
B
Step-by-step explanation:
We will use substitution method after writing 2 equations to solve for number of glass items.
Let number of glass items be g and number of plastic items be p
"The number of plastic items is 30 less than nine times the number of glass items":
We can write the equation as [tex]p=9g-30[/tex]
"The recyclables are 85% plastic":
This means that plastic (p) is 0.85 of the total (p+g). Thus we can write equation as [tex]p=0.85(p+g)[/tex]
We can substitute the expression for p in first equation into 2nd and solve for g:
[tex]p=0.85(p+g)\\(9g-30)=0.85((9g-30)+g)\\9g-30=0.85(10g-30)\\9g-30=8.5g-25.5\\0.5g=-25.5+30\\0.5g=4.5\\g=\frac{4.5}{0.5}\\g=9[/tex]
The number of glass items is 9
Answer:
b. 9
Step-by-step explanation:
x : glass items
9x - 30 : plastic items
(the equation will be set equal to [tex]\frac{15}{85}[/tex] because 85% of the recyclables are plastic, so that means 15% must be glass.)
[tex]\frac{x}{9x-30} =\frac{15}{85}[/tex]
[tex]85x=135x-450[/tex] (now subtract 135x from each side to isolate x to one side of the equation)
[tex]-50x=-450[/tex] (divide each side of the equation by -50 to isolate x)
[tex]x=9[/tex]
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Aubrey was offered a job that paid a salary of $45,000 in its first year. The salary was set to increase by 2% per year every year. If Aubrey worked at the job for 20 years, what was the total amount of money earned over the 20 years, to the nearest whole number?
Answers
Aubrey's total earnings over 20 years, given a starting salary of $45,000 and a 2% annual increase, would be approximately $1,157,357, calculated using the formula for an increasing annuity.
Explanation:The subject of this question is compound interest, which is a mathematical concept used to calculate the future value of an investment or loan. In this case, Aubrey's salary is subject to an annual increase of 2%, which is compounded yearly.
To calculate the total amount earned over 20 years, we need to use the formula for the future value of a salary subject to yearly increases: Future Value = Salary * ((1 + Rate)^Years). Substitute the given values into the equation: Future Value = $45,000 * ((1 + 0.02)^20). Calculating this gives a value of approximately $66,207.11, which would be Aubrey's salary in the 20th year.
To find the total earnings over 20 years, you would add each year's salary together. However, it is much more complex due to the increasing salary. In this case, an annuity formula can be used.
The formula is: Total Earnings = Pmt * ((1 - (1 + r) ^ -n) / r). 'Pmt' is the first period payment, 'r' is the interest rate, and 'n' is the number of payments. Here, Pmt = $45,000, r = 2% or 0.02, and n = 20 years. After substituting everything in, the result should be around $1,157,357 rounded to the nearest whole number.
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draw a modelto show that x + 3 is the same as x over 3
Answers
Answer:
Step-by-step explanation:
Your equation comes out to x + 3 = x/3. Multiplying all three terms by 3 results in 3x + 9 = x, which simplifies to 2x = -9, so that x = -9/2.
Unsure of what you're asking for by "model."
greatest common factor.
35+50
Answers
Answer:
GCF is 5
Step-by-step explanation:
The factors of 35 are: 1, 5, 7, 35
The factors of 50 are: 1, 2, 5, 10, 25, 50
Need help with a math question
Answers
ACD and ACE are supplementary angles that need to equal 180 degrees
ACE = 180 -100 = 80 degrees.
For this case we have by definition that, a flat angle is the space included in an intersection between two straight lines whose opening measures 180 degrees. So, the angle between A and B is 180 degrees.
If we are told that the ACD angle is 100 degrees, then the DCB angle should be 80 degrees.
The angle ACE is opposite by vertex to the angle DCB, then it is also 80 degrees; since by definition, two angles opposed by the vertex are congruent or equal.
Answer:
80 degrees
NEED HELP WITH A MATH QUESTION TO FIND THE VALUE OF X
Answers
Answer:
x=6.5 cm
Step-by-step explanation:
The tangent meets the circle at right angles.
Therefore the triangle formed is a right triangle.
From the Pythagorean Theorem;
[tex]x^{2} +20.2^2=(x+14.7)^2[/tex]
We expand to obtain:
[tex]x^{2} +408.4=x^2+29.4x+216.04[/tex]
We group like terms to get:
[tex]x^{2} -x^2+408.4-216.04=29.4x[/tex]
We simplify now to get:
[tex]192.36=29.4x[/tex]
We divide both sides by 29.4 to get:
x=6.5 to the nearest tenth.
Geometry PEOPLE HELP
Answers
Answer: second option.
Step-by-step explanation:
Given the transformation [tex]T:(x,y)[/tex]→[tex](x-5,y+3)[/tex]
You must substitute the x-coordinate of the point A (which is [tex]x=2[/tex]) and the y-coordinate of the point A (which is [tex]y=-1[/tex]) into [tex](x-5,y+3)[/tex] to find the x-coordinate and the y-coordinate of the image of the point A.
Therefore, you get that the image of A(2,-1) is the following:
[tex](x-5,y+3)=(2-5,-1+3)=(-3,2)[/tex]
You can observe that this matches with the second option.
Melissa sees a lighthouse from her sailboat. She knows the height of the lighthouse is 154 feet. She uses a measuring device and determines that the angle to the top of the lighthouse from her boat is 35°. How far is the sailboat from the base of the lighthouse?
Answers
Answer:
219.9 feet to the nearest tenth.
Step-by-step explanation:
Use trigonometry:
tan 35 = opposite / adjacent side
= 154/x
x = 154 / tan35
= 219.93
Answer:
219.9 ft
Step-by-step explanation:
After looking at pic, cross multiply to get x tan(35)=154
then divide both sides by tan(35) giving x=154/tan(35)
x is approximately 219.9 ft
A spinner with 6 equally sized slices is shown below. The dial is spun and stop on a slice at random . What is the probability that the dial stop at a grey side . Write your answer as a fraction in simplest form
Answers
One grey side or one gray side?
P(one grey side) = 1/6
Please explain how to solve step by step. Thank you.
Answers
3x-2 = 5x-14
Subtract 3x from each side:
-2 = 2x -14
Add 14 to each side:
12 = 2x
Divide both sides by 2:
x = 12/2
x = 6
Choose the system of equations which matches the following graph:
a line includes points 0 commas 2 and 5 commas 0
A) 2x − 5y = 10
4x − 10y = 20
B) 2x + 5y = 10
4x + 10y = 20
C) 2x + 5y = 10
4x − 10y = 20
D) 2x − 5y = 10
4x + 10y = 20
Answers
Answer:
B
Step-by-step explanation:
If you put (x,y) values in here
(0,2)
2x + 5y = 10
2.0 + 5.2 = 10
0 + 10 = 10
4x + 10y = 20
4.0 + 10.2 = 20
0 + 20 = 20
And the other is
(5,0)
2x + 5y = 10
2.5 + 5.0 = 10
10+0= 10
4x + 10y = 20
4.5 + 10.0 = 20
20 + 0 = 20
All of them is OK.
Answer:
2x + 5y = 10
4x + 10y = 20
Step-by-step explanation:
just took the test
Which of the following quadrilaterals have diagonals that are perpendicular to each other? Check all that apply.
Answers
Answer: Option B and option D.
Step-by-step explanation:
We know that a quadrilateral is a 2-dimensional closed shape that has four sides.
By definition the diagonals of a quadrilateral are the lines that connect two non-adjacent vertices.
The following quadrilaterals have diagonals that are perpendicular to each other (also known as perpendicular bisector diagonals), which means that they form four angles of 90 degrees (right angles): Rhombus and Square.
Therefore the answers are: the option B and the option D.
The quadrilaterals that have diagonals perpendicular to each other are:
a. Rectangle
b. Rhombus
d. Square
In a rectangle, the diagonals are always perpendicular to each other. The same applies to a rhombus, which is a special case of a parallelogram with all sides equal.
Similarly, a square is a special type of rectangle and rhombus, so its diagonals are also perpendicular. However, in a general parallelogram, the diagonals are not necessarily perpendicular. Therefore, the correct options are a, b, and d.
Therefore, The quadrilaterals that have diagonals perpendicular to each other are:
a. Rectangle
b. Rhombus
d. Square
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The coins in the stores cash register total $12.50. The cash register contains only nickels, dimes, and quarters. There are twice as many dimes and nickels. There are also twice as many quarters as dimes. How many dimes are in the cash register?
Answers
Answer:
20 dimes
Step-by-step explanation:
We can group the coins into groups that are ...
4 quarters + 2 dimes + 1 nickel
Then each group satisfies the ratio requirements, and the total value of a group is $1.25.
Since the total value in the register is $12.50, there must be 10 such groups, hence 20 dimes.
Felicity babysat 2 hours each night for 10 nights.She earned a total of $180 babysitting .Felicity wants to calculate her hourly rate.How much did felicity earn per hour babysitting
Answers
Answer:
$9 per hour
Step-by-step explanation:
given that falicity babysat for 2 hours each night for 10 nights
Total hours spent babysitting = 10 nights x 2 hours = 20 hours
hourly rate = total amount earned / total time spent babysitting
= $180 / 20 hrs = $9 per hour
ONLY PEOPLE WHO ANSWER CORRECTLY AND ANSWER ALL GET BRAINLIEST AND FULL POINTS
Q1: How do you identify the solution to a system of two linear equations in two variables from their graphs?
Q2: What causes a system of two equations in two variables to have no solution? What causes a system of two equations in two variables to have infinitely many solutions?
Q3: How do you determine whether to use substitution or elimination to solve a system of equations?
Answers
Q1: The solution of a system of two linear equations in two variables is the point where their graphs intersect. At that point, the (x, y) pair satisfies both equations.
__
Q2: There will be no solution when the lines representing the equations do not intersect. That will only happen when they are parallel. (We say the equations are "inconsistent.")
There will be infinitely many solutions when the lines overlap. That is, the equations for them are essentially the same equation. (We say the equations are "dependent.")
__
Q3: Elimination is easiest when the coefficients of one of the variables are opposites of each other, or if one is a factor of the other. Substitution is easiest if one of the equations is easily put in the form x = ( ) or y = ( ).
If neither or both conditions hold, the choice is by student preference. (In this latter case, solution using Cramer's rule may be simplest.)
A.
10,000
B.
23,000
C.
55,000
D.
155,000
Answers
The best and most correct answer among the choices provided by the question is B.) 23,000
Hope this helps :)