Two lines that intersect and form four right angles are perpendicular to each other. This is because they cross at a single point creating four 90 degree angles. Therefore, the lines are not parallel, the angles are not complementary, and their coplanar status is irrelevant.
Explanation:If two lines intersect and form four right angles, it means that the lines are perpendicular to each other. In geometry, when two lines are perpendicular, they intersect at one point forming four right angles. A right angle is an angle of 90 degrees, which is the total division of a straight angle. Therefore, the two lines are not parallel because parallel lines do not intersect. The angles would not be complementary because complementary angles are two angles that add up to 90 degrees. Lastly, the lines being coplanar or not has no bearing on the angles they form when they intersect.
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Two lines intersecting to form four right angles are perpendicular, which is reflected in B. the lines are perpendicular. Parallel lines don't intersect, complementary angles are about their sum, and not coplanar doesn't relate to angles formed by intersection.
Explanation:When two lines intersect and form 4 right angles, they possess a special relationship known as perpendicularity. These perpendicular lines meet to form 90-degree angles, also referred to as right angles. This fact is grounded in basic geometric principles.
The correct answer to the question is B. the lines are perpendicular. Choosing any of the other options would not accurately describe the relationship between the lines. Parallel lines do not intersect, complementary angles sum up to 90 degrees but do not describe the relationship between lines, and being not coplanar implies the lines do not lie in the same plane which is irrelevant to the intersection forming right angles.
It is important to recognize that according to Theorem 1, two straight lines cannot intersect in more than one point and Theorem 2 states that vertical angles, which are the angles opposite each other when two lines intersect, are equal. All this supports the fact that if the lines intersect in such a way to form 4 right angles, they are indeed perpendicular.
13 tenths plus 8 tenths plus 32 hundredths <,> =,to 2.42
Give 9.7814 correct to the nearest whole number
Final answer:
9.7814 rounded to the nearest whole number is 10, as the first digit after the decimal point is 7, which requires rounding up.
Explanation:
To find the nearest whole number to 9.7814, we need to look at the first digit after the decimal point. Since this digit is 7 (which is equal to or greater than 5), we round up the number. Rounding up changes 9.7814 to the next whole number, which is 10.
The general rule for rounding to the nearest whole number is:
If the first decimal place is 5 or greater, round up.If the first decimal place is less than 5, round down.Therefore, 9.7814 rounded to the nearest whole number is 10.
The equation of line KL is y=-1/2x-6. The equation line WX is 7x-14y=-42. Rewrite the equation of line WX in slope-intercept form and determine if the two lines are parallel.
The equation of line WX in slope-intercept form is,
⇒ y = 1/2x + 3
And, Lines WX and Kl are not parallel lines because its slopes are not equal to each other.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation of line KL is,
⇒ y = - 1/2x - 6.
And, The equation line WX is,
⇒ 7x - 14y = - 42
Now,
The equation of line WX in slope-intercept form is,
⇒ 7x - 14y = - 42
⇒ 7x + 42 = 14y
⇒ 14y = 7x + 42
⇒ y = 7x/14 + 42/14
⇒ y = 1/2x + 3
Hence, Slope of equation of line WX is,
⇒ y = 1/2x + 3
⇒ dy/dx = 1/2
⇒ m = 1/2
And, Slope of equation of line KL is,
⇒ y = - 1/2x - 6
⇒ dy/dx = - 1/2
⇒ m = - 1/2
We know that;
Slopes of parallel lines are equal.
Hence, Lines WX and Kl are not parallel lines because its slopes are not equal to each other.
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y times 6 for y = 2/3
Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 5(x + 8)2(x - 8)3
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3
B. -8, multiplicity 2; 8, multiplicity 3
C. -8, multiplicity 3; 8, multiplicity 2
D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1
The given polynomial has roots -8 with multiplicity 2 and 8 with multiplicity 3. Hence option B is correct.
Use the concept of polynomial defined as:
An expression that contains exponents, variables, and constants that is combined using mathematical operations such as addition, subtraction, multiplication, and division is known as a polynomial.
The given polynomial is:
f(x) = 5(x + 8)²(x - 8)³
To find its root equate this polynomial to 0.
Then,
5(x + 8)²(x - 8)³ = 0
(x + 8)²(x - 8)³ = 0
(x + 8)(x + 8)(x - 8)(x - 8)(x - 8) = 0
Therefore,
x = -8, -8, 8, 8, 8
Hence,
It has root -8 with multiplicity 2 and 8 with multiplicity 3 which is option B.
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The complete question is:
Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 5(x + 8)²(x - 8)³
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3
B. -8, multiplicity 2; 8, multiplicity 3
C. -8, multiplicity 3; 8, multiplicity 2
D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1
What is the prime factorization of 126
The prime factorization of the number 126 is 2,3,3, and 7.
What is prime factorization?Any number can be represented as a sum of prime numbers by prime factorization. A number with exactly two factors, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2,3, and 3.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the number is 126. The prime factorization of the number 126 will be calculated as:-
126 = 2 x 3 x 3 x 7
Hence, the prime factorization of the number 126 is 2,3,3, and 7.
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The hand on a clock shows 6:00pm what is the measure of the angle
Morgan calculated that he spent 305 minutes doing homework one week and 284 minutes doing homework the next week. How much more time did he spend doing homework the first week?
If h(x) = -3x - 10, find h(-3).
Answer
-1
2.3
-19
1
...?
XY is the perpendicular bisector of JK. which of the following statements must be true? check all that apply?
A. XY and JK form four right angles
B. P is the midpoint of XY
C. m
D. XP=YP
E.JP=KP
F. XY perpendicualr to JK
According to the properties of a perpendicular bisector, XY will form four right angles with JK, XY is perpendicular to JK, and it must bisect JK into two equal parts, making statements A, D, E, and F true.
Explanation:The question tells us that XY is the perpendicular bisector of JK. This tells us a few things about the relationship between the two lines and the points on them:
XY and JK form four right angles: Because XY is a perpendicular bisector, it intersects line JK at a 90° angle.XY perpendicular to JK: This simply restates that the angle formed by the intersection of XY and JK is a right angle.JP=KP: Perpendicular bisectors not only intersect the other line at a right angle, but they also bisect it, which means they cut it into two equal parts. Thus, point J is as far from the point of intersection as point K, making JP equal to KP.XP=YP: This is also a property of the perpendicular bisector. It means that the point of intersection P is the midpoint of XY, making segment XP equal to segment YP.The options regarding P being the midpoint of XY and the statement that includes an undefined variable 'm' were ignored due to lack of context.
Final answer:
The statements that must be true when XY is the perpendicular bisector of JK are: XY and JK form four right angles, P is the midpoint of XY, XP = YP, and XY is perpendicular to JK.
Explanation:
To determine which of the statements must be true, we need to understand the properties of a perpendicular bisector. A perpendicular bisector of a line segment is a line that divides the line segment into two equal parts and forms a right angle with the line segment.
From this definition, we can conclude that the following statements must be true:
A. XY and JK form four right angles - Since XY is the perpendicular bisector of JK, it forms a right angle with JK at each point of intersection.
B. P is the midpoint of XY - The perpendicular bisector passes through the midpoint of the line segment it bisects.
C. XP = YP - Since P is the midpoint of XY, XP and YP have equal lengths.
F. XY is perpendicular to JK - This is the definition of a perpendicular bisector.
Which of the following is the inverse of the function {(1,2),(3,4),(6,8)}
A. {(6,8),(3,4),(1,2)}
B. {(2,1),(4,3),(6,8)}
C. {(2,1),(4,3),(8,6)}
D. {(2,1),(3,4),(8,6)}
What is the solution of the equation?
4p/6+27=39
A. 22
B. 99
C. 4
D. 18
how to find a whole number in this question 4% of ... is 56?
In the formula A=\pi r^{2}, if the radius is 6 centimeters, what is the correct unit for the area of the circle?
A)\pi cm
B)cm^2
C)cm
D)cm^3
What number should be added to the expression x^2 + 2x to change it into a perfect square trinomial?
Write the standard form of the equation of the line that passes through the given points.
(5, 3) and (8, -2)
A fast food restaurant sells between 164 and 328 hamburgers per day. If the company profits $82.00 per 82 hamburgers sold, approximately how much does the company profit in one year from hamburgers?
PLZZZZZZ HELPPPP
Which equation shows the substitution method being used to solve the system of linear equations?
x – y = 7
x = y + 3
A.
(y + 3) – y = 7
B.
x = (7 – x) + 3
C.
x – (y + 3) = 7
D.
x – y = y + 3
What did the inventor of the 10 ton truck so often say
Answer:
This is an equation in which we have to find the slope of the line. We are supposed to draw the line for the two given points.
Step-by-step explanation:
The equation and the graph are solved as:
For graph One: B=(4,4)(1,2) for that m= 2/3. E=(2,0)(-4,4), for this m=-2/3. O=(1,-3)(-3,-4),m=1/4.for Second graph: I=(-1,-3)(2,3), m=2. E=(-4,-3)(-2,-1), m=-2. O=(-3,0)(-1,5),m=5/2. for the third graph:E=(0,2)(5,-1),m=-3/5. D=(5,6)(2,-1), m=7/3.L=(-5,2)(0,-3),m=-1.for the fourth graph: D=(0,0)(2,-6),m=-3. G=(4,5)(-2,4),m=1/6. S=(2,-3)(-5,-3), m=0.Now the Graphical data and the results are attached to the answer, given hope it helps out.
Assume the function has an inverse. Without solving for the inverse find the indicated function values: f(x)=x^3+4x-1, (a) f^-1 (-1) (b) f^-1 (4) ...?
To find the indicated function values of the inverse of a function, substitute the given values into the original function and solve for x.
Explanation:To find the indicated function values of the inverse of the function f(x)=x^3+4x-1, without solving for the inverse function, we substitute the given values into the original function and solve for x.
(a) To find f^-1(-1), we substitute -1 into the function: f(-1)=(-1)^3+4(-1)-1 = -1+(-4)-1 = -6.
(b) To find f^-1(4), we substitute 4 into the function: f(4)=(4)^3+4(4)-1 = 64+16-1 = 79.
the formula for finding the area of a circle is a equals pi r square. solve the formula for r.
A sneaker store salesman had $4,125 in total monthly sales last month. He made $165 in commission from those sales. What is the salesman's commission as a percent of his total monthly sales? Enter your answer in the box. %
Answer:
Salesman's commission 4% of total monthly sales.
Step-by-step explanation:
A sneaker store salesman had $4,125 in total monthly sales last month.
He made $165 in commission from those sales.
Suppose, it is x% of the total sale.
So, x% of $4125 will be,
[tex]=4125\times \dfrac{x}{100}[/tex]
According to the question it is equal to $165, so
[tex]\Rightarrow 4125\times \dfrac{x}{100}=165[/tex]
[tex]\Rightarrow x=\dfrac{165\times 100}{4125}[/tex]
[tex]\Rightarrow x=\dfrac{16500}{4125}[/tex]
[tex]\Rightarrow x=4\%[/tex]
Therefore, salesman's commission 4% of total monthly sales.
Answer: 4%
Step-by-step explanation:
Due to the fact that the salesman had $4,125 in total monthly sales the previous month, the answer would be 4%
How many millimeters are in 50 centimeters?
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The formula for rate is r=d/t . Solve for d.
Does antibiotics help kill the common cold??
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Dayla earns $108.75 for working 15 hours of holiday open rap at this rate how much money will see you earn if she works 18 hours the next week explain
graph the equation. y = 4x - 3
The width of a square-based storage tank is 3m less than its height. The tank has a capacity of 20 m3. If the dimensions are integer values in metres, what are they?