Answers
For the given diagram, it has been proved that angle A is congruent to angle B.
Given Information:
Angle A and Angle B are such that,
Ray AC ║ Ray BE
Ray AD ║ Ray BF
Proof:
Since a straight line is the shortest line connecting two points in a plane,
Extend ray AD and ray BE, such that both intersect at point G.
Now, since, angle A and angle 1 both make corresponding angles,
∠A = ∠1 .......... (1)
Ray ADG is parallel to the ray BF.
Thus, again, angle B and angle 1 make corresponding angles,
∠B = ∠1 ............ (2)
From (1) and (2), as per transitive relationship of angles,
∠A ≅ ∠B
Hence proved.
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Related Questions
Find parametric equation for the tangent line to the curve given by x(t)=e^-t cos(t), y(t) =e^-t sin(t), z(t)=e^-t and point p(1,0,1)
Answers
The parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.
For this question,
The curve is given as
x(t)=e^-t cos(t),
y(t) =e^-t sin(t),
z(t)=e^-t
The point is at (1,0,1)
The vector equation for the curve is
r(t) = { x(t), y(t), z(t) }
Differentiate r(t) with respect to t,
x'(t) = -e^-t cos(t) + e^-t (-sin(t))
⇒ x'(t) = -e^-t cos(t) - e^-t sin(t)
⇒ x'(t) = -e^-t (cos(t) + sin(t))
y'(t) = - e^-t sin(t) + e^-t cos(t)
⇒ y'(t) = e^-t ((cos(t) - sin(t))
z'(t) = -e^-t
Then, r'(t) = { -e^-t (cos(t) + sin(t)), e^-t ((cos(t) - sin(t)), -e^-t }
The parameter value corresponding to (1,0,1) is t = 0. Putting in t=0 into r'(t) to solve for r'(t), we get
⇒ r'(t) = { -e^-0 (cos(0) + sin(0)), e^-0 ((cos(0) - sin(0)), -e^-0 }
⇒ r'(t) = { -1(1+0), 1(1-0), -1 }
⇒ r'(t) = { -1, 1, -1 }
The parametric equation for line through the point (x₀, y₀, z₀) and parallel to the direction vector <a, b, c > are
x = x₀+at
y = y₀+bt
z = z₀+ct
Now substituting the (x₀, y₀, z₀) as (1,0,1) and <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get
x = 1 + (-1)t
⇒ x = 1 - t
y = 0 + (1)t
⇒ y = t
z = 1 + (-1)t
⇒ z = 1 - t
Hence we can conclude that the parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.
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HELP! A city pays a manufacturing company to produce more stop signs for the city due to an increase in traffic incidents at intersections. After doing some research, the company manager reads that a standard stop sign is a regular octagon that is 30 inches wide and 30 inches tall.
Answers
The apothem is 15 inches, the perimeter is calculated to be 99.41 while the area is given as 745.59
How to solve for the octagonThe side of the octagon is given by x inches
the interior side of the angles can be gotten by:
8-2 * 180 / 8 sides
= 135
We have to find the value of the angles
<abc = 180 - 135 = 45 degree
<acb = 180 - 135 = 45 degrees
x² = 2AB²
AB = x/√2
30 = x/√2 + x + x/√2
x = 30 / 1 + √2
The apothem = 30 / 2
= 15
perimeter = 8x
= 8(30 / 1 + √2)
= 99.4 inches
area = 0.5 x 15 x 99.4
= 745.59
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what is 5/8 divided by 1/2?
Answers
Answer:
5/4
Step-by-step explanation:
(5/8)(2/1)
(Reciprocal of 1/2 is 2/1 as shown above)
(5)(2)/(8)(1)=10/8
10/8=5/4
Let f (x) be a polynomial function with a zero of multiplicity of 1 at 2 and a zero of multiplicity of 2 at 1. Let g(x) be the radical function g of x equals the cube root of x minus 2 Part A: Using the Factor Theorem, determine the polynomial function f (x) in expanded form. Show all necessary calculations. (5 points) Part B: Let h (x) be the piecewise defined function of h of x is the piecewise function of f of x if x is less than 0 and g of x if x is greater than or equal to 0 Are there any breaks in the domain of h (x)? Explain why or why not. (5 points)
Answers
The polynomial functions in their expanded form is given as follows. It is right to state that there are no breaks in the domain of h(x).
What is a polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
For instance, the polynomial 3x+4 has an exponent of 1.
Part A: F(x) has zero at 2 and multiplicity of 1; and
1 at the multiplicity of 2
f(x) = x-2) (x-1)²
= (x-2) (x² - 2x + 1)
= x³ - 4x² + 5x -2
Part B: h (x) = [tex]\left \{ {{x^3 -4x^2 + 5x -2; X < 0} \atop {\sqrt[3]{x-2} ; X\geq 0 }} \right.[/tex]
The domain of X is X ∈ R
Hence it is correct to state that there are no breaks in the domain of h(x).
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Geometry: Write a formal proof, ASAP!!!
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
As we can see in the figure, lines m and n are parallel to each other. so we can apply Angle pair properties ~
So,
[tex]\qquad \sf \dashrightarrow \: \angle1 \cong \angle2[/tex]
[ they form corresponding angle pair ]
and it's given that :
[tex]\qquad \sf \dashrightarrow \: \angle2 \cong\angle 3[/tex]
therefore, by using above information. we can conclude that :
[tex]\qquad \sf \dashrightarrow \: \angle1 \cong \angle3[/tex]
PLEASE HELP!!
Find the value of the following expression:
(2^8 ⋅ 5^−5 ⋅ 19^0)^−2 ⋅ (5^-2/2^3)^4 ⋅ 2^28
Write your answer in simplified form. Show all your steps.
Answers
Answer:
25
Step-by-step explanation:
Cancel out 19^0, then exponentiate and simplify by multiplying exponents. Then simplify the terms. This leaves you with 2^-16*5^10*5^-8*2^16 which equals 5^2 which is 25
Use interval notation to express the set of real numbers x that satisfies the inequality (x+2)(x-5) < 0.
Answers
The interval notation to express the set of real numbers x that satisfies the given inequality is -2<x<5. You also can represent it as (-2,5)
Inequality
It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).
The solutions for inequalities can be given by: a graph in a number line or numbers.
For solving this exercise, it is necessary to find a number solution for the given inequality.
First, you should find the critical points of the inequality.
x+2=0
x = -2
and
x-5=0
x=5
Write, the intervals in between critical points. Therefore, -2<x<5.
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Jaquelyn wants to start getting to school on time more often. She is looking at some of her habits.
On Monday, she is late twenty percent of the time.
When she is late on Monday, she is late on Tuesday 60% of the time.
When she is not late on Monday, she is late on Tuesday 20% of the time.
What is the approximate probability that Jaquelyn will be late on Tuesday, given she was late to school on Monday?
Answers
Given that Jaquelyn was tardy on Monday, there is a 12 percent chance she will be late on Tuesday as well.
What is the Probability?
How likely it is that a stated event would occur is assessed using probability. The event would have a probability of 1 if it happened with certainty. The probability of an occurrence would be zero if it were absolutely guaranteed that it would not occur.
As getting late on Monday and Tuesday are independent events, their probabilities can be multiplied.
So the probability of getting late on Tuesday, given she was late to school on Monday = Probability of being late on Monday x Probability of she being late on Monday and she is late on Tuesday 60% of the time.
= 0.2 x 0.6
= 0.12
Thus the approximate probability that Jaquelyn will be late on Tuesday, given she was late to school on Monday will be 0.12
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A portion of the quadratic formula proof is shown. Fill in the missing statement ( the last answer choice is (x + b/2a = + b^2-4ac/a)
Answers
Answer:
[tex]x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac}}{2a}[/tex]
Step-by-step explanation:
So when it says simplify the right side, all it's doing is distributing the square root across division.
So when we distribute the square root we get the fraction
[tex]\frac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}[/tex]
And it's important to know that you cannot distribute the square root across addition/subtraction, but you can with multiplication.
There's a radical identity that states: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex] and this works both ways, so we can use this to combine like radicals or separate them into multiple. In this case we can separate the square root of 4a^2 into two radicals
[tex]\frac{\sqrt{b^2-4ac}}{\sqrt{4} * \sqrt{a^2}}[/tex]
And from here it's pretty easy to see that the square root of 4 is 2, and the square root of a^2 is a, since the square exponent and square root just cancel out.
So we get the following expression on the right side
[tex]\frac{\sqrt{b^2-4ac}}{2a}[/tex]
Three lorries each making five trips per day transport 2500 crates from a factory to a distributor in two days .how many lorries each making 6 trips a day are needed to transport 10000 such crates in a day
Answers
Step-by-step explanation:
3×5×2 = 30 lorry trips to deliver 2,500 crates.
3 lorries, 5 trips per day, 2 days
that means that one lorry trip transports
2,500 / 30 = 250/3 = 83.33333... crates = 83 1/3 crates.
now we need x lorries each making 6 trips per day in 1 day (so, 6 trips, period) to transport 10,000 crates.
that looks like
x × 6 × 83.33333... = 10,000
x × 6 × 83 1/3 = 10,000
x × (6×83 + 6 × 1/3) = 10,000
x × (498 + 2) = 10,000
500x = 10,000
x = 20
so, we need 20 lorries each doing 6 trips in one day to transport 10,000 crates in one day.
these are altogether 20×6 = 120 lorry trips.
that is 4 times the number of the original scenario (30 trips).
and logically, when doing 4 times the work, we achieve 4 times the result (10,000 crates instead of 2,500).
A square pyramid has a height of 6 units and a volume of 70 units3. if a square prism has the same base area and volume as the square pyramid, what is its height?
Answers
The height is 2 units.
What is a square pyramid?In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a polyhedron with three or more triangle faces that meet above its base. A square pyramid is a pentahedron, a three-dimensional form with a total of five faces.Find the area of the base of the square pyramid:
The volume of the square pyramid is equal to [tex]V=\frac{1}{3} BH[/tex]
B is the area of the base, and H is the height of the pyramid
[tex]H= 6 units[/tex]
[tex]V=70 units^{3}[/tex]
Solve: B
[tex]70=\frac{1}{3} B(6)\\ \\ B=\frac{70}{2} \\ \\ = 35units[/tex]
To find the height of the square prism:
The volume of the square prism is equal: [tex]V=Bh[/tex]
B is the area of the base and h is the height of the prism
[tex]B=35 units^{2}[/tex]
[tex]V=70units^{3}[/tex]
Solve: h
[tex]70=\frac{35}{h}[/tex]
[tex]h=2units.[/tex]
The height is 2 units.
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The height of the square pyramid exists 2 units.
How to estimate the area of the base of the square pyramid?Volume of the square pyramid
[tex]$V = \frac{1}{3}BH[/tex]
where B exists in the area of the base H lives at the height of the pyramid
we have H = 6 [tex]$$unit^3[/tex]
V = 70 [tex]$$unit^3[/tex]
substitute in the formula and solve for B, we get
[tex]$70 = \frac{1}{3}B(6)[/tex]
B = [tex]$\frac{70}{2}[/tex]
= 35 [tex]$$unit^3[/tex]
To estimate the height of the square prism
Volume of the square prism = Bh
Where B exists the area of the base
h exists the height of the prism
we have B = 35 and V = 70
substitute in the formula and solve for h
70 = (35)h
h = 2 units.
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Determine which of the following graphs does not represent a function
Answers
Explanation:
Assuming there are four answer choices, we can eliminate choices A through C because they are functions. This is because they pass the vertical line test.
The vertical line test is where we try to draw a single vertical line through more than one point on the curve. If such a task is possible, then it is said to "fail the vertical line test" and it's not a function.
For choice A, we cannot draw a single vertical line through more than one point on the parabola. Choice A passes the vertical line test. Hence, it is a function. The same goes for choices B and C.
Unfortunately choice D is not shown, but if it's the only thing left, then I'm assuming that it's some curve that fails the vertical line test.
The model of a trinomial is shown.
An algebra tile configuration. 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x, the 2 tiles below + x squared are labeled + x, and the 14 tiles below the negative x tiles are labeled negative.
What are the factors of the trinomial? Select two options.
x – 14
x + 7
x – 7
x – 2
x + 2
Answers
The factors of the trinomial based on the information given include:
C. x – 7
E. x + 2
What is a trinomial?It should be noted that a trinomial is an algebraic expression that has three non-zero terms. Here, the examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z. Also, 2a² + 5a + 7 is a trinomial in one variables.
In this case, the algebra tile configuration has 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x. Here, the trinomial is x² - 5x - 14.
The factors will be:
x² - 5x - 14.
x² + 2x - 7x - 14
x(x + 2) - 7(x + 2)
= (x + 2)(x - 7)
A polynomial with three terms is called a trinomial.
In conclusion, the correct options are C and E.
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Explain the conceptual and quantitative relationships between alpha risk and beta risk when testing hypotheses, and include the impact sample size plays in managing these risk levels
Answers
The conceptual and quantative relationship between Alpha risk and Beta risk is related to the probability of accepting Null hypothesis. They are also known as Type 1 and type 2 error.
Alpha Risk:
Alpha risk is the risk that in statistical test a null hypothesis will be rejected when it is actually true. This is also known as a type I error, or a false positive. The term risk refers to chance or likelihood of making an incorrect decission.
Beta risk:
Beta risk represents the probability that a false hypothesis in a statistical test is accepted as true. Beta risk contrast with alpha risk, which measures the probability that a null hypothesis is rejected when it is actually true.
Determining the type of risk in a quantitative relationship is primarily based on sample size. The Sample Size directly affect the Alpha and Beta risk. If Sample size is larger, the Alpha and Beta risk will lower, and if the sample size is lower the risk of Beta and Alpha increases.
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Which type of sediment deposit has an average rate of deposition (per 1000 years) of 1 centimeter (0.4 inch)?
Answers
The sediment deposit that has an average rate of deposition
(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.
Given that average rate of deposition is per 1000 years of 1 centimeter.
We are required to find the type of sediment deposit that has an average rate of deposition (per 1000 years) of 1 centimeter.
Biogenic ooze, which is also called biogenic sediment, is any pelagic segment that contains more than 30 percent skeletal material. These sediments can be made up of either carbonate ooze or siliceous ooze.
In plagic sediments feldspar is obtained from local volcanic sources, whereas quartz may be introduced from the continents by wind,upsetting simple patterns.A large number of accessory minerals occur in shales.
Hence if the sediment deposit that has an average rate of deposition
(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.
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A building has 63 apartments and 70 bathrooms. What is the ratio of apartments to bathrooms in the building?
Answers
Answer:
63:70
Step-by-step explanation:
The ratio of apartments to bathrooms in the building is 9:10.
Given that, a building has 63 apartments and 70 bathrooms.
The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
The ratio of apartments to bathrooms is 63:70
= 9:10
Therefore, the ratio of apartments to bathrooms in the building is 9:10.
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Someone help me please
30-60-90 triangles
Answers
Answer:
Short leg = 10
Longer leg = 10[tex]\sqrt{3}[/tex]
Hypotenuse = 20
Step-by-step explanation:
The given is a special right triangle, its angle measures are as follows:
30-60-90 and the side lengths will follow as:
x, x[tex]\sqrt{3}[/tex], 2x respectively.
The length of hypotenuse (sees angle measure 90) is represented with 2x and it's given as 20
We can conclude x = 10 from this
So the length of short leg is 10
Then the length of longer leg is 10[tex]\sqrt{3}[/tex]
The length of hypotenuse is already given as 20
Mrs. Greenaway has decided to open a new preschool in her town. To decide whether she will have enough students to be successful, she hires a researcher to conduct a survey of the town’s population. Which of the following groups would make up the best sample for this survey?
A. parents of preschool children
B. parents of elementary school children
C. registered voters in the town
D. members of the town council
Answers
The answer choice which represents the group which makes up the best sample for the researcher's survey as described in the task content is; Choice A; Parents of preschool children.
Which answer choice best represents a sample for the intended survey by Mrs Greenaway's researcher?It follows from the task content that; Mrs. Greenaway has decided to open a new preschool in her town.
The need for a researcher therefore arises from the decision to either open the preschool or not.
Consequently, in a bid to choose a sample, Mrs. Greenaway's researcher must make sure the sample chosen is from the population space.
Therefore, answer choice A represents the correct sample.
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PLEASE HELP
debra has $5. She bought 3 cakes of the same price and has 0.80$ left. what is the pride of 1 cake.
Answers
Answer:
$1.40
Step-by-step explanation:
5.00-0.80=4.20
4.20 ÷ 3= 1.40
What is this? PLEASE LOOK BELOW.
Answers
Answer:
Trapezoidal prism
Step-by-step explanation:
As long as only two sides of two of the faces are parallel, and the other four faces have two sets of parallel sides, this is a trapezoidal prism.
Answer:
it is a Trapezoidal prism
Select the correct answer.
What is the exact value of cos 105°?
A √6-√2
B. √6 + √2
с. V2 - V6
D. -√2+√6
Answers
The exact value of cos 105° is equals to √2/4 - √6/4.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
In this case, 105 degrees, can be split into 45+60 (cos (45+60))
Use the sum formula for cosine to simplify the expression;
cos (A+B) = - (cos (A) cos (B) + sin (A) sin (B)).
The exact value of cos(60) is 1/2.
So, multiply 1/2 to cos (45) - sin (60) times sin (45).
The exact value of cos (45) is the square root of 2 over 2
(1/2) ⋅ (√2/2) - sin (60) ⋅ sin (45)
The Value of sin (60) is √3/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ sin (45)
The exact value of sin (45) is √2/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ √2/2
Therefore, The exact value of cos 105° is equals to √2/4 - √6/4.
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The variables x and y vary directly. If one pair of the values is x = 3 and y = 12, write an equation that shows the relationship between x and y.
A. y = 4x
B. x/y = 4
C. y = x/4
D. x = 4y
Answers
Given the system of equations, what is the solution? x 2y = 11 x - 2y = -1 {(-5, -3)} {(1, 1)} {(5, 3)}
Answers
Answer:
{(5, 3)}
Step-by-step explanation:
Consider the system :
x + 2y = 11
x - 2y = -1
We notice that :
5 + 2×3 = 11
5 - 2×3 = -1
We conclude that :
(5, 3) is the solution to the system.
A house and a lot are worth $210,000. If the house is worth 6.5 times as much as the lot, find out how much each are worth.
Answers
Answer:
H:182000
L=28000
Step By Step
H=House
L=Lot
H+L=210000
H(6.5)=L
L+(L(6.5)=210000
L=28000
28000(6.5)=H
H:182000
On average, mary has noticed that 18 trains pass by her house daily (24 hours) on the nearby train tracks. what is the probability that exactly 1 train will pass her house in a 3 hour time period?
Answers
The probability that exactly 1 train will pass Mary's house is 0.00889.
According to the given question.
On average, 18 trains pass by Mary's house daily i.e. in 24 hours.
As, we know that "Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event".
Therefore,
The probability that exactly one train will pass Mary's house in a 3 hour period
= [tex]\frac{^{18C_{1} } }{^{24} C_{3} }[/tex]
[tex]= \frac{\frac{18!}{1!\times17!} }{\frac{24!}{3!\times 21!} }[/tex]
[tex]= \frac{18}{\frac{24\times23\times22}{3\times2\times1} }[/tex]
[tex]=\frac{18}{8\times23\times\ 11}[/tex]
= 18/2024
= 0.00889
Hence, the probability that exactly 1 train will pass Mary's house is 0.00889.
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Please help!! due in 2 hours!!
Answers
Answer:
i think 80 copies
Step-by-step explanation:
Use the drawing tool(s) to form the correct answers on the provided number line. plot the value(s) on the number line where this function is equal to zero: f(x) = (x 5)(x − 1).
Answers
Plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.
What is a parabola?A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.To plot the value(s) on the number line where the given function is equal to zero:
The equation is written as: y = (x+5)(x-1)
This is further written as:
(x+5)(x-1) = 0 and x+5 = 0x- 1 = 0Giving x = -5 and x = 1.The highest point occurs when x = 0, which is (5)(-1) = -5
Therefore, plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.
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The correct question is given below:
Use the drawing tool(s) to form the correct answers on the provided number line. plot the value(s) on the number line where this function is equal to zero: f(x) = (x + 5)(x − 1).
30 POINTS TO WHO EVER ANSWER THIS QUESTION!!!!
Answers
Explanation:Since these are similar triangles it means each contrasting side length has a ratio and the ratio for the side lengths is 1:3 based on 4:12 so you would multiple the side length of Db times 3 to find Ed and your answer is 15
Please Help its a math question i will mark brainlist !! plsss look at attached image below ...blessings
Answers
Answer:
-2
Step-by-step explanation:
Every point would flip over the y axis the same distance it is from the y axis now, but just on the other side of the y axis.
In the original equation, when y = 0, x is 2, so when we flip it over the y axis, it is now at -2 when y = 0.
Carly takes three steps to walk the same distance as jim walks in four steps. each of carly’s steps covers 0. 5 metres. how many metres does jim travel in 24 steps?
Answers
The distance travelled by Jim in 24 step is 9 miles by unitary method.
According to the given question.
The number of steps travelled by Jim = 24
Also, it is given that "Carly takes three steps to walk the same distance as Jim walks in four steps".
Therefore, by unitary mehod we can say that
The number of steps walked by Carly = 3 × (24/4) = 3 × 6 = 18
So, the distance travelled by Carly in 18 steps
= 18 × 0.5miles
= 9 miles
Since, the Carly's 18 steps is equals to Jim's 24 steps.
Therefore, the distance travelled by Jim in 24 step is 9 miles.
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