Answers
Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.
By being congruent, the corresponding angles and sides are equal.
Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].
By using [tex]\angle A = \angle F[/tex]
So, [tex]100^\circ = \angle 1[/tex]
Therefore, the measure of angle 1 is 100 degrees.
So, Option B is the correct answer.
Related Questions
I am first going to try finding the tangent line at this point:
Take the derivative:
dy/dx = (3x^2 - e^x)/2y
Solve using (0, 1)
dy/dx = (0 - 1)/6 = -1/6
I believe that -1/6 is the slope of the tangent line, so the slope of the normal line should be +6, right?
Answers
[tex]e^x-x^3+y^2=10[/tex]
[tex]y^2=x^3-e^x+10[/tex]
Take the derivative of both sides.
[tex]2y \dfrac{dy}{dx} = 3x^2-e^x [/tex]
[tex]\dfrac{dy}{dx}= \dfrac{3x^2-e^x}{2y}[/tex]
Plug in (0, 3) and you get -1/6.
The derivative of a function at a certain point is the slope of the tangent of that point.
This is because the derivative is supposed to represent the rate of change for the function, and the slope of a line represents a constant rate of change. The rate of change of a function at a certain point is constant, so a line can be used to represent it. This line is the tangent line.
It is a property of perpendicular lines to have slopes that are negative reciprocals of another. The negative reciprocal of -1/6 is 6, so you are correct.
The slope of the normal is 6.
A bag contains 5 5 green marbles, 10 10 yellow marbles, 4 4 red marbles. two marbles are drawn without replacement which means that once the first marble is selected it is not put bag into the bag. it is not replaced. what is the probability of drawing a green marble then a red marble?
Answers
Number of green marbles = 5
Number of red marbles = 4
P(Green, then red) = (4/19)(5/18) = 5/28
Answer: 5/28
An item that originally cost $100 is decreased by 8%. The reduced price is then increased by 8%.
The resulting price is _____.
Answers
100 x 0.08 = 8
100-8 = 92 ( reduced price )
now multiply reduced price by 8% and add:
92 x 0.08 = 7.36
92 + 7.36 = $99.36
Answer:
The resulting price is $99.36.
Step-by-step explanation:
Original cost of the item = $100
The decrease percentage is 8% or 0.08
So, the reduced price becomes :
[tex]100-(0.08\times100)=92[/tex] dollars
Now again the reduced price is increased by 8%.
So, multiplying the reduced price by 8% and adding it again we get;
[tex]92+(0.08\times92)[/tex] =$99.36
So, the resulting price is $99.36.
Haley measured the distances between her house and two of her friends' houses. ellen's house is 1.41 miles away from haley's, and dirk's house is 6,547 feet away from haley's. whose house is farther away from haley's, and how many feet farther away is it, to the nearest whole foot?
Answers
H = Haley's house
E= Ellen's house
D = Dirk's house
In the figure below we can see the representation of this problem.
Given that there are two measurements with different units, namely, the distance between Haley and Ellen's houses is in miles and the distance between Haley and Dirk's houses is in feet, we need to convert one of these units.
As the final question demands which house is farther away from Haley's, we will convert the distance between Haley and Ellen's houses from miles to feet, so:
[tex]1mi = 5280ft[/tex]
[tex]1.41mi(\frac{5280ft}{1mi}) = 7444.8ft[/tex]
So:
The distance between Haley and Ellen's houses = [tex]7444.8ft[/tex]
The distance between Haley and Dirk's houses = [tex]6547ft[/tex]
Then Ellen's house is farther away from haley's, and the nearest whole foot is:
[tex]7444ft[/tex]
Answer: Ellen's house is farther away by 898 feet.
Step-by-step explanation:
Given: The distance between Haley's house and Ellen's house = 1.41 miles
We know that 1 mile = 5,280 feet
Then, [tex]1.41\text{ miles}=1.41\times5,280\text{ feet}=7,444.8\text{ feet}[/tex]
The distance between Haley's house and Dirk's house = 6,547 feet
Clearly, 6,547<7,444.8
And [tex]7444.8-6547= 897.8\approx898[/tex]
Therefore, Ellen's house is farther away by 898 feet.
How to find all values of x where the tangent line is horizontal?
Answers
To find x-values where a function's tangent line is horizontal, find the derivative, set it to zero, and solve for x considering any function's restriction.
Explanation:To find all the values of x where the tangent line is horizontal, we need to understand that these are the points where the derivative of the function is zero. This is because the derivative of a function at a point gives us the slope of the tangent line at that point. And, for a line to be horizontal, its slope needs to be zero.
So, to find these values:
Find the derivative of the given function. Set this derivative equal to zero.Solve the equation for x.The solutions will give you the x-values where the tangent line is horizontal. Do note that you need to be aware of the domain and any restrictions of the original function to have valid solutions.
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jen is thinking of a number. the product of this number and 3.4 is 176.8. find jens number.
Answers
The product of the number and 3.4 is 176.8, so we can write the equation as:
3.4x = 176.8
Dividing by 3.4 on both sides, we get:
x = 52
Thus, Jen is thinking of 52 as his number
Let the unknown number equal X. We are given that the product of X and 3.4 is equal to 176.8. The term "product" implies the use of multiplication. With this knowledge, we can represent the problem using the following formula:
3.4x = 176.8
Now divide both sides of the equation by 3.4:
x = 52
We have now proven that Jen is thinking of the number 52.
I hope this helps!
Techechtium-99m has a half-life of 6 hours. If 1000mg is in use, in how many hours will 62.5mg remain?
Answers
One half life 500 mg to 500/2 = 250 mg
One half life 250 mg to 250/2 = 125 mg
Etc .......
Techechtium-99m has a half-life of 6 hours. It will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
Explanation:To determine how many hours it will take for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg, we can use the concept of half-life.
Techechtium-99m has a half-life of 6 hours, which means that after every 6 hours, half of the initial amount will decay.
So, to find the number of half-lives required to reach 62.5 mg, we can divide the initial amount by the remaining amount:
1000mg / 62.5mg = 16.
Since each half-life is 6 hours, we can multiply the number of half-lives by 6 to find the total number of hours:
16 x 6 = 96.
Therefore, it will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
n circle A shown below, m Arc BC is 61° and m Arc EF is 76°: Points B, C, E, F lie on Circle A. Lines BE and CF pass through point D creating angle EDF. Measure of arc BC is 61 degrees and What is m∠FDE?
Answers
m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°
So the answer is 68.5°
Answer:
The correct answer is 68.5°
The calculated result of the angle FDE is 68.5°. Whenever two chords cut across a circle, the resulting angle is equivalent to half of the sum of the measurements of the arc the angle intersects and that which the angle vertical to the first angle intercepts.
m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°
Give Brainliest if you please
Help me please.
Luke Skywalker's height is 68 inches. The mean height for all Jedi is 66.5 inches and the standard deviation of the Jedi heights is 2.4 inches. What is the z score for Luke Skywalker's height?
Round to the nearest thousandth
Answers
[tex]z=\frac{x-\mu }{\sigma }=\frac{68-66.5}{2.4}=0.625[/tex].
The z-score is 0.625.
The z-score for Luke Skywalker's height is 0.625, indicating that his height is 0.625 standard deviations above the mean.
Z-score Formula: The z-score for Luke Skywalker's height can be calculated using the formula: z = (x - μ) / σ, where x is the individual's height, μ is the mean height, and σ is the standard deviation.
Plugging in the values, we get z = (68 - 66.5) / 2.4 = 0.625 (rounded to the nearest thousandth).
Suppose two fair six-sided dice are rolled. what is the probability that they will both come up with the same number?
Answers
The measure of an angle is two times the measure of a supplementary angle. what is the measure of each angle
Answers
Let 2x = 180-x.
Then 3x = 180, and x = 60. One angle is 60 degrees and the other is 180-60, or 120, degrees.
Answer:
60 and 120 have a good day!
Step-by-step explanation:
Which represents a quadratic functionWhich represents a quadratic function? f(x) = 2x3 + 2x2 – 4 f(x) = –7x2 – x + 2 f(x) = –3x + 2 f(x) = 0x2 + 3x – 3
Answers
Answer:
[tex]f(x) = -7x^2 -x +2[/tex] represents a quadratic function.
Step-by-step explanation:
A polynomial of degree two is called quadratic function,
Also, degree of polynomial is the highest power of its monomial ( individual term with non zero coefficient ),
Since, [tex]f(x) = 2x^3 + 2x^2 -4[/tex] has degree 3,
⇒ [tex]f(x) = 2x^3 + 2x^2 -4[/tex] is not a quadratic function,
[tex]f(x) = -7x^2 -x +2[/tex] has degree 2,
⇒ [tex]f(x) = -7x^2 -x +2[/tex] is a quadratic function,
[tex]f(x) = -3x+2[/tex] has degree 1,
⇒ [tex]f(x) = -3x+2[/tex] is not a quadratic function,
[tex]f(x) = 0x^2 + 3x -3[/tex] has degree 1,
⇒ [tex]f(x) = 0x^2 + 3x -3[/tex] is not a quadratic function,
A museum charges a school $200 to hold a trip + $2 entrance fee per person. The students must share the total cost of the trip equally include the entrance feee for 8 teachers. What is the function Y(x) that gives that gives the cost per X person attending the trip?
Answers
This is because 16 needs to be added to the base amount since the teachers cost is automatically added in.
The endpoints of one diagonal of a rhombus are (-5,2) and (1,6). If the coordinates of the 3rd vertexare (-6,10), what arethe coordinates of the 4th vertex?
A.(2,-2)
B.(-8,0)
C.(4,8)
D.(-9,8)
Answers
[tex]E\left(\dfrac{-5+1}{2};\ \dfrac{2+6}{2}\right)\to E\left(\dfrac{-4}{2};\ \dfrac{8}{2}\right)\to E(-2;\ 4)[/tex]
[tex]\vec{BE}=[-2-(-6);\ 4-10]=[4;\ -6][/tex]
[tex]D(x;\ y)\\\\\vec{ED}=[x-(-2);\ y-4]=[x+2;\ y-4]\\\\\vec{ED}=\vec{BE}\ therefore\\\\ \ [x+2;\ y-4]=[4;\ -6]\to x+2=4\ and\ y-4=-6\\\\x=2\ and\ y=-2\\\\Answer:\ \boxed{A.\ (2;\ -2)}[/tex]
Answer:
A. (2,-2)
Step-by-step explanation:
That is the right answer. Hope this helps!!!
There is an expression some people use that says, “What you put into it is what you get out of it.” People might use this expression to describe your skills at a sport or activity and how that relates to the amount of time and effort you spend practicing that activity. Does this expression apply to functions? How? Give an example to support your answer.
Answers
The phrase 'What you put into it is what you get out of it' applies to functions in mathematics, where given an value x (input) into a function, you get an output y. It also applies to real life examples, like sports practice, where your input of time and effort has a corresponding output of skill level.
Explanation:Yes, the expression “What you put into it is what you get out of it” can be applied in mathematics, particularly to functions. In mathematical context, this statement represents the fundamental concept of a function, where an input (what you put into it) mapped to an output (what you get out of it). For example, consider a linear function y = 2x + 3. The value of y (output) depends on the value chosen for x (input). Thus, if x = 2 (input), y = 7 (output). The output here is a result of the input 'fed' into the function.
The same idea can be extrapolated to functions in everyday life, such as practicing a sport. The input to the 'function' is the time and effort you put in, and the output is the proficiency you achieve. As with mathematical functions, each 'input' in life tends to have a corresponding 'output', reinforcing the idea of causes having effects.
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The expression 'What you put into it is what you get out of it' applies to functions such that what you put into the function (input) directly influences what you get out of the function (output).
Explanation:Yes, the expression 'What you put into it is what you get out of it' can indeed be applied to the concept of functions in mathematics. A function is a special relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. The input you 'put into' a function is the independent variable and the output or 'what you get out of' the function is the dependent variable.
As an example, consider an equation of a function like y = 2x. Here, 'x' represents the inputs and 'y' the outputs. If you 'put into' this function x = 3 (input), you 'get out of' the function y = 6 (output). Thus, what you 'put into' the function (input) directly influences what you 'get out of' the function (output), demonstrating the principle of 'What you put into it is what you get out of it'
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Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j
Answers
a.b = (6i + 5j).(-5i+4j)
a.b = 6(-5)+5(4)
a.b = -30 + 20
a.b = -10
The dot product results in a scalar quantity, so you only get a magnitude not a vector.
Answer:
-10
Step-by-step explanation:
took the test
Find the area of the rectangle below (3x-2) (4x-7)
Answers
-> 12x^2-21x-8x+14
= 12x^2 - 29x + 14
So the area of the rectangle would be 12x^2 - 29x + 14.
Hope this helps. If you have any questions, place it in the comment section below.
If and only if this assumption is correct, then the area is L * W, or
(3x-2)(4x-7) = 12x^2 -13x + 14.
Which sequence is modeled by the graph below? Coordinates are 1,1 2,2 3,4 4,8
Answers
1,1
2,2
3,4
4,8
The first point indicates the number of term and second points indicate the value of the term in the sequence.
So, the sequence we get is:
1, 2, 4, 8, ...
Notice that each term of the sequence is obtained by multiplying the previous term by 2. A sequence with such a relation is known as Geometric Sequence or a Geometric Progression (G.P)
Then the sequence is:
For the x-coordinate:1,2,3,4,5,6,7...
For the y-coordinate:1,2,4,8, which is 2^0,2^1,2^2,2^3... so there for the next y-coordinates are 16,32,64,128, ...
So the sequence is: 1,2,4,8,16,32,... 2^x.
What is the measure of the angle?
Answers
Measure of the angle=65°+90°=155°
We can conclude that the measure of the bigger angle in the picture is 155°
So the angle is 90 degrees + 65 degrees = 155 degrees
The fourth one is the answer
Wai recorded the length of each wire needed for a science project. What is the total length of wire needed?
Answers
we know that
the attached figure is a frequency table
Multiply each number of Length by its frequency
The product is the total amount for that value
Add the products
so
(1/8)*1+(1/4)*1+(1/2)*3+(3/4)*8+(1)*4+1 3/8*(2)
1 3/8----> 11/8
=(1/8)*1+(1/4)*1+(1/2)*3+(3/4)*8+(1)*4+11/8*(2)
=(1/8)+(1/4)+(3/2)+(6)+(4)+11/4
=(1+2+12+48+32+22)/8
=117/8-----> 14.625-----> 14 5/8 ft
the answer is
14.625 ft or 14 5/8 ft
Answer:
14 5/8
Step-by-step explanation:
multiply each number by it's frequency the product is the total value .
Solve the inequality. Graph the solution set.
2r−9≤−6
Answers
2r−9≤−6------> 2r ≤ -6+9-------> 2r ≤ 3-----> r ≤ 1.5
the solution is the interval (-∞, 1.5]
using a graph tool
see the attached figure
The first step to solving this inequality is to change the equation. We'll change the equation by adding plus nine to both sides of the equation. This will help us get 2r on its own.
Original Equation :
2r - 9 ≤ -6
New Equation {Added Plus 9 to Both Sides} :
2r - 9 + 9 ≤ -6 + 9
Now we'll simplify the equation by solving -9 + 9 and -6 + 9.
Old Equation :
2r - 9 + 9 ≤ -6 + 9
New Equation {Old Equation Simplified} :
2r ≤ 3
Once again we'll have to change the equation. We'll do this by adding divide both sides by two. This will give us the variable ( r ) on its own.
Old Equation :
2r ≤ 3
New Equation {Added Divide 2 to Both Sides} :
[tex] \frac{2r}{2} [/tex] ≤ [tex] \frac{3}{2} [/tex]
Now we simplify.
Old Equation :
[tex]\frac{2r}{2}[/tex] ≤ [tex]\frac{3}{2}[/tex]
New Equation {Old Equation Simplified} :
r ≤ [tex] \frac{3}{2} [/tex]
Now, that is, in fact, the solution but since I'm not sure which form you need, I've written it in other forms as well.
Solution → r ≤ [tex] \frac{3}{2} [/tex]
Decimal → 1.5
Interval Notation → [tex](-[/tex] ∞[tex], \frac{3}{2} )[/tex]
Below, I have also attached a graph that shows how this inequality should be graphed.
Hope this helps!
- Lindsey Frazier ♥
Am I correct in thinking that the answer to this derivative problem is B?
dy/dx = y/x^2
dy/y = dx/x^2
ln y * ln c = -1/x
cy = e^(-1/x)
y = ce^(-1/x)
Answers
dy/dx = x(1+y)
dy/(1+y) = x dx .... separate variables
int[dy/(1+y)] = int[x dx] ... apply integral to both sides
ln(1+y) = (1/2)x^2+C ... see note below
1+y = e^{(1/2)x^2+C}
1+y = e^C*e^{(1/2)x^2}
1+y = Ce^{(1/2)x^2}
y = Ce^{(1/2)x^2}-1
Answer is actually choice C (not choice B)
note: we would use absolute value bars for the natural log on the left side, but because y > -1, this means 1+y > 0. So there's no need to worry about if 1+y is negative
-----------------------------------------------------
Checking the answer:
y = Ce^{(1/2)x^2}-1
dy/dx = d/dx[ Ce^{(1/2)x^2}-1 ]
dy/dx = d/dx[(1/2)x^2]*Ce^{(1/2)x^2}
dy/dx = (1/2)*2x*Ce^{(1/2)x^2}
dy/dx = x*Ce^{(1/2)x^2} ... we get some messy expression
x*(1+y) = x*(1+Ce^{(1/2)x^2}-1)
x*(1+y) = x*Ce^{(1/2)x^2} .... we get the same messy expression as before
So this shows that dy/dx = x*(1+y) is a true equation for y > -1 and y = Ce^{(1/2)x^2}-1, which confirms the right answer.
Q: what is the complete factorization of the polynomial below x^3+4x^2-x-4?
A. (x+1)(x-1)(x+4)
B. (x-1)(x-1)(x-4)
C. (x+1)(x-1)(x-4)
D. (x-1)(x-1)(x+4)
Answers
The solution is Option A.
The factorized form of the polynomial equation A = x³ + 4x² - x - 4 is given by B = ( x + 1 ) ( x - 1 ) ( x + 4 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the factorized equation be represented as = B
Now , let the equation be A
The value of A is given by A = x³ + 4x² - x - 4
On simplifying the equation , we get
A = x³ + 4x² - x - 4
Taking x² as the common term in the first two terms of the equation ,
A = x² ( x + 4 ) - x - 4
The equation can be further simplified as
A = x² ( x + 4 ) - ( x + 4 )
Taking ( x + 4 ) as the common term in the first two terms of the equation ,
A = ( x² - 1 ) ( x + 4 )
Now , ( x² - 1 ) can be simplified as ( x + 1 ) ( x - 1 )
So , the value of B is
B = ( x + 1 ) ( x - 1 ) ( x + 4 )
Therefore , the value of B is ( x + 1 ) ( x - 1 ) ( x + 4 )
Hence , the factorized equation is ( x + 1 ) ( x - 1 ) ( x + 4 )
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what is the following product 3 sqrt 2(5 sqrt 6-7 sqrt 3)
Answers
Answer:
[tex](30\sqrt{3}-21\sqrt{6})[/tex]
Step-by-step explanation:
We have to find the product of the expressions.
[tex]3\sqrt{2}(5\sqrt{6}-7\sqrt{3})\\[/tex]
= [tex]3\sqrt{2}\times 5\sqrt{6}-7\sqrt{3}\times 3\sqrt{2}[/tex] ( By distributive rule)
= [tex]3\times 5(\sqrt{2})(\sqrt{6})-7\times 3(\sqrt{3})(\sqrt{2})[/tex]
= [tex]15\sqrt{12}-21\sqrt{6}[/tex]
= [tex]15\sqrt{4\times 3}-21\sqrt{6}[/tex]
= [tex]30\sqrt{3}-21\sqrt{6}[/tex]
= [tex](30\sqrt{3}-21\sqrt{6})[/tex]
New York City gift shop sells miniature Statue of Liberty sculptures that are 7.8 inches tall. the scale of the model to the actual statue is 1:232. what is the height of the actual statue to the nearest foot?
Answers
The base of a triangle is 15 centimeters and its height is 6 centimeters. What is the area of the triangle?
a.21 cm2
b.45 cm2
c.90 cm2
d.180 cm2 Submit
Answers
To calculate the area, multiply 15 and 6, then divide the product by 2.
15 × 6 = 90
90 ÷ 2 = 45
The area of this triangle is 45.
a garden patio is covered with grey slabs and yellow slabs. 1/5 is grey. 1/4 is yellow. there’s 55 slabs in total. what is the number of yellow slabs
Answers
Answer:
44
Step-by-step explanation:
1:4
4+1=5
55/5=11
11*4=44
the answer is 44
The dot product of u with itself is 12. what is the magnitude of u?
Answers
we know it's dot product is 12, thus
[tex]\bf \ \textless \ a,b\ \textgreater \ \cdot \ \textless \ a,b\ \textgreater \ \implies (a\cdot a)+(b\cdot b)\implies \boxed{a^2+b^2=12}\\\\ -------------------------------\\\\ ||\ \textless \ a,b\ \textgreater \ ||=\sqrt{a^2+b^2}\implies \sqrt{\boxed{12}}[/tex]
Answer: The magnitude of the vector u is √12 units.
Step-by-step explanation: Given that the dot product of a vector u with itself is 12.
We are to find the magnitude of the vector u.
Let <a, b> represents the vector u.
That is, u = <a, b>
Then, according to the given information, we have
[tex]u.u=12\\\\\Rightarrow <a, b>.<a, b>=12\\\\\Rightarrow a^2+b^2=12\\\\\Rightarrow \sqrt{a^2+b^2}=\sqrt{12}\\\\\Rightarrow |u|=\sqrt{12}.[/tex]
Thus, the magnitude of the vector u is √12 units.
(need help!) A dart is thrown at the board shown. It hits the board at a random point. Find the probability that it will land in the unshaded region. Round to the nearest percent.
20%
33%
17%
25%
Answers
[tex] |\Omega|=360\\
|A|=120\\\\
P(A)=\dfrac{120}{360}=\dfrac{1}{3}\approx33\% [/tex]
If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?
4/7 = 10/AC
7/4 = 10/AC
4/11 = 10/AC
7/11 = 10/AC
Answers
The ratio of similar sides to triangles should be equal AC/XC=BC/YC BC=BY+YC BC=4+7=11
AC/10=11/7 or 7/11=10/AC the ratio above should be used for calculation of AC
Answer:
The correct option is 4.
Step-by-step explanation:
In triangle ABC and XYC,
[tex]\angle BAC=\angle YXC=60^{\circ}[/tex] (Given)
[tex]\angle BCA=\angle YCX[/tex] (Reflexive Property)
By AA rule of similarity,
[tex]\triangle ABC\sim \triangle XYC[/tex]
The corresponding sides of similar triangles are proportional.
Since triangle ABC and XYC, therefore
[tex]\frac{XC}{AC}=\frac{YC}{BC}[/tex]
[tex]\frac{XC}{AC}=\frac{YC}{BY+YC}[/tex]
[tex]\frac{10}{AC}=\frac{7}{4+7}[/tex]
[tex]\frac{10}{AC}=\frac{7}{11}[/tex]
Therefore option 4 is correct.