Given m∠1≅m∠2
Proof m∠3≅m∠4
Complete the flow chart to proof m∠3≅m∠4
The flow chart to prove m∠3≅m∠4 is given below.
What is the vertical angle theorem?
The Vertical Angle Theorem states that when two straight lines cross, they create two linear pairs. Due to the fact that their angles add up to 180 degrees, the adjacent angles created when two lines intersect are known as supplementary angles.
Given, m∠1≅m∠2
Then, m∠1≅m∠3 ( vertical angles theorem)
m∠2≅m∠3 (Given)
Then, m∠2≅m∠4 (vertical angle theorem)
Hence, m∠3≅m∠4 (transitive property of congruence) proved
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Organize the angles from largest to smallest.
Sum of 3x + 2 and 8x
What is the solution to x2 – 9x < –8?
x < 1 or x > 8
x < –8 or x > 1
1 < x < 8
–8 < x < 1
Answer:
1 < x < 8
Step-by-step explanation:
x² - 9x + 8 < 0
(x-8)(x-1) = 0
x = 8
x = 1
these are the points where the parabola intercepts the x axis. We have to find when it is under x axis
1 < x < 8
At what values of x does the graph of y=e−x+2xe−x+x2e−x have a point of inflection?
Where the voice rises and falls. But inflection also describes a departure from a normal or straight course.
What is inflection point and how to find an inflection point?
Inflection points for the given equation x^2e^{-2x} are
f'(x) =[tex]2x2xe^{(-2x)}-2{(x2)} e^{(-2x)}[/tex]
f'(x) =[tex]-2(x-1)xe {(^-2x)}[/tex]
The point of inflection, also known as the inflection point, is when the function's concavity changes. Changing the function from concave down to concave up, or vice versa, signifies that. In other words, an inflection point is the location at which the rate of slope shift from a growing to a decreasing way, or vice versa, occurs. There is no doubt that those positions are neither local maxima nor minima. They are fixed points.On a curve, an inflection point is when the concavity changes, according to definition. (i.e., a shift in the sign of curvature). We are aware that the function is concave up if f " > 0, and that it is concave down if f " 0. The point of inflection on a graph is where the function switches from positive to negative, or from negative to positive, at a particular value of x = c.x= -b±√(b^2 - 4ac)/2a
x=4±√(16+16)4
x=4±4√2/4
x=[tex]\sqrt{2+2/2}[/tex]
x=[tex]\sqrt{2-2/2}[/tex]
We get,
x=[tex]\sqrt{(2+2)/2^{2}*\sqrt{2+2}[/tex]
so, inflection points are,
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an exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is currently 100 feet below the sea level. How deep was the diver 15 minutes ago?
25% of 24 is what number
Answer: 6
Step-by-step explanation: you can ask siri
which ordered pair is the solution y=(1/3)x-4
To find the ordered pair that is the solution to the equation y = (1/3)x - 4, we need to solve the equation for x.
To do this, we can first add 4 to both sides of the equation to get y + 4 = (1/3)x. Then, we can multiply both sides of the equation by 3 to get 3y + 12 = x.
Therefore, the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 3y).
Note that the value of y is unknown in this solution. In order to find the exact solution, we would need to know the value of y. For example, if y = 2, then the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 6).
Cameron invests money in a bank account
which gathers compound interest each year.
After 4 years there is $736.80 in the account.
After 7 years there is $788.82 in the account.
Work out the annual interest rate of the bank
account.
Give your answer as a percentage to 1 d.p.
The annual interest rate of the bank account is 2.3%
Let's check the equation for each year.
Compound Interest earned amount
A = P( 1 + r/n)ⁿˣ
A = accumulated amount
P = original amount deposited
r = interest rate
n = times it compounds per year
x = years
when Amount = $736.80, x = 4 years and r% → r/100
736.80 = P(1 +[(r/100)/1] ¹×⁴
736.80 = P(1 + r/100)⁴
when Amount =$788.82 , x = 7 years and r% → r/100
788.82 = P(1 +[(r/100)/1] ¹×⁷
788.82 = P(1 + r/100)⁷
using the 1st equation:
736.80 = P(1 + r/100)⁴
P = 736.80 /[(1 + r/100)⁴]
Substitute on the Using 2nd equation
788.82 = P(1 + r/100)⁷
788.82 = 736.80 /[(1 + r/100)⁴] * (1 + r/100)⁷
788.82 = 736.80 * [(1 + r/100)⁷/(1 + r/100)⁴]
788.82 = 736.80 * (1 + r/100)³
788.82/736.80 = (1 + r/100)³
∛788.82/736.80 = ∛ (1 + r/100)³
∛788.82/736.80 = (100 + r)/100
100 ∛788.82/736.80 = 100 + r
100 ∛788.82/736.80 - 100 = r
r ≈ 2.3%
Hence, the annual interest rate of the bank account is 2.3%
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What is calculas of variations?
Answer:
Hey there!
Step-by-step explanation:
This is ur answer...
The calculus of variations is a field of mathematics about solving optimization problems. This is done by minimizing and maximizing functionals. The methods of calculus of variations to solve optimization problems are very useful in mathematics, physics and engineering.
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Find the amount that results from the given investment.
$600 invested at 6% compounded quarterly after a period of 4 years
After 4 years, the investment results in $.
(Round to the nearest cent as needed.)
We can tell that the investment results after 4 years will be $761 with the help of compound interest.
What is compounding?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it so that interest is generated the next period on the principal amount plus any accumulated interest.
In finance and economics, compound interest is common.
So, we have an initial investment of %600.
And the interest is 6% which will be compounded quarterly for 4 years.
Then the amount we will receive after 4 years is:
(Refer to the table attached below)
So, the amount we will get after 4 years is $761.39.
Rounding off: $761
Therefore, we can tell that the investment results after 4 years will be $761 with the help of compound interest.
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The nth term of a sequence is n²+20
a) Work out the first three terms of the sequence.?
b) How many terms in the sequence are less than 50 ?
The graph shows a system of inequalities.
Graph of two inequalities.
Which system is represented in the graph?
y > x2 + 4x – 5
y > x + 5
y < x2 + 4x – 5
y < x + 5
y ≥ x2 + 4x – 5
y ≤ x + 5
y > x2 + 4x – 5
y < x + 5
The system of inequalities shown by the graph are
y > x² + 4x – 5y > x + 5How to identify inequality graphsThere are some points that help in interpreting inequality graphs.
The first part is to arrange the equation in the form so that y is the subject of the formula and to the left
Then watch out for dashed lines or solid lines
dashed lines means there is no equality sign in the inequality > OR <solid line means there is equality in the inequality ≤ OR ≥Another part is the shaded portion
shading above the line defines greater thanshading below the line defines less thanEquipped with tis information, it is clear that the two lines of the graph are both dashed and shaded above the line,
Hence we look out for equations having no equality sign in the inequality and due to the shading must be greater than.
This makes the first option the best choice
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if c is (5x-7) degrees and b is (8x-55) degrees what is the value of x
The value of x is 18 if ∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.
What are vertically opposite angles?
It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
It is given that:
∠C and ∠D are vertical angles.
From the definition of the vertically opposite angles:
5x-7 = 8x-55
After solving we get:
-7 = 3x -55
3x = 48
x = 16
Thus, the value of x is 18 if ∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.
The complete question is:
∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55. What is m∠D ?
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23. For the data in the table, does y vary directly with x? If it does, write an equation for the direct (1 point) variation.
yes; y=2 x
yes; y=5 x
yes; y=7 x
no; y does not vary directly with x.
The ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.
What is the constant of variation?
The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.
We have,
x y
2 10
4 24
6 36
To determine whether y varies directly with x, you need to see if the ratio of y to x is constant for all the data points.
If y varies directly with x, then the ratio y/x will be constant for all the data points. In this case, you can write an equation for the direct variation in the form y = kx, where k is the constant of variation, which is equal to the ratio y/x.
If the ratio y/x is not constant for all the data points, then y does not vary directly with x.
so, let's see the k constant of variation,
k = y/x
k = 2/10 =1/5
k = 4/24 = 1/6
k = 6/36 = 1/6
so, k = 1/5, k=1/6, k=1/6.
Hence, the ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.
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hi if someone wouldn’t mind doing this that would be great!!! 100 points im just desperate i need a whole bunch of stuff done tomorrow, thank you! :)
Answer:
1. y=2x−5
2. y=-x-4
3. y=-1/2x+1
Step-by-step explanation:
First Question:
We are given (3, 1) and (1, -3)
The slope is the difference of y-values over x-values. From this we get:
(1−−3)/(3−1)=4/2=2
Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b
Plugging in (3, 1) gives us 1=3∗2+b ⇒ b=1−6 = −5
We have our slope and y-intercept now, so the equation is y=2x−5.
Second Question:
We are given (-4, 0) and (1, -5)
The slope is
(-5-0)/(1--4)=-5/5=-1
Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b
Plugging in (-4, 0) gives us 0 = -1∗-4+b ⇒ b = -4
We have our slope and y-intercept now, so the equation is y=-x-4.
Third Question:
We are given (-6, 4) and (-2, 2)
The slope is
(4-2)/(-6--2)=2/48=-1/2
Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b
Plugging in (-2, 2) gives us 2 = -1/2∗-2+b ⇒ b = 2-1 = 1
We have our slope and y-intercept now, so the equation is y=-1/2x+1
Ramesh took a loan of Rs 50,000 from Urmila at the rate of 10% p.a. If he paid a
half of the principal and all the interest at the end of 3 years, in how many years
should he pay the remaining amount with total interest of Rs 20,000 from the
beginning?
Answer:
Below
Step-by-step explanation:
In three years the interest will be
50 000 * .1 * 3 = 15 000
He pays this and 25 000 so his remaining loan is 25 000
we want to know how long will it be before this remaining loan
incurs 5 000 interest ( for a total of 20 000)
25000 * . 1 * n = 5000 shows n = 2 years more
( 5 years from original loan date)
Name the three types of triangles that deal with the measure of the sides
Solve one eighth times quantity x plus 32 end quantity equals negative 7.
HURRY 100 PTS
x = 56
x = 7
x = −88
x = −24
The solution of the expression will be;
⇒ x = - 88
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
'' one eighth times quantity x plus 32 end quantity equals negative 7.''
Now,
Since, The algebraic expression is,
'' one eighth times quantity x plus 32 end quantity equals negative 7.''
Hence, We can formulate;
⇒ 1/8 (x + 32) = - 7
⇒ x + 32 = - 56
⇒ x = - 56 - 32
⇒ x = - 88
Thus, The solution of the expression will be;
⇒ x = - 88
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If g'(x) = (2-x)x² So how many extreme points does the function g(x) has?
There are 3 extreme points does the function g(x) = (2 - x) x².
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The function is,
⇒ g ' (x) = (2 - x) x²
Now,
Since, The function is,
⇒ g ' (x) = (2 - x) x²
We know that;
The extreme points are find as;
⇒ g ' (x) = 0
So, We get;
⇒ g ' (x) = 0
⇒ (x - 2) x² = 0
This gives two values as;
⇒ (x - 2) = 0
⇒ x = 2
And, x² = 0
⇒ x = 0, 0
Thus, The extremes values are;
⇒ x = 2 , 0, 0
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What’s the slope for x<-3
Answer:As you can see, this line is vertical! It goes directly up. We know that because the equation says that X is equal to -3. It is telling us that no matter what the Y value is, X will be -3.
Step-by-step explanation:
The equation to find slope is to take two points
(A,B) and (C,D) and to do the following equation: D−B
______
C−A
So, let's take two points. Let's say that Y is equal to 3 and 2. In that case, since X is always -3, our points would be (−3,2) and (−3,3).
Now, let's substitute into our formula.
3−2 1 1
------ = ----- = ---
3 (−3) (subtract) -3 + 3 0
As you can see, the final slope is 1/0
. If you put that into your calculator, it will come out as undefined, because any number divided by zero is undefined. And so your slope for any vertical line is undefined.
Triangle congruence
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Solve the following inequalities 1/2 x ≥ 3
x[tex]x\geq 6[/tex].
Step-by-step explanation:1. Write the expression.[tex]\frac{1}{2}x \geq 3[/tex]
2. Divide both sides by 1/2.[tex]\frac{\frac{1}{2}}{\frac{1}{2} } x\geq \frac{3}{\frac{1}{2} }[/tex]
Dividing by a fraction of the same as multiplying by its multiplicative inverse. Since the multiplicative inverse of 1/2 is 2/1, we may rewrite as:
[tex]\frac{2}{1} *\frac{1}{2} x\geq \frac{2}{1} *3[/tex]
3. Simplify.[tex](1)x\geq(6)\\ \\x\geq6[/tex]
4. Verify.[tex]\frac{1}{2}(6) \geq 3\\ \\3\geq 3[/tex]
Correct!
5. Express the final result.x[tex]x\geq 6[/tex].
[tex]-16x^{\frac{-3}{2}[/tex]
The expression -16x^(-3/2) represents a term that has a coefficient of -16 and a variable x raised to the power of -3/2.
What is an expression?Generally, The expression -16x^(-3/2) represents a term that consists of a coefficient of -16 and the variable x raised to the power of -3/2.
In general, the exponentiation operator (^) represents the idea of raising a number (called the base) to a certain power (called the exponent). For example, x^2 means "x raised to the power of 2" and can be calculated as x * x = x^2.
Similarly, x^3 means "x raised to the power of 3" and can be calculated as x * x * x = x^3.
The exponent -3/2 means that the base (in this case, x) is raised to the power of -3/2. This can be simplified as follows:
x^(-3/2) = 1 / x^(3/2) = 1 / (x^(3/2))
The expression -16x^(-3/2) can then be simplified as follows:
-16x^(-3/2) = -16 * 1 / x^(3/2) = -16 / x^(3/2)
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The complete Question was not found
Write a
system of equations with the solution (4, -3).
Answer:
A (0, -3) translated to the right 4 units.
Step-by-step explanation:
If you go right 4, you get (4, -3)
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 7 liters of synthetic oil. In order to make 825 liters of Petrolyn oil, how many liters of natural oil are needed?
The natural oil that will be needed to make make 825 liters of Petrolyn oil is 300 liters.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this situation, Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 7 liters of synthetic oil. In order to make 825 liters of Petrolyn oil, the natural oil will be:
= 4 / (4+7) × 825
= 4 / 11 × 825
= 300
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Write a linear function f with f (0)
7 and f(3) = 1.
f(x) =
Answer:
f(x) = -2x +7
Step-by-step explanation:
The 2-point form of the equation for a line is suitable for this. For points (x1, y1) and (x2, y2), the equation is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
For the given points (0, 7) and (3, 1), the equation is ...
y = (1 -7)/(3 -0)(x -0) +7
y = -6/3x +7 . . . . . . . . simplify.
We can use f(x) for y to get ...
f(x) = -2x +7
PLEASE HELP!!
At school athletic events you can buy 3 drinks and 2 hot dogs for $4.80, or you can buy 1 drink and 1 hot dog for $2.00. How much does 1 hot dog cost?
A. $0.80
B. $0.96
C. $1.00
D. $1.20
1 hot dog cost is $1.20 .
What is costs?
A cost is the value of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.
Let's say that each drink costs $x and each hot dog costs $y.
Using the provided information, 3 drinks and 2 hot dogs cost $4.80. In equation form, it reads as follows:
3 x+2 y=4.80
1 drink and 1 hot dog costs $2.00. In equation form, we can write it as:
x+y=2
x=2-y
Using this value of x in first equation, we get:
3(2-y)+2 y=4.80
6-3 y+2 y=4.80
6-y=4.80
y=6-4.80
y=1.20
Thus the cost of one hot dog is 1.20$
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A force of 400 newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion.
The equation of motion for the mass attached to the spring
x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2
What is the equation of motion?Generally, The equation of motion for a mass on a spring is given by Hooke's law, which states that the force exerted by a spring is proportional to its displacement from equilibrium. The proportionality constant is known as the spring constant, which is denoted by the letter k.
In this case, the force exerted by the spring is 400 newtons, and the displacement from equilibrium is 2 meters. Therefore, the spring constant is given by:
k = F/x = 400 N/2 m = 200 N/m
The equation of motion for a mass on a spring is given by:
F = ma = -kx
where F is the force exerted by the spring, m is the mass of the object, a is the acceleration of the object, and x is the displacement of the object from equilibrium.
Substituting the values for the spring constant and the mass, we get:
-kx = -(200 N/m)(50 kg)(x'')
Solving for the acceleration, we get:
x'' = -k/m = -200 N/m / 50 kg = -4 m/s^2
This is the equation of motion for the mass attached to the spring. The negative sign indicates that the acceleration is in the opposite direction of the displacement, as is expected for a mass on a spring.
Finally, to find the equation of motion, we need to take into account the initial velocity of the mass. The equation of motion for an object with initial velocity is given by:
x = x_0 + v_0t + (1/2)at^2
where x is the displacement of the object, x_0 is the initial displacement (in this case, the equilibrium position of the spring), v_0 is the initial velocity, t is time, and a is the acceleration.
Substituting the values for the acceleration and the initial velocity, we get:
x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2
This is the equation of motion for the mass attached to the spring. The initial displacement, x_0, is the equilibrium position of the spring, which is assumed to be at x=0 in this case.
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the perimeters of the square and the rectangle below are the same. Write and solve an equation to find the value of x area= 121inches squared the rectangle is 3x and x-2
the area of the square is 121 in. Squared.
The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The borders of the square and the square shape underneath are something similar.
Perimeter of the square = Perimeter of the rectangle
4a = 2(L + W)
2a = L + W
If the area of the square is 121 square inches. Then the side length of the square is given as,
a² = 121
a = 11 inches
And the dimension of the rectangle is 3x and x - 2. Then the equation is given as,
3x + x - 2 = 11 (2)
4x - 2 = 22
4x = 24
x = 6
The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.
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