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The value of x from the diagram is 18degrees
An angle is a line where two or more lines meet.
The magnitude of two lines is known to be parallel if they have the same magnitude.
From the diagram shown, we can see that line BC is parallel to line ED
This shows that the following are true:
<C = <D8x and 2x are supplementaryIf the two angles are supplementary, then:
8x + 2x = 180
10x = 180
x = 180/10
x = 18 degrees
Hence the value of x is 18degrees
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State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change. Round to the nearest whole percent. original: 84, new: 96
Answer:
Then we divide that amount by the original older value and get 1.3035. Now we must convert that number
A collection of nickels, dimes, and quarters consist of 16 coins with a total of $1.90. If the number of dimes is equal to the number of nickels, find the number of each type of coins.
Answer:
There would be 6 nickels, 6 dimes, and 4 quarters.
(X) + log (X+4)=log 32 for x
The value of x from the logarithmic expression is 4 and -8
Given the logarithmic expressionLogarithm are inverse of exponential function. Given the logarithmic function below;
log (X) + log (X+4)=log 32
Since positive will become multiplication, hence;
X(X+4) = 32
Expand
X^2 + 4x = 32
x^2 + 4x - 32 = 0
x^2 + 8x - 4x - 32 = 0
x(x + 8) - 4(x + 8) = 0
(x-4)(x+8) = 0
X = 4 and -8
Hence the value of x from the logarithmic expression is 4 and -8
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Which equation is equivalent to 2 Superscript 4 x Baseline = 8 Superscript x minus 3?
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 3
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 6
2 Superscript 4 x Baseline = 2 Superscript 3 x minus 3
The equivalent exponential equations are given as follows:
\(2^{4x} = 2^{3(x - 3)}\)
How to obtain the equivalent exponential expression?The exponential expression for this problem is defined as follows:
\(2^{4x} = 8^{x - 3}\)
The number eight is the third power of 3, that is:
8 = 2³.
The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:
\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)
Meaning that the correct option is given by the fourth option.
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HELP ASPAPP The general form of an equation is x2+y2−25x+3y+1=0.
What is the equation of the circle in standard form?
Answer:
the first (top) answer option. ... = 129/100
Step-by-step explanation:
the for me qualifying or disqualifying term is the constant term as the product and sum of all the constant parts.
the general form has the constant parts
... + 1 = 0
so, all the constant terms from the squares on the left side minus the constant term on the right side must be 1.
let's start from the bottom : the 4th answer option.
the constant parts are
... + (-1/5)² + ... + (3/2)² = 121/100
... + 1/25 + ... + 9/4 = 121/100
... + 0.04 + ... + 2.25 = 1.21
... + 2.29 - 1.21 = ... + 1.08
and NOT 1. so, this is wrong.
the 3rd answer option.
... + (-1/3)² + ... + (-3/2)² = 221/100
... + 1/9 + ... + 9/4 = 221/100
... + 0.111111... + ... + 2.25 = 2.21
... + 0.111111... + ... + 2.25 - 2.21 = 0
... + 0.111111... + ... + 0.04 = 0
... + 0.111111 + 0.04 = 0.15111111...
and NOT 1. so, this is wrong.
the 2nd answer option.
... + (-1/5)² + ... + (3/2)² = 229/100
... + 1/25 + ... + 9/4 = 229/100
... + 0.04 + ... + 2.25 = 2.29
... + 2.29 - 2.28 = ... + 0
and NOT 1. so, this is wrong.
the first answer option.
... + (-1/5)² + ... + (3/2)² = 129/100
... + 1/25 + ... + 9/4 = 129/100
... + 0.04 + ... + 2.25 = 1.29
... + 2.29 - 1.29 = ... + 1
this IS 1. so, this is correct.
this corresponds now to the original
... + 1 = 0
Answer: Choice A (May vary from test to test)
Step-by-step explanation:
(x-1/5)^2 + (y+3/2)^2 = 129/100
Just an FYI:
I can't stress this enough... Add equation symbols when applicable, for example: √,^,/, etc. You can't expect to have someone give the correct answer when you literally typed the equation out incorrectly.keep in mind significant figures. 6.020*0.0510=?
Answer:
3.072×10^-1
Step-by-step explanation:
please mark me as brainlest
Answer:
0.307
Step-by-step explanation:
6.020 multiplied by 0.0510 is 0.30702 and when we multiply, we round the answer to the least sig figs. That would be 3 since 0.510.
(Here's a free one )
In the example shown, would you get the same sum if you used 12 as the common denominator? Explain. Alex rode his scooter from his house to the park. Later, he rode from the park to baseball practice. How far did Alex ride? ( 1/2 mile to the park from the house and 1/3 mild from the park to baseball practice)
Answer:
5/6
Step-by-step explanation:
Please help I am so so confused thank you all
y-(-9) = -6(x-(-4)), y = -6x-33
the correlation between years of education and salary in a sample of 20 people from a certain company is .4. is this correlation statistically significant.
Complete Question:
The correlation between years of education and salary in a sample of 20 people from a certain company is .4. Is this correlation statistically significant at the .05 level?
Answer:
We accept \(H_o\) hence no significant evidence
Step-by-step explanation:
From the question we are told that
sample correlation n= 20
population correlation = 4
level of significance \(\alpha =0.05\)
Generally we are task to understand existing difference between sample correlation and population correlation
Generally null hypothesis is given by \(H_o : p=0\)
alternative hypothesis \(H1_1 : p\neq 0\)
generaly the mathematical representation of test statics
\(t= r\sqrt{\frac{n-2}{1-r^2} }\)
\(t= 0.04\sqrt{\frac{20-2}{1-0.4^2} }\)
\(t= 1.85\)
Generally for table the p value is given by \(p= 0.08056\)
p value > the null hypothesis
Therefore
We accept \(H_o\) hence no significant evidence
What is the domain if the rational expressions X(x-2/(x- 2)(x+ 3) and x/x+3 are equivalent? A. all real numbers except -3 B. all real numbers except -2 C. all real numbers except -3 and 2 D. all real numbers except 2
Answer:
C. all real numbers except -3 and 2
Step-by-step explanation:
These two numbers will make the denominator equal to zero.
The domain of the rational expression is all real numbers except -3 and 2. The correct option is C.
What is a domain?The domain of the function is defined as the set of all the possible values of the function. The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
Given rational expression is,
E = x(x-2/(x- 2)(x+ 3)
For the above rational expression when we substitute the values of x as 2 and -3 the rational expression will give undefined values.
Therefore, the domain of the rational expression is all real numbers except -3 and 2. The correct option is C.
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If y = 9x − 7, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs? A) {(0, −7), (1, 2), (−1, −16)} B) {(−7, 0), (2, 1), (−16, −1)} C) {(1, 9), (2, 7), (3, 16)} D) {(7, 9), (8, 10), (9, 11)}
Answer:
0,-7 8,567;7,57,6,6,6,6,6,78,3,5
The graph below shows the solutions to which inequality?
A. x^2-3x+3 ≥0
B. x² + 3x-3 <0
C. x²-3x+3<0
D. x² + 3x-3>0
The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.
option B.
What is the solution of the inequality?The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;
The solution of the graph,
x > -4 and x < 1
The first equation with "≥" is ruled out because the graph doesn't have a thick dot.
Let's simplify the second expression;
x² + 3x - 3 < 0
solve using quadratic formula;
x > -3.79 or x < 0.79
The third expression is ruled out since its solution will be complex.
For the last expression;
x² + 3x - 3 > 0
x < -3.79 or x > 0.79
Thus, the correct inequality expression is x² + 3x - 3 < 0.
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Write the expression as a square of a monomial. 4/9b^6
Answer:
Step-by-step explanation:
It just so happens that all the numbers and variables in that expression are perfect squares. 4 has a square root of 2; 9 has a square root of 3; and b^6 has a square root of b^3. Putting that altogether into one simplified expression that we can square is:
\((\frac{2}{3}b^3)^2\)
The expression as a square of a monomial (4/9b⁶) is (2²/3²b³)²
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
A monomial is a polynomial that has only one term.
Given, a monomial (4/9b⁶).
To write this monomial in terms of as a square of a monomial we'll factor out the power of 2 from each f the constants and variables contained in the monomial which is,
= (2²/3²b³)²
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What is the exact value of sin pi/3?
The exact value of sin(pi/3) is √3. By definition, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, sin(pi/3) = √3/1 = √3.
The exact value of sin(pi/3) can be determined using trigonometric properties and identities.
First, we know that pi/3 is equivalent to 60 degrees. In a unit circle, the point corresponding to 60 degrees forms an equilateral triangle with the origin and the x-axis. This triangle has side lengths of 1, 1, and √3.
To find the sine of pi/3, we consider the side opposite the angle (pi/3) in the triangle. In this case, the opposite side has a length of √3. The hypotenuse of the triangle is 1, as it is the radius of the unit circle.
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In a certain Algebra 2 class of 28 students, 7 of them play basketball and 5 of them play baseball. There are 18 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
2 students play both
Step-by-step explanation:n(u)=28
n(b)=7,n(b)=5,n(who play neither sport)=18
HERE,
n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)
28=7+5-n(BnB)+18
28=30-n(BnB)
n(BnB)=30-28
=2 answer
There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?
Answer:
hvgf m g n HCF kvvfgfhhjfj
Find y
A)10
B)2
C)15
D)4
Answer:
y = 4Step-by-step explanation:
3y = y + 8
3y - y = 8
2y = 8
y = 8÷2
y = 4
Answer:
4
Step-by-step explanation:
Write an equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).
Line CD is shown. C is at 1, 1. D is at 3, 5.
y = −0.5x − 5.5
y = −0.5x + 5.5
y = 2x + 13
y = 2x − 13
Answer:
its b
Step-by-step explanation:
i took the test
y = - 0.5x + 5.5 is the equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).
What is the slope-intercept form of a straight line?The slope-intercept form of a straight line is y = mx + c.
Here, x and y are coordinates, m is the slope and c is the y-intercept of the line.
Given, two points are C(1, 1) and (3, 5).
Therefore, equation of the line CD is:
\(\frac{x - x_{1} }{y-y_{1} }\) = \(\frac{x_{1}-x_{2}}{y_{1}-y_{2}}\)
⇒ \(\frac{x - 1}{y-1}\) = \(\frac{1-3}{1-5}}\)
⇒ \(\frac{x - 1}{y-1}\) = \(\frac{-2}{-4}}\)
⇒2(x - 1) = (y - 1)
⇒ y = 2x - 1
Let, line AB is perpendicular to the line CD and passes through the point (-1, 6).
Therefore, slope of the line CD is = 2.
We know, slope of CD × slope of AB = -1
Therefore, slope of AB = -1 / slope of CD = \(-\frac{1}{2}\).
Now, line AB has a slope of \(-\frac{1}{2}\) and passes through the point (-1, 6).
Therefore, equation of the line AB is:
(y - y₁) = m(x - x₁)
⇒ [y - (6)] = \(-\frac{1}{2}\)[x - (- 1)]
⇒ 2(y - 6) = (-x - 1)
⇒ 2y - 12 + x + 1 = 0
⇒ x + 2y = 11
⇒ y = - 0.5x + 5.5
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i need help now i have like so much questions that need to be done
The measure of ∠M and ∠N = 76
Define an isoscales triangle?An isosceles triangle is a triangle that has two sides of equal length and two equal angles opposite those sides.
Given:- ∠NLM = 28°
The given triangle is an isosceles triangle as sides LM and LN are equal.
Therefore ,∠LMN and ∠LNM will be equal.
Let us assume ∠M as x
Therefore,
∠LMN = ∠LNM = x
Sum of all angles of a triangle =180°
Therefore,
∠NLM + ∠LNM + ∠LMN = 180°
28 + x + x = 180
28 + 2x = 180
2x = 180 – 28
2x = 152
x = 152/2
x = 76
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Choose the point-slope form of the equation of this line.
Answer:
y= -5x +7
Step-by-step explanation:
We can see points on the graph:
(2, -3) and (3, -8)The function in general form is:
y= mx+bLet's find the slope and y-intercept as per identified points on the graph:
m= (y1-y1)/(x2-x1)m= (-8+3)/(3-2)= -5b= y- mx
b= - 3 -(-5)*2= -3 +10= 7Based on the found values of m and b, the given line is:
y= -5x +7Answer:
The answer is C: y + 8 = -5(x - 3)
Step-by-step explanation:
I took the assignment on Edge
mathmatically indication example with solution
A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.
How to solve the equation ?Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.
The equation would be 3 x + 2 = 14.
So we can solve for the equation to be :
3x + 2 - 2 = 14 - 2
3x = 12
3 x / 3 = 12 / 3
x = 4
In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.
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) 65 people were asked on the activities they engage in during their free time. The results showed that 23 visit national parks, 26 engage in cycling while 22 engage in swimming. Furthermore 9 engage in swimming and visit national parks, 9 engage in swimming only while 11 visit national parks only. How many engage in
i. Swimming and cycling
Answer:
Step-by-step explanation:
i am working on the assumption that nobody does all three of them
i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.
the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.
so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4
A semicircle of diameter 1 sits at the top of a semicircle of diameter 2, as shown. The shaded area inside the smaller semicircle and outside the larger semicircle is called a lune. Determine the area of this lune.
a. π/6 - √3/4
b. √3/4 - π/12
c. √3/4 - π/24
d. √3/4 + π/24
e. √3/4 + π/12
The required area of the lune is (D) √3/4 - π/24.
What is the area?The measurement that expresses the size of a region on a flat or curved surface is termed area.
Surface refers to the area of a surface or the boundary of a tri structure, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
So,
The lune's area is equal to the smaller semicircle's area minus the segment's area.
The area of the segment is equal to the sum of the areas of the sector and the triangle formed by the intersection points and the larger semicircle's center.
Additionally, because all of the sides are one unit, the triangle thus constructed is an equilateral triangle.
Area of the lune = π * 1/8 (60/360 * π * 1² - √3/4 * 1²)
Area of the lune = π/8 - π/6 + √3/4
= √3/4 - π/24
Therefore, the required area of the lune is (D) √3/4 - π/24.
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1. Find the new value after the old value of 56 is increased by 8%.
Answer:
60.48
Step-by-step explanation:
Answer:51.52
Step-by-step explanation:
A family spends $450 every month on food. If the family’s income is $1,800 each month, what percent of the income is spent on food?
The total of h and b is split into 5 equal groups?
Answer: (h + b) ÷ 5
Step-by-step explanation:
First add h + b (h +b)
Then divide by 5. (h + b) ÷ 5
Can someone help please?
ASAP
Answer:
Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)
Step-by-step explanation:
As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.
11^2 + 5^2 = AC^2
121 + 25 = AC^2
146 = AC^2
sqrt(146) = AC^2
Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)
What the meaning of "f is order-preserving if x < y implies f(x) < f(y)"?
An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.
In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.
Order-Preserving Function:
A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.
Increasing Function:
If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).
Isomorphism:
A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:
a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).
b. f is onto (surjective): Every element in Q has a pre-image in P.
When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.
Automorphism:
An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.
These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.
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The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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