The value of angle A when A and B are vertical opposite angles is 96°.
How to illustrate the information?It should be noted that vertical angles are equal. Based on the information illustrated, it should be noted that angle A = 4x - 4 and angle B = 5x - 29.
Then, we will equate the equations and this will be:
Angle A = Angle B
4x - 4 = 5x - 29
Collect like terms
5x - 4x = -4 + 39
x = 25
Since angle A = 4x - 4 = 4(25) - 4 = 100 - 4 = 96°
Angle A is 96°.
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Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4;
zeros: -4-5i; - 5
multiplicity 2
Let a represent the leading coefficient. The polynomial is f(x) = a(________)
(Type an expression using x as the variable. Use integers or fractions for any
numbers in the expression. Simplify your answer.)
Answer: [tex]x^4 +2x^3 -14x^2 +210x+1025[/tex]
Step-by-step explanation:
By the conjugate root theorem, -4+5i is also a root.
[tex]f(x)=a(x+4-5i)(x+4+5i)(x+5)^2\\\\=a(x^2 -8x+41)(x+5)^2\\\\ =a(x^2 -8x+41)(x^2 +10x+25)\\\\=a(x^4 +2x^3 -14x^2 +210x+1025)[/tex]
Find the area of a circle with a radius of 9 inches. Use 3.14 for n. Hint: A = nr2 9 in. Area = [?] square inches Enter the number that goes in the green box. Do not round your answer.
Answer:
56,52
Step-by-step explanation:
take n as 3.14 multiples with 9 and multiples with 2
are the angles on, inside, or outside the circle
nswer
First image
Angle ABC covers around the inside and outside of the circle.
Second image
Angle x l
hird image
Angle DBE l
ngle of arc DE l
ngle of arc AC l
ourth angle
ll the angles at U lie inside the circle.
ngle 78° l
ngle 114° l
ope this Helps!!!
Find the difference in the latitudes of Athens, Greece, Latitude 38° N, and Sydney, Australia, latitude 34° S.
The difference in the latitudes of Athens, Greece, Latitude 38° N, and Sydney, Australia, latitude 34° S is 72° .
We have two different coordinates, 38° N and 34° S
We can find the differnce in two different coordinates by following a few steps.
We have to consider South as negative North. So, we can write 34° S as -34° N.
Hence, we can determine the difference in between two coordinates.
Difference in coordinates ≡ 38° N - 34° S = 38° N - ( - 34° N ) = 38° N + 34° N = 72° N
So, we can conclude that, the difference is 72°.
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Counterexamples
Instructions: Show that the conjecture is false by finding a counterexample. Change the value of n below in order to make it a counterexample.
"For every integer n, n3 is positive."
n=1
n=−3
n=2
n=5
n= Answer
Counterexample
A counterexample is an example that meets the mathematical statement's condition but does not lead to the statement's conclusion. It is used to check the validity of an argument.
We have been given the conjecture:-
"For every integer n, [tex]n^3[/tex] is positive."
We have to show that the conjecture is false by finding a counterexample.
Let us take an integer n = - 5
Finding its cube we, get
[tex]n^3[/tex] = -125
We know that,
-125 is not positive, it is negative.
Hence, the conjecture "For every integer n, [tex]n^3[/tex] is positive." is proven wrong by finding a counterexample which states otherwise.
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please help im really stuck
The director of a marching band asks the band members to line up in rows of six, but there are three band members in the last row. Then she tries to line them up in rows of seven, but there are four band members in the last row. Finally, she tries to line them up in rows of eight, but there are five band members in the last row.
The band has fewer than 200 members.
How many members are there?
Using divisibility rules, it is found that there are 165 members in the band.
How to determine how many members are there in the band?The number of students in the last row gives the remainder of the division of the total number of members by the number of members in each row.
Hence:
The number of members in the band divided by 6 has a remainder of 3The number of members in the band divided by 7 has a remainder of 4.The number of members in the band divided by 8 has a remainder of 5.It is also stated that the band has fewer than 200 members.
From the third bullet point, the possible values, that is, values that when divided by 8 have a remainder of 5, are given as follows:
{5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 125, 133, 141, 149, 157, 165, 173, 181, 189, 197}.
The number is 165, because:
165/6 = 27 with a remainder of 3.165/7 = 23 with a remainder of 4.More can be learned about divisibility rules at https://brainly.com/question/9462805
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mcdonald's sells the big mac for $2.50 in 1998, while a competing restaurant, burger king, sold the whopper for $0.75. The management of Mcdonalds develops a business plan for future growth that projects an increase in the price of big macs of $0.25 per year, while the management of burger king develops a plan aimed at increasing the price of the whopper by 15% each year.
What would be the function of both burger king and mcdonalds
The function of both burger king and mcdonalds cost are respectively; C(n) = 0.75(1.15)ⁿ and C(n) = 2.5 + 0.25n
How to find the function sequence?The formula for the nth term of an arithmetic sequence is given as;
aₙ = a + (n - 1)d
where;
a is first term
n is position of term
d is common difference
For McDonald's, we are told that the initial price is $2.50 and the common difference is $0.25. Thus, the function will be;
C(n) = 2.5 + 0.25n
where n is number of years after 1998
We are told that the cost in burger king increases by 15% each year. Thus, using formula for geometric progression, the function is;
C(n) = 0.75(1 + 0.15)ⁿ
C(n) = 0.75(1.15)ⁿ
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Theodora had practiced playing table tennis for hours by the end of the week. If each day the practice lasted for of an hour, how many days did she practice during the week?
Answer:
7 hours
Step-by-step explanation:
each day she practices 1 hour and there are 7 days in a week so 7 hours by the end of the week
HELP PLS LAST ONE
Simplify (4y³ – 2y +9) − (2y³ − 3y² + 4y + 7).
find the 6th term of the sequence 4, 6, 9,...
Answer:
30.375
Step-by-step explanation:
this is a geometric sequence, meaning it has a common growth factor
to find the growth factor, you divide a term by the previous term (example: 9/6)
so for this problem:
9/6 = 1.5
6/4 = 1.5
so 1.5 is the common growth factor
then you just multiply so:
9 • 1.5 = 13.5
13.5 • 1.5 = 20.25
20.25 • 1.5 = 30.375
4, 6, 9, 13.5, 20.25, and 30.375
so 30.375 is your 6th term
hope this helps :)
Make x the subject of the equation. Y=2x-a
Answer:
1/2y+1/2a=x
Divide both sides by2, then but the a value on the other side.
Question 4 (1 point)
THIS RELATION IS A FUNCTION:
(1,-2), (1,1), (1,6),(1,11)
O True
O False
Answer: False
Step-by-step explanation:
The x-value of 1 maps onto 4 different y values.
2. What is the value of x when y = 17 for the quadratic function
f(x) = x² + 6x + 10?
A. -7 only
B. 1 only
C. 7 only D. -7 and 7
E. -7 and 1
Value of x when y = 17 for the quadratic function f(x) = x² + 6x + 10 is -7 and 1. That is option E.
Given, y=17 :
17 = x² + 6x + 10
Move 17 to RHS (right-hand side) :
0 = x² + 6x - 7
Using the Middle Splitting method:
0 = x² + (7x - 1x) - 7
0 = x(x + 7) - 1(x+7)
0 = (x - 1) (x + 7)
Now, equate both the equations (x-1) and (x+7) separately with 0.
The first value of x is
(x - 1) = 0
x = 1
The second value of x is
(x + 7) = 0
x = -7
∴ The values of x are -7 and 1. According to the question, that is option E.
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Answer the questions in the photo ( will mark brainliest if correct )
Angles of a polygon add to 360 degrees. To find the measure of each exterior angle of a regular n-gon. divide 360 by n.
18) 27.719) 36020) 12021) 36022) 4523) 20HELP ME PLEASE !!!!!!
5. The value of x = 15
6. The converse that must be used is: C. Same-side exterior ∠s converse.
7. The proof is completed in the explanation part.
8. Slope of AB = 7/4; Slope of CD = -4/7, they are perpendicular.
What is the Same-Side Exterior Angles Theorem?The same-side exterior angles theorem states that same-side exterior angles that are on the same side of a transversal are supplementary to each other. Its converse states that if same-side interior angles are supplementary, then the lines they lie on are parallel to each other.
5. 10x - 22 + 3x + 7 = 180 [same-side exterior angles theorem]
13x - 15 = 180
13x = 180 + 15
13x = 195
x = 15
6. The converse that must be used to show that lines y and x are parallel to each other is: C. Same-side exterior angles converse.
7.
Statements Reasons
1. ∠6 ≅ ∠8 1. Given
2. y║z 2. Corresponding ∠s converse
3. ∠2 and ∠3 are supplementary 3. Same Side Interior ∠s
8. Given:
A(-3, 8)
B(1, 15)
C(10, -9)
D(3, -5)
Slope = change in y / change in x
Slope of AB = (8 - 15)/(-3 - 1) = -7/-4 = 7/4
Slope of CD = (-9 -(-5))/(10 - 3) = -4/7
-4/7 is the negative reciprocal of 7/4. Perpendicular lines have slope that are negative reciprocals of each other.
Therefore, CD and AB are perpendicular.
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If m = 8 and 3m + 72=4y – 56, then by the Substitution Property of Equality, 3(8) + 72 = 4y − ???
Answer:
56
Step-by-step explanation:
3m + 72 = 4y - 56
3(8) + 72 = 4y - 56
24 + 72 = 4y - 56
96 = 4y - 56
4y = 152
y = 38
3(8) + 72 = 4y - x
24 + 72 = 152 - x
96 = 152 - x
-56 = -x
x = 56
find the derivative of the function
f(x) = √2^3 + ln(x^3) - 2x^3 - log_3(729) - 2/x^4
Applying the rules for the constant, logarithm and exponents, the derivative of the given function is of:
f'(x) = 3/x - 6x² - 8/(x^5).
What is the derivative of the function?The function is given by:
f(x) = √2^3 + ln(x^3) - 2x^3 - log_3(729) - 2/x^4
The derivative of a sum is the sum of the derivatives, hence:
f'(x) = (√2^3)' + (ln(x^3))' - (2x^3)' - (log_3(729))' - (2/x^4)'
The derivative of a constant is of zero, hence:
(√2^3)' = 0.(log_3(729))' = 0.Hence:
f'(x) = (ln(x^3))' - (2x^3)' - (2/x^4)'.
The derivative of the logarithm is given by:
ln(h(x))' = (1/h(x)) x h'(x).
Hence:
(ln(x^3))' = 3x²/x³ = 3/x.
The derivative of the power of x is given by:
[x^n]' = nx^(n-1).
Hence:
(2x³)' = 6x². (2/x^4)' = (2x^(-4))' = -8x^(-5) = -8/(x^5).Hence the derivative of the function is given by:
f'(x) = 3/x - 6x² - 8/(x^5).
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Which ordered pair could you remove from the relation {(–1, 0), (1, 3), (2, 2), (2, 3), (3, 1)} so that it becomes a function
Answer:(3,1)
Step-by-step explanation:
Because you cant have (1,3) and (3,1).
Answer:
(2,3)
or (2,2) if the function does not need to be continuous.
Step-by-step explanation:
For a set of points to be considered a function, it must be true that for every X value, you have only a single Y value solution.
In other words, looking through your points listed, you would remove any point where an X value appears twice with different Y values.
[tex](X,Y)\\(-1,0)\\(1,3)\\(2,2) < -\\(2,3) < -\\(3,1)\\\\[/tex]
Notice the two points with arrows, both have 2 as their X value, but different Y values. Removing either one of them would make this a function. Although, by removing (2,3) the function has the potential to also be continuous, because having two of the same Y value for different X values would cause a piece-wise function which is generally non-continuous.
A 12-ounce can of soda contains 14 grams of sugar. How many grams of sugar are in 1 ounce of soda?
Write the answer as an improper fraction (fraction greater than one) in lowest terms.
[tex]1 \frac{1 \\ }{6} [/tex]
There are 1.17 grams of sugar are in 1 ounce of soda.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
A 12-ounce can of soda contains 14 grams of sugar.
Now,
Since, A 12-ounce can of soda contains 14 grams of sugar.
Hence, The amount of soda for 1 ounce of can = 14/12
= 1.17 grams
Thus, There are 1.17 grams of sugar are in 1 ounce of soda.
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kumon level C pages please i dont want to waste my time
Answer:
Image result for kumon level C
This award is presented to a student who has completed Level C10 or higher during or before their 1st-grade year. Math Level C covers multiplication and division.
Step-by-step explanation:
Find the surface area of the rectangular prism
Answer:
48
Step-by-step explanation:
Simplify.
3c + 6d + 3d = ?
Answer 3c+9d
Step-by-step explanation: add 3c 9d
Enola bought 14 chicken wings for $29.40. How much would it cost for 5 wings?
Answer:
x=10.50
Step-by-step explanation:
14 = 5
________
29.40 = x
cross multiply - 29.40 x 5 = 147
Then u would divide like this
14/14=1 147/14=10.5
Which equation compares the number of computers in b to the number a?
Answer:
3 × 5 = 15
Step-by-step explanation:
5 is the common number
How many centimeters are there in 12 yards?
O 10.9728 cm
O 36 cm
O 91.44 cm
O 1097.28 cm
Answer:
Answer is 1097.28 cm
Step-by-step explanation:
prove me wrong
Answer:
1097.28
Step-by-step explanation:
There are 91.44 centimeters per yard
12 x 91.44
Five less than the quotient of eighteen and a number n in algebraic expression
The provided sentence "Five less than the quotient of eighteen" is converted into an algebraic expression as 18/x - 5.
What is defined as the algebraic expression?Algebraic expressions are mathematical statements that result from operations on variables and constants including such addition, subtraction, multiplication, and division. We simply combine like terms to explain an algebraic expression. As a result, similar variables will be combined. A same powers will now be combined from the like variables.Five less than the quotient of eighteen and a number
We must convert the provided sentence into an algebraic expression.
Let "x" represent the number.
Therefore,
Five less than that of the quotient of eighteen and "x"
The term quotient refers to the outcome of division.
Therefore,
18/x - 5
That is, Five less than the quotient of eighteen and x.
As a result, the provided sentence is converted into an algebraic expression.
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HELP ASAP HAS TO BE DONE BY TONIGHT
Answer:
first drop down is, doesn't matter. Second one is, must be the negative reciprocal of the slope of the original line. Third is, must be different from the y intercept of the original line. If the y intercepts are the same, the two lines will intersect as proven by one of the questions asked by the user.
Step-by-step explanation:
Hope this helps! :)
can you help me solve me this math problems?
1. 200 - 7/21
2. 50 - 4/7
3. 24 1/4 - 20 3/5
4. 10 5/8 - 6 4/9
5. 6 1/2 - 5 3/4
Step-by-step explanation:
1.
200 - 7/21 = (200×21 - 7)/21 = (4200 - 7)/21 =
= 4193/21 = 599/3 = (199×3 + 2)/3 =
= 199 2/3
we could have seen that 7/21 = 1/3.
so, then this problem was
200 - 1/3 = (200×3 - 1)/3 = 599/3 = 199 2/3
(see above)
2.
50 - 4/7 = (50×7 - 4)/7 = (350 - 4)/7 =
= 346/7 = (49×7 + 3)/7 = 49 3/7
3.
24 1/4 - 20 3/5 = (24×4 + 1)/4 - (20×5 + 3)/5 =
= 97/4 - 103/5
to calculate this we need to bring both fractions to the save denominator. the LCM (lowest common multiple) of 4 and 5 is 20.
so,
97/4 - 103/5 = (97×5)/(4×5) - (103×4)/(5×4) =
= 485/20 - 412/20 = 73/20 =
= (3×20 + 13)/20 = 3 13/20
4.
10 5/8 - 6 4/9 = (10×8 + 5)/8 - (6×9 + 4)/9 =
= 85/8 - 58/9
the LCM of 8 and 9 is 72.
85/8 - 58/9 = (85×9)/(8×9) - (58×8)/(9×8) =
= 765/72 - 464/72 = 301/72 =
= (4×72 + 13)/72 = 4 13/72
5.
6 1/2 - 5 3/4 = (6×2 + 1)/2 - (5×4 + 3)/4 =
= 13/2 - 23/4
the LCM of 2 and 4 is 4.
13/2 - 23/4 = (13×2)/(2×2) - 23/4 =
= 26/4 - 23/4 = 3/4
Bonjour, je vous demande de l'aide pour ce gros exercice de maths niveau seconde merci d'avance.
Answer:
type in english
Step-by-step explanation:
english please
Can someone help p.l.z?? 50 pts
State all 4 ways to represent the Functions showing the slope and Y-intercept for each method.
Please help as much as you can, t.h.x. <3
Four ways to find the slope and y–intercept of straight line equation are;
Making use of the graph to find the slopeObtaining the coordinates of the x–intercept, Looking for the y–intercept when the slope and a point is knownSolving for the slope when two points are givenWhat is a straight line equation?A straight line equation is of the form, y = m•x + c
Where;
m = The slope of the graph of the equation
c = The point the graph intersects the x–axis.
The process by which the slope–intercept form of a straight line equation can be found from the above ways are as follows;
1. Making use of the graph of the equation
When the graph is given, the y–intercept is found from the point the graph crosses the y–axis
Note the y–intercept
Find two points on the graph where coordinates can be obtained
Find the ratio of the rise to the run to get the slope of the graph
[tex] \displaystyle{ Slope, \: m = \frac{ rise}{run} } = \frac{ \triangle y }{\triangle x} [/tex]
With the slope and y–intercept, the equation of the line can be written as; y = m•x + c
2. Obtaining the coordinates of the x–intercept
Given the slope and the y–intercept, the x–intercept can be found by plugging in the values of the slope, m, and the y–intercept, c, in the equation, y = m•x + c, to get the equation of the line
From the equation, the x–intercept can be found by plugging y = 0, to get;
0 = m•x + c
The x–intercept becomes, [tex] \displaystyle \frac{-c}{m} [/tex]
The graph can then be plotted by drawing a line through the x and y–intercept
3. Finding the y–intercept given the slope and the x–intercept
When the slope and the x–intercept and the slope is known, whole number part of the numerator can be added to the x–value of the x–intercept to obtain the x–coordinates of a second point on the graph
The process is repeated to find the y–coordinate of the second point
The slope is calculated using the two points and the equation for the slope given in the first method
4. When two points are known, the slope is calculated using the equation in method 1
The two are joined with a straight line and the y–intercept is obtained from the point the graph intersects the y–axis
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