Answer:
Each person will be getting [tex]2\frac{2}{5}[/tex] pieces of licorice
Step-by-step explanation:
If we have 12 pieces of licorice
To divide it equally among 5 people following formula will be used
Pieces to be given to each person = [tex]\frac{total\, pieces}{total\,people}[/tex]
= [tex]=\frac{12}{5} \\2.4\\[/tex]
So
Each person will be getting [tex]2\frac{2}{5}[/tex] pieces of licorice
Keywords: Algebra
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PLEASE HELP!
First determine the degree of each polynomial expression below. Explain how you determined this on each expression.Then organize the expressions from least to greatest based on their degree
I. 6x^2
II. 18x^3+5ab-6y
III.8a-5
IV. 4x^3y+3x^2-xy-4
Degree of polynomials:
[tex]6x^2 = 2\\\\18x^3+5ab-6y = 3\\\\4x^3y +3x^2-xy-4 = 4\\[/tex]
Least to greatest based on degree:
[tex]6x^2[/tex]
[tex]18x^3+5ab-6y[/tex]
[tex]4x^3y +3x^2-xy-4[/tex]
Solution:
The degree of the polynomial is the highest degree of any of the terms
Know that the degree of a constant is zero
Option I
[tex]6x^2[/tex]
Here the highest degree is 2 ( x power 2)
In this case, degree of polynomial is 2
Option II
[tex]18x^3+5ab-6y[/tex]
To find the degree of the polynomial, add up the exponents of each term and select the highest sum.
[tex]Degree\ of\ 18x^3 = 3[/tex]
[tex]Degree\ of\ 5ab = 5a^1b^1 = 1+1 = 2[/tex]
[tex]Degree\ of\ 6y = 6y^1 = 1[/tex]
Thus the highest degree is 3
Option III
[tex]8a^{-5}[/tex]
This is not a polynomial
A polynomial does not contain variables raised to negative
Option IV
[tex]4x^3y +3x^2-xy-4[/tex]
To find the degree of the polynomial, add up the exponents of each term and select the highest sum.
[tex]Degree\ of\ 4x^3y = 4x^3y^1=3+1 = 4\\\\Degree\ of\ 3x^2 = 2\\\\Degree\ of\ xy = x^1y^1 = 1+1 = 2\\\\Degree\ of\ 4 = 0[/tex]
Thus highest degree is 4
Then organize the expressions from least to greatest based on their degree
Least to greatest based on degree:
[tex]6x^2[/tex]
[tex]18x^3+5ab-6y[/tex]
[tex]4x^3y +3x^2-xy-4[/tex]
Urgent!
Write a polynomial, P(x), in factored form given the following requirements.
Degree: 3
Zeros (roots) at (−2,0) with multiplicity 2 and (3,0) with multiplicity 1
P(x) passes through the point (2,80)
Answer:
The polynomial will be P(x) = - 5 (x + 2)²(x - 3)
Step-by-step explanation:
The degree of the polynomial P(x) is 3 and it has zeros at x = - 2 with multiplicity 2 and at x = 3 with multiplicity 1.
Therefore, (x + 2)² and (x - 3) are the factors of the equation.
Let the polynomial is
P(x) = a(x + 2)²(x - 3) ........... (1)
Now, the polynomial passes through the point (2,80).
So, from equation (1) we gat,
80 = a(4)²(-1)
⇒ a = - 5
Therefore, the polynomial will be P(x) = - 5 (x + 2)²(x - 3) (Answer)
The required polynomial is [tex]P(x) = - 5 (x + 2)^{2} (x - 3)[/tex]
Any polynomial have number of roots equal to its degree of polynomial.
Since, the degree of the polynomial P(x) is 3. it means that it has 3 roots.
it has zeros at x = - 2 with multiplicity 2, it means that factor (x - 2) have power 2 and at x = 3 with multiplicity 1 means that factor (x - 3) have power of 1 .
Thus, [tex](x + 2)^{2}[/tex] and (x - 3) are the factors of the equation.
Let us consider the polynomial is [tex]P(x) = k(x + 2)^{2} (x - 3) .[/tex]
Since, the polynomial passes through the point (2,80).
So, substituting point (2, 80) in above polynomial equation.
We get, [tex]80 = a(4)^{2} (-1)[/tex]
a = - 5
Therefore, the polynomial is [tex]P(x) = -5(x + 2)^{2} (x - 3) .[/tex]
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solve for x: 3(9-8x-4x)+8(3x+4)=11
Answer:
x=4
Step-by-step explanation:
3(9-8x-4x)+8(3x+4)=11
Subtract 4 x from − 8 x
3 ( 9 − 12 x ) + 8 ( 3 x + 4 ) = 11
Distribute
27 − 36 x + 24 x + 32 = 11
Simplify
− 12 x + 59 = 11
Subtract 59 to both sides
− 12 x = − 48
Divide by -12
x=4
What is 12 percent of 29
Answer:
3.48
Step-by-step explanation:
12%=0.12
0.12*29=3.48
Use the distributive property to clear parentheses.
-6(3x+4)
Answer:-18x-24
Step-by-step explanation:Use the PEMDAS method
explanation:-18x-24
Let n represent the position of a term in the sequence below.
8, 11, 14, 17, 20, 23,
Which algebraic expression can be used to find the nth term of the sequence
The algebraic expression can be used to find the nth term of the sequence is:
[tex]a_n = 5+3n[/tex]
Where, [tex]n\geq 1[/tex] and n is a positive whole number
Solution:
Given sequence is:
8, 11, 14, 17, 20, 23
Let us find the common difference between terms
11 - 8 = 3
14 - 11 = 3
17 - 14 = 3
20 - 17 = 3
23 - 20 = 3
Thus the common difference between successive term and previous term is constant
Thus this is a arithmetic sequence
The formula for nth term term of arithmetic sequence is given as:
[tex]a_n = a_1+(n-1)d[/tex]
Where,
[tex]a_n[/tex] is the nth term of sequence
[tex]a_1[/tex] is the first term of sequence
d is the common difference between terms
Here in this sequence, 8, 11, 14, 17, 20, 23
[tex]a_1 = 8\\\\d = 3[/tex]
Therefore,
[tex]a_n = 8+(n-1)3\\\\a_n = 8+3n -3\\\\a_n = 5+3n[/tex]
Where, [tex]n\geq 1[/tex] and n is a positive whole number
Thus algebraic expression can be used to find the nth term of the sequence is found
The tree diagram represents an experiment consisting of two trials.
P(A and C) = [?]
Yo sup??
P(A)=0.5
P(C|A)=0.4
Therefore
P(A and C)=0.5*0.4
=0.2
Hope this helps.
The required probability is P(A and C) is 0.2 which is represented in the tree diagram.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The given tree diagram represents an experiment consisting of two trials.
The tree diagram represents an experiment consisting of two trials. In this case, the probability of event A and event C occurring is represented by the intersection of branches A and C in the tree diagram.
This probability can be calculated by multiplying the probability of each individual event together.
As per the given question, we have
P(A) = 0.5
P(C|A) = 0.4
So, P(A and C) = 0.5 × 0.4 = 0.2
Thus, the required probability is P(A and C) is 0.2
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how to find the height of a square based pyramid when you are given the length of the base sides and the slant height?
Answer:
use the Pythagorean theorem
Step-by-step explanation:
The slant height is the hypotenuse of a right triangle whose legs are the height of the pyramid and the distance from the edge of the base to the center of the pyramid (where the height segment reaches the base).
For h = pyramid height, b = base edge length, s = slant height, the Pythagorean theorem tells you ...
h² + (b/2)² = s²
Solving for h gives ...
h = √(s² -(b/2)²) . . . . . the height of the pyramid
Tina is fixing a rectangular sign. She plans to place a metal trim around the sign edges. The rectangle measures 32 inches by 9 inches. How much trim will Tina need?
Answer:288
Step-by-step explanation:32 x 9 = 288
RSTV is a parallelogram. Line RT and Line SV intersect at Q. RQ = 5x+1 and QT = 3x+15. Find QT
QT = 36
Step-by-step explanation:
Step 1 :
Lines RT and SV are the diagonals of the parallelogram RSTV.
Step 2 :
The diagonals of a parallelogram bisect each other . (Properties of a parallelogram)
Step 3 :
Given that the diagonals RT and SV intersect at Q, we have QT = RQ.
=> 5 x + 1 = 3 x + 15
=> 5 x - 3 x = 15 -1
=> 2 x = 14
= > x = 7
Step 4:
QT = 3 x + 15
=> QT = 3 * 7 + 15
=> QT = 21 + 15 = 36
Applying the properties of the diagonal of a parallelogram, the length of QT = 36 units.
Diagonals of a ParallelogramThe diagonals of a parallelogram are always congruent to each other.When the diagonals intersect, they bisect each other, that is, they cut each other into equal segments.Therefore,
RQ = QT
Substitute5x + 1 = 3x + 15
Add like terms5x - 3x = -1 + 15
2x = 14
x = 7
QT = 3x + 15
Plug in the value of xQT = 3(7) + 15
QT = 36
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Use the multiplier method to increase 258 by 43
Answer:
368.94
Step-by-step explanation:
New value =
258 + Percentage increase =
258 + (43% × 258) =
258 + 43% × 258 =
(1 + 43%) × 258 =
(100% + 43%) × 258 =
143% × 258 =
143 ÷ 100 × 258 =
143 × 258 ÷ 100 =
36,894 ÷ 100 =
368.94
To increase 258 by 43% using the multiplier method, multiply 258 by 1.43. The result is 369.14.
Explanation:To use the multiplier method to increase 258 by 43, you simply need to calculate 258 times the multiplier. The multiplier is 1 plus the rate of increase, which is 43% in this case. So, the multiplier is 1+0.43=1.43.
Here is the calculation:
258 * 1.43 = 369.14
So, 258 increased by 43% is approximately 369.14.
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A circle has a circumference of 56π centimeters (cm). What is the radius of the circle?
Answer:
if C = 56pi, you do plug in the given by using the formula C = 2pi(r)
56pi = 2pi(r)
56/2 = r
r= 28
the radius is 28
Identify all the sets to which the number belongs. Choose from Rational Number, Irrational number, whole number, and integer. 1.256...
A. Rational number
B. Irrational number
C.Integer, and rational number
D. Whole number, Integer, and rational number
Answer:
The number 1.256 is A)rational number.
Step-by-step explanation:
A whole number is a non-negative number without any digits behind the decimal. An integer is a set of negative and non negative numbers that don't have any digits behind the decimal.A number that can be shown as a fraction of two whole numbers is a rational number.And the numbers that are not rational are irrational numbers.Here, 1.256 is a fraction of whole numbers 1256 and 1000 , so it is a rational no.[tex]\frac{1256}{1000} =1.256[/tex]
But since it has digits behind the decimal it is neither a whole number, or an integer.The number 1.256... is a rational number because it can be expressed as a ratio of two integers. It is not an integer, whole number, or irrational number.
Explanation:The number 1.256 repeated is a rational number because it can be expressed as the ratio of two integers, which fits the definition of a rational number as ratios of integers such as 2/1, 3/4, and so on.
Even though the decimal representation may appear to continue forever, if the pattern of digits repeats indefinitely, it is still rational.
This number is not an integer, whole number, or irrational number, so it does not belong to those sets. An integer is a whole number without any fractional or decimal part, positive or negative, including zero.
Therefore, the correct option that defines the sets to which the number 1.256... belongs is Option A: Rational number.
Make Q the subject of formula.
[tex]T=\sqrt{\frac{PQ}{R} }-R^{2}Q[/tex]
Answer:
Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))
Step-by-step explanation:
Solve for Q:
T = sqrt((P Q)/R) - Q R^2
T = sqrt((P Q)/R) - Q R^2 is equivalent to sqrt((P Q)/R) - Q R^2 = T:
sqrt((P Q)/R) - Q R^2 = T
Add Q R^2 to both sides:
sqrt((P Q)/R) = Q R^2 + T
Raise both sides to the power of two:
(P Q)/R = (Q R^2 + T)^2
Expand out terms of the right hand side:
(P Q)/R = Q^2 R^4 + 2 Q R^2 T + T^2
Subtract Q^2 R^4 + 2 Q R^2 T + T^2 from both sides:
(P Q)/R - Q^2 R^4 - 2 Q R^2 T - T^2 = 0
Collect in terms of Q:
-Q^2 R^4 - T^2 + Q (P/R - 2 R^2 T) = 0
Divide both sides by -R^4:
Q^2 + T^2/R^4 - (Q (P/R - 2 R^2 T))/R^4 = 0
Subtract T^2/R^4 from both sides:
Q^2 - (Q (P/R - 2 R^2 T))/R^4 = -T^2/R^4
Add (P/R - 2 R^2 T)^2/(4 R^8) to both sides:
Q^2 - (Q (P/R - 2 R^2 T))/R^4 + (P/R - 2 R^2 T)^2/(4 R^8) = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4
Write the left hand side as a square:
(Q - (P/R - 2 R^2 T)/(2 R^4))^2 = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4
Take the square root of both sides:
Q - (P/R - 2 R^2 T)/(2 R^4) = sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
Add (P/R - 2 R^2 T)/(2 R^4) to both sides:
Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:
Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt((P^2)/(4 R^10) - (P T)/(R^7)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
Add (P/R - 2 R^2 T)/(2 R^4) to both sides:
Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4))
(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:
Answer: Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))
The rations that are equivalent to 16:12
Answer:
4:3, 32:24, 8:6
Step-by-step explanation:
for 4:3, you divide both sides of 16:12 by 4
for 32:24 you mutiple both sides by 2
for 8:6 you multiply both sides by 2
Hope this helps :)
Pirate Jack has an equal number of gold and silver coins. If Pirate Jack splits all of his coins into 7 equal piles for his parrots, he has 4 coins left. Or, if he splits all of his coins into 11 equal piles for his shipmates, he has 4 coins left. Assuming every pile has at least 1 coin, what is the least possible number of coins Pirate Jack has?
Answer:
The least possible number of coins that Pirate Jack has is 77.
Step-by-step explanation:
i) let the number of coins in the piles for the parrots be x.
ii) therefore we can say that the total number of coins be 7x + 4
iii) let the number of coins in the piles for for the pirates be y.
iv) therefore we can say that the total number of coins be 11y + 4
v) therefore we can say that 7x + 4 = 11y + 4
vi) therefore 7x = 11y
vii) therefore the least possible number of coins that Pirate Jack has is equal to the LCM of 11 and 7 which is 77.
viii) x = 11 and y = 7
Answer:
158 coins
Step-by-step explanation:
Jack's number has to be an even number, because he can split his gold and silver coins evenly.
77 is the LCM of 11 and 7 and add 4 (the remainder) to get 81.
But it has to be an even number since he can split his coins evenly.
You can then do 77 times 2, and add 4 to get 158, which is the answer.
How many solutions y=x^2-10x+25
Step-by-step explanation:
Given,
y = [tex]x^2[/tex] - 10x + 25
To find, the total number of solutions = ?
∴ y = [tex]x^2[/tex] - 10x + 25
⇒ y = [tex]x^2[/tex] - 2(x)(5) + [tex]5^2[/tex]
⇒ y = [tex](x-5)^{2}[/tex]
There are infinite solution of y.
Thus, there are infinite solution of y.
A handyman charges $150 plus $25 per hour for painting a house. How much will the costumer have to pay if he paints the house for 13 hours in total?
A.325
B.475
C.1,950
D.1,975
Answer: B
Step-by-step explanation: you multiply 25 x 13 + 150
need helpppppppppppppppppppppppppppp
Answer:
lower case p
Step-by-step explanation:
The law of sines: [tex]\frac{sinA}{a} = \frac{sinB}{b}[/tex]
Therefor look for which sides and angles are accounted for. If we are given angle P, Angle R, and Side r, then Side p is the last term that fits into the law of sines equation.
What is the average rate of change for ƒ(x) = −4x + 40 over the interval 1 ≤ x ≤ 3?
Answer:
The average rate of change is = - 4
Step-by-step explanation:
If y = f(x) is a function then the average rate of change for f(x) between the interval a ≤ x ≤ b is given by
[tex]\frac{f(b) - f(a)}{b - a}[/tex].
Now, in this case the function is given by f(x) = - 4x + 40 and the interval is 1 ≤ x ≤ 3.
Therefore, f(1) = - 4(1) + 40 = 36 and f(3) = - 4(3) + 40 = 28
So, the average rate of change is = [tex]\frac{28 - 36}{3 - 1} = - \frac{8}{2} = - 4[/tex] (Answer)
Answer:
−30
Step-by-step explanation:
−30 is the average rate of change for ƒ(x) = −4x + 40 over the interval 1 ≤ x ≤ 3.
ƒ(b) − ƒ(a)
b − a
= ƒ(3) − ƒ(1)
3 − 1
= −24 − 36
2
= −60
2
= −30
mike rides his bike with a constant speed of 12 miles per hour how far can he travel in 3 1/2 hours?
Answer:
42 miles
Step-by-step explanation
Distance = Speed * Time
X=12mph*3.5h
X=42 miles
Distance he can travel is 42 miles.
Step-by-step explanation:
Step 1: Given speed = 12 miles/hour and time = 3 1/2 hours = 7/2 hoursStep 2: Calculate distance using the formula Distance = Speed × Time⇒ Distance = 12 × 7/2 = 42 miles
Use the following paycheck to answer the question.
What percent of Zachary's pay do his deductions comprise?
To calculate the percentage of Zachary's pay that his deductions comprise, divide the total amount of deductions by the total pay, then multiply by 100.
Explanation:To find out what percent of Zachary's pay his deductions compromise, you need to divide the total amount of deductions by the total amount of his pay, and then multiply by 100 to get the percentage.
Let's use an example. If Zachary's total deductions are $300 and his total pay is $1000, you would do the following calculation:
Divide 300 by 1000. This will give you 0.3. Multiply 0.3 by 100. This will give you 30.
In this example, Zachary's deductions comprise 30% of his total pay.
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If y = -x² + 14x + 7 , then x = 10 is a counterexample for which conjecture?
A.
y is always positive.
B.
y is always negative.
C.
y is a function of x.
D.
The graph of y is a parabola.
Answer:
The correct answer is B
Step-by-step explanation:
If we plug in x=10 to the equation, we get y=47
Since y is positive, A is not an counterexample
Since y is a function of x, C is not an counterexample
Since the graph of y is a parabola, D is not an counterexample
Hope this helped and mark as brainliest!
You have 3 quarters, 7 dimes, and 5 nickles in your pocket. A coin is chosen at random. What is the BEST answer for the probability of drawing a quarter?
A) impossible
B) unlikely
C) very likely
D) certain
Answer:
B) Unlikely
Step-by-step explanation:
Your chance drawing a quarter is a low 20%
Answer:
B:Unlikely
Step-by-step explanation:
Because you have 7 dimes and 5 nickels so those ones would be more likely to be picked than the quarter but it is still possible.
A rectangle is eight inches and diagonal is ten
inches. What's the width of the rectangle?
Answer: Its width is 6inches.
Step-by-step explanation:
The given information can be used to construct a right angled triangle. Now applying the Pythagoras theorem,
10^2 = W^2 + 8^2
where w represents the width.
100 = w^2 + 64
100 - 64 = w^2
36 = w^2
find the square root of both sides,
6 = w
Therefore, w = 6 inches
Thus the width of the rectangle is 6 inches.
Can anyone help me please
Angle A and Angle B are identical, so AC and BC are also identical.
ABC = AC
3x -7 =20
Add 7 to both sides:
3x = 27
Divide both sides by 3:
x = 9
Paul's family drove 377 mi to the beach averaging 58 mi/h on the way there. On the return trip home, they averaged 65 mi/h.
What was the total time Paul's family spent driving to and from the beach?
11.3 h
11.6 h
12.3 h
13 h
Answer:
12.3 hours
Step-by-step explanation:
So other person can get brainliest
What is 38.96 × 15.7 with work
6 yd
Area:
Circumference:
From the problem above, if
you doubled the length of the
radius, what would be the
ratio of the area of the
smaller circle to the larger
circle?
Answer:
Pie
Step-by-step explanation:
Answer:
pi
Step-by-step explanation:
What is r/32=5/8=30/t
Step-by-step explanation:
[tex] \frac{r}{32} = \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: \frac{r}{32} = \frac{5}{8} \\ \\ \therefore \: r = \frac{32 \times 5}{8} \\ \\\therefore \: r = 4 \times 5\\ \\ \huge \orange{ \boxed{\therefore \: r = 20}} \\ \\ \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: t = \frac{8 \times 30}{5} \\ \\ \therefore \: t = 8 \times 6 \\ \\ \huge \purple{ \boxed{ \therefore \: t = 48}}[/tex]