The associative property of adding or multiplying can be represented by (a + b) + c = a + (b + c) and a * (b * c) = (a * b) * c
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The associative property states that when adding or multiplying it can be represented by:
(a + b) + c = a + (b + c)
For multiplication:
a * (b * c) = (a * b) * c
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Determine the area of a sector with√20 radius meters, and central angle 30°.
I will mark brainliest!
Answer Options:
20πm²
5π/3m²
30πm²
π/3²
Answer: [tex]\frac{5\pi}{3}[/tex]
Step-by-step explanation:
[tex]A=(\sqrt{20})^{2}(\pi)\left(\frac{30}{360} \right)=\boxed{\frac{5\pi}{3}}[/tex]
Equations Of Parabolas (Conics) Unscramble
The match is shown in the picture for the function of a parabola and the graph of a parabola.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
As we know the standard form of the parabola is:
y = a(x - h)² + k
If a > 0 (parabola opens upwards)
If a < 0 (parabola opens downwards)
or
x = a(y - h)² + k
If a > 0 (parabola opens right side)
If a < 0 (parabola opens left side)
Here (h, k) is the vertex of the parabola and a is the leading term.
Thus, the match is shown in the picture for the function of a parabola and the graph of a parabola.
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any solutions will each system of linear equations have? Match the systems with the correct number of
Solutions
Based on the information given, the correct options will be
y = x + 6 and 3x - 3y = -18 .... Infinitely many solutions.
y = -2x + 5 and 2x + y = -7 .... No solution.
y = -4x + 11 and -6x + y = 11 ... One solution.
Solving equations
y = -4x + 11 ....... equation i
-6x + y = 11 ...... equation ii
Put equation i into ii.
-6x + y = 11
-6x + (-4x + 11) = 11
-6x - 4x + 11 = 11
-6x - 4x = 11 - 11
-10x = 0
x = 0
Therefore, x = 0 and y = 11. This gives a solution for each variable.
y = -2x + 5 ..... i
2x + y = -7 ..... ii
Put equation I into ii
2x + y = -7
2x + (-2x + 5) = -7
2x - 2x = -7 - 5
0 = -12
This indicates no solution.
y = x + 6 ..... i
3x - 3y = -18 ..... ii
Put equation I into ii
3x - 3y = -18
3x - 3(x + 6) = -18
3x - 3x - 18 = -18
3x - 3x = - 18 + 18
0 = 0
This implies that there are infinitely many solutions.
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Here is the histogram of a data distribution. All class widths are 1.
SO
4
3
2-
2 3
Which of the following numbers is closest to the mean of this distribution?
A. 2
OB. 3
O C. 10
OD. 5
5 6 7 8 9 10
E. 4
The correct answer is option B which is 3
What is mean?
Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Given data:-
4,3,2
The mean will be calculated as:-
Mean = (4 + 3 + 2) / 3
Mean = 9 / 3
Mean = 3
Therefore the correct answer is option B which is 3
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Please answer this question i really want answers :(
Step-by-step explanation:
[tex] \sqrt{10} = 3.2 \\ then \: the \: sign \: there \: is \: = \\ \sqrt{10 } = 3.2 \\ \\ \: \sqrt{12} = 3.5 \\then \: the \: sign \: there \: is \: = \\ \: \sqrt{12} = 3.5 \\ \\ 6 \frac{1}{3} = 6.3 \: and \: \sqrt{40 } = 6.3 \\ therefore \: 6 \frac{1}{3} = \sqrt{40} \\ \\ 2 \frac{2}{5} = 2.4 \: and \: \sqrt{5.76} = 2.4 \\ then \: \: 2 \frac{2}{5} = \sqrt{5.76} \\ \\ 5 \frac{1}{6} = 5.16 \: and \: 516 \: \: therefore \: \\ 5 \frac{1}{6} = 5.16 \\ \\ \sqrt{6.2} = 2.5 \\ and \: 2.4 \: therefore \: \\ \sqrt{6.2} > 2.4[/tex]
What is the solution of
x²-1
2
x2 +5X+4
<0?
Answer:
Step-by-step explanation:
The value of the expression 2x2/x+(100-15x) when x=5 is
Answer:
27
Step-by-step explanation:
Find the time diffrence.
If u click there will be pic (very easy im just lazy lol)
Step-by-step explanation:
2 hours and 45 minutes.
8:45am + 2 hours = 10:45am
10:45am + 45 minutes = 11:30 am
Find the x- and y-intercepts of the parabola y=x2+10x+4
Answer:
x-intercepts: -5 +/-[tex]\sqrt{21}[/tex]. y-intercept: 4
Step-by-step explanation:
For x-intercepts use the quadratic equation
[tex]x= (-b +/-\sqrt{b^2-4ac} )/2a[/tex]
Fill in your values:
[tex]x= (-10 +/-\sqrt{100-16} )/2[/tex]
And solve
[tex]x=-5 +/- \sqrt{21}[/tex]
For y-intercepts set x=0 and solve. In this case, setting x= 0 gives you y=4.
What’s the vertex of this graph??
Answer:
(4, -3)
Step-by-step explanation:
A vertex is just a point at which 2 lines going in different directions meet, hence (4, -3)
Which statement is true about this equation Y=-3x2+4x+-11
Answer:
For plato users, the answer would be letter C.
Step-by-step explanation:
A.
It represents neither a relation nor a function.
B.
It represents a relation only.
C.
It represents both a relation and a function.
D.
It represents a function only.
This equation represents both a relation and a function.
Took the test, hope this helps!
Step-by-step explanation:
(x-8)^2 i need step by step please like eveyone gets x2 -16x +64 i dont get
how
Answer:
x²-16x+64
use formula =a²-2ab+b²x²-2.x.8+8² (for knowledge 2 × 8 = 16)x²-16x+64Answer:
(x -8)² = x² -16x +64
Step-by-step explanation:
A lot of math is about pattern recognition. For many of the patterns you are asked to recognize, it is helpful to be very familiar with basic math facts: addition facts, multiplication facts, and the squares and cubes of small integers.
All of algebra is based on a few properties of arithmetic and equality. One that is important here is the distributive property.
__
expanding a product of binomialsOne of the patterns that is used with quadratics is the square of a binomial.
(a - b)² = a² -2ab +b²
This is the result of applying the distributive property several times.
First of all, the exponent indicates repeated multiplication:
(a -b)² = (a -b)×(a -b)
The distributive property tells you each term outside parentheses multiplies each term inside:
= a×(a -b) -b×(a -b)
= a·a -a·b -b·a +b·b . . . . . and again
Now, we collect terms, recognizing that ab=ba.
= a² -2(a·b) +b² . . . . . . . using exponents for repeated multiplication
So, the pattern for the square of a binomial is ...
(a -b)² = a² -2ab +b²
__
using the patternFor your specific case, ...
a = xb = 8(x -8)² = x² -2(x)(8) +8² . . . . . . using the above pattern
(x -8)² = x² -16x +64
_____
Additional comment
If you want to do this without using the pattern, just make use of the distributive property:
[tex](x-8)^2=(x-8)(x-8)\\\\=x(x -8) -8(x-8)\\\\=x^2-8x-(8x-64)\\\\=x^2-8x-8x+64\\\\\boxed{(x-8)^2=x^2-16x+64}}[/tex]
__
While the distributive property is the fundamental property involved, some find it helpful to remember a mnemonic that gets you to the same result for the product of binomials: FOIL. The letters refer to First, Outer, Inner, Last, and they remind you of the terms that make up the expansion of the product:
(x -8)(x -8) -- First: x·x = x²(x -8)(x -8) -- Outer: x·(-8) = -8x(x -8)(x -8) -- Inner: (-8)·x = -8x(x -8)(x -8) -- Last: (-8)(-8) = 64Then the product is ...
(x -8)² = x² -8x -8x +64 = x² -16x +64
__
Of course, the distributive property is involved in what we call "collecting terms."
-8x -8x = (-8-8)x = -16x
The variable is factored out using the distributive property, then the coefficients are added to simplify the expression in parentheses.
whats the GCF of x^6 and x^4
if 300 equals 9 and 500 equals 16 what is the pattern? and what will 7 and 18 equal?
Step-by-step explanation:
hope you can understand
probability of independent events: decimal answers (probability and counting)
The probability that both are smokers is 6903/180000
How to determine the probability?The given parameters are:
Male smoker = 177
Female smoker = 78
Total student = 78 + 522 = 600
The probability of a male smoker is
P(Male) = 177/600
The probability of a female smoker is
P(Female) = 78/600
The probability that both are smokers is
P(Smoker) =P(Male) *P(Female)
So, we have:
P(Smoker) = 177/600 * 78/600
Simplify
P(Smoker) = 177/600 * 39/300
Evaluate the product
P(Smoker) = 6903/180000
Hence, the probability that both are smokers is 6903/180000
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3
cky has a board that is 2 feet long. She needs to cut the board into 11 pieces of equal length. How long
ould each piece be?
0.223 feet
0.25 feet
0.5 feet
0.75 feet
ase select the best answer from the choices provided
A
В
C
D
Answer:
0.223 is the answers for the question but I got this answer 0.181
Step-by-step explanation:
please mark me as brainlest
URGENT 30 points I need help
Answer:
- 112 + 100 n
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d
~~~~~~~
[tex]a_{1}[/tex] = - 12
d = 100
[tex]a_{n}[/tex] = - 12 + 100( n - 1 )
[tex]a_{n}[/tex] = - 12 + 100n - 100
[tex]a_{n}[/tex] = - 112 + 100 n
Find the inverse of the function.
y = -3x - 9
Write your answer in the form ax + b. Simplify any fractions.
y =
Answer: [tex]y=-\frac{1}{3} x-3[/tex]
Step-by-step explanation:
To find the inverse of a function you must first swap the places of x and y
[tex]x=-3y-9[/tex]
Now solve for y
Step 1: Flip the equation.
[tex]-3y-9=x[/tex]
Step 2: Add 9 to both sides.
[tex]-3y-9+9=x+9\\-3y=x+9[/tex]
Step 3: Divide both sides by -3.
[tex]\frac{-3y}{-3} =\frac{x}{-3} +\frac{9}{-3} \\y=-\frac{1}{3} x-3[/tex]
NEED HELP ASAP !!
Which equations are equivalent to 2 + 2 12-x1=1? Check all that apply.
Answer:
[tex]\frac{2}{3}|2-x|=\frac{1}{15}[/tex]
Step-by-step explanation:
[tex]\frac{1}{5} + \frac{2}{3} |2-x| = \frac{4}{15} \\\\\frac{1}{5}*(\frac{3}{3}) = \frac{3}{15}\\\\\frac{3}{15}-\frac{3}{15} + \frac{2}{3}|2-x| =\frac{4}{15}-\frac{3}{15}\\\\\frac{2}{3}|2-x|=\frac{1}{15}[/tex]
Which is the equation of the line with slope 0 passing through the point (-3, -1)?
manual spent 4.56 on a sandwich and 2.98 on a drink How much did he spend in all? If he paid with a 10$ bill how much change did he get
Manual paid with a $10 bill and he got $2.46 as a change.
What is subtraction?Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, −.
Money spent on sandwich=$4.56 and money spent on drink=$2.98.
We need to find out how much did he spend in all.
That is, the total money spent=4.56+2.98=$7.54
He paid with a $10 bill, he gets change as 10-7.54=$2.46
Hence, he paid with a $10 bill and he got $2.46 as a change.
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what are the coordinates of this point help plssssssssssssssss
Answer:
(-2, -4)
Step-by-step explanation:
Use the (x,y) thing:
x = -2
y = -4
therefore, (-2, -4)
Find the volume of a cylinder that has a diameter of 7 and a height of 8.
28 Pi
392 Pi
448 Pi
98 Pi
Therefore,
Radius (r) = d / 2Radius (r) = 7/2We know that :
V = πr^2hSubstituting the values :
>> V = π × (7 / 2)^2 × 8
>> V = π × (49 / 4) × 8
>> V = π × 49 × 2
>> V = 98π
Henceforth,
98 pi is the answer.We know , the volume of a cylinder is given by the formula – πr²h, where r is the radius of the cylinder and h is the height.
Diameter - 7Height - 8radius = 7/2Therefore, putting the values, we get,
[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: {r}^{2}h[/tex]
[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \times \: \bigg(\frac{7}{2} \bigg)^{2} \: \times \: 8 \\ [/tex]
[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{2} \: \times \: 8 \\ [/tex]
[tex] \Large \mathcal \purple {Volume } \large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{ \cancel2} \: \times \: \cancel{8} \: ^{ \orange4} \\ [/tex]
[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{ \cancel2} \: \times \: {7} \: \times \: \cancel4 \: ^{ \orange2} \\ [/tex]
[tex] \\ \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: 7 \: \times \: 7 \: \times \: 2[/tex]
[tex]\Large \mathcal \purple {Volume }\ \large\red\implies \tt \large \:\pi \: \times \: 49 \: \times \: 2[/tex]
[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:98 \:\pi[/tex]
Hence , the volume of cylinder is 98 pi
The weight of corn chips dispensed into a 24-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 25 ounces and a standard deviation of 0.8 ounce. What proportion of the 24-ounce bags contain more than the advertised 24 ounces of chips?
The percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
What is the z score?The z-score is a numerical assessment of a value's connection to the mean of a set of values, expressed in terms of standards from the mean, that is used in statistics.
Given data;
Mean,μ = 25
Standard deviation,σ=0.8
The Z score is found as;
[tex]\rm Z = \frac{x-\mu}{ \sigma } \\\\ Z = \frac{24-25}{0.8} \\\\ Z= -1.25[/tex]
The P-value for the obtained z score is .2113.
Hence the percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
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(a) Solve the following formula for b.
1
A = Zab
6
(b) Evaluate b when A= 18 and a = 5
1
(a) The formula A = ab solved for b is b =
6
(b) Evaluate b when A= 18 and a =
5
b = (Type an integer or a simplified fraction.)
Answer:
J Trump has to be a great day of school and I have a great
Step-by-step explanation:
you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you for your loss of school and I have a great day of school ii
The volume of a tree stump can be modeled by considering it as a right cylinder. Jin measures its radius as 11 in and its volume as 13685 cubic inches. Find the height of the stump in inches. Round your answer to the nearest tenth if necessary.
If the radius of tree stump is 11 inches and volume is 13685 cubic inches then the height will be equal to 36 inches.
Given Radius of tree stump is 11 inches and volume is 13685 cubic inches.
We know that the volume of cylinder will be equal to π[tex]r^{2} h[/tex].
Volume which is given as 13685 cubic inches.
13685=π[tex]r^{2}h[/tex]
π=22/7
13685=π[tex](11)^{2}[/tex]h
h=13685*7/22*121
h=95795/2662
h=35.98
if we round it to nearest tenth then the value of h be 36 inches.
Hence if radius is 11 inches, volume is 13685 cubic inches then the height of tree stump will be 36 inches.
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Answer:36
Step-by-step explanation:
Classify this triangle. (image down below)
(Acute scalene triangle. (Obtuse isosceles triangle. (Right isosceles triangle (Right scalene triangle?
Answer: Right iscoleces triangle
Step-by-step explanation: The square on the left bottom side means it is a right angle. The lines means that a side is congruent to the other side. By definition, iscoleces triangles have two congruent sides, so this must be it.
Answer:
right isosceles
Step-by-step explanation:
the right angle and the two sides that are equal make the triangle a right isosceles
5
14
6
3
1
2
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If
it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a
probability of winning.
B. Yes. Each friend has a
probability of winning.
C. No. Andrew has a probability of winning and Liz has a
probability of winning.
D. No. Andrew has a probability of winning and Liz has a
probability of winning.
The question is incomplete. Below you will find the missing figure.
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a 1/4 probability of winning.
B. Yes. Each friend has a 1/6 probability of winning.
C. No. Andrew has a probability of 1/4 winning and Liz has a probability of 1/6 winning.
D. No. Andrew has a probability of 1/3 winning and Liz has a probability of 1/4 winning.
The correct option is Option A: Yes. Each friend has 1/4 probability of winning.
Probability is the possibility of an event to happen which is the ratio of no. favorable outcomes and no. of total outcomes.
P = no. of favorable outcome/ total no. of outcome
Here given in the question,
If the spinner touches region 2 or 3, Andrew wins
If the spinner touches region 4, Liz wins.
This is fair play because both have the same size of region for winning.
If we cut the circle into 8 pieces,
as region 1 is the sum of 2 sub-parts of the circle,
possibility of spinner touching region 1= 2/8= 1/4
possibility of spinner touching the small region = 1/8
So the possibility of the spinner touching the region 2or 3= 1/8+1/8= 2/8= 1/4
Hence the possibility of Andrew wins= possibility of the spinner touching region 1= 1/4
possibility of Liz wins= possibility of the spinner touching the region 2 or 3= 1/4
Therefore the correct option is Option A: Yes. Each friend has 1/4 probability of winning.
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The function f(x) = x2 + 6x +7 is graphed below.
Drag the correct word and the the appropriate value to the box with each given interval to indicate whether the function is increasing or decreasing on that interval
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the function f(x) = x² + 6x + 7. This is a quadratic equation,that is of degree two.
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
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IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Find the probability, rounded to four decimal digits, that the person has an IQ greater than 120. Below is a sketch of the normal curve showing the area to be determined
The probability that the person has an IQ greater than 120 is 0.2524 of 25.24%
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
IQ is normally distributed with a mean of 100 and a standard deviation of 15.
probability that the person has an IQ greater than 120,
P(x >120)
= P(Z > 120-100/ 15)
= P(Z > 0.667)
P(x >120) = 1- P(Z < 0.667)
= 1-0.7476
= 0.2524
= 25.24%
Hence, the probability is 0.2524.
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