150
The median is where the line inside the box sits. That's the halfway point between all of the data. (Halfway in terms of "if you line everything up and it's the data point in the middle.")
f) Find the area of one small triangle
Answer:
Where is the triangle?
Step-by-step explanation:
-30 = m divided by 13
Answer:
If you're looking for the equivalent of m then it is -390
Step-by-step explanation:
-30 = m divided by 13 is the same as -30 times 13 = m
Finally m is equal to -390
Answer:
m = -390
Step-by-step explanation:
Given statement,
→ -30 = m divided by 13.
Forming the equation,
→ -30 = m/13
Now the value of m will be,
→ -30 = m/13
→ m/13 = -30
→ m = -30 × 13
→ [ m = -390 ]
Hence, value of m is -390.
use a=6 and b=30 to work out the value of these expression.(a+b)^2
Answer:
1296
Step-by-step explanation:
(6+30)²=36²=1296
Answer:
1296
Step-by-step explanation:
(6+30)^2
(36)^2
1296
Solve: log2(3x + 8) = 5 which is an equivalent equation? 25 = 3x + 8 52 = 3x + 8 25 = [log2(3x + 8)]2 52 = [log2(3x + 8)]5.
The mathematical function known as a logarithm expresses the degree to which a base number must be raised in order to obtain a specific value. The symbol logb(x), where b is the logarithm's base and x is the value being evaluated, stands for the logarithm of a number. The natural logarithm, which has a base of e, is the most widely used logarithm (approximately 2.71828). The inverse function of exponentiation is the logarithm, according to this definition. The exponent to which we must raise b in order to obtain a number x is its logarithm to base b.
It reads log2(3x + 8) = 5.
logb(a^n) = n * logb(a) where b is the base of the logarithm, is a property of logarithms that can be used to rewrite expressions. Since the base in this instance is 2, we obtain log2(3x + 8) = 5.
corresponding to 2^5 = 3x + 8
Now that x is on one side of the equation, we can solve for it.
32 = 3x + 8
After deducting 8 from both sides, we arrive at 24 = 3x, which we then multiply both sides by to get 8
Thus, x = 8 is the corresponding equation.
and the solution is 8.
Therefore, the x=8 is the solution of this problem .
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Answer:
1. a 2. 8
Step-by-step explanation:
What percent of 70 is 10?
what percent of 2.8 is 20?
18 is what percent of 90?
55 is what percent of 10?
Part A: percent of 70 is 10.
x% of 70 = 10
70x / 100 = 10
x = 1000 / 70
x = 14.28 %.
Part B: percent of 2.8 is 20.
x% of 2.8 = 20
2.8x/ 100 = 20
x = 2000/ 2.8
x = 714.28%
Part C: percent of 90 is 18.
x% of 90 = 18
90x/100 = 18
x = 1800 / 90
x = 2 %
Part D: percent of 10 is 55.
x% of 10 = 55
10x / 100 = 55
x = 5500/ 10
x = 550%.
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Supplementary angles are two angles that have measures with a sum of 180°. Angles 1 and 2 are supplementary and the measure of angle 2 is 3° more than twice the measure of angle 1.
The measure of Supplementary angles is ∠1 is 59° and ∠2 is 121°.
What are Supplementary angles?The word "supplementary" refers to two angles coming together to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles. If two angles complement one another.
It has an acute angle on one side and an obtuse angle on the other.
The angles are both right angles.
Given ∠1 and ∠2 are supplementary angles,
let ∠ 1 = x°
∠1 + ∠2 = 180°
so ∠2 = 180 - x
angle 2 is 3° more than twice the measure of angle 1,
and ∠2 = 3 + 2x
substitute the values
∠2 = 180 - x
3 + 2x = 180 - x
2x + x = 180 - 3
3x = 177
x = 177/3
x = 59°
∠2 = 180 - x
∠2 = 180 - 59
∠2 = 121°
Hence the value of ∠1 is 59° and ∠2 is 121°.
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Clocks the minute hand of a grandfather clock is 3 feet long, and the hour hand is 2 feet long. Is the distance between their ends greater at 3:00 or at 8:00?
Answer:
8:00
Step-by-step explanation:
This is probably extremely late
distance between their ends greater at 8.00
What is the distance between?from 0 we know that when the clock is 3.00 the distance between minute and hour hand is a=√a²+b²=√2²+3²=√13 from 2 we know that angle is 120 degree the clock is 360 degree and average divide into 12 large cells every cell is 360/12=30 90+30=120First note that a clock is a circle made of 360 degrees, and that each number represents an angle and the separation between them is 360/12 = 30. And at 2:00, the minute hand is on the 12 and the hour hand is on the 2. The correct answer is 2 * 30 = 60 degrees.We can say that any one of the hands is a complete clock circle. Therefore the angle between the hands of a clock at twelve o'clock is zero degreesTo learn more about angle of clock refers to:
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Given the functions f(x) = 4x2 - 1, g(x) = x2 - 8x + 5, and h(x) = -3x2 - 12x + 1, rank them from least to greatest based on their axis of symmetry. (2 points)
The axis of symmetry for a parabola in the form of f(x) = a(x - h)^2 + k is x = h.
For f(x) = 4x^2 - 1, the axis of symmetry is x = 0.
For g(x) = x^2 - 8x + 5, the axis of symmetry is x = 4.
For h(x) = -3x^2 - 12x + 1, the axis of symmetry is x = -4/3
So, the ranking from least to greatest based on their axis of symmetry would be:
h(x) = -3x^2 - 12x + 1 with x = -4/3
g(x) = x^2 - 8x + 5 with x = 4
f(x) = 4x^2 - 1 with x = 0
What is the y-intercept of y =- 2 3x 7?.
The y-intercept of y =- 2/3x + 7 is 7.
The equation, y = mx + b, is the slope-intercept form of a straight line.
Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.
y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.
The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.
Thus, The y-intercept of y =- 2/3x + 7 is 7.
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You buy a car for $22,000 and every year your car depreciates by 14% (in other words, you car decreases in value by 14% every year). What is your car worth in 4 years?
(Create an exponential function to solve this problem.)
Question options:
$18,920
$37,157
$12,034
$25,080
$12034 is the worth of the car after 4 years.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given that we purchased a car for $22,000
Every year your car depreciates by 14%
We have to find the worth of the car after 4 years.
[tex]A=P(1-r)^{t}[/tex]
P is the principal amount=$12000
r is rate of interest =14%=0.14
t is time =4 years
A=22000(1-0.14)⁴
A=22000(0.86)⁴
A=22000×0.547
A=$12034
Hence, $12034 is the worth of the car after 4 years.
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Beatrice and Marshall are salespeople who earned the same
amount this week, although Marshall made 5 more sales than
Beatrice. Beatrice earns a base of $276 plus $11 per sale. Marshall
earns a base of $29 plus $23 per sale. How many sales did Beatrice
make this week?
Beatrice made 11 sales this week. The solution has been obtained using linear equations.
What is linear equation?
A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.
Let the sales of Beatrice be 'x'.
Since, Marshall made 5 more sales than Beatrice, we get
Sales of Marshall= x+5
Thus, Earnings of Beatrice = $276 + $11x
Earnings of Marshall = $29 + $23(x+5)
We are given that Beatrice and Marshall have earned the same amount this week, therefore,
⇒$276 + $11x = $29 + $23(x+5)
⇒$276 + $11x = $29 + $23x + $115
⇒$12x = $132
⇒x = $132/$12
⇒x = 11
Hence, Beatrice made 11 sales this week.
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How do you write a solution set answer?.
We can demonstrate the solution set in a number of different ways. Number line, interval notation, and set notation are all options for accomplishing this.
Depending on the question, these methods may or may not be used.
There are two ways to write the interval notation solution set.
The closed interval is the first. The solution is enclosed by square brackets and includes the endpoints in a closed interval.
The form [a, b] is used to indicate this. The set notation, on the other hand, is x a x b. This indicates that the solution set runs from a to b, with the second interval being open. The endpoints are not included in the solution when an open interval is enclosed by round brackets ().
The format used for this is (a, b). The set notation, on the other hand, is x a x b. The solution set is therefore situated between a and b.
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A circle of radius 3cm has the center at (-2, 3) . Find the equation of the circle in the form of x2+y2+Px+qy+c=0
The equation of the circle in the form of x^2 + y^2 + Px + qy + c = 0
The standard form of the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.
Given the center of the circle is (-2,3) and the radius is 3cm.
Substituting the given values we get (x + 2)^2 + (y - 3)^2 = 3^2
Expanding and simplifying we get x^2 + 4x + 4 + y^2 - 6y + 9 = 9
x^2 + 4x + y^2 - 6y + 5 = 0 is the equation of the circle in the form of x^2 + y^2 + Px + qy + c = 0
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How do you graph an absolute value function example?.
The one example of absolute value function is x =|y| , and the graph is sketched below .
What is Absolut value Function ?
The absolute value function is defined as a function in algebra that consists of the variable in the absolute value bars. The general form of absolute value function is written as f(y) = a |y - h| + k .
let the absolute value function be : x = |y| ;
we put y = -1 , we get ⇒ x = 1 ;
we put y = 1 , we get ⇒ x = 1 ;
we put y = 0 , we get ⇒ x = 0 ;
from the above points we observe that , what ever we put in the function , the result "x" is always positive .
Therefore , the graph of the function x = |y| , is a V shaped graph that faces Right .
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3100 dollars is placed in an account with an annual interest rate of 7.25%. To the
how long will it take for the account value to reach 25300 dollars?
nearest year,
Answer: 8.46 years
Step-by-step explanation:
To find out how long it will take for the account value to reach $25,300, you would need to use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (25,300)
P is the initial amount (3,100)
r is the annual interest rate (7.25%)
n is the number of times the interest is compounded per year
t is the number of years
In this case, we can assume that the interest is compounded annually, so n=1.
We can then plug in the values and solve for t:
25,300 = 3,100(1 + 0.0725)^t
t = (ln(25,300/3,100)) / (ln(1 + 0.0725))
t ≈ 8.46 years
So it would take approximately 8.46 years, rounded to the nearest year.
Answer:
The correct answer would be 30
Step-by-step explanation:
8. Please help
Below are the results for
finding the solution to a
system of equations. State
how many solutions the
different results yield and
explain why.
X = -5
y = 2
The results for X = -5 and y = 2 yield one solution.
What is equation?An equation is an expression that states the equality of two values using mathematical operators. It is a mathematical statement consisting of an expression involving variables and constants, connected by an equal sign. Equations are used to solve problems in a wide range of fields, such as science, engineering, and economics.
This is because a system of equations will always have either one solution, no solutions, or infinitely many solutions. Since the equations are equal to a single value, the solution is unique, yielding one solution.
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How do you graph two equations with two variables?.
Find the x and y-intercepts of the line. Let y and solve for x. Let x and solve for y. Find a third solution to the equation. Plot these three coordinates and check that they line up. Draw the line.
Let the equation be y = Px + Qz. P and Q are constants, and x and z are 2 variables.
Firstly, make one variable 0, z = 0. This implies that you are dealing with only two variables, so you can make a graph(1) on X and Y axis. A simple line passes through the origin. Now take z = 1, and plot on the same plane, i.e., Plot y = Px + Q (this will be graph 2). Similarly, for all z. You will get a set of parallel lines separated by B.
Then you realize that only Graph(1) belongs to the z = 0 plane. and Graph(2) belongs to z = 1 plane and so on for z = 2, 3, 4….
So all you get is a Plane with slope P with respect to the x-axis and slope Q with respect to slope Q.
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What is a 140 degree angle called?.
Answer:
Obtuse
Step-by-step explanation:
An angle that is measured more than 90 degrees is an obtuse angle. Although an angle that measures 180 degrees is a straight angle or a half angle, and an angle that measures 360 degrees is a straight angle or a complete angle. However, when it's 360 degrees it's a full circle because a circle measures 360 degrees. If you want to measure an angle to determine which one it is, you must use a protractor.
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Answer:
obtuseStep-by-step solution:
Let's first familiarize ourselves with the basic types of angles out there.
The simplest angles are:
Acute AnglesRight AnglesObtuse AnglesIn a nutshell, acute angles are angles whose measure is less than 90 degrees, right angles are the ones whose measure is exactly 90 degrees, and obtuse angles are the ones whose measure is greater than 90 degrees.
Here's what an obtuse angle looks like.
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\linethickness{.4mm}\qbezier(1,1)(1,1)(5.5,1)\qbezier(1,1)(1,1)( -1,4)\qbezier(0.65,1.55)(1.5,1.8)(2,1)\put(3,3){\rm Obtuse Angle :}\put(3,2.5){\it measures more than}\put(3,2){\sf 90 degrees}\end{picture}[/tex]
--
Now, since 140 measures more than 90 degrees, it's an obtuse angle.
[tex]\therefore\quad\underline{\boxed{\sf{The~angle~is~obtuse}}}[/tex]
Why do trigonometric ratios only depend on the angle?.
Trigonometric ratios depend only on angles as they remain constant no matter what.
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides relate to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. The sin, cos, and tan functions can be used to obtain the other significant trigonometric ratios, cosec, sec, and cot.
Even if the sides of the triangle increases or decreases in a specific ratio, the angles of the triangle will always remain the same no matter what.
Trigonometric ratios in right triangles are therefore independent of the side lengths and solely depend on the magnitude of the angles.
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A quare play area ha an area of 81 q ft. Lyla want to put fencing around to keep the dog out. How many feet of fencing will he need?
36 feet of fencing will be needed
The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square metres serving as the standard unit (m2).
Area of a Square = Side × Side
Therefore, the area of square = Side2 square units
and the perimeter of a square = 4 × side units
Area of square field = 81 hectare
1 hectare = 10000 sq.m.
So, 81 hectare = 810000 sq.m.
So, Area of square field = 810000 sq.m.
Area of square=Side²
side²=810000
side =√810000
side=900
So,
Perimeter of square = 4× side
Perimeter of square field = 4 × 900 =3600m
Therefore 36 feet of fencing will be needed
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What is not a perfect square trinomial?.
In a perfect square trinomial, two of your terms will be perfect squares. If you do not have two perfect square terms, then this trinomial is not a perfect square trinomial.
The general shape of a really perfect rectangular trinomial is (x + y)^2, in which x and y are the roots of the trinomial. to check if a trinomial is perfectly rectangular, we will try to the component it into the rectangular binomial. We also can whole the square technique, which involves adding and subtracting the rectangular of 1/2 of the x-coefficient of the linear time period after which grouping the resulting phrases.
It's far essential to note that for a trinomial to be a super rectangular trinomial, the regular time period has to be a square of an integer and the linear time period should be an excellent variety.
Perfect rectangular trinomials are used in fixing quadratic equations and expertise their solutions, they also have programs in algebra, geometry, and trigonometry. Factoring them is an essential talent in algebra and is utilized in solving exceptional types of mathematical troubles.
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8. The population of a small village is in the following ratios:
• Adult Males: Children = 11:3
• Adult Women: Children = 5:2
The difference between the number of Adult Males and Adult Females is 28.
Find the number of children in the village.
Answer:
24 children
Step-by-step explanation:
Given ratios:
Adult Males: Children = 11 : 3Adult Females : Children = 5 : 2Multiply the first ratio by 2 and the second ratio by 3 so that the ratios of children are the same:
Adult Males: Children = 11 × 2 : 3 × 2 = 22 : 6Adult Females : Children = 5 × 3 : 2 × 3 = 15 : 6Therefore the combined ratio is:
Adult Males : Adult Females : Children = 22 : 15 : 6So the ratio of Adult Males to Adult Females is 22 : 15.
If the difference between the number of Adult Males and Adult Females is 28 then:
[tex]\implies \dfrac{22}{22+15}x-\dfrac{15}{22+15}x=28[/tex]
[tex]\implies \dfrac{22}{37}x-\dfrac{15}{37}x=28[/tex]
[tex]\implies \dfrac{7}{37}x=28[/tex]
[tex]\implies 7x=1036[/tex]
[tex]\implies x=148[/tex]
Therefore:
[tex]\implies \textsf{Adult Males}=\dfrac{22}{37} \times 148=88[/tex]
[tex]\implies \textsf{Adult Females}=\dfrac{15}{37} \times 148=60[/tex]
If the original ratio of Adult Males to Children is 11 : 3, and the number of Adult Males is 88:
[tex]\implies 11:3=88:c[/tex]
[tex]\implies \dfrac{11}{3}=\dfrac{88}{c}[/tex]
[tex]\implies 11c=264[/tex]
[tex]\implies c=24[/tex]
Therefore, the number of children in the village is 24.
What is a solution to this system of equations?.
A system of equations is an arrangement of one or more equations with many variables.
The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.Consequently, x = 1, y = -1, and z = 2 make up the solution set of the given system of linear equations. Eliminate all possible solutions to the following system of linear equations. In order to better understand systems of linear equations and methods for solving them, we can categorize these systems as inconsistent, dependent, or independent and consistent based on the quantity of solutions. Equation systems without any solutions are inconsistent, whereas equation systems with an infinite number of solutions are dependent.To know more about equations here
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What is a 20 degree angle called?.
A 20 degree angle called an acute angle.
Any angle which is less than 90 degree but greater than 0 degree is called an acute angle. For example - 20, 30, 40 , 50 etc are acute angles.
Polygons with at least one acute angle include triangles, parallelograms, trapezoids, and so on.The acute angle that are present in the triangle they are known as acute angle triangle.
Properties of acute angle triangles:
Acute triangles are all equilateral triangles. An equilateral triangle has three equal-length sides and three equal-measure angles, i.e. 60°.The longest side of an acute triangle is opposite the highest angle.Isosceles, equilateral, and scalene triangles are examples of acute triangles.To know more about acute angles visit: https://brainly.com/question/28451077
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What does it mean when an observational study is prospective?
- A prospective study requires that individuals took hack in time or require the researcher to look at existing records - A prospective study collects the data over time.
- A prospective study is a list of all individuals in a population along with certain characteristics of each individual.
Prospective observational studies involve collecting data from participants before an event or outcome occurs, while retrospective observational studies collect data after the event has already taken place.
A prospective observational study is a type of observational study that involves collecting data from participants before an event or outcome occurs. This type of study is used to predict and measure outcomes in the future.
In this type of study, the researcher can control the variables, such as when and how the data is collected, and can also observe the effects of any changes in the environment.
On the other hand, a retrospective observational study is a type of observational study that involves collecting data after an event or outcome has already taken place. This type of study is used to study the causes of a given outcome.
In this type of study, the researcher looks back in time and collects data from the past. This type of study is more limited than a prospective observational study, since the researcher cannot control the variables of the study or observe any changes in the environment.
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Can someone please help me with this math problem? ASAP!
The math problem is in the picture, THANKS!
Domain:
Range:
Answer :
Domain: Domain of a functions is defined as set of all values of x taken by the function, Which means all the values of x taken by the graph.
From the figure, we can see that all values of x taken from [-1, - 4]. So domain is [-1, - 4].
Range: Set of all values produce of by function, Which means all y's values taken by the graph.
From the graph, we can see that between - 2 to - 4 all values are taken by graph Hence, Range is given as [-2,-4].
1. For the following system of equations, what is the x-value of the solution?
-r+2y= 6
6y =x+18
The value of x for the two expressions will be 0.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two equations are (-x+2y= 6) and 6y =x+18. The equations can be solved as below,
-x+2y= 6 or x = 2y - 6
6y = x + 18
Substitute the value of x in the second equation,
6y = 2y - 6 + 18
4y = 12
y = 3
x = 2y - 6
x = ( 2 x 3 ) - 6
x = 0
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What is an example of equivalent expression in math?.
An example of Equivalent Expressions in math is
2(x² -1 ) - 1 and 2x² - 3 , because the value both remains same for any value of x.
Equivalent expressions are defined as the expressions that work the same even though they look different. Two expressions are equivalent when they can be simplified to the same third expression or if one of the expressions can be written like the other. In other words we can say that two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(p) for the variable(x). Let's consider an example for better understanding, let 2( x² - 1) - 1 be an algebraic expression and we want to determine its equivalent expression.
Simplify, the expression, 2( x² - 1) - 1 --(1)
=> 2x² - 2 -1
=> 2x² - 3 --(2)
if x= 1 , 2( x² - 1) - 1 = 2( 1² - 1) - 1 = -1 and 2x² - 3 = 2(1)² - 3 = -1
Now, expression (1) and (2) looks different but we get same value when substitute the same value of variable(x). By using definition, both expressions are equivalent.
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One evening, Emilia and her brother each needed to ue the family computer for part of their homework. They worked on their homework for 3 hour, and agreed to hare the computer equally for that time. How long did each peron ue the computer?
Emilia and her brother used the computer for 1.5 hours.
When Emilia and her brother need to use the family computer for their homework, they have agreed to share the computer equally. On this particular evening, they both needed the computer for 3 hours. To understand how much time each of them used the computer, we need to divide the total time by the number of users.
Dividing the total time of 3 hours by the number of users which is 2, we get 3 hours / 2 = 1.5 hours. This means each person, Emilia, and her brother, use the computer for 1.5 hours each.
It's important to note that this is possible because they both agreed to share the computer equally. If one of them needed more time than the other, they might have to work out a different arrangement.
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a necklace is made from 164 purple and blue beads. there are 8 more purple beads and blue beads how many of each colour bead are there.
Answer:74 blue beads and 90 purple beads
Step-by-step explanation:
first you need to take the total number of beads 164 divide by the 2 colors so 164÷2=86 then you subtract the 8 more purple from 1/2 of 86 and you get 74 then you add 8 more to the other half of 82 and get 90 purple and 74 blue.