ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.
What is congruent ?
In geometry, congruent refers to the condition where two or more figures have the same size and shape. Congruent figures have the same dimensions, angles, and proportions. Two figures are congruent if they can be superimposed exactly on each.
1) If, C.) Angle B is congruent to angle E then ∆ABC and ∆DEF are congruent by the ASA criterion.
2) If, D.) Angle A is congruent to angle D then ∆ABC and ∆DEF are congruent by the SAS criterion.
3) ∆ABC and ∆DEF are congruent if B.) AB=DE
ASA criterion: If in two triangles, two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.
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5. The new playground at the park will be 45 ft. by
62 ft. What is the area of the playground?
Answer:
2790 ft²
Step-by-step explanation:
Area of rectangle with length L and width W:
area = LW
area = 45 ft × 62 ft
area = 2790 ft²
How do you graph a quadratic equation in factored form?
The steps to convert the graph a quadratic equation in factored form is explained below.
Factored form in math is defined as the process of expressing a given number or algebraic expression as the product of its factors is called factoring.
Here we need to explain the process of graph a quadratic equation in factored form.
There are three ways are defined to convert them.
The very first way to When every term of the equation has GCD ≠ 0 then it can be factored by taking out GCD as a common factor.
the next way is to use the Identity that is a² - b² = (a + b) (a - b)
The last way is to use the Identity (x + a)(x + b)
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Find the length of each leg.
The length of each leg, just divide the hypotenuse, 12 , by the square root of 2. Then to remove the radical from the denominator, multiply both numerator and denominator by square root of 2.
Find the length of each leg?
A strict anatomical definition of leg length (LL) is the length of the femur + tibia. Due to the bipedal nature of the human species, “leg length” often is measured as: (femur + tibia + the height of the foot, from the tibia-talus articulation to the ground).Applying the Geometric Mean (Leg) Theorem (or Leg Rule) we can find the length of the legs if we know the length of the two segments. The hypotenuse is the sum of the two segments: c = n + m = 2 + 8 = 10 cmLeg lengths should be measured to determine if there is a difference from side to side. It is important to distinguish a true versus apparent leg length deficiency. With apparent or functional leg length discrepancy, the deficiency may be due to a pelvic obliquity, contractures, or scoliosis.To learn more about length refers to:
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please help!
Use the quadratic formula to find both solutions to the quadratic equation
given below.
*photo provided for easy access*
The solutions to the given quadratic equation are 1/4 and -1.
The correct options are Options E and F.
What is Quadratic Formula?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The coefficient of x² must be a non-zero term (a ≠ 0) in order for an equation to meet the definition of a quadratic equation. The easiest method for locating a quadratic equation's roots is the quadratic formula:[tex]x = \frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex] and [tex]x = \frac{-b - \sqrt{b^{2} -4ac} }{2a}[/tex]
Given equation :
4x² + 3x -1 = 0
Here,a = 4, b = 3, and c = -1.
[tex]x = \frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex]
The roots of the equation are:
[tex]x = \frac{-3 + \sqrt{3^{2} -4(4)(-1)} }{2(4)}[/tex] and [tex]x = \frac{-3 - \sqrt{3^{2} -4(4)(-1)} }{2(4)}[/tex]
[tex]x = \frac{-3 + \sqrt{25} }{2(4)}[/tex] and [tex]x = \frac{-3 - \sqrt{25} }{2(4)}[/tex]
[tex]x = \frac{2}{8} = \frac{1}{4}[/tex] and [tex]x = \frac{-8}{8} = -1[/tex]
Hence the roots of the equation are 1/4 and -1.
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given a student earned an a, what is the chance they attend class regularly? cond - numeric answer .8834 you are incorrect hint: p(r|a) round to four decimal places.
Answer: Probability that she attended class regularly given that she receives A grade is 0.9286.
Step-by-step explanation: i looked it up man ♀️
4y+x=15 x=8y+3?
Elimination
Graphing
Consistent’
Substitution
The solution to the system of equation 4y + x = 15 and x = 8y + 3 is (11, 1)
What is an equation?An equation shows the relationship between numbers and variables in an expression.
The standard form of a linear equation is:
Ax + By = C
Where A, B and C are constants
Given that:
4y + x = 15
multiply by 2:
8y + 2x = 30 (1)
Also:
x = 8y + 3
8y - x = -3 (2)
Subtract equation 2 from 1 to solve using elimination method:
3x = 33
x = 11
put x = 11 in equation 2:
8y - 11 = -3
y = 1
The solution is (11, 1)
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Answer the statistical measures and create a box and whiskers plot for the following set of data. 6 , 8 , 8 , 9 , 10 , 11 , 11 , 12 , 13 , 14 , 14 , 15 , 16 , 16 , 17 6,8,8,9,10,11,11,12,13,14,14,15,16,16,17 Min: Q1: Med: Q3: Max: Create the box plot by dragging the lines:
Note that the box and whisker plot is attached accordingly and the measure are given as follows:
Min: 6Q1: 9Median: 12Q3: 15Maximum: 17What is a box and whisker plot?A box plot is a figure that depicts the distribution of data by showing where the majority of values reside and those values that deviate significantly from the norm, known as outliers. Box plots are sometimes known as box and whisker plots or box and whisker diagrams.
The bottom of the box indicates the first quartile, while the upper side represents the third quartile. As a result, the inter-quartile deviation is represented by the vertical width of the middlebox.
The median is the horizontal line inside the box. The vertical lines projecting from the box extend to the data set's minimum and highest values, as long as these values are not outliers. Two shorter horizontal lines represent the ends of the whiskers.
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Consider a sequence whose first five terms are : -1.75, -0.5, 0.75, 2, 3.25
Which function ( with domain all integers n>1) could be used to define and continue this sequence
The function that could be used to define and continue this function is f(n) = 1.25n -3
How to determine which function could be used to define and continue the sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
Thus, the nth term of arithmetic sequence is given by:
Tₙ = a + (n-1)d (for all positive integer values of n)
where a is the first term, n is the number of term and d is common difference
d is the constant difference between each subsequent terms. That is:
d = -0.5 - (-1.75) = 1.25
Tₙ = -1.75 + (n - 1)1.25
Tₙ = -1.75 + 1.25n - 1.25
Tₙ = 1.25n - 3
If we take Tₙ = f(n) , then the function that gives the nth term is:
is f(n) = 1.25n + 3
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Arisia puts $500.00 into a savings account with an annual simple interest rate of 4.5%
If the interest rate stayed the same, how much interest would Arisia’s account earn after 15 years?
A factory make profit of Rs 1000,000 per month.At the end of the years 5% of it's profit is distributed as a dividend among it's 500 shareholder with equal number of Shares. Find the dividend received by each Share holders.
If the factor distributes 5% of its profits as dividends among its 500 shareholders with an equal number of shares, the dividend per shareholder is Rs. 1,200.
What are the dividends?Dividends refer to the profits declared for sharing among partners or more specifically among shareholders.
Dividends are a means for repaying shareholders for their shareholding interest in the company.
Companies declare dividends when sufficient profits are generated.
The profit per month = Rs 1,000,000
The total profit for the year = Rs 12,000,000 (Rs. 1,000,000 x 12)
Dividends payout = 5%
Dividends declared = Rs. 600,000 (Rs. 12,000,000 x 5%)
The number of shareholders with equal shares = 500
Dividends per shareholder = Rs. 1,200 (Rs. 600,000/500)
Thus, the dividends per shareholder is the quotient of the total dividends and the number of shareholders.
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-2x + 5y =52 x + 4y =26
The solution for the system of equations is x = -6 and y = 8.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given the equations,
-2x + 5y = 52
x + 4y = 26
solving by elimination method,
multiply by 2 in equation x + 4y = 26
= 2x + 8y = 52
now add both equations,
-2x + 5y + 2x + 8y = 52 + 52
13y = 104
y = 104/13
y = 8
substitute the value of y in equation x + 4y = 26
x + 4(8) = 26
x = 26 - 32
x = -6
Hence the solution of an equation is at x = -6 and y = 8.
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f(x)=2x+1
g(x)=x^2+2
Find g(f(x))
Answer:
4x²+4x+3
Step-by-step explanation:
g(f(x))= (2x+1)²+2
= 4x²+4x+1+2
=4x²+4x+3
Triangle OPQ, with vertices O(3,4), P(8,3), and Q(4,8), is drawn inside a rectangle, as
shown below.
What is the area, in square units, of triangle OPQ?
The area of triangle OPQ is 44 square units.
How to find the area of tringle?
There are different ways to find the area of a triangle, depending on the information given. Here are a few common methods:
Using the base and height: To find the area of a triangle using the base and height, you can use the formula: A = (1/2)bhwhere A is the area, b is the base and h is the height.The height is the perpendicular line segment drawn from the vertex of the triangle to the line containing the base of the triangle.Using the 3 sides of the triangle: Heron's formula is a method to find the area of a triangle when the lengths of all three sides are known. The formula is:A = √(s(s-a)(s-b)(s-c))where A is the area, a, b and c are the sides of the triangle, and s is the semi-perimeter of the triangle.s = (a+b+c)/2There are different methods to find the area of a triangle, but one common method is to use the coordinates of its vertices and the distance formula. The distance formula is
d = √((x2-x1)^2 + (y2-y1)^2)
We can use the distance formula to find the lengths of the sides of the triangle OPQ, which are:
OP = √((8-3)^2 + (3-4)^2) = √((5)^2 + (-1)^2) = √(25+1) = √26
OQ = √((4-3)^2 + (8-4)^2) = √((1)^2 + (4)^2) = √(1+16) = √17
PQ = √((4-8)^2 + (8-3)^2) = √((-4)^2 + (5)^2) = √(16+25) = √41
Once we have the lengths of the sides of the triangle, we can use the Heron's formula to find its area:
s = (OP + OQ + PQ)/2
Area = √(s(s-OP)(s-OQ)(s-PQ))
s = (√26 + √17 + √41)/2 = (√44)/2 = 4√11
Area = √(4√11(4√11-√26)(4√11-√17)(4√11-√41))
Area = √(4√11 * √(44-26) * √(44-17) * √(44-41))
Area = √(4√11 * √18 * √27 * √3)
Area = √(4√11 * 3√2 * 3√3 * √3)
Area = 4*11 = 44 square units
Hence, the area of triangle OPQ is 44 square units.
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Subtract 5/6 - 7/12 Simplify your answer.
The value on simplifying the fraction expression 5/6 - 7/12 is obtained as 1/4.
What is a fraction?
In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
The fraction expression is given as 5/6 - 7/12.
5/6 - 7/12
First take the LCM of the denominator -
LCM = 12
Now, multiply 2 by 5 in first fraction numerator, as 6 multiplied by 2 is 12 (LCM) -
10/12 - 7/12
Now, use the arithmetic operation of subtraction -
(10 - 7)/12
3/12
Divide numerator and denominator by 3 -
1/4
Therefore, the final value as a fraction is obtained as 1/4.
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Use these four expressions to make a hypothesis about the closure property of integers under each operation. select yes or no for each operation. operation example expression is the set of integers closed under the operation? addition -8 5 yes no subtraction 9 − (-11) yes no multiplication 3 · (-4) yes no division -1 ÷ 6 yes no
The answer is: Yes, Yes, Yes, No.
The expression -8 + 5 shows the sum of two integers. This expression has a value of -3. Because -3 is also an integer, the set of integers appears to be closed under addition.
The expression 9 − (-11) shows the difference between two integers. This expression has a value of 20. Because 20 is also an integer, the set of integers appears to be closed under subtraction.
The expression 3 · (-4) shows the product of two integers. This expression has a value of -12. Because -12 is an integer, the set of integers appears to be closed under multiplication.
The expression, -1 ÷ 6, shows the quotient of two integers. This expression has a value of -1/6, Because -1/6 is not an integer, the set of integers is not closed under division.
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write a rule that explains the ordered pairs:
(1,2/3), (2,4/9),(3,8/27),(4,16/81),(5,32/243)
The rule of the functions for the ordered pairs will be f(x) = (2/3)².
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values written in parentheses in a specific order. In order to understand a point visually, it can be helpful to locate it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.
Given that the ordered pairs are (1,2/3), (2,4/9),(3,8/27),(4,16/81) (5,32/243).
x y
1 2/3 = (2/3)^1
2 4/9 = (2/3)^2
3 8/27 = (2/3)^3
4 16/81 = (2/3)^4
5 32/243 = (2/3)^5
Function rule is f(x) = (2/3)²
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I need help ASAP on questions 3. 4. 5. 6. 7. 8. With steps for those
It is been proved that c(a+b) = ab.
Prove:-
c(a+b) = ab.
it is given that ∠ ABD = ∠ XYD = ∠ CDB = 90°
So, Lines AB, XY, and CD are parallel to Each other.
→ AB || XY || CD
Now In ΔABD, we have,
→ AB || XY
So,
→ DY/BD = c/a
→ DY = (c/a)*BD ----------------------- Equation (1)
In Δ BDC we have
→ CD || XY
So,
→ BY/BD = c/b
→ BY = (c/b)*BD ----------------------- Equation (2)
______________________
Adding Equation(1) and Equation(2) now, we get
→ DY + BY = (c/a)*BD + (c/b)*BD
taking (c * BD) common From LHS, we get,
→ BD = c * BD(1/a + 1/b)
BD will be canceled from both sides,
→ 1/c = 1/a + 1/b
→ 1/c = (a+b)/ab
→ c(a+b) = ab
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The Question is incomplete although I've found a similar question of it.
: Picture attached:
A rectangle has a length of 27 yards less than 9 times its width. If the area of the rectangle is 360 square yards, find the length of the rectangle.
The length of the yard as calculated from the given data is found out to be as 5 yards long.
let the length of the yard be , 27 - 9x
and the width of the yard is x.
Given , the are of the yard = 360.
Therefore, we can say that
=>x(27 - 9x) = 360
=>27x - 9x² = 360
=> 3x - x² = 40
=> x² - 3x + 40 = 0
=>x² + 5x - 8x + 40 = 0
=> x ( x - 5) -8 ( x - 5 )
Therefore, the value of x will be 5 or 8.
On putting these values in the equation we get that , the length being 5 is the correct answer.
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The line graph shows the poluution rate of a certain lake from 1950 to 2000. Use the graph to answer the question. Percentage of pollution by Volume (+ SP) 4.0% 3.0% 2.0% 1.0% 0.0% 1950 1960 1970 1980 1990 2000 Find an estimate for the percent of pollution by volume of the lake in 1960. A. 3% OB. 2.5% OC. 2% D. 1%
The introduction of harmful chemicals into the air is known as air pollution.
What are the primary sources of air pollution?The chief causes of man-made air pollution include vehicle emissions, fuel oils and natural gas used to heat houses, byproducts of manufacturing and electricity generation, notably coal-fueled power plants, and odors from chemical manufacture.Industrial emissions, automobile emissions, and any other place where fossil fuels are burnt are all sources of atmospheric pollution, or air pollution. Another major contaminant that can cause ozone depletion is methane, which is released by landfills and cattle.
Air pollution can have long-term harmful consequences, such as acid rain, which pollutes the Earth’s bodies of water and ruins infrastructure.
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the principal would like to assemble a committee of 4 students from the 14-member student council. how many different committees can be chosen?
There are 1001 different committees can be chosen.
The problem is asking how many different committees can be chosen or the number of ways to select 4 students out of a group of 14 without regard to order. This is a combinatorics problem, and it can be solved using the combination formula:
nCr = n!/(r!(n-r)!)
Where n is the total number of items to choose from (14 students in this case) and r is the number of items to choose (4 students).
Plug in the values and solve.
14C4 = 14!/(4!(14-4)!)
14C4 = 14!/(4!10!)
14C4 = 1001
Therefore, the number of different committees that can be chosen is 1001.
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To reach the Powai lake picnic spot from star apartments Sagar went 13km665m by bus ,1km220m by autorickshaw and500m by foot what is the total distance
The total distance cover by Sagar is, 15 km 385 m.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
To reach the Powai lake picnic spot from star apartments,
Sagar went 13 km 665m by bus ,1 km220 m by autorickshaw and 500 m by foot.
Now, Total distance cover by Sagar is,
⇒ 13 km 665 m + 1 km 220 m + 500 m
We know that;
1 km = 1000m
Hence, We get;
⇒ 13665 m + 1220 m + 500 m
⇒ 15,385 m
⇒ 15 km 385 m
Thus, The total distance cover by Sagar = 15 km 385 m.
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Let g represent the total number of hours Greg will travel on his trip across the country to attend his cousin's wedding. The first day he travels 8 hours. The second day he travels 9 hours. The third day he had mechanical problems and only drove 4 hours. Write an algebraic expression to represent how much time he has left to drive.
The algebraic expression to represent how much time he has left to drive as function is given as f(g) = g - 21.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Greg will travel on his trip across the country to attend his cousin's wedding. The first day he travels 8 hours. The second day he travels 9 hours. The third day he had mechanical problems and only drove 4 hours.
We can write an algebraic expression to represent how much time he has left to drive as function f(g). We can write -
f(g) = g - (8 + 9 + 4)
f(g) = g - 21
Therefore, the algebraic expression to represent how much time he has left to drive as function is given as f(g) = g - 21.
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What is the easiest way to find the distance between two points?
To find the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).
What is the distance?The distance of an object is its overall motion, regardless of direction.
Distance is the amount of space that an object has covered, regardless of where it began or concluded.
By understanding how far an object is from us, we may calculate its actual size.
It is possible to calculate the area that an object takes up in the sky.
The actual size of an object can then be determined by taking into account its distance.
The further away something is, the smaller it appears.
The distance between two locations on a plane is the length of the line segment connecting them.
The formula d=((x2 - x1)² + (y2 - y1)²) is frequently used to calculate the separation between two points.
Therefore, to find the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).
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(ASAPPPP!!!! POINTS INCLUDEDDDD!!!! ) An object attached to a spring oscillates around a position and is represented by the function y = 2 cos (x -0.02), with
time in a seconds. What is the maximum height of the object in inches, and how many times does the maximum occur on
the interval 0 < x < 20?
- 3times, 8inches
- 4times, 8inches
- 3times, 2inches
- 4times, 2inches
4times, 2inches occur on the interval 0 < x < 20
Find the maximum interval?y=2cos (x-0.02)(0<x<20)y max=2 inches-1<cos<1/-0.02<x<-0.02<1998when x - 0.02=0 2π 4 π4 times In mathematics, a interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in betweenIntervals are written with rectangular brackets or parentheses, and two numbers delimited with a comma. The two numbers are called the endpoints of the interval. The number on the left denotes the least element or lower bound. The number on the right denotes the greatest element or upper bound.To learn more about interval refers to:
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I need help please!!!
For f(-7), it's 20. For determining x, it's 8.
For f(-7), plug-in -7 to x, and you get -3(-7), which is 21, and minus 1 is 20.
For determining x, plug in 8, you get -3(8), which is -24, minus 1 is -25.
PLS HELP ASAP
GIVING BRAINLIEST + 30 POINTS EACH
Answer:12
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
12
Suppose you drink a cup of coffee that has 150mg of caffeine. The caffeine in your body drops by 15% each hour. Write an equation for this problem and tell me if the Equation is Exponential or Rational?
help pls desperate times
If the caffeine in the body drops by 15% each hour then the equation for this problem is [tex]f(t) = 150\times (0.85)^{t}[/tex] and the equation represents a exponential decay problem .
the amount of caffeine present in the cup of coffee (a) = 150 mg ;
the percent drop in caffeine in body each hour (r) = 15% = 0.15 ;
Since the percent of caffeine is dropping in the body , the exponential decay function will be used to represent this situation ;
the exponential decay equation is written as : [tex]f(t) = a\times (1-r)^{t}[/tex] ;
substituting the given values of "a" and "r" in the equation ,
we get ;
⇒ [tex]f(t) = 150\times (1-0.15)^{t}[/tex]
⇒ [tex]f(t) = 150\times (0.85)^{t}[/tex]
Therefore , the exponential decay equation is [tex]f(t) = 150\times (0.85)^{t}[/tex] .
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1/5x+1/2(3/5x−20) . Write your fractions in simplest form.
Answer:
1/2x-10
Step-by-step explanation:
[tex]\frac{1}{5} x+\frac{1}{2} (\frac{3}{5}) +\frac{1}{2}(-20)\\\frac{1}{5} x+\frac{3}{10} x-10\\\frac{1}{2} x-10\\[/tex]
Hope this helped! :)
Hey there!
1/5x + 1/2(3/5x - 20)
DISTRIBUTE 1/2 within the PARENTHESES:
= 1/5x + 1/2(3/5x) + 1/2(-20)
= 1/5x + 3/10x - 10
COMBINE the TERMS
= (1/5x + 3/10x) - (10)
= 1/5x + 3/10x - 10
= 1/2x - 10
Therefore, your should be:
1/2x - 10
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
what is the absolute value of the difference between its additive inverse and its complex conjugate?
The additive inverse of a complex number is the opposite of the complex number. The complex conjugate of a complex number is which is the real part plus the opposite of the imaginary part of the complex number.
The additive inverse of a number is its opposite number. If a number is added to its additive inverse, the sum of both numbers becomes zero.
When the sum of two real numbers is zero, then each real number is said to be the additive inverse of the other. So, we have R + (-R) = 0, where R is a real number.
A complex conjugate of a complex number is another complex number whose real part is the same as the original complex number and the magnitude of the imaginary part is the same with the opposite sign.
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What must be added to x³ 3x 8 to get 3x³ X² 6?
The polynomial 2x³ + x² -3x +14 must be added to (x³ + 3x -8) to obtain (3x³ + x² +6).
Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The general form of the quadratic equation is: ax² + bx + c = 0,
where x is an unknown variable and a, b, c are numerical coefficients.
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.
Let a polynomial P must be added.
Therefore, according to the question,
P+ (x³ + 3x -8) = (3x³ + x² +6)
=> P= (3x³ + x² +6) - (x³ + 3x -8)
=> P= (3-1)x³ + x² -3x +(6-(-8) )
=> P= 2x³ + x² -3x +14
Thus, the polynomial 2x³ + x² -3x +14 must be added to (x³ + 3x -8) to obtain (3x³ + x² +6).
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