In order to prove triangles are congruent using the sas postulate, the two sides and one angle of the one triangle should be equal to the two sides and one angle of second triangle
Here the given postulate is sas postulate
The sas stands for Side - Angle - Side postulates
The congruent is defined as the two shapes that has same size and shape.
Two triangles can be proved congruent by using the sas, sss, asa postulates
According to sas postulate of the triangle, if two sides and one angle of the triangles must be equal to the two sides and one angle of second triangle
Hence, In order to prove triangles are congruent using the sas postulate, the two sides and one angle of the one triangle should be equal to the two sides and one angle of second triangle
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Activity 6: What Property does 1 Exhibit? Directions: Complete the table by determining the property of operations on integers that justifies each statement. (Note: a xb can also be written as ab.)
Given:
1. 0 + (-3) = = -3
2. 2(3-5) = 2(3)3) - 2(5)
3. (-6) + (-7) = (-7) + (-6)
4. 1(-9) = = -9
5.(-4) [tex]( - \frac{1}{4} )[/tex] = 1
6. 2 (3 x 7) = (2 X 3) x 7
7. 10 + (-10) = 0
8. 2(5) 5(2)
9. 1 [tex]( - \frac{1}{4}) [/tex] = = [tex] - \frac{1}{4} [/tex]
10. (-3)(4 + 9) = (-3)(4) + (-3)(9)
1). 0 + (-3) = = -3 is Additive Inverse
2).2(3-5) = 2(3)3) - 2(5) is Associative Property
3). (-6) + (-7) = (-7) + (-6) is Commutative Property
4).1(-9) = = -9 is Multiplicative Identity
5).(-4) (-1/4) = 1 is Commutative Property
6). 2 (3 x 7) = (2 X 3) x 7 is Associative Property
7). 10 + (-10) = 0 is Additive Inverse
8). 2(5) 5(2) is Commutative Property
9).1(-1/4)= -1/4 is Multiplicative Identity
10). (-3)(4 + 9) = (-3)(4) + (-3)(9) is Distributive Property
What is Additive inverse ?
To get a result equal to 0, add the original number and the additive inverse by simply changing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
What is Commutative Property ?
This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution. Division and subtraction do not work interchangeably.
A+B=B+A
What is Multiplicative Identity ?
An element of a set that remains intact after being multiplied by any other element of the set. In the set of real numbers, 1 is a multiplicative identity.
What is Distributive Property?
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
What is Associative Property?
A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.
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At a local high school, gpa's are normally distributed with a mean of 2. 9 and standard deviation of 0. 6. What is the gpa of the highest 2. 5% of the students?.
At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6.
x=4.25 is the GPA highest 2.5% of the students.
We have to find the GPA of the highest 2.5% of the students.
Mean = μ = 2.9
Standard deviation = σ = 0.6
Finding the z value for corresponding area 0.9750
For 95% confidence interval ,
z = 1.96
For 97.5% confidence interval,
We get z = 2.25
From
Z = ( x - μ ) / σ
For 2.5% of the students
To solve for x
x = Z*σ + μ
x = 2.25*0.6 + 2.9
x = 1.35 + 2.9
x = 4.25 GPA of highest 2.5% of students
Hence the answer is, x=4.25 is the GPA highest 2.5% of the students.
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Hercules had to clean out a stable for King Augeas. The king had 3,000 cattle. Hercules said he would clean the stable in one day if the king paid him by giving him 1/10 of the cattle. How many cattle did Hercules want for his work?
Hercules got 300 cattle from the King for cleaning out his stable
FractionsMultiplying fractions is defined as the product of a fraction with a fraction or with an integer or with the variables. The procedure to multiply the fractions are: Multiply the numerator with numerator. Multiply the denominator with the denominator. Simplify the fractions, if required.
To find how many cattle Hercules got for his work, we can simply multiply 3000 by 1/10 and get the value.
3000 * 1/10 = 300.
He got 300 cattle for his work.
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Solve each problem by writing and solving an equation. use "x" for the variable and type with no spaces. during the spring car wash, asb washed 14 fewer cars than during the summer car wash. they washed a total of 96 cars during both car washes. how many cars did they wash during the spring car wash?
Answer:
55 cars
Step-by-step explanation:
x + (x-14) = 96
what is 5.37 divided by 3 equal put 5.37 at the top and 3 at the bottom PLEASE EXPLAIN YOUR ANSWER. my lil sister need help
Answer:
5.37/3 = 1.79
Step-by-step explanation:
Given statement,
→ 5.37 divided by 3 equals?
Forming the problem,
→ 5.37/3
Let's solve the problem,
→ 5.37/3
→ (5.37 ÷ 3)
→ 1.79
Hence, the answer is 1.79.
2x+y=1 and y=2x+1 how many solutions
The expression 2x + 1 = y and y = 2x + 1 has no solution.
Expression:
The expression means a mathematical statements that have two terms at least that contain variables, numbers, or both connected by the arithmetic operators.
Given,
Here we have the expressions 2x + 1 = y and y = 2x + 1.
Now, we have to find the number of solution for this expression.
When we try to find the solution(s) graphically, you would plot both of the equations as straight lines. The solution(s) lies where the lines intersect.
But here we looking into the given equation both are equal.
And if we plot these on the graph then it will simply present the straight line. And there is no intersection in it.
Which also states that there is no solution for this expression.
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A tank ha 120 gallon of water and i being drained at a rate of 1/2 gallon each econd. Another tank ha 100 gallon of water and i being drained at a rate of 1/4 gallon each econd. Which equation could be ued to determine x, the number of econd, when the two tank have the ame amount of water?
The equation that could be used to determine x, the number of seconds, when the two tanks have the same amount of water is 120 - 1/2(x) = 100 - 1/4(x) or x = 80.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x be the number of seconds at the moment that the two tanks have the same amount of water.
If a tank has 120 gallons of water and is being drained at a rate of 1/2 gallon each second, the the amount of water left after time = x is "120 - 1/2(x)".
If another tank has 100 gallons of water and is being drained at a rate of 1/4 gallon each second, the the amount of water left after time = x is "100 - 1/4(x)".
Equate the two expressions to determine the time, x , at which the two tanks have the same amount of water left.
120 - 1/2(x) = 100 - 1/4(x)
20 = 1/4 x
x = 80
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(Real-World Proportional Problems MC)
The time it takes to read 5 pages of a book can be represented with the equation y equals 4.5 divided by 5 times x, where y represents the total time in minutes and x represents the number of pages read.
Determine how long it will take to read a book that has 218 pages.
242.22 minutes
218.63 minutes
196.2 minutes
54.5 minutes
Answer:
C. 196.2 minutes===========================
Equationy = (4.5 / 5) xGivenx = 218Find yy = (4.5/5)*218 y = 0.9*218y = 196.2Correct choice is C
Answer:
c) 196.2 minutes
Step-by-step explanation:
Forming the equation,
→ y = (4.5/5) × 218
Now required value of y will be,
→ y = (4.5/5) × 218
→ y = 981/5
→ [ y = 196.2 min ]
Hence, the value of y is 196.2.
Solve: (1+i)^14. And show workings
Step-by-step explanation:
(1 + i)¹⁴ = (1 + i)²×(1 + i)¹² = ((1 + i)²)⁷
(1 + i)² = 1 + 2i - 1 = 2i
((1 + i)²)⁷ = (2i)⁷ = 2⁷×i⁷ = 128×i²×i²×i²×i =
= 128×-1×-1×-1×i = -128i
Need help pls
I HAVE A BAD GRADE IN MATH HELP PLS
The rounded value of x² = 521/73 is ± 2.67 and already rounded to the nearest hundred.
What is a perfect square number?A perfect square number when taken the square root of it results in an integer.
Numbers that are not perfect squares when taken the square root of it are irrational numbers.
One method of obtaining square roots for perfect squares is prime factorization.
Given, x² = 521/73.
∴ x² = 7.13.
x = ± √7.13.
x = ± 2.67.
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is y=1/3x+5 proportional or non proportional
The following equation is not proportional.
What is equation?
An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.
Main Body:
we now that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=y/x or y= kx.
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have
y= 1/(3x+5)
This is the equation of the line in slope intercept form
where
m= 3
b= 5
The given equation not represent a proportional relationship, because the line not pass through the origin
In a proportional relationship the value of b (y-intercept) is equal to zero
Hence , equation is not proportional.
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In a certain Algebra 2 class of 24 students, 6 of them play basketball and 7 of them play baseball. There are 13 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
Answer:
P(basketball or baseball) = 11/24
Step-by-step explanation:
You want the probability that a randomly chosen student plays either sport, given the probability that 13 of the 24 students plays neither sport.
ComplementThe probability that a student plays at least one (of the two) sports is the complement of the probability they play neither sport. If 13 of 24 students play neither sport, then (24-13)/24 = 11/24 must play at least one of the two sports.
P(basketball or baseball) = 11/24
__
Additional comment
6+7-11 = 2 students play both sports.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed at the end of the 6 years duration is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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Find the 3rd degree equation that is divisible by x, (x − 3), (x+1)
The 3rd degree equation that is divisible by x, (x − 3), (x+1) is x³ - 2x² - 3x.
Define cubic polynomial.A cubic polynomial is a sort of polynomial that is based on the variable's largest exponent, or degree, in mathematical terms. As a result, a cubic polynomial is one in which the degree or maximum power of the variable is 3. An algebraic statement having variables, constants, and exponents that are whole integers is called a polynomial.
The given factors are x, (x - 3), (x + 1)
To find the 3rd-degree polynomial divisible by x, (x - 3), (x + 1) multiply the three expressions.
First multiply x, (x - 3)
x × (x - 3)
= x × x - 3 × x
= x² - 3x
Now multiply x² - 3x and (x +1)
(x² - 3x) × (x + 1)
= x²(x) - 3x(x) + x²(1) - 3x(1)
= x³ - 3x² + x² - 3x
= x³ - 2x² - 3x
So, this is the 3rd-degree equation that is divisible by x, (x − 3), (x+1).
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The dimensions of a room are 4.2 m by 6 m. On a plan, the longer side is equal to 4cm. What is the length of the shorter side on this plan?
The length of the shorter side on this plan is 2.8cm.
How to calculate the length?Based on the information illustrated, let the length of the shorter side on this plan be represented by x.
In this case, the dimensions of a room are 4.2 m by 6 m and on a plan, the longer side is equal to 4cm.
This will be illustrated as:
x/4 = 4.2 / 6
Cross multiply
6x = 4 × 4.2
x = (4 × 4.2) / 6
x = 2.8cm
The length is 2.8 cm.
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factorise 16-(5y-2)^2
The factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)
The expression is
16 - [tex](5y-2)^2[/tex]
The expression is a mathematical statement that consist of different variables, numbers and the arithmetic operators
The expression is
The expression is
16 - [tex](5y-2)^2[/tex]
We know the identity
[tex](a+b)^2= a^2+2ab+b^2[/tex]
Apply this identity on the expression
= 16 -( [tex]25y^2[/tex]- 20y + 4)
Apply the distributive property
= 16 - [tex]25y^2[/tex]+ 20y - 4
Subtract the like terms
= - [tex]25y^2[/tex]+ 20y + 12
Take common term outside
= -1([tex]25y^2[/tex]- 20y - 12)
Split the middle term and apply factorization
= -1 ([tex]25y^2[/tex]+ 10y -30y - 12)
Take common term outside
= -1 ( 5y(5y+ 2) -6(5y +2)
Take common term outside
= -1(5y+2)(5y-6)
Hence, the factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)
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Which two points should the line of best fit go through to best represent the data in the scatterplot?
A graph with points (1, 3), (2, 7), (3, 8), (4, 11), (5, 12), (6, 13).
(1, 3) and (2, 7)
(1, 3) and (6, 13)
(3, 8) and (5, 12)
(5, 12) and (6, 13)
The best line fit go through to represent the data is (3,8) and (5,12)
The correct option is Option c)
What is best fit line?
A straight line that minimises the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.
We are given some points we will plot the graph on the points
From that if we plot the line through the point (3,8) and (5,12)
That will leave 2 points above the line and 2 point below the line
Hence it is the best fit line
The correct option is option C)
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A line's slope is 6,and its y -intercept is–4 . What is its equation in slope -intercept form?
Answer:
slope: 6
y-intercept: -4
easy: y = 6x -4
The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards did chloe cut the correct amount of fabric white or why not
The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error, Chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards,
Given that the directions on a sewing pattern say to cut an extra 15% of fabric to account for an error, and Chloe needs a 0.75 yard of fabric to make a skirt, so she cuts 0.1125 yard, to determine if Chloe cut the correct amount of fabric the following calculation must be made:
0.75 x 1.15 = X
0.8625 = X
0.8625 - 0.1125 = 0.75
Therefore, the amount of fabric that Chloe cut is correct.
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Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model. Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth. What are the coordinates of the point that represents the weekly average per run for Week 7?
The coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = aˣ
where a is a constant and a>1
It is given that:
Jason decided to begin a workout program. He wants to start running three times a week.
As we know, the exponential function can be represented as:
f(x) = abˣ
The weekly average per run is 1 mi.
He increases his weekly average per run by 17% each week,
The exponential function:
f(x) = 1(1.17)ˣ
Plug x = 7
f(7) = 1(3.0012)
f(7) = 3.00
Thus, the coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).
The complete question is:
Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model. Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth. What are the coordinates of the point that represents the weekly average per run for Week 7?
options:
A. (7, 3.2)
B. (7, 2.7)
C. (7, 3.0)
D. (7, 4.6)
E. (7, 4.1)
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Answer:
7,3,0
Step-by-step explanation:
Rectangle QPRS i dilated about the origin by a cale factor of 12, then tranlated 2 unit up to form rectangle Q′P′R′S′. What are the coordinate of S′?
Repone
(1,1)
( 1 , 1 )
(1,3)
( 1 , 3 )
(5,2)
( 5 , 2 )
(7,2)
The new coordinates for point S are (84,24), for a dilation centered around the origin,
Dk (x,y) = (kx, ky) ,
K is the dilated scale factor that is multiplied by points vertices of a rectangle,
then rectangle QPRS where vertices were,
P = (1,1)
Q = (1,3)
R = (5,2)
S = (7,2)
To get the dilation of this QPRS to Q'P'R'S' with a scale factor of 12 you have to multiply each and every coordinate of its vertices by 12.
Q' = (12,12)
P' = (12,36)
R' = (60,24)
S' = (84,24)
Hence, The new coordinates for point S are (84,24)
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A salami is 2 3/5 inches long. The salami is cut into 1/8 inch thick slices.
How many slices of salami were cut?
Answer:
20 slices
Step-by-step explanation:
2 3/5 = 13/5
13/5 / 1/8
(13/5)(8/1) = 20.8
about 20 slices
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equations in quadratic will be:
a) x⁴ – 6x² – 27 = 0
d) 6(2x + 4)² = (2x + 4) + 2
e) 6x⁴ = -x² + 5.
What is a quadratic equation?The quadratic equation au² +bu + c=0 can be written as a formula. where u is an algebraic expression. In each of these examples, doubling the exponent of the middle term equals doubling the exponent of the leading term.
The quadratic function f(x) = a(x - h)² + k is said to be in standard form if an is not equal to zero. If an is positive, the graph will open upward; if an is negative, it will open downward. The vertical line x = h is the line of symmetry, and the point is the vertex (h,k)
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Please help ASAP!!! I need help! More points coming!
Answer:
x=2
y=-4
Step-by-step explanation:
a) we isolate y
18=7x-y
+y. +y
y+18=7x
-18. -18
y=7x-18
b) now fill this in
3x+(7x-18)=2
10x-18=2
+18. +18
10x=20
/10. /10
x=2
Now fill in X to find y
3(2)+y=2
6+y=2
-6. -6
y=-4
Hopes this helps
Please help! Four transformed absolute value functions are shown in the graph. Write the name of the function that matches each equation on the blank.
The name of the function that matches each equation on the blank is,
-|x-7|= h(x)
0.5|x-3|= g(x)
|x-3|-2= f(x)
-5|x-7|=j(x)
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.
The name of the function that matches each equation on the blank is,
-|x-7|= h(x)
0.5|x-3|= g(x)
|x-3|-2= f(x)
-5|x-7|=j(x)
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A chef's specialty calls for one-twentieth of an ounce of a spice per serving. The chef has a digital scale that shows the weight as a decimal. What scale reading
does the chef need to see for this spice when preparing the specialty for 19 people?
The scale of reading that the chef needs to see for this spice when preparing the specialty for 19 people would be = 4.5 ounce.
Who is a chef?A chef is a trained individual in various aspects of preparation of dishes, who has the knowledge of combination of food products to achieve an adequate meal.
The quantity of spice per serving= 1/20 ounce.( For an individual)
The quantity of people to prepare specialty for = 90 people
The quantity of spice that would be used to prepare specialty for 90 people would be;
= 1/20 × 90
= 90/20
= 4.5 ounce.
Therefore, the scale reading the chef needs to see for preparing of specialty for 90 people would be = 4.5 ounce.
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In triangle EFG, m∠E = 95.2° and m∠F = 43.7°. Determine the measure of the exterior angle to ∠G.
138.9°
84.8°
51.5°
41.1°
The measure of the exterior angle to ∠G is 138.9°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Given, In triangle EFG, m∠E = 95.2° and m∠F = 43.7°.
We know the sum of all the interior angles in a triangle is 180°.
We also know that the measure of an exterior angle in a triangle is the sum of the two opposite interior angles.
∴ The measure of the exterior angle to m∠G is = m∠E + m∠F.
= 95.2° + 43.7°.
= 138.9°.
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Carmen has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters long. How long is the remaining piece of rope?
In a case whereby Carmen has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters long the lenght of the remaining piece of rope is 9.84 metres.
What is distance?Distance can be described as the space that exist between two or more point, the concept that willbe used in the question is the concept of distance.
The total distance of the rope is 18 meters long , and she cut 8.16 meters long awya which implies that the remaining lenght of the rope will be ( 18 - 8.16)= 9.84 metres
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Why is 27/22 as a decimal rounded to the nearest hundredth?
The division of the fraction 27/22 will result to 1.22 rounded to the nearest hundredth.
How to divide fractions using long divisionTo divide the fraction using long division, we first divide the dividend with the divisor, write the whole number result, and then multiply it by the divisor, subtract the result from the dividend to get a new dividend. Repeat the process for the new dividend until you arrive at a remainder of zero, or continue to a given place value.
27/22 = 1 whole number and a remainder of 5
1 × 22 = 22
27 - 22 = 5
drop the value for the tenth digit of 27.00 which is 0 to yeild 50{ new dividend}
50/22 = 2 whole number and a remainder of 6
2 × 22 = 44
50 - 44 = 6
drop the value for the hundredth digit of 27.00 which is 0 to yeild 60{ new dividend}
60/22 = 2 whole number and a remainder of 16
2 × 22 = 44
69 - 44 = 16
we are rounding up to the nearest hundredth, we stop with the quotient of 1.222.
Hence, the fraction 27/22 is equal 1.22 rounded up to the nearest hundredth using the long division process.
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a plumber charges $12.00 per hour for her work, plus a $32.00 materials fee. If you pay her $74.00, how many hours did the plumber work?
Answer:
3.5 hours
Step-by-step explanation:
74-32=42
42/12=3.5
