3√2x is the simplified form of the given expression by rationalizing the denominator.
What is the justification?In the form p q, where p and q are integers and q0, rational numbers can be expressed. The distinction between fractions and rational numbers is that the numerator or denominator of a fraction cannot be negative.
What does a math denominator mean?In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.
What does common factor mean?A common factor is a whole number that is a factor of at least two other numbers. The greatest common factor is the biggest factor that may be divided into two or more integers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).
Make the denominator simpler.
12/2√2x
Reject the 12/2 common factor.
6/√2x
Multiply the numerator and denominator by √2x
(6√2x⋅√2x/√2x)
Combine and make the denominator simpler.
6√2x/2x
= 3√2x
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Help!! Can someone state all the statements and reasons to prove that triangle WXY is congruent to triangle WZY!! It’s geometry proofs.
Whoever gives me the answer I’ll give them 20!
It is true that WXY ≅ WZY.
What is a congruent?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
Properties of Congruence
Reflexive Property: An angle is congruent to itself.
Symmetric Property: The order of congruence does not matter.
Transitive Property: If two angles are both congruent to a third angle, then the first two angles are also congruent.
Here, It is given that
Angle ZWY is congruent to angle XWY
Segment WZ is congruent to Segment WX
Segment WY is congruent to Segment WY - Reflexive Property of Congruence (which states that one thing is congruent to itself.
Hence, Triangle WXY is congruent to Triangle WZY because of Side Angle Side (SAS) postulate.
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quadrilateral rstu has vertices R(2,4) ,s (-2,2), T(-1,0)and (3,2)
Verify:
i) quadrilateral rstu is a rectangle
ii) the diagonals of the rectangle bisect each other and are equal in lengths .
As RS=TU and ST=UR by distance formula, The given quadrilateral RSTU is rectangle and The diagonals RT=US so they are equal and bisect each other at right angle.
What is rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.
Here,
Calculate the length of sides by distance formula.
RS=√(y2-y1)²+(x2-x1)²
=√(2-4)²+(-2-2)²
=√4+8
=√(12
=2√3 units
ST=√(y2-y1)²+(x2-x1)²
=√(0-2)²+(-1-(-2))²
=√(4+1)
=√5 units
TU=√(y2-y1)²+(x2-x1)²
=√(2-0)²+(3-(-1))²
=√(4+8)
=√12
=2√3 units
UR=√(y2-y1)²+(x2-x1)²
=√(4-2)²+(3-2)²
=√(4+1)
=√5 units
RT=√(y2-y1)²+(x2-x1)²
=√(0-4)²+(-1-2)²
=√(16+9)
=√25
=5 units
US=√(y2-y1)²+(x2-x1)²
=√(2-2)²+(-2-3)²
=√(0+25)
=√25
=5 units
Because the given quadrilaterals, RS=TU and ST=UR, are rectangles and the diagonals, RT=US, are equal and at right angles to one another, according to the distance formula.
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4. The drama club is printing t-shirts for its members. The printing company chargesa certain amount for each shirt plus a setup fee of $40. There are 21 students in the drama club.
a. If there are 21 students in the club and the t-shirt order costs a total of $187, how much does each t-shirt cost? Show your reasoning.
Answer:
$7
Step-by-step explanation:
You want the cost of a shirt when the cost of 21 shirts plus a $40 setup fee is $187.
CostThe total cost of the order is the sum of the setup fee and the extended cost of the shirts.
cost = (setup fee) + (number of shirts) × (cost per shirt)
187 = 40 + 21 × (cost per shirt)
Subtracting 40 gives ...
147 = 21(cost per shirt)
Dividing by 21, we have ...
7 = cost per shirt
Each T-shirt costs $7.
Given Two Points: Write the equation of the line with the two given point
5. (1, 3) and (-3, -5)
6. (1, 4) and (6, -1)
7. (-12, 14) and (6, -1)
8. (-4,-2) and (4, 0)
Writing Parallel & Perpendicular Equations
9. Write an equation parallel to y = 3x + 6 that passes through the point (4, 7).
Hooke's Law states that the displacement, d, that a spring is stretched by a hanging object varies directly as the mass, m, of the object. If the distance is 12cm when the mass is 4kg, what is the distance when the mass is 5kg.
The distance when the mass is 5kg is 15cm.
What is the distance?When two values vary directly, it means that both values move in the same direction. If one of the value increases, the other value increases and if one of the values decreases, the other value decreases.
The equation that is used to represent direct variation is:
d = km
Where:
d = distance k = constant of variation m = massThe first step is to determine the value of k:
12 = 4k
k = 12 / 4
k = 3
d = 3 x 5 = 15cm
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Please help me with this question
Answer: The ladder reaches 4.8 ft up the wall
Step-by-step explanation:
Sin 53°=0.80
Cos 53°=0.60
Tan 53°=1.33
Cos 58°/1 = X/8
0.60/1 = X/8
X=4.8
Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. Then, select the transversal that connects them.
∠1 and ∠14
corresponding
alternate interior
alternate exterior
consecutive interior angles
p
q
r
s
The identification of the missing angles and their congruency names are;
a. ∠4 and ∠7 = Consecutive interior
b. ∠2 and ∠11 = alternate exterior angles
c. ∠12 and ∠16 = corresponding angles
d. ∠8 and ∠13 = alternate interior angles
e. ∠11 and ∠15 = corresponding angles
f. ∠7 and∠10 = none
g. ∠1 and ∠14 = alternate exterior angles
h. ∠12 and ∠15 = Consecutive interior
i. ∠6 and ∠7 = none
j. ∠1 and ∠3 = corresponding angles
k. ∠12 and ∠16 = corresponding angles
l. ∠6 and ∠15 = alternate exterior angles
m. ∠5 and ∠10 = alternate interior angles
n. ∠8 and ∠14 = corresponding angles
How to classify congruent angles?Corresponding angles are defined as the angles which are formed in corresponding corners with the transversal in a case where two parallel lines are intersected by any other line.
Alternate interior angles are defined as the angles formed when a transversal intersects two coplanar lines.
Alternate exterior angles are defined as the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.
Therefore, the angles given can be classified similarly using the image as:
a. <4 and <7 are Consecutive interior angles
b. <2 and <11 are alternate exterior angles
c. <12 and <16 are corresponding angles
d. <8 and <13 are alternate interior angles
e. <11 and <15 are corresponding angles
f. <7 and <10 are none
g. <1 and <14 are alternate exterior angles
h. <12 and <15 are Consecutive interior
i. < 6 and <7 are none
j. <1 and <3 are corresponding angles
k. <12 and <16 are corresponding angles
l. <6 and <15 are alternate exterior angles
m. <5 and <10 are alternate interior angles
n. <8 and <14 are corresponding angles
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31.24 to 1 deecimal place
Round 31.24 to 1 decimal place:
31.2
Answer:31.2
Step-by-step explanation:
you remove the 4 because it is less than 5.
A coffee company surveyed 40 potential customers to see where they would
like the company's new organic coffee sold. Respondents were given the
following four locations and asked to choose as many as they liked: grocery
stores, drugstores, health food stores, and big box stores. The results are
summarized in the bar graph below, with the number of times each location
was chosen noted above the corresponding bar.
According to the statistics presented in the bar graph of responders of four locations per 40 potential customers, the average number of places chosen per potential client is 2.5.
We are given;
Total number of potential customers =40
From the bar graph number of respondents are following;
At grocery stores = 40
At drugstores respondents = 32
At health food stores = 8
At big box stores = 20
So,
The average number = Total number of respondents / Total number of potential customers
The average number = (40 + 32 + 8 + 20) / 40
The average number = (100) / 40
The average number = 2.5
Thus, according to the statistics presented in the bar graph of responders of four locations per 40 potential customers, the average number of places chosen per potential client is 2.5.
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If the public debt of a country in 2009 was $11,982,000,000,000and the
budget for 2010 was in deficit by $101,347,000,000 , what was the public debt
in 2010? Do not include commas in your answer.
If a country's public debt in 2009 was $11,982,000,000,000 and its budget for 2010 was $101,347,000,000 in deficit, the public debt in 2010 is $12083347000000.
What is public debt?Government obligations, particularly those evidenced by securities, to pay certain sums to holders at some future time. Private debt, which includes the obligations of individuals, businesses, and nongovernmental organizations, is distinct from public debt. A debt-to-GDP ratio compares a country's total debt to its economic productivity. Divide a country's debt by its GDP to calculate the debt-to-GDP ratio. Governments can use public debt to raise funds to expand their economies or pay for services. Politicians would rather increase the national debt than raise taxes. The national debt includes public debt, and when the national debt reaches 77% or more of GDP, the debt begins to slow growth.As given
if the public debt of a country in 2009 was $11,982,000,000,000 and the budget for 2010 was in deficit by $101,347,000,000 .
Total public debt in 2010 = Public debt in 2009 + Amount by which 2010 budget deficit .
= $ 11982000000000 + 101347000000
= $ 12083347000000
Therefore the public debt in 2010 is $12083347000000.
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we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can i. change the z value to a smaller number. ii. take a larger sample. iii. take a smaller sample.
Using the concepts of errors and measurement, we got that by taking a larger sample 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence.
In science, experimental errors may be caused due to the human inaccuracies like a wrong experimental setup in the science experiment or choosing the wrong set of people for the social experiment. Systematic error refers to that error which is actually inherent in the system of experimentation.
Hence, if we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can take a larger sample.
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Can anyone state the vertex of the graph?
Given the graph, the vertex does not exist and the transformations from are
Vertical shift down 2Horizontal shift left 4How to calculate the vertex of the graph?The graph represents the given parameter
In the above graph, we can see that the graph is a cubic function
By definition, cubic functions do not have vertex. This is because they have no minimum or maximum
So, we can conclude that the graph has no vertex
The transformation from the parent functionIn (a), we have
We can see that the graph is a cubic function
This function is represented as
y = ∛x
In this graph, we can see that the graph is 4 units to the left
i.e. y = ∛(x - 4)
And 2 units below the origin
i.e. y = ∛(x - 4) + 2
So, the transformation is (b) and (c)
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Solve for the value of v.
50⁰
(V-7)
The value of v as required to be solved for in the task content is; 47.
What is the value of according to the right triangle?It follows from the complete task content that a right triangle in which case the angle measures are; 50°, (v - 7)° and 90° is to be solved for variable v.
Recall from triangle geometry that the algebraic sum of angles in a triangle is; 180°.
Therefore, we have;
50° + (v - 7)° + 90° = 180°
v - 7 + 140 = 180
v = 180 - 140 + 7
v = 47.
On this note, the value of variable, v as required to be determined is; 47.
Completed question; The complete question is such that a right triangle with two other angles 50° and (v - 7)° is given.
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write down the value of 9 and a half?
The value of 9 and a half will be 9 1/2.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Here, we want to find the value of 9 and half. This will be:
= 9 + 1/2
= 9 1/2
The value is 9 1/2.
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Four
Four students, Ryan, Angel, Evan and Oliver were
shipwrecked on an island. Having no food they went to
work gathering pineapples. After gathering pineapples,
they were tired and all fell asleep. After another while,
Angel woke up and was very hungry and so she ate 1/3
of the pineapples - more than her proper share.
Shewent back to sleep. Evan woke up and, being
hungry, ate 1/3 of the remaining pineapples and went
back to sleep.Oliver did the same. When Ryan woke up,
he only took his rightful share of the remaining
pineapples. Then there were 6 pineapples left. How
many pineapples did they all gather?
Pineapple originally gather is 27
Quadratic equations are what?
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.
Step-by-step explanation:
Working Backward strategy
Remaining Pineapple = 3
[tex]\frac{2}{3}x+3=x[/tex]
x=9
Remaining Pineapple now = 9
ATQ [tex]\frac{1}{4}x+9=x[/tex]
x = 12
Remaining Pineapple now = 12
ATQ [tex]\frac{x}{3}+12=x\\[/tex]
x=18
Remaining Pineapple now =18
ATQ [tex]\frac{x}{3}+18=x[/tex]
x=27
hence The ans is 27
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What is the sum of the 9th square number and the 5th cube number?
Answer:
Step-by-step explanation:
which equation represents the graph below?
y = −1/5x − 3y
y = 5x − 3y
y = −1/5x + 3
Answer:
y=-1/5x+3
Step-by-step explanation:
I think this the answer
Answer:
y = -1/5x - 3
Step-by-step explanation:
→ Find the x intercept
( - 15 , 0 )
→ Find y intercept
( 0 , -3 )
→ Find gradient
y = -1/5x + c
→ Substitute coordinate pair in
y = -1/5x - 3
please help me with this.
Answer:
Option A
Step-by-step explanation:
→ Multiply both sides by 2
2s = a + b + c
→ Minus b and c from both sides
2s - b - c = a
Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
The formula of nth term is = 10 - 3n
What is AP?
A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. Take the numbers 5, 7, 9, 11, 13, and 15 as an example. . . is a sequence of numbers having a common difference of two.The n-th term of the sequence is given by:, if the beginning term of an arithmetic progression is and the common difference between succeeding members is, thenIf the AP contains m phrases, then denotes the final term, which is given by:The term "finite arithmetic progression" or "arithmetic progression" refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.Acc to our question-
For the nth term in an algebraic seriesU(n) = a + (n - 1)dthe number of terms is n.The first term is a.d is the typical differenceFrom the preceding sequencea = 7d = 4 - 7 = - 3The nth term's formula isU(n) = 7 + (n - 1)-3= 7 - 3n + 3The ultimate solution is= 10 - 3nHence,The formula of nth term is = 10 - 3n
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question the probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. is avery interpreting the probability correctly? responses yes, because 2 out of 5 is equal to 40%. yes, because 2 out of 5 is equal to 40%. yes, because participants in the survey are selected at random. yes, because participants in the survey are selected at random. no, because there could be voluntary response bias. no, because there could be voluntary response bias. no, because only 40% of all people will visit the site. no, because only 40% of all people will visit the site. no, because 0.40 represents probability in the long run over many visits to the site.
Out of the next 5 visitors, 2 will be asked to attempt the survey. (A) yes, because 2 out of 5 is equal to 40%.
It is given the probability that the randomly selected person is asked to participate in an online survey is 0.4
This means that there is a 40% chance of a visitor being asked to join the survey.
Probability of an event = no. of favorable outcomes / total no of outcomes
P(E) = n(E) / n
Therefore, if the number of visitors to the website is 5,
n = 5
P(E) = 0.4
Hence,
n(E) / 5 = 0.4
or, n(E) = 0.4 X 5
or, n(E) = 2
Therefore, out of the next 5 visitors, 2 will be asked to participate in the survey.
Correct Question
The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. is Avery interpreting the probability correctly?
(A) yes, because 2 out of 5 is equal to 40%.
(B) yes, because participants in the survey are selected at random.
(C) no, because there could be voluntary response bias.
(D) no, because only 40% of all people will visit the site.
(E) no, because 0.40 represents probability in the long run over many visits to the site.
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On average, Logan drinks 2/3 of a 6-ounce glass of water in 1 4/5 hours. How much water does he drink, in glasses per hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
[tex]\frac{3}{4}[/tex] of a 6-ounce glass will be drink by Logan in one hour.
What is Quantity?
Quantity is any number or variable and any algebraic combination of other quantities.
Define Average?
The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values .
Explanation for the answer:
Given time [tex]= \frac{2}{3}[/tex] of hours
= [tex]\frac{2}{3}\times 60[/tex] ([tex]\because[/tex] 1hrs = 60min)
[tex]= \frac{120}{3}[/tex]
= 40 minutes
Given quantity of water [tex]=\frac{1}{2}\ of\ 6\ ounce[/tex]
[tex]= \frac{1}{2}\times6\\ =3 ounce[/tex]
So,
In 40 mins, water intake is 3 ounce
In 1 min, water intake is [tex]\frac{3}{40}[/tex]
In 60 mins, water in take is [tex]\frac{3}{40}\times 60 = 4.5\ ounce[/tex]
Quantity of water intake in 60 mins:
4.5 ounce or 3/4 of 6-ounce glass
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What is the speed of a jet plane that travels 3,000 meters in 100 seconds?
Answer:
Step-by-step explanation:Answer: 108,000m/h (108km/h or 30m/s)
Karl bought 1.6 pounds of oranges and 2.4
pounds of pears. They each cost $1.48 per pound
Use properties to find the total cost.
Answer:
$5.92
Step-by-step explanation:
1.6 lbs. + 2.4 lbs. = 4 lbs.
4 x 1.48 = 5.92
Since it doesn't specify whether the oranges and apples cost differently you can add both of them. Then you multiply it by 1.48 because that's the cost per pound.
Please help! The total cost after tax to buy floor tiles is represented by 14f+0.096(14f), where f represents the number of square feet of tile are need to cover the floor.
a. What part of the expression represents the amount of tax that must be paid? Explain. (3 pts)
b. What would the expression be if the cost per square foot was $15 (plus tax)? (3 pts)
Considering the expression in this problem, it is found that:
a) The part of the expression that gives the amount of taxes that has to be paid is: 0.096(14f).
b) The expression would be of: C(f) = 15f + 0.096(15f).
What is the meaning of the expression?The expression for the total cost in this problem is presented as follows:
C(f) = 14f + 0.096(14f).
The meaning of each term is given as follows:
14f means that the cost of each square feet of tile is of 14 f.0.096 x 14f means that an additional 0.096 = 9.6% is paid of tax for each square feet of tile purchased.If the cost per square foot was of $15 instead of $14, the complete expression would be as follows:
C(f) = 15f + 0.096(15f).
That is, the two instances of 14 in the equation were replaced by 15.
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f(x)=-1²-3x+ 20
Find f(5)
Answer:
6
Step-by-step explanation:
-1^2-3(5)+20
1-15+20
1+5
6
hopes this helps
At the beginning of the lesson, Jacob determined that there was a problem with the sail length measurements of 7.5 meters, 4.8 meters, and 2.5 meters. Explain how Jacob was able to determine there was a problem with the specifications of the triangular sail.
Answer:
Jacob was able to determine there was a problem with the specifications of the triangular sail because of the Pythagorean theorem.
Step-by-step explanation:
Assume the triangular sail is a right triangle.
The Pythagorean theorem says: [tex]A^{2} + B^{2} = C^{2}[/tex]
If A = 4.8, B = 2.5, and C = 7.5, then [tex]4.8^{2} + 2.5^{2} = 7.5^{2}[/tex].
[tex]4.8^{2} + 2.5^{2} = 23.04 + 6.25 = 29.29[/tex]
[tex]7.5^{2} = 56.25[/tex]
In conclusion, [tex]29.29 \neq 56.25[/tex], so there is a problem with the sail.
Can someone help me with this please! I really need it done PLS
increase the amount of the ingredients by 5 and by 20
Answer:
it's 50 g
Step-by-step explanation:
it's like a multiplying assberry kehe
the ages of five randomly choose cars in the parking lot are determined to be 7, 9, 3,4, and 6 years old. if we consider these 5 cars in groups of 3, how many groups can be formed?
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Let d represent:
I do not drink bottled water.
Lett represent:
I eat pizza.
What is the symbolic representation of the following statement?
I do not eat pizza or I do not drink bottled water
I eat pizza or drink bottled water, for example, is a symbolic representation of the following statement.
What is meant by symbolic representation?Traditionally, symbolic representation is defined as the representation of a principal, such as a nation, through a symbol, such as a flag, that evokes specific meanings and emotions about the nation. The use of physical or psychological processes to represent an object (either another object or an idea) in a symbolic form is referred to as symbolic representation (Carlson, Sroufe, & Egeland, 2004). A written character or mark that is used to represent something; a letter, figure, or sign that is traditionally used to represent some object, process, etc. (Oxford English Dictionary). Figures denoting the planets, signs of the zodiac, and so on are examples of something visible that represents something else that is invisible by association or convention. Synonyms include symbol, symbolization, and symbolization.To learn more about symbolic representation, refer to:
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a researcher counts the number of students who agree, disagree, or are indifferent concerning a recent school policy change. what are the degrees of freedom for this chi-square goodness-of-fit test?
The number of degrees of freedom for the chi-square goodness-of-fit test is of:
2.
How to obtain the number of degrees of freedom for a chi-square test?The number of degrees of freedom for a chi-square goodness-of-fit test is obtained according to the multiplication presented as follows;
df = (r - 1) x (c - 1).
In which the variables are listed as follows:
r is the number of rows from the table.c is the number of columns from the table.The table in this problem has three rows, given as follows:
Students who agree with the recent school policy change.Students who disagree with the recent school policy change.Students who are indifferent with the recent school policy change.The table has two columns, which are given as follows:
Student's opinions.Absolute frequencies of the student's opinions.Hence the number of degrees of freedom of the test is given as follows:
df = (3 - 1) x (2 - 1) = 2 x 1 = 2.
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