The resulting perfect square using the given trinomial is found as (4y + 9)².
Explain the term perfect square?If a number's square root is indeed an integer—that is, if it is the product of an integer and itself—it is a perfect square and perhaps a square number.We need to ensure that our producing trinomials have the following form since we want to add an one term (monomial) here to given binomial (16y^2+__+81) so that the producing trinomial may be represented as the square of some other binomial:a²-2ab+b² or a²+2ab+b²
since:
a²-2ab+b² = (a-b)²
and
a²+2ab+b² = (a+b)²
A trinomial is written as the square of the a binomial in the equations above.
Knowing that the aforementioned equations are correct, we may use the binomial that has been provided and proceed backwards from there:
= (4y)² +__+ (9)² ....eq 1
a = 4y and b = 9.
Thus, 2ab = 2(4y)(9) = 72y
Put in eq 1;
= (4y)² + 72y + (9)²
The resulting perfect square:
= (4y + 9)²
Thus, resulting perfect square using the given trinomial is found as (4y + 9)².
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Solve for x ?
Not drawn to scale
Answer: 3
Step-by-step explanation:
The triangles are similar using the angle-angle similarity theorem.
Using the fact that similar triangles have proportional side lengths yields:
[tex]\frac{5x-7}{4}=\frac{18}{9}\\\\\frac{5x-7}{4}=2\\\\5x-7=8\\\\5x=15\\\\x=3[/tex]
-2x+y=-7
how do you do this problem
if f (x) = 4x - 1, what is f (-2)
PLEASE HELP!
Answer: -9
Step-by-step explanation: If you subtitutie -2 in for x, ask yourself , what is 4*-2 which is -8 which is then subtracted by 1 which gets you -9 so, this means f (-2)=-9
Hope this helped!
A pizza lover wants to compare the average delivery times for four local pizza restaurants. Over the course of a few weeks, he orders a number of pizzas from each restaurant, and he records the time it takes for each pizza to be delivered.
a) When performing an ANOVA with this data, what is the alternative hypothesis?
- All of the restaurants have different mean delivery times
- At least two of the restaurants have different mean delivery times
- Two of the restaurants have different mean delivery times
- One of the restaurants has a different mean delivery time than the others
b) A partial ANOVA table for his data is shown below. What is the value of B?
Source DF SS MS F P-value
Treatment B 19.31 D F G
Error C 15.667 E
Total 18 34.977
What is the value of C in the ANOVA table?
d) What is the value of D in the ANOVA table? Give your answer to three decimal places.
e) What is the value of E in the ANOVA table? Give your answer to three decimal places.
f) What is the value of F in the ANOVA table? Give your answer to two decimal places.
g) What is the value of G in the ANOVA table? Give your answer to four decimal places.
h) Using a 0.1 level of significance, what should his conclusion be in this case?
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is less than 0.1.
- He should fail to reject the claim that at all of the restaurants have the same mean delivery times because the P-value is greater than 0.1.
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is greater than 0.1.
- He should conclude that at all of the restaurants have the same mean delivery times because the P- value is less than 0.1.
There are at least two restaurants with varying mean delivery times. The required hypothesis are ,
H0: The mean delivery time for all restaurants is the same.
H1: The average delivery time varies between at least two restaurants.
If the data are put through an ANOVA, a different mean delivery time for at least two of the restaurants would be the alternative hypothesis.
According to the alternative hypothesis (Ha), there is a significant statistical association between two variables. As opposed to the null hypothesis, which claims that there is no statistical connection between the two variables.
The analysis of variance procedure, or ANOVA, includes examining the validity of mean hypotheses in light of variances. The equality mean, or H0. All means are equal, is used as the null hypothesis in an ANOVA. Alternative hypothesis, however, includes at least two means that are not equal.
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Please Help with this.
i need answers and explanations for the stuff in the picture
Point= (1, -1)
Hence, this is not the solution of the desired answer.
What is inequality?inequality is defined as declaration of the relation of greater, greater than or equal to, smaller, or less than or equal to between two numbers or the algebraic expressions. Either queries or the declarations of fact in the form of theorems can be used to formulate and solve inequality problems.
Shaded Region represents y<2x-3
Given Point= (1, -1)
Hence, this is not the solution of the desired answer,
As it not defines the equality part.
As for example (2,-2) is the solution of the desired inequality and it satisfies the condition y<2x-3.
And given point (1, -1) is not the solution of the desired equation as it does not satisfy the inequality portion.
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A boat can travel 302.9 miles on 23.3 gallons of gasoline. How far can it travel on 13.7 gallons?
Answer:
178.7 miles
Step-by-step explanation:
First, determine the miles per gallon:
[tex]\frac{302.9\ miles}{23.3\ gallons}\\13.0\frac{miles}{gallon}[/tex]
Then, use that value to find miles traveled on 13.7 gallons:
[tex]13.7\ gallons(\frac{13\ miles}{1\ gallon})\\178.7\ miles[/tex]
Anthony and joan have $10 to buy apples and oranges at the market. They will buy a total of 25 pieces of fruit. Apples cost 50 cents each and oranges cost 25 cents each. Which of these systems best represents this situation?.
The system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10
Define System of Equation
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given,
Total money Anthony and Joan have to buy apples and oranges = $10
Total pieces of fruit the Anthony and Joan buy is = 25 pieces of fruit
Each Apple's cost = 50 cents
Each orange's cost = 25 cents
Let, x = be the apples
and, y = be the oranges
The equation applied for the number of pieces of fruit they will buy,
x + y = 25
And, the equation applied for cost is,
0.50x + 0.25y = 10.00 (Keep everything in same decimal places)
Hence, the system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10
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How far must the outfielder throw the ball to return it to the pitcher? round to the nearest foot.
Using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.
What are the laws of cosines?The square of a side of a plane triangle is equal to the sum of the squares of the other sides minus twice the product of those sides and the cosine of the angle between them, according to a trigonometry rule.
So, it is a given that the distance between the home plate and the pitcher's mound on a softball field is 43 feet.
27° east of the pitcher's mound is the angle at which a ball is struck.
Before an outfielder catches the ball, it travels 162 feet.
Using the law of cosines, we may now:
a² = b² + c² - 2bcosA
When b=43, c=162, and A=27° are entered, we get:
a² = 43² + 162² - 2(43)(162)cos27°
a² = 1849 + 26244 - 12413.4
a² = 15679.6
a = 125.21
a = 125ft
Therefore, using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.
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Complete question;
On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(A) Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.
15PTS HELP ASAP PLEASE! A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 160 ounces of a mixture that is 70% salt. How many ounces of each solution should she use?
Answer:
Step-by-step explanation:
68 Ounces B - 61.2
92.4 Ounces A - 60.06
70% of 160 = 112
A+B estimated 112
What is the midpoint of (1,5) and (7,11)
Answer:
(4,8)
Step-by-step explanation:
First, Let us see the midpoint formula:
m(x,x /2, y,y/2) (That probably looks really confusing online)
Let us label our cords
A: (1x,5y)
B: (7x,11y)
Now, Add the x's together
7x + 1 = 8
8÷2 = 4
Now, Add the y together
11 + 5 = 16
16÷2 = 8
(4,8)
For positive angles A and B, it is known that tan A = 5/12 and sin B = 3/5. Find the value of cos(A-B) in simplest form.
This question has me stumped. can anyone help?
The value of the cos(A - B) in simplest form would be 273/100.
What are the trigonometric angles?
Trigonometry angles are the angles given by the ratios of the trigonometric functions. Trigonometry deals with the study of the relationship between angles and the sides of a triangle. The angle value ranges from 0-360 degrees. The important angles in trigonometry are 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°.
sin B = 3/5
tan A = 5/12
We have find cos(A - B)
first, let’s hope these are both all-integer triangles:
In a 3-4-5 Right triangle,
sinB = 3/5, cos B = 4/5
For tanA = 5/12 the hypotenuse turned out to be 13.
sin A = 5/12
cos A = 12/13
So now we just use the identity for cos ( A + B )
cos(A - B) = cosAcosB + sinAsinB
= (12/13)(4/5) + (5/12)(3/5)
= (60 + 52/65) + (25 + 36/60)
= (112/65) + (61/60)
= 273/100
Hence, the value of the cos(A - B) in simplest form would be 273/100.
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What is the hcf of 315 and 42
Answer: 21
the hcf of 315 and 42 is 21.
Answer:
HCF of 315 and 42:
Your answer is 21 !
The first few terms of a geometric
sequence are given by 2, 4, 8, 16... What is
the value of the 28th term divided by the
26th term?
Answer:
4
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{4}{2}[/tex] = 2
then
a₂₈ = 2 [tex](2)^{27}[/tex]
a₂₆ = 2 [tex](2)^{25}[/tex]
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{a_{28} }{a_{26} }[/tex]
= [tex]\frac{2(2)^{27} }{2(2)^{25} }[/tex] ( cancel 2 on numerator/ denominator )
= [tex]\frac{2^{27} }{2^{25} }[/tex]
= [tex]2^{(27-25)}[/tex]
= 2²
= 4
write the equation of a polynomial of least degree in standard form that has zeros at x=2i & x=3 what is the constant form?
The equation of a polynomial that has zeros at x = 2i and x = 3 is given as follows:
x³ - 3x² + 4x - 12.
How to obtain the cubic polynomial?We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.
The zeros are given as follows:
x = 2i.x = -2i, as if a complex number is a root, then it's conjugate also is.x = 3.Then the polynomial is obtained as the product of it's linear factors, due to the Factor Theorem, as follows:
(x - 2i)(x + 2i)(x - 3)
(x² + 4)(x - 3)
x³ - 3x² + 4x - 12.
(as the base complex number relation is i² = -1).
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The equation of the graphed line is x+2y=5. What is the x-intercept of the graph?
Answer:
(5,0)
Step-by-step explanation:
When graphed the x-intercept meaning the line touching x
is 5 so then your answer is (5,0) because the x-value comes first so then you'd put the 5 in front.
A group of cubes are arranged in a pattern with the same number of cubes in each row and column. There are 225 cubes in the shape. How many cubes are in one row?.
Using square roots, we know that there are (A) 15 cubes in a row.
What is square root?The value that a number produces when it is multiplied by itself is known as the square root of the number.
The square root is denoted by the radical sign. For instance, √16 = 4.
The root symbol or surds is another name for the radical symbol.
So, let x be the total number of cubes in a row.
The number of cubes in each row and column is equal because they are organized in a pattern with the same number of cubes in each.
Now,
Total cubes = x * x
Total cubes = x²
We know that the total number of cubes is 225.
So, we got:
x² = 225
Taking square roots:
x² = 225
x = √225
x = 15
Therefore, using square roots, we know that there are (A) 15 cubes in a row.
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Complete question:
A group of cubes is arranged in a pattern with the same number of cubes in each row and column. There are 225
cubes in the shape. How many cubes are in one row?
A) 15
B) 25
C) 56
D) 75
For each of the following questions solve for the variable.
supposed to questions
Step-by-step explanation:
people say the climate is changing
3. Amara was given the formula for the volume of a half-cylinder, V=h, and asked to sok
the formula for h, the length of the half-cylinder.
Which equation below is a correct rearrangement of the formula Amara was given?
The equation for the length, h is h= ( 2V ) / ( πr² )
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.
Volume of a half-cylinder:
V= (1/2)πr²h
Move 2 to the left
=> 2V= πr²h
Solve for h
=> 2V/πr² = h
=> h= ( 2V ) / ( πr² )
Thus, the equation for h is h= ( 2V ) / ( πr² )
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Use a graphing calculator to find the equation of the line of best fit for the data in the table below. Find the value of the correlation coefficient r. Then predict the number
of movie tickets sold in 2014
years- 1998,1999,2000,2001,2002,2003,2004,2005,2006,2007
tickets sold(millions)- 1282,1312,1317,1324,1365,1381,1383,1423,1449,1462
The value of the correlation coefficient is 0.9866.
By the end of 2014, the number of movie tickets sold would be equal to 1,600,000,000 movie tickets.
How to find the value of the correlation coefficient?In order to determine value of the correlation coefficient and line of best fit that models the data points contained in the table, we would use a graphing calculator (scatterplot).
In this scenario, the year would be plotted on the x-axis of the scatterplot while the number of tickets sold (in millions) would be plotted on the y-axis of the scatterplot.
On the Excel worksheet, you should right click on any data point on the scatterplot, select format trend line, and then tick the box to display an equation and correlation coefficient for the trend line (line of best fit) on the scatterplot.
From the scatterplot (see attachment) which models the relationship between the data points in the table, a linear equation for the line of best fit (trend line) is given by:
y = 20.012x - 38704
Correlation coefficient, R² = 0.9757.
By the end of 2014, the number of movie tickets sold is given by:
y = 20.012x - 38704
y = 20.012(2014) - 38704
y = 40,304.168 - 38704
y = 1,600.168 × 1,000,000 ≈ 1,600,000,000 movie tickets.
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(05.01)
The graph below shows a system of equations:
y=x+4
3y = -2x + 2
The x-coordinate of the solution to the system of equations is
Answer:
x= -2
Step-by-step explanation:
since we know what y equals we fill it into the second equation
3(x+4)= -2x+2
3x+12=-2x+2
-12. -12
3x=-2x-10
+2x +2x
5x=-10
/5. /5
x= -2
hopes this helps please mark brainliest
b) 4 machines of a factory can finish the required amount of production in 6 days. If one machine had machinery defect and stopped functioning, in how many days would the remaining machines finish the same quantity of production at the same rate of production?
Answer:
Answer = 8 days
Step-by-step explanation:
Step 1: Find how long one machine takes to finish
1. 6 ∙ 4 = 24 days
Step 2: Divide 24 by 3 to get the rate of speed of 3 machines
2. 24 / 3 = 8 days
Draw all the lines of symmetry for this shape.
Line 1
Answer:
Line down the middle
Step-by-step explanation:
There is only one line of symmetry in this shape because there is no rotational symmetry. Its a line down the middle.
Find the distance between the two points rounding to the nearest tenth (if necessary). ( 1 , 4 ) and ( − 2 , 8 )
Distance between (1,4) and (-2,8) is 5 units.
How to find distance between two points?The separation between two points. The coordinates of two points in space are used in the formula.
In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula.
Let distance between two points ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) be 'd' then,
d = [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
We are given two points (1,4) and (-2,8)
So, using formula for distance we get,
d= [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
=[tex]\sqrt{(-2-1)^{2} + (8-4)^{2} }[/tex]
d [tex]\sqrt{(-3)^{2} + 4^{2} } \\=\sqrt{25} \\=5[/tex]
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Nolan is going to a carnival that has games and rides. Each game costs $2.50
and each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and
rides. Write a system of equations that could be used to determine the
number of games Nolan played and the number of rides Nolan went on.
Define the variables that you use to write the system.
Hence, the equation is of the form [tex]2.5x+3.5y=52.50[/tex].
What is the system of equation?
A system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions.
Here given that,
Nolan is going to a carnival that has games and rides. Each game costs $[tex]2.50[/tex] and each ride costs $[tex]3.50[/tex]. Nolan spent $[tex]52.50[/tex] altogether on [tex]17[/tex] games and rides.
So, let us assume that the number of games are [tex]x[/tex] and the number of rides are [tex]y[/tex].
So, the equation is of the form
[tex]2.5x+3.5y=52.50 ........(1)[/tex]
And Noaln spent altogether $[tex]52.50[/tex] on [tex]17[/tex] games and rides.
So,
[tex]x+y=17[/tex]
Then,
[tex]2.5x+2.5y=2.5(x+y)\\As,\\x+y=17\\So,\\=2.5(17)\\\\=42.5.....(2)[/tex]
Now, subtract equation [tex](2)[/tex] from equation [tex](1)[/tex], we get
[tex]x=52.5-42.5\\\\x=10[/tex]
[tex]y=17-10\\y=7[/tex]
So the equation is of the form
[tex]2.5(7)+3.5(10)=52.50\\17.5+35=52.50\\52.50=52.50[/tex]
Hence, the equation is of the form [tex]2.5x+3.5y=52.50[/tex].
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. Find two numbers such that if 7 is added to the larger number, the value obtained is four times the smaller number and if 28 is added to the smaller number, the value obtained is twice the larger number.
Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.
We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:
x + 28 = 2(y + 7)
x + 28 = 2y + 14
x - 2y = -14
Then, we can substitute the second equation into the first equation to eliminate the other variable:
y + 7 = 4(x + 28)
y + 7 = 4x + 112
y - 4x = -105
Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:
x - 2y = -14
y - 4x = -105
If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:
x - 2(4x - 105) = -14
x - 8x + 210 = -14
-7x = -224
x = 32
Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.
Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).
Compare 0. 3 and 0. 8 uing >,=, or <. Draw a model or number line to upport your olution
On solving the provided question, we got that - 0.8 > 0.3, 0.8 is greater as , it is more closer to 1 than 0.3.
What is Number Line?The term "number line" refers to a horizontal line with numbers placed equally apart. Depending on the numbers present, you can choose how to respond to the numbers on the line. The corresponding question dictates how to use numbers. B. When arranging the points.
From the provided question,
we have to compare between 0.3 and 0.8.
Here,
Obviously, 0.8 is greater than 0.3.
as on number 0.8 is closer to 1 than 0.3,
and 0.3 is more closer to 0 than 0.8.
Therefore,
0.8 > 0.3.
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Select all of the equations that represent linear relationships. 5 + 2y = 13, y=1/2x^2+7, y – 5 = 2(x – 1), y/2=x+7, x = –4
5+2y=13, y-5=2(x-1), y/2 = x+7, x=-4 are linear equations.
What is linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1.
Another name for it is a one-degree equation.
A linear equation with one variable has the conventional form Ax + B = 0.
In this case, the variables x and A are variables, while B is a constant.
A linear equation with two variables has the conventional form Ax + By = C.
Here, the variables x and y, the coefficients A and B, and the constant C are all present.
As explained above about linear equation from given option we can verify that
5+2y = 13 can be written as 2y = 8 or 2y-8=0 which represents linear equation in one variable.
[tex]y = \frac{1}{2x^{2} +7}[/tex] cannot be written in any linear form and its highest degree is 2. So, it is not linear equation.
y-5= 2(x-1) can be written as 2x-y=-3 which is in the form of linear equation in two variables. So, it is linear equation in two variables.
x = -4 can be written as x + 4 = 0 which represents linear equation in one variable.
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In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister.
The probability that a randomly selected student has a brother given they have a sister is 8/30.
What is the probability calculation formula?We have provided that.
A class of 30 pupils has 13 brothers, 8 sisters, and 3 students who have both brothers and sisters.
The probability of an occurrence is calculated by dividing the total number of outcomes in the sample space by the proportion of favorable events.
Considering that there are 30 pupils overall and that 8 of them have both a brother and a sister,
The probability of a student having a brother given that they have a sister would then be 8/30 (8 out of the 30 students).
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JP Sports sold football boots on its first day of release. SoccerWorld sold 3 as many boots as JP Sports. DirectSportz sold 5 more boots than JP Sports. Each pair of football boots costs £70 The amount of sales from this particular boot totalled £7000
Work out how many pairs were sold by SoccerWorld.
The total number of pairs sold by SoccerWorld is 57
How to determine the total number of pairs sold by SoccerWorld?From the question, we have the following parameters that can be used in our computation:
SoccerWorld sold 3 as many boots as JP SportsDirectSportz sold 5 more boots than JP Sports. Cost of each pair = £70 Amount in sales = £7000The above parameters means that
s = 3j
d = 5 + j
70(s + d + j) = 7000
Where
j = JP Sports
s = SoccerWorld
d = DirectSportz
Divide both sides of 70(s + d + j) = 7000 by 70
s + d + j = 100
Substitute s = 3j and d = 5 + j
3j + 5 + j + j = 100
Evaluate the like terms
5j = 95
Divide by 5
j = 19
Substitute j = 19 in s = 3j
s = 3 * 19
So, we have
s = 57
Hence, the number of pairs is 57
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vy = a sin( k ( x - d)) + c and y = a cos( k ( x - d)) + c
The equation Vy = a sin(k(x - d)) + c is an equation for a sine wave. A sine wave is a periodic function that describes a periodic oscillation or vibration. It is commonly used to model periodic phenomena in many fields, such as sound, light, and electricity.
In this equation, Vy is the vertical position of the sine wave at a given point in time (x), a is the amplitude of the sine wave (the maximum distance from the midline), k is the wave number (the number of complete cycles per unit distance), x is the horizontal position (time or distance), d is the phase shift (the horizontal shift of the wave), and c is the vertical offset (the distance from the midline).
The equation y = a cos(k(x - d)) + c is similar to the equation for a sine wave, but it describes a cosine wave instead. A cosine wave is also a periodic function, but it is shifted by 90 degrees in phase compared to a sine wave.
Like a sine wave, a cosine wave can be used to model periodic phenomena and is commonly used in many fields. In this equation, y is the vertical position of the cosine wave at a given point in time (x), a is the amplitude of the cosine wave, k is the wave number, x is the horizontal position, d is the phase shift, and c is the vertical offset.
What is sin and cosine sum?
sin(x) + cos(x) = √2 * sin(x + 45°)
To learn more about sin and cosine
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