(a+√8)^2 can be written in the form c+d√2, where a c and d are integers. Find in terms of a an expression for c and an expression for d
Thank you so much
Please respond when you can in your own convenience
Answers
The expression for c and d in terms of a are c = a²+8 and d = 4a
How to write (a+√8)² in the form c+d√2?An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.
(a+√8)²can be written in the form c+d√2 by expand the bracket. That is:
(a+√8)² = (a+√8)(a+√8)
(a+√8)² = a(a+√8) + √8(a+√8)
(a+√8)² = a² + a√8) + a√8 + 8
(a+√8)² = a² + 2a√8 + 8
(a+√8)² = a² + 4a√2 + 8
(a+√8)² = (a²+8) + 4a√2
Thus, c = a²+8 and d = 4a
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Related Questions
You are throwing a party and you need 7 liters of soda for every 12 guests. If you have 90 guests, how many liters of soda do you need?
Answers
Using proportion, the number of liters of soda needed would be 52.5 liters.
How to Use Proportion to Solve Word Problem?Proportion can be described as an equation that relates two equal ratio to each other.
If you need 7 liters of soda for every 12 guests, and you have 90 guests, you can use the proportion:
7 liters / 12 guests = x liters / 90 guests.
To find the number of liters of soda you need, you can cross-multiply and solve for x:
12x = 7(90)
12x = 630
x = 630/12
x = 52.5
So, you need 52.5 liters of soda for 90 guests.
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A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
A. The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.
B. The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.
C. The confidence interval from the first simulation is (0.191, 0.233), and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.213 and 0.257.
D. The confidence interval from the first simulation is (0.191, 0.233), and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.213 and 0.257.
Answers
The correct option regarding the 95% confidence interval for this problem is given as follows:
A. The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for the first simulation are given as follows:
[tex]n = 1000, \pi = \frac{212}{1000} = 0.212[/tex]
Hence the lower bound of the interval is of:
[tex]0.212 - 1.96\sqrt{\frac{0.212(0.788)}{1000}} = 0.187[/tex]
The upper bound is of:
[tex]0.212 + 1.96\sqrt{\frac{0.212(0.788)}{1000}} = 0.237[/tex]
For the second simulation, the parameters are given as follows:
[tex]n = 1000, \pi = \frac{235}{1000} = 0.235[/tex]
Hence the lower bound of the interval is of:
[tex]0.235 - 1.96\sqrt{\frac{0.235(0.765)}{1000}} = 0.209[/tex]
The upper bound is of:
[tex]0.235 + 1.96\sqrt{\frac{0.235(0.765)}{1000}} = 0.261[/tex]
This means that option A is the correct option.
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A student weighs 565 N, She climbs 3. 25m vertically up a flight of stairs. It takes her 12. 6 s what is her power output?
Answers
The work done by student is 145.9 W.To calculate the work done by the student:
Work = Force x Distance = 565 N x 3.25 m = 1841.25 J
Calculate the power output:
Power = Work/Time = 1841.25 J/12.6 s = 145.9 W
Power is the quantity of energy that is transported or transformed per unit of time in physics. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as activity in ancient writings. A scalar quantity is power.
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multiply (x+6)(x^2-3x-4)
Answers
The required Product of the given two expression is x³ - 9x² - 22x - 24.
What is multiplication of two expression?The process of multiplying two provided expressions made up of variables and constants is known as the multiplication of algebraic expressions. An expression that uses integer constants and variables together is called an algebraic expression.
According to question:We have given,
(x+6)(x²-3x-4)
= x(x²) - x(3x) - 4x + 6x² - 6(3x) - 24
= x ³ - 3x² - 4x - 6x² - 18x - 24
= x³ - 9x² - 22x - 24
Thus, required product of the given two expression is x³ - 9x² - 22x - 24.
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The two expression given has a necessary Product of x3 - 9x2 - 22x - 24.
What does a two-fold phrase mean?Algebraic expression multiplication is the operation of multiplying two supplied expressions made consisting of variables and constants.Algebraic expressions combine variables and integer constants to form sentences.The information that we have provided,(x+6)(x²-3x-4)= x(x²) - x(3x) (3x) - 4x + 6x² - 6(3x) - 24= x ³ - 3x² - 4x - 6x² - 18x - 24= x³ - 9x² - 22x - 24As a result, the required product of the two expressions supplied is x3 - 9x2 - 22x - 24.To learn more about multiplication refer::
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Find X, Y, and Z.
TEACHING TEXTBOOKS GEOMETRY
Answers
The required values of x, y and z are 58°, 29° and 60°
What is an angle?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Given are two triangles with unknown angles, we are asked to find, value of x, y and z.
Since, the lines are given parallel,
Therefore,
2y = 58° [alternate interior angles]
y = 29°
Now,
2y = x [alternate interior angles]
x = 58°
Since, we know that, the sum of interior angles of a triangle is 180°
Therefore,
x + z + 62° = 180°
58° + 62° + z = 180°
z = 180° - 120°
z = 60°
Hence, the required values of x, y and z are 58°, 29° and 60°
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John needs 23 boards to build rafters for his house. He can use 16-foot or 20-foot length boards. He needs seven fewer 16-foot boards than 20-foot boards. Write and solve a system of equations to determine how many of each board John needs
Answers
The equation which is required to solve how many of each board John needs is x + x - 7 = 23.
The number of 20-foot boards is 15.
The number of 16-foot boards is 8.
As per the given data, John needs 23 boards to build rafters for his house.
He can use 16-foot or 20-foot length boards.
He needs seven fewer 16-foot boards than 20-foot boards.
Here we have to determine how many of each board John needs.
Let the number of 20-foot boards be x.
Then the number of 16-foot boards be x - 7.
Total number of boards are 23.
Equation to determine how many of each board John needs:
x + x - 7 = 23
2x - 7 = 23
2x = 23 + 7
2x = 30
x = 15
The number of 20-foot boards are 15.
The number of 16-foot boards are x - 7
= 15 - 7
= 8
The number of 16-foot boards are 8.
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Select the correct answer. Given: Prove: Two parallel lines passing the vertices with red line r at points (c, d) at (2, 10) and (O, b) at (0, 6) and blue line s intercepts (c, O) at (2, 0) and (O, a) at (0, minus 4) Statements Reasons 1. given 2. application of the slope formula 3. distance from to equals the distance from to definition of parallel lines 4. application of the distance formula 5. substitution property of equality 6. inverse property of addition 7. substitution property of equality The table and corresponding image show the proof of the relationship between the slopes of two parallel lines. What is the missing statement in step 2? A. B. C. D.
Answers
Answer: its A
Step-by-step explanation:
Answer:
step 6
Step-by-step explanation:
Ben decides to build a rabbit to keep his children rabbits in. The run will be a rectangular with a width of 4cm. He has a maximum of 34m of fencing to use but wants the area to be greater than 50msquared. Find the range of values for the length of the run using inequalities
Answers
For the given case, the the range of values for the length of the run using inequalities is 4 < l < 8.5.The equation for the area of a rectangle is A = w x l, where w is the width and l is the length.
To find the range of values for the length of the run, we need to set up an inequality equation. We know the width is 4cm, so A = 4l > 50m2. This can be rearranged to 4l > 50m2, and then divided by 4 to get l > 50/4m2, which gives us l > 12.5m. This means that the length of the run must be greater than 12.5m.
We also know that Ben has a maximum of 34m of fencing to use, so l < 34/4m, which gives us l < 8.5m. This means that the length of the run must be less than 8.5m. Therefore, the range of values for the length of the run using inequalities is 4 < l < 8.5m.
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72
1
5
10
23
t(n)
1
-7
-17
What’s the t(n) for 4
Answers
N(u) = 4, where N is the function and u is the independent variable, is the function that is provided.
Find the solution ?The input values for a particular function are shown by the independent variable (x).An experiment involves controlling the independent variables while it is being conducted.
The results of the function are shown by the dependent variable (y). In an experiment, a variable that stands in for a variable being changed is known as an independent variable.As the independent variable in an equation, x is frequently employed as its symbol.
N(u) = 4, where N is the function and u is the independent variable, is the function that is provided.
Since u is no longer a variable, the value of the function N(u) is now a constant.
As a result, the N(u) function will always equal 4 for all values of the variable u, making it a constant function.
Thus, N(4) = 4. ( Answer )
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Solve the iniquality below. Use the drop - down menus to describe the solution and it’s graph. -7x+13>41
Answers
Step-by-step explanation:
-13 on both sides
/ by -7 on both sides
flip the ineq sign bcus u divided by a negative
x < -5.86
Kris is making cookies.
He has 4/3 cups of sugar.
He needs 2/3 cup of sugar to make one whole batch of cookies.
Use the drop-down menus to complete the statements below about the cookies that Kris can make.
Answers
Answer: With 4/3 cups of sugar, Kris can make (4/3) / (2/3) = 2 batches of cookies.
Step-by-step explanation:
The Mccay's purchase a home in a flood zone for $265,00.
Unfortunately, due to location the house depreciates in value by
2. 5% per year. What will the value of the house be in 5 years?
Round to the nearest cent
Answers
If Mccay purchased a home in a flood zone for $26500 , and the value depreciates by 2.5% , then the value of house after 5 years will be $23349 .
the current value of Mccay's house is = $26500 ;
the percent decrease in the value of the house is = 2.5% per year ;
let the number of years be = "n" years ;
we know that 2.5% is = 0.025 ;
the Depreciated Value(V) of the house can be written as :
V = 26500(1 - 0.025)ⁿ ;
to find the value of house after 5 years we substitute n = 5 ;
V = 26500(0.975)⁵ = 23349.035
V = 23349 .
Therefore , the value of the house after 5 years will be $23349 .
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An 8 feet tall stop sign creates a shadow that is 2.5 feet long. At the same time, a utility pole creates a shadow that is 10 feet long. How tall, in feet, is the utility pole?
Answers
The height of the utility pole casting a shadow 10 ft is 32 feet.
What is the height of the utility pole?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
Given that;
Height of stop sign = 8ftShadow of stop sign = 2.5ftShadow of utility pole = 10ftHeight of utility pole = xRatio of height of utility pole and its shadow = x / 10
Ratio of height of sign post and its shadow = 8/2.5
Equate to determine the height of the utility pole.
x/10 = 8/2.5
Solve for x
x × 2.5 = 8 × 10
2.5x = 80
x = 80 / 2.5
x = 32 ft
Therefore, the height of the utility pole is 32 ft.
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Work out the value of x.
Answers
Answer:
x = 4 . . . cm
Step-by-step explanation:
You want the measure of the segment CE from external point C to circle O, given several other dimensions of chords and segments in the circle.
Crossing chordsAs in the attachment, we can extend segment DO across the circle to make diameter DX. Then we can use the relation for chord lengths to find the radius of the circle (r).
Segments of crossing chords have the same product:
FA·FE = FD·FX
7·4 = 2·(2r -2) . . . . . use given segment values
14 = 2r -2 . . . . . . divide by 2
16 = 2r . . . . . . . add 2
r = 8 . . . . . . . divide by 2
The radius of the circle is 8 cm.
SecantsWe can also extend radius EO across the circle to make diameter EY, as shown in the attachment.
The relation involving the product of secant segments can be used to find x:
CE·CY = CB·CA
x(x +16) = 5(5+4+7)
x² +16x = 80 . . . . . . . . simplify
x² +16x +64 = 144 . . . . . . . add 64 to complete the square
(x +8)² = 12² . . . . . . . . . write as squares
x +8 = 12 . . . . . . . . positive square root
x = 4 . . . . . . . . subtract 8
The value of x is 4.
__
Additional comment
The attachment is accurately drawn.
L
6cm
10cm
X
if the shaded area is 112 cm²,
then the length x in the figure is 口。
cm.
Answers
If the shaded area is 112 cm², then the length x in the figure is 7cm.
What is Area of Rectangle?The area of Rectangle is length times of width.
Split the shape into two rectangles:
then you have two areas:
x×10 and x×6
the shaded area is given as 112cm²
10x+6x=112
Add the like terms
16x=112
Divide both sides by 16
x=112/16
x=7 cm
Hence, if the shaded area is 112 cm², then the length x in the figure is 7cm.
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What is the quotient of 154,504 divided by 28 with long division
Answers
5518 is the quotient of 154,504 divided by 28.
What is Division?A division is a process of splitting a specific amount into equal parts.
The quotient of 154, 504 divided by 28 is 5518 after applying the arithmetic operation.
Long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals that is simple enough to perform by hand.
Hence, 5518 is the quotient of 154,504 divided by 28.
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Please help me ASAP please please please
Answers
The quadrilateral is parallelogram because the opposite sides are parallel and congruent
What is a parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.
Since WZ and XY are congruent and XW and YZ are congruent and Also, WZ and XY are parallel and XW and YZ are parallel, we can therefore say that the quadrilateral obeys the property of a parallelogram.
parallel lines are two straight lines that can not meet at a point.
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What type of solutions does this equation have?
y² = 0
one real solution
two imaginary solutions
two real solutions
no solutions
Answers
Answer:
the last one
Step-by-step explanation:
Answer: One real solution (0)
Step-by-step explanation:
The only thing square which equals 0 is 0 itself.
Which of the follow is a solution set for the following graph
Answers
The solution set for the given graph is (2,1). The solution has been obtained using linear equations.
What is a linear equation?
It is a linear equation that has the greatest degree of one. In a linear equation with an exponent greater than one, this indicates that there are no variables. A straight line is produced on the graph by this equation.
We are given two lines on the graph
The points of the red line are (3,0) and (0,3)
So, the equation of the line comes out to be
y=−x+3 ...(1)
The points of the blue line are (3,2) and (-1,-2)
So, the equation of the line comes out to be
y=x−1 ...(2)
To find the solution set, we need to solve the equations
Substituting (1) in (2), we get,
⇒−x+3 = x−1
⇒−2x = -4
⇒x = 2
So, y = 1
Hence, the solution set for the given graph is (2,1).
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3. Suppose that your goal is to build a credit history by establishing a FICO score. How should
you approach payments on a long-term loan, such as an auto loan?
OPay the minimum amount required each bill.
OMake multiple small payments toward each bill.
OSkip payments occasionally.
OPay as much as you can afford each bill.
Answers
Suppose that your goal is to build a credit history by establishing a FICO score. you should approach payments on a long-term loan, such as an auto loan by: A. pay the minimum amount required each bill.
What is credit history?Credit history can be defined as the record that help to show a creditworthiness of a person which is the ability to pay back a loan.
FICO score on the other hand is as well used to determine the creditworthiness of a borrower based on the fact that this score help to show whether a borrower used to pay the amount loan to him/her on time or delay it.
Therefore the correct option is A.
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I need help quickly Pleasee
Answers
The volume of a pyramid with a base area of 15 square inches and a height of 7 inches will be 35 cubic inches.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (L × B × H) / 3
V = (Base area x H) / 3
The volume of a pyramid varies jointly with the base area of the pyramid and its height.
The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.
Then the volume of a pyramid with a base area of 15 square inches and a height of 7 inches will be
V = (15 x7) / 3
V = 35 cubic inches
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x = -2 graphed please!!!
Answers
see attachment..........
hope it helps<3
The four 6th grade math teachers decide they want to go to McDonald's
for lunch. They each order big mac for $3.99 and a drink. If they spent
$20.32, how much was each drink? Create an equation using distributive
property and solve.
Answers
Let x be the cost of each drink.
The total cost for all four teachers' meals can be represented using the distributive property:
4(3.99 + x) = 20.32
Expanding and solving for x:
15.96 + 4x = 20.32
Subtracting 15.96 from both sides:
15.96 -15.96 + 4x = 20.32 -15.96
4x = 4.36
Dividing both sides by 4:
x = 1.09
Hence, each drink cost $1.09
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The sum of double a number and six times a number is 48. Find the number. show your work
Answers
The equation is 2x + 6x = 48. Then the unknown number will be 6.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The sum of double a number and six times a number is 48.
Let the unknown number be 'x'. Then the equation is given as,
2x + 6x = 48
Simplify the equation, then the value of 'x' is given as,
2x + 6x = 48
8x = 48
x = 48 / 8
x = 6
The equation is 2x + 6x = 48. Then the unknown number will be 6.
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Which of the following graphs is described by the function given below?
y=x²-4x-12
-20
18
A. Graph A
B. Graph B
C. Graph C
D. Graph D
jy v
-20
SUBMIT
Answers
Answer:
Step-by-step explanation:
grew graph B for graph A
a bakery needs to make 10 batches of bagels before opening in 6 hours ech batch of bagels takes 3/4 of an hour to make will the bakery have enough time to bake 10 bagels
Answers
The bakery will not have enough time to bake 10 batches of bagels in 6 hours.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
Given that,
There is a time limit of 6 hours to make 10 batches of bagel.
Time needed to make 1 batch of bagel = 3/4 hour
Time needed to make 10 batches of bagel = 10 × (3/4)
= 30 / 4
= 7.5 hours
Hence at least 7.5 hours is needed to make 10 batches of bagel.
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18. What is the equation for the relation? HELPPPPP
Answers
The line crosses the vertical axis at 400, so the equation has to be "C = something + 400".
If you pick any point and go up 100 and over 200, you get back on the line, so the slope is 100/200 or 1/2
Option C: C = 1/2 N + 400
Answer:
C. 1/2N +400
Step-by-step explanation:
So the 400 is reqiured in the equation as
x =0 , y= 400.
To find the slope you can do rise over run:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] =
[tex]\frac{500-400}{200-0} =\frac{100}{200} =\frac{1}{2}[/tex]
y = -5x - 21
-4x + y = 6 Solve each system of equations. Show all your work.
Answers
The solution of the system of equations:
y = -5x + 21-4x + y = 6is (-3, 6)
How to solve the system of equations?
Here we want to solve the system of equations below:
y = -5x + 21
-4x + y = 6
We can use the elimination method to solve this if we take the difference between the two equations, we will get:
y - (-4x + y) = -5x - 21 - 6
4x = -5x - 27
Now we can solve this for x.
4x + 5x = -27
9x = -27
x = -27/9 = -3
And the value of y is given by:
y = -5x - 21 (we need to evaluate that on x = -3)
y = -5*-3 - 21
y = 15 - 21 = 6
The solution is (-3, 6).
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Answer: Elimination : (-3,-6) Substitution : (5/3,38/3)
Step-by-step explanation: Elimination : y = -5x + 21;-4x + y = 6 y - (-4x + y) = -5x - 21 - 6 4x = -5x - 27 4x + 5x = -27 9x/9 = -27/9 x = -3 y = -5x - 21 y = (-5) (-3) - 21 y = 15 - 21 y = -6 (-3,-6) Substitution : y = -5x + 21;-4x + y = 6 −4x + −5x + 21 = 6 −9x + 21 - 21 = 6 - 21 -9x/-9 = -15/-9 x = 5/3 y = −5x + 21 y = −5 (5/3) + 21 (-25) (1) + (21) (3) / (3) (1) -25/3 + 63/3 y = 38/3 (5/3,38/3)
g(x)=1/2x-3 find g (12)
Answers
Answer:
g(12) = 3
Step-by-step explanation:
g(12) means to put 12 in place of x.
g(x) = 1/2x - 3
g(12) = 1/2(12) - 3
Mulitply 1/2 and 12.
= 6 - 3
subtract.
= 3
g(12) = 3
Write the pair of fractions as a pair of fractions write a common denominator 1/8 and 2/6