We want to find a quadratic equation with the following roots:
[tex]\begin{gathered} x_+=2+i\sqrt{\frac{3}{2}} \\ x_-=2-i\sqrt{\frac{3}{2}} \end{gathered}[/tex]Then we have:
[tex]\begin{gathered} y=(x-x_+)\cdot(x-x_-) \\ y=(x-2-i\sqrt{\frac{3}{2}})\cdot(x-2+i\sqrt{\frac{3}{2}}) \\ y=x^2-2x+i\sqrt{\frac{3}{2}}x-2x+4-i2\sqrt{\frac{3}{2}}-i\sqrt{\frac{3}{2}}x+i2\sqrt{\frac{3}{2}}+\frac{3}{2} \\ y=x^2-4x+\frac{11}{2} \end{gathered}[/tex]want is the constant out if these options 16.2 - 3(4) + 14/2
Given the expression :
[tex]16.2-3\mleft(4\mright)+\frac{14}{2}[/tex]so, the result will be as following:
[tex]\begin{gathered} 16.2-3\mleft(4\mright)+\frac{14}{2} \\ \\ =16.2-12+7 \\ \\ =11.2 \end{gathered}[/tex]the term 16.2 is a constant
Hey there!
Whenever, you hear or see the word “constant” think of the definition ‘a specific number or value that never changes in a particular equation’
16.2 - 3(4) + 14/2
= 16.2 - 12 + 14/2
= 16.2 - 12 + 7
= 4.2 + 7
= 11.2
Now, that we have that information out the way, we can answer your equation
Your CONSTANTS aren’t:
• -3(4) because we had to simplify it and convert it to: -12
• 14/2 because we had to simplify that as well and it converted it to: 7
(That’s how we figured out to make the equation much easier to breakdown)
(By the way, you can use PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, & Subtraction) to solve for the overall problem, like how I did for you :))
This leaves the constant to: 16.2 because we didn’t have to anything to it.
Therefore, your answer should be:
16.2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The proportional relationship between cost and pints of blueberries is shown in the table.
Blueberries (in pints) 2 5
Cost (in dollars) 6.80 17
Describe what a graph of the proportional relationship would look like.
A coordinate plane with the x-axis labeled Cost (in dollars) and the y-axis labeled Blueberries (in pints) shows a line going through (0, 0) and (5, 17).
A coordinate plane with the x-axis labeled Cost (in dollars) and the y-axis labeled Blueberries (in pints) shows a line going through (0, 0) and (2, 6.80).
A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (6.80, 2).
A graph of what the proportional relationship would look like is: C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
What is a graph?In Mathematics, a graph is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Generally speaking, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).
In this context, the x-axis of this graph would be labeled Blueberries (in pints) while the y-axis would be labeled Cost (in dollars), with the data points starting from the origin (0, 0) and passes through (5, 17) as shown in the image attached below.
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Answer:
C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
Step-by-step explanation:
Find the volume of this sphere.Use 3 for TT..V ?20 ftV ==Tr3Hint: The radius (r) is1/2 of the diameter.
From the problem, the diameter of the sphere is 20 ft.
Note that radius is half of diameter, so the radius will be r = 20/2 = 10 ft
Using the volume formula of a sphere.
[tex]V=\frac{4}{3}\pi r^3[/tex]where π = 3
[tex]\begin{gathered} V=\frac{4}{3}(3)(10)^3 \\ V=4000 \end{gathered}[/tex]The answer is 4000 ft^3
Write about a time you have used numbers and operations in your everyday life (outside ofmath class).
When going to the movies and we pay the ticket, most of the times (if we pay in cash) we will receive change for the bill we use.
For example, if the ticket costs $7 and we pay with $10, we will receive 10-7 = $3 as change.
We then have used math to know that the change we receive is correct.
Is y=x(x+1) a valid equation?
y = x(x + 1)
Yes, it's a valid equation, there are 2 values for x and two values for y.
In my opinion it's a continuous function because if we graph it there would not be gaps on it.
What is the domain of the square root function graphed below?
On a coordinate plane, a curve opens down to the right in quadrant 1. The curve starts at (3, 1) and goes through (4, 2) and (7, 3).
Answer:
3 ≤ x < ∞
Step-by-step explanation:
You want the domain of a square root function shifted right 3 units and up 1 unit. It goes through points (3, 1), (4, 2) and (7, 3).
DomainThe domain of a function is the set of values of the independent variable for which the function is defined. It is the horizontal extent of the graph.
The graph of the given square root function extends to the right from x=3.
The domain is 3 ≤ x < ∞. In interval notation, it is [3, ∞).
A theme park guest takes an innertube into the wave pool. The innertube moves up and down in a way such that the height h of the innertube, in meters, above the floor of the pool can be modeled by the function h = asinbx + 5. When the wave pool is turned on, the innertube's height fluctuates between 2 meters and 8 meters, with an interval of 12 seconds between maximums. Based on the context of the problem, what are the values of a and b?
So we are told that the height of the innertube in meters is given by:
[tex]h(x)=a\sin (bx)+5[/tex]The minimum height is 2 meters, the maximum is 8 meters and the time between two consecutive maximums is 12 seconds. Here is important to note a few properties of the sine. First of all, the minimum value of sin(bx) is -1 and its maximum value is 1. Then the height of the innertube is minimum when sin(bx)=-1 and maximum when sin(bx)=1. With these two values we can build two equations for a:
[tex]\begin{gathered} \min (h)=2=a\cdot(-1)+5 \\ \max (h)=8=a\cdot1+5 \end{gathered}[/tex]So we have:
[tex]\begin{gathered} 2=-a+5 \\ 8=a+5 \end{gathered}[/tex]Substracting 5 from both sides of the second equation we get:
[tex]\begin{gathered} 8-5=a+5-5 \\ 3=a \end{gathered}[/tex]Using this in the first equation gives us:
[tex]\begin{gathered} 2=-3+5 \\ 2=2 \end{gathered}[/tex]Which confirms that a=3. Now we have to find b. For this purpose we can recal another property of the sine. Its period i.e. the distance (in this case the time) between two consecutive maximums is given by:
[tex]\frac{2\pi}{b}[/tex]Since we know this time is 12 seconds we get:
[tex]\frac{2\pi}{b}=12[/tex]If we multiply both sides by b and divide them by 12 we get:
[tex]\begin{gathered} \frac{2\pi}{b}\cdot\frac{b}{12}=12\cdot\frac{b}{12} \\ \frac{2}{12}\pi=b \\ \frac{\pi}{6}=b \end{gathered}[/tex]So we have:
[tex]a=3\text{ and }b=\frac{\pi}{6}[/tex]Which means that the answer is the second option.
Meals in a hospital cafeteria are discounted 15% for all hospital employees what will an employee pay for the grilled chicken lunch which cost a non employee $8.00
Given that the meals in a hospital cafeteria are discounted 15% for all hospital employees,
The price an employee will pay for the grill chicken lunch worth of $8.00 will be,
[tex]\text{ \$8.00}-(15\text{ \% of \$8.00)}[/tex][tex]\begin{gathered} \text{ \$8.00-(}\frac{\text{15}}{100}\times\text{ \$8.00)} \\ \text{ \$8.00-(0.15}\times\text{ \$8.00)}=\text{\$8.00- \$1.2=\$6.8} \end{gathered}[/tex]Hence, the hospital employee will pay $6.8 for the grilled chicken lunch.
2,361÷59
What is the answer with a remainder
Answer:
40 R 1.
Step-by-step explanation:
Graph the solution set of the second linear any quality
Solution
- The inequality is:
[tex]7y\ge6x+21[/tex]- The graph of the inequality is graphed using a graphing calculator as follows:
To analyze the variation of vitamin supplement tablets, you randomly select and weigh 14 tablets. The results are shown below: 500.000 499.995 500.010 499.997 500.015 499.988 500.000 499.996 500.020 500.002 499.998 499.996 500.003 500.000 a. Assume this sample is taken from a normally distributed population. Construct a 90% level of confidence for the population variance and population standard deviation. b. For quality control, the population standard deviation of the tablets weights should be less than 0.015 milligrams. Does the confidence interval you constructed for the population standard deviation suggest that it is at an acceptable level? Explain your reasoning.
Answer:
a.
[tex]\begin{gathered} 0.000041\leq\sigma^2\leq0.00015 \\ 0.0064\leq\sigma\leq0.0125 \end{gathered}[/tex]b. The standard deviation is at an acceptable level
Explanation:
The confidence interval for the variance can be calculated as:
[tex]\frac{(n-1)s^2}{\chi^2_{\frac{\propto}{2}}}\leq\sigma^2\leq\frac{(n-1)s^2}{\chi^2_{1-\frac{\propto}{2}}}[/tex]Where n is the size of the sample, s² is the variance of the sample, (1-∝) is the level of confidence, and χ² is the value of chi-square with n-1 degrees of freedom.
In this case, we get that n is 14 tablets, s² is 0.000071, and 1-∝ = 90%, so ∝ is 10%.
Then, the values of chi-square with 13 (14 -1) degrees of freedom is:
[tex]\begin{gathered} \chi^2_{\frac{\propto}{2}}=22.36 \\ \chi^2_{1-\frac{\propto}{2}}=5.89 \end{gathered}[/tex]Therefore, the interval of confidence for the population variance is:
[tex]\begin{gathered} \frac{(14-1)(0.000071)}{22.36}\leq\sigma^2\leq\frac{(14-1)(0.000071)}{5.89} \\ 0.000041\leq\sigma^2\leq0.00015 \end{gathered}[/tex]Then, the standard deviation is the square root of the variance, so the interval of confidence for the population standard deviation is:
[tex]\begin{gathered} \sqrt[]{0.000041}\leq\sigma\leq\sqrt[]{0.00015} \\ 0.0064\leq\sigma\leq0.0125 \end{gathered}[/tex]Finally, since the upper limit of the interval for the standard deviation is less than 0.15 milligrams, we can say that the population standard deviation is at an acceptable level with a confidence level of 90%
if 5% more than A is B, and B is 15% less than C, what is the ratio of A to C?
For the given condition when B is 5% more than A and B is 15% less than C then ratio of A to C is equal to 17 : 21.
As given in the question,
Let value of A is equal to 100
As per given condition we have,
B is 5% more than A
5% of 100
= (5/100) × 100
= 5
So B is equal to
= 100 +5
= 105
A:B = 100/105
= 20/21
B is 15% less than C
let C= 100
15 % of 100
= (15/100) × 100
= 15
Value of B is equal to
= 100 - 15
= 85
B:C = 85 : 100
= 17 : 20
Ratio A : B : C
= 340 : 357 : 420
Ratio A : C = 340 : 420
= 17 :21
Therefore, for the given condition when B is 5% more than A and B is 15% less than C then ratio of A to C is equal to 17 : 21.
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the amount of water a washing machine uses varies directly with the number of loads of laundry washed. if a machine uses 65 gallons of water to wash 5 loads, how much water will be used to was 8 loads?
Let g represent gallons of water and let L represent loads.
Here, the gallons of water varies directly with the number of loads, thus we have:
g ∝ L
Now introduce a constant k:
g = kL
65 gallons is used to wash 5 loads, thus we have:
65 = k * 5
Let's solve for k:
65 = 5k
Divide both sides by 5:
[tex]\begin{gathered} \frac{65}{5}=\frac{5k}{5} \\ \\ 13=k \end{gathered}[/tex]To find the amount of water that will be used to wash 8 loads, we have:
g = kl
We are to find g, substitute 13 for k and 8 for l:
g = 13 x 8
g = 104
Therefore, to wash 8 loads, 104 gallons of water is needed.
ANSWER:
104
Round 21.897 to the nearest hundredth. Underestimate
Answer:
21.9
Step-by-step explanation:
it rounds up
-45g – 9g
Factor the algebraic expression
Answer:
-54g or -9g(5+1)
Step-by-step explanation:
-45g - 9g
-9g(5+1)
I'm not sure which form you want it in lol. -9g(6)
:]
Answer:
-9g ( 5 + 1 )
Step-by-step explanation:
-45g - 9g
-(45g - 9g)
common factor or less number = 9
-9g (5 + 1)
I SEEN HELP ASAP. are these following triangles similar? Yes or no and explain
Given data:
The given length of the EC is CD=9.
The given length of the CD is CD=10.
The given length of TV is TV=27.
The given length of TU is TU=30.
The ratio of the corresponding sides is,
[tex]\frac{EC}{CD}=\frac{TV}{TU}[/tex]Susbtitute the given values in the above expression.
[tex]\begin{gathered} \frac{9}{10}=\frac{27}{30} \\ =\frac{9}{10} \end{gathered}[/tex]Thus, the ratio of the corresponding sides is equal so they are similar.
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y < 2x - 5 y ≤ -x - 2
First, we need to graph the lines:
[tex]\begin{gathered} y=2x-5\text{ (slope = 2 and y-intercept = -5)} \\ y=-x-2\text{ (slope = -1 and y-intercept = -2)} \end{gathered}[/tex]In the solution of the first inequality, the points on the line are not included, then this line must be dashed. On the other hand, in the solution of the second inequality, the points on the line are included, then this line must be solid.
In both cases, the solution to each inequality is the area below each line.
Combining this information we get the next graph:
where the solution is the orange area.
From the above graph, one point in the solution set is (1, -7). We can check if this point is part of the solution by replacing it into the inequalities, as follows:
[tex]\begin{gathered} -7<2(1)-5 \\ -7<-3\text{ (True)} \\ \text{And} \\ -7\le-1-2 \\ -7\le-3\text{ (True)} \end{gathered}[/tex]Given that the point satisfies both inequalities, then it is part of the solution set.
Task 3: Solve the following quadratic equation by extracting the square root.
Given -
(2s - 1)² = 225
To Find -
s =?
Step-by-Step Explanation -
(2s - 1)² = 225
Now, on removing square =
(2s - 1) = √225
2s - 1 = 15
2s = 15 + 1
2s = 16
s = 16/2
s = 8
Final Answer -
s = 8
simplifylog(z) - log(18)
You have the following expression:
log(z) - log(18)
By the properties of logarithms, consider that the subtraction of two logarithms is equal to the logarithm of the quotient of the arguments:
log(z) - log(18) = log(z/18)
Hence, the answer is log(z/18)
A student bank balance at the beginning of month was $843 during the month she deposits $92’ $404’ $39 and $51 also she made withdrawal of $70 $87 and $221 what was the student’s balance at end of month?
The account balance at the end of the month is $1051.
How is the balance estimated in a bank account?To estimate the balance in a bank account, one has to add the credit to the available balance of the account and subtract the debited amount from the same.
It is given that the account balance initially is $843.
The deposited balances are $92, $404, $39 and $51.
Add the credited amount to the account balance.
So, the current amount is = $843+ $92+ $404+ $39+ $51= $1429
The withdrawal amount is $70, $87 and $221
Subtract the debited amount to the account balance.
So, the current amount is = $1429 - $70 -$87 - $221 = $1051.
So, the account balance at the end of the month is $1051.
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What is this answer 467 x 48=
Long Multiplication
1. Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand.
This will be written as follows:
467
x 48
---------------
2. Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number.
This product is 8*7 = 56
3. If that answer is greater than nine, write the ones place as the answer and carry the tens digit.
We should write 6 and carry 5:
467
x 48
---------------
6 (carry 5)
4. Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so.
The next product is 8*6 = 48. Adding the carry: 48+5=53, Write 3, carry 5:
467
x 48
---------------
36 (carry 5)
Multiply 8*4 = 32. Add the carry 5: 32+5 = 37. Write the full number because it's the last of the products of this step:
467
x 48
---------------
3736
5. When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.
Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.
Multiply 4*7 = 28. Write 8, carry 2.
467
x 48
---------------
3736
8 (carry 2)
Multiply 4*6=24. Add 2: 24+2=26. Write 6, carry 2:
467
x 48
---------------
3736
68 (carry 2)
Multiply 4*4=16. Add 2: 16+2=18. Write the full number:
467
x 48
---------------
3736
1868
6. When you finish multiplying, draw another answer line below your last row of answer numbers.
467
x 48
---------------
3736
1868
----------------
7. Use long addition to add your number columns from right to left, carrying as you normally do for long addition.
467
x 48
---------------
3736
1868
----------------
22416
The graph below represents the number of siblings each student in a class has.
Given;
There are given that the graph represents the number of siblings.
Explanation:
According to the given graph:
The frequency of the number of siblings is:
[tex]6,7,4,4,3,2[/tex]Now,
We need to find the value of the range:
So,
From the concept of range:
The value of the difference between the highest data and lowest data will be representing the value of the range:
So,
The highest number is 7 and the lowest data is 2:
So,
[tex]\begin{gathered} Range=7-2 \\ =5 \end{gathered}[/tex]Final answer:
Hence, the value of the range is 5.
Assume a normal distribution and that the average phone call in a certain town lasted 9 minutes, with a standard deviation of 2 minutes. What percentage of the calls lasted less than 5 minutes?
Given the sample mean of the distribution as 9 minutes.
Also, the sample deviation as 2 minutes;
Given the z-score formula;
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where;
[tex]x=5,\text{ }\mu=9\text{ and }\sigma=2[/tex][tex]\begin{gathered} z=\frac{5-9}{2} \\ z=-\frac{4}{2} \\ z=-2 \end{gathered}[/tex]Now, from the Z-table;
[tex]P(x<-2)=0.02275[/tex]Thus, the percentage of the calls lasted less than 5 minutes is 2.3%
describe the transformation from f to g where f(x)=x² and g(x)=(1/3)x²
describe the transformation from f to g where f(x)=x² and g(x)=(1/3)x²
In this problem we have a dilation of the y-coordinate
so
the rule is
(x,y) -------> (x,ay)
where
the scale factor a=1/3
Describe a series of transformations Matt can perform to device if the two windows are congruent
Congruent shapes are produced when the three transformations—rotations, reflections, and translations—are combined. Any pair of congruent shapes can actually be matched to one another by combining one or more of these three transformations.
Definition of transformationsAn object's shape and/or location can vary in each of the four possible transformations of a point, line, or geometric figure. Pre-Image refers to the shape of the object before transformation, whereas Image refers to the location and shape of the object after transformation.
Data Presented
We now understand that stiff transformations preserve the size and shape of the figures (reflections, translations, and rotations). The pre-image and the actual image always concur.
The following transformational skills belong to Matt:
Reflection
A reflection maintains its initial form because the Comparable locations from the pre-image to the picture remain at the same distance from the line of reflection.
Rotations as a Congruence Transformation
A rotating figure twists. Despite being the same size and shape as before, the figure appears to have toppled over. A clock is an excellent example of how the globe actually rotates. Every hour or every day, a clock's connecting arms revolve around its axis. The degree of a rotation determines what kind of rotation it is; popular rotations include those of 90, 180, and 270 degrees. Before going back to its original position, the figure rotates a full 360 degrees. the clockwise or counterclockwise direction in which a revolution happens. This data can be used to determine the degree, amount, and a revolution's speed and direction.
Congruence translational transformation
When an object or shape is transferred from one location to another without altering its size, shape, or orientation, we refer to the transfer as a movement. A translation, often known as a slide, involves moving every point on an object or shape uniformly and in one direction.
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how do I find the correct answer? ( the top says "Triangles ABC and DEF are right triangles, as shown, ABC is similar DEF.)
The cosine relation is defined by the length of the adjacent side over the length of the hypotenuse.
So, for triangle ABC, the cosine of B is defined as:
[tex]\cos (B)=\frac{BC}{AB}[/tex]And for triangle DEF, since the triangles are similar, the cosine of B is equal the cosine of its corresponding angle E:
[tex]\cos (E)=\frac{EF}{DE}[/tex]So the correct options are the first and fifth ones.
Write each trinomial in factored form (as the product of two binomials) by showing the steps used to factor.
You have the following trinomial given in the exercise:
[tex]p^2-8p+7[/tex]Notice that is is a trinomial because it is a polynomial that has three terms.
In order to factor it (as the product ot two binomials) you can find two numbers whose sum is -8 and whose sum is 7. These numbers would be -1 and -7, because:
[tex]\begin{gathered} -1-7=-8 \\ \\ \\ (-1)(-7)=7 \end{gathered}[/tex]Then, you can factor it
[tex](p-1)(p-7)[/tex]The answer is:
[tex](p-1)(p-7)[/tex]When using a counterexample to prove a conditional statement false, which must be true about the counterexample?
There must be infinite counterexamples.
The counterexample must satisfy the hypothesis of the conditional statement.
There must be at least one example under which the conditional statement is true.
The counterexample must satisfy the conclusion of the conditional statement.
The counterexample must satisfy the hypothesis of the conditional statement which is the correct answer would be option (B).
What is a Counterexample?A counterexample is an example in which the hypothesis is correct but the conclusion is incorrect.
Since A counterexample is used to show that a conditional assertion is untrue.
So, just one counterexample is required to prove a statement untrue.
Also, when employing a counterexample to prove a conditional assertion untrue.
The counterexample must then meet the hypothesis of the conditional statement.
As a result, the correct statement concerning the counterexample is;
The conditional statement's hypothesis must be satisfied by the counterexample.
Hence, the correct answer would be option (B).
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Solve the system. Tell how many solutions the system has.-2x + 6y = 8x-3y=-3solution(s).The system has (select)(select)onenoinfinitely many
We have
-2x + 6y = 8 ...(1)
x-3y=-3 ....(2)
we need to solve the system of equations
we will multiplicate the second equation by 2
[tex]2x-6y=-6[/tex]then we sum the equation above with the first equation
[tex]-2x+2x+6y-6y=8-6[/tex]we sum similar terms, and we obtain
[tex]0=2[/tex]that's an inconsistency
so we don't have a solution
the answer is no
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]