The equation of smallest degree with integer coefficients will be f(x) = x^2 - (3 + √7)x + 3√7
How to explain the equationIt should be noted that to begin, let us establish the following:
x = √(8 - 1) which is equal to √7.
y = √(8 + 1) which is equivalent to √9. Therefore, y equals 3.
For the value of x, its conjugate coincides with √7; hence:
(x - x') × (x - y') = (x - √7)(x - 3)
Equation expansion yields:
f(x) = x^2 - (3 + √7)x + 3√7
By substituting for both values x and y in the equation above, we can show that f(x) satisfies the given specifications:
When x takes on a value of √7:
f(√7) = (√7)^2 - (3 + √7)√7 + 3√7 = 7 - 7 = 0
With an input value of 3:
f(3) = 3^2 - (3 + √7)(3) + 3√7 = 9 - 9 - 3√7 + 3√7 = 0
The lowest degree polynomial with rational coefficients having √(8 - 1) and √(8 + 1) as its roots is: f(x) = x^2 - (3 + √7)x + 3√7
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witch values are solutions to the inequlity [tex]x^{2} \leq 8[/tex]
Answer:
x ≤ [tex]\sqrt[2]{2}[/tex]
Step-by-step explanation:
x² ≤ 8
[tex]\sqrt{x^{2} }[/tex] ≤ [tex]\sqrt{8}[/tex]
x ≤ [tex]\sqrt[2]{2}[/tex]
Can someone help me pleasee
Answer:
The answer is 50% or 1/2
Step-by-step explanation:
There are four outcomes on that chart: 1,2,3,3
There are two threes which means 2/4=.5 or 1/2
Answer:
1/2 chance of landing on a 3.
Step-by-step explanation:
Out of the 4 sections on the spinner, 2 of them have the number 3. This means that there is a 2/4 chance that the spinner lands on a three. This fraction can be simplified into 1/2.
3 subtracted from quarter of g is 6
Answer: G=36
Step-by-step explanation:
Step 1: Write out the equation
1/4g-3=6
Step 2: Add 3 to both sides
1/4g=9
Step 3: Divide both sides by 1/4, or 0.25
G=36
Complete the sentences to compare the intervals for which each function is decreasing
The intervals for which each function is decreasing are f(x) = [0, ∝) and g(x) = (-∝, ∝)
Completing the sentences to compare the intervalsFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
From the graph of the functions, we can see that
The function g(x) decreases all through because it is a linear function with a negative slopeThe function f(x) decreases at [0, ∝) because it a quadratic function with a maximum vertex at (0, 5)Read more about functions at
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In the data set below, what is the upper quartile?
24 28
28 47 53 55 58 78 79
Submit
Answer:
68
Step-by-step explanation:
the median is the term in the middle (53) the upper quartile is the median of the terms above the median. Since there are an even number of terms, you need to average them (58+78)/2
what 7 coins make 82 cents
Answer:
1 quarter, 2 dimes, 1 nickel, and 3 pennies can be used to make 82 cents.
Step-by-step explanation:
One possible set of 7 coins that make 82 cents is:
1 quarter (25 cents)
2 dimes (10 cents each)
1 nickel (5 cents)
3 pennies (1 cent each)
Adding up the values of these coins:
25 + 10 + 10 + 5 + 1 + 1 + 1 = 82
Therefore, a set of 1 quarter, 2 dimes, 1 nickel, and 3 pennies can be used to make 82 cents.
What is the solution to this system?
(1, 0)
(1, 6)
(8, 26)
(8, –22)
Find the dot product for the pair of vectors
The result of -3u + 5v is the vector (12, -34).
Let's start by defining the two given vectors u and v:
u = (1, 3)
v = (3, -5)
To find the dot product of two vectors, we need to multiply their corresponding components and then add up the results. The formula for the dot product of two vectors can be written as:
u · v = u₁v₁ + u₂v₂ + ... + uₙvₙ
where u₁ and v₁ are the first components of vectors u and v, u₂ and v₂ are the second components, and so on up to un and vₙ, which are the nth components.
Using this formula, we can find the dot product of u and v as follows:
u · v = (1)(3) + (3)(-5)
= 3 - 15
= -12
So, the dot product of vectors u and v is -12.
Next, we need to calculate -3u + 5v. To do this, we need to multiply each component of vector u by -3 and add it to the corresponding component of vector v multiplied by 5. We can write this as follows:
-3u + 5v = (-3)(u₁, u₂) + (5)(v₁, v₂)
= (-3)(1, 3) + (5)(3, -5)
= (-3, -9) + (15, -25)
= (12, -34)
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How many ways to paint a house with 3 different colors from a pool of 12 distinct colors
PLEASE HURRY!!!!
The height h in feet of an object shot straight up with initial velocity v in feet per second is given by h = −16t^2 + vt + c, where c is the initial height of the object above the ground. A model rocket is shot vertically up from a height of 6 feet above the ground with an initial velocity of 22 feet per second. Will it reach a height of 10 feet? Identify the correct explanation for your answer.
A. No; The discriminant is positive so the rocket will reach a height of 10 feet.
B.Yes; The discriminant is positive, so the rocket will reach a height of 10 feet.
C.No; The discriminant is negative, so the rocket will not reach a height of 10 feet.
D.Yes; The discriminant is zero, so the rocket will reach a height of 10 feet.
Answer:
B.
Step-by-step explanation:
We can use the given formula to find the time it takes for the rocket to reach a height of 10 feet:
10 = -16t^2 + 22t + 6
Rewriting the equation in standard quadratic form:
16t^2 - 22t + 4 = 0
Using the quadratic formula:
t = (22 ± sqrt(22^2 - 4(16)(4)))/(2(16))
t = (22 ± sqrt(36))/32
t = 3/4 or 1/4
Since the rocket reaches a height of 10 feet at two different times (3/4 and 1/4 seconds), it must pass through that height twice during its flight. Therefore, the rocket will reach a height of 10 feet. The correct answer is B.
The growth of a colony of bacteria is modeled by the function below, where t is the
is time in hours after the culture is begun and f(t) is the number of bacteria present.
After how many hours will there be 2000 bacteria in the colony? Round your answer
to the nearest hundredth (two decimal places).
f(t) = 500e^0.195t
namely, what is "t" when f(t) = 2000
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(t)}{2000}=500e^{0.195t}\implies \cfrac{2000}{500}=e^{0.195t}\implies 4=e^{0.195t} \\\\\\ \log_e(4)=\log_e\left( e^{0.195t}\right)\implies \log_e(4)=0.195t\implies \ln(4)=0.195t \\\\\\ \cfrac{\ln(4)}{0.195}=t\implies 7.11\approx t[/tex]
complete the table on the relation
Given u = 4i - 7j and v = -6i + 9j, what is u • v?
-87
-82
26
39
The letters of "EAGLES" should be evenly spaced across a 63 inch wide banner, with no margins. Each letter is 8 inches wide. How many inches (x) should exist between each pair of letter?
Answer:
1 inch
Step-by-step explanation:
A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 13. Find the numbers. (If applicable, write your answers in the form p±q√r)
Triangle ABC
A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?
Answer:
19cm
Step-by-step explanation:
I think it's 19cm as sides BC on the green triangle measure 15cm, and EF is 25cm on the blue triangle. It also mentions that they are similar, meaning that ∆ DEF is just a translated and enlarged version of ∆ ABC
25 - 15 = 10cm
9 + 10 = 19cm
Hope this helped :)
How do you find Exponential Decay Rate?
1+b
1-b
Answer:
Exponential decay is represented by the equation:
y = a * e^(-bx)
where:
y is the final value
a is the initial value
b is the decay rate
x is the time variable
The exponential decay rate, b, can be found by taking the natural logarithm (ln) of both sides of the equation, then rearranging to isolate the decay rate:
ln(y/a) = -bx
b = -ln(y/a)/x
So, to find the exponential decay rate, you would need to know the initial value (a), the final value (y), and the time elapsed (x). Then, you can use the formula above to calculate the decay rate, b.
The expressions "1+b" and "1-b" are not sufficient to find the exponential decay rate, as they do not contain enough information about the specific scenario or data set.
if this helps, can you please mark my answer brainliest?
Paola has enough mulch to cover 48 square feet. She wants to use it to make three square vegetable gardens of equal sizes. Solve the equation 3s2 = 48 to find s, the length of each garden side (in feet).
The length of each garden side is 4 ft.
Given that, Paola has 48 ft² of mulch, she wants to make three square vegetable gardens of equal sizes, we need to find the length of each garden side.
Let s be the length of the side of the gardens,
Since, she need 3 gardens,
So,
3 × side² = 48
3s² = 48
s² = 16
s = 4
Hence, the length of each garden side is 4 ft.
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Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex] units. What is a simplified expression for the difference in the areas of Circle A and Circle B
The simplified expression for the difference in the areas of Circle A and Circle B is = 12π/(x+2)²
Area of a Circle:The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is [tex]A = \pi r^2[/tex], where r is the radius of the circle. The unit of area is the square unit, for example, [tex]m^2, cm^2, in^2[/tex], etc.
We know that :
The formula of circle's circumference is = 2πr
We have :
Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units
and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex]
Now, First we calculate the area of circle A is:
8π/x+2 = 2πr
r = 8π/x+2 × 1/2π
r = 4/x+2
Area = πr² = (4/x+2)²π
Now, for circle B
4π/x+2 = 2πr
r = 4π/x+2 × 1/2π
r = 2/2x+2
Area =( 2/2x+2)²π
Simplified expression for the difference in the areas of Circle A and Circle B are:
(4/x+2)²π - ( 2/x+2)²π
= π/(x+2)²( 4²-2²)
= π/(x+2)²(16-4)
= 12π/(x+2)²
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In a choir, the number of girls is twice the number of bovs. The avera height of the boys is 150 cm and the average height of the girls is 159 cm
What is the average height of all the choir members?
Answer:
Step-by-step explanation: mark me brainliest
Determine if the statement is true or false.
Angle AEC and DEB are complementary angles and therefore add up to 180 degrees.
1. True
2. False
The statement "Angle ∠AEC and ∠DEB are complementary angles" is false.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Angle ∠AEC and ∠DEB are supplementary angles because the sum is 180 degrees.
Thus, the given statement is false.
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Determine which of the following statements is true concerning the values described in column #1 and column #2. (1 point)
Column #1
Column #2
The x-coordinate of the vertex of the graph of The x-coordinate of the vertex of the graph of
y=-2x² - 4x + 12
y=x²-4x+3
O The value found in column #1 is greater than the value found in column #2.
The value found in column #1 is less than the value found in column #2.
O The value found in column #1 is equivalent to the value found in column #2.
The relationship between column #1 and column #2 cannot be determined by the information given.
8
The statement which is true concerning the values described in column #1 and column #2 is: B. The value found in column #1 is less than the value found in column #2.
How to determine the x-coordinate of the vertex of the graph?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = -2x² - 4x + 12, we have:
Axis of symmetry, Xmax = -(-4)/2(-2)
Axis of symmetry, Xmax = 4/-4 = -1.
For the vertex of f(x) = -2x² - 4x + 12, we have:
f(-1) = -2(-1)² - 4(-1) + 12 = 14.
For the given quadratic function f(x) = x²-4x+3, we have:
Axis of symmetry, Xmax = -(-4)/2(1)
Axis of symmetry, Xmax = 4/2 = 2.
For the vertex of f(x) = x²-4x+3, we have:
f(2) = (2)²-4(2) +3 = -1.
Therefore, 2 is greater than -1.
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Problem 5:
Find the missing side using
trigonometry:
52
18 H
AWO
Drag&Drop the correct trig function:
Cos
Tan
Rati
Circle which shortcut you use.
Multiply
Round your answer to the nearest tenth:
Give Feedback to Micrones
Sin
%
or
IN
Divide
Ans
Ans
The missing length is 11.0818 unit.
We have,
Angle = 52 degree
H = 18
Using Trigonometry
cos 52 = B/H
cos 52 = x / 18
0.615661 = x /18
x = 11.0818 unit
Thus, the missing length is 11.0818 unit.
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26=-9w-2w-18?????????????????
Answer:
w = -4
Step-by-step explanation:
Hope this helps
Sophia wishes to retire at age 65
with $1,600,000
in her retirement account. When she turns 28
, she decides to begin depositing money into an account with an APR of 9%
compounded monthly. What is the monthly deposit that Sophia must make in order to reach her goal? Round your answer to the nearest cent, if necessary
Answer:
To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:
FV = P * ((1 + r/n)^(nt) - 1) / (r/n)
where:
FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)
P = monthly deposit
r = annual interest rate (which is 9%)
n = number of times interest is compounded per year (which is 12 for monthly compounding)
t = number of years until retirement (which is 65 - 28 = 37)
Substituting the given values, we get:
1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)
Simplifying and solving for P, we get:
P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)
P ≈ $524.79
Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.
Step-by-step explanation:
Val's whole-house central air conditioner uses 4,000 watts when running. Val runs the AC 7 hours per summer day. Electricity costs (10 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
The electricity cost for the Val's AC to run for a summer month of 30 days is $84.
Given that,
Val's whole-house central air conditioner uses 4,000 watts when running.
Val runs the AC 7 hours per summer day.
Electricity costs (10 cents)/(1 kilowatt-hour).
Total electricity used for the whole house = 4000 watts = 4 kilowatts
Number of hours that the AC runs = 7 hours
Cost of electricity = (10 cents)/(1 kilowatt-hour).
Cost of electricity for 4 kilowatts for 1 hour = 10 × 4 = 40 cents
Cost of electricity for 4 kilowatts for 7 hours = 40 × 7 = 280 cents
= $2.80
Cost of electricity for a summer month of 30 days = $2.80 × 30
= $84
Hence the total cost for the electricity is $84.
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perimeter of a tabe is 228 inches and the length is 18 inches which is more than twice the width. How do I find the length and width of the worktable
The width of the worktable is 32 inches, and the length of the worktable is 82 inches.
Let's assume that the width of the worktable is "w" inches.
We are given that the length is 18 inches more than twice the width, which can be expressed as:
Length = 2w + 18
The perimeter of the worktable is the sum of the lengths of all four sides.
We know that the perimeter of the worktable is 228 inches, so we can write an equation:
Perimeter = 2 × (Length + Width)
228 = 2 × (2w + 18 + w)
228 = 2 × (3w + 18)
Dividing both sides by 2:
114 = 3w + 18
Subtracting 18 from both sides:
96 = 3w
Dividing both sides by 3:
w = 32
So, the width of the worktable is 32 inches.
Now we can use this value to find the length:
Length = 2w + 18
Length = 2 × 32 + 18
Length = 82
So, the length of the worktable is 82 inches.
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :)
Step-by-step explanation:
5 (4x^8) ^(-1/2) - 2 x^-3
p ^(1/2)
r ^5/3
In the figure to the right, you are given a square ABCD. Each of its sides is divided into two segments, such that AE = BF = CG = DH. Prove that quadrilateral EFGH is a square.
First to answer gets brainliest
Answer:proving that EFGH is a square: points E,F,G,H
separate the sides of the square ABCD into two lines. if AE=BF=CG=DH then
AH=DG=EB=FC and it shows that if we connect the points E,F,G,H to each other with line we will have a square
HAE~EBF~FCG
A geography teacher assigns each student to write a report about one of the first 13 colonies. Students select the name of a colony by "blindly" drawing a colony's name from a bag. Once a colony has been drawn, it is not replaced.
What is the probability that the first student selects Pennsylvania and the second student selects Virginia? Round your answer to the nearest hundredth of a percent.
The probability that the first student selects Pennsylvania and the second student selects Virginia to the nearest hundredth of a percent is 0.64%.
Probability problemThe probability that the first student selects Pennsylvania is 1/13. Once Pennsylvania has been drawn, there are only 12 colonies left in the bag, so the probability that the second student selects Virginia is 1/12.
To find the probability that both events occur, we multiply the probabilities:
(1/13) x (1/12) = 1/156
To express this probability as a percentage, we multiply by 100:
(1/156) x 100 ≈ 0.64%
Therefore, the probability that the first student selects Pennsylvania and the second student selects Virginia is approximately 0.64%.
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