The quadratic equation with roots 5 + i√2 and 5 - i√2 is:
x^2 - 10x + 27 = 0
To write a quadratic equation with roots 5 + i√2 and 5 - i√2, we can use the fact that complex roots occur in conjugate pairs. Therefore, the equation will have the form:
(x - root1)(x - root2) = 0
Substituting the given roots:
(x - (5 + i√2))(x - (5 - i√2)) = 0
Now, we expand the equation:
(x - 5 - i√2)(x - 5 + i√2) = 0
Using the difference of squares formula:
((x - 5)^2 - (i√2)^2) = 0
Simplifying the equation:
(x - 5)^2 + 2 = 0
Expanding the square:
x^2 - 10x + 25 + 2 = 0
Combining like terms:
x^2 - 10x + 27 = 0
Therefore, the quadratic equation with roots 5 + i√2 and 5 - i√2 is:
x^2 - 10x + 27 = 0
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variable of 10(n+3)=1,000,00
Answer: Distribute the 10 on the left side of the equation:
10n + 30 = 1,000,000
Subtract 30 from both sides of the equation to isolate the term with n:
10n = 1,000,000 - 30
10n = 999,970
Divide both sides of the equation by 10 to solve for n:
n = 999,970 / 10
n = 99,997
Therefore, the value of the variable n that satisfies the equation 10(n + 3) = 1,000,000 is n = 99,997.
Step-by-step explanation:
What is B^2+8b+7??
Can someone explain it step by step please?
Step-by-step explanation:
B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).
To factor a quadratic expression, you can use the following steps:
1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).
2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.
In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:
(b+7)(b+1)
This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).
Here is a step-by-step explanation of how to factor B^2+8b+7:
1. The coefficient of the middle term is 8.
2. The constant term is 7.
3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.
4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).
a pyramid and a cone are both 10 centimeters tall and have the same volume what statement
Answer: "The pyramid and the cone have the same volume despite their different shapes."
Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:
"The pyramid and the cone have the same volume despite their different shapes."
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Graph the equation shown below by transforming the given graph of the parent
function.
Answer:
Step-by-step explanation:
it is only moving 3 to the right, so shift the green dot to (3,0)
I used desmos . com for the graph
Multiply the following binomials (2x - 3y)(8x - y)
Answer:
16x + [tex]3y^{2}[/tex] - 26xy
Step-by-step explanation:
PEMDAS
(2x - 3y)(8x - y)
= 16x - 2xy - 24xy + [tex]3y^{2}[/tex]
= 16x + [tex]3y^{2}[/tex] - 26xy
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Angle C of the triangle measures 68°.
Side AC = 22.90
Side BC = 14.26
Given triangle,
∠A = 37°
∠B = 75°
AB = 22
Now,
Sum of all the interior angles of triangle is 180.
So,
∠A + ∠B +∠C = 180°
37° + 75° + ∠C = 180°
∠C = 68°
Now,
According to sine rule,
Ratio of side length to the sine of the opposite angle is equal.
Thus,
a/SinA = b/SinB = c/SinC
Let,
BC = a
AC = b
AB = c
So,
a/Sin37 = b/Sin75 = c/Sin68
a/0.601 = b/0.965 = 22/0.927
Solving,
BC = a = 14.26
AC = b = 22.90
Thus with the properties of triangle side length and angles can be calculated.
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Ochenta y nueve en número romano ??
Answer:
LXXXIX
Step-by-step explanation:
ochenta y nueve es 89.
89 en numero romano es LXXXIX.
Change 0.12 to a ratio.
Answer:
3:25
Step-by-step explanation:
The photo shows how it's solved.
Answer: 3:25
Step-by-step explanation:
Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator
0.12 = 0.12/1
Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100
------------ = 12/100
1 x 100
Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)
12 ÷ 4
--------- = 3/25
100 ÷ 4
Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:
3
25 = 3:25
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
B. 108 ft³
Step-by-step explanation:
solution given:
We have Volume of solid = Area of base * length
over here
base : 9ft
height : 6 ft
length : 4ft
Now
Area of base : Area of traingle:½*base*height=½*9*6=27 ft²
Now
Volume : Area of base*length
Volume: 27ft²*4ft
Therefore Volume of the solid=108 ft³
Descrive in words the rule that is used to determine the term value from its position in the sequence
The rule used to determine the term value from its position in the sequence is often referred to as the "nth term" rule.
What is the nth-term rule?The nth-term rule involves identifying a pattern or relationship between the position (n) of a term in the sequence and the value of that term.
By analyzing the pattern, such as the common difference or common ratio, the nth-term rule allows us to express the value of any term in the sequence based on its position.
This rule provides a formula or equation that relates the position of a term to its corresponding value in the sequence.
Mathematically, the rule is:
T(n) = a + (n - 1) * d
where:
T(n) represents the value of the term at position n.a represents the first term in the sequence.n represents the position or index of the term in the sequence.d represents the common difference (for arithmetic sequences) or the common ratio (for geometric sequences) between consecutive terms.More on sequence and series can be found here: https://brainly.com/question/15583579
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geometry worksheet find the measure of the arc or angle indicated
The value of the measure of the arc or angle indicated are,
⇒ m ∠DCE = 54°
⇒ m ∠MON = 53°
Now, We can simplify as,
4) As shown in figure,
m arc DE = 360° - (121° + 131°)
m arc DE = 360° - 252°
m arc DE = 108°
So, We get;
⇒ m ∠DCE = m DE / 2
⇒ m ∠DCE = 108 / 2
⇒ m ∠DCE = 54°
4) As shown in figure,
m arc MN = 360° - (109° + 145°)
m arc MN = 360° - 254°
m arc MN = 106°
So, We get;
⇒ m ∠MON = m MN / 2
⇒ m ∠MON = 106 / 2
⇒ m ∠MON = 53°
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100 Points! Geometry question. Photo attached. Use the Pythagorean Theorem to find x. Please show as much work as possible. Thank you!
The value of x is,
⇒ x = 21.65
We have to given that,
A right triangle is shown in image.
Since, The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Hence, We get;
⇒ 25² = 12.5² + x²
⇒ 625 = 156.25 + x²
⇒ x² = 625 - 156.25
⇒ x² = 468.75
⇒ x = 21.65
Thus, The value of x is,
⇒ x = 21.65
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A truck travels from warehouse A at (–4,8) to warehouse B at (–4,–1). If each unit represents 20 miles per hour, how long will it take the truck to travel this distance?
It will take the truck 9 hours to travel from warehouse A to warehouse B.
To determine the time it takes for the truck to travel from warehouse A at (-4, 8) to warehouse B at (-4, -1), we need to calculate the distance between these two points and then convert it to time using the given unit of 20 miles per hour.
First, let's find the vertical distance between the two points. The y-coordinate of warehouse A is 8, and the y-coordinate of warehouse B is -1. So the vertical distance is 8 - (-1) = 9 units.
Next, we convert the vertical distance to miles. Since each unit represents 20 miles per hour, we multiply the vertical distance by 20: 9 units × 20 miles/unit = 180 miles.
Now, we can calculate the time it takes to travel this distance. We divide the distance by the speed of the truck, which is 20 miles per hour: 180 miles / 20 miles per hour = 9 hours.
Therefore, it will take the truck 9 hours to travel from warehouse A to warehouse B.
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(02.02 MC)
If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′′′ lie?
Trapezoid formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at 0, 1.
(1, −1)
(−4, 1)
(1, 1)
(−4, −1)
The location of point A''' after the three transformations would be (-4, 1).
To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.
When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.
So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).
When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).
When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).
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Multiplying polynomials 4n2(n2 + 5n - 8)
Answer:
4n^4 + 20n^3 - 32n^2
Step-by-step explanation:
We have to distribute 4n2 to each term.
4n2 x n2. We can multiply the two n2 together resulting in 4n^4.
Now we do 4n2 x 5n. Here we multiply 4 x 5 which equals 20. Then, we multiply the n2 and n. Which results in n^3. Now we put them together; 20n^3.
Finally, we multiply 4n2 by -8. Since 8 doesn't have any variables, we just multiply the 4 and -8. Which equals to -32, now we just combine -32 and the variable; -32n2.
Now we combine these terms together. Our final answer is, 4n^4 + 20n^3 -32n^2.
^ represents an exponent.
find the quotient of 5/31 divided by 15/23 . reduce your answer to the lowest fraction
4
(1 pa
10. The table shows the results from home games for a specific team during the season leading up
to the World Series. The team's home field has a roof that can be closed for weather. If it is
closed, the fans could make more noise for the home team and possibly give them an
advantage. Find the test statistic needed to test independence for the contingency table.
Closed roof
Open roof
034.215
00.093
00.798
03.841
Win
36
15
Loss
17
11
The test statistic χ² is approximately 1.47.
We have,
To test independence for the contingency table, we need to calculate the test statistic.
The most commonly used test statistic for testing independence in a 2x2 contingency table is the chi-square test statistic.
The chi-square test statistic (χ²) is calculated using the formula:
χ² = Σ [(Observed - Expected)² / Expected]
Where:
Σ represents the sum over all cells of the contingency table.
Observed is the observed frequency in each cell.
Expected is the expected frequency in each cell if the variables were independent.
First, we calculate the expected frequencies for each cell. To do this, we use the formula:
Expected frequency = (row total x column total) / grand total
Grand total = sum of all frequencies = 36 + 17 + 15 + 11 = 79
Expected frequency for the cell "Closed roof - Win" = (53 * 51) / 79 = 34.49
Expected frequency for the cell "Closed roof - Loss" = (53 * 28) / 79 = 18.51
Expected frequency for the cell "Open roof - Win" = (26 * 51) / 79 = 16.51
Expected frequency for the cell "Open roof - Loss" = (26 * 28) / 79 = 9.49
Now, we can calculate the test statistic using the formula:
χ² = [(36 - 34.49)² / 34.49] + [(17 - 18.51)² / 18.51] + [(15 - 16.51)² / 16.51] + [(11 - 9.49)² / 9.49]
Calculating each term and summing them up:
χ² ≈ 0.058 + 0.482 + 0.58 + 0.35 ≈ 1.47
Therefore,
The test statistic χ² is approximately 1.47.
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For Exercises 24-29, find each value.
24. Sin x
25 cos x
26 tan x
27. Sin y
28. Cos y
29. Tan y
All the values of expressions are,
24. Sin x = 1/√17
25 cos x = 4/√17
26 tan x = 1/4
27. Sin y = 4/√17
28. Cos y = 1/√17
29. Tan y = 4
We have to given that,
A right triangle is shown in figure.
Now, We can simplify all the values,
24. Sin x = Opposite / Hypotenuse
sin x = 2 / 2√17
sin x = 1/√17
25) cos x = Base / Hypotenuse
cos x = 8 / 2√17
cos x = 4/√17
26) tan x = Opposite / Base
tan x = 2 / 8
tan x = 1/4
27. Sin y = Opposite / Hypotenuse
sin y = 8 / 2√17
sin y = 4/√17
28. Cos y = Base / Hypotenuse
cos y = 2 / 2√17
cos y = 1/√17
29. Tan y = Opposite / Base
tan y = 8 / 2
tan y = 4
Thus, All the values of expressions are,
24. Sin x = 1/√17
25. cos x = 4/√17
26. tan x = 1/4
27. Sin y = 4/√17
28. Cos y = 1/√17
29. Tan y = 4
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The length of the arc LM is 8.72 cm.
We have,
The length of an arc is the distance that runs through the curved line of the circle making up the arc.
The length of an arc is expressed as;
l = tetha/360 × 2πr
tetha = R
R = 100°
and, radius = 5 units
so, we get,
l = 100/360 × 2 × 3.14 × 5
l = 8.72 cm (1.dp)
therefore the length of the arc LM is 8.72 cm
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pedro walks at a rate of 4 miles per hour and runs at a rate of 8 miles per hour. Each Week, his exercise program requires him to cover a total fist of 20 miles with some combination of walking and/or running.
A. write an equation that represents the different amounts of time pedro can walk, x, and run, y, each week.
B. graph the equation
C. what is the y- intercept? what does this tell you?
The equation showing the problem is: 4x + 8y = 20
The graph is attached and the y intercept is (0, 2.5)
How to model the equationAssuming that:
Time spent walking x hoursTime spent running y hoursSince Pedro walks at a rate of 4 miles per hour, the distance he covers by walking would be
4x milesAlso Pedro runs at a rate of 8 miles per hour, the distance he covers by running would be
8y milesAccording to the given information, the total distance Pedro covers each week is 20 miles. Therefore, we can write the equation:
4x + 8y = 20
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Find the volume of a cone of radius 3.5cm and vertical height 12 cm.
Answer:
Volume ≈ 153.93804 cm^3
Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.
Step-by-step explanation:
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
8 feet
Step-by-step explanation:
Let b be the length of the base. Then the height is b+6 ft.
The area of the parallelogram is given by:
Area = b(b + 6) = 160
Solving for b, we get,
[tex]b^2 + 6b - 160 = 0[/tex]
Factoring the expression, we get:
(b - 8)(b + 20) = 0
Therefore, b = 8 or b = -20.
Since the base cannot be negative, b = 8.
Therefore, the length of the base of the parallelogram is 8 feet.
which table does not show y as a function of x?
Answer:
I am confident the answer is H.
For what value of x is the rational expression below undefined?
x-3
3+x
A. 3
OB. -1
O C. 0
OD. -3
Answer:
x= -3
Step-by-step explanation:
x-3
-----------
x+3
This expression is undefined when the denominator is zero.
x+3 =0
x= -3
The centre of a circle is the point with coordinates (-1, 2)
The point A with coordinates (5, 9) lies on the circle.
Find an equation of the tangent to the circle at A.
Give your answer in the form ax + by + c = 0 where a, b and c are integers.
The equation of the tangent to the circle at point A is 6x + 7y - 93 = 0
How do we solve for the equation of the tangent to the circle?The equation of a circle in standard form is (x-h)² + (y-k)² = r²,
(h,k) is the center of the circle
r is the radius.
The radius formula ⇒ √((x₂ - x₁)² + (y₂ - y₁)²).
Here,
x₁ = -1, y₁ = 2 (center of the circle),
x₂ = 5, y₂ = 9 (point A on the circle).
∴
r = √((5 - (-1))² + (9 - 2)²) = √(36 + 49) = √85.
Now, we have the equation of the circle: (x - (-1))² + (y - 2)² = 85, or (x + 1)² + (y - 2)² = 85.
The slope of the radius from the center of the circle to point A ⇒ (y₂ - y₁) / (x₂ - x₁)
= (9 - 2) / (5 - (-1)) = 7/6.
tangent line is the negative reciprocal of the slope of the radius, ∴ -6/7.
The equation of a line in point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
The slope of the tangent line (m) is -6/7 and it passes through point A(5,9). Substituting these values in, it becomes
y - 9 = -6/7 (x - 5).
Multiplying every term by 7 to clear out the fraction and to have the equation in the ax + by + c = 0 form, we get:
7y - 63 = -6x + 30,
or
6x + 7y - 93 = 0.
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Which of the following answers to the question below is correct (multiple answers can be chosen)?
Question: Let s(t) be the position of a moving particle at time t. Choose ALL that represent the average speed of the particle over the time interval [0,4]?
1. s(4)/4
2. s(4)-s(0)/4
3. The slope of the secant line from (0, s(0)) to (4, s(4))
4. The slope of the tangent line at (0, s(0))
Answer:
The average speed of a particle over a time interval is defined as the total distance traveled divided by the time elapsed. In this case, the average speed of the particle over the time interval [0,4] is represented by options 2 and 3. Option 2 represents the change in position over the time interval [0,4] divided by the time elapsed. Option 3 represents the slope of the secant line connecting the points (0,s(0)) and (4,s(4)), which is equivalent to the average rate of change of position over the time interval [0,4].
the correct answers are, 2 and 3
Two cars leave towns 850 kilometers apart at the same time and travel toward each other. One car's rate is 16 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car? Do not do any rounding.
Answer:9.5
Step-by-step explanation:
Phil spends no more than 12 hours per week knitting. It takes him 2 hours to knit a hat and
3 hours to knit a scarf. He uses 150 yards of yarn for each hat and 400 yards of yarn for each
scarf. Which combinations of complete hats and scarves can Phil knit if he has 900 yards of yarn?
Select all of the correct answers.
A. 1 hat, 1 scarf
B. 3 hats, 2 scarves
C. 6 hats, 0 scarves
D. 4 hats, 1 scarf
E. 0 hats, 4 scarves
F. 2 hats, 1 scarf
The correct options regarding the inequality are:
A. 1 hat, 1 scarf
D. 4 hats, 1 scarf
F. 2 hats, 1 scarf
How to explain the inequalityBased on the time constraint, Phil can spend a maximum of 12 hours knitting, so we can set up the following inequality:
2h + 3s ≤ 12,
Phil can knit at most 6 hats per week, because 6 hats * 2 hours/hat = 12 hours.
Phil can knit at most 4 scarves per week, because 4 scarves * 3 hours/scarf = 12 hours.
Phil can use at most 900 yards of yarn, because he has 900 yards of yarn.
Phil can knit 1 hat and 1 scarf, because 1 hat * 150 yards/hat + 1 scarf * 400 yards/scarf = 550 yards < 900 yards.
Phil can knit 4 hats and 1 scarf, because 4 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 900 yards.
Phil can knit 2 hats and 1 scarf, because 2 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 700 yards < 900 yards.
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The slop of the graphed line is 2/3
The formulas that represent the linear function in this problem are given as follows:
y - 2 = 2/3(x - 1).y - 4 = 2/3(x - 4).f(x) = 2x/3 + 4/3.How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The line has a slope of 2/3, hence:
y = 2x/3 + b.
When x = 1, y = 2, hence the intercept b is obtained as follows:
2/3 + b = 2
b = 6/3 - 2/3
b = 4/3.
Hence the slope-intercept equation of the line is given as follows:
f(x) = 2x/3 + 4/3.
The line goes through points (1,2) and (4,4), hence the point-slope equations to the line are given as follows:
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Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
6543/2
-24
1-3-
Answer:
x intercept at( -2)
y intercept at (4)
The x-intercept and the y-intercept are -2 and 4 respectively.
The X-intercept is the point where the line of an equation intersects the X-axis. While y-intercept is the point where the line of an equation intersects the Y-axis. Here, the X-axis is the horizontal axis, and the Y-axis is the vertical axis.
Since the given graph shows the line intersecting the X-axis i.e. the horizontal axis at -2, the x-intercept of the line would be -2. Whereas, since the line intersects the Y-axis at 4, the y-intercept is 4. The points that show these intercepts are (-2,0) for the x-intercept and (0,4) for the y-intercept.
∴ The intercepts are -2,4 respectively.
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