The volume of the new box is 30 units³.
We can infer the roots are rational integers from the response options, thus this polynomial ought to be simple to factor. The coefficients of x must multiply by 10, hence they must be in some sequence of 5, 2, 1 or 10, 1. Since we can try each one separately, we can express the factored form as follows:
(5x-p)(2x-q)(x-r)
Due to the fact that p, q, and r must multiply to 6, they must be either 3, 2, 1 or 6, 1, 1 in some sequence. Once more, we may test each one in a different place to determine if they multiply properly.
When we multiply the x-terms and attempt (5x - 2)(2x - 1)(x - 3), the answer is 29. Try adding the x² terms together, they equal -39. Consequently, the roots are 2/5, 1/2 and 3 Now if you add 2 to each root, you get the volume is
= 12/5 × 5/2 × 5 = 30 units³
Therefore, The volume of the new box is 30 units³.
The question is incomplete. The complete question is:
"the roots of the polynomial 10x³ - 39x² + 29x - 6 are the height, length, and width of a rectangular box (right rectangular prism). a new rectangular box is formed by lengthening each edge of the original box by 2 units. what is the volume of the new box?"
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Determine the equation of a line in standard form which passes through the
point (2,-8) and perpendicular to the line-3x -9y-12.
Answer:
3x - y - 2 = 0
Step-by-step explanation:
The line-3x - 9y - 12 is given in the general form of the equation of a line, Ax + By + C = 0, where A = -3, B = -9, and C = -12.
To find the equation of the line that passes through the point (2, -8) and is perpendicular to the line-3x - 9y - 12, we need to find the slope of the perpendicular line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The slope of the line-3x - 9y - 12 can be found using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Rearranging the general form equation:
-3x - 9y - 12 = 0
9y = 3x + 12
y = (3/9)x + 4
The slope of the line is m = 3/9. To find the slope of the perpendicular line, we find the negative reciprocal:
m_perpendicular = -1 / (3/9) = -9 / 3
We have the slope of the perpendicular line, now we need to find its equation. To do this, we use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is the point through which the line passes and m is the slope of the line. Plugging in the values for the point (2, -8) and the slope -9/3:
y - (-8) = -9/3 (x - 2)
y + 8 = -3x + 6
3x - y - 2 = 0
A nurse is preparing to administer dextrose 5% in water (D5W) 750 mL IV to infuse over 6 hr. The nurse should set the IV pump to deliver how many mL/hr? (Round the answer to the nearest whole number. Do not use a trailing zero. )
The nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.
Determine IV pump settingThe nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr. To calculate the infusion rate, you can use the formula:
Infusion rate (mL/hr) = Volume to be infused (mL) / Infusion time (hr)
In this case, the volume to be infused is 750 mL and the infusion time is 6 hr. Plugging these values into the formula, we get:
Infusion rate (mL/hr) = 750 mL / 6 hr = 125 mL/hr
Therefore, the nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.
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A swimming pool is 50 m in length, 30 m in breadth, and 2.5 m in depth. find the cost of cementing its floor and walls at the rate of rupees 27 per square metre?
Answer:
51,300 rupees
Step-by-step explanation:
Surface area of the 2 short walls = 2 x 30 x 2.5 = 150
Surface area of the 2 long walls = 2 x 50 x 2.5 = 250
Surface area of the floor = 50 x 30 = 1500
Total surface area = 150 + 250 + 1500 = 1900 m²
27 rupees/m² x 1900 m² = 51300 rupees
The tax rate is
5.1%. How much is
the tax on $675?
Round to the nearest cent.
For what value of x is the given parallelogram a rhombus?
The value of x the given parallelogram a rhombus is 18
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The quadrilateral that is a rhombus
The diagonals of rhombus bisect each other
Using the above as a guide, we have the following:
Angle 1 = A
Substitute the known values in the above equation, so, we have the following representation
5x - 30 = 3x + 6
Evaluate
2x = 36
Divide
x = 18
Hence, the value is 18
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A tiling pattern is defined by the pattern rule equation n = 5+ 3p, where p is the
position number and n is the number of tiles. How many tiles would there be in
position 26?
Step-by-step explanation:
n=5+3p
when p=26,
n=5+3×26=83
Show all work to multiply (2+√-25)(4-√-100).
Product of multiplication of (2+√-25) and (4-√-100) is 58.
What are complex numbers?Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1).
For example, 6+7i is a complex number, where 6 is a real number and 7i is an imaginary number.
Given complex numbers
(2+√-25) and (4 -√-100)
√-25 = √(5² . -1) = 5√-1
i = √-1
√-25 = 5i
√-100 = √(10² . -1)
√-100 = 10i
Multiplying both numbers
(2+√-25) . (4 -√-100)
then
= (2 + 5i) . (4 - 10i)
Using FOIL method
(a + b)(c + d) = ac + ad + bc + bd
= 8 - 20i + 20i - 50i²
= 8 - 50i²
i² = -1
= 8 + 50
= 58
Hence, 58 is the product of multiplication of (2+√-25)(4-√-100)
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How do you write 0.11111 as a fraction?
Answer:
Step-by-step explanation:1/9
Need help on this exit ticket
Using the secant-secant and tangent-secant formulas, the indicated measures are:
1. x = 1
2. y = 10.
3. SU = 30
4. x = 4
5. x = 1
6. CD = 12
How to Apply the Secant-secant and Tangent-secant Formula?The secant-secant and tangent-secant formulas relates the lengths of the segments formed when two secants or a secant and a tangent intersect outside a circle.
Using the formula, we can solve for the indicated measures as explained below.
1. To find x, apply the secant-secant formula:
(7 + 17) * 7 = (13x + 8x) * 8x
168 = 168x²
168/168 = 168x²/168
1 = x²
x = 1
2. To find y, apply the tangent-secant formula:
20² = y * (y + 30)
400 = y² + 30y
y² + 30y - 400 = 0
Factorize:
(y - 10)(y + 40) = 0
y = 10 or y = -40
y cannot be negative so, y = 10.
3. Apply the secant-secant formula to find the value of x:
(x + 10 + 9) * 9 = (x + 6 + 10) * 10
(x + 19) * 9 = (x + 16) * 10
9x + 171 = 10x + 160
9x - 10x = -171 + 160
-x = -11
x = 11
SU = x + 19 = 11 + 19
SU = 30
4. Apply the tangent-secant formula:
6² = x(x + 5)
36 = x² + 5x
x² + 5x - 36 = 0
Factorize:
(x - 4)(x + 9) = 0
x = 4 or x = -9
x must be positive, therefore, x = 4
5. Apply the secant-secant formula to find x:
18*10 = 20x * 9x
180 = 180x²
1 = x
x = 1
6. Apply the tangent-secant formula:
AB² = (CD + AC) * AC
Substitute the values:
8² = (CD + 4) * 4
64 = 4CD + 16
64 - 16 = 4CD
48 = 4CD
48/4 = CD
12 = CD
CD = 12
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Which rational function has the most solutions in common with the function y=2x+6
Answer: Rational functions are defined as the ratio of two polynomials. A rational function has the most solutions in common with the function y = 2x + 6 if their graphs intersect at the most points.
If a rational function has the same degree as the polynomial function y = 2x + 6, which is degree 1, and has a leading coefficient that is the same sign as the leading coefficient of y = 2x + 6, then their graphs will intersect at the most points.
One such rational function that has the same degree as y = 2x + 6 and has a leading coefficient that is the same sign is:
y = (2x + 6) / 1
So the rational function y = (2x + 6) / 1 has the most solutions in common with the function y = 2x + 6.
Step-by-step explanation:
please help!! i’m confused
The method that can be used to prove that the triangles are congruent is B. AAS.
How to prove the congruence ?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
There are two angles in the two triangles that are shown to be equal and there is also a side of one triangle that is equal to anther side. These triangles are therefore congruent.
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An item has a listed price of 30$. If the sales tax rate is 8%, how much is the sales tax (in dollars)?
Answer:
32.4
Step-by-step explanation:
8% of 30 is 2.4. So, 2.4 + 30 is 32.4.
A triangle has integer side lengths 2, 5 and x. What is the median of all possible
values of x?
The median of all possible values of x is 5.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
To find the median of all possible values of x, we need to find all the possible values of x first.
By the triangle inequality, we know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, we can write:
2 + 5 > x
2 + x > 5
5 + x > 2
Simplifying each inequality, we get:
7 > x
x > 3
x > -3
The smallest possible integer value for x is 4 and the largest possible integer value for x is 6.
Therefore, the possible integer values for x are 4, 5, and 6.
Since we have an odd number of values, the median is simply the middle value, which is 5.
Therefore, the median of all possible values of x is 5.
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Suppose that you would like to select a sample of 50 students at your school in order to learn something about how many hours per week, on average, students at your school spend engaged in a particular activity (such as studying, surfing the web, or watching TV)
To select a sample of 50 students at your school in order to learn something about how many hours per week, on average, students at your school spend engaged in a particular activity, you could use random sampling.
Random sampling involves selecting a sample of individuals from a larger population in a way that ensures each individual has an equal chance of being selected. This helps ensure that the sample is representative of the larger population and can provide accurate results.
Here are the steps you could follow to select a random sample of 50 students at your school:
1. Obtain a list of all the students at your school. This could be a roster or a directory.
2. Assign each student a unique number.
3. Use a random number generator to select 50 numbers from the list of student numbers.
4. Select the students whose numbers were chosen by the random number generator as your sample.
By following these steps, you can ensure that your sample is randomly selected and representative of the larger population of students at your school. This will allow you to accurately estimate how many hours per week, on average, students at your school spend engaged in a particular activity.
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How do you find Van t Hoff?
The formula for Van 't Hoff's law, which is also known as the law of osmotic pressure, is: П = iMRT, where: Π is the osmotic pressure of the solution,
i is the van 't Hoff factor, which is a measure of the number of particles a solute molecule dissociates into in solution, M is the molar concentration of the solute, R is the gas constant, and T is the absolute temperature. Van 't Hoff is a term used to refer to a Dutch chemist named Jacobus Henricus van 't Hoff, who was known for his work on solutions, chemical equilibrium, and the laws of thermodynamics. To find Van 't Hoff, you can do any of the following: Research: You can learn about Van 't Hoff by doing research on his life and work. There are many online and offline resources available that provide information about his contributions to chemistry and his scientific achievements. Education: If you are a student of chemistry, you are likely to encounter Van 't Hoff's name in your coursework. You can learn about his theories and concepts in your chemistry classes or by consulting your textbooks. Application: You can apply Van 't Hoff's laws and principles in solving problems related to chemical equilibrium, colligative properties of solutions, and other thermodynamic concepts. This may involve using mathematical formulas and equations that are based on his work. In summary, Van 't Hoff refers to a Dutch chemist known for his work in thermodynamics, solutions, and chemical equilibrium. You can learn about his contributions to chemistry through research, education, and application of his principles in problem-solving.
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The student council has $100 to spend on decorations for the school dance. If streamers cost $3. 50 per roll and balloons cost $0. 75 each, write an inequality that represents the number of streamers x and balloons y the student council can buy.
The inequality that represents the number of streamers x and balloons y the student council can buy is given as follows:
3.50x + 0.75y ≤ 100.
How to model the inequality?Each streamer costs $3.50, hence the total cost of purchasing x streamers is given as follows:
3.5x.
Each balloon costs $0.75, hence the total cost of purchasing y balloons is given as follows:
0.75y.
Then the total cost of purchasing x streamers and y balloons is given as follows:
3.50x + 0.75y.
The amount spent can be of at most $100, hence the inequality is given as follows:
3.50x + 0.75y ≤ 100.
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if Joaquin bought a lawn mower for $519.20 on a 20% off sale what was the original price of the mower
Answer: The original price of the lawn mower was $649
Step-by-step explanation:
If Joaquin bought the lawn mower for $519.20 after a 20% discount, it means that he paid only 80% of the original price. We can use this information to calculate the original price of the mower by setting up the following equation:
0.8x = 519.20
where x is the original price of the lawn mower. To solve for x, we can divide both sides of the equation by 0.8:
x = 519.20 / 0.8
x = $649
A
65%
B
Reflex Angle B =
degrees.
The reflex of angle A is 295 therefore, angle B is 295°
What is a reflex angle?A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.
Given that angle B is the reflex angle of angle A, angle is measuring 65°
We need to find the measure of reflex Angle B
We know that,
To find the reflex angle of a given angle, we need to subtract the given measure from 360 degrees.
For example, the reflex angle of 110 degrees = 360 – 110 = 250.
Therefore,
Reflex Angle B = 360° - 65° = 295°
Hence, the reflex of angle A is 295 therefore, angle B is 295°
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3
The volume of a sphere is given by V = Tr³, where r is the radius.
Find the inverse function. Describe what it represents.
The inverse function is v⁻¹ = ( v/T)^1/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that the formula of the volume of the sphere is,
⇒ v = 4/3 πr³
T = 4/3π
Now,
To determine the inverse function we can solve the formula for the term r as;
⇒ v = 4/3 πr³
Multiply by 3/4 we get;
⇒ 3v/4 = πr³
Divide by π both side, we get;
⇒ 3v/4π = r³
Substitute r = v⁻¹ in above equation, we get;
⇒ v⁻¹ = ( v/T)^1/3
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What is the cost of nuclear, coal, gas, wind, hydel, and sun electricity separately
Step-by-step explanation:
Nuclear: 6-20 cents per kWh
Coal: 5-17 cents per kWh
Gas: 5-15 cents per kWh
Wind: 2-9 cents per kWh
Hydro: 5-20 cents per kWh
Solar: 10-20 cents per kWh
1. Which expression defines the arithmetic series 10 +7+4+... for six terms?
your question is incomplete!
line u - Line v, what is the value of x?
Rewrite in simplest terms: 6(4y+8)−2y
The simplification process of the expression 6(4y+8)−2y involves distributing '6' to '4y' and '8', and then combining like terms, yielding the simplified expression as 22y+48.
Explanation:To rewrite the given expression in simplest terms, distribute the 6 to the terms inside the parentheses:
6 * 4y = 24y6 * 8 = 48Now subtract 2y:
24y + 48 - 2y = 22y + 48So, the expression 6(4y+8)−2y can be simplified to 22y + 48.
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z=-4+5i what is |z|=√
Answer:


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Class 11
>>Applied Mathematics
>>Number theory
>>Complex Numbers
>>The complex number z satisfying the equa
Question

The complex number z satisfying the equations ∣z∣−4=∣z−i∣−∣z+5i∣=0, is
This question has multiple correct options
A
3−i
B
23−2i
C
−23−2i
D
0
Medium
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Updated on : 2022-09-05
Solution

Verified by Toppr
Correct options are B) and C)
We have two equation ∣z∣−4=0 and ∣z−i∣−∣z+5i∣=0
Putting z=x+iy i.e x2+y2=16 ....(1)
and ∣x+iy−i∣=∣x+iy+5i∣
⇒x2+(y−1)2=x2+(y+5)2
⇒y=−2 ...(2)
Putting y=−2 in (1),
x2+4=16⇒x=±2
Step-by-step explanation:
Hence the complex numbers z satisfying the given equation are
z1=23−2i and z2=−23−2i
A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on top, where the radius of the hemisphere is to be the same length as the radius of the base of the cylinder, which is 15 feet. The height of the cylinder is 30 feet.
The farmer would like to paint the outside of the silo blue when he is finished. How much area will he have to cover to paint the outside of the silo? (Use 3.14 for pi.)
Answer:
Step-by-step explanation:
To find the surface area of the silo, we need to calculate the areas of the cylinder and hemisphere separately, and then add them together.
The formula for the surface area of a cylinder is:
A_cylinder = 2πrh + 2πr^2
where r is the radius of the base of the cylinder, and h is the height of the cylinder.
In this case, r = 15 feet and h = 30 feet, so we have:
A_cylinder = 2π(15)(30) + 2π(15)^2
A_cylinder = 900π + 450π
A_cylinder = 1350π
The formula for the surface area of a hemisphere is:
A_hemisphere = 2πr^2
where r is the radius of the hemisphere.
In this case, the radius of the hemisphere is also 15 feet, so we have:
A_hemisphere = 2π(15)^2
A_hemisphere = 450π
To find the total surface area of the silo, we add the surface areas of the cylinder and hemisphere:
A_total = A_cylinder + A_hemisphere
A_total = 1350π + 450π
A_total = 1800π
Using 3.14 for π, we can approximate the total surface area as:
A_total ≈ 5652 square feet
Therefore, the farmer will need to cover approximately 5652 square feet of surface area to paint the outside of the silo.
You sell bracelets for $2 each and necklaces for $3 each at a local flea market. You collect $95, selling a total of 37 jewelry items. How many of each type did you sell?
Answer: You sold 16 bracelets and 21 necklaces
Step-by-step explanation
X# Bracelets x+y=37 -2(x+y=37) -2x-2y= -74 x+21=37
Y# Necklaces 2x+3y=95 [tex]\frac{+(2x+3y=95)}{y=21}[/tex] x=16
You sold 16 bracelets and 21 Necklaces
Lavaughn wraps a gift box in the shape of a right rectangular prism. The figure below shows a net for the gift box. 9 m 9 m 8 m 8 m 15 m 8 m 8 m How much wrapping paper did he use, in square meters?
The length of paper he used for wrapping paper is, 702 meters²
What is surface area ?Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.
To calculate the amount of wrapping paper needed, we need to find the total surface area of the gift box. The surface area of a right rectangular prism is given by the formula:
surface area = 2(lw + wh + lh)
where l, w, and h are the length, width, and height of the prism, respectively.
In this case, the dimensions of the gift box are 9 meters, 9 meters, and 15 meters, so:
surface area = 2(9 x 9 + 9 x 15 + 15 x 9)
= 2(81 + 135 + 135)
= 2(351)
= 702 square meters
Therefore, Lavaughn used 702 square meters of wrapping paper for the gift box.
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Using the Rule of 70, what approximate interest rate would be needed for an investment
of $14,000 to double by the end of 32 years?
A22.49
B 45.7%
C 2.19%
A town's population of 25000 is expected to decrease at a rate of 6.5% per year. What will the population be in 10 years. Round your answer to the nearest whole number.
The population of the town after 10 years is expected to be about 12766
What will the population be in 10 years.We can use the formula for exponential decay to find the population of the town after 10 years.
The formula is:
P = P₀ * (1 - r)^t
Where P₀ is the initial population, r is the annual decay rate as a decimal (in this case, r = 0.065), t is the time in years, and P is the population after t years.Substituting the given values into the formula, we get:
P = 25000 * (1 - 0.065)^10
Simplifying and evaluating using a calculator:
P = 12766
Hence, the population is expected to be about 12766 .
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Exponents power of power multiplication properties
(4a³b^4)³
The expression (4a³b^4)³ when evaluated is 64a^9b^12
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
(4a³b^4)³
When expanded, we have
(4a³b^4)³ = 4³ * (a³)³ * (b^4)³
Evaluate the exponents
So, we have the following representation
(4a³b^4)³ = 64a^9b^12
Hence, the solution si 64a^9b^12
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