Mathematics College
Answers
Answer 1
To translate miles per gallon to kilometres per litre, multiply all of these summaries by 0.425.
This is because the measurements are changing from being expressed in kilometres to being expressed in units of volume (liters).
The conversion of the median fuel economy of 21 miles per gallon to 8.83 kilometres per litre, the mean fuel economy of 22 miles per gallon to 9.3 kilometres per litre, the maximum fuel economy of 51 miles per gallon to 21.53 kilometres per litre, and the interquartile range of 7 miles per gallon to 2.97 kilometres per litre. 2.84 kilometres per litre equals the 6.69 miles per gallon standard deviation.
Therefore, to convert from miles per gallon to kilometres per litre, each of these summary statistics will be multiplied by 0.425.
Complete Question:
The fuel economy in miles per gallon for 2015 model cars in the U.S.is summarized in the table below.
mean= 22.0
s = 6.69
Q1= 18
median=21
marimum =51.
IQR=7
To compare these U.S. models to European cars, these statistics will be converted to km per liter by multiplying the numerical mpg rating for each car by 0.425. Which of the following statements is true?
A. The standard deviation and IQR will remain unchanged, but the other summary statistics will be multiplied by 0.425.
B. The mean and median will be multiplied by 0.425, but the other summary statistics will remain unchanged.
C. The standard deviation and IQR will be multiplied by 0.425, but the other statistics will remain unchanged.
D. All of these summary statistics will remain unchanged.
E. All of these summary statistics will be multiplied by 0.425.
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Related Questions
or
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Two kids at a summer camp, Lester and Kyle, are competing in a potato sack race. Lester is younger, so he is given a head start of 29 yards. When the race starts, Lester hops at a rate of 3 yards per second, and Kyle hops 4 yards per second. Eventually, Kyle will overtake Lester. How long will that take? How far will Kyle have to hop?
Answers
29 mins will that take. 116 yards will Kyle have to hop.
What is the rate?
A rate is a broader measure that involves dividing one quantity by another, where neither quantity necessarily needs to have the same unit of measurement as the other. It is capable of being equal to any value, even a negative one. It can be expressed as a number or a percentage, just like proportions.
Given that, Lester is younger, so he is given a head start of 29 yards.
The rate of hops of Lester is 3 yards per second.
The rate of hops of Kyle is 4 yards per second.
The equation that represents the distance covered by Lester is
L = 3t + 29 ......(i)
The equation that represents the distance covered by Kyle is
K = 4t ......(ii)
Kyle will overtake Lester. Then the time of overtaking L = K
Equate equations (i) and (ii)
4t = 3t + 29
t = 29
After 29 mins, Kyle will overtake Lester.
Putting t = 29 in equation (ii):
K = 4×29
K = 116 yards
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The radius of a circle is 3 m. Find its area in terms of pi.
Answers
Answer:
A = 9π m²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius )
= π × 3²
= 9π m²
A volcanologist rappels 1200 feet into a volcano. He wants to climb out of the
volcano in less than 4 hours. He climbs the first 535 feet in 100 minutes. Graph an inequality
that represents the average rates at which he can climb the remaining distance and meet his
goal.
Answers
The linear equation will be y=535+4.75x where y is distance climbed and x is time in minutes and average rate of climbing the remaining distance will be 4.75 feet/minute.
What exactly is a linear equation?
A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the following standard form:
Ax + B = 0
e.g. x-10=0. In this equation, x is a variable, A is a coefficient, and B is constant.
A linear equation in two variables has the following standard form:
Ax + By = C
e.g. 2x-4y=10. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.
Now,
Total distance to climb=1200 feet in 4 hours or 240 minutes
Climbed 535 feet in 100 minutes and left distance=1200-535=665
and time left =240-100=140 minutes
average rate with which remaining distance will be covered in time=665/140
=4.75 feet/minute
and linear equation for the graph will be
y=535+4.75x where where y is distance climbed and x is time in minutes
Hence,
The linear equation will be y=535+4.75x and average rate of climbing the remaining distance will be 4.75 feet/minute.
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find the volume of the solid obtained by rotating the region in the first quadrant bounded by x=0, y=1, x=y^4 about the line y=10
Answers
The volume of the solid obtained by rotating the region in the first quadrant bounded by x=0, y=1, x=y^4 about the line y=10 is 678.53 units cubed.
Here we can use the formula for the area of the circle which is A = pi*r^2 to calculate the area of the cylindrical shell. since the volume of the solid formed by rotating the given region about the line y=10 can be found by using the method of cylindrical shells, it states that the volume of the solid of revolution is equal to the integral of the cross-sectional area of the solid with respect to the axis of rotation.
in order to calculate the volume, we first need to find the radius of the cylindrical shell, this can be done by subtracting the distance from the line of rotation. in this case, the distance from the line of rotation to the axis of rotation is 10, thus the radius of the cylindrical shell is y-10.
while using the formula for the area of the circle, here subsituting the radius of the cylindrical shell into this formula will give us the area of the sylindrical shell, then integrate the area of the cylindrical shell with respect to the axis of rotation, which will given us the volume of the solid, so the volume of the solid by rotating the region in the first quadrant bounded by v about the line y=10 given by the integral of the I*(y-10)^2 from y=1 to y=10, which gives us the aprroximately 678.54
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Which equations are equal to this equation? Select all that apply. 1/4 (8x + 56) = 20
Answers
The equations that are equal to the given equation are 56 + 8x = 80 and 2x = 6.
How to find the equations
From the question,
We are to determine the equations that are equal to the given equation
The given equation is 1/4 (8x + 56) = 20
Multiply both sides of the equation by 4,
We get
4 x 1/4 (8x + 56) = 20
This gives
8x + 56 = 80
OR
56 + 8x = 80
∴ Option a. 56 + 8x = 80 is equal to the given equation
Simplifying further
56 + 8x = 80 becomes
8x = 80 - 56
8x = 24
Now, divide both sides by 4
This gives
2x = 6
Therefore, 2x = 6 is equal to the given equation
Hence, the equations that are equal to the given equation are 56 + 8x = 80 and 2x = 6.
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The table below indicates the number of labor hours required in Countries X and Y to produce one unit of food or one unit of clothing.
Country Food Clothing
X 20 hrs. 50 hrs.
Y 10 hrs. 20 hrs.
Given this information, which of the following statements is correct?
Select one:
a. X has comparative advantage in the production of both food and clothing.
b. Y has comparative advantage in food production, whereas X has a comparative advantage in clothing production.
c. Neither country has a comparative advantage in the production of either good.
d. X has comparative advantage in food production, whereas Y has a comparative advantage in clothing production.
e. Y has comparative advantage in the production of both food and clothing.
Answers
The correct statement is d. X has a comparative advantage in food production, whereas Y has a comparative advantage in clothing production.
Comparative advantage refers to a country's ability to produce a good at a lower opportunity cost than another country. Opportunity cost is the next best alternative that must be given up in order to produce a certain good. In this case, we can compare the opportunity cost of producing food and clothing in both countries.
In Country X, the opportunity cost of producing one unit of food is 50/20 = 2.5 units of clothing. This means that in order to produce one unit of food, 2.5 units of clothing must be given up. In Country Y, the opportunity cost of producing one unit of food is 20/10 = 2 units of clothing.
Thus, in Country Y, the opportunity cost of producing food is lower compared to that in Country X. Hence, Y has a comparative advantage in clothing production.
On the other hand, the opportunity cost of producing one unit of clothing in Country X is 20/50 = 0.4 units of food. In Country Y, the opportunity cost of producing one unit of clothing is 10/20 = 0.5 units of food.
In this case, Country X has a lower opportunity cost of producing clothing compared to Country Y, and therefore, X has a comparative advantage in food production.
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Find the distance around the figure by using the appropriate formula. Round approximate answers to the least accurate of the given measurements. (Assume a = 0.3 cm, b = 1.0 cm, c = 1.7 cm, d = 1.8 cm, e = 1.0 cm, and f = 3.6 cm.)
Answers
The distance around the given figure above which is its perimeter would be = 17.6cm.
How to calculate the distance around the given figure?
The distance around the given figure can be calculated using the formula for perimeter= addition of all the sides of the shape which is made up of three different figures.
That is =
Figure 1 = a+a+d+d
= 0.3+0.3+1.8+1.8
= 4.2cm.
figure 2 = 3a + 3a + 2e
=6(0.3) + 1.0(2)
= 1.8+2 =2.8cm
figure 3 = 2c + 2f
= 2(1.7) + 2(3.6)
= 3.4 + 7.2 = 10.6cm.
Therefore the perimeter of the figure = 4.2+2.8+10.6 = 17.6cm.
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NO LINKS!!! URGENT HELP PLEASE!!!
For #13 and 14, order the angles from least to greatest.
Answers
Answer:
13. ∠N < ∠R < ∠Q
14. ∠G < ∠H < ∠J
Step-by-step explanation:
In a triangle:
The largest angle is opposite the longest side.The smallest angle is opposite the shortest side.
Question 13
From inspection of triangle NQR:
As ∠N is opposite the shortest side, it is the smallest angle.As ∠Q is opposite the longest side, it is the largest angle.
Therefore, the angles in order from least to greatest are:
∠N < ∠R < ∠Q
Question 14
From inspection of triangle GHJ:
As ∠G is opposite the shortest side, it is the smallest angle.As ∠J is opposite the longest side, it is the largest angle.
Therefore, the angles in order from least to greatest are:
∠G < ∠H < ∠J
Alan multiplies a 4-digit number by 36. How can you tell the
number of partial products Alan will have?
Answers
Answer:
Step-by-step explanation:
The number of partial products in this calculation will be equal to the number of digits in the 4-digit number being multiplied by 36. Since 36 has two digits, there will be 2 partial products for each digit in the 4-digit number, for a total of 2 * 4 = 8 partial products.
When will Marc and Prisha meet?
Answers
Answer: who is Marc and Prisha?
What is the area of a rectangle with a width of 2.5 feet and a length of 8.25 ft
Answers
Multiply 2.5 and 8.25 which equals 20.65
Mario had
이윽
8
07 cookies
11
5
18
cookies. He gave his brother 4
4호
5
18
cookies
cookies
cookies. How many cookies does Mario have left?
Answers
Answer: he had 17/5 over 3 times 2
Step-by-step explanation:
Question 1
At the end of the 2000 WNBA regular season, the Houston comets had 22 more
victories than losses. The number of victories they had was three less than six
time the number of losses. How many regular season games did the Houston
comets play during the 2000 WNBA season?
Answers
Answer:Its 54
Step-by-step explanaon:
Express the function graphed on the axes below as a piecewise function.
Answers
y = 2/3x +6 for x < -3
y = 2/3x +1 for x > 3.
This can be solved using the concept of slope-intercept form.
What is slope-intercept form?
The equation for a straight line is y = mx + b, where m stands for the slope and b for the y-intercept of the line. The slope-intercept formula, y = mx + b, is used when the slope of the line under study is known and the specified point also serves as the y-intercept (0, b). The y value of both the y-intercept point is represented by b in the formula.
The graph is a line for x < -3
(-6,2) and ( -3,4)
The slope is m= ( y₂ - y₁)/(x₂-x₁)
m = ( 4-2)/(-3 - -6)
m = 2/ ( -3+6)
m = 2/3
∴ The slope is 2/3
Using point slope form:
y-y₁ = m (x-x₁) and the point ( -6,2)
y -2 = 2/3 (x - -6)
y -2 = 2/3 (x +4)
y-2 = 2/3 x + 6
y = 2/3x +6 x< -3
The graph is a line for x > 3
(3,3) and ( 6,5)
The slope is m= ( y₂-y₁)/(x₂-x₁)
m = ( 5-3)/(6-3) = 2/ (3) = 2/3
The slope is 2/3
Using point slope form:
y-y₁ = m(x-x₁) and the point (6,5)
y -5 = 2/3(x - 6)
y-5 = 2/3 (x -4)
y = 2/3x +1 x> 3
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This is answer choice d for question 6
Answers
The proportional relationship that defines the graphed function is given as follows:
y = 40x.
What is a proportional relationship?
A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
A proportional relationship is a special case of a linear function, with an intercept of zero.
For this problem, when x = 2, y = 80, hence the constant k is given as follows:
k = y/x
k = 80/2
k = 40.
Meaning that the equation is given as follows:
y = 40x.
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If t varies directly with s and inversely with the square of r, and s = 48 when t = 8 and r = 3. Find s
when t = 12 and r = 5.
Answers
[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{llll} \textit{"t" varies directly}\\ \textit{with "s" and}\\ \textit{inversely with }r^2 \end{array}\qquad t=\cfrac{ks}{r^2}\hspace{5em}\textit{we also know that} \begin{cases} s=48\\ t=8\\ r=3 \end{cases} \\\\\\ 8=\cfrac{k(48)}{(3)^2}\implies 8=\cfrac{16k}{3}\implies \cfrac{3}{16}\cdot 8=k\implies \cfrac{3}{2}=k~\hfill \boxed{t=\cfrac{ ~~ \frac{3}{2}s ~~ }{r^2}} \\\\\\ \textit{when t=12 and r=5, what's "s"?}\qquad 12=\cfrac{\frac{3}{2}s}{5^2}\implies 300\cdot \cfrac{2}{3}=s\implies 200=s[/tex]
William bought a plant and planted it in a pot near a window in his house. The initial
height of the plant was 6 inches and it grew at a rate of 3 inches per month. Make a
table of values and then write an equation for H, in terms of t, representing the
height, in inches, of the plant t months after William bought the plant.
Answers
Answer:
Step-by-step explanation:
15 inch
Maya has savings of $30,000. She invests in a bond mutual fund that pays 5% interest each year. Ignoring compounding, what are Maya's total savings after 15 years?
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$30000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &15 \end{cases} \\\\\\ A = 30000[1+(0.05)(15)] \implies A = 52500[/tex]
a stereo speaker in the shape of a rectangular prism has a height of 10 inches the length of the base of the stereo speaker is 6.5 inches and width of the base is 7 inches what is the volume of the speaker in cubic inches
Answers
The volume of the rectangular, prism-shaped speaker is 455 cubic inches.
What is a prism?
In three-dimensional space, prisms is a polyhedron where two ends are similar.
Given:
A stereo speaker in the shape of a rectangular prism has a height of 10 inches the length of the base of the stereo speaker is 6.5 inches and the width of the base is 7 inches.
The volume of the rectangular prism-shaped speaker,
= Length x width x height
= 10 x 6.5 x 7
= 455 cubic inches.
Therefore, the volume is 455 cubic inches.
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a technician is asked to prepare a dilution of a common laboratory disinfectant. the label indicates that a 1:29 dilution in water is required prior to use. using the simple dilution method, calculate the volume in ml of disinfectant required to make 1.0 l. record the answer to one decimal place below
Answers
The required volume of disinfectant is 34.
To calculate the required volume of disinfectant, we need to use the simple dilution method.
To make a 1:29 dilution, we need one part disinfectant for every 29 parts water.
Since we want to make 1.0 L of the solution, we need to find out how many parts of the solution are water. We can calculate this by dividing 1.0 L by 29, which gives us 0.0345 L of water.
Now we need to figure out how many parts of disinfectant we need to get a 1:29 dilution. To do this, we can simply multiply 0.0345 L of water by 29, which gives us 1.0055 L of disinfectant.
Finally, we need to convert this to milliliters. We can do this by multiplying 1.0055 L of disinfectant by 1,000 to get 1,005.5 mL of disinfectant.
Rounding the answer to one decimal place, the required volume of disinfectant is 34.5 mL.
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Use the sum of cubes identity to find the factors of the expression 826 + 27³. Write your answer in the form
of the expression on the right of the sum of cubes identity.
Enter the correct answer in the box.
Answers
On solving the provided question, we can say that the expression 826 + 27³, value is = 826 + 27*27*27 = 20509
what is expression ?
In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
the expression 826 + 27³
value is = 826 + 27*27*27 = 20509
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How are exponential functions characterized? Exponential functions are characterized by the fact that: a. the graph will always be positive c. their growth rate is less than their value b. their growth rate is proportional to their value d. the value is greater than the growth rate Please select the best answer from the choices provided A B C D
Answers
Answer:
Option B.
Step-by-step explanation:
Their growth rate is more proportional to their value and exponential functions are mainly characterized by the fact that their rate of growth is proportional to their own value.
Data for a sample of 55 members of the baseball Hall of Fame in Cooperstown, New York, are shown here. Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R).
LPCH2PR1SS1
LPRPPPPRCSL
RPCCPPRP23P
HLP1CPPPS1L
RR12HS3H2LP
(a)
Construct frequency and relative frequency distributions to summarize the data. (Round the relative frequencies to three decimal places.)
PositionFrequencyRelative
Frequency
PitcherCatcher1st Base2nd Base3rd BaseShortstopLeft FieldCenter FieldRight FieldTotal(b)
What position provides the most Hall of Famers?
PitcherCatcher 1st Base2nd Base3rd BaseShortstopLeft FieldCenter FieldRight Field
(c)
What position provides the fewest Hall of Famers?
PitcherCatcher 1st Base2nd Base3rd BaseShortstopLeft FieldCenter FieldRight Field
(d)
What outfield position (L, C, or R) provides the most Hall of Famers?
Left FieldCenter Field Right Field
(e)
Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).
There are more infielders than outfielders.There is the same number of infielders and outfielders. There are more outfielders than infielders.
Answers
To Construct the frequency and relative frequency distributions to summarize the data, and determine the answers to the rest of the problem, let's go straight to the analysis below.
Step by step analysis of the problem
(a)
Frequency:
Pitcher: 21
Catcher: 11
1st Base: 5
2nd Base: 5
3rd Base: 3
Shortstop: 7
Left Field: 5
Center Field: 3
Right Field: 5
Relative Frequency:
Pitcher: 0.382
Catcher: 0.200
1st Base: 0.091
2nd Base: 0.091
3rd Base: 0.055
Shortstop: 0.127
Left Field: 0.091
Center Field: 0.055
Right Field: 0.091
(b) The position that provides the most Hall of Famers is Pitcher.
(c) The position that provides the fewest Hall of Famers is 3rd Base.
(d) The outfield position that provides the most Hall of Famers is Right Field.
(e) There are more infielders than outfielders.
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Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form of the equation of the quadratic function: Vertex = (-10,-6) Point = (3,-5)
Answers
The standard form of the equation of the quadratic function is y = 1/169x² + 20/169² - 5.41.
What is quadratic form of equation?
A polynomial with all terms of degree two is known as a quadratic form in mathematics ("form" is another termfor a hom*ogeneous polynomial). It is common to refer to a quadratic form over K when the coefficients are typically members of an external factors K, such as the real or complicated numbers.
The vertex form of the quadratic equation is given as:
y = a(x - h)² + k
Substitute the value of the vertex and the point to find the value of a:
-5 = a(3 + 10)² - 6
-5 = a(169) - 6
1 / 169 = a
Substitute the value of a in the equation along with the vertex:
y = 1/169(x + 10)² - 6
y = 1/169(x² + 20x + 100) - 6
y = 1/169x² + 20/169² + 100/169 - 6
y = 1/169x² + 20/169² - 5.41
Hence, the standard form of the equation of the quadratic function is y = 1/169x² + 20/169² - 5.41.
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Liz and Rick are squeezing lemons for a lemonade stand. Liz squeezed 18 lemons in 6 minutes. Rick squeezed 24 lemons in 12 minutes. Who squeezed lemons at a faster pace?
Answers
Answer:
Step-by-step explanation:
The department of designing the Death Star had a lot of money in the bank account and then received a large donation of 13,000 from George Lucas. They decided to spilt their money equally between the three research projects. iLife each research project for 25,000, how much money did the department of designing the Death Star have in the bank account originally? Please write equation and solve!!
Answers
The department of designing the Death Star originally had 62,000 dollars in the bank account.
What is Equation?
Two or more expressions with an Equal sign is called as Equation.
Let's call the original amount of money in the department's bank account as "A".
After receiving the donation of 13,000, the total amount of money in the account became A + 13,000.
Each project received (A + 13,000) / 3 dollars.
And since each project was funded with 25,000 dollars, we can write an equation to solve for M:
(A + 13,000) / 3 = 25,000
A + 13,000 = 75,000
A = 75,000 - 13,000
A = 62,000
Hence, the department of designing the Death Star originally had 62,000 dollars in the bank account.
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What is the volume of this figure? A three-dimensional figure that is composed of two rectangular prisms. Prism A has a length of 8 meters, a height of 5 meters. The width is unknown but can be determined by the width of prism B. Prism B has a length of 12 meters, a width of 4 meters, and a height of 5 meters. 400 m 320 m 240 m 80 m
Answers
The volume of this required figure is 190m³.
What is volume, exactly?
Volume is a term used in mathematics to describe the volume of three-dimensional space inhabited by an object or a closed surface.
Volume is measured in cubic units like m3, cm3, in3, etc. Volume and capacity may be used interchangeably.
Volume of a rectangular prism is the space inside the prism. It is calculated by multiplying its base area by its height.
Volume (v) = l × b × h, where l is the length, b is the breadth, and h is the height of the prism.
so volume of both the rectangular prism are to be found.
Volume of first rectangular prism = l×b×h = 5 × 4 × 5 = 100 m³.
volume of second prism = 2 × 9 × 5 = 90m³.
∴ the volume of the figure
= volume of first rectangular prism +volume of second prism
= 100m³ + 90m³
=190m³.
Thus, the volume of this required figure is 190m³.
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Make x the subject
✓a) z = 4x
Answers
The required expression is x = 4z/√a that the subject is x.
What is the expression?
Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression is given in the question, as follows:
√a/z = 4/x
We have to make x the subject,
As per the question, we have
√a/z = 4/x
Apply the cross-multiplication,
(√a)x = 4z
Isolate the term of variable x, and we get
x = 4z/√a
This is the required expression that the subject is x.
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Given the polynomial Q(x)=2x^3+3x^2+3x+1, and knowing the only real zero is x= -1/2, find the complex zeros
Answers
Given the polynomial Q(x)=2x^3+3x^2+3x+1, and knowing the only real zero is x= -1/2, the complex zeros are:
z1 = -3/4 + (√(3) / 2)i
z2 = -3/4 - (√(3) / 2)i
How to find the complex zeros?
Since the polynomial Q(x) has degree 3 and only one real zero, we know that it must have two complex zeros in the form of a complex conjugate pair, let's call them z1 and z2.
From Vieta's Formulas, we know that the sum of the zeros of a polynomial is equal to the negation of the coefficient of the linear term divided by the leading coefficient. So, in this case:
z1 + z2 = -3/2
Also, the product of the zeros of a polynomial is equal to the negation of the constant term divided by the leading coefficient. So, in this case:
z1 * z2 = -1/2
Since z1 and z2 are complex conjugates, they have the same magnitude and opposite phases. Hence, we can represent them in the form:
z1 = a + bi
z2 = a - bi
where a and b are real numbers and "i" is the imaginary unit.
Using the two equations above, we can find the value of "a" and "b":
a = -3/4
b = √(1/4 - (-1/2)) = √(3/4) = √(3) / 2
So, the complex zeros are:
z1 = -3/4 + (√(3) / 2)i
z2 = -3/4 - (√(3) / 2)i
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Answer:
Step-by-step explanation:
Given the polynomial Q(x)=2x^3+3x^2+3x+1, and knowing the only real zero is x= -1/2, the complex zeros are:
z1 = -3/4 + (√(3) / 2)i
z2 = -3/4 - (√(3) / 2)i
I need to solve for x
Answers
The value of x in the circle is x = 15
How to solve for the value of x in the circle?
Since the measure of angle BAC is m∠BAC = 3x-6. The measure of arc BC will be:
arc BC = 2 *(3x-6) (inscribed angle theorem)
arc BC = 6x-12
In a semicircle, the intercepted arc measures 180°. Thus:
27+5x + 6x-12 = 180°
11x + 15 = 180
11x = 180 - 15
11x = 165
x = 165/11
x = 15
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