The wonderful waffle cone holds more ice cream than super sundae cone.
In this question,
The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.
Volume of ice cream cone = volume of hemisphere + volume of cone
Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]
Volume of super sundae cone:
Radius of hemisphere = height of hemisphere = 0.5 in
Depth of the ice cream cone = 4 in
Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]
⇒ 0.2616+1.0466
⇒ 1.3082 ≈ 1.31 cubic in.
Volume of wonderful waffle cone:
Radius of hemisphere = height of hemisphere = 0.9 in
Depth of the ice cream cone = 3 in
Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]
⇒ 1.526+2.5434
⇒ 4.0694 ≈ 4.07 cubic in.
Thus volume of wonderful waffle cone > volume of super sundae cone.
Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.
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Please help!!!!!!!!!!
Answer: 18.7
Step-by-step explanation:
Find the lengths of AB, BC, and CA
AB = [tex]\sqrt{(4-(-1))^{2} + (-1-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1
BC = [tex]\sqrt{(0-(-1))^{2} + (-3-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1
CA = [tex]\sqrt{(0-4)^{2} + (-3-(-1))^{2} }[/tex] = 2[tex]\sqrt{5}[/tex] ≈ 4.5
7.1 + 7.1 + 4.5 = 18.7
Find a and k so that the given points lie on the parabola (An algebraic solution is required)
The value of a is -3 and the value of k is 10
A parabola is a U-shaped plane curve where any point is equidistant from a fixed point (known as the focus) and from a fixed line known as the directrix. The parabola is an integral part of the conic section topic
The section of a right circular cone by a plane parallel to the generator of the cone is a parabola. It is the location of a point that moves so that the distance from the fixed point (the focus) is equal to the distance from the fixed line (the directrix).
The fixed point is called the focus
A fixed line is called a directrix
Solving an algebraic equation is the process of finding a number or set of numbers that, when substituted for the variables in the equation, reduce them to an identity. Such a number is called the root of the equation
Here the equation y = a(x -2)^2 + k...........(1)
and two points A(1,7) and B(4, -2) is given
We need to find the value of a and k
Put A(1,7) in equation (1) , we get,
7 = a + k ,therefore k = 7 - a......(2)
Put B(4, -2) in equation (1), we get,
-2 = 4a + k........(3)
Put k= 7-a in (3)
-2 = 4a+7 -a
3a = -9
a= -3
From equation (2) , we get k = 7-(-3)= 10
Hence the value of k is 10 and the value of a is -3
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For the given points to lie on the parabola,
a = -3 and k = 10.
An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix).
According to the question,
Equation of parabola : y = a[tex](x-2)^{2}[/tex] + k
Points A(1,7) and B(4,-2)
For the points to lie on the parabola,
7 = a[tex](1-2)^{2}[/tex]+k
7 = a + k
Similarly,
-2 = a[tex](4-2)^{2}[/tex] + k
-2 = 4a + k
On solving the two equations simultaneously, we get,
a = -3
k = 10
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write 158/4 as a mixed number in simplest terms. thank you :)
158/4 as a mixed number in the simplest term is [tex]39\frac{3}{4}[/tex]
Converting improper fractions to mixed numberThe given fraction is 158/4
The number of times that 158 can be divided by 4 = 39
4 x 39 = 156
The remainder = 159 - 156
The remainder = 3
The mixed number is of the form:
[tex]Quotient\frac{Remaider}{Divisor}[/tex]
Therefore, the mixed number is [tex]39\frac{3}{4}[/tex]
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Determine the missing digit (denoted with*) for the American Express Traveler's Check identification number 783920*814 a) 3
b) 2
c) 6
d) 9
The missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.
In this question,
A Check Digit is a decimal (or alphanumeric) digit added to a number for the purpose of detecting the sorts of errors humans typically make on data entry.
A check digit is a digit added to a string of numbers for error detection purposes. Normally, the check digit is computed from the other digits in the string. A check digit helps digital systems detect changes when data is transferred from transmitter to receiver.
The last digit of a bar code number is a calculated check digit. The check digit is calculated from all the other numbers in the bar code and helps to confirm the integrity of your bar code number.
The American Express Traveler's Check identification number is 783920*814.
In Airline tickets, there are several digits plus a check digit.
Divide the ID number by 7. The check digit is the remainder.
Sum of digits = 7+8+3+9+2+0+8+1+4
⇒ 42
Now divide the sum by 7, the remainder is
⇒ 42 mod 7 = 42 - (5×7)
⇒ 42 mod 7 = 6
Hence we can conclude that the missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.
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I need to find the equation of the line
Answer:
y = 3x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = 3x + 3 ← equation of line
Answer:
y = 3x + 3
Step-by-step explanation:
See attached image.
Last week salazar played 13 more tennis games than perry. if they played a combined total of 53 games. How many games did salazar play?
If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.
Let the total number of games played by Perry be x.
It is given that, Salazar played 13 more tennis games than Perry.
⇒ Total games played by Salazar = x + 13
Also, Salazar and Perry played a combined of 53 games.
Hence, total number of tennis games played by Salazar and Perry = 53
⇒ Games played by Salazar + Games played by Perry = 53
⇒ x + (x + 13) = 53
2x + 13 = 53
2x = 53 - 13
2x = 40
x = 40 / 2
x = 20
Therefore, total number of games played by Salazar = x+13
= 20 + 13
= 33
Thus, Salazar played total 33 games.
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Part E:
Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form.
The equation for the graphed function is (x+20)(x+5)(x-15).
How to illustrate the equation?It should be noted that a graph shows the relationship between variables.
From the graph, the equation is x³+10x²-275x-1500.
In this case, this can be as - (x + 20)(x + 5)(x - 15)
The graph crosses the x axis. The coefficient is negative because the graph rises to the left.
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What additional information is obtained by measuring two individuals on an ordinal scale compared to a nominal scale
The direction of the difference between the 2 measurements.
What is nominal and ordinal scale with example?Examples of data for a nominal scale include a person's gender, ethnicity, and hair color. On the other hand, an ordinal scale requires putting data in a certain order, or in relation to one another and "ranking" each parameter (variable).What is the difference nominal and ordinal?Ordinal data has a preset or natural order, whereas nominal data is categorized without a natural order or rank. A number that can be measured, however, will always be present in numerical or quantitative data.What is an example of a ordinal scale?First place would go to a student with a score of 99 out of 100; third place would go to a student with a score of 92 out of 100; and so on.Learn more about ordinal scale and nominal scale here:
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According to the weather report, there is a 25% chance of snow in the mountains tomorrow. how likely is it to snow tomorrow in the mountains?
It is likely is it to snow tomorrow in the mountains is 1/4
A chance is the occurrence of events without apparent purpose or cause. It is simply the possibility that something will happen. When chance is defined in mathematics, it is called probability. Probability is the extent to which an event is likely to occur, measured by the ratio of favorable cases to the total number of possible cases. Mathematically, the probability that an event occurs is equal to the ratio of the number of cases favorable to a particular event to the number of all possible cases. The theoretical probability of an event is referred to as P(E). P(E) = number of outcomes more favorable to E/Nnumber of all possible outcomes of the experiment
We need to find that what is the chance that it will snow tomorrow in the mountains
According to the weather report, there is a 25% chance of snow in the mountains tomorrow.
Therefore the possible chance that it will snow tomorrow is 25/100 = 1/4
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A rectangle room has a perimeter of 70m.what would be the length of the longest side of the room?
Answer:
The longest side of room is 24m
Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
The rule which states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities is "Multiplicative rule".
What is Multiplicative rule?The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.
If A and B are dependent events, then the probability of both events occurring simultaneously is given by:
[tex]P(A \cap B)=P(B) \cdot P(A \mid B)[/tex]
The likelihood of both events occurring simultaneously in an experiment where A and B are two independent events is given by:
[tex]P(A \cap B)=P(A) \cdot P(B)[/tex]
Multiplication Theorem of Probability:
The multiplication guidelines that we use in probability have already been taught to us, including;
[tex]\begin{aligned}&P(A \cap B)=P(A) \times P(B \mid A) \text {; if } P(A) \neq 0 \\&P(A \cap B)=P(B) \times P(A \mid B) \text {; if } P(B) \neq 0\end{aligned}[/tex]
Therefore, the relationship between two events is explained by the probability multiplication rule.
Set AB represents the events in which both events A and B have occurred for two events A and B related to a sample space S.
Consequently, (AB) indicates that occurrences A and B happened at the same time. You can write the event AB as AB.
Using the characteristics of conditional probability, the likelihood of event AB is calculated.
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Which function could be a stretch of the exponential decay function shown on the graph?
f(x) = 2(6)x
f(x) = One-half(6)x
f(x) = 2(one-sixth) Superscript x
f(x) = One-half (one-sixth) Superscript x
We find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)
What function represents a stretch of a exponential decay function?
Exponential functions are trascedent functions whose form is described below:
[tex]y = a\cdot r^{x}[/tex] (1)
Where:
a - Stretch factorr - Growth rateThere are two conditions for a stretch factor and exponential decay: (i) a > 1, (ii) 0 < r < 1. Thus, we find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)
RemarkThe picture is missing and it cannot be found, but statement is still solvable as there is only one choice that responds the question.
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How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?
triangle(s)
How many distinct triangles can be formed for which m∠J = 129°, k = 8, and j = 3?
triangle(s)
Answer:
10Step-by-step explanation:
1.For two side measures and one angle measure to form one distinct triangle, the given angle must be between the given sides, or opposite the longest side.
When the given measures are ...
E = 64°g = 9e = 10The given angle is opposite the longest side, so one distinct triangle can be formed.
2.No triangle can be formed if the given angle is opposite the shorter given side, and either of ...
the angle is right or obtusethe ratio of shorter to longer sides is less than the sine of the given angle.__
Additional comment
As we can see from the above, the only ambiguous cases arise when the given angle is opposite the shorter given side. When that happens, the ratio of the shorter to longer given side relative to the sine of the given angle determines the nature of the solution:
two distinct triangles if the ratio is greater than the sineone right triangle if the ratio is equal to the sine.Answer:
1
0
Step-by-step explanation:
Write an expression using fractions to show how to determine the amount that each person will pay. Then calculate each person's contributions showing all steps in long division.
Me: $14.89
Friend 1: $7.27
Friend 2: $25.67
Friend 3: $11.59
The fraction based on the information given illustrated for each person.
How to illustrate the information?Me: $14.89
Friend 1: $7.27
Friend 2: $25.67
Friend 3: $11.59
Total = $59.42
The fraction for each person will be:
Me: $14.89 = 14.89/59.42 = 0.25
Friend 1: $7.27 = 7.27/59.42 = 0.12
Friend 2: $25.67 = 25.67/59.42 = 0.32
Friend 3: $11.59 = 11.59/59.42 = 0.195
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Jim jogged from his house to the gym at 15 km/hr. On the trip home on the same route he walked at 10 km/hr. Together the two trips took him two hours. What is the distance from his home to to the gym
The distance from Jim's home to the gym is 12 km.
What is Speed?Speed is defined as the rate at which the position of object is changed.
Speed = Distance / Time
Here, there are two different speeds given for the same distance.
Average speed is the total distance travelled by the total time taken.
If distance is a constant,
Average speed = 2xy / (x + y), where x and y are two different speeds for the same distance.
Average speed = (2 × 15 × 10) / (15 + 10)
= 12 km/hr
So, Total distance travelled = Average speed × total time taken
= 12 × 2
= 24
Distance = 24 / 2 = 12
Hence, the distance from Jim's home to the gym is 12 km when average speed is taken.
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What are the factors of 3x2 23x − 8? (3x − 4)(x 2) (3x − 2)(x 4) (3x − 8)(x 1) (3x − 1)(x 8)
Answer:
(3x − 1)(x 8)
Step-by-step explanation:
[tex]20-x-x^{2}[/tex]
solve this equation by class 9 course
The factored expression of the polynomial is (4 - x)(5 + x)
How to solve the polynomial?The polynomial expression is given as;
20 - x - x^2
Expand the expression
20 - 5x + 4x - x^2
Factorize the expression
5(4 - x) + x(4 - x)
Factor out 4 - x
(4 - x)(5 + x)
Hence, the factored expression of the polynomial is (4 - x)(5 + x)
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Solve the quadratic equation numerically (using tables of x- and y- values). x(x + 6) = 0 a. x = -1 or x = 3 c. x = 0 or x = -3 b. x = 0 or x = 6 d. x =0 or x = -6
Answer:
d. x =0 or x = -6
Step-by-step explanation:
x(x + 6) = 0
This is telling us that either x is 0 or x is -6, because:
1) when x = 0, 0*(0+6)=0, and
2) when x = -6, -6*(-6+6) = 0; -6(0) = 0
Solve for x:
[tex] \frak{2 ( 3x + 1 ) + 3 ( 5x + 2 ) = x - 1}[/tex]
[tex] \\ \\ \\ [/tex]
Thank uh -,-
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \:x = - \dfrac{ 9}{20} [/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:2(3x + 1) + 3(5x + 2) = x - 1[/tex]
[tex]\qquad❖ \: \sf \:6x + 2 + 15x + 6 = x - 1[/tex]
[tex]\qquad❖ \: \sf \:(6x + 15x - x) + (2 + 6 + 1) = 0[/tex]
[tex]\qquad❖ \: \sf \:20x + 9 = 0[/tex]
[tex]\qquad❖ \: \sf \:20x = - 9[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \:x =- \cfrac{ 9}{20} [/tex]
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
x = –9/20Step-by-step explanation:
________________________________
→ 2(3x + 1) + 3(5x + 2) = x – 1
→ 6x + 2 + 15x + 6 = x – 1
→ 21x + 8 = x – 1
→ 21x – x = – 1 – 8
→ 20x = – 9
→ x = –9/20
________________________________
Hope it helps you :')There are 86,400, frames of animation in 1 hour of anime.
How many frames are there per second?
There are 3,600, seconds in 1 hour.
Answer:
There are 24 frames of animation in 1 second of anime. Step-by-step explanation: There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.86400 ÷ 3600 = 24There are 24 frames of animation in 1 second of anime.
The table gives the populations of three countries in 2013.
United States Brazil Germany
3.16 × 108 1.96 × 108 8.0 × 107
1) Difference of the populations of Germany and Brazil = 1.16 X 10^8
2) Difference of the populations of Brazil and the United States = 1.2 X 10^8
3) Sum of the populations of Brazil and Germany = 2.76 X 10^8
4) Sum of the populations of the United States and Brazil = 5.12 X 10^8
According to the statement
we have given that the populations of three countries which are
United States is 3.16 × 10^8 and Brazil is 1.96 × 10^8 and Germany is 8.0 × 10^7
And we have to arrange the sums and differences in increasing order of their values.
so, we have to find the
a) the difference of the populations of Germany and Brazil
So,
Difference of the populations of Germany and Brazil = 1.96 X 10^8 - 8 X 10^7 = 116000000 = 1.16 X 10^8
And then we have to find the
b) the sum of the populations of the United States and Brazil
So,
Sum of the populations of the United States and Brazil = 3.16 X 10^8 + 1.96 X 10^8 = 512000000 = 5.12 X 10^8
And then we have to find the
c) the difference of the populations of Brazil and the United States
So,
Difference of the populations of Brazil and the United States = 3.16 X 10^8 - 1.96 X 10^8 = 120000000 = 1.2 X 10^8
And then we have to find the
d) the sum of the populations of Brazil and Germany
So,
Sum of the populations of Brazil and Germany: 1.96 X 10^8 + 8 X 10^7 = 276000000 = 2.76 X 10^8
NOW, we arrange the sum and difference in increasing order of their values.
So,
1) Difference of the populations of Germany and Brazil = 1.16 X 10^8
2) Difference of the populations of Brazil and the United States = 1.2 X 10^8
3) Sum of the populations of Brazil and Germany = 2.76 X 10^8
4) Sum of the populations of the United States and Brazil = 5.12 X 10^8
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Find the value of x in each figure
The length of a rectangle plus its width is 24 cm. The area is 135 cm. What are the length and width of the rectangle
Answer:
[tex]l = 5.63 \\ [/tex]
hope this helps
Choose the correct simplification of the expression ( expression in photo! )
A. G^7h
B. G^3h
C. G^7h^7
D. G^3/h^7
Use the rules of exponents to simplify the expression.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{g^{5}h^{4} }{g^{2}h^{3} } \end{gathered}$}[/tex]
To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.
[tex]\large\displaystyle\text{$\begin{gathered}\sf g^{5-2}h^{4-3} \end{gathered}$}[/tex]Subtract 2 from 5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf g^{3 }h^{3-2} \end{gathered}$}[/tex]Subtract 3 from 4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf g^{3 }h^{1} \end{gathered}$}[/tex]For any term t, t¹ =t.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf g^{3}h \end{gathered}$} }[/tex]Therefore, the correct option is "B".
Celia uses the steps below to solve the equation Negative StartFraction 3 over 8 EndFraction (negative 8 minus 16 d) + 2 d = 24.
Step 1 Distribute Negative StartFraction 3 over 8 EndFraction over the expression in parentheses.
3 minus 16 d + 2 d = 24
Step 2 Simplify like terms.
3 minus 14 d = 24
Step 3 Subtract 3 from both sides of the equation.
Negative 14 d = 21
Step 4 Divide both sides of the equation by –14.
d = StartFraction 21 over negative 14 EndFraction = Negative three-halves = negative 1 and one-half
Which corrects the error in the step in which Celia made the first error?
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over 2d, to get 3 minus 16 d + (negative three-fourths d) = 24.
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over –16d, to get 3 + 6 d + 2 d = 24.
In step 3, she should have added 3 to both sides of the equation to get Negative 14 d = 27.
In step 3, she should have first divided both sides by –14 to get 3 + d = 24
The error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
Simplifying linear equationsGiven the following equation as shown below
-3/8(-8-16d)+2d = 24
Step 1 Distribute -3/8 over the expression in parentheses
3 + 6d + 2d = 24
Simply the like terms
3 + 8d = 24
Subtract 3 from both sides of the equation.
8d = 24 - 3
8d = 21
d = 21/8
Hence the error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
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the half life of an element in the periodic table measured over a period of time, t, is modeled by the function f(t)=16(1/2)^t. what is the initial amount of the element
The initial amount of the element is 16
How to determine the initial amount?The function is given as:
f(t) = 16(1/2)^t
Set t = 0, to determine the initial amount
f(0) = 16(1/2)^0
This gives
f(0) = 16 * 1
Evaluate
f(0) = 16
Hence, the initial amount of the element is 16
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Of the last 16 people at a carnival booth, 6 won a prize. what is the experimental probability that the next person at the booth will win a prize? write your answer as a fraction or whole number. p(win)
The experimental probability that the subsequent booth competitor will receive a reward is 3/8.
Probability calculationThe possibility of an event occurring is determined by probability.
The probability of the occurrence ranges from 0 to 1.
If the event doesn't happen, it = 0;
otherwise, it = 1.
For instance, the likelihood that it will storm on Sunday ranges from 0 to 1. If it storms, the event is given a value of 1. If it doesn't, the event is given a value of zero.
Depending on the outcome of a study that has been run several times, the experimental probability is calculated.
The number of winners in the games divided by the total number of competitors in those games determines the probability that the following competitor will earn a reward.
So, here the probability = 6/16 = 3/8 (by dividing both the numerator and the denominator by 2).
Therefore, the final solution is P= 3/8 .
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Question is DOWN↓ PLS ANSWER I WILL MARK BRAINLIEST.....
Answer: Anita's
Step-by-step explanation:
Anita's shape would have the longest sides because she only has 4 total sides, while the others have 5, 6, and 10
This means that if the total perimeter for each of the shapes was 10 units,
Anita's shape would have side lengths of about 2.5 units while the others would have side lengths of 2, 1.6, and 1 units.
This means Anita's shape has the longest sides
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
The radius of the circle is 3 units. TRUE
The center of the circle lies on the x-axis. TRUE
The center of the circle lies on the y-axis. FALSE
The standard form of the equation is (x – 1)² + y² = 3. FALSE
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE
Step-by-step explanation:
x² + y² - 2x - 8 = 0
x² - 2x + y² = 8
Complete the square in x.
x² - 2x + 1 + y² = 9
(x - 1)² + y² = 3²
Center: (1, 0); radius: 3
The radius of the circle is 3 units. TRUE
The center of the circle lies on the x-axis. TRUE
The center of the circle lies on the y-axis. FALSE
The standard form of the equation is (x – 1)² + y² = 3. FALSE
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE
Bill and jenna are solving the quadratic equation x 2 - x = 12. bill solved this way jenna solved this way x 2 - x = 12 x(x - 1) = 12 x = 12 or 13 x 2 - x = 12 x 2 - x - 12 = 0 (x - 4)(x 3) = 0 x = 4 or x = -3 which student is correct? what error did the other student make when solving?
Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.
Form of quadratic equationThe form of quadratic equations is given as
ax2 + bx + c = 0
So, for the quadratic equation, we have
x² - x = 12
Let's make it into quadratic form
x² - x - 12 = 0
Bill solved it as
x(x - 1) = 12
This is wrong, because quadratic equations must be written in the form before solving for the variables
Jenna solved it as
x 2 - x - 12 = 0
Jenna is correct because she converted the equation to a quadratic form before solving for the variables.
Thus, Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.
Learn more about quadratic equations here:
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