MODELING REAL LIFE A cell phone plan costs $30 for each line.
a. Does the situation represent a function? If so, identify the independent and dependent variables.
the situation represent a function. The total cost of the cell phone plan is the
The domain is
b. You can have a maximum of four lines on a plan. Find the domain and range.
Yes :: No
The range is
:: independent variable :: dependent variable
and the number of cell phone lines is the
a. Yes, The situation represents a function.
The independent variable is number of lines and dependent variable is the total cost.
b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.
What is Domain?
The set of all inputs of the function is called Domain of set.
Given that;
A cell phone plan costs $30 for each line.
Now, Let the number of lines be x and total cost be y.
So, We can evaluate;
y = 30x
Thus, This equation represent Linear function.
So, The situation represents a function.
The independent variable is number of lines and dependent variable is the total cost.
Since, You can have a maximum of four lines on a plan.
So, The possible values are;
x = 0, 1, 2, 3, 4
After substitute all the value of x in equation y = 30x we get;
For x = 0
y = 30 × 0 = 0
For x = 1
y = 30 × 1 = 30
For x = 2
y = 30 × 2 = 60
For x = 3
y = 30 × 3 = 90
For x = 4
y = 30 × 4 = 120
Thus, The range of the function will be 0 ≤ x ≤ 4.
And, The domain of the function will be 0 ≤ y ≤ 120.
Therefore,
a. Yes, The situation represents a function.
The independent variable is number of lines and dependent variable is the total cost.
b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.
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All changes savedFor the three-part question that follows, provide your answer to each question in the given workspace.Identify each part with a coordinating response. Be sure to clearly label each part of your response asPart A, Part B, and Part C.A bag contains three blue marbles, five red marbles, and four green marbles.Part A: What is the probability of selecting a red marble?Part B: What is the probability of selecting three red marbles without replacement?Part C: In a short paragraph, explain in your own words your work to Step B.
If there are three blue marbles, five red marbles, and four green marbles, the probability of selecting a red marble is
[tex]P=\frac{5}{3+5+4}=\frac{5}{12}_{}[/tex]Remember that the probability is the ratio between the number of events and the total number of all the events. In this case, the number of events is 5 because there are 5 red marbles, and the total number of all events is the sum of all the marbles.
Therefore, the probability of selecting red marbles is 5/12.
Part B.[tex]P=\frac{5}{12}\cdot\frac{4}{11}\cdot\frac{3}{10}=\frac{5\cdot4\cdot3}{12\cdot11\cdot10}=\frac{60}{1320}=\frac{30}{66}=\frac{15}{33}[/tex]Notice that we have three different ratios, that is because each time we select a red marble it represents a different situation since we won't place back the red marble into the bag, that's why each event decreases by one and each denominator too.
Therefore, the probability of selecting three red marbles without replacement is 15/33.
Part C.As we said before, in Part B, we had to multiply each probability for each time we select a red marble. It's important to notice that the numerators decreased by 1 (5,4,3) because each time we select a marble we won't place it back, that's the reason why the denominator also decreased by 1.
Help its due in 5 hours. And I haven’t got the answer right for 2 hours.
Explanation
the volume of a cone is given by:
[tex]\text{Volume}=\frac{1}{3}\pi\cdot r^2\cdot h[/tex]Step 1
find the radius:
let
Circumference= 6n inches
radius= r
[tex]\begin{gathered} \text{Circumference = 2 }\cdot\pi\cdot radius \\ \text{replace} \\ 6n\text{ inches=2}\cdot\pi\cdot\text{ r} \\ \text{divide both sides by 2}\pi \\ \frac{6n\text{ }}{2\pi}\text{=}\frac{\text{2}\cdot\pi\cdot\text{ r}}{2\pi} \\ so \\ r=\frac{6n\text{ }}{2\pi}=\frac{3n}{\pi} \\ r=\frac{3n}{\pi} \end{gathered}[/tex]Step 2
apply the formula for the volume of the cone:
let
h=13 inhces
[tex]\begin{gathered} r=\frac{3n}{\pi} \\ h=13\text{ inches} \end{gathered}[/tex]replace.
[tex]\begin{gathered} \text{Volume}=\frac{1}{3}\pi\cdot r^2\cdot h \\ \text{Volume}=\frac{1}{3}\pi\cdot(\frac{3\text{ n}}{\pi})^2\cdot13 \\ \text{Volume}=\frac{1}{3}\pi\frac{(9n^2)}{\pi^2}\cdot13 \\ \text{Volume}=\frac{3n^2}{\pi}\cdot13 \\ \text{Volume}=\frac{39n^2}{\pi}in^3 \end{gathered}[/tex]so, the answer is
[tex]\begin{gathered} \text{Volume}=\frac{39n^2}{\pi}in^3 \\ \text{Volume}\approx\frac{39n^2}{\pi}in^3 \\ \text{Volume=}12.41n^2inches^3 \end{gathered}[/tex]I hope this helps you
what is the constant of prportionality in the equation y= 5x
The constant of proportionality on the equation is 5.
What is constant of proportionality?
Constant of proportionality is defined as the ratio that relates two given value. When two values are directly or indirectly proportional to one another, there relation is expressed as y = kx.
We compare the general direct proportionality relation with the equation given.
The equation given : y = 5x
The direct relationship between y and x is :
y α x
y = kx - - - (1)
Where, y and x are variables and k is the constant of proportionality.
Comparing equation (1) with the equation given :
y = kx
y = 5x
We can observe that, k in the equation (1) equals to 5 in the given equation.
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George finished 1/4 of a level of his computer game in 1/3 of an hour. At this rate, how many levels can he finish in one hour?
Let x be the number of game he can finish in 1 hour
1/4 = 1/3 hour
x = 1 hour
cross-multiply
1/3 x = 1/4
Multiply both-side of the equation by 3
x = 3/4 of his level game
He can finish 3/4 of his level game in an hour
A train starts from rest and accelerates uniformly at 1.5m/s²
until it attains a speed of 30m/s. Find the time taken and the
distance travelled.
Answer:
V= 30m/s u=0 A=1.5, time t=? distance S=?
Step-by-step explanation:
to find time:
A=v-u/t
t=v-u/a
t =30-0/1.5
t = 20 secs
to find distance S
S= UT +½at²
S= 0×20+ 1.5×20²/2
s= 300m
Please help me to do this problem please.
In order to find the solution of this compound inequation, let's first divide it in two inequations:
[tex]\begin{cases}-2\le3x+4 \\ 3x+4<13\end{cases}[/tex]Solving the first inequation, we have:
[tex]\begin{gathered} -2\le3x+4_{} \\ -2-4\le3x \\ -6\le3x \\ -2\le x \end{gathered}[/tex]Now, for the second inequation, we have:
[tex]\begin{gathered} 3x+4<13 \\ 3x<13-4 \\ 3x<9 \\ x<3 \end{gathered}[/tex]Putting both solutions together:
[tex]-2\le x<3[/tex]So the correct option is C.
The airport parking lot charges $2.00 to enter and $3.00 per hour after that. Carmen has N dollars and wants to be able to determine the maximum number of hours she can park. How can Carmen determine the length of time she can afford to park her car in the parking lot?
Carmen can determine the length of time she can afford to park her car in the airport parking lot by first deducting the entrance fixed charge from her N dollars and then dividing the balance by the hourly rate.
What are the mathematical operations?The standard mathematical operations that combine numbers, variables, and operands to arrive at a defined output value are addition, subtraction, division, and multiplication.
In this situation, we can use the mathematical operations of subtraction and division to determine the length of time Carmen can park her car.
The fixed charge for entering the airport parking lot = $2
Hourly charger after the initial entrance = $3
The total amount of dollars possessed by Carmen = N dollars.
Let the length of time she can park there = l.
The maximum number of hours she can park is given by the function, F(l) = (N - 2)/3.
Thus, the best strategy for Carmen to determine her parking time at the airport parking lot based on her N dollars, the fixed entrance fee, and the variable cost per hour, is using the mathematical operations of subtraction and division.
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The area of a rectangular living room is 450 square feet. The length of the room is 15 feet less than three times the width.
The length of the rectangle is 30 feet and the width of the rectangle is 15 feet.
Let l be the length l the rectangle and w be the width of the rectangle.
The area of a rectangular living room is 450 square feet.
⇒ A = l × w
⇒ 450 = l × w ................(1)
The length of the room is 15 feet less than three times the width.
So we get an expression,
l = 3w - 15
Substitute above vale of l in equation (1)
450 = (3w - 15) × w
450 = 3w² - 15w
3w² - 15w - 450 = 0
w² - 5w - 150 = 0
(w - 15)(w + 10) = 0
w - 15 = 0 or w + 10 = 0
w = 15 or w = -10
But width of the rectangle cannot be -10
So, w = 15 feet
and l = 3(15) - 15
l = 30 feet
Therefore, the length of the rectangular living room is 30 feet and the width is 15 feet.
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8. If a triangle has the given side lengths of
16 and 24, determine the range of
values for the possible length of the 3rd
side.
Answer:
8 < L < 30
Step-by-step explanation:
The third side (L) can't be longer than or equal to the sum of the other two.
So. L < 30.
Also, it must be greater than 24-16 ie > 8
How to solve for 27-30 (X, Y, Z, and W)
27)
Opposite angles are equal.
x° angle is the opposite angle of the 90° angle.
Therefore, x°=90°.
28)
The 90° angle marked in the figure and the y° angles forms a linear pair.
Hence, both angles are supplementary. Supplementary angles sum upto 180°.
Therefore, we can write
[tex]\begin{gathered} y\degree+90\degree=180\degree \\ y\degree=180\degree-90\degree \\ y\degree=90\degree \end{gathered}[/tex]Therefore, y°=90°.
29)
In the figure, let z°+46°=p°.
From figure, we can see that the p° angle is the opposite angle of y° angle.
Since opposite angles are equal, we can write
[tex]\begin{gathered} p\degree=y\degree \\ z\degree+46\degree=y\degree \end{gathered}[/tex]Since from part 28, y°=90°, we get
[tex]\begin{gathered} z\degree+46\degree=90\degree \\ z\degree=90\degree-46\degree \\ z\degree=44\degree \end{gathered}[/tex]Therefore, zh=44e.
30)
From figure,
[tex]\begin{gathered} w\degree=y\degree+90\degree+z\degree \\ \end{gathered}[/tex]Substitute the known values.
[tex]\begin{gathered} w\degree=90\degree+90\degree+44\degree \\ w\degree=224\degree \end{gathered}[/tex]Therefore, w°=224°
What is the value of the expression -83 + (-56)
what’s the inverse of Y equals X squared -10 X
The inverse of the function y equals x squared - 10x (y = x² - 10x) is 5 ±√(x + 25).
What is an inverse function?An inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
First of all, we would translate the given word sentence into a function as follows:
y equals x squared - 10x ⇒ y = x² - 10x
In order to determine the inverse of this function f(x) = x² - 10x, we would interchange both the input value (x) and output value (y) as follows:
y = x² - 10x
x = y² - 10y
Next, we would add (half the coefficient of the y-term)² to both sides of the function as follows:
x + (-10/2)² = y² - 10y + (-10/2)²
x + 25 = y² - 10y + 25
x + 25 = (y - 5)²
±√(x + 25) = y - 5
Adding 5 to both sides of the function, we have:
5 ±√(x + 25) = y - 5 + 5
y = f⁻¹(x) = 5 ±√(x + 25)
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school children shared oranges as follows .Jonas got 1/3 of the total and the remaining were shared between Mary and Rejoice in the ratio 3:2. if Rejoice got 24 oranges How many did Jonas get
The appropriate choice of ratio will be given by
Jonas got 30 oranges
What is ratio?
Ratio determines the comparision among many quantities with the same unit.
Here,
Let Mary got 3x oranges and Rejoice got 2x oranges
By the Problem,
[tex]2x = 24[/tex]
[tex]x = \frac{24}{2}[/tex]
[tex]x = 12[/tex]
Number of oranges Mary got = [tex]12 \times 3[/tex]
= [tex]36[/tex]
Number of oranges shared between Mary and Rejoice = [tex]24 + 36[/tex]
= [tex]60[/tex]
Fraction of oranges shared between Mary and Rejoice = [tex]1 - \frac{1}{3}[/tex]
= [tex]\frac{3 - 1}{3}[/tex]
= [tex]\frac{2}{3}[/tex]
Total number of oranges = [tex]\frac{60}{\frac{2}{3} }[/tex]
= [tex]60 \times \frac{3}{2}[/tex]
= [tex]90[/tex]
Number of oranges Jonas got = [tex]90 \times \frac{1}{3}[/tex]
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What is 12 2/3 times 19 1/4? Put in your answer as a mixed number.
243.83
Step-by-step explanation:
Multiple: 38/
3
* 77/
4
= 38 · 77/
3 · 4
= 2926/
12
= 1463 · 2/
6 · 2
= 1463/
6
Answer:
[tex]243 \frac{5}{6}[/tex]
Step-by-step explanation:
Given multiplication:
[tex]12 \frac{2}{3} \times 19 \frac{1}{4}[/tex]
Convert the mixed numbers to improper fractions:
[tex]\implies \dfrac{12 \times 3+2}{3} \times \dfrac{19 \times 4+1}{4}[/tex]
[tex]\implies \dfrac{36+2}{3} \times \dfrac{76+1}{4}[/tex]
[tex]\implies \dfrac{38}{3} \times \dfrac{77}{4}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{ab}{cd}:[/tex]
[tex]\implies \dfrac{38\times77}{3\times4}[/tex]
[tex]\implies \dfrac{2926}{12}[/tex]
Divide the numerator and denominator by 2:
[tex]\implies \dfrac{2926 \div 2}{12 \div 2}[/tex]
[tex]\implies \dfrac{1463}{6}[/tex]
Convert to a mixed number:
[tex]\implies 243 \frac{5}{6}[/tex]
For x = -5, what is the value of 4x²-11x ?
Answer:
155
Step-by-step explanation:
4(-5)^2-11x
-5 squared is 25, times 4 =100, -11times-5 is 55 (positive) so 100+55=155
What is the linear equation of (1, -7); slope = -1
The linear equation of given point (1, -7) and slope -1 is y = -x - 6.
What is the point-slope form of linear equations?One of the three forms we can use to express a straight line is the point-slope form, also referred to as the point-gradient form. The general form of a linear equation is y - y₁ = m(x - x₁) where m is the slope and (x₁, y₁) is the point.It draws attention to the line's slope and one of the line's points (that is not the y-intercept).Given:
Point(x₁ , y₁) = (1, -7)
Slope = -1
By using the Point-slope form of the linear equations, we get
y - y₁ = m(x - x₁)
⇒ y - (-7) = -1(x - 1)
⇒ y + 7 = -x + 1
⇒ y = -x + 1 - 7
⇒ y = -x - 6
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Simplify (write without the absolute value sign) :
Problem 1 : |5-x|-|x+8|, if x>5
Problem 2 : |x − 2| + |8 − x| + 2, if 2 ≤ x < 8
Problem 3 : |x − 5| − |2 − x| + |x + 1|, if x ≥ 5
Problem 4 : |7 − x| + |4 − 2x| − |x − 8, if x < 2
Simplification of the given problems without absolute value sign:
1. |5-x|-|x+8|, if x>5 is equal to -13.
2. |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.
3. |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.
4. |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.
As given,
Simplification of the given problems without absolute value sign:
1. |5-x|-|x+8|, if x>5
= x - 5-(x+8)
= x-5 -x-8
= -13
2. |x − 2| + |8 − x| + 2, if 2 ≤ x < 8
= x -2+ 8 -x+2
=8
3. |x − 5| − |2 − x| + |x + 1|, if x ≥ 5
= x-5-(x-2)+(x+1)
=x-5-x+2+x+1
=x-2
4. |7 − x| + |4 − 2x| − |x − 8, if x < 2
= 7-x +4-2x-8 +x
=3-2x
Therefore, simplification of the given problems without absolute value sign:
1. |5-x|-|x+8|, if x>5 is equal to -13.
2. |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.
3. |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.
4. |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.
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Logan starts an IRA (Individual Retirement Account) at the age of 24 to save for retirement. He deposits $300 each month. Upon retirement at the age of 65. his
retirement savings is $1,510,293.29. Determine the amount of money Logan deposited over the length of the investment and how much he made in interest upon
retirement.
Total deposited = $147600
Interest earned = $1362693.29
Total no. of years for saving = 65-36-24 = 41
years saving no. of months = 41 x12
= 492 Month
deposit for 1 month = $300 deposit for 492 month = 492 x $300= $147600
Total deposited = $147600
Total saving after retirement = $1,510,293.29 interest = total saving - total deposit= $1,510,293.29 - $147600
= $1362693.29
What is the Interest Rate ?Interest is a periodically paid interest amount related to the amount borrowed, deposited or borrowed (the so-called capital amount). The total interest on the amount borrowed or borrowed depends on the principal amount, the interest rate, the frequency of the interest and the time of loan, deposit or borrowing.
Annual interest is interest for one year. Other interest rates apply to different periods of time, such as a month or a day, but are usually calculated annually.
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P, R and S are points on a circle
centre O. If PÔR = 150°, calculate PSR
The measure of angle PSR is 105°.
What does the Angle Subtended by an Arc of a Circle Theorem state?An arc's angle at the center of the circle is twice as large as its angle at any other point on the circumference.
Given:
The centre of the circle is O.
P, R, and S are points on a circle.
∠POR = 150°
Let Q be a point on the circumference of the circle with centre O.
By half angle property,
∠POR = 2∠PQR
∠PQR = [tex]\frac{1}{2} * 150[/tex] = 75°
In the figure, the points on the circle PQRS form a cyclic quadrilateral.
A cyclic quadrilateral has opposite angles that measure a total of 180 degrees.
∠PQR + ∠PSR = 180°
∠PSR = 180° - 75°
∠PSR = 105°
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f(x)=7x-9, f(a +9),what’s the answer HELPME
Step-by-step explanation:
substitute a+9 in place of x in f(x) f(a+9)= 7(a+9) -9 = 7a+63-9 = 7a+54Be Precise An orchard contains 12 rows of Granny Smith apple trees, 10 rows of Fuji apple trees, 15 rows of Gala apple trees, 2 rows of Golden Delicious apple trees, and 2 rows of Jonathan apple trees. Write each ratio in three ways.
Ratio in three ways are given below.
What is ratio?The ratio is the number that can be used to represent one quantity as a percentage of another, to put it simply. A ratio's two numbers can only be compared if they share the same unit. Ratios are used to compare two objects. a connection between two values that is typically expressed as the quotient of one value divided by the other. For instance, the ratio of red to blue marbles is 6:4, or six red to four blue marbles, in the case of a box containing six red and four blue marbles. A decimal or percentage can also be used to indicate a ratio.
Given Data
An orchard contains 12 rows of Granny Smith apple trees, 10 rows of Fuji apple trees, 15 rows of Gala apple trees, 2 rows of Golden Delicious apple trees, and 2 rows of Jonathan apple trees.
a) Rows of Gala apple trees to Granny apple smith trees:
Ratio
First way = 15 to 12
Second way = 15:12
Third way = [tex]\frac{15}{12}[/tex]
b) Rows of Fuji apple trees to total number of apple trees
Total number = 12 + 10 + 15 + 2 +2
Total number = 41
Rows of Fuji apple trees = 10
First way = 10 to 41
Second way = 10: 41
Third way = [tex]\frac{10}{41}[/tex]
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Identify the domain and range of y = [x] + 2.
DOMAIN X CAN BE ALL REAL NUMBERS.
NO MATTER THE VALUE OF X YOU INSERT IT WILL ALWAYS TURN POSITIVE PLUS A POSTIVE TWO. MEANING THERE IS NO WAY THAT YOUR Y CAN BE EQUAL TO 0 OR A NEGATIVE NUMBER THE FUNCTION IS ALWAYSINCREASING FOR ANY VALUE OF Y.RANGE: Y IS ALL THE REAL NUMBERS GREATER THAN 0.
The price of silver dropped a total of $14 in 3 and a half hours. What was the average change in price per hour?
average change in price of silver per hour is $ 4 .
WHAT IS UNITARY METHOD ?With the unitary method, you can solve issues by first calculating the value of a single unit, then multiplying that value by the quantity of units required.
CALCUATION$14 price dropped in 3 and half hours i.e. in 3.5hrs
so in 1 hour price dropped will be = 14 / 3.5
= $ 4 per hour
therefore average drop rate of price of silver per hour is $ 4 .
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Rachel can finish the job in 5 hours, while Carl can finish the same job in 8 hours.
How long will it take them to finish the job together?
Answer:
use keywords together. So I think all you have to do is multiply or add them both together. Try multiplying or adding but I know that those are part of the answer.
Step-by-step explanation:
To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars.
The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.
What is meant by expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
The dollar amount the club would contain if they reached half of their goal T + 50.
The dollar amount the club would contain if every student at the school donated 50 cents to the cause 0,5T.
The dollar amount the club could donate if they earned $50 more than their goal of 0.25n.
The dollar amount the club would still require to expand to achieve its goal after every student at the school donated 50 cents 0.5n.
The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.
The complete question is:
To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars. Match each quantity to an expression, an equation, or an inequality that describes it. A: the dollar amount the club would have if they reached half of their goal 1: B: the dollar amount the club would have if every student at the school donated 50 cents to the cause 2: C: the dollar amount the club could donate if they made $50 more than their goal 3: D: the dollar amount the club would still need to raise to reach its goal after every student at the school donated 50 cents 4: E: the dollar amount the club would have if half of the students at the school each gave 50 cents 5: Which statement matches with T + 50?
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Help me Plss is very hard and i need an answer
Line C has the constant of proportionality between y and x of 2/3.
What is defined by constant of proportionality?The proportionality constant is the constant value of the ratio of two proportional quantities. When the ratio or product of two varying quantities yields a constant, they are said to be in a proportional relationship.For the given question;
Constant of proportionality = change in y / change in x
Check for each line;
Line A; select any coordinate from the graph.
(7, 3); Put in the formula
Constant of proportionality = 7/3
Thus, Line A has Constant of proportionality between y and x of 7/3.
Line B; select any coordinate from the graph.
(4, 3); Put in the formula
Constant of proportionality = 4/3
Thus, Line B has Constant of proportionality between y and x of 4/3.
Line C; select any coordinate from the graph.
(2, 3); Put in the formula
Constant of proportionality = 2/3
Thus, Line C has Constant of proportionality between y and x of 2/3.
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17. Marlene drove 540 miles to visit a friend. She drove 3 hours and stopped
for gas. She then drove 4 hours and stopped for lunch. How many
more hours did she drive if her average speed for the trip was 60 miles
per hour?
0.5 hours
Step-by-step explanation:
60 mph for 7 hours = 60×7= 420 miles
540-420=120 miles left
60mph÷120miles= 0.5 hours
The measures of the exterior angles of a triangle are 5x°, 9x°, and 10x°. Find the
measure of the largest exterior angle.
The measure of largest exterior angles is 150 degrees
What are exterior angles?Exterior angles are defined as angles of a polygon formed or created by two the sides of that polygon and sharing a common endpoint.
It is important to note that the exterior angle of a triangle is congruent to the sum of the two non-adjacent interior angles that are opposite to each other.
They are also known to be angles formed by a transversal line as it cuts through one of two lines and it is located on the outside part of the line.
Given the angles as;
5x°9x°10x°Note that the sum of exterior angles are 360degrees
5x° + 9x° + 10x° = 360°
collect like terms
24x = 360
Make 'x' the subject of formula by dividing both sides by 24
x = 360/24
x = 15
But the largest angle is 10x = 10(15) = 150°
Hence, the value is 150°
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Find the circumference of a circle with area
[tex] \frac{1}{ 4} \pi \: d {}^{2} cm {}^{2} [/tex]
The circumference of circle is [tex]\pi[/tex]d
What is a circle ?
A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or center, and the fixed distance between each point and the origin is referred to as the radius.
Given that : the circle with area =[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]
area of circle is =[tex]\pi r^{2}[/tex]
[tex]\pi r^{2}[/tex]=[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]
on comparing we get
r = [tex]\frac{d}{2}[/tex]
circumference of circle is 2[tex]\pi r[/tex]
= 2×[tex]\pi[/tex]×[tex]\frac{d}{2}[/tex]
=[tex]\pi[/tex]d
The circumference of circle is [tex]\pi[/tex]d
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