The First One Is True Then The Next One Is A.B=3 And The Last One Is D.A=3.48
Hope It Helps And PLEASE MARK ME THE BRAINLYEST
A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm. What is the area of the pentagon, rounded to the nearest tenth? 13.8 cm2 17.3 cm2 32.7 cm2 69.0 cm2
plz dont ask for a pic i cant put one
Answer:
[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]
Step-by-step explanation:
Given that a regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.
we have to find the area of pentagon.
Apothem=a=3 cm
Perimeter=s=21.8 cm
[tex]\text{Area of regular pentagon=}\frac{1}{2}\times apothem\times perimeter[/tex]
[tex]\frac{1}{2}\times s \times a[/tex]
[tex]=\frac{1}{2}\times 21.8\times 3[/tex]
[tex]=\frac{65.4}{2}=32.7 cm^2[/tex]
[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]
Option 3 is correct.
To estimate 179% of 41 by rounding use the expression
Answer:
To estimate 179% of 41 by rounding, use the expression
✔ 180%(40)
.
Using the distributive property, the expression is equivalent to
✔ (100%)(40) + (80%)(40)
.
179% of 41 is about
✔ 72
.
Step-by-step explanation:
The sum of the squares of two consecutive positive even integers is 340. what are the integers?
While driving your rental car on your trip to Europe, you find that you are getting 12.4 kilometers per liter of gasoline. What does this correspond to in miles per gallon? PLEASE HELP ME!!!!
A circle could be circumscribed abut the quadrilateral below
Answer:
B. False.
Step-by-step explanation:
We have been given an image of a quadrilateral. We are asked to determine whether a circle could be circumscribed about the given quadrilateral.
We know that opposite angles of a cyclic quadrilateral are supplementary.
Let us check is this true for our given quadrilateral or not.
[tex]m\angle B+m\angle D=180^{\circ}[/tex]
[tex]80^{\circ}+60^{\circ}=180^{\circ}[/tex]
[tex]140^{\circ}\neq 180^{\circ}[/tex]
Now let us check other pair of angles.
[tex]m\angle A+m\angle C=180^{\circ}[/tex]
[tex]110^{\circ}+110^{\circ}=180^{\circ}[/tex]
[tex]220^{\circ}\neq 180^{\circ}[/tex]
Since opposite angles of our given quadrilateral are not supplementary, therefore, a circle could not be circumscribed about the given quadrilateral.
Subtract. (x2+3x−7)−(3x2−5x+3) Express the answer in standard form.
Answer is -2x^2+8-10 hope this helps!!!!
What is the length of the diagonal of a square with side lengths 7 square root of 2 ? round to the nearest tenth if necessary?
The length of the diagonal of a square with side lengths 7√2 is approximately 14.1 units.
Explanation:The length of the diagonal of a square can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides. Since a square has all sides equal, the length of each side can be represented as 7√2. Substituting this value into the Pythagorean theorem, we get:
Diagonal² = (7√2)² + (7√2)²
Diagonal² = 98 + 98 = 196
Taking the square root of 196, we find the length of the diagonal to be approximately 14 units. Rounding to the nearest tenth gives us 14.1 units.
1. if a dozen eggs (12 eggs) are worth 3 cowry shells, how much would 6 dozen be worth?
a. 9 cowry shells
b. 36 cowry shells
c. 18 cowry shells
d. 15 cowry shells
2. I have 7 cowry shells. If a dozen eggs (12 eggs) cost 3 cowry shells, how many dozens can i purchase?
a. 21 dozen
b. 2 dozen
c. 9 cowry dozen
d. 3 dozen,
Explain in a short paragraph how the figure below shows this is a right triangle, by the converse of the Pythagorean Theorem.
Arthur borrowed $380 for six months, with $67 monthly payments. How much interest will he pay on this loan?
Given is the borrowed amount = 380 dollars.
Repayment period = 6 months.
Monthly installments = 67 dollars.
After six months, total repaid amount would be sum of all six monthly installments i.e. 6 x 67 = 402 dollars.
The interest to be paid on this loan would be difference of total repaid amount and borrowed amount.
Interest paid = Repaid amount - Borrowed amount
Interest = 402 dollars - 380 dollars
Interest = 22 dollars.
So, he would pay 22 dollars as interest on this loan.
Which of these statements is true for f(x)....
Answer:
B. the y -intercept is (0,3)
Step-by-step explanation:
If b is the midpoint of ac and the length of ac is 23.8 what is the length of ab
Line AB and BC for a right angle at point B. If A(-3,4) and B(4,4) what is the equation of line BC?
Answer: The required equation of line BC is [tex] x=4.[/tex]
Step-by-step explanation: As shown in the attached figure, lines AB and BC meet at right angle at the point B. The co-ordinates of point A and B are (-3, 4) and B(4, 4).
We are to find the equation of line BC.
We know that the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the line AB will be
[tex]m=\dfrac{4-4}{4-(-3)}\\\\\Rightarrow m=0.[/tex]
Therefore, the equation of the line AB is
[tex]y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.[/tex]
Since y = constant is the equation of a line parallel to X-axis, so its perpendicular line will be parallel to Y-axis.
So, its equation will be of the form
x = constant.
Since the line BC is perpendicular to AB passing through the point (4, 4), so we must have
[tex]x=4.[/tex]
Thus, the required equation of line BC is [tex] x=4.[/tex]
A customer who opens a savings account at a bank, in turn, becomes a(n) _____.
A. lender
B. investor
C. insurer
D. borrower
@lulu22,
Write this number in standard form.
1 x 1 + 8 x 1/100 + 9 x 1/1000,
The following set of numbers is going to be graphed on a histogram.
3, 19, 11, 29, 4, 6, 10, 16, 2, 21, 15, 22, 13, 9, 1, 17, 2, 26, 18, 7
If there are going to be six intervals in the display, what is the length of each interval?
1.) 5
2). 6
3.) 3
Answer:
The answer is 5.
Step-by-step explanation:
Are the number of steps in a stairway continuous or discrete data
Answer:
The number of steps in a stairway is discrete.
Step-by-step explanation:
A discrete data is that, which can take only integer values like number of apples in a basket.
But the continuous data is that, which can take on any value like a decimal. For example, the weight of patients in a hospital.
So, the number of steps in a stairway will be a discrete data. As stairs are counted in whole numbers and not decimals.
In the diagram below of right triangle ACB, altitude CD is drawn by hypotenuse AB. if AB= 36 and AC= 12, what is the length of AD?
The length of AD is 18 units.
To find the length of AD, we can use the fact that the altitude from the right angle of a right triangle divides the triangle into two smaller similar triangles.
Let's denote the length of AD as x.
Since triangle ADC and triangle CDB are similar to triangle ACB, we can set up the following proportions:
For triangle ADC:
AD / AC = CD / AB
For triangle CDB:
BD / AC = CD / AB
We already know that AC = 12, AB = 36, and CD = x. So, let's substitute these values into the proportions:
For triangle ADC:
x / 12 = CD / 36
For triangle CDB:
(36 - x) / 12 = CD / 36
Now, let's solve these equations:
From the first equation:
x / 12 = CD / 36
x = (12 * CD) / 36
x = CD / 3
From the second equation:
(36 - x) / 12 = CD / 36
36 - x = (12 * CD) / 36
36 - x = CD / 3
Now, let's solve for CD using the second equation:
36 - x = CD / 3
36 - (CD / 3) = CD / 3
36 = (2 * CD) / 3
CD = (36 * 3) / 2
CD = 54
Now that we have found CD, we can substitute it into the first equation to find x:
x = CD / 3
x = 54 / 3
x = 18
So, the length of AD is 18 units.
A bank offers a CD that pays a simple interest rate of 5.5%. How much must you put in this cd now in order to have $8000 for a kitchen remodeling project in two years? Could you please show work?,
NASA cameras film a rocket launcher vertically
which of the following statements is not always true ?
a. if a function contains the origin , then its inverse contains the origin.
b.if a function has 3 x-intercepts, then its inverse has 3 y-intercepts.
c.if a function contains no points in the fourth quadrant, then its inverse contains no points in the second quadrant.
d.if the slope of a linear function is less than 1, then the slope of its inverse is greater than 1.,
Which expression represents the sixth term in the binomial expansion of (2a - 3b)10?
10C5(2a)5(-3b)5
10C5(-2a)5(3b)5
10C6(2a)4(-3b)6
10C6(-2a)4(3b)6
10C6(2a)6(-3b)4
10C6(-2a)6(3b)4
Answer:
[tex]^{10}C_5(2a)^{5}(-3b)^5[/tex]
Option 1 is correct.
Step-by-step explanation:
Given: [tex](2a-3b)^{10}[/tex]
We need to find 6th term of binomial expansion.
Formula:
[tex]T_{r+1}=^nC_rx^{n-r}y^{r}[/tex]
We need to find 6th term, [tex]T_6[/tex]
[tex]T_6=T_{r+1}[/tex]
So, r=5
Put r=5 into formula
[tex]n=10, x=2a \text{ and }y=-3b[/tex]
[tex]T_6=^{10}C_5(2a)^{10-5}(-3b)^5[/tex]
Now we will simplify it to calculate 6th term
[tex]T_6=^{10}C_5(2a)^{5}(-3b)^5[/tex]
Hence, The 6th term of binomial is [tex]^{10}C_5(2a)^{5}(-3b)^5[/tex]
The expression that represents the sixth term in the binomial expansion of (2a - 3b)¹⁰ is expressed as ¹⁰C₆(2a)⁴(-3b)⁶.
To find the sixth term in the binomial expansion of (2a - 3b)¹⁰, we can use the binomial theorem,
which states that the k-th term in the expansion of (a + b)ⁿ can be calculated using the following formula:
T(x) = C(n, x) × (aⁿ⁻ˣ) × (bˣ)
Where:
T(x) is the x-th term in the expansion.
C(n, x) is the binomial coefficient, also denoted as "n choose x," and it is equal to n! / (x! × (n-x)!), where "!" denotes factorial.
a is the first term in the binomial (2a in this case).
b is the second term in the binomial (-3b in this case).
n is the exponent of the binomial (10 in this case).
x is the term we want to find (the sixth term in this case).
Now, let's calculate the sixth term:
x = 6
n = 10
a = 2a
b = -3b
First, calculate the binomial coefficient:
C(10, 6) = 10! / (6! × (10-6)!)
C(10, 6) = 210
Now, plug these values into the formula:
T(6) = 210 × (2a)¹⁰⁻⁶ × (-3b)⁶
Simplify the exponents:
T(6) = 210 × (2a)⁴ × (-3b)⁶
T(6) = 210 × 16a⁴× 729b⁶
Now, multiply the constants:
T(6) = 30,240a⁴b⁶
Therefore, the sixth term in the binomial expansion of (2a - 3b)¹⁰ is 30,240a⁴b⁶ which is written as ¹⁰C₆(2a)⁴(-3b)⁶.
learn more about binomial expansion here
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A complex number, will, in general, have ____ fifth roots.
What is the blank?,
What we know about prime and common factors help us to find the ___________ of two or more numbers.
Answer:
greatest common factor the largest factor that any given numbers have in common
Step-by-step explanation:
so the answer is greatest common factor
Final answer:
Knowledge of prime and common factors is essential for finding the greatest common divisor (GCD) or greatest common factor (GCF) of two or more numbers, a key element in simplifying fractions and understanding ratios.
Explanation:
Understanding prime and common factors is instrumental in finding the greatest common divisor (GCD) or greatest common factor (GCF) of two or more numbers. The GCD is the highest number that divides evenly into each of the numbers in question. For example, the GCD of 48 and 60 is 12 since 12 is the largest number that can divide both 48 and 60 without leaving a remainder. Finding the GCD is crucial in simplifying fractions, solving problems involving ratios, and is also a fundamental concept in more advanced mathematics including algebra and number theory.
The process often involves factoring the numbers down to their prime factors, identifying the common primes, and then multiplying these common prime factors together to find the GCD. This method not only highlights the importance of prime numbers in the mathematical hierarchy but also underlines the indelible role of factorization in simplifying and solving numerical problems.
Claudia dumped her 200-penny coin collection on the floor and counted the number of pennies that landed heads up. Claudia repeated this process 5 times and had an average of 84 pennies landing heads up on each try. Which of the following statements is true?
If Claudia had repeated this process fewer times, the average number of pennies landing heads up would be closer to 100.
Each penny has a greater probability of landing heads up than tails up.
The theoretical probability of a penny landing heads up is
If Claudia had repeated this process more times, the average number of pennies landing heads up would be closer to 100.
Find all the zeros of the equation. Need help finding the zeros.
-3 x^{4} } +27 x^{2} +1200=0
Final answer:
The zeros of the equation -3x^4 + 27x^2 + 1200 = 0 can be found by substituting y = x^2 to create a quadratic equation, solving for y using the quadratic formula, and then solving for x for each y value found.
Explanation:
To find all the zeros of the equation -3x^4 + 27x^2 + 1200 = 0, we can treat the equation as a quadratic in form by substituting y = x^2, which reduces the equation to -3y^2 + 27y + 1200 = 0. This is now a standard quadratic equation that can be solved using the quadratic formula, y = (-b ± sqrt(b^2 - 4ac))/(2a), where a = -3, b = 27, and c = 1200. Once we find the values for y, we substitute back x^2 = y to get the values of x which are the zeros we are looking for.
The quadratic equation would provide us with two values for y, say y1 and y2. For each y value found, we solve for x by taking the square root, resulting in two x values for each y, giving us a total of four zeros for the original quartic equation.
we can re-write our expression as:
-3a^2+27a+1200=0
-3(a^2-9a-400)=0
a^2-9a-400=0
factorizing the above we have:
a^2+16a-25a-400=0
a(a+16)-25(a+16)=0
(a+16)(a-25)
thus replacing back x^2 we have:
(x^2+16)(x^2-25)
=(x^2+16)(x-5)(x+5)
factorizing (x^2+16) we get
x^2=+/-√-16
x=+/-4i
thus the zeros of the expression are:
x=-5, x=5 , x=-4i, x=4i
Find the missing value to the nearest whole number of tan x° =0.9
We have to find the missing value to the nearest whole number of tan x° =0.9.
Since, tan x° =0.9
To evaluate the missing value of 'x', we will take [tex] \arctan (0.9) [/tex]
So, [tex] x^{\circ}=\arctan (0.9) [/tex]
Now, we will find the value of [tex] \arctan (0.9) [/tex]using the calculator, we get,
[tex] x^{\circ}=\arctan (0.9)=41.9^{\circ}=42^{\circ} [/tex]
So, the missing value of 'x' to the nearest whole number is [tex] 42^{\circ} [/tex].
PLEASE HELP ASAP!!!!!!!!!!!!!!
Properties of Parallelograms
find x.
An organization president conducts a survey to see where the next convention should be held. She uses a list of 1008 members in alphabetical order and selects every 10th member to participate in the survey. An organization is conducting a survey to see where their next convention should be held. They use a list of their 1008 members listed in alphabetical order and selects every 10th member to participate in the survey Is this sample valid or not valid, and why? A not valid; Since 1008 divided by 10 is not a whole number, there are 8 members who are not accounted for. B not valid; The survey chooses only members of the organization. C valid; There is no bias in the survey. D not valid; The survey chooses only every 10th member.
Answer:
The correct option is:
Option: C
C valid; There is no bias in the survey.
Step-by-step explanation:
It is given that:
An organisation president uses a list of 1008 members in alphabetical order and selects every 10th member to participate in the survey.
So, the sample used by her is a valid sample.
Since, she sets a random rule to choose the members to participate in the survey.
The sample used by her is unbiased.
( Since, the aim of our survey questions are to capture an unbiased opinion to capture the true sentiments of the survey taker )
Hence, the correct statement regarding her survey is:
C. valid; There is no bias in the survey