Answer:
The number 540 has the following divisors
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
Step-by-step explanation:
The number 540 has the following divisors
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
Therefore, the number 540 is not a prime number or a deficient number
A deficient number is one that is larger than the sum total of its possible dividing numbers less the number 540 itself that is we have;
1+ 2+ 3+ 4+ 5+ 6+ 9+ 10+ 12+ 15+ 18+ 20+ 27+ 30+ 36+ 45+ 54+ 60+ 90+ 108+ 135+ 180+ 270 = 1140.
Answer:
[tex]540 = 3 ^{3} \times 2 {}^{2} \times 5[/tex]
so, it is 4*3*2= 24
In the triangles, Line segment B C is-congruent-to line segment D E and Line segment A C is-congruent-to line segment F E. Triangles A B C and F D E are shown. The lengths of sides A C and F E are congruent. The lengths of sides B C and D E are congruent. If m Angle C is greater than m Angle E, then Line segment A B is ________ Line segment D F. Congruent to longer than shorter than the same length as
Answer:
Longer than
Step-by-step explanation:
The lengths of sides A C and F E are congruent. The lengths of sides B C and D E are congruent. Therefore:
AC = FE, BC = DE
Also m∠C is greater than m∠E
∠C is the angle opposite to line AB and ∠E is the angle opposite to line DF. Since AC = FE, BC = DE and m∠C is greater than m∠E. The length of a side of a shape is proportional to its opposite angle, since the opposite angle of AB is greater than the opposite angle of DF therefore AB is greater than DF
From the given two triangles under the given conditions of congruency, we can say that;
Line segment AB is longer than Line segment FD.
CongruencyThe image showing both triangles is missing and so i have attached it.
From the attached image, we see that BC is congruent to DE and AC is congruent to FE. Thus, if Angle BCA was congruent to angle DEF, then the it means that both triangles would be congruent as well, because it would satisfied the Side Angle Side (SAS) congruence postulate.Therefore, we can say that line AB and line FD do not have the same length.
Now, we see that angle BCA is larger than angle DEF, and as such we can say that the line segment AB is longer than line segment FD.
Read more about congruency at; https://brainly.com/question/3168048
The 4th term of an exponential sequence is 108 and the common ratio is 3. Calculate the value of the eighth term of the sequence.
Answer:
The eighth term is 8748Step-by-step explanation:
Since the sequence is a geometric sequence
For an nth term in a geometric sequence
[tex]A (n) = a ({r})^{n - 1} [/tex]
where
a is the first term
r is the common ratio
n is the number of terms
To find the eighth term we must first find the first term
4th term = 108
common ratio = 3
That's
[tex]A(4) = a ({r})^{4 - 1} [/tex]
[tex]108 = a ({3})^{3} [/tex]
[tex]27a = 108[/tex]
Divide both sides by 27
a = 4The first term is 4For the eighth term
[tex]A(8) = 4 ({3})^{8 - 1} [/tex]
[tex]A(8) = 4({3})^{7} [/tex]
The final answer is
A(8) = 8748The eighth term is 8748Hope this helps you
To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade? 14% 17% 55% 67%
Answer: 14%
Step-by-step explanation:
Complete question is provided in the attachment below:
Probability that members of the junior varsity swim team wear glasses = 55%=0.55
Given: P(wear glasses) = 0.55
P(not wear glasses) = 1-0.55 = 0.45
P(member in 10th grade | not wear glasses) = 30%
Using conditional probability formula:
[tex]P(B|A)=\dfrac{P(A\text{ and } B)}{P(A)}[/tex]
[tex]\Rightarrow\ 0.30=\dfrac{P(\text{not wear glasses and in 10th grade})}{0.45}\\\\\Rightarrow\ P(\text{not wear glasses and in 10th grade})=0.45\times0.30\\\\0.135=13.5\%\approx14\%[/tex]
Hence, the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade = 14%.
So, the correct option is "14%".
I REALLY need help with these 3 questions plz!!!!
Answer:
6. No. See explanation below.
7. 18 months
8. 16
Step-by-step explanation:
6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.
Let's find the GCF of 85 and 99:
85 = 5 * 17
99 = 3^2 + 11
5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.
Answer: No because the GCF of 85 and 99 is 1.
7.
We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.
6 = 2 * 3
9 = 3^2
LCM = 2 * 3^2 = 2 * 9 = 18
Answer: 18 months
We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.
Month Charlie Dasha
1 home home
2 home home
3 home home
4 home home
5 home home
6 trip home
7 home home
8 home home
9 home trip
10 home home
11 home home
12 trip home
13 home home
14 home home
15 home home
16 home home
17 home home
18 trip trip
Answer: 18 months
8.
First, we find the prime factorizations of 96 an 80.
96 = 2^5 * 3
80 = 2^4 *5
GCF = 2^4 = 16
Answer: 16
The height of the sail on a boat is 7 feet less than 3 times the length of its base. If the The area of the sail is 68 square feet, find its height and the length of the base.
Step-by-step explanation:
It is given that,
The height of the sail on a boat is 7 feet less than 3 times the length of its base.
Let the length of the base is x.
ATQ,
Height = (3x-7)
Area of the sail is 68 square feet.
Formula for area is given by :
[tex]A=lb\\\\68=x(3x-7)\\\\3x^2-7x=68\\\\3x^2-7x-68=0[/tex]
x = 8 feet and x = -3.73 feet
So, length is 8 feet
Height is 3(8)-7 = 17 feet.
So, its height and the length of the base is 17 feet and 8 feet respectively.
A company ships coffee mugs using boxes in the shape of cubes. The function g(x) = gives the side length, in inches, for a cube with a volume of x cubic inches. Suppose the company decides to double the volume of the box. Which graph represents the new function?
Answer:
The graph is attached below.
Step-by-step explanation:
The volume of the box containing the coffee mugs is,
[tex]V=x^{3}[/tex]
Then the function representing the side length, in inches, for the box is:
[tex]g(x)=x[/tex]
Now, it is provided that the company decides to double the volume of the box.
That is, the new volume will be:
[tex]V_{n}=2x^{3}[/tex]
Then the side length, in inches, for the box will be:
[tex]g_{n}(x)=\sqrt[3]{2x^{3}} =\sqrt[3]{2}x[/tex]
Then the graph representing the function, formed using the following points is:
[tex]x\ \ \ \ \ \ \ \ \ g_{n}(x)\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\0\ \ \ \ \ \ \ \ \ \ \ 0\\1\ \ \ \ \ \ \ \ \ \ \ 2^{1/3}[/tex]
Answer:
c
Step-by-step explanation:
Choose all true statements.
All real numbers are rational numbers.
Some rational numbers are natural numbers.
No real numbers are irrational numbers.
All whole numbers are integers.
Some integers are natural numbers.
No rational numbers are integers.
Answer:
- All real numbers are rational numbers. FALSE
- Some rational numbers are natural numbers. TRUE
- No real numbers are irrational numbers. FALSE
- All whole numbers are integers. TRUE
- Some integers are natural numbers. TRUE
- No rational numbers are integers. FALSE
Answer: B,D, and E
Step-by-step explanation:
A. All real numbers are rational numbers.
B. Some rational numbers are natural numbers
C.No real numbers are irrational numbers.
D.All whole numbers are integers.
E. Some integers are natural numbers.
F. No rational numbers are integers.
Initial Knowledge Check
Question 2
Suppose that $4000 is placed in an account that pays 11% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year
sc
(b) Find the amount in the account at the end of 2 years.
?
Answer:
Step-by-step explanation:
We first need to figure out what the equation is for this set of circumstances before we can answer any questions. We will use the equation
[tex]A(t)=P(1+r)^t[/tex] which is just another form of an exponential equation where
(1 + r) is the growth rate, P is the initial investment, and t is the time in years. We will fill in the values we know first to create the equation:
[tex]A(t)=4000(1+.11)^t[/tex] which simplifies to
[tex]A(t)=4000(1.11)^t[/tex]
Now we'll just sub in a 1 for t and solve, then a 2 for t and solve.
When t = 1:
A(t) = 4000(1.11) so
A(t) = 4440
When t = 2:
[tex]A(t)=4000(1.11)^2[/tex] which simplifies to
A(t) = 4000(1.2321) so
A(t) = 4928.40
Find the missing the side of the triangle. A. 0 yd B. 30−−√ yd C. 25–√ yd D. 17−−√ yd
Answer:
Step-by-step explanation:
This a right triangle so we will use the Pythagorian theorem. x is the hypotenus.
■■■■■ Pythagorian theorem ■■■■■
● x^2 = √10^2 + √10^2
● x^2 = 10 + 10
● x^2 = 20
● x = √20 yd
If today is Friday, what day will it be in 51 days?
Show your thinking.
Answer:
SundayStep-by-step explanation:
Each weekday repeats every 7 days.
51 = 49 + 2 = 7•7 + 2
So 49 days from now also will be Friday .
Two days later will be Sunday.
So in 51 days will be Sunday.
Which of the following equations has roots x = 3 (multiplicity 3) and x = -i?
A. f(x) = x3 - 3x2 + x - 3
B.f(x) = x + 9x4 + 28x3 + 36x2 + 27x + 27
C.f(x) = x - 9x4 + 28x3 – 36x2 + 27x – 27
D.f(x) = x3 + 3x2 + x + 3
Answer:
The first and third polynomials have roots in x = 3 and x = -i. (A, C)
Step-by-step explanation:
The quickest form to determine if [tex]x = 3[/tex] and [tex]x = -i[/tex] are roots consist in evaluating each polynomial and proving that result is zero.
A. [tex]f(x) = x^{3}-3\cdot x^{2}+x-3[/tex]
x = 3
[tex]f(3) = 3^{3}-3\cdot (3)^{2}+3-3[/tex]
[tex]f(3) = 27-27+3-3[/tex]
[tex]f(3) = 0[/tex]
x = -i
[tex]f(-i) = (-i)^{3}-3\cdot (-i)^{2}-i-3[/tex]
[tex]f(-i) = i + 3-i-3[/tex]
[tex]f(-i) = 0[/tex]
B. [tex]f(x) = x^{5}+9\cdot x^{4}+28\cdot x^{3} + 36\cdot x^{2}+27\cdot x +27[/tex]
x = 3
[tex]f(3) = 3^{5}+9\cdot (3)^{4}+28\cdot (3)^{3}+36\cdot (3)^{2}+27\cdot (3)+27[/tex]
[tex]f(3) = 2109[/tex]
x = -i
[tex]f(-i) = (-i)^{5}+9\cdot (-i)^{4}+28\cdot (-i)^{3}+36\cdot (-i)^{2}+27\cdot (-i)+27[/tex]
[tex]f(-i) = -i+9 -28\cdot i +36-27\cdot i +27[/tex]
[tex]f(-i) = -56\cdot i +64[/tex]
[tex]f(-i) = 64 -56\cdot i[/tex]
C. [tex]f(x) = x^{5}-9\cdot x^{4}+28\cdot x^{3} - 36\cdot x^{2}+27\cdot x -27[/tex]
x = 3
[tex]f(3) = (3)^{5}-9\cdot (3)^{4}+28\cdot (3)^{3}-36\cdot (3)^{2}+27\cdot (3)-27[/tex]
[tex]f(3) = 0[/tex]
x = -i
[tex]f(-i) = (-i)^{5}-9\cdot (-i)^{4}+28\cdot (-i)^{3}-36\cdot (-i)^{2}+27\cdot (-i)-27[/tex]
[tex]f(-i) = -i - 9+28\cdot i+36-27\cdot i-27[/tex]
[tex]f(-i) = 0[/tex]
D. [tex]f(x) = x^{3}+3\cdot x^{2}+x+3[/tex]
x = 3
[tex]f(3) = (3)^{3}+3\cdot (3)^{2}+(3)+3[/tex]
[tex]f(3) = 60[/tex]
x = -i
[tex]f(-i) = (-i)^{3}+3\cdot (-i)^{2}+(-i)+3[/tex]
[tex]f(-i) = -i+3-i+3[/tex]
[tex]f(-i) = 6-i\,2[/tex]
The first and third polynomials have roots in x = 3 and x = -i. (A, C)
What is the volume of the rectangular prism 3 1/2, 5 1/4,4 in
Answer:
73.5in³
Step-by-step explanation:
You multiply the three numbers.
3.5x5.25x4=73.5in³
What is the coefficient of the variable in the expression 6 − 4x − 8 + 2
Answer:
-4
Step-by-step explanation:
6 − 4x − 8 + 2
The variable is x
The coefficient is the number in front of the variable ( it will include the sign)
-4 is the coefficient
Answer:
-4
Step-by-step explanation:
One of the students in the class scored 100 on the midterm but got overconfident, slacked off, and scored only 15 on the final exam. No other student in the class "achieved" such a dramatic turnaround. If the instructor decides not to include this student’s scores when constructing a new regression model, will the slope of the new line increase or decrease?
Answer:
Increase
Step-by-step explanation:
Since your not including the bad mark, it'd increase.
Quina is cooking fish for a group of travelers quina has 78 huge fish and each fish can feed 3 travelers. how many travelers can Quina feed?
Answer:
234 people
Step-by-step explanation:
1 fish = 3 people
Multiply each side by 78
1*78 = 3 *78
78 fish = 234 people
Answer:
234 traveling people
Step-by-step explanation:
78 times 3 equals 234
Find the length of RA. A. 42 B. 84 C. 14 D. 7
Answer:
[tex]\large \boxed{\mathrm{B. \ 84}}[/tex]
Step-by-step explanation:
[tex]LU[/tex] bisects [tex]RU[/tex] and [tex]UA[/tex].
[tex]RU=UA[/tex]
[tex]3m+21=6m[/tex]
Solve for m.
Subtract 3m from both sides.
[tex]21=3m[/tex]
Divide both sides by 3.
[tex]7=m[/tex]
Calculate [tex]RA[/tex].
[tex]RA=3m+21+6m[/tex]
[tex]RA=9m+21[/tex]
Put m = 7.
[tex]RA=9(7)+21[/tex]
[tex]RA=63+21[/tex]
[tex]RA=84[/tex]
Answer:
B) 84
Step-by-step explanation:
ΔLRU ≅ ΔLAU {SAS congruent}
Therefore, UA = UR {CPCT}
6m = 3m +21
Subtract 3m from both sides
6m - 3m = 3m + 21 -3m
3m = 21
Divide both sides by 3
3m/3 = 21/3
m = 7
RA = RU + UA
= 3m + 21 + 6m {add like terms}
= 9m + 21 {Plug in m =7}
= 9*7 + 21
= 63 + 21
RA = 84 units
30 PTS!! Can someone PLEASE rephrase this? The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students.
Answer:
Step-by-step explanation:
This study investigated three mathematics teachers' construction process of geometric structures using compass and straightedge. The teacher-student-tool interaction was analysed. The study consists of the use of a compass and straightedge by the teachers, the ideas of the teachers about their use, and the observations regarding the learning process during the construction of the geometric structures. A semi-structured interview was conducted with the teachers about the importance of the use of a compass and straightedge to construct geometric structures. It was found that teachers taught compass and straightedge constructions in a rote manner where learning is little more than steps in a process. The study concludes with some suggestions for the use of a compass and straightedge in mathematics classes based on the research results. SUMMARY Purpose and significance: For more than 2,000 years, the way in which geometric structures could be constructed with the help of compasses and straightedges has caught the attention of mathematicians. Nowadays, mathematics curriculums place an emphasis on the use of the compass and straightedge. The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students. However, 'doing compass and straightedge construction early in the course helps students to understand properties of figures'
Help, Answer ASAP; will give brainliest
Answer:
a = 2, b = 3
Step-by-step explanation:
The diagonals of a rectangle bisect each other, thus
5a² = 4a² + 4 ( subtract 4a² from both sides )
a² = 4 ( take the square root of both sides )
a = [tex]\sqrt{4}[/tex] = 2
Also
6b - 8 = 4b - 2 ( subtract 4b from both sides )
2b - 8 = - 2 ( add 8 to both sides )
2b = 6 ( divide both sides by 2 )
b = 3
In 1 through 3, what is the relationship between the values of the given digits?
1. The 7s in 7,700
2. The 2's in 522
Answer:
7000 (7 thousand)
700 (7 hundred)
20 (2 tens)
2 (2 units)
Step-by-step explanation:
what is the relationship between the values of the given digits?
1. The 7s in 7,700
2. The 2's in 522
From the knowledge of place values;
7,700 could be broken down thus :
7000 + 700 + 0 + 0
The first 7 depicts thousands as it has 3 trailing digits (7000)
The second 7 depicts hundred as it has 2 trailing digits (700)
522 could be broken down thus :
500 + 20 + 2
From 522
The first '2' has one trailing digit = tens
The ending / last digit ia always = Unit value
a cone with base radius 7 cm has a volume of 308 cm cube find the vertical height of the cone take π 22/7
pls now
Answer:
h=6.003 cm
Step-by-step explanation:
[tex] \frac{1}{3} \pi {r}^{2} h \: \: is \: the \: volume \: of \: cone[/tex]
1/3×22/7×7×7×h=308
h=308/51.3
Answer:
h = 6 cm
Step-by-step explanation:
r = 7 cm
Volume of cone = 308 cm³
[tex]\frac{1}{3}\pi r^{2}h=308\\\\\\\frac{1}{3}*\frac{22}{7}*7*7*h=308\\\\\\h=\frac{308*3*7}{22*7*7}\\\\\\h=2*3[/tex]
h = 6 cm
12 farmers harvest the crops in a field in 20 hours. How much workers will be required to do the same work in 8 hours?
Answer:
x2 # of farmers
y2 # of hours
x1# unknown workers
x2# amount wanted
x1 y1 = x2 y2
x1 (8) = 12(20)
x1 = 12(20)/8
x1 = 30
30 Farmers needed to complete the same work in 8 hours.
Solve the system of equations.
y=-2x
y= x2 - 8
A. (-4, 8) and (2, -4)
B. (-2,-4) and (4,8)
C. (-4,-8) and (2, 4)
D. (-2, 4) and (4, -8)
Answer:
A. (-4,8) and (2,-4)
Step-by-step explanation:
Because you already have a value for "y" you can plug in that value of "y" into the next equation and then solve for Y and X
The expression f(x) = 12(1.035)* models the monthly growth of membership in the new drama club at a school. According to the function, what is the monthly growth rate?
Answer:
The monthly growth rate is 3.5%.
Step-by-step explanation:
The exponential growth function is given as follows:
[tex]y=a(1+r)^{x}[/tex]
Here,
y = final value
a = initial value
r = growth rate
x = time taken
The provided expression for the monthly growth of membership in the new drama club at a school is:
[tex]f(x) = 12\cdot(1.035)^{x}[/tex]
Comparing this function with the exponential growth function:
[tex]a(1+r)^{x}=12(1.035)^{x}\\\\a(1+r)^{x}=12(1+0.035)^{x}[/tex]
Then value of r is 0.035 or 3.5%.
Thus, the monthly growth rate is 3.5%.
NASA is painting the nose cone of a sounding rocket with a special sealant which reduces the air-drag on the rocket. If they need to do two coats of the sealant, how many square feet are they painting? Use π = 3.14.
Answer:
The formula for the lateral surface area (LSA) of a right cone is:
LSA = π x r x l
where: r as radius, and l as the slant height of the cone
If NASA need to do two coats of the sealant, the number of square feet that they are painting is: 2 x LSA = 2 x π x r x l
Step-by-step explanation:
Answer:
56.5 ft^2
Step-by-step explanation:
After you calulate the the surface area and double it, subtract the area of the circle.
-4 = BLANK - 9 what is BLANK
Answer:
5
Step-by-step explanation:
Let be blank be a
-4=a-9
-4+9=a
9-4=a
a=5
Proof:
-4=a-9
-4=5-9
-4=-4
Hope this helps ;) ❤❤❤
The value of BLANK in the given expression is 5.
To solve the equation "-4 = BLANK - 9",
Isolate the variable on one side of the equation.
To do this, we can add 9 to both sides of the equation:
-4 + 9 = BLANK - 9 + 9
This simplifies to:
5 = BLANK
So the value of BLANK is 5.
To solve the equation "-4 = BLANK - 9",
We can add 9 to both sides of the equation to isolate the variable.
This gives us the solution of BLANK = 5.
To learn more about equations visit:
https://brainly.com/question/29174899
#SPJ2
On the following number line, two rational numbers are graphed. Represent the two numbers as fractions (or mixed numbers) in lowest terms, and write two different expressions to represent the difference between them. Then, find the difference, showing all of your work.
Answer:
see explanation
Step-by-step explanation:
point on left is -1 and 3/6 = -9/6 = -3/2
point on right is 5/6
Difference 5/6 - -3/2 = 14/6 = 7/3
How would you write Five times the difference of a number and 7
Answer:
5(x-7)
Step-by-step explanation:
5(x-7) or 5x-35
Hope this helps!
P.S. Please give me brainliest. Thanks :)
Answer: 5*(x-7)
Step-by-step explanation:
no work needed
difference of a number means x
SOMEONE PLZ HELP ME ON THIS PROBLEM!!!!! I WILL GIVE BRAINLIEST TO THE BEST ANSWER!!!!!
Answer:
D
Step-by-step explanation:
End behaviour refers to the asymptotes, which both exponential functions have the same one at y = 2. However, they have different y - intercepts. The first one has a y - intercept of 4 and the second one has a y - intercept of 6. Thus, the answer is D.
Answer:
D. They have different y-intercepts but the same end behaviorStep-by-step explanation:
Let's name the function from graph: f
for f:
y-intercept = f(0) = 4
for x → ∞, f(x)→2
for g:
y-intercept = f(0) = 4(¹/₄)⁰+2 = 4•1+2 = 4+2 = 6 ≠4
f(1) = 4(¹/₄)¹+2 = 4•¹/₄+2 = 1+2 = 3
f(2) = 4(¹/₄)2+2 = 4•¹/₁₆+2 = ¹/₄+2 = 2¹/₄
f(3) = 4(¹/₄)³+2 = 4•¹/₆₄+2 = ¹/₁₆+2 = 2¹/₁₆
f((5) = 4(¹/₄)⁵+2 = 4•¹/₁₈₂₄+2 = ¹/₅₁₂+2 = 2¹/₅₁₂
....
so for x x → ∞, f(x)→2
select the shape of the graph of this two variable equation. y=4x^(2)-1
Answer:
The highest power of the equation is 2, since the equation is y = 4x^2 - 1. That means that the graph is a parabola. And because the 4 is positive, the parabola curves into a smile.
You can use the Math is Fun Function and Calculator to graph the parabola.
Hope this helps!
Find the midpoint of NP⎯⎯⎯⎯⎯ given N(2a, 2b) and P(2a, 0).
Answer:
(2a, b )
Step-by-step explanation:
Given the endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ [tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
Here (x₁, y₁ ) = N(2a, 2b) and (x₂, y₂ ) = P(2a, 0), thus
midpoint = [ [tex]\frac{1}{2}[/tex](2a + 2a), [tex]\frac{1}{2}[/tex](2b + 0 ) ] = (2a, b )
