Answer:
[tex]\textsf{area of a sector}=\dfrac{\theta\pi r^2}{360\textdegree} \mathsf{\ \ (where\ \theta \ is\ in\ degrees)}[/tex]
Given:
radius (r) = 6 cm[tex]\theta[/tex] = 60°[tex]\implies \textsf{area}=\dfrac{60\textdegree \times\pi \times 6^2}{360\textdegree}[/tex]
[tex]\implies \textsf{area}=\dfrac{2160\pi}{360}[/tex]
[tex]\implies \textsf{area}=6\pi \textsf{ cm}^2[/tex]
[tex]\implies \textsf{area}=18.85\textsf{ cm}^2 \textsf{ (nearest hundredth)}[/tex]
Factor completely 16x8 − 1. (4x4 − 1)(4x4 1) (2x2 − 1)(2x2 1)(4x4 1) (2x2 − 1)(2x2 1)(2x2 1)(2x2 1) (2x2 − 1)(2x2 1)(4x4 − 1).
The factors of the expression specified is given by: Option B: [tex](2x^2 - 1)(2x^2 + 1)(4x^4 + 1)[/tex]
What are some basic properties of exponentiation?If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c[/tex]
What is the product result of (a+b)(a-b) ?Suppose two numbers are there as 'a' and 'b'.
Then, we get:
[tex](a+b)(a-b) = a(a-b) + b(a-b) = a^2 -ab + ab - b^2 = a^2 - b^2\\(a+b)(a-b) = a^2 - b^2[/tex]
For the considered case, factoring the considered expression [tex]16x^8 - 1[/tex] by rewriting it as:
[tex]16x^8 - 1 = (4 \times 4 \times x^4 \times x^4) - 1^2 = (4x^4)^2 -1^2\\\\\\[/tex]
Now, since we've got [tex](a+b)(a-b) = a^2 - b^2[/tex], therefore,
[tex]16x^8 - 1 = (4x^4)^2 -1^2\\16x^8 - 1 = (4x^4 +1 )(4x^4 - 1)[/tex]
The second term can also be factored using same property, as shown below:
[tex]16x^8 - 1 = (4x^4 +1 )(4x^4 - 1) = (4x^4 + 1)((2x^2)^2 - 1^2) \\16x^8 - 1 = (4x^4 + 1)(2x^2 + 1)(2x^2 - 1)\\\\\text{Rearranging the terms, we get}\\16x^8 - 1 = (2x^2 - 1)(2x^2 + 1)(4x^4 + 1)[/tex]
Therefore, the factors of the expression specified is given by: Option B: [tex](2x^2 - 1)(2x^2 + 1)(4x^4 + 1)[/tex]
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Answer:
Option B
Step-by-step explanation:
I took the test.
161,743 vinyl records were sold in 1967.
Answer:
yes thats right 161,743 vinyl records were sold in 1967.
Choose the student who modeled the relationship correctly in a table.
Beatriz makes $7.80 per hour.
Zohar's work. A 2-column table with 3 rows. Column 1 is labeled Dollars (x) with entries 7.80, 15.60, 23.40. Column 2 is labeled hours (y) with entries 1, 2, 3.
Felipe's work. A 2-column table with 3 rows. Column 1 is labeled hours (x) with entries 1, 2, 3. Column 2 is labeled dollars (y) with entries 7.80, 15.60, 23.40.
Leonie's work. A 2-column table with 3 rows. Column 1 is labeled 1 (x) with entries 2, 3, 4. Column 2 is labeled 7.80 (y) with entries 1, 2, 3.
Answer:
The second choice
Step-by-step explanation:
Answer: Felipe's work!
Step-by-step explanation:
Blake is signing a lease for a studio apartment that rents for $425/month. How much will Blake pay to move in if he must pay the first and last months’ rent and a security deposit equal to 50% of his monthly rent? $637. 50 $850. 00 $1062. 50 $1275. 0.
Answer:
(c) $1062.50
Step-by-step explanation:
The total of the rental and security deposits amounts to two and a half months' rent:
2.5 × $425 = 1062.50
It will cost Blake $1062.50 to move in.
please help im struggling so much
Answer:
B. y=-10,250
C. 6 payments
Sorry for my terrible handwriting.. Hope this helps tho! Have a great day/night!
PLS HELP GIVEING BRANLIEST
Answer:
25
Step-by-step explanation:
2 to the power of 4 + 16
3 to the power of 2 = 9
so, 16 + 9 is 25...
Step-by-step explanation:
[tex] {2}^{4 + } {3}^{2} [/tex]
=2x2x2x2+3x3
=16+9
=25
NEED HELP ASAPP
A car uses fuel at a rate of 15 miles per gallon. Predict how many miles the car can travel on 31.5 gallons of fuel.
Answer:
472.5 Miles
Step-by-step explanation:
1:15
10:150
20:300
30:450
.5:7.5
30x+1x+5x=450+15+7.5=472.5 miles
What is 6 out of 120 expressed as a percentage
Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should the length of the third side be). Write the inequalities for each case. 22 and 15
Answer: 7<x<37
Step-by-step explanation:
help!
(1) x-m/n+m=x-n/n-m
(2) simplify:
(3)
Answer:
x=0,(m+n)
Step-by-step explanation:
what is the measure of angle y ?
Answer:
163 degrees
Step-by-step explanation:
because the whole circle is 360 degrees and the other side would be 163 as it's the same angle.
PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS
Answer:
DC
Step-by-step explanation:
DC is the diameter AE is the radiusDB is a chordBC is very short cordSo the series is
DC>DB>AE>BCAnswer:
b. DC
b. 15
Step-by-step explanation:
Point A = center of circle
The widest part of the circle is the diameter. The diameter is a straight line that touches the circumference of the circle and passes through the center of the circle. Therefore, the diameter is DC, and this is the longest line segment.
The radius of a circle is a straight line from the center of the circle to a point on the circumference. Therefore, AE = radius of the circle.
The radius of a circle is half the length of the diameter.
Therefore, if AE = 7.5, then DC = 2 × 7.5 = 15
what is(12^2)^7*12 as single exponent?
Answer:
12^15
Step-by-step explanation:
(12^2)^7 would be 12^14 because the two exponents (2 and 7) will multiply each other. Then, you do 12^14 * 12, which would be 12^15 because you are multiplying 12 by itself one more time.
Suppose that p partners equally share the profits from a sale of $3,600. Which algebraic expression represents this situation?
3600 + p
3600 minus p
3600 p
StartFraction 3600 over p EndFraction PLEASE ASAP
Answer:
3600/p
Step-by-step explanation:
i think it's the last option because you cannot add or subtract the partners from the profit.
Solve the quadratic equation x2 − 4x = 21 by factoring.
Answer:
[tex]x=7, x=-3[/tex]
Step-by-step explanation:
Bring the 21 on the LHS:
[tex]x^2-4x-21=0[/tex]
At this point we need to find two numbers whose product is -21, and whose sum is -4.
From the product we can tell that one has to be positive, and one is negative.
From the sum, we can tell that the greater of the two is negative.
At this point we look at the factors of 21: 1,3,7,21.
In particular, 3 and -7 added togheter do -4, which is what we need. At this point we can factor the trinomial as
[tex](x-7)(x+3)=0[/tex]
Considering that a product is zero if any of the factors is zero, it's:[tex]x-7=0 \rightarrow x=7\\x+3=0 \rightarrow x=-3[/tex]
Solve the following word problems using the BUCKS strategy. Remember to show your work.
Pete rented a bike from Bob’s Bikes. It costs $13 plus $5 for every hour. If Pete paid $23, then how many hours did he rent the bike for?
Answer:
5 is the answer of the question
Answer:
He rent the bike for 2 hours.
Step-by-step explanation:
5x + 13= 23
I honestly just 13+5= 18
Then 18+5= 23
That is how I knew it was 2 hours.
It probably wasn't the right way to do it, but it was the way I thought it through. Sorry if this doesn't help. Have a great day.
In Rectangle ABCD diagonals AC and BD intersect at point P. If PD = 4x and AC = 88, solve for x.
Answer: 11
In rectangle diagonals are equal and bisect each other.
Therefore,
2×4x=88
8x=88
x=88÷8
x=11
Step-by-step explanation:
Please help me solve this. its very simple. you will get a lot of points too.
The equation has one solution and it is x = 91/30
Let's take a glimpse at the solution
[tex]6 + 9( - 3x + 9) = \frac{3}{2} (2x + 4) - 10[/tex]
[tex]6 - 27x + 81 = \frac{3}{2} \times 2(x + 2) - 10[/tex]
[tex]6 - 27x + 81 = 3(x + 2) - 10[/tex]
[tex]6 - 27x + 81 = 3x + 6 - 10[/tex]
[tex] - 27x + 81 = 3x - 10[/tex]
[tex] - 27x - 3x = - 10 - 81[/tex]
[tex] - 30x = - 91[/tex]
[tex]x = \frac{91}{30} [/tex]
The hardware store sells white buckets, which hold 5 liters of water, and red buckets, which hold 6 liters.
Jayce bought 10 buckets. His buckets will hold 55 liters in total. How many of each type of bucket did
Jayce buy?
white buckets
red buckets
Submit
Please help!!! I’ll mark you brainliest if you answer!!!
Answer:
The cordinate is (7,6)
Step-by-step explanation:
First you count how many squares (units) until you are directly under P. Then you cound how many squares up it is till you get to P.
Have an amazing day!
Please rate!
Answer:
7,6
Step-by-step explanation:
cuz yes
Fill in the missing statement and reason for the proof below.
Given: AB = AC and BE = CE
Prove: BDE = CDE
The length of adult parakeets is normally distributed. If the mean length is 8 inches with a standard deviation of 0.25 inches, what is the probability that a randomly selected adult parakeet will be less than 7.55 inches long?
There is a probability of 3.95% that the randomly selected adult parakeet will be less than 7.55 inches long
What is z score?Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
Given that:
Mean = 8 inches, standard deviation = 0.25 in, For < 7.55 in:
z = (7.55 - 8) / 0.25 = -1.8
P(z < -1/8) = 0.0395
There is a probability of 3.95% that the randomly selected adult parakeet will be less than 7.55 inches long
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Aaron is having his birthday party at King's Castle Laser Tag. He is making crowns for his guests to wear. He opens a bag of 100 stick-on gems. His sister asks for some, so he gives her 12 gems. He evenly divides the remaining gems among the 8 crowns.
Answer: 11 gems
Step-by-step explanation:
After Aaron gives 12 gems to his sister, he is left with 100-12 gems = 88 gems.
If he divides the gems evenly among the crowns, each one will have 88/8 gems = 11 gems.
HELPPP FOR BRIANLEST???!
Answer:
3/17
Step-by-step explanation:
multicolored and 1 passenger (3) over total (17)
3/17 doesn't simplify
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,596 was collected on the sale of 1,216 tickets. How many of each type of ticket were sold?
Step-by-step explanation:
Suppose adult tickets are x ticket
Student tickets are 1216 - x ticket
x(5) + (1216 - x)(1) = 2596
5x + 1216 - x = 2596
4x = 2596 - 1216
4x = 1380
x = 345
Adult tickets have 345 tickets
and student tickets have 1216 - 345 = 871 tickets.
Find the equation of the line that passes through the point (8, - 3) and is perpendicular to the line y = 1/2x - 2.
Answer: y+3=0.5(x-8)
Step-by-step explanation:
Find the measure of b.
Answer:
I'm not so sure but it's 90°
PLEASE HELP DUE SOON! THANK YOU ( Will give brainliest!!!)
Consider that a barn loft is shaped like a rectangular pyramid, as ahsown. Calculate the volume of the loft.
A)2,750 ft3
B)4,375 ft^3
C)6,425 ft^3
D)13,125 ft^3
Answer:
B
Step-by-step explanation:
answer is B, 4,375 ft^3
[tex]V= \frac{lwh}{3}=\frac{25 x 35 x 15}{3} = 4 ,375ft^3[/tex]
(x = multiplication symbol)
what is the output on this graph when the input is 2?
How to find input and output from the co-ordinates on the graph?
If a pair be (x,y) then x is the input and y is the outputHere the co-ordinate having x=2 is
(2,0)So the output is 0
Every pair have ( x , y ) which means x is input and y is output .
Here , input is 2 (x)
then , let output be y ( indicate with 0 )
So , the co- ordinates are ( x , y ) = ( 2 , 0 ) .
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
These two triangular prisms are similar. Figure 2 is similar to figure 1 by a scale factor of 4.
If the perimeter of [tex]ABC[/tex] is 21 cm, the perimeter of [tex]PQR[/tex] is cm.
The perimeter of the face PQR is 84 cm.
What is perimeter?The perimeter of an object is the sum of the lengths of the sides of the object.
Given that, there are two similar triangular prisms. Figure 2 is similar to figure 1 by a scale factor of 4.
We know that, the ratio of the perimeters of similar objects is equal to their scale factor.
Therefore,
P(ABC) / P(PQR) = 1/4
21 / P(PQR) = 1/4
P(PQR) = 84
Hence, the perimeter of the face PQR is 84 cm.
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