Answer:
Step-by-step explanation:
by using formula (a+b)^2=a^2+2ab+b^2
in these two we have to just open the formula
(3x+2y)^2
=(3x)^2+2(3x)(2y)+(2y)^2
=9x^2+12xy+4y^2
(3y+2x)^2
=(3y)^2+2(3y)(2x)+(2x)^2
=9y^2+12xy+4x^2
Which function g(x) or f(x) has the equation y=x^2-4
Answer:
f x
Step-by-step explanation:
the equqtion's y intercept is -4 , and f (x) has that intercept
Answer:
f(x)
Step-by-step explanation:
The equation says -4 meaning that it moved down 4 spaces on the y-axis.
i ned help with this asap. im not well with percentages
Answer:
160
Step-by-step explanation:
Add up all the numbers
48 + 67 + 16 + 29 = 160
Answer: D. 160
Step-by-step explanation:
Find the area of the shaded figure
Answer:
its 56 units square.
Step-by-step explanation:
(count the tiles in the shaded figure, you'll get the area)
A messenger earns 2640 per year and pays tax at the rate of 10k On a naira how much tax does he pay in the year
Answer:
264 naira
Step-by-step explanation:
Given that:
Amount earned per year = 2460
Rate of interest paid : 10k per naira earned
Tax paid by messenger per year :
100k = 1 naira
10k = (100/10) = 0.1 naira
Hence 0.1 naira is paid as tax on every naira earned
Total amount paid on 2640 Naira :
Amount paid per naira * total amount earned
(0.1 * 2640) = 264 naira
Regular hexagon ABCDEF is inscribed in circle X and has an apothem that is 6√3 inches long. Use the length of the apothem to calculate the exact length of the radius and the perimeter of regular hexagon ABCDEF. In your final answer, include your calculations.
Answer:
Part A
[tex]The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}[/tex]
Plugging in the given values we get;
[tex]The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12[/tex]
R = 12 inches
The radius of the circumscribing circle is 12 inches
Part B
The length of each side of the hexagon, 's', is;
[tex]s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)[/tex]
Therefore;
[tex]s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12[/tex]
s = 12 inches
The perimeter, P = n × s = 6 × 12 = 72 inches
The perimeter of the hexagon is 72 inches
Step-by-step explanation:
The given parameters of the regular hexagon are;
The length of the apothem of the regular hexagon, a = 6·√3 inches
The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;
[tex]a = R \cdot cos \left(\dfrac{\pi}{n} \right)[/tex]
Where;
n = The number of sides of the regular polygon = 6 for a hexagon
'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;
Part A
Therefore, we have;
[tex]The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}[/tex]
Plugging in the values gives;
[tex]The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12[/tex]
The circumradius, R = 12 inches
Part B
The length of each side of the hexagon, 's', is given as follows;
[tex]s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)[/tex]
Therefore, we get;
[tex]s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12[/tex]
The length of each side of the hexagon, s = 12 inches
The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches
The perimeter of the hexagon = 72 inches
Answer: radius = 12, perimeter = 72
Step-by-step explanation:
We know that in 30-60-90 right triangles, the hypotenuse is exactly twice the length of the short leg and the long leg is the short leg times √3.
so therefore, if the long leg (apothem) is equal to 6√3, the short leg is equal to 6
long leg = 6√3
long leg = short leg √3
short leg = 6
hypotenuse (radius) = 2(short leg)
hypotenuse (radius) = 2(6)
hypotenuse (radius) = 12
The radius of hexagon ABCDEF = 12 inches
Perimeter = r (sides)
Perimeter = r (6)
Perimeter = 12 (6)
Perimeter = 72
The perimeter of hexagon ABCDEF = 72 inches
At a team meeting, 80% of the tennis team was there. If there were 12
people at the meeting, how many
people are on the team?
Answer:
15 people
Step-by-step explanation:
let x=total # of people on the team
80%=12
80/100=12/x
cross multiply
80x=1200
division property of equality (divide both sides by 80)
x=15
There are 15 people on the team.
g(n) = -72*(1/6)^n-1 complete the recursive formula
The recursive formula for g(n) is:
g(1) = -72 (base case)
g(n) = [tex]g(n-1) \times (-1/6)[/tex] (for n > 1)
A recursive formula is a formula that defines a sequence or function by expressing each term in terms of one or more previous terms.
It is a way of defining a sequence or function iteratively, where each term or value depends on the previous terms or values.
To find the recursive formula for [tex]g(n) = -72\times (1/6)^{(n-1)} ,[/tex] we need to express the function in terms of its previous term, g(n-1).
Notice that g(n) can be obtained by multiplying g(n-1) by -1/6.
This is because:
[tex]g(n) = -72\times (1/6)^{(n-1)}[/tex]
[tex]g(n-1) = -72\times (1/6)^{(n-2) }[/tex]
So we can write:
[tex]g(n) = g(n-1) \times {(-1/6) }[/tex]
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Find P(A') given that P(A) = 0.75
Answer:
I'm not sure what you're asking if P (A) = 0.75 P(A) is equal to 0.75
1
y>
5x + 3
What is the y-intercept
(xy)
What is the slope
Will the line be solid or dotted
Given:
The inequality is:
[tex]y>5x+3[/tex]
To find:
The y-intercept, slope and type of line (solid or dotted).
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept.
We have,
[tex]y>5x+3[/tex]
The relation equation is:
[tex]y=5x+3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=5[/tex]
[tex]b=3[/tex]
It means the slope is 5 and the y-intercept is 3.
The sign of the inequality in the given inequality is ">". It means the boundary line is not included in the solution set. So, the boundary line is a dotted line.
Therefore, the slope is 5, the y-intercept is 3 and the line is a dotted line.
What is the length of AC?
Answer:
2nd option
;)
I did this before-
Step-by-step explanation:
What is the equation of a circle with center (−3, 0) and radius 20?
Answer:
(x + 3)^2 + y^2 = 20^2
Step-by-step explanation:
If the center is (-3, 0), then the standard equation of a circle, (x - h)^2 + (y - k)^2 = r^2 becomes (x + 3)^2 + (y - 0)^2 = 20^2, or
(x + 3)^2 + y^2 = 20^2
helpp!!! i need help with this!
Answer:
51
Step-by-step explanation:
The two tangent lines can be set equal to each other
10x - 19 = 4x + 23
Solve for x
10x - 19 = 4x + 23
-4x -4x
6x - 19 = 23
+19 +19
6x = 42
6 6
x = 7
Plug in x and solve for FE
10x - 19 = 10(7)-19 = 51
Find the sum of (x + 5), (–4x –2), and (2x – 1).
PLEASE HELP!!!
Answer:
-x-2
Step-by-step explanation:
x+5 + -4x -2 + 2x -1 = -x -2
Answer:
-x + 2
Step-by-step explanation:
(x + 5), (-4x -2), and (2x -1)
x + (-4x) + 2x) + (5 + -2 + -1)
= -x + 2
2 x + y = 25 3 x − y = 15
Answer: Yeah and ?
Step-by-step explanation:
Answer:
(15,-5)
Step-by-step explanation:
I need an answer! NOT A LINK!!! ASAP!
Answer:
im pretty sure its 14
Step-by-step explanation:
A bag contains 30 ping-pong balls, each with a different number written on it from 1 to 30. What is the probability of selecting a ball with a number that is less than 13?
Answer:
...
Step-by-step explanation:
Answer:
so you have a 40% chance or 2/5 chance
Step-by-step explanation:
30 numbers in total
12 are less than 13
so you have a 12/30
simplify
2/5 = 0.4 or 40%
What is the equation used to find the nth term of the arithmetic sequence:
-8, -5 -2, 1, 4
Answer:
aₙ = 3n - 11Step-by-step explanation:
The equation of the nth term of the arithmetic sequence is: [tex]a_n =a_1+d(n-1)[/tex]
d = -5 - (-8) = - 5 + 8 = 3
a₁ = -8
Therefore:
[tex]a_n =-8+3(n-1)\\\\a_n =-8+3n-3\\\\a_n =3n-11[/tex]
x-3=2x-3-x
Please solve with answer and how you got the answer
Answer:
3x-3
Step-by-step explanation:
You have to combine like terms. x and 2x have the same variable, so this equals 3x, and then you subtract 3 so:
x-3=2x-3-x
=3x-3
The first four terms of an arithmetic sequence are shown below.
1, 5, 9, 13,......
(a) Write down the nth term of the sequence (general formula).
(b) Calculate the 100th term of the sequence.
(c) Find the sum of the first 100 terms of the sequence.
Answer:
a) n = 4(n-1)+1
b) 397
c) 19900
Step-by-step explanation:
Plz help me solve and show your work.
Hi there!
[tex]\large\boxed{h = \frac{15x}{y}}[/tex]
Recall the volume of a pyramid is:
V = 1/3(bh)
We are given the volume and side length of the base. Find the area of the base:
A = s²
A = (5xy²)² = 25x²y⁴
Plug in the solved for base:
125x³y³ = 1/3(25x²y⁴)h
To isolate for h, begin by multiplying both sides by 3:
375x³y³ = (25x²y⁴)h
Divide both sides by 25x²y⁴. Use the following exponent property:
xᵃ / xᵇ = xᵃ⁻ᵇ
Thus:
375x³y³ / 25x²4⁴ = 15x/y.
The height must be equal to:
[tex]h = \frac{15x}{y}[/tex]
You're a quality control manager in a fruit juice company. You want to choose
a sample size for a quality check on the cans used to package the juice. From
a batch of 30,000 cans, you want a sample size that will allow you to closely
approximate the population parameters for the entire batch. Which sample
size will most likely produce the least variability among different samples?
Answer:
246.
Step-by-step explanation:
a) The 95% confidence level two-tail confidence interval for the mean value of the key index of this batch is between 98.22 and 99.78
b) The minimum sample size to achieve this is 246.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find the margin of error M as such
In which is the standard deviation of the population(square root of the variance) and n is the size of the sample. So in this question,
The lower end of the interval is the sample mean subtracted by M. So it is 99 - 0.78 = 98.22
The upper end of the interval is the sample mean added to M. So it is 99 + 0.78 = 99.78.
a) The 95% confidence level two-tail confidence interval for the mean value of the key index of this batch is between 98.22 and 99.78
(b) (5 points) If we want the sampling error to be no greater than 0.5, what is the minimum sample size to achieve this based on the same confidence level with part (a)
We need a sample size of n
n is found when
Then
Rounding up
The minimum sample size to achieve this is 246.
the base of a jewelry box is a square with a side length of 5 1/2 inches. the box is 2 inches high. what is the volume of the box?
The volume of the jewelry box is 60 1/2 cubic inches.
The area of a square with a side length of 5 1/2 inches can be found by multiplying the length of one side by itself, giving:
Area = (5 1/2) × (5 1/2) = 30 1/4 square inches
The height of the box is 2 inches.
Therefore, the volume of the jewelry box can be found by multiplying the area of the base by the height of the box, giving:
Volume = Area x Height = (30 1/4) × 2 = 60 1/2 cubic inches
Thus, the volume of the jewelry box is 60 1/2 cubic inches.
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Which expression is equivalent to
5(3x+3)−7x?
Answer:
38x
Step-by-step explanation:
A hexagonal aquarium needs to hold 10 gallons of water and be 24 inches tall. What should be the area of the hexagon?
Answer:
240
Step-by-step explanation:
7th grade simple solutions math 85-88
Answer:
-3 85-88 lets turn that around 88-85 is 3 but the problem is 85-88 so its -3
Step-by-step explanation:
Answer:-3 (88-85=3
Step-by-step explanation:
Find the unit rate 5 cars for 20 people
Answer:
4 people per car
Step-by-step explanation:
To find the unit rate we would have to do
20/5=4
a penny is dropped from a height of 144 ft. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is h(t) = 16t^2 - 144.
answers
t = 9seconds
t = 3 seconds
t = 18 seconds
t = 10 seconds
Answer:
The time of fall is 9 seconds
Step-by-step explanation:
We are asked to find the time between when the penny was dropped and when it landed.
To do this, we have to start with what we are given and see how we can relate it to find what we are looking for.
From the problem, we are given the equation which represents the height which the penny travels as it falls. It is given by
[tex]h(t) = 16t^2 - 144.[/tex] ----------- equation 1
in addition to that, we are also given that h = 144ft at the end of the fall; that is, where t = t max, and h = hmax
Hence, it is safe to say that at the end of the fall, that the heigh is no more changing. This means that dh/dt = 0
We can now differentiate equation 1 above to get
h max = 16t - 0 ------------- equation 2
recall that h max = 144
plugging the value of h max into equation 2, we have
144 = 16t
t = 9 seconds
Therefore the time of fall is 9 seconds
Answer:
t= 3 seconds
Step-by-step explanation:
I took the quiz and this is the answer
This box is 3/4 inch long, 1/2 inch wide, and 1/4 inch deep. What is the volume of the box?
A: 3/16 inch ^3
B: 3/8 inch ^3
C: 3/32 inch ^3
D: 1 1/2 inch ^3
The volume of the box is 3/32 inch³. The correct option is C: 3/32 inch ^3
Calculating VolumeFrom the question, we are to determine the volume of the box
The volume of a box is given by the formula,
V = l × w × h
Where V is the volume
l is the length
w is the width
h is the height or depth
From the given information,
l = 3/4 inch
w = 1/2 inch
h = 1/4 inch
Thus,
Volume of the box = 3/4 × 1/2 × 1/4
Volume of the box = 3/32 inch³
Hence, the volume of the box is 3/32 inch³. The correct option is C: 3/32 inch ^3
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Please answer correctly !!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
For every 7 books Ethan read, Sadie read 3 books.
Step-by-step explanation:
For every 21 books Ethan read, Sadie read 9 books.
Unsimplified Ratio = 21:9
21 and 9 have a common factor of 3.
Because 21 and 9 share a common factor we can simplify the ratio
21 / 3 = 7
9 / 3 = 3
The new ratio is 7 to 3
So for every 7 books Ethan read, Sadie read 3 books.
In 2000 there were about 2172000 farms in the United States twenty four thousand of the farms were in South Carolina what percent of the farms were in South Carolina
Answer:
the percentage of the farms were in SOuth caroline is 1.10%
Step-by-step explanation:
The computation of the percentage of the farms were in SOuth caroline is shown below:
= NUmber of farms in south carolina ÷ number of farms in united states
= 24000 ÷ 2172000
= 1.10%
Hence, the percentage of the farms were in SOuth caroline is 1.10%
We simply used the above formula so that the percentage could come