what's the exact circumference of the circle
a. 7p cm
b. 5p cm
c. 10p cm
d. 4p cm
Answers
Answer:
B
Step-by-step explanation:
not sure
Related Questions
Determine whether the sequence shown are arithmetic or geometric 1,8,15,22,29
Answers
8 <--- 1 + 7
15 <--- 8 + 7
22 <--- 15 + 7
29 <--- 22 + 7
is simply adding "7" to get the next value, so is an arithmetic sequence, whose common difference is 7.
The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v 0 feet per second is r = 1 v 20 sin 2θ where r is measured in feet. a golfer strikes a golf ball at 120 feet per second. 32 ignoring the effects of air resistance, at what angle must the golfer hit the ball so that it travels 140 feet? (round answer to nearest angle.)
Answers
There are already derived equations for this so it is already convenient. However, your given equation for range is incomplete. The correct equation is:
R = v₀²sin2θ/g
where
R = 140 ft
v₀ = 120 ft/s
g = 32.2 m/s²
Substituting the values,
sin 2θ = Rg/v₀²
sin 2θ = (140)(32.2)/(120²)
sin 2θ = 0.313
2θ = sin ⁻¹ (0.313)
2θ = 18.24°
θ =18.24°/2
θ = 9.12°
The point (-2, 6) is on the line given by which of the equations below?
A.
y = 4x
B.
y = 2x
C.
y = 3x
D.
y = -3x
Answers
for (-2, 6) = (x, y) which also means that x = -2 and y = 6
A/ y = 4x => 6 = 4.(-2) <=> 6 = (-8) Absurd
B/ y = 2.x => 6 = 2.(-2) <=> 6 = (-4) Absurd
C/ y = 3x => 6 = 3.(-2) <=> 6 = (-6) Absurd
D/ y = -3x => 6 = (-3).(-2) <=> 6 = 6 Right Answer
The parabola has a vertex of (1,-16) and y intercept of (0,-15) that crosses the x axis in two places. one x intercept is (5,0) what is the other x intercept
Answers
y = a(x - 1)^2 - 16 where a is a cosntant
at y intercept we have
-15 = a^2 - 16
a^2 = 1
so equation of the parabola is y = (x-1)^2 - 16
the equation of symmetry is x = 1 and both roots are same distance either side of the point (1,0) so the other x-intercept is 1 - 4 = (-3,0)
the leg of a right triangle is 5 units and the hypotenuse is 8 units.what is the length in units of the other leg of the triangle
Answers
If you don't know, the Pythagorean Theorem states that for any right triangle the sum of the squares of both of the legs is equals to the hypotenuse.
[tex]a^2 + b^2 = c^2[/tex]
Where the variables a and b are the legs and c is the hypotenuse.
The variables a and b are interchangeable but not c.
Plug in the values that we know.
[tex]5^2 + b^2 = 8^2[/tex]
[tex]25 + b^2 = 64[/tex]
[tex]b^2 = 39[/tex]
[tex]b = \sqrt{39}[/tex]
So, the other leg is equal to the square root of 39 units.
The square of the hypotenuse is equal to the sum of the square of other two sides. The length in units of the other leg of the triangle is 6.2 units
What is Pythagoras theorem?The square of the hypotenuse is equal to the sum of the square of the other two sides.
Mathematically;
l^2 = a^2 + b^2
Given
l = 8 units
a = 5 units
Substitute
8^2 = 5^2 + b^2
64 - 25 = b^2
b^2 = 6.2units
Hence the length in units of the other leg of the triangle is 6.2 units
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The length of a rectangle is eight times it's width. If the length was decreased by 10 meters and the width decreased by 2 meters the area would be decreased by 162 m. Find the original dimensions.
Answers
(l-10)*(w-20)=a-162
Substituting l for 8w and a for l*w and then 8w*w, we have
(8w-10)(w-20)=8w^2-162=8w^2-160w-10w+200=8w^2-170w+200
8w^2-170w+200=8w^2-162 , so we subtract 8w^2 from both sides as well as subtract 200 to both to get -170w=-362, so w=362/170 and
l= 8*362/170=2896/170
PQRS is an isosceles trapezoid and m angle Q=127. Find M angle P.
Answers
so m<Q = m<P =127
answer
127
Answer:
[tex]m<P=127\°[/tex]
Step-by-step explanation:
we know that
If the trapezoid PQRS is an isosceles trapezoid
then
[tex]PS=QR[/tex] ----> congruent sides
[tex]m<P=m<Q[/tex] -----> congruent angles
In this problem we have
[tex]m<Q=127\°[/tex]
therefore
[tex]m<P=127\°[/tex]
How you know when there is only one solution triangle possible from a side-side-angle?
Answers
Answer:
There will be only on solution if either of these conditions is met:
the given angle is opposite the longest sidethe triangle is a right triangle (the ratio of the side opposite the angle to the other given side is equal to the sine of the angle)Step-by-step explanation:
Consider the SSA geometry with the angle placed in standard position at the origin and its adjacent given side (the second side of SSA) extending along the +x axis. Draw a circle having a radius equal to the length of the first side of SSA, centered on the vertex between the two segments on the +x axis.
There are three possibilities for the way this circle intersects the other ray of the angle (the ray that is not the x-axis):
the first side is as long or longer than the second side, so there is one point of intersection (one solution to the triangle, purple in the attachment)the first side is just long enough to be tangent to the other ray, so there is one point of intersection (one solution to the triangle, green in the attachment)the first side is between these lengths, so intersects the other ray in two places, giving two solutions to the triangle, red in the attachment.Find the value of x for which abcd must be a parallelogram 5x-1 2x+5
Answers
5 x - 1 = 2 x + 5
5 x - 1 + 1 = 2 x + 5 + 1
5 x - 2 x = 2 x - 2 x + 6
3 x = 6
x = 6 : 3
Answer:
x = 2
What polynomial identity should be used to prove that 20 = 36 − 16
Answers
Diffrence of squares is the correct answer just score pract q
What is
5.63×
10
−6
in decimal form?
a. 0.00000563
b. 0.000000563
c.5,630,000
d. 56,300,000
Answers
A basketball is thrown with an initial upward velocity of 25 feet per second from a height of 8 feet above the ground. The equation h=−16 t 2 +25t+8 h=−16t2+25t+8 models the height in feet t seconds after it is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?
Answers
-16t^2 + 25t - 2 = 0
t = 1.48 seconds
The area of a rectangular wall of a barn is 75 75 square feet. its length is 10 10 feet longer than the width. find the length and width of the wall of the barn.
Answers
A = 75
L = W + 10
75 = W(W + 10)
75 = W^2 + 10W
W^2 + 10W - 75 = 0
(W + 15)(W - 5) = 0
W + 15 = 0
W = -15...not this one because it is negative
W - 5 = 0
W = 5 <=== width is 5 ft
L = W + 10
L = 5 + 10
L = 15 <=== length is 15 ft
First, represent the unknown width as 'x'. Then, because the length is 10 feet more than the width, represent the length as 'x + 10'. Since the area is 75 square feet, set up and solve the equation x*(x + 10) = 75 for 'x'. This will give the width and the length will be this width plus 10 feet.
Explanation:This problem can be solved using algebra. First, let's denote the width of the wall as x in feet. If the length of the wall is 10 feet longer than the width, then we can express the length as x + 10. We're told that the area of the rectangle formed by the wall is 75 square feet. The area of a rectangle is calculated by multiplying its length by its width. Therefore:
x*(x + 10) = 75
You can solve this quadratic equation for x. The positive solution will be the width of the wall and the length will be that value plus 10 feet.
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Sue took a taxi from her home to her friends house. It cost $3.58 per mile and she gave the driver a $5 tip. If she paid $87.34, how many miles does she live from her friend?
Answers
87.34-5 = 82.34
82.34/3.58 = 23
she lives 23 miles away
The sum of six consecutive odd numbers is 204. What is the fourth number in the sequence
Answers
6x + 30 = 204
6x = 174
x = 29
six consecutive odd numbers are 29,31,33,35,37,39
answer
the fourth number in the sequence is 35
2n+1 , 2n+3, 2n+5, 2n+7, 2n+9,2n+ 11 and these add up to 204
12n + 36 = 204
12n = 168
n = 14
so fourth number in the sequence is 2(28) + 7 = 63
What is 5.928301 to 2 decimal places?
Answers
Final answer:
To round 5.928301 to 2 decimal places, we observe the third decimal place. It's 8, so we round up, making the answer 5.93.
Explanation:
When rounding the number 5.928301 to 2 decimal places, we need to look at the third decimal digit to decide whether to round up or down. Since the third decimal digit (8) is greater than 5, we round up. Therefore, the number 5.928301 rounded to 2 decimal places is 5.93.
Rounding a number to two decimal places involves examining the third decimal digit to determine whether to round up or down. In the case of 5.928301, the third digit is 8, which is greater than 5. Consequently, rounding up is necessary. Thus, the rounded value of 5.928301 to two decimal places is 5.93, emphasizing the role of the third digit in the rounding decision.
(06.06) Which of the following demonstrates the Commutative Property of Multiplication? 3(4a − 2) = 12a − 6 3(4a − 2) = (4a − 2) ⋅ 3 12a − 6 = (4a − 2) ⋅ 3 (3 ⋅ 4a) − 2 = 3(4a − 2)
Answers
3(4a - 2) = (4a - 2) * 3 <==
so its the second option:-
3(4a - 2) = (4a - 2).3
Use the given graph to determine the limit, if it exists.
limf(x)
x-->2
Answers
Answer:
Step-by-step explanation:
4
The limit as x tends to 2 is -1
How to find the limit
The limit is sought by investigating the graph. More attention is directed to when the domain or the x-value is at 2.
It can be observed that at this point we have 2 open dots and one closed dot.
The closed dot implies there is a value for x = 2, hence we trace the y coordinate at this point.
Tracing the y coordinate shows that the value is -1
find the value of x if f(x) equals 7 f(x) equals 4x minus 1
Answers
if M and N are midpoints in a diagram below, determine values for x and y
Answers
AС = 2*MN
3x + 10 = 2(x+5)
3x + 10 = 2x + 10
3x - 2x = 10 - 10
x = 0
M is a midpoint of AB ⇒
AM = BM
3y - 8 = 2(y+1)
3y - 8 = 2y + 2
3y - 2y = 2 + 8
y = 10
Where do the following graphs intersect? Show how you can find the intersection point algebraically.
1) y-2x=3
2) y-3= x^2
Answers
y-2x = 3
y-2x+2x = 3+2x
y = 2x+3
Plug that into equation (2)
y - 3 = x^2
2x+3 - 3 = x^2
2x = x^2
Get everything to one side
2x = x^2
2x-2x = x^2-2x
0 = x^2-2x
x^2-2x = 0
Now factor and use the zero product property to find the solutions for x
x^2-2x = 0
x(x-2) = 0
x = 0 or x-2 = 0
x = 0 or x = 2
If x = 0, then y is...
y = 2x+3
y = 2(0)+3
y = 3
So (x,y) = (0,3) is one solution of the system. This is one point where the graphs intersect.
If x = 2, then y is...
y = 2x+3
y = 2(2)+3
y = 4+3
y = 7
So (x,y) = (2,7) is another solution to the system. This is another point where the graphs intersect.
See the attached image for a visual. The two curves cross at point A and point B
A = (0,3)
B = (2,7)
The distance from earth to the moon is about 22^4 miles. the distance from earth to neptune is22^7 miles. which distance is the greatest and by how much
Answers
22^7=22x22x22x22x22x22x22
This means that 22^7 is greater and by the amount of 22^3
Select the additive inverse of 51
Answers
What can we add to 51 to make it equal to 0. Set up an equation.
Let x = the additive inverse of 51
x + 51 = 0
Solve for x.
x + 51 = 0
x = -51 <-- Subtract 51 from both sides
So, -51 is the additive inverse of 51.
Don is 6 feet tall. at a given time of day, he measures his shadow to be 13 feet long. at the same time, he measures the shadow length of a nearby tree to be 51 feet. how tall is the tree
Answers
the equation for this problem would be...
6/13=x/51
you then multpli the denominators on both sides and get...
6*51=13x
you then solve...
306=13x
and then you divide 13 on both sides...
x=23.54ft
the tree is 23.54ft tall
(leave a thanks and a rating if i helped) c:
The height of the tree maintaining the given ratio is 23.54 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Don height = 6 feet
His shadow = 13 feet
The ratio of height to shadow = 6/13
Tree height = x (let's say)
Tree shadow = 51 feet
Ratio = x/51
Both ratios must be the same, therefore,
x/51=6/13
x=23.54 feet
Hence "The height of the tree maintaining the given ratio is 23.54 feet".
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A point on an ellipse is 11 units from one focus and 7 units from the other. What is the length of the major axis?
Answers
VW is the major axis
ST is the minor axis
P is a point on the ellipse
A and B are the foci (or focus)
The length of major axis is given by either VA+AW or AP+BP
One useful fact to know that AP+BP is constant wherever the point P is on the ellipse
We know that the distance of the point 'P' from one focus is 11 units and from the other focus is 7 units, so we know the length of AP and BP.
Hence, the length of major axis is 11+7=18 units
The sum of two real numbers is 18 and the product is 70. what are the two numbers?
Answers
x+y=18......i
xy=70.........ii
from i
y=18-x.....iii
from ii
y=70/x......iv
substituting iii in iv we get:
70/x=18-x
multiplying through by x;
70=18x-x^2
x^2-18x+70=0
x=12.3 or 5.7
thus:
x=12.3 and y=5.7
Which of the following sets is not finite?
Answers
1. In how many different ways can 5 people be seated at a round table?
2. Each block on the grid is 1 unit by 1 unit. We wish to walk from A to B via 7 unit path but we have to stay on the grid. How many different paths can we take?
3. How many different "words" can be made from the given word by re-arranging the letters?
a) VECTOR
B) TRUST
Answers
Assume the people A, B, C, D and E are sitting in a row.
since there are 5 positions, they can sit in 5*4*3*2*1=120 ways.
consider 1 certain sitting position, for example ABCDE, that is B has A to his right, C to his left. D has C to his right and E to his left. And so on.
the positions
ABCDE
BCDEA
CDEAB
DEABC
EABCD
while in a row are different positions, in a round table they are the same thing.
(read the letters starting from A, and when the letters finish, continue reading from the beginning of the row. They all read "ABCDE")
This means that any arrangement in a round table, is converted to 5 arrangements in a row.
So there are in total [tex] \frac{5!}{5}=4*3*2*1=24 [/tex] arrangements of 5 people around a table.
2. check picture.
Consider the case where A is at (2, 2) and B is at (5, 6)
A can move to B through 3 horizontal units to the right, we call them E (for East) and 4 vertical units up, which we call N (for north).
the total path is 7 units.
it can be done in several ways, for example:
ENNNENE (the red path shown in the figure)
NNEEENN (the black path shown in the figure)
In total there are
[tex] \frac{7!}{3!*4!}= \frac{7*6*5*4!}{3!*4!}= \frac{7*6*5}{3!}= 35 [/tex] paths.
Remark: 7! is the number of arrangements if the letters were different. We divide by 3! because of the 3 E's and 4! because of the 4 N's.
Another possibility could be A'(3, -5), B'(8,-3).
From A' to B' we go by a total of 5 E and 2 N, so there are
[tex] \frac{7!}{2!*5!}= \frac{7*6*5!}{2!*5!}= \frac{7*6}{2}= 42 [/tex] paths in total.
there is one more possibility
[tex] \frac{7!}{1!(6!)}=7 [/tex]
C.
a) consider the letters {V,E,C,T,O,R}
we can form 6*5*4*3*2*1=720 words, as the first digit can be any of the 6 letters, combined with 5 for the second letter and so on.
b) the difference with a is that we have 5 letters and we have 2 T.
we have in total 5*4*3*2*1=120 arrangements of these letters, if the 2 T's were considered as separate.
consider the arrangements:
[tex]T_1RUST_2[/tex] and [tex]T_2RUST_1[/tex].
We read bth as just TRUST, but the permutation formula 5*4*3*2*1 considers these as 2 different.
this is why we need to divide 120 by 2, to get the actual number of words that can be formed. So the number is 60.
Answers:
1) 24
2) 7, 35 or 42. it depends on the positions of A and B, check the solution
3) a-720, b-160
a bag contains 5 red marbles, 3 yellow marbles, and 2 blue marbles. Once a marble is drawn, it is not replaced.what is the probability of drawing a blue on the first draw and a second blue marble on the next draw ?
Answers
P(first one being blue) = 2/10 which reduces to 1/5
not replaced
P(second one is blue) = 1/9...because u already pick a blue, meaning there is only 1 left, and there is one less marble, so there is a total of 9 marbles.
P(both events happening) = 1/5 * 1/9 = 1/45 <==
if a metal tool chest has the shape of a prism with a pentagonal base of 6194in squared in area, calculate the volume of the metal chest and pick where length c = 6 inches and length m = 19 inches
Answers
The volume of the metal tool chest is 37,164 cubic inches. To calculate the volume of the metal tool chest, we use the formula for the volume of a prism: Volume = Base area × Height
Given that the pentagonal base has an area of 6194 square inches, and the length c (which represents the height) is 6 inches, we can calculate the volume as follows:
Volume = 6194 in² × 6 in
Volume = 37,164 cubic inches
So, the volume of the metal tool chest is 37,164 cubic inches.
As for the lengths provided:
c = 6 inches (height)
m = 19 inches (unknown side length of the pentagon)
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