The additional of a triangle's degree measure will always equal 180˚
When the question asks you if a triangle with 112˚, 57˚, and 11˚, you have to add them up and make sure they equal to 180˚
In this case, 112˚ + 57˚ + 11˚ DO add up to 180˚, and is indeed a triangle.
Which expression is equivalent to
5(3x+3)−7x?
Answer:
38x
Step-by-step explanation:
Solve for the surface area
Answer:
210.7
Step-by-step explanation:
7x8 (and multiply that by 3 for the 3 sides)
7x6.1 (times 2 for the 2 sides and divided by 2 because it is a triangle)
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
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]
For similar question on recursive formula.
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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]
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.
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
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 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
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:
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.
Learn more about the volume here:
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you deposit $1050 into an account that pays 7.25% interest per year. find the amount after six year given the following:
a) compounded semiannually b) compounded monthly
please send help my way please!!
Answer:
14
Step-by-step explanation:
Answer:
area = 153.94
circumfrence = 43.98
Step-by-step explanation:
A=πr2=π·72≈153.93804
C=2πr=2·π·7≈43.9823
pls help pls help!!!!! ok ty
Answer:
D
Step-by-step explanation:
Indepedent values basically means the x-values
Also sorry for last answer
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
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
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:
the volume of a sphere is 4851 cubic cm find its diameter
Answer:
The diameter is 21 cm
Step-by-step explanation:
The formula for the volume of a sphere is V = (4/3)πr³, or (in terms of the diameter) V = (4/3)π(d/2)³. This simplifies to
4πd³ πd³
V = ----------- = -----------
3·8 6
Now equate V = (πd³/6) to 4851 cm³. We must first solve this for d³ and then take the cube root of the result:
πd³ = 4851(6) = 29106.
Dividing this result by π yields 9264.7,
and taking the cube root of this is 21. The diameter is 21 cm
2 x + y = 25 3 x − y = 15
Answer: Yeah and ?
Step-by-step explanation:
Answer:
(15,-5)
Step-by-step explanation:
What number makes the equation true? 35 + = 42
Answer:
7
Step-by-step explanation:
42 - 35 = 7
The time required to drive a fixed distance varies inversely as the speed. It takes 40 hr at a speed of 10 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 8 km/h?
Answer:
50 hours
Step-by-step explanation:
Given data
Time=40hr
Speed=10km/hr
Let us find the fixed distance first
Speed= distance/Time
10= distance/40
distance= 10*40
distance= 400miles
Now our speed= 8km/h
hence the time is
8= 400/time
time= 400/8
time=50 hours
Hence the time is 50 hours
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.
Help me plz pretty please
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%
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
PLS HELPPPPPP!!!!!!!!!!
Answer:
x = 30
ABC = 90
ACB = 30
Step-by-step explanation:
We know that if we add the 3 angles of a triangle together, it will come out to be 180 degrees, so..
60 + x + 3x = 180 subtract 60 from both sides and simplify
4x = 120 divide both sides by 4
x = 30
ABC = 3x
ABC = 3(30)
ABC = 90
Preform the indicated operation. Be sure the answer is reduced.
Answer:
D. [tex]\frac{2x+1}{x-8}[/tex]
Step-by-step explanation:
[tex]\frac{x+1}{x-8} - \frac{x}{8-x} = \\\\\frac{x+1 + x}{x-8} = \\\\\frac{x+1}{x-8} +\frac{x}{x-8} =\\\\\frac{x+1+x}{x-8} =\\\\\frac{2x+1}{x-8}[/tex]
Correct choice is D
I need an answer! NOT A LINK!!! ASAP!
Answer:
im pretty sure its 14
Step-by-step explanation:
What is the length of AC?
Answer:
2nd option
;)
I did this before-
Step-by-step explanation: