Answer:
[tex]a_{n}[/tex] = 5n - 2
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₄ = 18 and a₁₀ = 48 , then
a₁ + 3d = 18 → (1)
a₁ + 9d = 48 → (2)
subtract (1) from (2) term by term to eliminate a₁
6d = 30 ( divide both sides by 6 )
d = 5
substitute d = 5 into (1) and solve for a₁
a₁ + 3(5) = 18
a₁ + 15 = 18 ( subtract 15 from both sides )
a₁ = 3
Then
[tex]a_{n}[/tex] = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2
Which expression is equivalent to Cosine (StartFraction pi Over 2 EndFraction r) for all values of r?.
The expression that is equivalent to [tex]Cos(\frac{\pi }{2}+r )[/tex] is [tex]-Sinr[/tex].
Given trigonometric expression is:
[tex]Cos(\frac{\pi }{2}+r )[/tex]
What is the value of [tex]Cos(\frac{\pi }{2}+\theta )[/tex]?The value of [tex]Cos(\frac{\pi }{2}+\theta )[/tex] is [tex]-Sin\theta[/tex] because [tex]\frac{\pi }{2} +\theta[/tex] lies in the second quadrant and the cosine function is negative in the second quadrant.
So, [tex]Cos(\frac{\pi }{2}+r )= -Sin r[/tex]
The range of sine and cosine functions is the same i.e. [-1,1].
Both the functions are periodic functions with periods 2π.
Hence, the expression that is equivalent to [tex]Cos(\frac{\pi }{2}+r )[/tex] is [tex]-Sinr[/tex].
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David’s family is driving from New York to Florida. They know the distance they will travel is about 1100 miles. If a map has a scale of 1 in. = 80 mi, about how far will the trip be on the map? StartFraction 8 over 110 EndFraction inches 11 inches 13 and three-fourths inches 88 inches.
Answer:
13 and three-fourths inches
Step-by-step explanation:
The map distance can be found using a proportion with the map scale.
__
map distance / (1100 mi) = (1 in) / (80 mi)
map distance = (1100×1)/80 in = 13 3/4 in . . . multiply by 1100 mi; cancel mi
The trip will be about 13 3/4 inches on the map.
help! please! now!.............
Answer:
The answer is 133.5
Step-by-step explanation:
See the image above
help please and please hurry this assignment is due 11:59
A triangle has sides with lengths of 63 miles, 64 miles, and 85 miles. Is it a right triangle? Yes or no?
Answer:
no it is not a right angled triangle.
Step-by-step explanation:
forthetra
A salesperson earned x dollars last year. The salesperson earned 25% more money this year than last
year. Which expressions represent the amount, in dollars, the salesperson earned this year?
Drag and drop each correct expression into the box.
HELP PLS
More earnings:-
25% of x0.25xTotal earnings this year
x+0.25x(1+0.25)x$1.25xAnswer:
[tex]\$ \huge{\text{(} \dfrac{x}{4} \ + \ \dfrac{4x}{4} \huge{\text{)}[/tex]
Step-by-step explanation:
Given:
Last year: $x
Determining the money earned for this year:
This year = 25% more than last year
= $25x/100 + $x
= $x/4 + $4x/4
The expression that represents the money earned this year is $x/4 + $4x/4.
what is the surface area of the a cylinder with base radius 3 and height 8.
Bonjour,
πr² *h
3,14 * 3² *8
= 3,14 *9 *8
=>226, 08 ....²
Answer:
66π square units
Step-by-step explanation:
Which is equivalent to 4 (9) 1/2 ^x
O 9^2x
O 9 1/8 ^x
O (9)^x
O 6(9) ^x
Answer:
36/2^x
Step-by-step explanation:
= 4 X 9 x 1/2^x
= 36/2^x
Hello, the point (-2,k) lies on the line. Determine the value of k. please answer this. ty
Answer:
0
Step-by-step explanation:
This problem is impossible if the x value is -2. However, if the x value is 2, find where the line meets x=2 and record the y value.
A lake has a surface area of 11. 0 square miles. What is its surface area in square meters?
Answer:
11mi² = 28489869m²
Step-by-step explanation:
m² = mi² / 0.00000038610
The relative frequency of Event A in an experiment is 13.
If the experiment is performed 30 times, how many times should you expect Event A to occur?
Enter your answer as a number, like this: 42
!!PLEASE HELP ME IM NOT GOOD AT MATH AT ALL!!
Based on the relative frequency and the number of times the experiment is to be performed, the number of times Event A should occur is 10 times.
How many times should Event A occur?The relative frequency in this regard is 1/3.
The number of times it will occur can be found as:
= Relative frequency x Number of times event was performed
Solving gives:
= 1/ 3 x 30
= 10 times
Find out more on relative frequency at https://brainly.com/question/3857836.
what are the solutions to the equation?
Answer:
x = -2 and 1
Step-by-step explanation:
Given :
f(x) = x+2
g(x) = -x²+4
The solution to the equation f(x) = g(x)
=> x+2 = -x²+4
=> x²+x = 4-2
=> x²+x -2 = 0
By factorisation
=> x²+2x-x -2 = 0
=> x(x+2) -1(x+2)
=> (x+2) (x-1)
x = -2 and 1
So if I have 6,000 dollars and I need 20,000 how much money do I need to earn to reach 20,000?
Answer14,000
Step-by-step explanation:
20,000-6,000=14,000
Answer:14000
Step-by-step explanation:
20000 - 6000, not sure why ur doing these type of problems in highschool
Can anyone solve this correctly?
Answer:
24 cm³
Step-by-step explanation:
The volume of a triangular prism with triangular face 4 cm by 2 cm and height 6 cm is the product of the triangle area and the prism height:
V = BH
V = ((1/2)bh)H = 1/2(2 cm)(4 cm)(6 cm) = 24 cm³
The volume of the prism is 24 cubic centimeters.
_____
Additional comment
Note that this is half the volume of a rectangular prism of the same dimensions.
what are the slope and y - intercept of the equation 6x+3y=-12
Answer:
Slope= -2
y-intercept= -4
Step-by-step explanation:
To find the slope and y-intercept of a given equation, first rearrange the equation such that it is in the slope-intercept form. In the slope-intercept form, the coefficient of y is 1 and the rest are moved to the left hand side of the equation.
[tex]\textcolor{steelblue}{\text{Slope-intercept form}}[/tex]
y= mx +c, where m is the slope and c is the y-interceptGiven equation: 6x +3y= -12
Let's leave the y term on the left of the equation and bring the rest to the right.
3y= -6x -12
To ensure that the coefficient of y is 1, divide both sides by 3.
y= -2x -4
The equation is now in the slope-intercept form.
The slope is the coefficient of x (the number that comes before x), thus the slope is -2. The y-intercept is -4.
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
A rectangular prism with the width as three and a half feet, the length as two and a half feet and the height as one and a half feet. i need help
Answer:
The volume is approximately 13 1/8 feet.
Step-by-step explanation:
Volume of a rectangular prism is calculated by multiplying the width, length, and height together.
3.5w × 2.5l × 1.5h = 13.125
13.125 = 13 1/8. The fraction cannot be reduced any further, so this is its simplest form.
If the circumference is 50 cm what is radius of the circle?
Answer:
7.96
Step-by-step explanation:
C=2πr undo it
R=C/2π=50/2×π≈7.5775 rounded is 7.96
Hope this helps!
Have a nice day!! :D
The radius of the circle is 7.96 cm.
What is the radius of the circle?The radius of a circle is the distance from the center of the circle to any point on its circumference. It is usually denoted by ‘R’ or ‘r’.
The circumference of the circle is given by;
[tex]\rm Circumference = 2\pi r[/tex]
Where r is the radius of the circle.
Substitute all the values in the formula
[tex]\rm Circumference = 2\pi r\\\\50 = 2\pi r\\\\r = \dfrac{50}{2\times 3.14}\\\\r=7.96[/tex]
Hence, the radius of the circle is 7.96 cm.
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PLEASE HELP I NEED TO TURN THIS IN QUICKK
Answer:
QUienn quieres ser mi ami
Step-by-step explanation:
xd
What is the area of the shaded sector of the circle? 20pi units squared 40pi units squared 180pi units squared 400
The area of the sector with a radius of 20 units and a central angle of 162° is 180π unit².
What is the sector of a circle?
A sector is the portion of a circle enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger is the major sector.
The radius of the sector =20 units
Central angle subtended by sector = 162° = 162π/180 radians
As we know the area of a sector= 0.5r²α
where r is the radius and α is the central angle.
So, the area of the given sector = 0.5*20²* 162π/180
The area of the given sector = 180π unit²
Therefore, The area of the sector with a radius of 20 units and a central angle of 162° is 180π unit².
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Answer:
its c
Step-by-step explanation:
25 cows produce 4 2/3 literes of milk how much milk is this in total
Answer:
116 2/3 liters of milk
Step-by-step explanation:
4 2/3 liters of milk per cow * 25 cows = 350/3 liters of milk = 116 2/3 liters of milk
I hope this was good enough. Happy mathing!
Friction creates heat and lowers the _______
Answer:
energy
Step-by-step explanation:
Answer:
energy
Step-by-step explanation:
What’s 70x56,000+65,000,000
An electrician has an income of $41,500. The income tax the electrician has to pay is 12%. What is the amount of income tax that the electrician has to pay? A) $3,840 B) $4,164 C) $4,980 D) $5,210.
Answer:
he has to pay 4980$ in tax So its C) 4,980
The amount of income tax that the electrician has to pay is $4980. Then the correct option is C.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
An electrician has an income of $41,500.
The income tax the electrician has to pay is 12%.
Then the amount of income tax that the electrician has to pay will be
Amount of income tax = 0.12 × $41500
Amount of income tax = $ 4980
Thus, the amount of income tax that the electrician has to pay is $4980.
More about the percentage link is given below.
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Nidah writes down two different prime numbers.
She adds together her two numbers.
Her answer is a square number less than 30
Find two prime numbers that Nidah could have written down.
Mathematician
Answer:
2 and 3
Step-by-step explanation:
prime numbers=2,3,4,5,...
taking 2 and 3
2+3=5
5²=25
hence the different prime numbers are 2 and 3
The numbers can be (2, 7), (2, 23), (3, 13), (5, 11)
What are Prime Numbers?A prime number is a whole number greater than 1 whose only factors are 1 and itself.
Given that, Nidah writes down two different prime numbers.
She adds together her two numbers.
Her answer is a square number less than 30
Square numbers less than 30 are = 1, 4, 9, 16, 25
The pairs of numbers that can satisfy the given condition are;
2 + 7 = 9
2 +23 = 25
3 + 13 = 16
5 + 11 = 16
Hence, Nidah could have chosen from these numbers (2, 7), (2, 23), (3, 13), (5, 11)
For more reference on Prime numbers, click;
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#SPJ2
Multiplication and __are inverse operations. addition subtraction O division
Answer:
Division is the opposite of multiplication
Step-by-step explanation:
Opposites:
Addition and subtraction
multiplication and division
differentiation and integration.
a + b =c a + b + c = 36 given that a and b have the same value what is a,b and c
Answer:
a = 9 b = 9 c = 18
Step-by-step explanation:
a+b = c
a+ b + c = 36 but we know a+b = c sub that in
c + c = 36
c = 18 now a + b = c and a and b are the same
so a and b are = 9
Answer:
a is 9
b is 9
c is 18
Step-by-step explanation:
Let's list the information provided
a + b =c
a + b + c = 36
a=b
Knowing that a=b we can replace b with a in the equations
a+a is the same as 2a since a is being doubled
2a=c
Knowing this we can replace c with 2a
2a+2a=36
Now solve for a
[tex]2a+2a=36\\4a=36\\\frac{4a}{4} =\frac{36}{4} \\a=9[/tex]
Now let's sub this value of a into the equations to see what the other values are
a=b
9=b
2a=c
2(9)=c
18=c
heres another one of those impossible looking problems for another chance for a brainly no links please
Answer:
B. X=6 onlyStep-by-step explanation:
Isolate the term of x from one side of the equation.
[tex]\sf{\sqrt{2x-3}=x-3}[/tex]
2x-3=x²-6x+9
Solve.
[tex]\sf{2x-3=x^2-6x+9=\boxed{\sf{x=6}}[/tex]
Therefore, the solution is x=6, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
help me please thank you
Answer:
o = 20.18; b = 13.51i = 12.68; n = 27.19Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relations between sides and trig functions in right triangles. These can be used to solve the triangles shown.
__
1.Sin = Opposite/Hypotense
sin(48°) = 15/o
o = 15/sin(48°) ≈ 20.18 . . . . . . . . . multiply by o/sin(48°)
Cos = Adjacent/Hypotenuse
cos(48°) = b/o
b = o·cos(48°) = 20.18·cos(48°) ≈ 13.51
For triangle BOX, o = 20.18, b = 13.51.
__
2.Sin = Opposite/Hypotense
sin(25°) = i/30
i = 30·sin(25°) ≈ 12.68
Cos = Adjacent/Hypotenuse
cos(25°) = n/30
n = 30·cos(25°) ≈ 27.19
For triangle TIN, i = 12.68, n = 27.19.
find the highest common factor (HCF) of 30 and 45
Answer:
The highest common factor of 30 and 45 is 15.
Step-by-step explanation:
factors of 30 = 1, 2, 3, 4, 5, 6, 10, 15, 30 ; factors of 45 are = 1, 3, 5, 9, 15, 45)
Greatest common factor is 15
Answer:
15.
Step-by-step explanation:
HCF is also called GCD. So, you divide both numbers with a common number that can divide both numbers at the same time without a remainder.
3 30 45
5 10 15
2 3
3 × 5 = 15
A triangle has angles measureing 40 and 30. What is the measure of the third angle
Answer: 110 degrees
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees, so the third angle is 180-40-30=110 degrees.