Answer:
The 7th term is 10 and the 9th term is 16
(and the common difference d = 3)
Step-by-step explanation:
If by calculate the numbers, you mean the 7th term and 9th term, first, you will determine the common difference.
The nth term of an A.P is given by the formula
Tₙ= a+(n-1)d
Where Tₙ is the nth term
a is the first term
and d is the common difference
From the question,
a = -8
T₇ : T₉ = 5:8
From the formula
T₇ = a + (7-1)d = a + 6d
and T₉ = a + (9-1)d = a + 8d
Then.
a + 6d : a + 8d = 5:8
But a = -8
∴ -8 + 6d : -8 + 8d = 5:8
We can write that
(-8 + 6d) / (-8 + 8d) = 5/8
Cross multiply
8(-8+6d) = 5(-8+8d)
-64 + 48d = -40 + 40d
48d - 40d = -40 + 64
8d = 24
d = 24/8
d = 3
∴ The common difference is 3
Now, for the 7th term
From
T₇ = a + 6d
T₇ = -8 + 6(3)
T₇ = -8 + 18
T₇ = 10
and for the 9th term
T₉ = a + 8d
T₉ = -8 + 8(3)
T₉ = -8 + 24
T₉ = 16
Hence, the 7th term is 10 and the 9th term is 16
A jet travels 1198 miles against the wind in 2 hours and 1438 miles with the wind in the same amount of time. What is the rate of the jet in still air and what is the rate of the jet wind?
Rate of the jet still in the air: x mi/h
Rate of the wind: x mi/h
Answer: tbh jets arent really a good way to travel man. you better start walking ur lazy butt and get movin.
Step-by-step explanation:
If 18 is subtracted from twice the square of an integer, the result is equal to nine times the integer. What is the value of the integer?
Answer:
6 or -1.5
Step-by-step explanation:
We can let this integer be x.
Therefore, according to the question we have:
[tex]2x^2-18=9x[/tex]
Subtracting 9x, we have a quadratic:
[tex]2x^2-9x-18=0[/tex]
Plugging into the quadratic equation:
[tex]\frac{9+\sqrt{81+144}}{4}, \frac{9-\sqrt{81+144}}{4},[/tex]
the square root of 81+144 is 15, so the answer is either 6 or -1.5
Evaluate.
10 3/4 plus 8 3/4 subtract 6 1/2
Answer:
13
Step-by-step explanation:
add 3/4 and 3/4 to get 6/4 then get 1/2 times the bottom and the top but 2 to get 2/4 so then do 6/4 - 2/4 to get 4/4 or 1
add 10,8 to get 18 then subtract 6 to get 12 then all the 1 and you get your answer. Hope this helped
Answer:
13
Step-by-step explanation:
Convert 10 3/4
to an improper fraction.
43/4 + 8 3/4 − 6 1/2
Convert 8 3/4
to an improper fraction.
43/4 + 35/4 − 6 1/2
Convert 6 1/2
to an improper fraction.
434 + 354 − 132
Combine fractions.
78/4 + −13/2
Simplify each term.
39/2 − 13/2
Combine fractions.
13
PLEASE ANSWER ILL GIVE 5 STARS AND A HEART!!!
Answer:
120
Step-by-step explanation:
5x6 = 30
30x4= 120
What is the solution to this system?
8
Answer:
(2,2)
Step-by-step explanation:
The solution to a system is the point on the graph where both lines intersect.
1 divided by 11/2 as a fraction
Answer:
1.375 decimal to fraction.
2/7 Fraction to Decimal
Step-by-step explanation:
what is the equation of a line whose slope is -2 and whose y-intercept is 4?
Answer:
y=-2x+4
Step-by-step explanation:
if y is 4..it means x intercept is 0
gradient is -2
and we know gradient is the change in y /change in X
so: we let the second intercepts to be (x,y)
so y-4/x-0=-2
multiply by x-0 both sides then collect like terms together
it will be y= -2x+4
How many solutions does the system of equation have?
2x + 3y = 9 and y = 2/3x - 2
A.
One solution
B.
Two solutions
C.
Infinitely many solutions
D.
No solutions
Answer:
A. One solution
Step-by-step explanation:
y = 2/3x - 2 has slope of 2/3
2x + 3y = 9
3y = -2x + 9
y = (-2/3)x + 3 has slope of -2/3
lines with different slopes have only ONE intersection
what is the sum of 2/3,1/2and1/4=
Answer:
17/12
Step-by-step explanation:
In order to add fractions, you have to have a common denominator. The denominators in these fractions are 3, 2, and 4 (the bottom numbers). To get a common denominator, figure out what number all three of them can go into. Their common factor would be 12 because all three numbers go into 12.
Multiply each numerator in the fraction (the top number) by how much it takes to get from our current denominators (3,2,4) to our final denominator (12).
For example, in 2/3 we know that 3 times 4 equals 12. Multiply the top number by 4 to get 8/12.
In 1/2 we know that 2 times 6 equals 12. Multiply by 6 to get 6/12.
In 1/4 we know that 4 times 3 equals 12. Multiply by 3 to get 3/12.
Add the fractions to get 17/12.
an expression that is equivalent to 10x - 8 +0.5(2x - 3)?
-
Answer:
......................
What is the value of the expression
Answer:
Step-by-step explanation:
2 1/2
opposite = 1.5.
adjacent = 4.
find the acute angle
Answer:
Step-by-step explanation:
tanθ = opp/adj
θ = arctan(1.5 / 4)
θ = 20.55604521958346...
θ = 20.6°
Answer
20.56
Step-by-step explanation:
tan∅=opposite/adjacent
=1.5÷4
=0.375
then to get ∅ find the tan inverse of 0.375 you'll get 20.55604...
put it in two decimal point...20.56°
every week james skis 8 miles and swims 12 miles, write an order that represents the miles he skies and swims in 8 weeks.
Answer:
Every eight weeks, James skis 64 miles and swims 96 miles.
Step-by-step explanation:
12×8=96
8×8=64
A video game is on sale for 30% off the
regular price of $50. What is the sale
price of the video game
A.$20
B.$30
C.$33
D.$35
Answer:
d! 35 ......!!!!!!!!!!!!
As a restaurant, you and four friends divide the bill evenly. Each person pays $7.35. How much is the total bill?
Answer:
29.4
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2750.
What was the rate charged per hour by each mechanic if the sum of the two rates was $205 per hour?
-Whats the First mechanic: $ -----per hour
-Whats the Second mechanic: $ ---- per hour
Y=3x-1 i need help now right now.
2. Kiant is having a sale on ketchup. All
ketchup is 70% of its original
price. You want to buy Meinz' ketchup with an original price of $8.90.
What is the sale price?
Answer: $2.67
Step-by-step explanation:
$8.90 - $6.23 = $2.67
Brainliest? Im just trying to get to a higher rank
How would you write the quotient as a simplified fraction?
A) 851÷46 = 18 23/36
B) 851÷46 = 18 1/2
C) 851÷46 = 18.5
D) 851÷46 = 17 23/46
Answer:
The answer is b
Step-by-step explanation:
Find the measure of the angle marked and indicated in bold
How do I find the degree measure?
Answer:
The Degree Measure of the Angle = Radian x (180/)
Write an equation in point-slope form for the line that passes through the given points (1,-3),(4,-15)
Answer: b=7
Step-by-step explanation:
please help! ASAP I need help fast!!
Answer: 4.8
Explanation: divide total needed of blue paint (3) by 1/2 to find the ratio, which is 6. then multiply that by 4/5 to get the total of yellow paint, which is 4.8
I need help with pre calculus.
Problem 1
Answer: Choice A. (0,9)---------------------
Explanation:
The first task is to determine the function for f(x). Because it's linear, it's in the form y = mx+b. Let's find the slope m.
Select any two columns to pick out (x,y) points from the f(x) function. I'll pick the first two columns to select the points (-6,15) and (-4,11). Apply the slope formula to these two points to get...
m = (y2-y1)/(x2-x1)
m = (11-15)/(-4-(-6))
m = (11-15)/(-4+6)
m = -4/2
m = -2
Then use this m value along with any of the points of the table to determine the y intercept b. I'll use the point (-6,15)
y = mx+b
b = y-mx
b = 15-(-2)*(-6)
b = 15-12
b = 3
The y = mx+b equation becomes y = -2x+3 and that leads directly to the function f(x) = -2x+3.
Repeat all of those steps but do so for g(x) this time. I'll skip those steps over but you should get the function g(x) = 5x-6.
The y intercepts of f(x) and g(x) found were 3 and -6 respectively. Subtract those values to find the y intercept of h(x) = (f-g)(x) = f(x)-g(x).
So we get 3-(-6) = 3+6 = 9 which leads to the location (0, 9).
=========================================================
Problem 2
Answer: Choice Ax is any real number but x cannot equal -2, -1 or 1.---------------------
Explanation:
Through trial and error, the factor by grouping method, or using your graphing calculator, factor the denominator to get
g(x) = x^3+2x^2-x-2 = (x+2)(x+1)(x-1)
The factors (x+2), (x+1) and (x-1) lead to the roots of x = -2, x = -1, and x = 1 in that order. Those three roots of g(x) will make g(x) = 0 and cause a division by zero error in the denominator. So we must kick out those three values from the domain. Every other real number is allowed in the domain. So that's how we get the notation for choice A. It starts off saying x is a real number. Then it goes onto say that -2, -1 and 1 aren't allowed.
So overall the domain is described as: "x can be almost any real number except x cannot be -2, cannot be -1, and it cannot be 1".
Side note: We don't involve the numerator function at all.
=========================================================
Problem 3
Answer: Choice B. 2x+1 and x-3---------------------
Explanation:
The height is x, which we can factor out like this
2x^3-5x^2-3x
2x^2*x - 5x*x - 3*x
x(2x^2-5x-3)
Effectively you would use the distribution rule in reverse.
Now let's factor the remaining expression in the parenthesis.
I'll use the factor by grouping method.
2x^2-5x-3
2x^2-6x+1x-3
(2x^2-6x) + (1x-3)
2x(x-3) + 1(x-3)
(2x+1)(x-3)
Therefore, the full factorization is
x(2x+1)(x-3)
which shows we have the dimensions of x, (2x+1) and (x-3). The order doesn't matter so we could easily have (2x+1) the length and (x-3) the width, or we could have it the other way around.
You can verify that (2x+1)(x-3) expands out to 2x^2-5x-3 using either the FOIL method or the box method.
How many days are in 52 weeks?
Answer:
A year but -1.
Step-by-step explanation:
52x7=364.
Hope this helps!
Answer:
there are 364 days in 52 weeks.
Step-by-step explanation:
To find out how many days are in 52 weeks you have to multiply the amount of days there are in a week by 52, there are 7 days in a week and 7 times 52 is 364 so the answer is 364
A room has a rectangular floor 5.5 m long and 4.5 m wide. The room is 2.5 m in height.
A. What is the area of wall space in the room?
B. How much paint is required to paint the
walls with two coats if one litre of paint
can cover 11.25 m??
Answer:
Length=8 m,Breadth=6 m,Height=3 m
We know,
LSA=2(l+b)×h
LSA=2×14×3=84 m
2
Therefore, cost of painting = 84×60=Rs.5040.
Over the summer, Paulo opens a dog-washing business and begins with $32. The table shows how much he earns and spends each week. He works for 8 weeks washing dogs. When he starts back at school, he budgets $60 to spend each week. How many weeks pass before he needs to wash more dogs?
Chandra has 15 feet of ribbon to make bows for 6 teams how much ribbon can she use for each bow if she cuts the ribbon into equal pieces
Answer:
2.5 feet for each bow
Step-by-step explanation:
15/6= 2.5
The quotient of 2 numbers, p and q
Answer:
2p/q
2q/p
q/p=2
p/q =2
Step-by-step explanation:
Here are some possible answers. The way your statement is formated in does not ask a question nor does it provide enough information for one to deduce what the question was.
Jason stands in the corner of a very large field. He walks, on a bearing of 030°,
a distance of d metres. Jason then changes direction and walks twice as far on a new
bearing of 120°. At the end of the walk Jason calculates both the distance he must
walk and the bearing required to return to his original position. Given that the total
distance walked is 120 metres, what answers will Jason get if he is correct?
Answer:
Step-by-step explanation:
d + 2d = 120
3d = 120
d = 40 m
east distance was 40cos30 + 80cos120 = -5.35898 m
north distance was 40sin30 + 80sin120 = 89.282032
as 30° and 120° bearings are 90° apart, Jason needs to walk
D = √(d² + (2d)²) = d√5 or 40√5 meters or about 89.44 m to return to his original position.
we could also use √(-5.35898² + 89.282032²) = 89.44 m
direction will be
θ = arctan -89.28/5.359 = -86.565° or a bearing of 273.4°
