Answer:
[tex]T_n = -97n[/tex]
Step-by-step explanation:
The actual sequence is: -97, -194, -291, -388
Required
Determine the nth term
nth term of an arithmetic progression is:
[tex]T_n = T_1 + (n - 1)d[/tex]
Where
[tex]T_1 = First\ Term = -97[/tex]
[tex]d = Common\ Difference = -194 - (-97) =-97[/tex]
So:
[tex]T_n = T_1 + (n - 1)d[/tex] becomes
[tex]T_n = -97 + (n - 1) * -97[/tex]
[tex]T_n = -97 -97n + 97[/tex]
Collect Like Terms
[tex]T_n = -97n + 97-97[/tex]
[tex]T_n = -97n[/tex]
Hence, a term of the sequence is:
[tex]T_n = -97n[/tex]
A3ft board weighs 2 pounds. How much
does a 12 ft board weigh?
Answer:
8 pounds
Step-by-step explanation:
3 ft board = 2lb
12 ft board is 4 times more so
2x4 = 8 lb
i need help quick!!!!! Ive been trying to figure this out for 20 mins now.
Whats one plus one?
A: 2
B:11
C:0
or D: not this one
Answer:
take one finger and than the other and how may fingers do you have now 2
What is angle U?
A) 129
B) 42
C) 34
D) 43
Step-by-step explanation:
4x+2+95=-7+17x
104=13x
x=8
for angle U=34 degrees
the answer is C
Need Help ASAP
Slope = -7;(4,-30)
Answer:
y=-7x-2
Step-by-step explanation:
I assume you need the equation for the line, so that's what I'm solving for here.
1. Start by putting the slope and the coordinates into point slope form, which is y-y1=m(x-x1)
y+30=-7(x-4)
2. Distribute -7 to (x-4) (or multiply x and -4 by -7).
y+30=-7x+28
3. Subtract 30 from both sides to get y by itself.
y=-7x-2
a.
Missing x:-2
Missing y:0
c.
Missing x:-2
Missing y:2
b.
Missing x:0
Missing y:1
d.
Missing x:-1
Missing y:1
Answer:
B
Step-by-step explanation:
The pattern is x/-3
25 points, will mark brainliest!!
Step-by-step explanation:
Alex buys x oranges and Bobbie buys x + 2 oranges. Together they buy 2x + 2 oranges.
$4.20 / $0.21 = 20 oranges.
2x + 2 = 20
2x = 18
x = 9
Hence the value of x is 9.
Answer:
x=9
Step-by-step explanation:
The total number of oranges purchased is x + x+2 = 2x+2
They cost 21 cents each
(2x+2) *.21
This is equal to 4.20
(2x+2) *.21 =4.20
Divide each side by .21
(2x+2) *.21/.21 =4.20/.21
2x+2 = 20
Subtract 2 from each side
2x+2-2 =20-2
2x= 18
Divide by 2
2x/2 =18/2
x =9
A line with a negative slope is perpendicular to one of the lines shown. What is its slope? Use the graph shown below. The slope is:
Given:
A line is perpendicular to the given line and having negative slope.
To find:
The slope of the line.
Solution:
We know that, product of slopes of two perpendicular lines is -1.
[tex]m_1\cdot m_2=-1[/tex]
[tex]m_1=-\dfrac{1}{m_2}[/tex]
It means, one slope is opposite and reciprocal of other.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given graph it is clear that, blue line passes through (0,3) and (2,4). So, slope of blue line is
[tex]m_B=\dfrac{4-3}{2-0}[/tex]
[tex]m_B=\dfrac{1}{2}[/tex]
The slope of blue line is [tex]\dfrac{1}{2}[/tex]. So, slope of the line which is perpendicular to the blue line is -2, which is negative.
From the given graph it is clear that, red line passes through (0,4) and (4,3). So, slope of red line is
[tex]m_R=\dfrac{3-4}{4-0}[/tex]
[tex]m_R=\dfrac{-1}{4}[/tex]
The slope of blue line is [tex]-\dfrac{1}{4}[/tex]. So, slope of the line which is perpendicular to the blue line is 4, which is positive.
Therefore, the slope of the line which is perpendicular to the given line and having negative slope, is -2.
6. Which expression is equivalent to (14442,6 for all positive values of k and r? OF 12kr7 O G.726?-14 OH 144kry O J. 126-14
Answer:
the answer is 12k²r¹⁴.........
Can someone help me in this question
Answer:
The average speed of the athlete for the entire competition is approximately 21.23 km/hr
Step-by-step explanation:
The given parameters of the athlete performance in the triathlon are;
The length the athlete swims = 750 m = 0.75 km
The time the athletes spends swimming = 15 minutes = 0.25 hours
The speed with which the athlete cycles = 40 km/hr.
The time the athletes spends while cycling = 30 minutes = 0.5 hours
The distance the athlete ran = 5 km
The average speed with which the athlete ran = 3 m/s = 10.8 km/hr.
The formula for average speed, s is Average speed = Total distance/(Total time)
The distance, ∑d, the athlete covered in the entire competition is given as follows;
∑d = 0.75 km + 0.5 hr. × 40 km/hr. + 5 km = 0.75 km + 20 km + 5 km = 25.75 km
The distance, ∑t, the athlete spends in the entire competition is given as follows;
∑t = 0.25 hr. + 0.5 hr. + 5 km/(10.8 km/hr.) = 0.25 hr. + 0.5 hr. + 0.463 hr. ≈ 1.213 hr.;
Therefore;
The average speed of the athlete for the entire competition, s = ∑d/∑t = 25.75 km/(1.213 hr.) ≈ 21.23 km/hr.
coach purchased footballs and basketballs from two different stores.
Each football costs the same amount, and each basketball costs the same
amount.
At the first store, the coach paid $110 for 5 footballs and 14 basketballs.
At the second store, the coach paid $82.50 for 10 footballs and 6
basketballs.
What was the cost in dollars of each basketball?
Answer:
$6.25Step-by-step explanation:
Let football cost be f and basketball cost be b
We have two equations as per given:
5f + 14b = 11010f + 6b = 82.50We need to find b, therefore we'll eliminate f
To do so we'll double the first equation and subtract the second one:
2(5f + 14b) - (10f + 6b) = 2(110) - 82.5028b - 6b = 220 - 82.5022b = 137.5b = 137.5/22b = 6.25Each basketball costs $6.25
Question:
Coach purchased footballs and basketballs from two different stores.
Each football costs the same amount, and each basketball costs the same amount.
At the first store, the coach paid $110 for 5 footballs and 14 basketballs.
At the second store, the coach paid $82.50 for 10 footballs and 6 basketballs.
What was the cost in dollars of Each basketball?
Answer:
Probably 7
REAL Answer:
6.25
Your Welcome! (^·^)
#TeamTrees #TeamSeas #TeamEducation #TeamWorkMakesDreamWork #TeamSpirit #NoSleep #TeamIPhone #TeamBrainly
y+1=5(x−9) is it linear or non-linear?
Answer:
yes its linear
Step-by-step explanation:
When creating your budget, make sure the amounts (both income and expenses)
a. are for the same time period.
b. total to zero.
c. create a negative balance.
d. are for the same amount.
Answer:
a. are for the same time period
PLEASE HELP VERY URGENT!!!!
Which of the following is equal to 16.4 ?
A. 16 • 4
B. 32
D. 64
Answer:
A or B
Step-by-step explanation:
Also i need help to
Answer:
A. [tex]\sqrt{16}[/tex] × [tex]\sqrt{4}[/tex]
I hope this helps!
Which of the following is an equation of the line through (3, −1) and (−2, 14)?
y=1/5x+ 13/5
y= -1/5 x+ 17/5
y = -3x + 8
y = 3x + 8
Given the graphed function below, which of the following ordered pairs are
found on the inverse function?
Answer: Option B.
Step-by-step explanation:
A linear function can be written as:
y = a*x + b
where a is the slope and b is the y-intercept.
if the line passes through the points (ax, ay) and (bx, by) then the slope is:
a = (bx - ax)/(by - ay)
In this case, we can see that the line passes through the points:
(1, 3) and (2, 1)
Then the slope is:
a = (1 - 3)/(2 - 1) = -2
y = -2*x + b
In the graph we also can see that the line intersects the y-axis at y = 5, then b = 5.
The line is:
y = f(x) = -2*x + 5.
the inverse function is such that:
g( f(x)) = x
to find the inverse function of a linear equation, we just could isolate x.
y - 5 = -2x
-y/2 + 2.5 = x
Then we could write the inverse function as:
g(x) = - x/2 + 2.5
Now we need to see which pairs belong to this line. I just will evaluate the function g(x) in different values of x, and see which points belong to the line.
g(9) = -9/2 + 2.5 = -4.5 + 2.5 = -2
(9, -2) belongs to the line.
g(7) = -7/2 + 2.5 = -3.5 + 2.5 = -1
Then (7, -1) belongs to this line.
g(5) = -5/2 + 2.5 = 0
Then the point (5, 0) belong to this line.
We can already see that all these points are in option B, then option B is the correct one.
PLEASE HELP ME!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!
Equations and inequalities fall under the umbrella of algebra. Algebra is the category of math where letters, like x and y, are used to represent numbers. These letters are called variables, and the goal of equations and inequalities is to find the value of the variable. An equation is a statement that two expressions or values are equal, shown by an equal sign, which looks like this: =. An inequality is a statement that two expressions or values are not equal, shown by an inequality sign. The four inequality signs look like this: > (“greater than”), 437
A= y - 78
B x = 46 + y
C= 4x + 5 = 950
D= 2b - 17 > 437
Answer:
b
Step-by-step explanation:
Answer:
the answer is D.
Step-by-step explanation:
Divide the polynomials.
right answers only
Answer:
x+9
Step-by-step explanation:
I got it right on the quiz
-3( 2r + 7) = 3 pls help
Answer:
R=-4
Step-by-step explanation:
-3(2r+7)=3
-6r-21=3
-6r=24
r=-4
I hope this is correct and have a great day
i need help!! please
========================================================
Explanation:
The old dimensions of the rectangle were 30 by 15.
The new dimensions are 30+x by 15+x, where x is some positive number.
The new rectangle dimensions multiply to 1000
(30+x)(15+x) = 1000
Use the FOIL rule to expand out the left side like so
(30+x)(15+x) = 1000
450+30x+15x+x^2 = 1000
450+45x+x^2 = 1000
x^2+45x+450
Then lets get everything to one side
x^2+45x+450 = 1000
x^2+45x+450-1000 = 0
x^2+45x-550 = 0
---------------------
From here we use the quadratic formula
Plug in a = 1, b = 45, and c = -550.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(45)\pm\sqrt{(45)^2-4(1)(-550)}}{2(1)}\\\\x = \frac{-45\pm\sqrt{4225}}{2}\\\\[/tex]
[tex]x = \frac{-45\pm65}{2}\\\\x = \frac{-45+65}{2} \ \text{ or } \ x = \frac{-45-65}{2}\\\\x = \frac{20}{2} \ \text{ or } \ x = \frac{-110}{2}\\\\x = 10 \ \text{ or } \ x = -55\\\\[/tex]
Earlier we defined x to be a positive number. This means we ignore x = -55. It makes no sense to add on a negative amount to each dimension.
The only practical answer is x = 10.
So each dimension is increased by 10 feet.
--------------------------
If x = 10, then the old dimensions of 30 by 15 bump up to 30+10 = 40 by 15+10 = 25
Then note how 40*25 = 1000, which helps confirm we have the correct dimensions.
--------------------------
Now go back to the question at hand: we want to find the new width. The old width was 30 feet. The new width is 30+x = 30+10 = 40 feet
Which situation leads to a unit cost of $6 per
football ticket?
Select one:
1)$6 paid for 2 football tickets
2)$6 paid for 6 football tickets
3)12 football tickets for $72
4)6 football tickets for $24
Can somebody tell me the equation to this please ?? ASAP
Answer:
y= -5/1 + 1.90
Step-by-step explanation:
The y-intercept is hard to tell
But the rest is right
Answer:
I have a picture if that helps
Step-by-step explanation:
The gardening store sells clay flower pots, which hold 2 litres of dirt, and ceramic flower pots, which hold 7 litres. Tara bought 35 flower pots, which will hold a total of 150 litres of dirt. How many of each flower pot did she buy?
Answer:
The number of clay flower pots = x = 19
The number of ceramic flower pots = y = 16
Step-by-step explanation:
Let
The number of clay flower pots = x
The number of ceramic flower pots = y
Tara bought 35 flower pots
= x + y = 35
x = 35 - y
The gardening store sells clay flower pots, which hold 2 litres of dirt, and ceramic flower pots, which hold 7 litres. Tara bought 35 flower pots, which will hold a total of 150 litres of dirt.
Hence:
2x + 7y = 150.... Equation 2
Substitute 35 - y for x in Equation 2
2 (35 - y) + 7y = 150
70 - 2y + 7y = 150
-2y + 7y = 150 - 70
5y = 80
y = 80/5
y = 16 flower pots
x = 35 - y
x = 35 - 16
x = 19 flower pots
The number of clay flower pots = x = 19
The number of ceramic flower pots = y = 16
Answer:
The number of clay flower pots = 19
The number of ceramic flower pots = 16
Step-by-step explanation:
1.
(03.01 LC)
The leg of a right triangle is 2 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle? (5 points)
2 units
6 units
Square root of 12 units
Square root of 20 units
Answer:
[tex]\sqrt{12}[/tex] units
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let x be the other leg, then
x² + 2² = 4²
x² + 4 = 16 ( subtract 4 from both sides )
x² = 12 ( take the square root of both sides )
x = [tex]\sqrt{12}[/tex] units
which can be simplified to 2[tex]\sqrt{3}[/tex] units , if required.
√2x-7+X= 5
Solve the equation with work shown below
Answer:
[tex]x=12(\sqrt2-1)[/tex]
Step-by-step explanation:
The given equation is :
[tex]\sqrt{2} x-7+x=5[/tex]
Add 7 to both sides of the equation.
[tex]\sqrt{2} x-7+x+7=5+7\\\\\sqrt{2} x+x=12[/tex]
Taking x common from both sides of the equation.
[tex]x(\sqrt{2} +1)=12\\\\x=\dfrac{12}{\sqrt2+1}[/tex]
Multiplying both numerator and denominator by [tex]\sqrt2-1[/tex]
[tex]x=\dfrac{12}{\sqrt2+1}\times \dfrac{\sqrt2-1}{\sqrt2-1}\\\\=\dfrac{12(\sqrt2-1)}{2-1}\\\\=12(\sqrt2-1)[/tex]
Hence, the value of x is [tex]12(\sqrt2-1)[/tex].
A pair of new headphones cost $20 to make. They get marked up in price 250% by a retail store before they are sold. How much will the headphones cost?
Answer:
$50
Step-by-step explanation:
Change 250 to a decimal:
250/100 = 2.50
multiple the price by this decimal to find the new price:
$20 x 2.50 = $50
The graph of a linear relationship passes
through (0, 2), (1,5), and (3, 11) but not
through (2, 7). Which of the following is
the equation for this linear relationship?
A y= 2x + 3 Cy=5x
B y = 3x + 2
Dy= 4x - 1
Answer:
The equation of the linear relationship is y = 3x + 2 ⇒ B
Step-by-step explanation:
To solve the question substitute the x in the equation by the x-coordinate of each point to find y, if y equals the y-coordinate of the point, then the point is on the graph of the equation
A.
∵ y = 2x + 3
→ Use the first point (0, 2)
∵ x = 0
→ Substitute x by 0 in the equation
∴ y = 2(0) + 3
∴ y = 0 + 3 = 3
∵ The y-coordinate is 2
∴ The point (0, 2) does not lie on the graph of the relationship
∴ The equation y = 2x + 3 doesn't represent the equation of the relationship
B.
∵ y = 3x + 2
→ Use the first point (0, 2)
∵ x = 0
→ Substitute x by 0 in the equation
∴ y = 3(0) + 2
∴ y = 0 + 2 = 2
∵ The y-coordinate is 2
∴ The point (0, 2) lies on the graph of the relationship
→ Use the second point (1, 5)
∵ x = 1
→ Substitute x by 1 in the equation
∴ y = 3(1) + 2
∴ y = 3 + 2 = 5
∵ The y-coordinate is 5
∴ The point (1, 5) lies on the graph of the relationship
→ Use the third point (3, 11)
∵ x = 3
→ Substitute x by 3 in the equation
∴ y = 3(3) + 2
∴ y = 9 + 2 = 11
∵ The y-coordinate is 11
∴ The point (3, 11) lies on the graph of the relationship
→ Use the fourth point (2, 7)
∵ x = 2
→ Substitute x by 2 in the equation
∴ y = 3(2) + 2
∴ y = 6 + 2 = 8
∵ The y-coordinate is 7
∴ The point (2, 7) doesn't lie on the graph of the relationship
∴ The equation of the linear relationship is y = 3x + 2
help me please! ill make you brainliest.
Someone please help with this question please
Step-by-step explanation:
Since Angle DAE = Angle BCE, lines AD amd BC are parallel (by Z-angles).
This means that Angle ADE = Angle CBE (by Z-angles).
We have 2 congruent angles and 1 congruent side (AD = BC, given).
By ASA congruence, triangles AED and CEB are congruent.
B.P. Mathur v. Union Of India
YALL I NEED HELP, I’m BEGGINGGGGGF
Answer:
the first one
Step-by-step explanation:
☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️
Can someone plz tell me the coordinates for D’