Answer:
Question!! What is the relationship between A and B?
Step-by-step explanation:
The sum of three terms in AP is 15. If the first two terms are each decreased by 1 and the last is increased by 1 then the resulting terms are in GP. find the numbers.
Answer:
3, 5, ,7 or 9, 5, 1
Step-by-step explanation:
Let the three terms in AP be a - d, a & a + d
where a = First term and d = Common difference.
Condition 1: sum of three terms in AP is 15.
a - d + a + a + d = 15
3a = 15
a = 15/3
a = 5
Condition 2: When first two terms are each decreased by 1 and the last is increased by 1 then new terms so obtained will be as follows:
a - d - 1, a - 1, a + d + 1
These terms are in G.P.
[tex] {(a - 1)}^{2} = (a - d - 1)(a + d + 1) \\ \\ {(5 - 1)}^{2} = (5 - d - 1)(5 + d + 1) \\ \\ {(4)}^{2} = (4 - d)(6 + d) \\ \\ 16 = 24 + 4d - 6d - {d}^{2} \\ \\ 0 = 8 - 2d - {d}^{2} \\ \\ {d}^{2} + 2d - 8 = 0 \\ \\ {d}^{2} + 4d - 2d - 8 = 0 \\ \\ d(d + 4) - 2(d + 4) = 0 \\ \\ (d + 4)(d - 2) = 0 \\ \\ d + 4 = 0 \: \: or \: \: d - 2 = 0 \\ \\ d = - 4 \: \: or \: \: d = 2 \\ \\ when \: d = - 4 \\ \\ a - d = 5 - ( - 4) = 9 \\ a = 5 \\ a + d = 5 - 4 = 1 \\ \\ when \: d = 2 \\ a - d = 5 - 2 = 3 \\ a = 5 \\ a + d = 5 + 2 = 7 \\ \\ thus \: three \: terms \: in \: AP \: are: \\9, \: 5, \: 1 \: \: or \: \: 3, \: 5, \: 7[/tex]
PLEASE HELP ASAP! harold makes a plan to save $500 per month for the next 5 years. He is depositing it in an interest bearing account at 2% APR (compounded monthly). What will be Harold’s balance at the end of 5 years?
Answer:
50
Step-by-step explanation:
Find a polynomial f(x) of degree 4 that has the following zeros. -7, 0, 1, 6
leave your answer in factored form.
please help! its my exam study guide and i need to finish it!
[tex]\begin{cases} x=-7\implies &x+7=0\\ x=0\implies &x=0\\ x=1\implies &x-1=0\\ x=6\implies &x-6=0 \end{cases}\qquad \implies (x+7)(x)(x-1)(x-6)=\stackrel{y}{0} \\\\\\ (x+7)(x)\stackrel{using~\mathbb{FOIL}}{(x^2-7x+6)}=0\implies (x^2+7x)(x^2-7x+6)=0[/tex]
[tex]\begin{array}{llll} x^2-7x+6\\ \qquad \times ~x^2\\\cline{1-1} x^4-7x^3+6x^2 \end{array}\qquad +\qquad \begin{array}{llll} x^2-7x+6\\ \qquad \times ~7x\\\cline{1-1} 7x^3-49x^2+42x \end{array} \\\\\\ (x^4-7x^3+6x^2)+(7x^3-49x^2+42x)=0 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x^4-43x^2+42x=y~\hfill[/tex]
Determine the largest integer that makes 2 - 3(x+8) > 12 - x true.
Answer:
2
Step-by-step explanation:
Because if you add 1 to 8 you get 9 then subtract 9 by 7 then and your answer is
Solve the equation. -10=2y
Answer:
y=-5
Step-by-step explanation:
-10/2=2y/2
-5=y
y=-5
Answer:
y = - 5
Step-by-step explanation:
You have yo divided the numbers
Cancel terms that are in both the numerator and denominator
Move the variable to the left
One kilometre is about 0.62 miles. It is 12 kilometres from Noah's house to the
ice skating rink. About how many miles is it from Noah's house to the ice
skating rink?
u'll get extra points if u answer guys!! pls help!!!!!
Answer:
7.44miles
Step-by-step explanation:
1km = 0.62miles
12km will be ; 0.62 × 12
= 7.44miles
which among the following
We have:
[tex]1-\frac{1}{3} >0[/tex] ; [tex]1- \frac{11}{17}>0[/tex] ; [tex]1-\frac{132}{157}>0[/tex] ⇒ right
[tex]\frac{-1}{7}, \frac{-51}{107},\frac{-347}{949} <0[/tex] ⇒ wrong
[tex]\frac{7}{5}, \frac{131}{47} ,\frac{945}{711} >1[/tex] ⇒ wrong
ANSWER: [tex]\frac{1}{3} ,\frac{11}{17} ,\frac{132}{157}[/tex]
ok done. Thank to me :>
Write -37.75 as a mixed number.
Answer:
[tex]-37\frac{3}{4}[/tex]
Step-by-step explanation:
0.75 is equivalent to three quarters, or (3/4).
3/4 would be the fraction. -37 would be the whole number.
[tex]-37.75 = \boxed{-37\frac{3}{4}}[/tex]
Hope this helps.
Answer:
- 37 3/4
Step-by-step explanation:
What is the answer to 1010 + 0101? (Binary) *
Answer:
1111 is the answer to your question.
30 POINTS!!!! SOMEONE PLEASE HELP ME!!!
Answer:
60 nickels
Step-by-step explanation:
When a ratio between coins is given, I like to consider the problem in terms of groups of coins. Here, each group would consist of 1 nickel and 0.20 quarters. The value of that group is
5¢ +0.20×25¢ = 10¢
Then the number of groups is ...
(total value)/(value of 1 group) = number of groups
600¢/10¢ = 60
Since each group has 1 nickel, there are 60 nickels.
__
Check
60 nickels + 12 quarters = $3.00 +3.00 = $6.00
_____
Additional comment
If you want to see this with equations and variables, you can do this.
Let n and q represent the numbers of nickels and quarters, respectively. The given relations are ...
0.05n +0.25q = 6.00
q = 0.20n
Substituting for q in the first equation gives ...
0.05n +(0.25)(0.20n) = 6.00
Simplifying gives ...
0.10n = 6.00
n = 6.00/0.10 = 60
HELPPPP ASAPPPPPPPPPPPP
Answer:
C
Step-by-step explanation:
- z > 8 equivalent inequality
Answer: z < -8
Step-by-step explanation:
Since z is negative, divide both sides by -1, which leaves you with z > -8.
Multiplying or dividing an inequality by a negative number flips the sign, thus the answer is z < 8.
Correct me if I am incorrect.
Example 8: Over the track-and-field season, the height Fred cleared in the high jump increase from 1.81 m to 1.96 m. a) Find Fred's percent increase in height. W b) What final height would Fred have to clear for a 20% increase in height over the track-and-field season?
Answer:
a. about 8.3%
b. 2.172 m
Step-by-step explanation:
a. 1.81 * x = 1.96
x = 1.083
Percent increase is approximately 8.3%
b. 1.81 * 1.2 = x
x = 2.172 m
1 minute is equal to 60 seconds. How many seconds are in 3 minutes, 37 seconds?
Answer:
217 Seconds.
Step-by-step explanation:
The answer is 217 seconds because 60x3+37=217.
expand and simplify
5(3y+2)+5(5y+2)
Answer:
Step-by-step explanation:
15y + 10 + 25y + 10
Answer:
Solution here,
Step-by-step explanation:
For simplify
First multiply the terms inside the brackets with the term outside the bracket i.e 5.
5(3y+2)+5(5y+2)
15y+10+25y+10
35y+20
B+8/2=6
How do I do this
Answer:
B = 2.
Step-by-step explanation:
First work out 8/2. Okay so how many 2's go into 8? 4.
We now have B + 4 = 6.
Now that we've simplified it a bit we can do a reverse equation and turn it into subtraction.
Take the answer (6) and 4 and put them into a subtraction equation,
6 - 4. And simple subtraction should be easy so 6 - 4 = 2.
So B equals 2. Let's check it! 2 + 4 = 6. I think that sounds right so that will be the answer. B=2.
Hope that helps. x
x + 7 when x = -11
What is the answer
find the slope
a line that passes between (-5, 8) and (2,4)
Answer:
Step-by-step explanation:
formula : m=(y2-y1)/(x2-x1)
(4 - 8) / (2 - - 5)
-4 / 7
m = -4 / 7 = -0.57143
review the proof (not in order) of the identity tan(0/2) = + √1-cos(0)/1+cos(0)
which is the correct sequence of steps
Answer:
1-3-4-2-5
Step-by-step explanation:
[tex]tan\frac{\theta}{2}[/tex] <== Given
[tex]\frac{sin\frac{\theta}{2}}{cos\frac{\theta}{2}}[/tex] <== Step 1
[tex]\frac{\frac{\sqrt{1-cos\theta}}{2}}{\frac{\sqrt{1+cos\theta}}{2}}[/tex] <== Step 3
[tex]\frac{\sqrt{1-cos\theta}}{\sqrt{1+cos\theta}}[/tex] <== Step 2 (as a result of Step 4)
[tex]\pm\sqrt{\frac{1-cos\theta}{1+cos\theta} }[/tex] <== Step 5
(x - y + z) : (y - z + 2w) : (2x + z - 10) = 2:3:5 Then ( 3x + 3z - 2w) : w = ?pgvzcmckyc?
Answer:
19
Step-by-step explanation:
in question given ,x = 2, y = 3, z = 5 in this way
(3x+3z+2w) and find the value of w . according to given values and put
Answer:
4 +30/w . . . . for any w≠0
Step-by-step explanation:
The given constraints resolve to 2 equations in 4 unknowns. There are an infinite number of solutions.
The ratio requirement means ...
(x -y +z)/2 = (y -z +2w)/3 = (2x +z -10)/5
Considering the first equality, we can multiply by 6 and subtract the right side.
3(x -y +z) -2(y -z +2w) = 0 ⇒ 3x -5y +5z -4w = 0
Considering the first and last expressions, we can multiply by 10 and subtract the right side.
5(x -y +z) -2(2x +z -10) = 0 ⇒ x -5y +3z = -20
These two equations have solutions ...
x = 10 -z +2w
y = 6 + 0.4z +0.4w
Using these expressions in the ratio of interest, we have ...
(3x +3z -2w) : w = (3(10 -z +2w) +3z -2w) : w = (30 -3z +6w +3z -2w) : w
= (30 +4w) : w
Expressed as a mixed number, the ratio of interest is ...
(30 +4w)/w = 4 +30/w . . . . an infinite number of solutions
__
For positive values of w that are divisors of 30, there are 8 possible values:
(w, ratio) = (1, 34), (2, 19), (3, 14), (5, 10), (6, 9), (10, 7), (15, 6), (30, 5)
_____
Check
It might be interesting to substitute the expressions for x and y into our original equation(s).
(x -y +z)/2 = ((10 -z +2w) -(6 +0.4z +0.4w) +z)/2 = (2 -0.2z +0.8w)
(y -z +2w)/3 = ((6 +0.4z +0.4w) -z +2w)/3 = (2 -0.2z +0.8w)
(2x +z -10)/5 = (2(10 -z +2w) +z -10)/5 = (2 -0.2z +0.8w)
All of these expressions are identical, as they should be.
Xavier has 29 baseball
cards he'd like to share
with his 3 best friends.
Each friend gets an equal
number of cards. How
many baseball cards will
be left over?
Math
Answer:
2
Step-by-step explanation:
29 % 3 = 9
3x9 = 27
29 - 27 = 2
Help help help help math math
Answer:
Yes, it is a function
Step-by-step explanation:
Each x value in the domain has its own output, and it does not have more than 1
The vertices of quadrilateral PQRS are listed.
P(3,7), Q(6,-2), R(0,-4), S(-3,5)
Which of the following is the strongest classification that identifies quadrilateral PQRS
A.
Quadrilateral PQRS is a square.
B.
Quadrilateral PQRS is a trapezoid.
C.
Quadrilateral PQRS is a rectangle.
D.
Quadrilateral PQRS is a parallelogram.
Answer:
It's C. for plato. It's a rectangle
Step-by-step explanation:
FILE BELOWAnswer:
its a rectangle .
Step-by-step explanation:
[tex]{ \color{darkred}{(2+√3)+(4-√3)}} = ?[/tex]
︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎
[tex](2 + \sqrt{3} ) + (4 - \sqrt{3} ) \\ = 2 + \sqrt{3} + 4 - \sqrt{3} \\ = 2 + 4 \\ = 6[/tex]
Answer:
6
Hope you could get an idea from here.
Doubt clarification - use comment section.
[tex]\huge \bf༆ Answer ༄[/tex]
Here's the solution ~
[tex] \sf(2 + \sqrt{3} ) + (4 - \sqrt{3}) [/tex][tex] \sf2 + \cancel {\sqrt{3} } + 4 - \cancel{\sqrt{3} }[/tex][tex] \sf6[/tex]Aarón rides his bike away from home at a constant speed he stops at the park for a while before riding back home at a constant speed
Answer:
Step-by-step explanation: This is the answer
The triangle and rectangle have the same perimeter.find the value of x.
Answer:
[tex]x + 5 \: + \: x \: + 6 \: + x + 7 = 2x - 1 + x + 7 + x + 7 + 2x - 1[/tex]
[tex]3x + 18 = 6x + 12[/tex]
[tex]18 = 3x + 12[/tex]
[tex]6 = 3x[/tex]
[tex]x = 6 \div 3 = 2[/tex]
[tex]x = 2[/tex]
I hope this helps you !!The base of a triangle is 4 ft more than the height. If the area is 30ft2, find the base and the height.
Answer:
Base = 10 ft. and the height = 6.
Step-by-step explanation:
Area of triangle = 1/2bh
base is 4 + h ⇔ base = 4 + h
height = h
Using the formula for the area of triangle substitute into the formula the given facts.
A = 1/2bh
30 = 1/2(4 + h) (h)
30 = 1/2(4h + h²) Multiply both sides by 2
60 = 4h + h²
-60 = -60 Add -60 to both sides
0 = h²+ 4h -60
(h + 10)(h - 6) = 0 Factor
h + 10 = 0 h - 6 =0
h = -10 h = 6
reject any negative number and use the positive answer for h.
So h = 6 and the base = 4 + 6 ; base = 10
I NEED HELP WITH THESE
I am pretty sure of my answers, so I just need someone to double check. Explanation is not needed because I know how to solve it, just needs to be checked. You can put one it you want.
Answer:
(b) 500 km (b) 6 secondsStep-by-step explanation:
1.The semi-major axis length is √47196900 = 6870 km. That distance from the center of the Earth means the satellite is ...
6780 -6370 = 500 . . . km
from the surface of the Earth.
The satellite is a maximum of 500 km from the Earth.
(It is a minimum of 250 km from Earth.)
__
2.The equation has a zero at t=6. When the car's velocity is zero, it is at a complete stop.
The car comes to a complete stop when time is 6 seconds.
(The car is still being accelerated, so it doesn't stay stopped.)
__
I prefer a graphing calculator for a quick solution. You can also solve this equation algebraically.
0 = 0.5t^2 -10.5t +45 . . . . t when v(t) = 0
t^2 -21t +90 = 0 . . . . . . . multiply by 2
(t -6)(t -15) = 0 . . . . . . . . factor
t = 6 or t = 15 . . . . . . . only t=6 is in the domain of the function
9
11 (a) Grapes cost £2 per kilogram.
Calculate the cost of 380g of grapes.
Answer:
£0.76
Step-by-step explanation:
1kilogram = 1000grams
1000g of grapes costs £2
380g costs = (380 × 2)/ 1000
760/1000 = £0.76
0.081 to the nearest hundredth
Answer:
0.08
Step-by-step explanation:
a 1 in the thousandths place is dropped in standard rounding to the nearest hundredth.
Answer:
0.08
Step-by-step explanation:
In 0.081, 0 is the tenth, 8 is the hundredth, and 1 is the thousandth. So as you want to approximate to the nearest hundredth, you have to look at the number behind 8 which is 1. And, 1 is less than 5, so you don't have to round up.