Answer:
1,187
Step-by-step explanation:
The nth term of an arithmetic sequence is expressed as;
an = a + (n-1)d
a is the first term
n is the number of terms
d is the common difference
Given the sequence 3, 11, 19, 27...
a = 3
d = 11-3 = 19-11 = 8
n = 149 (since we need the 149th term)
a149 = 3 + (149-1)(8)
a149 = 3+(148)(8)
a149 = 3+1,184
a149 = 1,187
Hence the 149th term is 1,187
Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.
~Thanks in advance !
Answer:
[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]
Step-by-step explanation:
We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.
First, we will need the distance formula, given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let the point on the locus be P(x, y).
So, the distance from P to (0, 2) will be:
[tex]\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}[/tex]
And, the distance from P to (0, -2) will be:
[tex]\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}[/tex]
So sum of the two distances must be 6. Therefore:
[tex]d_1+d_2=6[/tex]
Now, by substitution:
[tex](\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6[/tex]
Simplify. We can subtract the second term from the left:
[tex]\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}[/tex]
Square both sides:
[tex](x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)[/tex]
We can cancel the x² terms and continue squaring:
[tex]y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4[/tex]
We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:
[tex]-8y=36-12\sqrt{x^2+(y+2)^2}[/tex]
We can divide both sides by -4:
[tex]2y=-9+3\sqrt{x^2+(y+2)^2}[/tex]
Adding 9 to both sides yields:
[tex]2y+9=3\sqrt{x^2+(y+2)^2}[/tex]
And, we will square both sides one final time.
[tex]4y^2+36y+81=9(x^2+(y^2+4y+4))[/tex]
Distribute:
[tex]4y^2+36y+81=9x^2+9y^2+36y+36[/tex]
The 36y will cancel. So:
[tex]4y^2+81=9x^2+9y^2+36[/tex]
Subtracting 4y² and 36 from both sides yields:
[tex]9x^2+5y^2=45[/tex]
And dividing both sides by 45 produces:
[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]
Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.
Stella wnats to buy an atlas that costs 510, a novel that costs $8, and a comc that costs $6. She saved 516 from her pocket money. How much
more money does she need to save? What equation is correct?
Answer:
where are the equations
Step-by-step explanation:
m is how much more she needs to save
510+8+6=516+m
m=8
Please help me ASAP
Answer:
BOTH SIDES ARE 12
Step-by-step explanation:
Answer:
x and y is equal to 33° as x and y are the equal angles of the isosceles triangle given in the figure.
find the rate of change /slope between its ordered pairs
(-5,13) and (1,1)
(-5,14)and (12,-21)
(1,1)and(12,-21)
Answer:
1.) -2
2.) -2
3.) -3
Step-by-step explanation:
Since we can't make a graph, we can make a table
(-5,13) and (1,1)
x y
-5 13
1 1
From 13 to 1, you subtract 12 ( y-section)
From -5 to 1, you add 6 (x-section)
Now we can do y/x
y/x = 12/6 = -2
The slope for this first one is (-2).
(-5,14) and (12,-21)
x y
-5 14
12 -21
From 14 to -21, you subtract 34
From -5 to 12, you add 17
Now we can do y/x
y/x = -34/17 = -2
The slope for this second one is (-2)
(1,1 )and (12,-21)
x y
1 12
12 -21
From 12 to 21, you subtract 33
From 1 to 12, you add 11
Now we can do y/x
y/x = -33/11 = -3
The slope for this third one is (-3)
Hope this helped!
Have a supercalifragilisticexpialidocious day!
16q3-48q2+32q what would be the steps on how to do this? please?
Answer:
Its nothing complicated, you just have to combine all the like terms, just make sure the lvariables are the same before combining of course.
so assuming the gaps missng are exponents
the solution is the same exact thing
it can’t be simplified anymore since 16q^3 or -48q^2 can’t due to different exponents which thefore can’t combine
same with 32 q, nothing combines
The answer is the original expression
In a high school football stadium, there are 3,892 seats. The stadium has 14 sections. Each section has the same number of seats.
How many seats are in each section?
PLZ help!!!!!! :(
Answer:
278, pls brainliest
Step-by-step explanation:
Answer:
278 seats per section
Step-by-step explanation:
Division
The division allows us to divide or 'share' numbers to find the answer to a problem.
For example, to evenly share 10 sweets between 5 kids, we use division to find 10/5 = 2 sweets per kid.
It's given a high school football stadium has 3,892 seats distributed in 14 sections and each section has the same number of seats.
To find the number of seats in each section we use division:
3,892 seats / 14 sections = 278 seats per section
Solve.
3/5x - 7 = 23
A. x = 40
B. x = 45
C. x = 50
D. x = 55
Answer:
(C) x=50
Step-by-step explanation:
[tex]\frac{3}{5 }x -7=23[/tex]
[tex]\frac{3x}{5} -7=23[/tex]
[tex]\frac{3x}{5} -7+7=23+7[/tex]
[tex]\frac{3x}{5}=30[/tex]
[tex]3x=30* 5[/tex]
[tex]3x=150[/tex]
[tex]x=50[/tex]
Answer:
(C) X = 50
Step-by-step explanation:
(3/5)*x-7 = 23 // - 23
(3/5)*x-23-7 = 0
3/5*x-30 = 0 // + 30
3/5*x = 30 // : 3/5
x = 30/3/5
x = 50 (Sorry if it's wrong)
If water freezes at 0ᴼC, which temperature is above freezing
Answer:
32 F
Step-by-step explanation:
Find the surface area of the cuboid shown below
Answer:
Surface area of cuboid = 352 cm
Step-by-step explanation:
Given that:
Height of cuboid = 8 cm
Length of cuboid = 12 cm
Width of cuboid = 4 cm
Surface area = 2lw + 2lh + 2hw
Putting all the values;
Surface area = 2*12*4 + 2*12*8 + 2*8*4
Surface area = 96 + 192 + 64
Surface area = 352 cm
Hence,
Surface area of cuboid = 352 cm
Fill in the missing numbers to complete the pattern:
5.81, ,5.91,5.96, ,6.06
Write each percent as a fraction in simplest form.
12%
Elisa is saving an equal amount each week for 8 weeks to buy a video game that costs $40. How much is she saving each week?
A $4
B $5
C $32
D $48
Jesse chose C as the correct answer. How did he get that answer?
Answer:
Jesse must have subtracted the 8 weeks from $40 to get $32 but the answer should be b $5
Step-by-step explanation:
Drag each number to show whether it is equal to 50% , 0.2 , or neither
Answer:
Step-by-step explanation:
50% = 1/2, 0.5
0.2 = 2%
Other = 20%, 20/100, 1/5
Answer:
I put this, Its correct.
Step-by-step explanation:
50% : 1/2, 0.5.
0.2 : 20/100, 20%, 1/5.
Other : 2%
What is the value of 20+6•5/-2
Answer:
The answer is 25
Step-by-step explanation:
6•5=30
30+20=50
50/-2=25
Pls help my brain is fried and this is my last question
Answer: 14, 16, 18, 20 in that order
Step-by-step explanation:
If the bottom response square is asking for a general equation, it would be y=x+7
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
the middle sign
Step-by-step explanation:
x+3y=6
3x+9y=72
cdxddxdxfcfcgcffcffcfchcfcfhxhc
Answer:
No solution
Step-by-step explanation:
1) 3(x+3y=6)
3x+9y=72
2) 3x+9y=18
3x+9y=72
3) 3x+9y=18
-
3x+9y=72
____________
-54
40.8-10 to the power of 2
Answer:
-4
Step-by-step explanation:
8-10 = -2
-2^2 = -4
948.64
Subtract then multiply by itself
No offense but can't you use a calculator?
Solve the system of equations using elimination, or write “no solutions” or “infinite solutions” where applicable
4x-y = 7
Answer:
no solutions
Step-by-step explanation:
i guess im
Zoe went shopping for a new pair of pants. The listed price of the pair of pants was
$45, but the price with tax came to $46.35. Find the percent sales tax.
ASAP!
Answer:
3%
Step-by-step explanation:
46.35 - 45 = 1.35 (change)
change/original price X 100
1.35/45 = 0.03
0.03 X 100 = 3
sales tax 3%
x-3y=7
2х-6у=12
Solve the following systems
Answer:
Step-by-step explanation:
this system doesnt have any solutions
if you multiply the first equation by 2 you will get
2x-6y=14
second equation is
2x-6y=12
the result will -12=14
no solutions
Given right triangle XYZ with altitude WZ, let WY = 10 cm and XY = 13 cm. Find the
length of WZ.
A.5.4
B.11.4
C.7.3
D.3
Which of the following statements is false?
8<8
2>8
2<8
2<8
Answer:
8<8 and 2>8 are both false
Answer:
B
Step-by-step explanation:
Part 1
Washington, DC, was warmer in February (4.3°F)than in December (44°F). Write an inequality for this relationship.
Answer:
Step-by-step explanation:
4.3 °F > 4 1/4 °F
Find the value of x. Your answer must be exact.
х
45° 18
Answer:
x = 63
Step-by-step explanation:
Simplifying
x + -18 = 45
Reorder the terms:
-18 + x = 45
Solving
-18 + x = 45
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '18' to each side of the equation.
-18 + 18 + x = 45 + 18
Combine like terms: -18 + 18 = 0
0 + x = 45 + 18
x = 45 + 18
Combine like terms: 45 + 18 = 63
x = 63
Simplifying
x = 63
the measure of the angles in a heptagon measure 95 107 132 138 145 and 158 what is the measure of the 7th angle
Answer:
ANSWER:123
Step-by-step its very simple its puttin x+11 is how u get ur answer by adding the numbers close to that one angle
The measure of the seventh angle in the heptagon is 125 degrees.
What is Polygon?A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
We are given the measures of six angles in the heptagon, which are:
95, 107, 132, 138, 145, and 158 degrees
Sum of angles in Heptagon is 900 degrees.
To find the measure of the seventh angle, we can subtract the sum of the six known angles from the sum of all the angles in the heptagon:
Measure of the seventh angle = Sum of angles - Sum of known angles
Measure of the seventh angle = 900 degrees - (95 + 107 + 132 + 138 + 145 + 158) degrees
Measure of the seventh angle = 900 degrees - 775 degrees
Measure of the seventh angle = 125 degrees
Therefore, the measure of the seventh angle in the heptagon is 125 degrees.
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help for last one please
Answer:
the slope is one since the line rises once and runs once
Which of the following fraction pairs is equivalent?
6/12 and 8/20. 16/20 and 20/35. 2/6 and 7/21. 8/24 and 8/20
Answer:
2/6 and 7/21
Step-by-step explanation:
thi is due at 9:00 please help
Answer:
-2 -4
Step-by-step explanation:
saying to use 20 letters lol hope that helps
PLEASE HELP!!
Which inequality describes all the solutions to -5x + 6 -9
B. x 4
Answer:
-5x-3
Step-by-step explanation:
-5x+6-9=-5x-3
The inequality that describes all the solutions to the given inequality expression is x > 4
Given the inequality expression -5x + 6 < 2(-3 − x)
Expand the right-hand side of the ineqality
-5x + 6 < -6 - 2x
Collect the like terms
-5x + 2x < -6 - 6
-3x < -12
Divide both sides by -3
-3x/-3 > -12/-3
x > 4
Hence the inequality that describes all the solutions to the given inequality expression is x > 4
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