Answer:
4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....
Step-by-step explanation:
Fifth term (a₅) = [tex]\frac{1}{4}[/tex]
Common ratio (r) = [tex]\frac{1}{2}[/tex]
n = 5
The formula to find the [tex]n^{th}[/tex] term of a geometric sequence is
a₅ = a₁r⁽ⁿ⁻¹⁾
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(5-1)}[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(4)}[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁* [tex]\frac{1*1*1*1}{2*2*2*2}[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{16})[/tex]
Flip the sides of the equation
a₁*[tex](\frac{1}{16})[/tex] = [tex]\frac{1}{4}[/tex]
Multiply both sides by 16
a₁*[tex](\frac{1}{16})[/tex]*16 = [tex]\frac{1}{4}[/tex]*16
Cancelling out the 16's from the top and bottom of the left side
a₁ = [tex]\frac{16}{4}[/tex]
=> a₁ = 4
So, first term of the geometric sequence is 4.
Common ratio = [tex]\frac{1}{2}[/tex]
Second term = First term * Common ratio
= 4* [tex]\frac{1}{2}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
Third term = Second Term * Common ratio
= 2 * [tex]\frac{1}{2}[/tex]
= [tex]\frac{2}{2}[/tex]
= 1
Fourth term = Third Term * Common ratio
= 1 * [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{2}[/tex]
Fifth term (given) = [tex]\frac{1}{4}[/tex]
So, the geometric sequence would be
4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....
Which of the following is a factor of 2[tex]x^{4}[/tex] + 22x[tex]x^{3}[/tex] + 60x[tex]x^{2}[/tex]?
[tex]x^{3}[/tex]
[tex]x^{4}[/tex]
x + 4
x + 5
[tex]2x^4+22x^3+60x^2=2x^2(x^2+11x+30)=2x^2(x^2+6x+5x+30)\\\\=2x^2[x(x+6)+5(x+6)]=2x^2(x+6)(x+5)\\\\Answer:\ x+5[/tex]
Answer:
(x+5) is the final answer.
Step-by-step explanation:
We have to find the factors of [tex]2x^4+22x^3+60x^2[/tex]
Then select correct choice or choices from the given options.
[tex]2x^4+22x^3+60x^2[/tex]
[tex]=2x^2(x^2+11x+30)[/tex]
[tex]=2x^2(x^2+6x+5x+30)[/tex]
[tex]=2x^2(x(x+6)+5(x+6))[/tex]
[tex]=2x^2((x+5)(x+6))[/tex]
[tex]=2x^2(x+5)(x+6)[/tex]
From above factors, we see that only (x+5) is correct.
Hence (x+5) is the final answer.
A store owner bought a pair of headphones fo$150. He wanted to sell them for a profit of 30%. What price would he have to mark the headphones in order to make a profit?
Answer:
180
Step-by-step explanation:
30% of 150 = 30
because
30% of 15 = 3
30 + 150 = 180
Answer:
Step-by-step explanation:150+30=180
Which of the following is the equation of a circle whose center is at the origin and whose diameter has end (-1,2) and (1,-2)
Answer:
x² + y² = 5
Step-by-step explanation:
The circle with center (h, k) and radius r has equation ...
... (x -h)² + (y -k)² = r²
You can find r² using the Pythagorean theorem or the distance formula, or you can simply calculate what it needs to be to make one or the other of the points lie on the circle.
For (h, k) = (0, 0), the equation is ...
... (x -0)² + (y -0)² = r²
Using (-1, 2) for (x, y), we can find r² as ...
... (-1 -0)² + (2 -0)² = r² = 1 + 4 = 5
Then the circle equation is ...
... x² + y² = 5
the graph below shows the relationship between the number of cookies made and the number of pans used:
Which statement best describes point A on the graph?
A: four pans make 16 cookies
B: four pans make 32 cookies
C: One pan makes 16 cookies
D: One pan makes 32 cookies
Answer:
B four pans make 32 cookies
Which equations have a value less than 6,766? A. one fourth x 6,766 = ________ B. 6 x 6,766 = ________ C. one half x 6,766 = ________ D. 1 x 6,766 = ________ A and C D and B A and B C and D
The values less than 6,766 are one fourth x 6,766 and one half x 6,766 (A and C options are correct)
What is an expression?Numbers, symbols and operators (such as and times) grouped together that show the value of something.
Given is an expression, 6,766
The values less than 6,766 are,
i) 1/4x6,766 = 1691.5
1691.5 < 6,766
ii) 1/2x6,766 = 3383
3383 < 6,766
Hence, one fourth x 6,766 and one half x 6,766 are correct answers.
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Tabitha walked 13.5 miles in 3 hours. at that speed how many miles will she wallk in seven hours?
Answer: 31.5 miles
Step-by-step explanation: know how many miles tabitha walked per hour, which is 4.5 miles. then multiply 13.5 x 2, and add 4.5 to receive your answer - 31.5.
Answer:
Step-by-step explanation: The answer is 31.5 miles. The way I got it is by multiplying 13.5 by 2 because that will be 6 hours already. That gives me 27. Then you divide 13.5 to get how much she walk for just 1 hour which is 4.5. When you add that to 27, you get 31.5. Hope this helps!!!!!
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What is the length of if ?
8 in.
8.75 in.
10.25 in.
14 in.
Answer:
Diagram attached
AJ = 8.75 in.
Step-by-step explanation:
Since triangles HBA & HKJ are similar,
BH/AH = KH/JH
3 in /5.25 in = 8 in /JH
JH = 14 in
JA = JH - AH = JH - 5.25 in = 8.75 in
HJ = 14 in.
AJ = 14 in - 5.25 in
AJ = 8.75 in.
Which equation is a point slope form equation for line AB ? y+1=32(x−1) y+1=−32(x−1) Four-quadrant Cartesian graph with integer tickmarks from -9 to 9 (or -10 to 10) for x and y axes, with a straight line with arrowheads drawn through two points labeled A and B. Point A is at (-3,5) and point B is at (1,-1).
Answer:
The second option is correct. The point slope form of AB is [tex]y+1=\frac{-3}{2}(x-1)[/tex].
Step-by-step explanation:
The given points are A(-3,5) and B(1,-1).
Slope of a line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of AB is
[tex]m=\frac{-1-5}{1-(-3)}[/tex]
[tex]m=\frac{-6}{4}[/tex]
[tex]m=\frac{-3}{2}[/tex]
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is slope of the line.
Case 1: The slope of the line is [tex]\frac{-3}{2}[/tex] and the point is (-3,5). The point slope form of AB is
[tex]y-5=\frac{-3}{2}(x+3)[/tex]
Case 1: The slope of the line is [tex]\frac{-3}{2}[/tex] and the point is (1,-1). The point slope form of AB is
[tex]y+1=\frac{-3}{2}(x-1)[/tex]
Therefore the point slope form of AB is [tex]y+1=\frac{-3}{2}(x-1)[/tex]. Option 2 is correct.
What is the value of x in the equation 2x + 3y = 36, when y = 6?
8
9
27
36
THE ANSWER IS.......
Answer:
x=9
Step-by-step explanation:
2x+3y =36
We know y =6, so we can substitute this into the equation
2x+ 3(6) = 36
2x+18 = 36
Subtract 18 from each side
2x+18-18 = 36-18
2x =18
Divide each side by 2
2x/2 =18/2
x=9
I really like that you put the answer out there for other people. that's pretty cool! B) 9
What is the y intercept of the line with the equation y=2x+8
Answer:
in the point slop form y=2x+8
the slope is 2
the y intercept is 8
The slope-intercept form of line:
y = mx + b
m - slope
b - y-intercept
We have y = 2x + 8. Therefore:
slope m = 2
y-intercept b = 8
Answer: y-intercept = 8.Please help with this ...Its very urgent..
Answer: q²x² - p³x + 3pqx + q = 0
Step-by-step explanation:
Since a and B are the roots of x² - px + q = 0, then x = a and x = B
⇒ (x - a)(x - B) = 0
⇒ x² - ax - Bx + aB = 0
⇒ x² - (a + B)x + aB = 0
Comparing this to the given equation of x² - px + q = 0, we discover that
p = a + Bq = aBNext, given the roots for the new equation as [tex]x = \dfrac{a}{B^2} \quad\text{and}\quad\ x=\dfrac{B}{a^2}[/tex]
⇒ [tex]\bigg(x - \dfrac{a}{B^2}\bigg)\bigg(x-\dfrac{B}{a^2}\bigg)=0[/tex]
⇒ (B²x - a)(a²x - B) = 0
⇒ a²B²x² - a³x - B³x + aB = 0
⇒ a²B²x² - (a³ + B³)x + aB = 0
Let's look at each term individually:
1st term: a²B²x² = (aB)²x² = q²x² (since q = aB)
2nd term: (a³ + B³)x cubic formula can be used
= [(a + B)(a² - aB + B²)]x
= [(a + B)(a² + (2aB - 3aB) + B²)]x
= [(a + B)(a² + 2aB + B² - 3aB)]x
= [(a + B)(a + B)² - 3aB)]x
= [( p )( p² - 3 q )]x since p = a + B and q = aB
= (p³ - 3pq)x distributed "p" into p² - 3q
= p³x - 3pqx distributed "x" into p³ - 3pq
3rd term: aB = q since q = aB
Put it all together:
q²x² - (p³x - 3pqx) + q = 0
⇒ q²x² - p³x + 3pqx + q = 0
Write the explicit formula for the sequence. -1, 4, -16, 64,... A) an = (4)(n-1) B) an = (-4)(n-1) C) an = -(4)(n-1) D) an = -(-4)(n-1)
Answer:
A
Step-by-step explanation:
Answer:
If on USA TEST PREP it is D
Step-by-step explanation:
6691 ÷28. solved by long divison
To calculate 6691 divided by 28 using long division, divide each set of numbers step by step to arrive at a quotient of 238 with a remainder of 27, resulting in a decimal of approximately 238.96 when rounded.
The question involves the process of long division which is a method used in arithmetic. The student is trying to divide 6691 by 28:
Divide 66 by 28, which goes 2 times. Write 2 above the division bar, to the right of the first quotient place.
Multiply 2 by 28, which is 56, and subtract that from 66 to get a remainder of 10. Bring down the next digit, 9, to make 109.
Divide 109 by 28, which goes 3 times. Write 3 on the division bar. Multiply 3 by 28 (equals 84) and subtract from 109 to get 25.
Bring down the next digit, 1, to make 251. Divide this by 28, which goes 8 times. Eight times 28 is 224. Subtract this from 251 to get 27.
27 is less than 28, so the division process stops here. The answer up to this point is 238, with a remainder of 27.
The long division calculation of 6691 divided by 28 is 238 with a remainder of 27 or as a decimal, 238.96.
10$ for 4 cans of soup ratio and unit rate
What is the seventh term of the sequence 2, 3, 4 1/2 …?
Answer:
22 25/32
Step-by-step explanation:
well you just dividde the number in half and add the half and continue this and that's the seventh term. please be grateful it took me five minutes to do this
The seventh term of this sequence is 34.17875
Given : Each consecutive term is calculated by adding the half of preceding term to the preceding term.
Like : 2 + 1/2 (2) = 2 + 1 = 3
3 + 1/2 (3) = 3 + 3 / 2 = 3 + 1.5 = 4.5 or 4 1/2
4.5 + 1/2 ( 4.5 ) = 6.75
Similarly :
6.75 + 1/2 (6.75) = 10.125
10.125 + 1/2 (10.125) = 15.1875
15.1875 + 1/2 (15.1875) = 22.78125
22.78125 + 1/2 (22.78125) = 34.17875
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Classify the sequence (an) =(1,16,31,46,...) as arithmetic, geometric, or neither. If there is not enough information to classify the sequence, choose not enough information.
The manager of a store orders model railroad sets that cost $390 and sells them for $429. What is the mark-up, as a percentage?
Answer:
10%
Step-by-step explanation:
We have been given that the manager of a store orders model railroad sets that cost $390 and sells them for $429.
We will use markup % formula for our given problem.
[tex]\text{Markup percentage}=\frac{\text{Selling price- Cost}}{\text{Cost}}\times 100[/tex]
[tex]\text{Markup percentage}=\frac{429-390}{390}\times 100[/tex]
[tex]\text{Markup percentage}=\frac{39}{390}\times 100[/tex]
[tex]\text{Markup percentage}=\frac{1}{10}\times 100[/tex]
[tex]\text{Markup percentage}=10[/tex]
Therefore, markup is 10% of cost.
if the cost of 3 pies is $20.What is the cost for 6 pies
one gallon is equal to about 3.785 liters .what is the greatest number of whole liters of water u could pour into a one-gallon container without it overflowing ? explain your answer
We know that there are about 3.785 liters in 1 gallon. From here we could pour 3 whole liters into a one-gallon container without overflowing since 3 < 3.285 liters. But if we try to pour the next whole liter( 4 liters) it would be too much since 4 is greater then 3.785 liters. So the answer is 3 liters.
Hope this helps. <3
A Youth chorus of 30 members. There are 14 boys in the chorus. What is the ratio of boys to girls in the simplest form?
A: 7/15
B: 8/15
C: 7/8
D: 8/7
Answer:
C PLEASE GIVE BRAINLIEST
Step-by-step explanation:
30 - 14 = 16girls
ratio is : 14/16 = 7/8
Answer:
C
Step-by-step explanation:
I took the test
Alice planted some corn in the back yard and measures it’s height regularly. The last time she checked, the stalks were 60 inches tall. Now they are 72 inches tall. What is the percent of increase in the height of the stalks?
The percentage increase in the height of the corn stalks is 20%. This was calculated by subtracting the old height from the new height, dividing by the old height, and then multiplying by 100.
Explanation:The question is asking about the percentage increase in the height of the corn stalks that Alice planted. The stalks were previously 60 inches tall and now, they are 72 inches tall.
The formula to calculate the percentage increase is:
[(New Value - Old Value) / Old Value] x 100%
Substituting the given values into the formula, we get
[ (72 - 60) / 60 ] x 100%
This simplifies to [12/60] x 100%, which equals to 20%.
Therefore, there has been a 20% increase in the height of the corn stalks.
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Miss Johnson drives to work everyday when she left for work one day the automator mileage gauge on her car read 38643.8 when she returned to her house at the end of the day the automator red 38 points 668.6 if she didn't drive anywhere else during the day but to work and back how many miles is it from her house to her work explain how you got your answer
Answer:
Distance from her house to her work = 12.4 Miles
Step-by-step explanation:
Given :-
==> Automator mileage gauge read 38643.8 Miles before she left to work.
==> Automator mileage gauge read 38668.6 Miles after she came home from work.
==> She didn't drive anywhere else during the day. home to work & work to home.
Car driven during the day = 38668.6 - 38643.8
= 24.8 Miles
Let the distance from home to work be X
*It is assumed that Distance from home to work = Distance from work to home
So, Distance from work to home = X
Total distance driven during the day = Distance from home to work + Distance from work to home
Total distance driven during the day = X + X
24.8 = 2X
24.8 ÷ 2 = X
12.4 = X
Distance from her house to her work = 12.4 Miles
Answer: I think the answer is 24.8
Step-by-step explanation:
Given: △AKL, AK=9 m∠K=90°, m∠A=60° Find: The perimeter of △AKL The area of △ AKL
Answer:
Perimeter of ΔAKL is, [tex]27 +9 \sqrt{3}[/tex] units.
Area of ΔAKL is, [tex]\frac{81\sqrt{3} }{2}[/tex] square units
Step-by-step explanation:
Given: In ΔAKL , AK = 9 units , [tex]m\angle K = 90^{\circ}[/tex] and [tex]m\angle A= 60^{\circ}[/tex].
In ΔAKL
[tex]\tan (A) = \frac{KL}{AK}[/tex]
Substitute the value AK = 9 units and [tex]m\angle A =60^{\circ}[/tex] to solve for KL ;
[tex]\tan(60^{\circ}) = \frac{KL}{9}[/tex]
[tex]\sqrt{3} = \frac{KL}{9}[/tex]
⇒[tex]KL = 9\sqrt{3} units[/tex]
In right angle ΔAKL,
Using Pythagoras theorem;
[tex]AL^2 = AK^2+KL^2[/tex] ......[1]
Substitute AK = 9 units and [tex]KL =9\sqrt{3} units[/tex] in [1] to solve for AL;
[tex]AL^2 = 9^2+(9\sqrt{3})^2[/tex]
[tex]AL^2 = 81+(81 \cdot 3)[/tex]
[tex]AL^2 = 81+243 = 324[/tex]
[tex]AL = \sqrt{324} = 18 units[/tex]
Perimeter of triangle is the sum of all the sides.
Perimeter of triangle AKL = AK +KL +AL = [tex]9 + 9\sqrt{3} + 18 = 27 +9 \sqrt{3}[/tex] units.
Formula for Area of right angle triangle is given by:
[tex]A = \frac{1}{2} Base \times Height[/tex]
Area of triangle AKL= [tex]\frac{1}{2} (9\sqrt{3}) \times (9)[/tex]
= [tex]\frac{81\sqrt{3} }{2}[/tex] square units
Final answer:
The perimeter of triangle AKL is approximately 29.09 m, and the area is 20.25 m², calculated using the properties of a 30°-60°-90° right triangle.
Explanation:
To find the perimeter of △AKL, we need to determine the lengths of all three sides. We know that AK = 9 m, ∠K = 90° (which makes △AKL a right triangle), and ∠A = 60°. Because the angles in a triangle add up to 180°, ∠L must be 30° (180° - 90° - 60°). In a 30°-60°-90° right triangle, the lengths of the sides are in the ratio 1:√3:2. Thus, if AK is the side opposite the 60° angle, AL must be half of AK, and KL must be AK times √3.
Therefore, AL = ½ × 9 m = 4.5 m, and KL = √3 × 9 m ≈ 15.59 m. The perimeter is the sum of AK, AL, and KL: 9 m + 4.5 m + 15.59 m ≈ 29.09 m.
The area of △AKL can be found using the formula for the area of a right triangle, which is ½ × base × height. AK and AL can serve as the base and height, respectively, so the area A is ½ × 9 m × 4.5 m = 20.25 m².
What is the simplified form of the rational expression below? 6x^2-54/5x^2+15x
The simplified form of the rational expression 6x^2-54/5x^2+15x is 6(x - 3)/5x. This was achieved by factoring the original expressions, cancelling out common terms, and applying the difference of squares formula.
Explanation:The subject here is the simplification of a rational expression. First, let's factor the numerator (6x^2 - 54) and the denominator (5x^2 + 15x). The common factor in the numerator is 6 and in the denominator is 5x. After factoring we get:
6x^2 - 54 = 6(x^2 - 9)
5x^2 + 15x = 5x(x + 3)
Now, we can use the property a^2 - b^2 = (a + b)(a - b) to further simplify x^2 - 9 to (x - 3)(x + 3). This gives our new numerator as 6(x - 3)(x + 3).
The denominator 5x(x + 3) remains the same. Therefore, the simplified form of the rational expression is 6(x - 3)(x + 3)/5x(x + 3). The (x + 3) terms can be cancelled out leaving us with the final simplified rational expression of:
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Find the coordinates of the midpoint for segment HX if is H(7, 10) and X (5, -8)
Answer:
(6,1)
Step-by-step explanation:
I used the Midpoint Formula.
3r-34r+80 please factor this
Answer:
(3r-10) (r+8)
Step-by-step explanation:
3r-34r+80
The first step is to combine like terms
3r - 34r
is -31r
-31r+80
We cannot factor since 31 is a prime number and 80 is not a multiple of 31
If you mean
3r^2-34r+80
(3r-10) (r+8)
Write -3/4x-6 in standard form using integers
A. -3x+4y=-24
B. 3x+4y=24
C. 3x+4y=-24
D. 3x+4y=-6
Answer:
[tex]3x+4y=-24[/tex]
Therefore, option C is correct.
Step-by-step explanation:
We have been given the equation:
[tex]y=\frac{-3x}{4}-6[/[/tex]
We will take LCM 4 on right hand side of the above equation:
[tex]y=\frac{-3x-24}{4}[/tex]
Now, we will multiply the 4 in denominator on right hand side to the y in left hand side pof the equation we get:
[tex]4y=-3x-24[/tex]
After rearranging the terms we get:
[tex]3x+4y=-24[/tex]
Therefore, option C is correct.
The area of a square is 729 square centimeter. How long is each side of the square?
Answer:
27 cm
Step-by-step explanation:
So the square root of 729 is 27
Harper knows he is 50 yards from the school. The map on his phone show that the school is 3/4 inches from current location. How far is Harper from home if map shows the distance as 3 inches
Answer: 200 yards
Step-by-step explanation:
So if 3/4 inches on the map is equal to 50 yards then you could divide the 3 inch distance from him to his home by 3/4 and then multiply that answer by 50. So 3 ÷ 3/4 = 4. 4 * 50 = 200. He is 200 yards from his home.
Answer:
Harper is 200 yards away home.Step-by-step explanation:
To solve this problem, we use the rule of three, if 50 yards represents 3/4 inches, how many yards would represent 3 inches?
[tex]x=3in\frac{50yd}{\frac{3}{4}in } =3\frac{200}{3}yd=200yd[/tex]
So, 3 inches represents 200 yards, that means Harper is 200 yards away home.
Remember that the rule of three is just about using the ratio that the problem already gave.
Therefore, the answer is 200 yards.
The regular price for a sweater is $48. The store is having buy one get one 1/2 off sale. If you buy 2 sweaters for that price what percent discount is that ?
Answer: 25%
Step-by-step explanation:
Hi, if you buy 2 sweaters at full price (100%)
$48 x 2 = $96
"Buy one get one 1/2 off sale"´price
48 + (48/2) = 48 +24 = $72
So, the normal price for both sweaters (96) multiplied by a percentage is equal to the "buy one get one 1/2 off sale” price.
96 x =72
x =72/96 = 0.75
Multiplying by 100 to obtain the percentage form
0.75 =75%
So, the sale price is %75 of the full price.
To obtain the percent discount.
100%-75% = 25%