Answer:
[tex]\huge\boxed{a_n=1\cdot(-2)^{n-1}}[/tex]
Step-by-step explanation:
[tex]a_n=a_1r^{n-1}[/tex]
We have the geometric sequence: 1, -2, 4, -8, ...
Find the common ratio:
[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}[/tex]
[tex]a_1=1,\ a_2=-2[/tex]
substitute:
[tex]r=\dfrac{-2}{1}=-2[/tex]
Substitute
[tex]a_1=1;\ r=-1[/tex]
to
[tex]a_n=a_1r^{n-1}[/tex]
[tex]a_n=1\cdot(-2)^{n-1}[/tex]
Answer:
[tex]a_{n}=1 (-2)^{n-1}[/tex]
Step-by-step explanation:
Hi there!
Let's do it,
1)[tex]1,-2,4,-8[/tex]
First let's find the q, the common ratio by dividing the second term by the anterior one.
-2:1 =-2
4:-2=-2
So the common ratio is -2. Plugging in on the General formula:
[tex]a_{n}=a_{1}q^{n-1}[/tex]
[tex]a_{n}=1 (-2)^{n-1}[/tex]
1. George want to score at least a 90% on his math tests this quarter. So far his test scores are 88, 97 and
80. What does George need to score on his last test to average at least 90%?
Define variable:
Equation:
Solution:
check my work please! it’s number 1 :)
Answer:
Yes you are correct.
Step-by-step explanation:
The best way to check theese types of questions is go back in plug in X with your answer so 88+97+80+90(which is x)=360 then divide by 4 and get 90! So yes you are correct good job!
please help attachment
Answer:
v = 7
Step-by-step explanation:
a. v = 5x + 2y
= 5 × 3 + 2 × -4
= 15 + -8
= 7
Sorry I know only the A one anyways , hope this helps :)
Answer:
Step-by-step explanation:
a v = 5x+ 2y = 5*3 + 2*-4 = 7
b 3p(p+5) = 3p^2 =15p
c 4k = 44
k=44/4 =11
i hope the person who had deleted my answer this much explanation is only required if not please say so that I can correct myself by ellaborating ...
The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°. a. Find the length of the diagonal. b. Find the length of the shorter base. Round your answers to the nearest hundredth. show work please!
Answer:
Step-by-step explanation:
as the non parallel sides are equal and it is a trapezoid.∴ base angles are equal.each base angle=1/2×140=70°let the foot of perpendicular from end of shorter side is at distance x from nearest end of longer side.[tex]\frac{x}{7}=cos ~70\\x=7 \times cos~70 \approx 2.394\\2x \approx 4.788 \approx 4.79\\[/tex]shorter side=22-4.79=17.21 ftto find diagonal use cos formula[tex]cos ~70=\frac{22^2+7^2-d^2}{2*22*7} \\308 cos~70=484+49-d^2\\d=\sqrt{533-308~cos~70} \approx~20.68\\where ~d~is~diagonal.[/tex]d=20.68 fta. The length of the diagonal is approximately 15.74 feet.
b. The length of the shorter base is approximately 27.77 feet.
a. To find the length of the diagonal (d), we can use the given information and the formulas mentioned. Let's substitute the values into the formula:
h = (7/2) * tan(140°)
h ≈ (7/2) * (-1.376381920471173)
h ≈ -4.796335681196056
Now, substitute the values into the formula for the diagonal:
[tex]d = \sqrt{(22 - x)^2 + [(7/2) * tan(140\°)]^2}\\\\d = \sqrt{(22 - 7)^2 + [(-4.796335681196056)]^2}\\\\d = \sqrt{15^2 + 23.011228900189124}\\\\d = \sqrt{225 + 23.011228900189124}\\\\d = \sqrt{248.011228900189124}\\\\d = 15.74[/tex]
Therefore, the length of the diagonal is approximately 15.74 feet.
b. To find the length of the shorter base (b), we can use the given information and the law of cosines:
[tex]b^2 = 7^2 + 22^2 - 2 * 7 * 22 * cos(140\°)\\\\b^2 = 49 + 484 - 2 * 7 * 22 * cos(140\°)\\\\b^2 = 533 - 308 * cos(140\°)\\\\b^2 = 533 - 308 * (-0.766044443118978)\\\\b^2 = 533 + 236.924\\\\b^2 = 769.924\\\\b = 27.77[/tex]
Therefore, the length of the shorter base is approximately 27.77 feet (rounded to the nearest hundredth).
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can someone help please? i’ll give brainliest
Answer:
Assuming that t = toppings, then the inequality is 9.25+0.75t ≤ 13.75. Solution is 6.
Step-by-step explanation:
Let's define toppings as [tex]t[/tex].
If the original cost of a pizza is $9.25 and each topping costs $0.75, we can find how much the toppings would cost by multiplying 0.75 by t, the amount of toppings. Adding this to 9.25 would give us the expression needed to find the cost.
[tex]9.25 + 0.75t[/tex]
If you want to spend NO MORE than 13.75, it's ok to spend $13.75, so we write the equation with a ≤ symbol (less than or equal to).
9.25+0.75t ≤ 13.75
Now lets solve the equation.
We can subtract 9.25 from both sides, which gets us
0.75t ≤ 4.5
Now we can divide both sides by 0.75 to isolate t.
t ≤ 6
So, the maximum number of toppings you can order is 6.
Hope this helped!
Answer:
6
Step-by-step explanation:
so default for pizza is 9.25
and toppings vary depending on number so 0.75x
so I guess 9.25+0.75x<=13.75-variable
equation-9.25+0.75x=13.75
solve to get 0.75x=4.5
x is 6 not sure
QUESTION 8
Simplify the expression
(5-4 (25)*)?
expressing the answer as a power of 5.
Step-by-step explanation:
Do you mean (5-4)*(25) or 5-4(25)
(5-4) * (25)
= 5^2
Or
5-4(25)
=5 - 100
=-95
?
Which of the following relations is not a function? x y 0 1 1 4 -1 4 x y 0 2 1 3 1 -3 x y 0 -2 1 -3 -2 5 x y 0 -2 1 -2 2 -2
Answer:
-1 4 x y
Step-by-step explanation:
A =3x2+4x+1,B=5x2−3x+8,C=4x2−7x−3, find the value of B + C –A.
Answer:
6x^2 - 14x + 4.
Step-by-step explanation:
5x^2 - 3x + 8 + 4x^2 - 7x - 3 - (3x^2 + 4x + 1)
= 5x^2 - 3x + 8 + 4x^2 - 7x - 3 - 3x^2 - 4x - 1
= 6x^2 - 14x + 4.
Which system of equations represents the matrix shown below?
11
2 -18
0 3 15
-2 4 18
1
x + 2y + Z-8
O A. x+y+3z = 15
x + 2y + 4z = 18
x+2y - z- 8
B. -x +32 - 15
x - 2y + 4z = 18
X+2y- Z=8
O C. -X+ y + 3z = 15
X-2y + 4z = 18
x+2y + z = 8
D. X+37 = 15
x +2y + 4z = 18
Answer:
its b.
Step-by-step explanation: 5n − 19 + n + 7 = 144 − 6n
6n − 12 = 144 − 6n
12n = 156
n = 13
m∠z = (144−6n)°
m∠z = (144−6×13)°
m∠z = 66°
HEYY! REALLY SIMPLE QUESTION : ) …..the strange creature moved slowly making terrifying sounds. It looked around…. (Write a story using the following cues somewhere in the story) I JUST NEED SUM IDEAS PLS : ) also ik this is not a math question but oh well I guess..... THANK U!
Answer:
so u could write about its teeth
Step-by-step explanation:
and its legs or its scary presence or its long arms and it erupted from a haunted house
hope this helps : )
i would appreciate it if you can heart and like this answer and maybe even give it 5 stars or brainliest
what is the area of 1/4 of a circle with a radius of 10
Answer:
78.5
Step-by-step explanation:
It is 78.5 because you first get the area of the circle, which is 314. Then divide 314 by 4 to get 78.5
The area of 1/4 of a circle with a radius of 10 is 78.5 units²
Given,
1/4 of a circle.
Radius = 10
π = 3.14
We need to find the area of 1/4 of a circle.
What is the area of a circle?It is given as:
Area = πr²
Find the area of 1/4 of a circle.
We have,
Area of a circle = πr²
Radius = 10
1/4 area of a circle:
= 1/4 x πr²
= 1/4 x 3.14 x 10²
= 1/4 x 3.14 x 100
= 78.5 units²
Thus the area of 1/4 of a circle is 78.5 units²
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Help me ASAP for this question the picture are the answers
If triangle BAT is similar to triangle ROD (ABAT AROD), which of the following statements is incorrect?
Answer:
I'm pretty sure it's the last one that is incorrect
Step-by-step explanation:
Answer:
The first one - “line segment TA is congruent to line segment DO” is incorrect
Step-by-step explanation:
Since the triangles are similar, the angle measurements would be the same (congruent), but the line segments are are only similar, not congruent, as they have different lengths. So the first statement is incorrect.
5. a) A business company made a profit of Rs 24,00,000 in the last year. The management decided to distribute 20 % bonus from the profit to its 30 employees.
( i ) Find the bonus amount received by each employee.
(ii) By what percent should the bonus be increased so that each employee can receive Rs 20,000?
(iii) What should be the profit of the company so that it can provide Rs 20,000 to each employee at 20 % bonus?
Answer:
a) = Rs 16000
b) = 5%
c) = Rs 30,000,000
10% = 24,000,00/10 = Rs 240,000
20% = 240,000 x 2 = Rs 480,000
480,000/30 = Rs 16000
b) The bonus percentage needs to be increased by 5%
explanation:
Since every worker needs Rs 20000 we need to times it by 30
20000 x 30 = Rs 600,000
600,000 - 480,000 = Rs 120,000
Now we need to find the percentage of Rs 120,000
10% = Rs 240,000
5% = 240,000 divide by 2 = Rs 120,000
This is the best I can do for now please let me know if you understood the answer!
Answer:
1.Rs.16000
2.Bonus rate:25%
3.profit:Rs.3000000
Step-by-step explanation:
Case 1
Profit=Rs.2400000
Bonus Rate:20%
No.of employees =30
Now,
Bonus = (Bonus Rate of Profit) / no. Of employees
= 20% of Rs.2400000 / 30
= Rs. 16000
Case 2
Bonus=Rs.20000
Profit=Rs.2400000
Bonus rate=?
Now,
Bonus=bonus rate of profit / no. Of employees
Or,Rs. 20000 = Bonus rate × Rs. 2400000/30
Or, Rs. 20000=Bonus rate × Rs. 80000
Or,Rs.20000/Rs.80000 = Bonus rate
Bonus rate = 1/4=25%
Case 3
Bonus=Rs.20000
Bonus Rate = 20%
Now,
Bonus = bonus Rate of profit / no.of employees
Or, Rs. 20000 = 20% × Profit / 30
Or, Rs. 20000 × 30 / 0.2 = profit
Profit= Rs. 3000000
I hope it helped you
Match the number with its opposite.
Answer:
3.2 matches with (A) -3.3
-2.3 matches with (C) 2.3
-1.5 matches with (B) 1.5
5.1 matches with (D) -5.1
Rose is making necklaces. She needs 7 sapphires and 6 rubies to make one necklace. Complete the double number line diagram to show the numbers of rubies and sapphires Rose needs to make 1 , 2 3 and 4 necklaces.
Answer:
B
Step-by-step explanation:
question 9: consecutive angles in a parallelogram are___ A: cute B: congruent C: parallel D: Supplementary E: Convex
Answer:
Consecutive angles in a parallelogram are, D supplementary.
Step-by-step explanation:
Consecutive angles in a parallelogram will always sum to 180 degrees.
Answer:
Supplementary
Step-by-step explanation:
Correct answer in Ap3x. Just took the quiz.
Write a word phrase that represents x + 5.
Answer:
5 added to a number, x.
Step-by-step explanation:
I phrased it like other ones I saw before so... :) (Also if you ask someone to write it, I'm sure they'd get x+5)
Answer:5 added to a number, x
Step-by-step explanation:
please hurry write a vector equation of a line that passes through p(-4,12) and is parallel to q=(14,-8)
The line containing the vector q can be obtained by scaling q by an arbitrary scalar t. To make this line pass through the point p, translate this line by a vector p pointing from the origin to p.
So the line we want has equation
r(t) = qt + p = (14, -8)t + (-4, 12) = (14t - 4, 12-8t)
where t is any real number.
The Vector Equation which passes through point p(-4, 12) and parallel to q(14, -8) is r(t) = (14t-4, 12-8t).
What is a vector equation?A vector equation is an equation involving a linear combination of vectors with possibly unknown coefficients.
Here, the line containing the vector q can be obtained by scaling q by an arbitrary scalar t. To make this line pass through the point p, translate this line by a vector p pointing from the origin to p.
r(t) = q*t + p
r(t) = (14, -8)t + (-4, 12)
r(t) = (14t - 4, 12-8t)
where t is any real number
Thus, the Vector Equation which passes through point p(-4, 12) and parallel to q(14, -8) is r(t) = (14t-4, 12-8t).
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If one factor of 6.x2 + 5x – 6 is
3.x - 2, the other factor is
A.
3.x + 3
B. 6x + 3
C. 2x + 3
D. 2.x - 3
simplify the expression
[tex]8p + 10 + - 2p - 1 + 10[/tex]
Answer:
6p+19
Step-by-step explanation:
combine like terms:
8p+10+-2p+-1+10
(8p+-2p)+(10+-1+10)
6p+19
HOPE THIS HELPS!!!!!!:)
Hi. Please i need help with these questions ; 1. I spent 7/32 of my income housing , 1/4 of it on food and 1/8 of it on transport . What fraction of my income do i have left a . 7/32 b 9/32 c. 13/32 d. 15/32 e. 19/32 workings please
Answer:
C: 13/32
Step-by-step explanation:
Change 1/4 and 1/8 into 4/32 and 8/32 and add them up with the 7/32 and then subtract the top and you have your answer
Answer:
13/32 left over.
Step-by-step explanation:
First, you would want to convert the 1/4 and 1/8 to ?/32. You would get: 7/32 on housing, 8/32 on food, and 4/32 on transportation.
To get those numbers this is what you do: 1/4 was spent on food. 32 divided by 4 is 8. So that would be 8/32. I hope you understand, because I'm not that good at explaining!
Then you add those up: 7/32 + 8/32 + 4/32. You would get 19/32 as your total, which means you have 13/32 left over. I hope this helped!
Which equation gives the length of the altitude of ABC?
Answer:
B. AD = sqrt(CD * BD)
Step-by-step explanation:
By the right triangle altitude theorem,
CD/AD = AD/BD
AD^2 = CD * BD
AD = sqrt(CD * BD)
Answer: B. AD = sqrt(CD * BD)
Answer:
B
Step-by-step explanation:
[tex]$\frac{CD}{AD} =\frac{AD}{BD} $[/tex]
[tex]AD^2=CD \cdot BD[/tex]
[tex]AD=\sqrt{CD \cdot BD}[/tex]
In this question, you are clearly supposed to use the geometric mean theorem or known as the right triangle altitude theorem. But note that there are other approaches to find the height of the triangle.
Using Pythagorean theorem:
[tex]AD^2+CD^2=AC^2 \Rightarrow AD=\sqrt{AC^2-CD^2}[/tex]
Also,
[tex]AD=AC\sin(c)[/tex]
Write an equation and solve it to answer each question:
A pile of 55 coins, consisting of nickels and dimes, is worth $3.90. find the number of each.
You have to Answer like this:
If there are x nickels, then the equation is______
The number of nickels is_____
the number of dimes is______
Answer:
there are 25 nickels and 30 dimes
(1 mark)
13.
The time to finish a certain work decreases as the number of worker increases
in number. What kind of proportion is illustrated in the situation?
Answer:
Inverse proportion
Step-by-step explanation:
Inverse proportion: in this type of relation, two quantities proportion such that one decreases and other increases or vice-versa.
So, in the given question when the number of workers increases, time is taken for certain work decreases.
So, Inverse proportion is the correct answer.
Right isosceles triangles are constructed on the sides of a 3−4−5 right triangle, as shown. A capital letter represents the area of each triangle. What is [tex]\frac{X+Y}{Z}[/tex]
Answer:
1
Step-by-step explanation:
because the triangles are isosceles, that means that the area of Z is 5x5x1/2, which equals 12.5
the area of X is 4.5
the area of y is 8
(8+4.5)/(12.5) = 1
Solve the inequality $2x - 5 \le -x +12$. Give your answer as an interval.
Answer:
[tex]$\left(-\infty, \frac{17}{3} \right]$[/tex]
Step-by-step explanation:
[tex]2x - 5 \le -x +12[/tex]
[tex]2x - 5 +5\le -x +12+5[/tex]
[tex]2x\le -x+17[/tex]
[tex]3x \le17[/tex]
[tex]$x \le \frac{17}{3} $[/tex]
We have
[tex]$\{x \in \mathbb{R}:x \le \frac{17}{3} \}$[/tex]
Interval notation:
[tex]$\left(-\infty, \frac{17}{3} \right]$[/tex]
please help with this
Answer:
158m^3
Step-by-step explanation:
First, let's figure out the total amount of water in the tank.
It measures 4.5m by 6m by 8m. The volume of a rectangular prism is V=lwh.
Therefore, the volume is:
[tex]V=(4.5)(6)(8)=216 m^3[/tex]
We are told is it filled to the brim, so we can conclude that there are 216 cubic meters of water in the tank.
We used 58 cubic meters of water, so we simply need to subtract that from 216:
[tex]216m^3-58m^3=158m^3[/tex]
There is still 158 cubic meters of water left in the tank.
Answer:
158 m^3
Step-by-step explanation:
Volume of the tank
= 4.5 * 6 * 8
= 216 m^3.
So amount left in the tank
= 216 - 58
= 158 m^3.
Isabella filled her pool with water at a constant rate. The table compares the remaining volume of water left to fill the pool (in liters) and the time since Isabella started filling the pool (in minutes).
Time (m) Remaining Volume (L)
4 148
6 112
8 76
What is the size of her pool?
Answer:
It was kinda hard to really understand your question but as of all the information that I received the answer is 220 liters
Step-by-step explanation:
Liam is making chocolate chip cookies. The recipe calls for 1 cup of sugar for every 3 cups of flour. Liam only has 2 cups of flour.
How much sugar should Liam use?
Explain why your answer is correct.
Answer:
2/3 cups of sugar
Step-by-step explanation:
Answer:
2/3 cups of sugar
Step-by-step explanation:
If 3 cups of flour: 1 cup of sugar
2 cups of flour: x cup of sugar
Cross multiply
3x = 2 × 1
3 3
x = 2/3
My answer is correct because every 3 cups of flour is a full cup (1) but because he has 2 cups of flour, the cup of sugar is going to be less than 1 because 3 cups of flour is bigger than 2 cups of flour.
I need a quick response! Please help!
A park ranger sees a fire from an observation deck 120 feet high. The fire is at an angle of
depression 2.5 degrees. How far is the fire from base of the observation deck ?
Answer: 2748.5 feet
Step-by-step explanation:
Given that the
Height h = 120 feet.
angle of depression = 2.5 degrees
The angle of depression is equal to the angle of elevation.
The base of the observation deck will be achieved by using trigonometry ratio.
Tan Ø = opposite/ adjacent
Opposite = height = 120 feet
Adjacent = base = ?
Substitutes the given parameters into the trigonometry ratio.
Tan 2.5 = 120 / adjacent
Adjacent = 120 / tan 2.5
Adjacent = 2748.452
Therefore, the base of the observation deck is 2748.5 feet
Write the equations after translating the graph of y = | 1 /2 x−2|+3 one unit down,
Answer:
[tex]y=|\frac{1}{2} x-2|+2[/tex]
Step-by-step explanation:
If your original function is:
[tex]y=|\frac{1}{2} x-2|+3[/tex]
the translation of its graph vertically down one unit, can be obtained by simply subtracting 1 from the whole functional expression:
[tex]y=|\frac{1}{2} x-2|+3-1=|\frac{1}{2} x-2|+2[/tex]