Final answer:
To find the height of the 7th bounce of a bouncy ball, where each bounce is 64% of the height of the previous one, use the geometric sequence formula. For the first bounce's height of 5.5 feet and a common ratio of 0.64, calculate the 6th power of 0.64, then multiply by 5.5 and round to the nearest tenth.
Explanation:
The student is asking about finding the height of the seventh bounce of a bouncy ball, which follows a geometric sequence in which each term is 64% of the previous one. To find the height of the 7th bounce, we will use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number.
The first term a1 is the height of the first bounce, which is 5.5 feet, and the common ratio r is 0.64 (since 64% is 0.64 in decimal form). Using this information, the height of the 7th bounce is calculated as follows:
Calculate the 6th power of the common ratio: 0.646
Multiply this value by the height of the first bounce: 5.5 × 0.646
Round the result to the nearest tenth
Calculating the exact value and rounding to the nearest tenth gives us the height of the seventh bounce.
Eliminate the parameter.
x = t - 3, y equals two divided by quantity t plus five
Answer:
y = 2/(x +8)
Step-by-step explanation:
Solve the first equation for t and substitute that expression into the second equation.
x = t -3
x + 3 = t
Then for y, we have
y = 2/(t +5)
y = 2/((x +3) +5) . . . . substitute for t
y = 2/(x +8) . . . . . . . . simplify
Can someone help me?
Thanks-Aparri
Answer:
10y
Step-by-step explanation:
9y + y = 10y
Answer:
[tex]10y[/tex]
Step-by-step explanation:
[tex]9y + y = y(9 + 1) = y(1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) = y \times 10 = 10y[/tex]
Graph the function.
y = –2x^2 + 6x – 2
Answer:
Step-by-step explanation:
At the start of the first down, the football was 30 yards from the Tigers' end zone. During three downs, the ball moved 9
yards farther from their end zone, then 14 yards closer to it, and then 2 yards closer to it. How many yards from their end
zone was the ball at the end of the third down?
Answer:
23
Step-by-step explanation:
30 + 9 = 39.
39 - 14 = 25.
25 - 2
= 23
Answer:
23
Step-by-step explanation:
((Please Answer with A B C or D))
If x = 3 inches, what is the perimeter of the figure above?
A. (36[tex]\sqrt{2}[/tex] + 36) inches
B. (6[tex]\sqrt{2}[/tex] + 12) inches
C. 72 inches
D. (6[tex]\sqrt{3}[/tex] + 12) inches
Answer:
B. (6√2 + 12) inches
Step-by-step explanation:
The length of the kite edge at upper left is ...
x/sin(45°) = x/(1/√2) = x√2
The length of the kite edge at upper right is ...
x/sin(30°) = x/(1/2) = 2x
The perimeter of the kite is double the sum of the lengths of these edges:
P = 2(x√2 +2x) = 2x(√2 +2)
For x=3 in, this is ...
P = 2·(3 in)(√2 +2)
P = (6√2 +12) in
_____
The sine of an angle is the ratio of the side opposite to the hypotenuse. Here, the side opposite is x, and the hypotenuse is the kite edge of interest.
x/hypotenuse = sin(angle)
hypotenuse = x/sin(angle) . . . . . solve for hypotenuse
Answer:
B
Step-by-step explanation:
I was told to put down A B C or D
And B was right
In which direction does the parabola open?
Answer:
up
Step-by-step explanation:
A graphing calculator, spreadsheet, or web site can help you with this one, or you can simply plot some points on a graph.
___
Only the highest-degree terms matter for answering this question. Leaving the others out, the form is ...
y = x^2
This tells you that y gets more positive for larger and larger values of x, regardless of their sign. Thus the graph of it is U-shaped, opening upward.
Please answer this multiple choice question correctly for 30 points and brainliest!!
Answer:
B. 12n + 2(25) ≤ 100
Step-by-step explanation:
The inequality you are asked for is intended to express ...
shirt cost + pant cost (is less than or equal to) Sandy's budget
The cost of n shirts at $12 each will be 12n. The cost of 2 pants at $25 each is 2(25). Then the inequality is ...
12n + 2(25) ≤ 100 . . . . . matches choice B
Which list shows the numbers in order from least to greatest? A. 53.783 B. 53.65 C. 53.09 D. 53.163 A) A, B, D, C B) C, D, B, A C) D, C, B, A D) B, C, A, D
Answer:
B) C,D,B,A
Step-by-step explanation:
Which products result in a perfect square trinomial? Check all that apply. (–x + 9)(–x – 9) (xy + x)(xy + x) (2x – 3)(–3 + 2x) (16 – x2)(x2 – 16) (4y2 + 25)(25 + 4y2)
Answer:
(xy + x)and (xy + x)
(2x - 3) and (-3 + 2x)
(4y² + 25) and (25 + 4y²)
Step-by-step explanation:
* Lets explain the meaning of the perfect square trinomial
- If a binomial multiply by itself, then the answer will be a perfect
square trinomial
- Example: if the binomial (ax + b) multiply by itself, then
(ax ± b)(ax ± b) = (ax)(ax) ± (ax)(b) ± (b)(ax) + (b)(b)
(ax + b)(ax + b) = (ax)² ± 2(axb) + (b)²
∵ (ax + b)(ax + b) = (ax + b)²
∴ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
* From the example above the perfect square trinomial has 3 terms
# 1st term is the square the first term in the binomial
# 2nd term is twice the product of the two terms of the binomial
# 3rd term is the square of the second term of the binomial
* Lets solve the problem
- The product of (-x + 9)and (-x - 9)
∵ -x + 9 ≠ -x - 9
∴ The product of (-x + 9) and (-x - 9) is not a perfect square trinomial
- The product of (xy + x)and (xy + x)
∵ xy + x = xy + x
∴ (xy + x)(xy + x) = (xy + x)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (xy + x) and (xy + x) is a perfect square trinomial
- The product of (2x - 3) and (-3 + 2x)
∵ (-3 + 2x) can be written as (2x - 3)
∴ 2x - 3 = -3 + 2x
∴ (2x - 3)(-3 + 2x) = (2x - 3)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (2x - 3)(-3 + 2x) is a perfect square trinomial
- The product of (16 - x²) and (x² - 16)
∵ 16 - x² can be written as -x² + 16
- If we take -1 common factor from -x² + 16
∴ -x² + 16 = -(x² - 16)
∴ (-x² + 16)(x² - 16) = -(x² - 16)(x² - 16) = -(x² - 16)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∵ -(x² - 16)² = -(x^4 - 32x² + 256) = -x^4 + 32x² - 256
∵ x^4 - 32x² + 256 is perfect square trinomial
∵ -x^4 + 32x² - 256 is not a perfect square trinomial
∴ The product of (16 - x²) and (x² - 16) is not a perfect square trinomial
- The product of (4y² + 25) and (25 + 4y²)
∵ 25 + 4y² can be written as 4y² + 25
∴ 4y² + 25 = 25 + 4y²
∴ (4y² + 25)(25 + 4y²) = (4y² + 25)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (4y² + 25) and (25 + 4y²) is a perfect square trinomial
Which expression is the radical form of m^2.5?
The expression [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .
What is a Radical form ?
If n is a positive integer greater than 1 and n is a real number, then
[tex]\rm \sqrt[n]{a}[/tex] = aⁿ
Here the index is represented by n, the radicand is represented by a , and the sign is called the radical.
Left side of the equation is called the radical form
Right side of the equation is called exponent form.
The given exponent form is
[tex]\rm m^{2.5}[/tex]
In radical form this will be written as
[tex]\rm \sqrt[2.5]{m}[/tex]
Therefore the expression [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .
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At 350 degrees Fahrenheit, an oven can cook approximately 3 pounds of turkey per hour. At 450 degrees Fahrenheit, it can cook approximately 4.5 pounds per hour. How many more ounces of turkey can the oven cook at 450 degrees than at 350 degrees in 10 minutes? (1 pound = 16 ounces)
A) 4
B) 6
C) 8
D) 12
Answer:
D
Step-by-step explanation:
Factor 60x2 – 155x + 100 completely.
A. 5(4x + 5)(3x + 4)
B. (20x – 25)(3x – 4)
C. 5(4x – 5)(3x – 4)
D. (4x – 5)(15x – 20)
Hey there! Thanks for asking your question here on Brainly.
First, we can factor a 5 out of each term in the trinomial. This leaves us with: 5(12x^2 - 31x + 20)
Second, we need to multiply 12 * 20 and find a factor pair of the product, 240, which equals -31. This factor pair would be -15 and -16. This now leaves us with: 5((12x^2 - 16)(-15x + 20))
Third, we need to simplify each binomial in parenthesis. By doing so, what is left inside of each parenthesis should be the same if this step is done correctly. This leaves us with: 5(4x(3x - 4)-5(3x - 4))
Fourth and finally, we construct our new factored trinomial! The outside number stays, as well as one of the inner parenthesis binomials. Use the terms you factored out of the parenthesis in step three to construct another
binomial. This leaves us with: 5(4x - 5)(3x - 4) and the correct answer is C.
Hope this helps! If there's anything else I can help you with, please let me know! :)
Which products result in a difference of squares? Check all that apply. (5z + 3)(–5z – 3) (w – 2.5)(w + 2.5) (8g + 1)(8g + 1) (–4v – 9)(–4v + 9) (6y + 7)(7y – 6) (p – 5)(p – 5)
Answer:
(w - 2.5)(w + 2.5)
(-4v - 9)(-4v + 9)
Step-by-step explanation:
* Lets explain what is the a difference of two squares
- If we multiply two binomial and the answer just two terms with
negative sign between them and the two terms are square numbers
we called this answer a difference of two squares
- Examples
# (a + b)(a - b)
- Lets multiply them
∵ (a × a) + (a × -b) + (b × a) + (b × -b)
∴ a² - ab + ba - b²
- Add the like term
∵ ab = ba
∴ -ab + ba = 0
∴ (a + b)(a - b) = a² - b² ⇒ difference of two squares
- From above the difference of two squares appears when we
multiply sum and difference of the same two terms
# (a + b) ⇒ is the sum of a and b
# (a - b) ⇒ is the difference of a and b
* Now lets solve the problem
- In (5z + 3)(-5z - 3)
∵ (5z + 3) ⇒ is the sum of 5z and 3
∵ (-5z - 3) ⇒ is the difference of -5z and 3
∵ 5z ≠ - 5z
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
- In (w - 2.5)(w + 2.5)
∵ (w - 2.5) is the difference between w and 2.5
∴ (w + 2.5) is the sum of w and 2.5
∴ They are the sum and difference of the same two terms
∴ The product result in a difference of squares
- In (8g + 1)(8g + 1)
∵ The two brackets are the sum of 8g and 1
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
- In (-4v - 9)(-4v + 9)
∵ (-4v - 9) is the difference between -4v and 9
∵ (-4v + 9) is the sum of -4v and 9
∴ They are the sum and difference of the same two terms
∴ The product result in a difference of squares
- In (6y + 7)(7y - 6)
∵ (6y + 7) is the sum of 6y and 7
∵ (7y - 6) is the difference between 7y and 6
∵ 6y ≠ 7y and 7 ≠ 6
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
- In (p - 5)(p - 5)
∵ The two brackets are the difference of p and 5
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
Answer:
option 2 and 4
Step-by-step explanation:
It costs 31.95d + 0.10m dollars to rent a car for d days and drive it m miles. How much does it cost to rent a car for 5 days if the car is driven a total of 600 miles ?
Answer:
$219.75
Step-by-step explanation:
Just plug in the values
x = final cost
31.95(5) + 0.10(600) = x
159.75 + 60 = x
219.75 = x
The airplane was 32,000 feet above sea level. It landed in a valley 100 feet below sea level. Write an integer to express the change in the altitude
Answer:
- 32,100 ft
Step-by-step explanation:
Initial Altitude = 32,000 ft above sea level = +32,000 feet
Final Altitude = 100 ft below sea level = -100 ft
Altitude change,
= final altitude - initial altitude
= - 100 - (32,000)
= - 32,100 ft
Please help me !! D is also an option but I couldn't get it in the picture
Answer: A) (-1, 0) to (1, 2)
Step-by-step explanation:
Complex numbers are written in the form of ai + b ; where "a" represents the x-coordinate and "b" represents the y-coordinate --> (a, b)
-i → -1i + 0 → (-1, 0)
2 + i → 1i + 2 → (1, 2)
Which graph connects those two coordinates? OPTION A
Tomas used 3 1/3 cups of flour and now has 1 2/3cups left. Which equation can he use to find f, the number of cups of flour he had to begin with?
f+3 1/3=1 2/3
f-3 1/3=1 2/3
3 1/3f=1 2/3
f/3 1/3=1 2/3
For this case we have that the variable "f" represents the number of cups of flour that Tomas had initially.
If of that amount Luis used [tex]3 \frac {1} {3}[/tex] of cups of flour, then we have the following expression:
[tex]f-3 \frac {1} {3}[/tex]
If Luis has[tex]1 \frac {2} {3}[/tex] cups of flour left, then we have the following equation:
[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]
Finally, the equation that represents the given situation is:
[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]
Answer:
Option B
Help with this question, please!
Answer:
see below
Step-by-step explanation:
Apart from the pictures being drawn with the axis at a funny angle relative to the edges of the solid, it should be pretty clear from the pictures that the figure has both plane and axis symmetry.
Every point on one side of the axis has a matching point on the other side at the same distance. Every point on one side of the plane of symmetry has a matching point on the other side at the same distance.
Using the table below, write a function rule for the balance in the CD account after any number of years. Let y represent the value of the investment at the end of any year x.
CD/Year
Beginning Balance
Interest Earned
Ending Balance
Savings Account/Year
Beginning Balance
Interest Earned
Ending Balance
1
$700
$22
$722
1
$700
$25.90
$725.90
2
$722
$22
$744
2
$725.90
$26.86
$752.76
3
$744
$22
$766
3
$752.76
$27.85
$780.61
4
$766
$22
$788
4
$780.61
$28.88
$809.49
5
$788
$22
$810
5
$809.49
$29.95
$839.44
Answer:
y = 700 +22x
Step-by-step explanation:
The CD account balance is 722 after the first year and increases by $22 each year. The function rule is a linear function with a y-intercept of 700 and a slope of $22 per year.
y = 700 +22x . . . . . . ending balance after x years
The sum of the digits of a two-digit number is 13. The units digit is one more than twice the tens digit. Find the number.
Answer:49
Step-by-step explanation: 9+4=13 4x2=8 8+1=9
9 is the units digit
4 is the tens digit
A national study found that a car's value decreases by 15 percent annually. If the car was purchased for $66,000, how much will the car be worth in 10 years? A. $12,993.71 B. $11,768.35 C. $18,429.50 D. $13,792.14
Answer:
A. $12,993.71
Step-by-step explanation:
Each year, the car's value is multiplied by 1-0.15 = 0.85. After 10 years, the car's value will be ...
$66,000×0.85^10 ≈ $12,993.71
The coordinates of vertex S are (_,_)
The area of rectangle PQRS is_____square units.
Answer:
vertex s is -2,-2
Step-by-step explanation:
and with the rectangle is q to p is 4cm coz one box is 1 cm and r to q is 3cm so you multiply them and the answer is 12cm
A can can be rented for $50 per day with unlimited mileage, or for $40 per day plus 25 cents per mile . For what daily mileages will be unlimited mileage plan save you money ?
Determine the principal value of the function: Arc sin(square root of 3/2)
Answer:
π/3
Step-by-step explanation:
We have to find the principal value of [tex]\text{arc sin}(\frac{\sqrt{3}}{2} )[/tex]
arc sin means sin inverse. The sin inverse is a one to one function with its range between [tex]-\frac{\pi}{2} \textrm{ to } \frac{\pi}{2}[/tex]
The principal value of the arc sin will lie within the above given range.
value of sin (60) or sin([tex]\frac{\pi}{3}[/tex]) is [tex]\frac{\sqrt{3}}{2}[/tex].
[tex]\frac{\pi}{3}[/tex] lies between [tex]-\frac{\pi}{2}\textrm{ and } \frac{\pi}{2}[/tex]
So, from here we can say that the Principal Value of Arc sin(square root of 3/2) is π/3
The principal value of the function Arc sin(√3/2) is,
⇒ π / 3
We have to given that,
⇒ Arc sin (√ 3/ 2)
Since, Value of arc sin lies between - π/2 and π/2.
Hence, The principal value of the function Arc sin(√3/2) is,
⇒ Arc sin(√3/2)
⇒ Arc sin(sin π/3)
⇒ π / 3
Therefore, The principal value of the function Arc sin(√3/2) is,
⇒ π / 3
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Charlie entered an elevator and ride up 10 floors and then down 2 floors before realizing he had not pressed the button for Floor 1. He then pressed the button for Floor 1 and rode down 14 floors and exited the elevator on Floor 1. On which floor did he begin?
Answer:
Floor 7
Step-by-step explanation:
He entered the elevator on floor x.
Then he rode up 10 floors. Now he is on floor x + 10.
Then he rode down 2 floors. Now he is on floor x + 10 - 2 = x + 8.
Then he pressed the Floor 1 button and rode down 14 floors to Floor 1. Now he is on floor x + 8 - 14 = x - 6 which is the same as Floor 1.
Floor x - 6 is the same as Floor 1, so we get the equation:
x - 6 = 1
Add 6 to both sides:
x = 7
Since we let x be the floor number he entered the elevator in, he entered the elevator on Floor 7.
Answer:
He began on floor 7
Step-by-step explanation:
This is a question where you have to use the question from the end and work your way backwards if that makes sense.
He had to go down 14 floors to get to floor 1. So 14 + 1 = 15. He was on the 15th floor.
Next he went down 2 floors. Since this is reverse, add two floors to the answer. 15 + 2 = 17. He was on the 17th floor.
And finally, he goes up 10 floors. Doing this in reverse, take away 10 floors to the answer. 17 - 10 = 7
He started on the 7th floor.Now to make sure it is correct, start from 7 and follow the original order of the question.
7 + 10 = 17
17 - 2 = 15
15 - 14 = 1
Need help with this math question
Answer:
120
Step-by-step explanation:
If those 2 polygons are similar, then their corresponding angles are the same. The thing that makes them similar as opposed to congruent is that their side lengths exist in proportion to one another instead of being the same.
Answer:
[tex]w = 120\°[/tex]
Step-by-step explanation:
In this case we know that
ABCD and FECG are similar polygons.
This means that their sides are proportional and their corresponding angles are equal.
So if the lines FG and AD are parallel and of proportional length then by definition the angle w is equal to 120 °
Thus
[tex]w = 120\°[/tex]
A chemist wants to mix a 66% alcohol solution with eight liters of 54% alcohol solution to produce a solution that is 65% alcohol. How many liters of the 66% alcohol solution should be used ?
Answer:
We have 8 liters of 54% alcohol.
We will add "x" liters of 66% alcohol to make "8 +x" liters of 65% alcohol.
54 * 8 + 66 x = 65 (8 + x)
432 + 66x = 520 + 65x
x = 88 liters
Step-by-step explanation:
Find the arc length intercepted by a central angle of radians in a circle whose radius is 18.4 inches. 13.8π 15.2π 24.5π
Final answer:
The arc length intercepted by a central angle of π radians in a circle of radius 18.4 inches is calculated as arc length = θ × radius, resulting in 18.4π inches.
Explanation:
To find the arc length intercepted by a central angle of θ radians in a circle with radius r, we use the formula:
arc length (s) = θ × r
Given that the central angle θ is π radians and the radius r is 18.4 inches, we can compute the arc length as follows:
arc length (s) = π × 18.4 inches
By multiplying, we get:
arc length (s) = 18.4π inches
Therefore, the arc length intercepted by a central angle of π radians in a circle with a radius of 18.4 inches is 18.4π inches.
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth.
Check the picture below.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{27.6}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{30^2-27.6^2}=h\implies \sqrt{138.24}=h\implies 11.76\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the triangle}}{\cfrac{1}{2}bh\implies \cfrac{1}{2}(27.6)(11.76)}\implies 162.288\implies \stackrel{\textit{rounded up}}{162.3}[/tex]
To find the area of the right triangle with a given hypotenuse and adjacent leg, use the Pythagorean theorem to calculate the other leg. Then, use the base and height (the two legs) in the area formula for a right triangle. The area of the triangle is approximately 148.7 cm².
To find the area of a right triangle, you need two perpendicular sides, known as the legs of the triangle. Since we are given the hypotenuse (30 cm) and one adjacent leg (27.6 cm) which is one of the legs, we need to find the other leg. Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In mathematical terms, this is expressed as a² + b² = c². Therefore, the length of the other leg (b) can be found using the equation b² = c² - a², where c is the hypotenuse and a is the given adjacent leg.
Substituting the given values, we have b² = 30² - 27.6². Calculating this gives b ≈ 10.8 cm.
Now, the area of the triangle can be calculated using the formula for the area of a right triangle, which is (1/2) × base × height. In this case, the base and height are the two legs of the triangle. Substituting the lengths of the legs we have, Area ≈ (1/2) × 27.6 cm × 10.8 cm. The result is approximately 148.7 cm², which is the area of the triangle rounded to the nearest tenth.
If fis a function and x is an element in its domain, which statement is true about the graph of f?
OA.
The graph of f is the graph of the equation f = x.
OB.
The graph of fis the graph of the equation x = f(y).
OC.
The graph of fis the graph of the equation y = x.
D.
The graph of f is the graph of the equation y = f(x).
Reset
Next
The right choice here is
"The graph of f is the graph of the equation y = f(x)."
Horizontal and vertical axes of the Cartesian plane are conventionally labeled and referred to as "x" and "y", respectively. When we talk about the graph of f(x) in that context, we usually mean the graph of y = f(x). However, this convention may not be followed in all cases. There may be no "y" label on the graph at all, or the horizontal axis may be labeled something other than "x".