Answer:
D) 8
Step-by-step explanation:
Given function for height = f(x) = 80(0.5)^x
It shows that the height of ball after any bounce can be calculated by putting bounce number in place of x in this equation.
so, height after first bounce f(1) is calculated by placing 1 in place of x
f(1) = 80(0.5)^1
f(1) = 80(0.5)
f(1) = 40
Similarly, the height after 4th bounce f(4)
f(4) = 80(0.5)^4
f(4) = 80(0.0625)
f(4) = 5
Therefore, the height of 1st bounce is 40/5 = 8 times higher than the fourth bounce. So, option D is correct.
The first bounce is 8 times higher than the fourth bounce. Option D (8) is correct.
The height of the bouncing ball is given by the function f(x) = 80(0.5)^x, where x represents the number of bounces. To find how many times higher the first bounce is than the fourth bounce, we'll calculate the heights for f(1) and f(4) and then compare them.
Calculate the height after the first bounce (x = 1):Therefore, the first bounce is 8 times higher than the fourth bounce, corresponding to option D (8).
Select the measures of the angles of a triangle whose angles have measures in the ratio 6:8:10
Answer:
45, 60, 75
Step-by-step explanation:
The ratio of the angles are 6:8:10
Multiply by x to get the angle measures
6x, 8x,10x
We know the sum of the angles is 180 for a triangle
6x+8x+10x = 180
Combine like terms
24x = 180
Divide each side by 24
24x/24 = 180/24
x =7.5
Each angle is
6x = 6(7.5) =45
8x = 8(7.5) =60
10x = 10*7.5 = 75
The measures of the angles of the given triangle are 54 degrees, 72 degrees, and 90 degrees.
Explanation:To find the measures of the angles of a triangle whose angles have measures in the ratio 6:8:10, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since the ratio of the angles is 6:8:10, we can set up the equation 6x + 8x + 10x = 180, where x is a common factor. Solving this equation, we find that x = 9. Therefore, the measures of the angles are 6x = 54 degrees, 8x = 72 degrees, and 10x = 90 degrees.
A roll of 40 quarters weighs 8 ounces. Which proportion can be used to find the weight in ounces, w, of 200 quarters?
Answer:
40oz
Step-by-step explanation:
just make it easy 20 quarters is 4 oz multiply that by 10 it would be 200 quarters and 40 oz
the weight of 200 quarters is 40 ounces.
The question asks to find the weight in ounces, w, of 200 quarters, given that a roll of 40 quarters weighs 8 ounces. To solve this problem, we can set up a proportion which is a statement that two ratios are equal. Since we know the weight of 40 quarters, we can compare this to the weight of 200 quarters. The proportion can be set up as follows:
40 quarters / 8 ounces = 200 quarters / w ounces
To find w, simply cross-multiply and divide:
(40)(w) = (8)(200)40w = 1600w = 1600 / 40w = 40 ouncesTherefore, the weight of 200 quarters is 40 ounces.
Write the expression as a square of a binomial if possible: 1/9 x^2+ 2/15 x y+ 1/25 y^2
Answer: [tex]\bold{\bigg(\dfrac{1}{3}x+\dfrac{1}{5}y\bigg)^2}[/tex]
Step-by-step explanation:
The square of the trinomial exists only if (a + b)² = a² + 2ab + b²
[tex]\dfrac{1}{9}x^2+\dfrac{2}{15}xy+\dfrac{1}{25}y^2\\\\\\a=\sqrt{\dfrac{1}{9}x^2}=\dfrac{1}{3}x\\\\\\b=\sqrt{\dfrac{1}{25}y^2}=\dfrac{1}{5}y\\\\\\2\cdot a\cdot b=2\cdot \dfrac{1}{3}x\cdot \dfrac{1}{5}y = \dfrac{2}{15}xy\\\\\text{So, }\dfrac{1}{9}x^2+\dfrac{2}{15}xy+\dfrac{1}{25}y^2=\bigg(\dfrac{1}{3}x+\dfrac{1}{5}y\bigg)^2\\[/tex]
Solve the system using elimination. Write the solution as an ordered pair. (1 point) SHOW YOUR WORK FOR FULL CREDIT! (2 points)
13x + y = 15
-9x - 3y = -15
Answer: (1,2)
Step-by-step explanation:
You must:
- Multiply the first equation by 3.
- Add both equations.
- Solve for the variable left. In this case will be x.
Then:
[tex]\left \{ {{39x +3y = 45} \atop {-9x - 3y = -15}} \right.\\------\\ 30x=30\\x=1[/tex]
Substitute x=1 into any of the original equtions and solve for y:
[tex]13(1)+y=15\\y=2[/tex]
The solution is: (1,2)
Answer:
The solution of the system of equation is (1 , 2)
Step-by-step explanation:
The system of equation is:
* 13x + y = 15 ⇒ (1)
* -9x - 3y = -15 ⇒ (2)
- By using elimination ⇒ we must make on of the
two variables in the two equations has the same value
with different sign
- So we will multiply equation (1) by 3 to eliminate y
∴ 3(13x) + 3(y) = 3(15)
∴ 39x + 3y = 45 ⇒ (3)
- Now add (2) and (3)
∴ 39x + -9x = 45 + -15
∴ 30x = 30 ⇒ ÷ 30 both sides
∴ x = 1
- Substitute the value of x in equation (1) or (2)
- Lets use (1)
∴ 13(1) + y = 15
∴ 13 + y = 15 ⇒ subtract 13 from both sides
∴ y = 15 - 13
∴ y = 2
∴ The solution of the system of equation is (1 , 2)
. Write an equation of the line that passes through
(3, 5) and is perpendicular to the graph of y = –3x +7. Write your final equation in slope-intercept form.
Answer:
y = 1/3 x + 4
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals. The given line is
y = -3x + 7
which is already in the slope-intercept form, y = mx + b, where m is the slope.
The slope of the given line is -3.
The slope of the perpendicular is the negative reciprocal of -3 which is 1/3.
The line we are looking for has an equation of the form
y = 1/3x + b
We need to find b. We use the x- and y-coordinates of the given point as x and y in the equation above, and we solve for b.
y = 1/3x + b
5 = (1/3)(3) + b
5 = 1 + b
4 = b
Now that we know that b = 4, we replace b with 4 in the equation
y = 1/3x + b to get the answer.
Answer: y = 1/3 x + 4
The equation of the line that is perpendicular to y=-3x+7 and passes through the point (3,5) is y = 1/3x + 4.
Explanation:To find an equation of the line that is perpendicular to the line represented by the equation y = -3x + 7 and also passes through the point (3, 5), we must first find the slope of this new line. In mathematics, the perpendicular line's slope is the negative reciprocal of the original line's slope. Here, the slope of the original line is -3, so our new line's slope will be 1/3. Now we can use the point slope form to find the equation of the line:
y - y1 = m(x - x1)
Substituting our values, it becomes y - 5 = 1/3(x - 3), which simplifies to y = 1/3x + 4. So, the equation of the line is y = 1/3x + 4.
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the surface area of a cone is 16.8pi in. the radius is 3 in what is the slant height
The slant height of a cone with a radius of 3 inches and a surface area of 16.8π square inches is 2.6 inches.
Explanation:In order to find the slant height of a cone, we need to understand the formula for calculating the surface area of a cone. The formula is πrs + πr². The given surface area is 16.8π and the radius is 3 in. This area consists of the area of the base (which is a circle of radius 3 in, hence area πr² = π(3)² = 9π) and the area of the side, which is πr times the slant height (s).
So, we subtract the base area from the total area to isolate the side area: 16.8π - 9π = 7.8π. This is equal to πrs, so we can set up the equation: 7.8π = 3πs (we replace 'r' with its given value 3). Solving for 's', we divide both sides of the equation by 3π, getting slant height 's' = 7.8π / 3π, which simplifies to 2.6 inches.
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(13 points) HELP PLEASEEE!
Subtract the equations
3x + 4y = 17
- (3x + 2y = 3)
Answer:
y = 7 x = -11/3
Step-by-step explanation:
3x + 4y = 17
- (3x + 2y = 3)
Distribute the minus sign and add together
3x + 4y = 17
- 3x - 2y = -3
------------------------
2y = 14
Divide by 2
2y/2 = 14/2
y = 7
Now find x
3x + 4y = 17
3x +4(7) = 17
3x +28 = 17
Subtract 28 from each side
3x+28 -28 = 17 -28
3x = -11
Divide each side by 3
3x/3 = -11/3
x = -11/3
Answer:
A.2y=14
Step-by-step explanation:
Apex
Hope this helps Have a nice day
Which is log x+ 6 log(x+7) written as a single logarithm.
Answer: option d.
Step-by-step explanation:
To solve this problem you must keep on mind the properties of logarithms:
[tex]log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a[/tex]
Therefore, knowing the properties, you can write the expression gven in the problem as shown below:
[tex]5logx+6log(x+7)=logx^5+log(x+7)^6=logx^5(x+7)^6[/tex]
Then, the answer is the option d.
Answer:
D
Step-by-step explanation:
We can use 2 properties of logs to write this as single logarithm:
1. [tex]Log(A^B)=BLog A[/tex]
2. Log x + Log y = Log (x*y)
We can use property #1 to write this as:
[tex]5Logx+6Log(x+7)\\=Logx^{5}+Log(x+7)^{6}[/tex]
Now we can use property #2 to write this as:
[tex]Logx^{5}+Log(x+7)^{6}\\=Log((x^5)((x+7)^6)\\=Logx^{5}(x+7)^{6}[/tex]
We see that answer choice D is right.
An equal number of men and women were randomly selected and asked how many hours per week they spend exercising
Answer:
1. Greater than
2 less than
3. More
Step-by-step explanation:
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 0.3x − 0.4y = 0.2 −0.2x + 0.5y = 0.1 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Answer:
One solution. It is (2, 1)
Step-by-step explanation:
Clear out all fractions right away by multiplying all terms by 10. Then:
0.3x − 0.4y = 0.2
−0.2x + 0.5y = 0.1
becomes
3x - 4y = 2
-(2x + 5y = 1)
Multiply the first row by 2 and the second row by 3, which produces:
6x - 8y = 4
-6x +15y = 3
Combining like terms results in: 7y = 7. Then y = 1.
Now subst. 1 for y in the first equation, to calculate x:
3x - 4(1) = 2
3x = 2 + 4 = 6. Then x = 2.
The solution is (2, 1). There is ONLY ONE SOLUTION.
How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively (y is considered a consonant)?
The 21 consonants are :
b c d f g h j k l m n p q r s t v w x y z
The 5 vowels are :
a e i o u
Now, to arrange the consonants there are 21! ways.
Now the vowels can be arranged in 22 ways because one vowel can be placed before 'b' and one after 'z' also.
It can be shown like this : (V represents vowels)
V b V c V d V f .......................
Therefor the ways to put vowels will be : [tex]22P5[/tex]
The complete order to place consonants without repeating vowels becomes: [tex]22P5*21![/tex]
There are 22! x 6! x 5! ways to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively.
Explanation:In order to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively, we can consider the vowels as a single block that needs to be placed in between the consonants. Firstly, let's count the number of ways to arrange the consonants C (21 consonants + 1 y) and the block of vowels V (5 vowels) as separate entities. This can be done in 22! x 6! ways. However, we need to consider that within the V block, the vowels can be rearranged in 5! ways. Therefore, the total number of arrangements is 22! x 6! x 5!.
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If you roll a number cube 22 times about how many times do you expect to roll a numeber Less than 4?
Answer:
About 7 times
Step-by-step explanation:
What is the frequency of the function f(x)?
f(x)=3cos(5x)+2
Enter your answer, in simplest fraction form, in the box.
Answer:
The frequency = 5/2π
Step-by-step explanation:
* Lets revise some facts about the trigonometry function
- If the function is f(x) = A sin (B x + C) + D
* A is the amplitude
- The amplitude is the height from highest to lowest points and
divide the answer by 2
* The period is 2π/B
- The period is the distance from one peak to the next peak
- Period and Frequency are related where frequency = 1/period
* C is the horizontal shift
- The horizontal shift is how far the function is shifted to left
(C is positive) or to right (C is negative) from the original position.
* D is the vertical shift
- The vertical shift is how far the function is shifted vertically up
(D is positive) or down (D is negative) from the original position.
* Lets solve the problem
∵ f(x) = 3 cos (5x) + 2
∵ f(x) = A sin (B x + C) + D
∴ A = 3 , B = 5 , C = 0 , D = 2
∵ The period = 2π/B
∴ The period = 2π/5
∵ The frequency = 1/period
∴ The frequency = 1/(2π/5) ⇒ multiply up and down by 5
∴ The frequency = 5/2π
The frequency of the function f(x) = 3cos(5x) + 2 is 5/2π, represented as 5 cycles per unit interval on the x-axis.
The frequency of the function f(x) = 3cos(5x) + 2 is determined by the coefficient of x inside the cosine function. In this case, the coefficient is 5, which represents 5 cycles per unit interval on the x-axis. The standard form for a cosine function's frequency is given when the function is written as cos(2πft), with f representing the frequency. To match this form, we can rewrite the function as cos(2π(5/2π)x), making it clear that f = 5/2π cycles per unit interval, which is the frequency.
In simplest fraction form, the frequency of the function f(x) is 5/2π.
The subway sold 439 tickets in one day. It wants to sell that amount each day over the next 13 days. How many tickets does the subway need to sell over the next 13 days?
Answer:
5707 tickets
Step-by-step explanation:
We want to sell 439 tickets each day for the next 13 days
439 * 13 =5707
We need to sell a total of 5707 tickets
Measure the length of the top of your desk in centimeters. Describe how you found the length
Answer:
55 centimeters
Step-by-step explanation:
Ok buddy, just say like 55 centimeters, and say you used a measuring tape.
What is the value of X?
Answer: 30 degrees
Step-by-step explanation:
well 60 divided by 2
Just do 60 divided by 2 and that would equal 30 degrees.
A box of granola is 3 inches wide 4 inches long and 6 inches high . The box is half empty.What is the volume of granola bar left in the box
Answer:
[tex]36\ in^{3}[/tex]
Step-by-step explanation:
we know that
If the box is half empty, then the box is half full
therefore
Find the volume of the box and then divide by two to calculate the volume of granola bar left in the box
The volume of the box is
[tex]V=(3)(4)(6)=72\ in^{3}[/tex]
The volume of granola bar left in the box is
[tex]72/2=36\ in^{3}[/tex]
Can someone help me ?
Answer:
• changing an interior angle to a reflex angle
Step-by-step explanation:
In order for the outline of the polygon to have a pair of sides that is concave (pointed inward, rather than outward), the corresponding interior angle must be a reflex angle. (It must measure more than 180°.) Draw one; you'll see.
Circle O has a circumference of 88 cm. What is the length of the radius of the circle?
Answer is 44cm
Step-by-step explanation:
Pl help me
WILL GIVE BRAINLIEST
Answer:
up
Step-by-step explanation:
Since this is written as y = function of x, it will open up or down
y = 3x^2 -5x -10
The coefficient of x^2 is positive so it will open up
3 out of every 5 picks are orange. If 12 picks are orange how many pivks are there in all
Answer: 20 picks
Step-by-step explanation: because orange is picked 3 out of every 5 picks, and 12 picks are orange, you multiply 3 by 4 to get 12, and 5 by 4 to get 20.
Answer:
I think the answer would be 20 picks. Good luck :)
Which transformation shows a translation of 3 units to the right?
A) B) C) D)
lionel wanted to share 4 muffins with his 5 friends. He separated the muffins into 6 equal parts
Answer:
24 muffins, each friend gets 4. There are 4 remaining
Step-by-step explanation:
True or false (Picture provided)
Answer:
The correct answer is F (false)
Step-by-step explanation:
Points to remember
Sin θ = Opposite side/Hypotenuse
Tan θ = Opposite side/Adjacent side
Sec θ = Hypotenuse/Adjacent side
To find Sin 45, Sec 45 and Tan 45
We have Sin 45 = 1/√2
Sec 45 = 1/Cos 45 = 1/(1/√2) = √2
Tan 45 = 1
To find Sec θ/Tan θ
Here θ = 45
Sec (45)/Tan (45) = √2/1 = √2 ≠ Sinθ
Therefore the correct answer is False(F)
Which graph represents the solution set of the system of inequalities?
Answer:
your first Graph :D Hope this helps
The first equation is greater than or equal to, so the line would be solid.
The second equation is less than so the line would be dotted.
Greater than or equal to would be above the solid line, less than would be to the left of the dotted line.
The top left graph is correct.
The radius of a circle is ________ to the tangent where the radius intersects the circle.
A. supplementary
B. perpendicular
C. parallel
D. congruent
Can sum1 help me with this plzz
Sure, but with what question
A circle centered at the origin contains the point (0,-9) does (8, 17) also lie on the circle
Answer:
No
Step-by-step explanation:
The magnitude of the distance from the origin to the point (8, 17) will be more than 17. That point is not on a circle of radius 9 centered at the origin. It is well outside the circle.
Using the linear equation 3x+2y=6, express y in terms of x
Answer: any number
Step-by-step explanation: 3x+2y=6, 2y=6-3x, we want y by itself, so divide by 2 from both sides, y=3-1.5x, then we plug it into the equation,3x+2(3-1.5)=6, then solve. 3x+6-3x=6, 3x-3x=0,so 6=6, y could be any possible answer
The expression for y in terms of x is y = 3 - (3/2)x the linear equation 3x+2y=6 .
To express y in terms of x using the linear equation 3x + 2y = 6, we need to isolate y on one side of the equation.
Step 1: Move the 3x term to the other side of the equation.
Subtract 3x from both sides:
3x + 2y - 3x = 6 - 3x
2y = 6 - 3x
Step 2: Now, to solve for y, divide both sides by 2:
y = (6 - 3x) / 2
Step 3: We can further simplify the equation:
y = 6/2 - (3x/2)
y = 3 - (3/2)x
So, the expression for y in terms of x is y = 3 - (3/2)x.
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Please help me with this.
Answer:
c
Step-by-step explanation:
cause i am a math mttition
It is a rhombus because when we join the different coordinates which forms a rhombus
The answer is rhombus