Answer:
Step-by-step explanation:
[tex]s=ut+\frac{1}{2}gt^2\\if ~the~body~falls~freely,~then~at~t=0,d=0\\s_{n}=d_n=\frac{1}{2}gn^2\\S_{n-1}=\frac{1}{2}g(n-1)^2\\distance~covered ~in~nth~second\\S(n)=d(n)-d(n-1)=\frac{1}{2}gn^2-\frac{1}{2}g(n-1)^2=\fracg[n^2-(n-1)^2]\\=\frac{1}{2}g{(n+n-1)(n-n+1)]\\=\frac{1}{2}g(2n-1)[/tex]
m/JHI =(2x+7)° and m/GHI = (8x - 2)° and m/JHG= 65°. Find m/JHI and m/GHI
The value of m/JHI and m/GHI is angle 19 and 46.
What is angle ?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
[tex]\begin{aligned}2 x+7+8 x-2 & =65 \\10 x+5 & =65 \\10 x & =60 \\x & =6\end{aligned}[/tex]
m/JHI =(2x+7) = (2* 6+7)=12+7=19.
m/GHI = (8x - 2)° = (8*6-2)=48-2=46
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4. Suppose y varies directly with x. If y = 6 when x = -2, find x when y = 15.
Answer:
x is -7.5 or -14/2 or -7½
Step-by-step explanation:
- Supposing y varies directly with x
[tex] { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} [/tex]
[k is a constant of proportionality (k ≠ 0)]
- When y is 6, x is -2
[tex] \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}[/tex]
- Therefore, the equation is;
[tex]{ \boxed{ \tt{y = - 2x}}}[/tex]
- What is x when y is 15
[tex]{ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}[/tex]
The value of x is -5
The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:
k = y/x
k = 6/-2
k = -3
Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation
15 = -3x
Then solve x,
x = [tex]\frac{-15}{3}[/tex]
x = -5
Therefore, when y = 15, x = -5.
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the top of an electric pole is s supported by a wire of 26 ft long on the ground level. how far is tightened spot from the foot of the pole if its height is 24 ft?
Answer:
The tightened spot is 10 feet away from the foot of the pole.
Step-by-step explanation:
1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.
2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.
⭐What is the Pythagoras' Theorem?
[tex](C)^2 = (A)^2 + (B)^2[/tex]An equation to find a 3rd side lengthC = hypotenuseA = one legB = another leg3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.
Let B= the distance from the tightened spot to the foot of the pole.
[tex](C)^2 = (A)^2 + (B)^2[/tex]
[tex]26^2 = 24^2 + B^2[/tex]
[tex]676 = 576 + B^2[/tex]
[tex]100 = B^2[/tex]
[tex]\sqrt{100} = \sqrt{(B)^2}[/tex]
[tex]10 = B[/tex]
∴ The tightened spot is 10 feet away from the foot of the pole.
Diagram:
A table of values of a linear function is shown below. Find the output when the input is n . Type your answer in the space provided.
Input 1 2 3 4 n
output -1 3 7 11
PLEASE ANYONE I NEED HELP ASAP THANK YOU!!
Answer:
input: n
output: 15
Step-by-step explanation:
⭐What is a linear function?
A linear function is an equation that increases by a constant, additive amount.A linear function looks like a straight line when graphed.⭐To find the output that corresponds to n, we can:
make a table of values to find the constant, additive amount of this linear functionuse said constant, additive amount to find the output that corresponds to n⭐Remember:
"input" = x-values"output" = y-values
A cryptographer uses a combination of two functions to develop the initial "key” in a sequence of coded numbers. The functions are:
f(x) = log5(x) – 8
g(x) = x3 + 3
Which is h(x) = f(x) – g(x)?
h(x) = log5(x) – x3 – 5
h(x) = log5(x3) – 3
h(x) = log5(x) – x3 + 11
h(x) = log5(x) – x3 – 11
The value of the function h(x) = f(x) – g(x) will be h(x) = log5(x) – x³ – 11. The correct option is D.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a cryptographer uses a combination of two functions to develop the initial "key” in a sequence of coded numbers. The functions are:
f(x) = log5(x) – 8
g(x) = x³ + 3
The value of the function h(x) = f(x) - g(x) is,
h(x) = f(x) - g(x)
h(x) = log5(x) – 8 - x³ - 3
h(x) = log5(x) – 8 - x³ - 11
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Answer:
D. h(x) = log5(x) – x3 – 11
Step-by-step explanation:
If 5/33 is expressed in decimal form, what digit is in the 92nd place to the right of the decimal point?
Answer: 5
Step-by-step explanation:
If you plug 5/33 into a calculator (or just solve with long division), you'll find that it makes 0.151515... (with 15 repeating forever.)
In every EVEN decimal place there's a 5, but in every ODD decimal place there's a 1. (The first decimal place is 1, the second is 5, etc.)
Since 92 is an even number, there is a 5 in the 92nd decimal place.
In 2003, the price of a certain automobile was approximately $30,600 with a depreciation of $1,440 per year. After how many years will the car's value be $19,080?
a) Write an equation to model the problem. Let t represent the number of years after 2003. For example, the year 2005 would be represented by t = 2.
Answer:
b)Solve the equation to find the answer to the question above. (Note: Include the units, in this case years.)
Answer:
Answer:
a) v(t) = 30600 -1440t
b) 8 years
Step-by-step explanation:
You want an equation that models the value of a car that is initially $30,600 and falls at the rate of $1440 per year. Then you want the number of years it takes for the value to fall to $19,080.
a) EquationSince the rate at which the value falls is a constant, we can use a linear equation for the model. Its form will be ...
value = initial value - (depreciation per year) × years
v(t) = 30,600 -1440t
b) TimeThe time it takes for the value to fall to 19080 can be found by solving for t:
19080 = 30600 -1440t
1440t = 30600 -19080 = 11520
t = 11520/1440 = 8
After 8 years the car's value will be $19,080.
Write the ratio 0.1 to 0.2 as a simplified fraction
What is the length of X Y? 5 units 4 units 3 units 2 units
The length of XY in the given figure is 3 units.
What does congruent mean?same in size and form
Congruent refers to things that are exactly the same size and form. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
What is an example of congruent?Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.
In the above question,
According to the congruency criteria
HI=XY
Hence, Value of XY is 3 units.
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is an altitude in triangle WXZ.
Triangle W X Z is shown. An altitude is drawn from point W to point Y on side Z X, forming a right angle. Angles Z W Y and W X Y are congruent.
If ΔYWZ ~ ΔYXW, what is true about AngleXWZ?
AngleXWZ is an obtuse angle.
AngleXWZ is a right angle.
AngleXWZ is congruent to AngleWXY.
AngleXWZ is congruent to AngleXZW.
Angle XWZ is a right angle if line WY is an altitude in triangle WXZ.
Define angle.In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees. In geometry, there are several different kinds of angles.
Given,
Triangle W X Z is shown. On side ZX, an altitude is drawn at a right angle from point W to point Y. The angles ZWY and WXY are congruent.
ΔYWZ ~ ΔYXW
Angle XWZ is a right angle is true about Angle XWZ.
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Answer:Angle XWZ is a right angle if line WY is an altitude in triangle WXZ.
Step-by-step explanation:
Got it right on edge
What value(s) of b will cause 27x2 + bx + 3 = 0 to have one real solution? Select all that apply.A. b = −18. B. b = −9. C. b = 9. D. b = 18.
The value of b is 18 that will cause equation 27x² + bx + 3 = 0 to have real solution.
What is a quadratic equation?A quadratic equation is an equation of second order. Quad implies the square power, it is also called equation of degree 2.
The standard form of a quadratic equation is ax² + bx + c = 0.
Where a, b and c are constants.
The given equation is,
27x² + bx + 3 = 0.
Compare the given equation from the standard quadratic equation
ax² + bx + c = 0
Compare both the equations,
a = 27, b = b , c = 3
To find the real solution of the quadratic equation,
Substitute discriminant of the equation equal to zero.
D = 0
b² - 4ac = 0
b² - 4 x 27 x 3 = 0
b² = 4 x 81
b = 2 x 9
b = 18.
The required value of b for the given equation is 18.
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Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?
How many visits for them to cost the same?
The number of visits Jim must make to make Plan A the cheaper option is 6 and 5 visits will cost the same.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Suppose n number of visits will make plan A cheaper than B.
The total cost of A < total cost of B
50 + 10n < 25 + 15n
15n - 10n > 50 - 25
5n > 25
n > 5
n = 6
At n = 5
Total cost of A = 50 + 10 x 5 = $100
Total cost of B = 25 + 15 x 5 = $100
Hence "Jim needs to visit 6 times, and 5 visits will cost the same, for Plan A to be more affordable".
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solve the equation 1 half 4s + 2 = 10. on a numberline thanks.
The product of x and 10 is greater then or equal to 23
Answer:
x ≥ 2.3
Step-by-step explanation:
Product means multiplication
10x ≥ 23 Divide both sides by 10
x ≥ 2.3
The relative frequency distribution describes the number of observations that fall within each class. O proportion of observations that fall within each class. O number of observations that are within or below each of the classes. O proportion of observations that are within or below each of the classes. O none of these is correct.
True statement is number of observations that are within or below each of the classes.
Describe relative frequency.A relative frequency describes how frequently a particular kind of event happens among all observations. It is a kind of frequency that employs fractions, percentages, and proportions. The ratio of the total number of events occurring in a scenario to the number of times an event occurs is known as relative frequency. Relative Frequency = Subgroup Frequency/Total Frequency is the formula for relative frequency. A relative frequency count is a way to count how many times an event happens compared to all the other events. It can be described as a percentage. It is frequently represented as a percentage as well.
Given
The relative frequency distribution describes the number of observations that fall within each class.
Statement which is true is,
Number of observations that are within or below each of the classes.
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What is the missing number, what property did you use? 0=–––×3×4
Answer:
0, zero product property
Step-by-step explanation:
Let X and Y be independent and identically distributed exponential random variables with rate λ.
Let U = X/Y and let V = XY . Find the joint desnity for (U, V ). Also find the marginal densities fU (u)
and fV (v).
The joint density for (U, V) is given by:
f(u,v) = fX/Y,XY(u,v) = fX(v/u) * fY(v/u) * |(v/u)|= λ^2 * v * e^(-λv/u) * |(v/u)|
The marginal density for U is given by:
fU(u) = ∫f(u,v)dv
= ∫λ^2 * v * e^(-λv/u) * |(v/u)|dv
= λ^2 * u * ∫ve^(-λv/u)dv
= λ^2 * u * (-(u/λ)^2 * e^(-λv/u))|v=0 to v=∞
= λ^2 * u * (-(u/λ)^2)
= λ^3 * u^2
The marginal density for V is given by:
fV(v) = ∫f(u,v)du
= ∫λ^2 * v * e^(-λv/u) * |(v/u)|du
= λ * v * ∫e^(-λv/u) * |(v/u)|du
= λ * v * (∫e^(-λv/u)du)|v=0 to v=∞
= λ * v * (-(u/λ) * e^(-λv/u))|u=0 to u=∞
= λ * v * (-1)
= λ * v
Therefore, the joint density for (U, V) is
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A triangle has one angle that measures 25 degrees, one angle that measures 104 degrees, and one angle that measures
51 degrees.
What kind of triangle is it?
OA. equilateral triangle
OB. right triangle
OC. acute triangle
OD. obtuse triangle
Answer:
D) Obtuse triangle
Step-by-step explanation:
Obtuse triangles have an angle greater than 90 degrees, and this triangle has an angle of 105.
DUE SOON PLEASE HELP! WHAT ANGLES SHOW THAT LINE 1 AND 2 ARE PARALLEL AND WHY!
Answer:
Both e and h and a and c
Step-by-step explanation:
e and h are corresponding angles on a transversal. Lines are parallel when the corresponding angles of a transversal have the some degree of measure
Same goes for a and c
e and g are not because g doesn't correspond to e because g is in 2 transversals.
Heather plans to make monthly payments of $800 for next 25 years and into it an annuity offering and annual interest rate of 4.8% how much money will she have in 25 years round to the nearest hundred
Answer:
formula
= Pmt [(1 + i/n)^nt - 1] / (i/n)
answer in picture hihi ^_^
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Fill in the blanks 30 = 27 __ ___x 9 = 54 81 / ___ = 92 = ___ / “” 58 x ___ = 32 “” 72 / ___ = 8 “” 7* __ = 49
Answer:
30 = 27 __ 3 x 9 = 54
81 / __9 = 9
2 = __4 / 8
58 x __6 = 32
72 / __8 = 9
7* __7 = 49
Step-by-step explanation:
the high temperature for the week were 50, 52, 71, 54, and 51. what is the mean of the temperatures without the outlier?
Answer: 55.6 or 55.60
Step-by-step explanation: Okay, so we have to add up all the numbers and divide by how many numbers there are, so we would add 50 + 52 + 71 (Including this outlier) + 54 + 51, to get 278. Now, since there are 5 numbers in the data set, we would divide 278 by 6, and you should get 55.6 or 55.60 (They are the same thing)
10. The figures below are similar.
State the ratio of similarity and then use it
to find the value of x. (2 points)
Answer:
x = 16.5
Step-by-step explanation:
the ratio of similarity is the ratio of corresponding sides, that is
ratio = [tex]\frac{18}{12}[/tex] = [tex]\frac{15}{10}[/tex] = 1.5
Then
[tex]\frac{x}{11}[/tex] = 1.5 ( multiply both sides by 11 to clear the fraction )
x = 16.5
Differentiate the function with respect to x. Answer is B. I need the step. Thank you
Answer:
y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.
Step-by-step explanation:
Rewrite the equation to -((6 c^2 - 20 x^3) dx)/(3 + 5 x^2) + dy = 0 and solve
Solve (dy(x))/(dx) = (6 c^2 - 20 x^3)/(5 x^2 + 3):
Integrate both sides with respect to x:
Answer: y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.
Here is an inequality: 7 x+6<3 x+2.
Select all values that are solutions.
(Select all that apply.)
x=1
x=0
x=-1
x=-2
x=-8
By solving a linear inequation, it can be calculated that
The values that are solutions are
x= -2 and x= -8
What is linear inequation?
Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤
A one degree inequation is known as linear inequation.
Here the inequation is 7x + 6 < 3x + 2
7x + 6 < 3x + 2
7x - 3x < 2 - 6
4x < - 4
x < [tex]-\frac{4}{4}[/tex]
x < -1
So the values that are solutions of the inequation are
x=-2 and x=-8
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Sybush
5 Resuelve como en el ejemplo.
TH
.-6+8-10 + 13 = +2 -10 + 13 = -8 + 13 = +5
b) 5-9+7-6
d) -8 + 12-9-2
a) 10-3-5 + 11
c) −2+2+7+8
The Answers for the four parts are
a) 5-9+7-6=-3
b) -8 + 12-9-2=-7
c) 10-3-5 + 11 =13
d) −2+2+7+8= 15
What are Integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
a) 5-9+7-6
= -4 +7-6
= 3-6
=-3
So, the value of 5-9+7-6 is (-3).
b) -8 + 12-9-2
= 4-9-2
= -5-2
=-7
So, the value of -8 + 12-9-2 is (-7).
c) 10-3-5 + 11
= 7-5+11
= 2+11
=13
So, the value of 10-3-5 + 11 is (13).
d) −2+2+7+8
= 0+7+8
= 7+8
= 15
So, the value of −2+2+7+8 is (15).
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The Translation of the Attached Question:
Solve as in the example
Write the tangent equation to solve for angle f
Answer:
Tan(f) = 24/7
Step-by-step explanation:
Tan is opposite over adjacent.
The opposite of angle F is 24 and the adjacent is 7.
could anyone help this is so confusing
Step-by-step explanation:
I and somebody else answered this already. how often did you post this ?
6. How much will you pay for 14.8 gallons of diesel fuel at $1.39 per gallon?
Round to the nearest cent
Answer:
$20.5
Step-by-step explanation:
A school bought 105 boxes of chocolate cookies and 22 boxes of vanilla cookies
for a fundraiser. Each box contained 12 cookies.
The school then repacked the cookies into smaller packs of 8 to sell.
How many small packs were there? How many cookies were left over?
Answer:190 small packs and 4 cookies left over
Step-by-step explanation:
Add the boxes of cookies together 105+22=127
Multiply each box by 12
127 x 12=1524
Because we need to put them into smaller packs of 8 cookies
we need to divide by 8
1524÷8=190 small boxes
This is a total of 190 x 8=1520 cookies there are 4 cookies left over