Answer:
The stone covers 36 m in the 5th second. Correct choice: A.
Step-by-step explanation:
Proportions
Two variables are said to be proportional if one of them can be calculated by multiplying the other by a constant of proportionality. If y and x are those variables, then:
y=k.x
There are other similar proportions where the relation is not linear. For example, if y is proportional to the square of x, then:
[tex]y=k.x^2[/tex]
According to the conditions of the question, the distance traveled by a stone dropped from a height of 5 Km varies directly with the square of the time taken to fall through that distance. If d is the distance and t is the time, then;
[tex]d=k.t^2[/tex]
To find the value of k, we use the given condition: The stone falls d=66 meters in t=4 seconds. Substituting:
[tex]64=k.4^2=16k[/tex]
Solving:
[tex]k=64/16=4[/tex]
Substitute the value of k into the equation to get the complete model.
[tex]d=4.t^2[/tex]
Now we calculate the distance when t=5 seconds:
[tex]d=4\cdot 5^2=4\cdot 25=100[/tex]
The stone has covered 100 m in 5 seconds. But we need to find the distance covered in the 5th second, that specific interval between 4 sec and 5 sec.
Since we already know the distance for t=4 sec (64 m), and the distance for t=5 sec (100 m), then:
distance in the 5th second = 100 m - 64 m = 36 m
The stone covers 36 m in the 5th second. Option A.
Which is one of the transformations applied to the graph of f(x) = x2 to produce the graph of p(x) = –50 + 14x – x2? a shift down 1 unit a shift left 7 units a shift right 1 unit a shift up 7 units
Answer:
Shift down one unit
Step-by-step explanation:
Correct for e2020
The transformation applied to the graph of f(x) to produce the graph of p(x) is:
A). a shift down 1 unit and a shift left 7 units.
What is transformation on the graphs?Let the functions f(x) and g(x) be two real functions.
And g (x) = f (x) + k, where k is real numbers.
The function can be sketched by shifting f (x), k units vertically.
The direction of shift can be found by the value of k:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
The function provided by the basic function f(x) and the constant
g(x) = f(x - k),
may be drawn by horizontally moving the f(x) k unit coordinates.
The shift's direction depends on the value of k. Specifically,
The base graph moves k units to the right if k > 0, and
The base graph moves k units to the left if k < 0.
To determine the transformation applied to the graph of f(x) = x² to produce the graph of p(x) = –50 + 14x – x², we can compare the general forms of the two functions:
f(x) = x²
p(x) = –x² + 14x - 50
The function p(x) can be written as,
p(x) = –(x² - 14x + 49) - 1
p(x) = -(x - 7)² - 1
Therefore, the transformation applied to the graph of f(x) to produce the graph of p(x) is:
A). a shift down 1 unit and a shift left 7 units.
So, the correct answer is A).
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PLEASE HELP ASAP I GIVE YOU BRAINLIEST AND 20 POINTS
can a system of linear equations be inconsistent and dependent? explain.
Answer:
No
Step-by-step explanation:
Inconsistent means it has no solution, which means they do not intersect
Dependent means it is the same line
You cannot have both the same line and not intersecting.
Find the standard deviation of the following data. Round your answer to one decimal place. x 00 11 22 33 44 55 P(X
Complete question :
Find the standard deviation of the following data. Round your answer to one decimal place.
X: 0 1 2 3 4 5
P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2
Answer:
1.833
Step-by-step explanation:
Given the data :
X: 0 1 2 3 4 5
P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2
Standard deviation (s) = Sqrt[Σx²*f(x) - E(x)²]
E(x) = (0*0.2) + (1*0.3)+(2*0.1)+(3*0.1) + (4*0.1) + (5 * 0.2) = 2.2
Sqrt[Σx²*f(x) - E(x)²]: [(0^2 * 0.2)+(1^2 * 0.3)+(2^2 * 0.1)+(3^2 * 0.1) + (4^2 * 0.1) + (5^2 * 0.2)] - 2.2²
Sqrt(8.2 - 4.84) = 1.833
1. Diane's Sweet Treats can make 24 cupcakes using 16 ounces of whipped
icing. How much icing is used on each cupcake?
a. 1/6 ounce of icing per cupcake.
b. 2/3 ounce of icing per cupcake.
c. 1/2 ounce of icing per cupcake.
d. 3/4 ounce of icing per cupcake.
Answer:
b. 2/3 ounce of icing per cupcake.
Step-by-step explanation:
Given parameters:
Number of cupcakes = 24 cupcakes
Ounces of whipped icing = 16 ounces
Unknown:
How much icing was used in each cupcake = ?
Solution:
To find the number icing used per cupcake;
= [tex]\frac{number of ounces of whipped icing}{Number of cupckakes}[/tex]
Input the parameters;
= [tex]\frac{16 ounce of icing }{24 cupcake}[/tex]
= [tex]\frac{2}{3}[/tex] ounce of icing per cupcake
Vincent is selling candy bars to raise money for his soccer team. He started with a full box of 20 candy bars and has sold 3/10 of them so far. If each candy bar costs $1.25, how much money has vincent raised?
Answer:
$7.25
Step-by-step explanation:
6*1.25
Answer:
7.50
Step-by-step explanation:
In a square, what is the relationship between the length of a side and the area?
A. proportional
B. cannot be determined
c. non proportional
d. ratio
The relationship between the length of a side and the area is non proportional. so option C is correct.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In a square, we need to find the relationship between the length of a side and the area.
The answer is non proportional because the side length is x, so is the other side lengths.
The side lengths are all equal and to find area you do x squared or x times x.
So they are not proportional because there will be different numbers for each.
For example. X= 2, area ( x squared ) is 4.
Hence, The relationship between the length of a side and the area is non proportional. so option C is correct.
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The graphed line can be expressed by which equation?
1. y+2=2/3(x×2)
2. y-2=3/4(x-1)
3. y-1=-3/4(x-2)
4. y-2=3/4(x-2)
Write the equation of the line that passes through the given points.
(0,5) and (-2,-4)
Answer:
[tex]y=\frac{9}{2}x+5[/tex]
Step-by-step explanation:
To find the equation of the a line that passes through the two given points, we must first find the slope between the two points. We can do this by using the slope formula. The slope formula is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where m is the slope and (x₁, y₁) and (x₂, y₂) are two points.
By plugging in (-2, -4) and (0, 5) for (x₁, y₁) and (x₂, y₂) respectively, we get:
[tex]y=\frac{5-(-4)}{0-(-2)}=\frac{9}{2}[/tex]
So the slope is 9/2. Now we that we have found the slope, we can write an equation. Normally, when we are given two points, we would pick one of the points and plug it into the point-slope form and then solve for slope-intercept form. Here, notice that one of the points give, (0, 5), is the y-intercept. Knowing this, we can plug in 5 for the y-intercept into the slope-intercept form to get our equation. Remember, slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
Pugging in 9/2 for m and 5 for b we get:
[tex]y=\frac{9}{2}x+5[/tex]
which would be our equation.
I hope this helps. Happy studying.
Find The Difference.
1) 8.5-7.6=
2) 2.5-17.8=
3)-2.9-(7.5)-
4) 3.5-1.9=
Answer:
0.9
-15.3
-10.4
1.6
Step-by-step explanation:
Let me know if I messed up I think I went to fast
Answer:
1. 0.9
2. -15.3
3. -10.4
4. 1.6
If we double the sum of the numbers x and -21, we get the number -100. What is x?
Step-by-step explanation:
2{x + (-21) }= –100
= 2x – 42 = –100
= 2x= –100 + 42
= 2x= –58
= x = –58/2
x= –29
What is the value of sin-1(cos(2pi/3))?
Answer:
-pi/6
Step-by-step explanation:
Answer:
-pi/6 c
Step-by-step explanation:
What is the value of x?
sin(x+22)°=cos(2x−7)°
Answer:
x is 25
Step-by-step explanation:
sin(x+22)° = cos(2x-7)°
since,
sin theta = cos(90 - theta)
we can substitute that in (let theta = x + 22)
sin(x + 22) = cos(90 - (x+22))
we also know
sin(x+22) = cos(2x-7)
thus cos(90 - (x+22)) = cos(2x-7)
cos(90 - (x +22)) = cos(2x-7)
cos(90 - x -22) = cos(2x - 7)
cos(68 - x) = cos(2x - 7)
68 - x = 2x - 7
68 + 7 = 2x + x
75 = 3x
x = 75/3
x = 25
Find the equation of a line passing through the point (6,9) and (0,0)
Answer:
y=3/2x
Step-by-step explanation:
The equation of the required line as per slope-intercept form is 3x - 2y = 0.
What is the equation of a line passing through two points?The equation of a line that passes through points (x₁, y₁) and (x₂, y₂) is defined as:
m = (y₂ - y₁)/(x₂ - x₁)
Here, 'm' is the slope and 'c' is the y-intercept of the given line.
Therefore, the slope of a line that passes through (6, 9) and (0, 0) is
= (0 - 9)/(0 - 6)
= 3/2
Now, the general form of a line is y = mx + c. Here, 'm' is the slope and 'c' is the y-intercept of the line.
The line passes through the point (0, 0).
Therefore, 0 = (3/2) × 0 + c
⇒ c = 0
Now, the equation of the straight line is
y = (3/2)x + 0
⇒ 2y = 3x
⇒ 3x - 2y = 0
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Barb’s Grandma is always creating math problems for her to solve. In one problem she gave Barb a store receipt that listed 72 identical items, each the same price, for a total cost of $*67.9* Barb’s grandma covered the first and last digits of the total price on the receipt with stars. Determine the value of the digits that Barb’s Grandma covered.
9514 1404 393
Answer:
367.92
Step-by-step explanation:
72 = 9·8
In order for the total cost to be divisible by both 8 and 9, it must meet a couple of requirements:
The sum of the digits must be divisible by 9. The last three digits must be divisible by 8.In order for the sum of digits to be divisible by 9, the first and last digits must total 5 or 14. (The total of existing digits is 22. The sum needs to be 27 or 36.)
In order for the last three digits to be divisible by 8, the last digit must be 2*. So, the first digit must be 5-2=3.
The first digit is 3; the last digit is 2.
The total cost is 367.92. Each item price is 367.92/72 = $5.11.
_____
* 790/8 = 98.75, so (790 + 2)/8 will be 99. 792 is the only number starting with 79 that is divisible by 8.
Jonae gets paid $16.50 an hour working at a furniture store. She also gets paid 20% of all of the store's furniture sales each week. This week, the store made $600 on a table and $400 on chairs. If Jonae worked 40 hours this week, how much will she be paid?
Answer:
$860
Step-by-step explanation:
Jonae makes $16.50 an hour and worked 40 hours. Multiply the hours worked by the amount of money she earned.
$16.50 × 40 = $660
The stored made $600 on a table and $400 on chairs, which, in total, is $1000. Since Jonae gets paid 20% of all of the furniture sales, multiply the total sales by the percentage.
$1000 × 0.2 = $200
Add together the earnings she made per hour and the earnings she made from the furniture store's sales.
$660 + $200 = $860
Help plz this is due at 11:59
Answer:
A
Hope this helps ;)
Can someone please help me I need help and I can’t understand this plsssss
step 1. Multiply the variable x with 13 .
step 2. Add 2 to it .
Solution (b) :Step 1 : Subtract 2 from both sides : 13x + 2 - 2 = 41 - 2 = 39
Step 2 : Divide both the sides by 13 : 13x ÷ 13 = 39 ÷ 13 = 3
x = 3
Solution (2) :Solution (a) :Step 1. Subtract 3 from the variable .
Step 2. Divide the result by 5 .
Solution (b) :[tex]Step \: 1. \: add\: 3 \: to \: both \: the \: sides : \frac{x - 3}{5} + 3 = - 1 + 3
[/tex]
Step 2 : Multiply both the sides by 5 : 5 × 1/5x = 5 × -2/5
x = -2
PLEASE HELP !!! Find the missing side lengths
Pls I need help ASAP
Answer:
the answer is 1/8
thank you
if you loved my answer then please like it and mark as brainliest
the mass of earth is approximately 5.9×10^24 kg,and the mass of venus is approximately 4.9×10^24 kg. a. find the combined mass b. given that mass of the sun is approximately 1.9 × 10^30 kg how many venues and earths would it take to equal the mass of the sun.
a) Combined mass of earth and venues is 10.8 × 10²⁴. b) There are total 18989.2 kg taking earth and venue to equal to the sun.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given that,
Mass of earth = 5.9 × 10²⁴ kg
Mass of venus = 4.9 × 10²⁴ kg
a) Combined mass of earth and venus
5.9 × 10²⁴ + 4.9 × 10²⁴ = 10.8 × 10²⁴
b) If the mass of the sun = 1.9 × 10³⁰
Let's say the total gain of earth and venus combined x so it will equal the mass.
Then,
10.8 × 10²⁴ + x = 1.9 × 10³⁰
x = 18989.2 kg
Hence "Combined mass of earth and venues is 10.8 × 10²⁴ and there are a total of 18989.2 kg taking earth and venue to equal to the sun.
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How do you Graph: -3x – 2y = -8
Answer:
I hope this helps!
Answer:
y = -2/3x +4 --> y = mx+b form
Step-by-step explanation:
-3x-2y = -8 --> add 3x to both side
-2y = 3x-8 --> divide by -2 on both side
y = -2/3x +4 --> y = mx+b form
the y intercept is 4 and the slope is -2/3, down 2, right 3.
therefore, the graph would contain a y intercept point of (0,4) and then from there u would start plotting down 2, going right 3 unit or up 2 and left 3 units. Then when u plotted at least 2/3/4 points, use a straightedge to draw the line.
In a population of 271 Dd parrots, predators kill 55. What is the approximate fitness of the genotype?
Fitness of Dd: 20%
Fitness of Dd: 40%
Fitness of Dd: 60%
Fitness of Dd: 80%
Answer:
60%
Step-by-step explanation:
They killed quite a bit and a lot were left.
put 0.12, 0.1225, 3/25, 7/125 in order from least to greatest
Answer:
Note: 3/25 and 0.12 are the same
0.12, 3/25, 0.056, 0.1225
OR
3/25 0.12, 0.056, 0.01225
Hope this Helps!
How many solutions does this system of equations have? Exactly one None Infinitely many Exactly two
Solve for X using Special Rights
Answer:
c) 10√2
Step-by-step explanation:
Two angles are same, means this is an isosceles triangle.
So,
x=10
Now, by using pythagoras theorem,
y=√(10²+10²)
=10√2
1. Mrs. Wendt called Drano Plumbing Company to fix a leak. Their fee is $35 for the
service call, and $42 per hour.
a) Build a table.
b) Write an equation for the amount she would pay for ‘x’ hours:
_________________________
c) Write and solve an equation to find out how long they worked if her bill was $140.
Equation:_________________________
Solution:_______________
Answer:
the equation is 140÷42 and the answer is 4
Find the
median
75,75,75,75,90,95,100,100,110,110,136, 136,136,136,180, 180,180
180,180,180
Answer:
110
Step-by-step explanation:
self explanatory
A taxi company charges $3 per ride plus $1.50 for each mile traveled. Andrea wants to spend no more than $24 on a taxi ride. How many miles can Andrea travel? Select all that apply.
Answer:
x=14
Step-by-step explanation:
3+1.50x=24
24-3=21
21/1.50=14
Answer is C which is 14
Which graph represents a function?
Write the ordered pair for point H.
1. 3, -5
2. 5, -3
3. -5, 3
4. -3, 5
5. -3, -5
Answer:
Number 4 is the correct answer: (-3, 5)