A rock climber throws a first aid kit to the another climber who is higher up the mountain, the initial velocity of the kit is 12 m/s at an angle of 71 above the horizontal, at the instant when the kit is caught, it is traveling horizontally, so its vertical speed is zero, height difference between climbers is 0.85 m.
What is velocity?Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by specific unit of time (for example, 60 km/h northbound). In kinematics, area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea.
Vertical motion of the first aid kit:
The Initial vertical velocity, u = 5.70 sin 45.7 = 4.08 m/s
Acceleration, g = -9.81 m/s²
When climber who is higher up the mountain catches the kit it's vertical speed is zero.
Final vertical velocity, v = 0 m/s
We have the equation of motion, v² = u² + 2as
Substituting
0² = 4.08² + 2 x -9.81 x s
s = 0.85 m
So kit travels 0.85 m vertically.
Height difference between the climbers = 0.85 m.
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Multiply −14y(7y − 5).
−98y2 + 70y
−98y2 + 70
−98y2 − 5
98y2 − 70y
Answer:
[tex]-98y^2+70y[/tex]
Step-by-step explanation:
Expand the equation [tex]-14y(7y-5)[/tex], we get
[tex](-14y*7)-(-14y*5)[/tex]
Which is equal t0:o
[tex]-98y^2+70y[/tex]
The product of given monomial by binomial is -98y²+70y.
Given that, -14y(7y - 5).
What is product of polynomials?To multiply two polynomials: multiply each term in one polynomial by each term in the other polynomial. Add those answers together, and simplify if needed.
Using distributive property, multiply given monomial by binomial. That is,
-14y(7y - 5)=-14y×7y - (-14y)(5)
= -98y²+70y
Therefore, the product of given monomial by binomial is -98y²+70y.
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Write a rule to describe the transformation.
E(-1-3), F(0,1), G(3,-2)
E'(-1.5,-4.5), F'(0,1.5), G' (4.5.-3)
Answer:
x= x1.5 y = x1.5
E' = E dilated by 1.5
Step-by-step explanation:
-1 x 1.5 =-1.5 -3 x 1.5 = -4.5 (-1.5,-4.5)
0 x 1.5 =0 1 x 1.5 = 1.5 (0,1.5)
3 x 1.5 = 4.5 -2 x 1.5 =-2 (4.5.-3)
SOLVE ASAP PLEASE!!!!
===================================
Explanation:
Recall that [tex]i = \sqrt{-1}[/tex]
Square both sides to get [tex]i^2 = -1[/tex]
So,
[tex](i\sqrt{5})^2 = i^2*(\sqrt{5})^2 = -1*5 = -5[/tex]
1. Given the sequence: {5, 7, 9, 11, ...}
Which explicit formula generates this sequence?
What’s the answer
Given that each term has a common difference, this is an arithmetic sequence as per the explicit formula that generates this sequence.
Arithmetic Sequence formula.In this instance, the next word in the sequence is obtained by adding 2 to the previous term. To put it another way, a n = a 1 + d (n – 1) This is the arithmetic sequence’s formula.
How are explicit formulas handled?Firstly, we have to find the initial phrase in a given series. Thereafter we have to find the shared difference between the following phrases in the sequence. For an explicit rule, replace the general form with the first term and common difference.
What in mathematics is an arithmetic sequence?The distance between succeeding terms in an arithmetic series is always the same.
The difference between consecutive terms in the sequence 3, 5, 7, 9…, for instance, is an example of an arithmetic sequence.
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9. A teacher assigns 4 points for a correct
answer, -1 points for an incorrect answer,
and 0 points for leaving the question
unanswered. What is the score for a
student who had 23 correct answers, 2
incorrect answers, and 1 unanswered
questions?
Answer:
90
Step-by-step explanation:
4 x 23 = 92
2 x (-1) = -2
1 x 0 = 0
92 + (-2) + 0 = 90
Write an equation for the line parallel to the given line that contains C.
8
C(-1,8); y=8/9x-7
y=
The equation for the line parallel to given line containing C:
y = 8/9x + 64 / 9
What is Parallel line ?
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Given that a line's equation is,
y = 8 / 9x - 7
If we contrast this equation with a line's slope-intercept,
this line's slope = 8/9
Since every line parallel to this one will have a same slope,
The parallel line's slope is equal to
The symbol for the line with the slope 'm' and the coordinates (x', y') is
y - y' = m(x - x')
As a result, the equation of the line through (-1, 8) with a slope will be,
y - 8 = 8/9 (x-1)
y =8/9x - 8/9 - 8
y = 8/9x + 64 / 9
Hence, The equation for the line parallel to given line containing C is
y = 8/9x + 64 / 9
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All of the following are equivalent fractions except
04/12
07/21
O 5/20
O9/27
Answer:
05/20 is not an equivalent fraction
Step-by-step explanation:
1) Write each fraction in its simplest form. To do this divide the numerator by the denominator.
04/12 becomes 1/3
07/21 becomes 1/3
05/20 becomes 1/4
09/27 becomes 1/3
2) all the fractions simplify to the same number except 05/20. So, we can conclude that 05/20 is not an equivalent fraction
Divide -2 1/8÷6 4/5 . Explain each step you used to find the quotient.
Answer: -85/272
Step-by-step explanation:
-17/8 divided by 34/5
then opposite reciprical
-17/8 x 5/34
-85/272 (check if you can simplify)
Solve the equation for y. Then find the value of y for each value of x. y + 2x = 5; x = -2, 0, 4
please help me
Answer: y=9 when x=-2
y=5 when x=0
y=-3 when x=4
Step-by-step explanation:
y+2x=5
y=5-2x
y=5-2(-2)
y=5-(-4)
y=5+4
y=9 when x=-2
y=5-2(0)
y=5 when x=0
y=5-2(4)
y=5-8
y=-3 when x=4
Zoe downloaded a trial game to her computer. She has at most 60 free minutes to
play the game. It takes 5 minutes to set up her character, and the instructions say
each level takes 8 minutes.
How many levels L is she estimated to complete on the free trial?
Show work or explain. Write your answer as an inequality. (here are inequality symbols you can
copy and paste < > ≤ ≥)
Answer:
6 levels
Step-by-step explanation:
60 - 5 (to set up the character)
55 total minutes
8(l) = 55
L = 55/8
L = 6.875
.˙. they can finish 6 levels
Write as
a Ratio : 18:11
Answer:
This is all ready written as a ratio. You could also write it as 11:18, but other than that, your good!
Step-by-step explanation:
Hope it helps! =D
7. You bought a Gatorade and 4 bags of apples for $5.50. Write the equation that determines how much
each bag of apples was if the Gatorade cost $2.50.
Answer: (5.50-2.50)/4 = 0.75. each bag of apples is $0.75
Step-by-step explanation:
first, you subtract $5.50 by $2.50 to get $3, the cost of the 4 bags of apples altogether ($5.50 - $2.50 = $3)
then you divide $3 by 4 to get the cost of each bag of apples. (3/4 = 75)
so each bag of apples is $0.75
i hope this helps!
Sophie has
1
2
cup of chocolate which can make
1
3
of a S’more recipe. How many cups of chocolate are needed to make one whole S’more recipe? EXTRA POINTS FOR A CORRECT ANSWER
Answer:
1 1/2 cups of chocolate
Step-by-step explanation:
Sophie has
1/2
cup of chocolate which can make
1/3
of a S’more recipe. How many cups of chocolate are needed to make one whole S’more recipe? EXTRA POINTS FOR A CORRECT ANSWER
1 1/2 cups of chocolate because 1/3 takes 3 times to get a whole so 1/2x3=
1 1/2
In the circle below, P is the center. If < APB measures 56 °, find the measure of < ACB.
Given the shown figure
since
The Central Angle Is Twice The Inscribed Angle
where
a= mACB
2a = mAPB=56
then
[tex]2a=56[/tex][tex]a=\frac{56}{2}[/tex][tex]a=28[/tex]a= mACB=28
Correct answer
option b
28
Suppose that you decide to buy a car for $27,635, including taxes and license fees. you saved $5000 for a down payment and can get a three-year car loan at 6.36%. Find the monthly payment and the total interest for the loan
the monthly payment of $ 668.75 will be paid for the loan for the car.
Total payment for the car = $ 27,635
Money for down payment = $ 5000
Interest for 3 year loan = 6.36 %
Amount on which this interest will be applied = $ 27,635 - $ 5000
Amount = $ 22,635
Interest = 6.36 % of $ 22,635
Interest = 6.36 / 100 × $ 22,635
Interest = 1440 (approx.)
Total amount of loan = $ 22,635 + $ 1440
= $ 24075
Number of months = 3 × 12 = 36 months
So, monthly payment = $ 24075 / 36
= $ 668.75
Therefore, we get that, the monthly payment of $ 668.75 will be paid for the loan for the car.
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A construction crew is lengthening a road. The road started with a length of 53 miles, and the crew is adding 4 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked.
Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 36 days.
Answer:
L = 4D + 53
After 36 days of work, the road will be 197 miles long.
Step-by-step explanation:
This question requests that an equation is found to represent the relationship between the length of a road and the days that the workers spend working on the road.
We are given that the road is 53 miles long prior to the work done by the construction crew. This means that this will be added in addition to what we will find.
L represents the length of the road after D days. Since the road is lengthened by 4 miles each day, this could be represented by 4 * D, or simply 4D.
Therefore, the equation we find can be written as L = 4D + 53.
Since we need to find how many miles the road will be after 36 days of work, substitute 36 days as D and solve for L:
L = 4(36) + 53
L = 144 + 53
L = 197
Therefore, the road will be 197 miles long after 36 days of construction.
which formula defines the sequence f(1)=2, f(2)=4, f(3)=8, f(4)=16, f(5)=32
please help !!
Ans: The formula that defines the sequence is Tn = 4n - 2
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Skippy got his first paycheck and his gross pay was $1200. He noticed he paid the federal
government $180, FICA $91.44, and a state tax of $60.
a) How much did he pay in taxes?
b) What percentage of his gross income went to taxes?
c) What is his net pay?
11.) You have $49.99 to spend for a pair of jeans. The sales tax is 7%. What is the
most the jeans can cost?
A) $46.49
B) $46.72
C) $29.41
D) $45.16
Answer:
B) $46.72
Step-by-step explanation:
Let j = cost of the jeans
j * 1.07 is the cost of the jeans with tax
j * 1.07 = 49.99
Divide each side by 1.07
j * 1.07 /1.07 = 49.99 / 1.07
j =46.72
The jeans can cost no more than 46.72
Answer:
B) $46.72
Step-by-step explanation:
The problem can be expressed as an equation you solve for "y"
y + y * 0.07 = 49.99
We factor out the "y" from the equation and we get
y * (1 + 0.07) = 49.99
Which is the same as
y * 1.07 = 49.99
We can then divide by 1.07 both sides
y = 49.99 / 1.07
Which yields
y = 46.719
If rounding is allowed the answer is B, otherwise the answer is A. I'll go with the rounded one
PLEASE HELP ASAP this stuff doesn’t make sense ;-;
The system of Inequality for the given graph is;
2x + 3y ≥ 12
3x - 5y ≥ 15
How to Interpret Inequality graph?
Inequalities that use < or > symbols are always plotted with a dashed line while Inequalities that use ≤ or ≥ symbols are always plotted with a solid line.
Now, if the shaded portion is above a dashed line, the the symbol is > but if it is shaded above a solid line, then the symbol is ≥. In this question, a solid line is used for both equations and shaded above the lines and so we will use ≥.
Equation of Line 1;
x-intercept = 6
y intercept = 4
Slope = -2/3
Thus, using the general equation of slope of line, the equation of this inequality is; 2x + 3y ≥ 12
Similarly, the equation of the second line will be;
3x - 5y ≥ 15
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Solve for x -
[tex]\sf 6+4x+3=6x-21[/tex]
Answer:
x = 15
Step-by-step explanation:
Let's start by copying down the equation.
6 + 4x + 3 = 6x - 21
Let's simplify this equation and we get,
4x + 9 = 6x - 21
Now, we can add 21 to both sides to isolate 6x on one side. Then, we get...
4x + 30 = 6x
Now, we minus 4x from both sides to get rid of it.
Then we get...
2x = 30
Thus, x = 15
6 + 4x + 3 = 6x - 21
We minus (4x+3) on both side.
6 + 4x + 3 - (4x+3) = 6x - 21 - (4x + 3)
6 = 2x - 24
2x = 30
x = 15.
Recheck : 6 + 60 + 3 = 90 - 21
69 = 69 (nice.)
Grand canyon tours offers air and ground scenic tours of the grand canyon. tickets for the 7-1/2 hr tour cost $169 for an adult and $129 for a child, and each tour group is limited to 19 people. on three recent fully booked tours, total receipts were $2931 for the first tour, $3011 for the second tour, and $2771 for the third tour. determine how many adults and how many children were in each tour. hint: use method of question 2 to find the number of adults and children in each tour (3 tours).
Using a system of equations, the number of people on each tour is given as follows:
First tour: 12 adults and 7 children.Second tour: 14 adults and 5 children.Third tour: 8 adults, 11 children.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the given problem.
For this problem, the variables are described as follows:
Variable x: number of adults in the tour.Variable y: number of children in the tour.All the tours were fully booked, hence the following equation is used in all cases:
x + y = 19.
Four the first tour, considering the values of the ticket and the total receipts, the following equation is built:
169x + 129y = 2931.
Using a calculator, the solution is:
x = 12, y = 7 -> 12 adults and 7 children.
For the second tour, the equation is:
169x + 129y = 3011.
Hence:
x = 14, y = 5 -> 14 adults and 5 children.
For the third tour, the equation is:
169x + 129y = 2771.
The solution is:
x = 8, y = 11 -> 8 adults, 11 children.
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Long division synthetic remainder theorem and factor theorem
[tex](4n^3 - 18n + 21 - 8n^2) ÷ (2n - 6)[/tex]
answer step by step:
hope this helps
which rational is qvuivalent to 0.86
The rational equivalent to 0.86 can be written as 43/50.
A rational number may be defined as the number which can be expressed in the form of p/q where p and q are integers, and the term q cannot be equal to zero. It can be either positive or negative or both. We can also say that any fraction which does not have zero in the denominator is called a rational number. Zero can also be regarded as a rational number as it can also be represented as a fraction. For example, 0/2, 0/5. In order to write 0.86 as a rational number, we have to convert it in fraction form. In fraction form it can be written as
0.86 = 86/100
This is also a rational number, but we simplify it further and we get
86/100 = 43/50 which is a rational number.
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please help. urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
From the given linear equation graph, we can tell that the equation of the line in slope intercept form is; y = 1.2x + 3
How to Interpret Linear Equation Graph?
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
From the given graph, we see that;
y - intercept = 3
x - intercept = -2.5
Now, we can find the slope by taking two coordinates;
(-2.5, 0) and (0, 3)
Slope = (3 - 0)/(0 - (-2.5))
Slope = 3/2.5
Slope = 1.2
Thus, the equation of the line is;
y = 1.2x + 3
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10 oranges and 20 grapefruits weigh 35 pounds total. 16 oranges and 10grapefruits weigh 23 pounds total. How much would 13 oranges and 15grapefruits weigh?A 28 poundsB 29 poundsC 30 poundsD 58 pounds20 Illuminate Education, Inc.
First, we will find the weight of each oranges and grape fruit
Let x be the unit weight of orange
Let y be the unit weight of grape fruit
If "10 oranges and 20 grapefruits weigh 35 pounds total"
Then this implies;
10x + 20 y = 35 -----------------(1)
And
If " 16 oranges and 10 grapefruits weigh 23 pounds total"
This implies;
16x + 10y = 23 ---------------------(2)
We can solve the two equations simultaneously.
Using elimination method;
we eliminate y and to do that, the y variables in the two equations must be same, Hence we can achieve that by multiply equation (1) by 10 and then multiply equation (2) by 20
100x + 200y = 350 ----------------------------(3)
320x + 200y = 460 ------------------------------(4)
subtract equation (3) from equation (4)
220x = 110
divide both-side of the equation by 220
x = 0.5
substitute x=0.5 into equation(1) and then solve for y
10(0.5) + 20y = 35
5 + 20y = 35
subtract 20 from both-side of the equation
20y = 35 - 5
20y = 30
divide both-side of the equation by 20
y = 1.5
"13 oranges and 15 grape fruits" = 13 x + 15y
substituting x = 0.5 and y= 1.5 in the above;
13(0.5) + 15(1.5)
=6.5 + 22.5
=29
Hence;
13 oranges and 15 grapefruits will weigh 29 pounds
Find the distance between points S(-2,4) and T(3,9). Round your answer to the nearest tenth.
Answer:
d^2=(x2-x1)^2+(y2-y1)^2
d^2=[3-(-2)]^2+(9-4)^2
d^2=(5)^2+(5)^2
d^2=25+25
d^2=50
d= [tex]\sqrt{50}[/tex]
d=7.07 units
Find the equation of the line.
Use exact numbers.
Answer:
y = (1/2)x + -3
Step-by-step explanation:
Point 1: (0, -3); Point 2: (6, 0)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 0 - (-3) 0 + 3 3 1
m = ------------- = ------------ = ---------- = -------- = --------
x₂ - x₁ 6 - 0 6 6 2
y - y₁ = m(x - x₁)
y - (-3) = (1/2)(x - 0)
y + 3 = (1/2)x
- 3 -3
----------------------------------
y = (1/2)x - 3
I hope this helps!
Answer: y=0.5x-3
Step-by-step explanation:
[tex]\displaystyle\\(0,-3)\ \ \ \ (6,0)\\ \frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=0\ \ \ \ x_2=6\ \ \ \ \ y_1=-3\ \ \ \ \ y_2=0\\\\\frac{x-0}{6-0} =\frac{y-(-3)}{0-(-3)}\\\\\frac{x}{6} =\frac{y+3}{0+3} \\\\\frac{x}{6} =\frac{y+3}{3}[/tex]
Multiply both parts of the equation by 3:
[tex]\displaystyle\\\frac{x}{2} =y+3\\\\0.5x=y+3\\\\0.5x-3=y+3-3\\\\0,5x-3=y\\\\Thus,\ y=0.5x-3[/tex]
Converting Units of Measure I - Item 35100
Ellie needs 24 cups of milk for a large recipe. How many gallons does she need?
2 c = 1 pint
(pt)
2 pt = 1
quart (qt)
4 qt = 1
gallon (gal)
Ellie needs 1.5 gallon of milk (that is 24 cups).
we are given 2 cup = 1 pint
we have 24 cup which will be equal to 24/2 i.e. 12 pint.
we are given 2 pint = 1 quart
we have 12 pint which will be equal to 12/2 i.e. 6 quart
we are given 4 quart = 1 gallon
we have 6 quart which will be equal to 6/4 i.e. 1.5 gallon.
Hence, we know 24 cups of milk is equivalent to 1.5 gallon of milk
what are conversions in maths?
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. When a conversion is required, the right conversion factor to an equivalent value must be applied. For instance, 12 inches equals 1 foot when converting between inches and feet.
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line m can be represented by the equation 3x-6y=18. Write an equation of the line perpendicular to line m that passes through the point (-4,1)
Step-by-step explanation:
the perpendicular line can be represented by bx-ay+k=0 ,So the second step Is Written
since the line passes through point (-4,1) ,the value of x and y is Substitute as written in answer
Answer:
y=-2x-7
Step-by-step explanation:
3x-6y=18 also equals 3x-18=6y
divide both sides by 3 to get x-6=2y or y=x/2-3 as same line then, to find inverse switch x and y, x=(y/2)=3 and solve for y, y-6=2x, -y=2x+6 is the inverse then to make it pass thru (-4,1) change b value, y=-2x-7