A rock climber throws a first aid kit to 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. How far apart are the two climbers (horizontally)?

Given the shown figure

since

The Central Angle Is Twice The Inscribed Angle

where

a= mACB

2a = mAPB=56

then

a= mACB=28

Correct answer

option b

28

Given that each term has a common difference, this is an arithmetic sequence as per the explicit formula that generates this sequence.

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.

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.

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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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

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

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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answer step by step:

hope this helps

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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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

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

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

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)

Ans: The formula that defines the sequence is Tn = 4n - 2

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From the given linear equation graph, we can tell that the equation of the line in slope intercept form is; y = 1.2x + 3

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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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!

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

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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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]

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)

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

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.

Using a system of equations, the number of people on each tour is given as follows:

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:

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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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

The system of Inequality for the given graph is;

2x + 3y ≥ 12

3x - 5y ≥ 15

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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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

===================================

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]

Answer:

90

Step-by-step explanation:

4 x 23 = 92
2 x (-1) = -2
1 x 0 = 0

92 + (-2) + 0 = 90

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.)

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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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).

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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