A child is flying a kite. If the string is pulled tight to its full length of 40 feet and is held at an angle of 71 degrees above the ground, how high is the kite? Round your answer to the nearest whole foot.

x^2 + y^2 - 10y + (-85) is equation of the circle with center (0, -5) containing the point (-√109,-6).

To find the equation of a circle with a given center and containing a given point, we can use the distance formula. The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the center of the circle and (x2, y2) is the point on the circle. In this case, the center of the circle is (0, -5) and the point on the circle is (-√109, -6). Plugging these values into the distance formula, we get:

d = √((-√109 - 0)^2 + (-6 - (-5))^2)

d = √((-√109)^2 + (-1)^2)

d = √(109 + 1)

d = √110

Since the point (-√109, -6) is on the circle, the distance from the center of the circle to this point is the radius of the circle. Therefore, the radius of the circle is √110.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (0, -5) and the radius is √110, so the equation of the circle is:

(x - 0)^2 + (y - (-5))^2 = (√110)^2

x^2 + y^2 - 10y + 25 = 110

x^2 + y^2 - 10y + (-85) = 0

This is the equation of the circle with center (0, -5) and containing the point (-√109, -6).

To learn more about circle equation refer :

https://brainly.com/question/1506955

#SPJ1

Answer:

Step-by-step explanation:

Example:

If you have the inequality 3<(x/9)+7

Begin with subtraction by subtracting 7 from both sides, rather than beginning with the parentheses x/9.

Do all processes to both sides of the inequality until you have solved for x.

Example: As mentioned in the previous step, you would begin by subtracting 7 from both sides.

So 3<(x/9)+7 becomes, -4<x/9

Now you would multiply both sides by 9 because the fraction x/9 is the same as x divided by 9, and the opposite of division is of course multiplication.

This process leaves you with the solution, -36<x, so x is greater than -36.

Remember that if your problem requires you to multiply or divide by a negative number, then you need to flip the inequality sign when you do so.

For example: If instead of multiplying by 9 in the previous problem you had to multiply by -9, you would get 36>x rather than 36<x.

The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.

What is Inequalities of equations ?

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.Inequality simply means that two things aren't equal. One of the items could be inferior to, superior to, greater than, or equivalent to the other things.
p ≠ q means that p is not equal to qp &lt; q means that p is less than qp &gt; q means that p is greater than qp ≤ q means that p is less than or equal to qp ≥ q means that p is greater than or equal to q
Different kinds of inequality exist. Important inequities include the following: the inequalities of polynomials
Inequalities in absolute values
Logic-based disparities
Calls made by Hazar = 2370
Calls recieved by Hazar = 1645Let the number of Calls by Huzan be x.
And the number of calls recieved by Huzan be y.
Then the inequalities arex&lt; 2370 and y&gt; 1645
The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.

To learn more about inequalities refer to : https://brainly.com/question/28823603
#SPJ1

Answer:

There are an infinte amount of whole numbers

Step-by-step explanation:

7 examples are, 0, 3, 7 , 8 ,9 14, 39

The solution of the given equation 2x + y = 10 is equal to option b. x = 2 and y = 6.

As given in the question,

Given equation is equal to :

2x + y = 10

Simplify and Check which given option represent the solution of the equation :

a. x = 9

2(9) + y = 10

⇒y = -8

Incorrect option.

b. x = 2

2(2) + y = 10

⇒y = 6

Correct option.

c. x = 1

2(1) + y =10

⇒y = 8

Incorrect option

d. x =4

2(4) + y = 10

⇒y = 2

Incorrect option

Therefore, for the given equation 2x + y = 10 , option b . x = 2 and y = 6 is the correct answer.

The given question is incomplete , the complete question is :

Which of the following is a solution of the equation 2x + y = 10?

a. x = 9 and y = 3

b. x = 2 and y = 6

c. x = 1 and y = 7

d. x = 4 and y = 3

Learn more about the equation here

brainly.com/question/29538993

#SPJ4

The numerator for the rational expression is 6

Let us assume the value of numerator to be x

[tex]\frac{2}{f} +\frac{4}{f} = \frac{x}{f}[/tex]

Since these are fractions with same denominators (like fractions),

[tex]= > \frac{2}{f} +\frac{4}{f} \\\\ = \frac{2 +4}{f}\\\\= \frac{6}{f}[/tex]

x = 6

The numerator for the rational expression is 6

To learn more about fractions, refer:

https://brainly.com/question/78672

#SPJ1

The expression which represents the sum of polynomials (9-3x²) and (-8x²+4x+5) is -11x² + 4x + 14

What is polynomial equation?

A polynomial equation is an algebraic equation that consists of variables and coefficients, which are often real numbers, and exponents which are non-negative integers. Polynomial equations can have one or more terms, and can involve addition, subtraction, multiplication, division, and exponentiation.

According to the given question:

The sum of polynomials can be calculated by combining like terms where there are multiple of the same variable.

= (9-3x²) + (-8x²+4x+5)

= 9 - 3x² - 8x² + 4x + 5

= -11x² + 4x + 14

Therefore, the expression which represents the sum of polynomials (9-3x²) and (-8x²+4x+5) is -11x² + 4x + 14

Complete question:

Which expression can be used to find the sum of the polynomials?

(9-3x²) and (-8x²+4x+5)

To know more about polynomials click-

brainly.com/question/2833285

#SPJ4

The three semantics models of parameter passing for subprograms are:  in mode, out mode, and inout mode

In this question we need to describe the three semantics models of parameter passing for subprograms.

The three semantics models of parameter passing for subprograms are:

1) in mode: They can receive data from corresponding actual parameters.

2) out mode: They can transmit data to the actual parameter.

3) inout mode: They can do both.

There are two conceptual models of how data transfers take places in parameter transmission: either an actual value is copied (to the caller, to the callee, or both ways), or an access path is transmitted.

Generally, the access path is a simple pointer or reference.

Therefore, in mode, out mode, and inout mode are 3 semantics models of parameter passing for subprograms

Learn more about semantics here:

https://brainly.com/question/30054863

#SPJ4

The system of equations of line parallel to y = -5x + 4 is y = -5x + c where c is any arbitrary value of y-intercept.

The linear equation y = -5x + 4 is a straight line with slope -5 and y-intercept 4.

The slope of parallel lines are equal. So any line with slope -5 is parallel to the line y = -5x + 4. So the equation of a line with slope -5 is

y = -5x + c

where c is a constant

c represent arbitrary value of y-intercept.

For example y = -5x + 2 is a straight line parallel to y = -5x + 4 but having value of y-intercept equal to 2.

--The question is incomplete, answering to the question below--

"What is parallel to y = -5x + 4?"

To know more on linear equations

https://brainly.com/question/30004506

#SPJ4

An asymptote is a line that a curve approaches but never touches, so it is not part of the curve itself. As a result, an asymptote is not a function. However, the curve that approaches an asymptote may or may not be a continuous function.

A function is continuous if it is defined for all values in its domain and there are no breaks or jumps in the graph of the function.

For example, consider the function f(x) = 1/x. This function has a horizontal asymptote at y = 0, but it is not continuous at x = 0 because the value of the function is undefined at this point (division by zero is not allowed).

On the other hand, consider the function f(x) = ². This function has no asymptotes and is continuous for all values of x.

To know more on asymptote

brainly.com/question/4084552

#SPJ4

Answer:

Eighth half-hour

Step-by-step explanation:

Given pattern:

Calculate the differences between the number of bows used:

[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16[/tex]

Therefore, the pattern for the bows used is:

If the pattern continues:

[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16\underbrace{}_{-3}13\underbrace{}_{+5}18\underbrace{}_{-3}15\underbrace{}_{+5}20[/tex]

Create a table with the given and found data, and add a cumulative total column:

[tex]\begin{array}{c|c|c}\vphantom{\dfrac12} \textsf{Half Hour} & \textsf{Bows used per half hour} & \sf Cumulative\; total\\\cline{1-3} \vphantom{\dfrac12} \sf 1st & 12 & 12\\\vphantom{\dfrac12} \sf 2nd &9 &21 \\\vphantom{\dfrac12} \sf 3rd & 14&35 \\\vphantom{\dfrac12} \sf 4th & 11& 46\\\vphantom{\dfrac12} \sf 5th & 16& 62\\\vphantom{\dfrac12} \sf 6th & 13& 75\\\vphantom{\dfrac12} \sf 7th &18 & 93\\\vphantom{\dfrac12} \sf 8th & 15& 108\\\vphantom{\dfrac12} \sf 9th & 20& 128\\\end{array}[/tex]

If Clifford has a total of 100 bows, he will run out of bows during the eighth half-hour.

Therefore  the probability that the chip belongs to bowl c is 1/3.

Probabilities can be expressed as proportions with a 0–1 range or as percentages with a 0%–100% range. If an event has a probability of 1, it is very certain to occur; if it has a probability of 0, it has no chance of occurring. There are 45 chances out of 100 that an event will occur when its probability is 0.45 (45%).

Here,

A : 2 Red chips

B : 2 White chips

C: One Red and one White chip

P(selecting any bowl) = 1/3

1) We have to find P(W).

The selected chip can be white if it is either selected from Bowl B or Bowl C.

Symbolically this can be written as

P(W) = P(Bowl B and White chips) + P(Bowl A and White chips)

P(W) = [(1/3) × 1/1)] + [(1/3) × (1/2)]

P(W) = (1/3) + (1/6)

P(W) = 1/2

P(W) = 0.5

2) There is only one bowl with both of white and red chips and that bowl is bowl C. So it is possible the other chips in the bowl to red only if it has been selected from Bowl C.

So ,We need to find P(Bowl C | W).

P(Bowl C | W) = P(Bowl C and W)/P(W)

P(Bowl C | W) = (1/3) × (1/2)/(1/2)

P(Bowl C | W) = 1/3

Hence, the required probability is 1/3.

To know more about probability , visit

brainly.com/question/11234923

#SPJ4

Answer:

y=1.4x

Step-by-step explanation:

Find the relationship.

1.4/1=1.4

2.8/2=2.8

and so on so we know it is 1.4

so y=1.4x

The nature of the roots of the given equation x^2 - 3x - 4 = 0 is real and unequal.

The general form of a quadratic equation is ax^2 + bx +c = 0.

Comparing the given equation x^2 - 3x - 4 = 0 with the general form of quadratic equations, we get that:

a = 1,  b = -3 and c = -4

If b^2 - 4ac > 0, then we say that the nature of the roots of the equation is real and unequal.

Therefore,  b^2 - 4ac = (-3) ^ 2 - 4 x 1 x (-4) = 25 >0

Hence, we conclude that the nature of the roots of the given equation is real and unequal.

The question is incomplete, the complete question is:

What is the nature of the roots of x² − 3x - 4 = 0?

To know more about the nature of roots:

https://brainly.com/question/12383696

#SPJ4

Answer:

Step-by-step explanation: it is b

Yes, you can claim sickness benefits on universal credit.

Here we have to find out if it is possible to claim the sickness benefit on Universal credit.

In order to find that, we must know the definition of universal credit,

The term universal credit refers to a payment to help with your living costs.

Here we have to know that as per the definition of universal credit here you can self-certify for up to the first 7 days of your claim by notifying Universal Credit that you have a health condition that prevents you from working. Then on the 8th day, your condition persists and if you have not already done so, then you will definitely need to submit medical evidence in order to claim for benefit.

To know more about claim here.

https://brainly.com/question/14541748

#SPJ4

Answer:

3

Step-by-step explanation:

The lower bound of f-g is 41.31 .

The upper bound of f-g is  41.49 .

Given,

A number 'f' rounded to 1 decimal point is Number = 49.2

A number 'g' rounded to 1 decimal point is  Number = 7.8

Now,

The range of f rounded to 1 decimal point is [49.15 , 49.24].

The range of g rounded to 1 decimal point  is [7.75 , 7.84].

So,

Lower bound of f-g = 49.15 - 7.84

Lower bound of f-g = 41.31

Next,

Upper bound of f-g = 49.24 - 7.75

Upper bound of f-g = 41.49

Therefore the lower bound of f - g is 41.31 and upper bound of f - g is 41.49.

Learn more about lower and upper bound, here:

https://brainly.com/question/32676654

#SPJ4

Answer:

exterior angle = 180° - 120°

                        = 60°

Answer:

60 degrees

Step-by-step explanation:

180-120=60

The z-score 30 points below the mean is -3

The normal distribution of scores has a standard deviation(σ) of 10

Below the mean is (X-μ)=-30

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Z=(X-μ)/σ

Z=-30/10

Z=-3

Therefore, the z-score is -3.

For such more questions about normal distribution

https://brainly.com/question/12421652

#SPJ4

No They can not because you need to be at least 62 years old

The median of 1,2,3,4,5 is 3.

The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

Here we have to find the median of 1,2,3,4,5.

Here we can see that there are 5 numbers given

so, n= 5  which is an odd number so we will use the formula for finding the median in the case of the odd number of data.

So, M = 5+1/2 = 3

Thus the median is the 3rd term which is 3.

Therefore, the median of 1,2,3,4,5 is 3.

To know more about the median visit: brainly.com/question/28060453

#SPJ4

The sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Let us assume: 3 consecutive integers are x, x+1 , x+2.

on adding these three numbers we get,

x + x+1 + x+2 = 3x + 3

which can be further reduced to the form 3(x+1).

If you add any 3 consecutive numbers together it will always equal a multiple of 3, e.g.

1+2+3=6

2+3+4=9

3+4+5=12

4+5+6=15

5+6+7=18

Thus , the sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.

Learn more about consecutive numbers at:

brainly.com/question/17296996

#SPJ4

The mean and standard deviation are 50.292 and 10.362 respectively.

The mean is the average of all available data value. And standard deviation is the measure of how far each data value apart from the mean value.

We are given, 7% of item are under 35 and 89% of item are under 63.

Let, M refers to mean, and SD refers to standard deviation.

As per given data, P(x<35) = 35%

P(z<Z1) = 0.07

hence, Z-score= Z1 = -1.4758 [obtained from Z table]

we know that the z-score = (observed value - mean)/ standard deviation

                      Z1 = (x - M)/ SD

       - 1.4758 = (35 - M)/ SD

-1.4758SD = 35 -M ......... equation 1

as per the 2nd condition in the given data

89% of items are under 63

so, X= 63, P(X<63)

hence, the z-score = 1.2265 [ obtained from Z table]

Z2= 1.2265= (X- mean)/ SD

1.2265SD = 63 - M.......equation 2

Solving equation 1 and 2, we get standard deviation = 10.362

                                   Mean value = 50.292

To know more about Mean and standard deviation visit:

https://brainly.com/question/23556021

#SPJ4

Answer:

9 :)))))))))))

Answer: 7/ -8

Step-by-step explanation:

The slope is rise/run

Our two points are (10,9) ( 2,16)

We see that y increased by 7, and the x decrease by 8

So the slope is 7/ -8

The graph of the equation y = 7.5x shows the proportional relationship.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

y = 7.5x.

The graph of the equation y = 7.5x is shown below.

At x = 1, the value of y = 7.5,

At x = 2, the value of y = 7.5 x 2 = 15

At x = 3, the value of y = 7.5 x 3 = 22.5

And so on.

The value of y multiplied by 7.5 by increasing value of x by 1.

Thus, the graph of the equation  y = 7.5x shows the proportional relationship.

To know more about Equation on:

https://brainly.com/question/187506

#SPJ1

Using system of linear equations, Amelia spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges

System of linear equations is the set of two or more linear equations involving the same variables. A linear equation can be defined as the equations of the first order, whereby the highest power of the variable in the equation is one.

To solve this problem, we have to write a system of linear equation;

Let;

We can represent the problem with two set of equations as;

x + y = 120 ...eq(i)

x = 3y + 10 ...eq(ii)

From equation 1

x + y = 120

x = 120 - y ..eq(iii)

Put eq(iii) into eq(ii)

120 - y  = 3y + 10

collect like terms

120 - 10 = 3y + y

110  = 4y

y = 110 / 4

y = 27.5 minutes

Put y = 27.5 in equ(i)

x + 27.5 = 120

x = 120 - 27.5

x = 92.5 minutes

She spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges.

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

The best estimate of your maximum cumulative funding needed, based on the projected revenue and the expenses is $ 4, 000.

The maximum cumulative funding needed would be the amount that would be total gap between revenue and expenses in the three years that the plan will be in effect.

In year 1, the gap is :
= 5, 000 - 9, 000

= $ - 4, 000

In year 2, the gap is:

= 8, 000 - 9, 000

= $ - 1, 000

In year 3, the gap is:
= 10,000 - 9, 000

= $ 1, 000

The cumulative funding needed is :
= ( -4,000 + - 1, 000 ) + 1, 000

= - $4, 000

You have a maximum cumulative funding needed of $ 4, 000.

Find out more on cumulative funding needed at https://brainly.com/question/14953890

#SPJ1