*URGENT + 100 POINTS*
A right triangle is shown in the graph.

right triangle on coordinate plane with hypotenuse labeled t and one endpoint of hypotenuse at r comma s and the other endpoint at x comma y, vertical line from point x comma y and horizontal line from r comma s that meet at right angle of triangle, horizontal dotted line from point r comma s to point s on y axis, horizontal dotted line from point x comma y to point y on y axis, vertical dotted line from point r comma s to point r on x axis, and vertical dotted line from right angle to point x on x axis

Part A: Use the Pythagorean Theorem to derive the standard equation of the circle with center at (r, s) and a point on the circle at (x, y). Show all necessary math work. (3 points)

Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle. (4 points)

Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence. (3 points)

Answer:

-8

Step-by-step explanation:

f(-3) = 2(-3)-2

f(-3) = -6 -2

f(-3) = -8

Answer:

[tex] \huge{f( - 3) = - 8}[/tex]

Step-by-step explanation:

[tex]f(x) = 2x - 2[/tex]

In order to find f(-3) we substitute the value of x that's -3 into f(x) that's wherever we find x in f(x) we substitute it with -3 and solve for f(-3).

We have

[tex]f( - 3) = 2( - 3) - 2 \\ = - 6 - 2 \\ = - 8[/tex]

We have the final answer as

[tex] \bold{f( - 3) = - 8}[/tex]

Hope this helps you

Answer:

x=9 (9,25)

Step-by-step explanation:

9*7=27

27-2=25

Answer:

x<1

Step-by-step explanation:

since the circle is not filled it will not be equal to one but either grater or equal to it

Since the arrow is pointing left than x is less than 1

x<1
hopes this helps please mark brainliest

The number of months after which she will be able to vault 11 feet is 30 months.

For a pole-vaulter in training, the height the athlete will be able to pole-vault after t months of training is given by a mathematical formula. The formula is given below.

H(t) = 17 - 11e^(-0.02t)

We need to find the number of months after which she will be able to vault a height equal to 11 feet. We will substitute the value of height in the given equation.

11 = 17 - 11e^(-0.02t)

11e^(-0.02t) = 17 - 11

11e^(-0.02t) = 6

e^(-0.02t) = 6/11

Now, we will take the natural logarithm on both sides of the equation.

-0.02t = -0.606

t = 0.606/0.02

t = 30.3

Thus, she will be able to vault 11 feet in approximately 30 months.

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Answer:140

Step-by-step explanation:

14 x 10=

Answer:

90% increase

Step-by-step explanation:

490-931=-441

931-490=441

931/490=1.9

therefore, 190% of 441=931

Answer:90% increase

The F Test statistic is 1.58.

Given data is

Source       SS           df          MS

between   21,000.00       2        6,000.00

within  442,500.00  117        3,782.00

The SStotal is sometimes easier to calculate than SSbetween Since ......

SSwithin +SSbetween = SStotal you can use SStotal to calculate SSbetween.

= 442,500+21,000 =  463,500

In ANOVA, the F test statistic is the  ratio of the between - treatments variance and the within-treatments variance. The value of the F test statistic is 1.58 when the null hypothesis is true , the F test statistics is closer to 1, when the null hypothesis is false, the F test statistic is most likely large in general, you should reject null hypothesis for larger values of the F test statistic.

Hence the answer is the F Test statistic is 1.58.

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1. It will take 5 hours for the five-gallon tank full of water to become empty at the drainage rate of 1/(1 + t) gallons per hour.

2. A correct setup of the equation problem above in terms of function is D. None of these will give the correct solution.

An equation is a mathematical statement that shows that two or more mathematical expressions share equality or are equivalent.

Functions, which are mathematical expressions involving one or more variables known as domain (or the independent variable) and range (or the dependent variable), using the equation symbol to show that two expressions are equal.

Drainage rate per hour = 1/(1 + t) gallons

t = 0

The capacity of the tank = 5 gallons

1/(1 + t) gallons

= 1/(1 + 0) gallons

= 1/1 gallons

= 1 gallon per hour

Since the tank is 5 gallons, it will take = 5 hours (5/1)

Thus, based on the drainage equation rate, the five-gallon tank will empty in 5 hours.

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Answer:

Step-by-step explanation:

-21 = -7x

-21 divided by -7 = -7 divided by -7

3=x

The number of eraser Stefanie bought is 10.

Stefanie bought a package of pencils for $1.75 and some erasers that cost $0.25 each. She paid a total of $4.25 for these items, before tax.

Therefore, the number of eraser Stefanie bought can be calculated as follows;

let

x = number of eraser bought

Therefore,

4.25 = 1.75 + 0.25x

subtract 1,75 from both sides of the equation

4.25 - 1.75 = 1.75 - 1.75 + 0.25x

2.5 = 0.25x

divide both sides by 0.25

x = 2.5 / 0.25

x = 10

Therefore,

number of eraser = 10

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The formula of the parabola is y = 2/35(x + 7)(x - 5)

The parameters in the question are given as

These parameters can be represented as

x₁ = -7 and x₂ = 5

(x, y) = (0, -2)

The quadratic function can be represented as

y = a(x - x₁)(x - x₂)

Substitute the known values in the above equation So, we have the following equation

y = a(x + 7)(x - 5)

At (x, y) = (0, -2), we have

-2 = a(0 + 7)(0 - 5)

Evaluate

a = -2/-35

Divide

a = 2/35

So, we have

y = 2/35(x + 7)(x - 5)

Hence, the equation is y = 2/35(x + 7)(x - 5)

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The probability that the next number pointing north is between 2 and 7 is 13/18 .

1) The circle is divided into 9 parts.

Now the parts are uneven.

So the data about the spins is required to calculate the probability .

The total number of items in the box = 18

favorable outcomes (between 2 and 7) = 13 possible outcome.

Required probability

= favorable outcome / total outcome

= 13 / 18

2) Using the Venn diagram we can calculate the various parts of the problem:

Shoppers at big-box store or online or local store = sum of all the shoppers = 109+57+107+18+17+38+34 = 380 shoppers

3) Shoppers made purchase online or locally owned shop but not at a big box store = 107 + 38 + 34 = 179 shoppers.

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In triangle QRS, ∠S=67⁰ if ∠R =∠S and ∠Q=46⁰

An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common endpoint, and are referred to as the sides of the angle. Two planes intersecting at an angle also produces an angle.

A measure of an angle or of a rotation is also referred to as an angle. The ratio of a circular arc's length to radius is known as this quantity. When it comes to a geometric angle, the arc's vertex serves as its center and its sides as its boundaries. When there is a rotation, the arc is defined by the rotation's image and any other point other than the rotation's center.

In triangle QRS,

And from the figure,

∠R=∠S

Therefore,

∠R+∠S+∠Q=180⁰

2∠S+46⁰=180⁰

2∠S=134⁰

∠S=67⁰

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The eastbound airplane traveled 44 miles far.

Given:

Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart.

Let x be the eastbound airplane traveled.

we know that,

north and east direction are perpendicular and with hypotenuse 55 miles it forms a right angle triangle with side = 33 miles.

According to pythagorean theorem:

[tex]33^2+x^2=55^2[/tex]

[tex]x^{2} =55^2-33^2[/tex]

= 3025 - 1089

x = [tex]\sqrt{1936}[/tex]

= 44 miles.

Therefore The eastbound airplane traveled 44 miles far.

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The lengths of the base of the triangle are 31cm while the height of the triangle is 39cm

A triangle is a polygon that has 3 sides, three angles and three vertices whose sum of angles equal to 180 degrees.

How to find the lengths and height of a triangle?

from the statement,

A=1/2bh

A=1/2 xbx(8+b)

cross multiplying,

713 = 8b+b²

rearrange the function

b²+8b-713=0

Simplyfying the equation,

(b²+23b)-(31b-713)=0

b(b+23)-31(b+23)=0

b-31=0 or b+23 =0

b=31 or b=-23

length cannot be negative. therefore base = 31cm

Recall the h= b+8

this implies that h=8+31

h=39cm

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After solving the linear programming problem, we get the answer as 250.

What is linear programming?

When a linear function is exposed to multiple restrictions, linear programming maximizes or minimizes the function. This method determines the best way to use the resources that are currently available and aids managers in using the process to make decisions about the most efficient use of scarce resources, such as money, time, materials, and machinery. Linear programming has been useful for guiding quantitative decisions in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.

Solution explained:

[tex]\left \{ {{2x + y = 12} \atop {x + y = 7}} \right.[/tex]            x=3, y=4    P(3,4)       Coordinates of the solution point

[tex]\left \{ {{x + y = 7} \atop {x + 2y = 10}} \right.[/tex]            x=4, y=3    Q(4,3)      

                                                           Coordinates of the simultaneous eqs.

[tex]\left \{ {{2x + y = 12} \atop {x + 2y = 10}} \right.[/tex]            x=14/3, y=8/3

Putting the values of x and y in the equation P = 30x + 40y and calculating we get

P(P) = 250, P(Q) = 240, P(R) = 246.67

So, the answer is 250

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Answer:

Step-by-step explanation:

they are asking for probability

so they want to know,  what's the probability of getting a "heads"  on a coin toss.   What do you think it is?  You probably know this intuitively.

P(H) = ?

P(T) = ?  

They are asking for fractions,    so just say what  you already know to be how often you'll get a "heads"   in words, then just make that a fraction.  :)

The solution is Option D.

Line plot , because a small number of scores are reported individually

What is a line plot?

A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.

If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions

Given data ,

Total number of athletes = 15

The score points of athletes = { 1 , 2 , 3 , 4 , 5 }

The number of athletes = { 1 , 2 , 3 , 4 , 5 }

The best option to plot the line plot because of the data set

The line plot , a data visualization chart that more accurately represents the small data set, is chosen.

And , to begin, unlike a line plot , a histogram involves data ranges or intervals. A line plot uses a dot to represent each observation, whereas a histogram divides the data into intervals, masking the identity of each observation

Furthermore, because line plots are one of the simplest statistical plots, they are better suited to small to moderate-sized data sets. They are more effective than histograms at highlighting clusters and gaps

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Answer:D

Step-by-step explanation:

Answer:

0.32

Step-by-step explanation:

[tex]\frac{780-532}{780}[/tex] = [tex]\frac{248}{780}[/tex] = 0.32 Rounded.

The approximate of √59 is 7.7 when rounded off to the nearest tenth place.

Given,  √59

we are asked to determine the approximation without using a square root button.

√59 is a decimal number since it is not a perfect square. Therefore, rather than finding a precise value, we will need to obtain a near approximation of 59 in decimal form.

the square root of the number 59 is:

7.6811

You rounded to the nearest tenths place. The 6 in the tenths place rounds up to 7 because the digit to the right in the hundredths place is 8.

= 7.7

When the digit to the right is 5 or greater we round away from 0.

7.6811 was rounded up and away from zero to 7.7

Hence we get the required approximation.

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The value of x in  the following equation: 3|x+3|−12=0 is -7 and 1

The equation is 3|x+3|−12=0

We need to rewite the equation above in standard form

The modulus function can be positive and negative

Considering it to be negative,

the equation is

3((-1)(x + 3) - 12

3(-x - 3) - 12

-3x - 9 - 12 = 0

3x + 21 = 0

3x = -21

x = -7

3(x + 3) - 12

3x + 9 - 12

3x - 3 = 0

3x = 3

x = 1

Therefore, the value of x in  the following equation: 3|x+3|−12=0 is -7 and 1

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[tex]-\frac{5}{2} (8a - 2b) = ...[/tex] the answer for this question is zero (0)

How can the answer is zero?

The first thing that we should do is simplify questions.

[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (- 2b)\\= - 20a + 5b[/tex]

After that, we will search for "a" and "b" to solve the question. For me, i will search for "b" first.

[tex]- 20a + 5b \\5b = 20a\\b = \frac{20}{5} a\\b = 4a[/tex]

Next step is find the "a" by enter the "b" into the same question.

[tex]- 20a + 5b =\\20a = 5b\\20a = 5 (4a)\\20a = 20a\\a = 1[/tex]

After we find the "a" and "b", the next step is to enter it into the main question to find the right answer.

[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a - 2[4a]) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (-8a)\\= - 4a + 4a\\= -4 (1) + 4 (1)\\= -4 + 4\\= 0[/tex]

So, the answer is zero (0).

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Answer:

[tex] - 20a + 5b[/tex]

Step-by-step explanation:

[tex] - \frac{5}{2} (8a - 2b)[/tex]

[tex] - \frac{5}{2} (8a) - \frac{5}{2} ( - 2b)[/tex]

[tex] - 20a + 5b[/tex]

Answer:

11

Step-by-step explanation:

Find the difference using subtraction:

18 - 7 = 11

So, the numbers are 11 units apart.

The volume V of the water in the cone as a function of the height h of the water is,

V = (1/48)πh³

Given, water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches.

We have to express the volume V of the water in the cone as a function of the height h of the water.

Now, at any instant let the height of the water in the cone be h and radius of the water in the cone be r,

So, using the concept of similarity in triangles

we get, r/4 = h/16

r = h/4

Now, the volume of the water in the cone be,

V = (1/3)πr²h

V = (1/3)π(h/4)²h

V = (1/48)πh³

So, the function expressing the volume of the water in the cone be,

V = (1/48)πh³

Hence, the volume V of the water in the cone as a function of the height h of the water is,

V = (1/48)πh³

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500

Step-by-step explanation:

research

The number of groups, using the combination formula, for each case, is given as follows:

a) Same number of students from each grade: 1,245,816,000

b) At least two grade nine students: 31,650,886,995.

c) James and Lucy are in it: 2,481,256,778.

The number of groups is obtained for the three cases using the combination formula, as the order in which the students are chosen is not important.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For item a, the same number of students is taken from each class, hence 3 students are taken from each class, as 12 students are taken from 4 classes, hence 12/4 = 3.

Hence the number of groups, considering the number of students in each class, is of:

[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]

For item b, we use complementary events, first obtaining the total number of students that can be taken, and then removing the combinations that do not have at least two grade nine students.

The total number of groups is obtained as follows:

[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]

(as there are 10 + 11 + 12 + 13 = 46 students, and 12 are taken).

The number of groups with none students from grade 9 is:

[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]

(removing the 10 students from grade 9).

The number of groups with one student from grade 9 is:

[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]

(one from grade 10 and the remaining from the other classes).

This the number of groups with at least two grade 9 students is calculated as follows:

38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.

For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set containing the 44 remaining students, hence:

[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]

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Answer:

[tex]y=-\frac{5}{7}+5[/tex]

Step-by-step explanation:

the goal is to isolate y on one side

5x+7y=35

-5x.     -5x

7y=35-5x

/7. /7.  /7

y=-5/7x+5

Hopes this helps please mark brainliest

The solutions of the equations are x = 1 and y = 2

The system of equations are

4x + 3y = 10

-4x + 5y = 6

Here we have to use the elimination method. Eliminate the x term and find the value of y term

Add both equation

3y + 5y = 10 +6

Add the like terms

8y = 16

y = 16 / 8

Divide  the terms

y = 2

Substitute the value of x in the first equation

4x + 3y = 10

4x + 3×2 =  10

Multiply the terms

4x + 6  = 10

4x = 10 - 6

4x = 4

x = 4 / 4

Divide the terms

x = 1

Hence, the solutions of the equations are x = 1 and y = 2

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