Solve for A in terms of I and P.
I=A–P

The length of the line segment defined by two endpoints; negative 3 comma 10 to 4 comma negative 1 as required in the task content is; 13.04.

It follows from the task content that the length of the line segment whose endpoints are as given in the task content is to be determined.

Recall; The length of a line segment whose endpoints are defined by; (x1, y1) and (x2, y2) is given as;

Length = √{ (y2 - y1)² + (x2 - x1)² }

Therefore, since the given endpoints are; (-3, 10) and (4, -1), it follows that the length of the line segment in discuss is;

Length = √{ (-1 - 10)² + (4 - (-3))² }

Length = √(121 + 49)

Length = √170

Length = 13.04.

Ultimately, the length of the line segment as required is; 13.04.

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The measure of ∠ YXR is 55 degrees.

Given that:-

m∠ XOY = 110 degrees

XR is a tangent to circle O at X.

We have to find the measure of ∠ YXR.

Draw the radii XO and OY to form the isosceles triangle XOY.

We know that the radius of the circle is perpendicular to the tangent.

Hence,  ∠OXR = 90 degrees.

Consider the triangle XOR, we know that XO and OY are the radii of the triangle and hence equal.

Let, ∠ OXY = OYX = x

Hence,

110 + x + x = 180 degrees

2x = 70 degrees

x = 35 degrees

Now, we know that,

∠ OXR = ∠ OXY + ∠ YXR

90 = 35 + ∠ YXR

∠ YXR = 90 - 35 = 55 degrees.

∠ YXR = 55 degrees.

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The solution of the double-ended inequality is -7/2 < x < -5/2

From the question, we are to solve the doubled ended inequality.

The given inequality is

2x - 5 < 4x + 2 < 2x -3

From the inequality, we can write that

2x - 5 < 4x + 2 and 4x + 2 < 2x - 3

Now, we will solve each of the inequalities separately

Solving 2x - 5 < 4x + 2

Add 5 to both sides

2x - 5 + 5 < 4x + 2 + 5

2x < 4x + 7

Subtract 4x from both sides

2x - 4x < 4x - 4x + 7

-2x < 7

Divide both sides by -2 and reverse the sign

x > -7/2

-7/2 < x

Solving 4x + 2 < 2x - 3

Subtract 2x from both sides of the equation

4x - 2x + 2 < 2x - 2x -3

2x + 2 < -3

Subtract 2 from both sides

2x + 2 -2 < -3 - 2

2x < -5

Divide both sides by 2

x < -5/2

Putting the two solutions together, we get

-7/2 < x and x < -5/2

-7/2 < x < -5/2

Hence, the solution is -7/2 < x < -5/2

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A stratified sample in this case can be selected as follows:

The rooms are divided by whether they overlook the ocean or the street, and 25 of each are selected.

The five most common classifications for sampling are listed as follows:

In this problem, the groups are given as follows:

50 rooms will be sampled, hence the number that is sampled from each group is given as follows:

50/2 = 25 rooms from each group.

The problem asks to describe a stratified sample for this situation.

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The equation of the graph is f(x) = |x - 3| + 5

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the graph has it minimum point located at the coordinate (3, 5)

This coordinate can then be interpreted as

(h, k) = (3, 5)

As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5

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The amount of energy that the ball will have at 10 m/s is; 600 J

From the given table, we see that when the velocity is 2 m/s, then the energy is 20 J.

If we take the square of the velocity, we get 2² = 4.

Thus, we need to multiply 4 by 6 to get the energy that is equal to 24 as 4 * 6 = 24.

Similarly;

For velocity equal to 3 m/s, the energy is given as:

E = 6 * 3²

E = 54 J

Thus, the general formula to find the energy is given as:

E = 6 * v²

where;

E is the energy

v is the velocity

Now, for velocity equal to 10 m/s, energy is given as;

E = 6 * 10

E = 60 J

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Using the properties of compound interest we can calculate that Jacob will have $1485 more than Brandon in his account.

Brandon invested $7,900 at the rate of 6 1/8% compounded daily.

Principal = $7900

Time = 15 years

Rate = 6 1/8% = 49/8 %

Amount earned after n years:

[tex]A=P (1+\frac{r}{n})^{nt}[/tex]  

Now we will use these values to find the amount at the end of 15 years.

P = 7900

r = 0.06625

n = 365

t = 15

[tex]A=P (1+\frac{.06125}{365})^{15\times 365}[/tex]

or, A = 19797.104...

or, A ≈ 19797.1

Again, Jacob invested the same sum at compound interest monthly at

6 5/8% .

Amount earned after 15 years:

P = 7900

r = 6.125

n = 12

t = 15

[tex]A=P (1+\frac{.06625}{12})^{15\times 12}[/tex]

or, A = 21282.383..

or, A ≈ 21282.38

Amount earned by Jacob more than Brandon

= $21282.38 - $19797.1

= $148785.283..

≈ $1485

Hence Jacob will have $1485 more than Brandon in his account.

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The value of x in the given figure is x = 22.56 m .

In the question ,

a figure is given where the measure of angle(C) = 70° and angle(A) = 30°

In the triangle ABC ,

By Angle Sum Property Of Triangle  

angleA + angleB + angleC = 180°

30° + angleB + 70° = 180°

angleB = 180° - 100°

angle(B) = 80°

By using Sine Law ,

a/Sin(A) = x/Sin(C)

From the figure ,

a = 12 m

we get ,

12/Sin(30°) = x/Sin(70°)

x = (Sin70° × 12)/Sin(30°)

x = 11.2763/0.5

x = 22.5526

x ≈ 22.56 m

Therefore , The value of x in the given figure is x = 22.56 m .

The given question is incomplete , the complete question is

Find the value of x in the given figure ?

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Using the linear function, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

In the given question,

Arianna is going to use a computer at an internet cafe.

The cafe charges an initial fee to use the computer and then an additional price per minute of usage.

Let C represent the total cost of using a computer for t minutes at the internet cafe.

We have to determine the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

The additional change per unit = Slope of the linear function

The linear function C(t) given as;

C(t)=mt+b...............(1)

where m=slope and b=vertical intercept

Then, Slope = change in C(t)/change in t

Slope = ∆C(t)/∆t

We taking he given two point to find the slope

C(t) = 9.90 for t=1

C(t) = 15.30 for t=7

∆C(t)=15.30-9.90

∆C(t)=5.40

∆t=7-1

∆t=6

So, The required slope=5.40/6

The required slope=0.9=m

Now finding the value of b.

As we know that,

C(t) = 9.90 for t=1

The equation using this should be

9.90=m×1+b

Now putting the value of m in this equation

9.90=0.9×1+b

9.90=0.9+b

Subtract 0.9 on both side, we get

b=9

Now finding the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

Putting the value in equation (1)

15.75=0.9t+9

Subtract 9 on both side

15.75-9=0.9t+9-9

0.9t=6.75

Divide by 0.9 on both side

0.9/0.9 t=6.75/0.9

t=7.5

Hence, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

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The volume of a frustum is equal to 445.3785 cubic units.

Mathematically, the volume of a cone can be calculated by using this formula:

Volume of a cone = 1/3 × πr²h

Where:

For the volume of the large cone, we have the following:

Volume of large cone = 1/3 × πr²h

Volume of large cone = 1/3 × 3.142 × 6² × 12

Volume of large cone = 3.142 × 36 × 4

Volume of large cone = 452.448 cubic units.

Since the height of the small cone is quarter of the height of the large cone, we have:

Height of small cone = 1/4 × 12 = 3 units.

Radius of small cone = 12/18 = 3/2 = 1.5 units (similar triangles by AAA).

For the volume of the small cone, we have the following:

Volume of small cone = 1/3 × πr²h

Volume of small cone = 1/3 × 3.142 × 1.5² × 3

Volume of small cone = 3.142 × 2.25

Volume of small cone = 7.0695 cubic units.

Mathematically, we know that the volume of a frustum is made by subtracting the volume of a small cone from the volume of a similar large cone cone:

Volume of the frustum = Volume of large cone - Volume of small cone

Volume of the frustum = 452.448 - 7.0695

Volume of the frustum = 445.3785 cubic units.

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A total of 549 of people at the convention are bored by the cable news

From the question, we have the following parameters that can be used in our computation:

Not bored = 122

Bored = 9/11 of the people

This means that

Not bored = 1 - Bored

So, we have

Not bored = 1 - 9/11

Evaluate

Not bored = 2/11

Recall that Not bored = 122

So, we have

2/11 * x = 122

Where x = the number of people

This gives

x = 122 * 11/2

Evaluate

x = 671

Recall that

Bored = 9/11 of the people

So, we have

Bored = 9/11 * 671

Evaluate

Bored = 549

Hence, the number of people at the convention that are bored is 549

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Answer:

A/ 80 grams

Step-by-step explanation:

We know that 430 - 280 = 150,  so each marble weights 5 grams. Then we take 5 times 40 = 200 grams. Then we take 280 subtract 200 = 80 grams

2/5÷2 3/4

0.4 / 2.75

= 0.14545...

The number of balcony seats sold is 110

Finding Unknown quantity using Linear equation:

The linear equation is an equation that is used to find an unknown quantity or an unknown number. In this, we will represent the Uknown value with a variable like x, y, z, etc.  

Here we have

Tickets for a community theater cost $11 for each main-floor seat
and $6 for each balcony seat.

There are 400 seats on the main floor, which are sold out for the evening performance  

The total revenue from ticket sales was $5060.

Here we don't know the number of balcony seats.

Let us assume that number of balcony seats = x

Then total revenue = 400(11) + 6x = 5060

=> 4400 + 6x = 5060

=> 6x = 5060 - 4400

=> 6x = 660

=> x = 110  

Therefore,

The number of balcony seats sold = 110

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The time taken for Wilson to paint the bookcase is 50 minutes.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, Wilson paints 40% of a bookcase in 20 minutes. It should be noted that 40% = 0.4

Therefore, the time taken to paint the whole bookcase will be:

= Number of minutes / Percentage painted

= 20 / 0.4

= 50

He'll use 50 minutes.

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The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

the graph of the line is shown below .

In the question ,

point on the line and slope of the line is given

So , equation will be

Part(1)

(-6, -3), m = -1

(y -(-3)) = -1(x -(-6))

y + 3 = -1(x + 6)

y + 3 = -x - 6

y = -x -6 -3

y = -x -9

the equation is y = -x -9  .

Part(2)

(-7, 6), m = 0

(y - 6) = 0(x -(-7))

y - 6 = 0(x + 7)

y - 6 = 0

y = 6

the equation is y = 6

Part(3)

(-2, 11), m=4/3

(y - 11) = (4/3)(x -(-2))

y - 11 = (4/3)x + 8/3

y = (4/3)x + 8/3 + 11

y = (4/3)x + 41/3

the equation is y = (4/3)x + 41/3

the graph of all the three equations are shown below .

Therefore , The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

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Answer:

[tex]1.8 \times {10}^{2} = 180[/tex]

Step-by-step explanation:

[tex] \frac{9 \times {10}^{5} }{5 \times {10}^{3} } = \frac{9}{5} \times \frac{ {10}^{5} }{ {10}^{3} } = 1.8 \times {10}^{2} = 1.8 \times 100 = 180[/tex]

At b= 24 will complete the square in the expression x^2 + bx + 144.

What is perfect square trinomial?

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b^2 = 4ac has the form ax^2 + bx + c, it is said to be a perfect square. The formula for the perfect square trinomial is (ax)^2 + 2abx + b^2 = (ax + b)^2.

Consider the given expression

x^2 + bx + 144

For this type of expression [tex]b = 2\sqrt{c}[/tex] will complete the square.

Here, c = 144

√144 = 12

So, b√c = 2(12) = 24

The expression becomes,

x^2 + 24x + 144 = (x + 12)^2

This is the perfect square.

Hence, b = 24  will complete the square in the expression x^2 + bx + 144.

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Answer:

-1,4

Step-by-step explanation:

move the point to the left 7 times

The cost of an adult ticket is £17 and a child ticket is £9.

Let's assume 'a'  for an adult ticket and 'c' for a child ticket

The cost of tickets for the Smith family of 2 adults and 3 children is £61

Equating, [tex]2a+3c=61[/tex]

[tex]2a=61-3c[/tex]

Dividing by 2, [tex]a=30.5-1.5c[/tex]        (equation 1)

Now, the cost of tickets for the Jones family of three adults and five children is £96

Equating, [tex]3a+5c=96[/tex]                 (equation 2)

Using equation 1, [tex]3(30.5-1.5c)+5c=96[/tex]

[tex]91.5-4.5c+5c=96[/tex]

[tex]91.5+0.5c=96[/tex]

[tex]0.5c=96-91.5[/tex]

[tex]0.5c=4.5[/tex]

[tex]c = \frac{4.5}{0.5}[/tex]

[tex]c=9[/tex]

Similarly, putting the answer of equation 2 in equation 1

we get, [tex]a=30.5-1.5c[/tex]

[tex]a=30.5-1.5(9)[/tex]

[tex]a=17[/tex]

Therefore, adult tickets cost £17 and child tickets cost £9

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The phrase [tex]f (x)[/tex] denotes a formula with [tex]x[/tex] serving as its input variable. Not multiply f and x, though!

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable .

The x in [tex]f(x)[/tex] is referred to the argument of the function or simply the argument in function notation. Therefore, the response is just 2 if they ask for a argument and give you the equation [tex]f(2)[/tex].

Hence,  the phrase [tex]f (x)[/tex] represents a formula with [tex]x[/tex] serving as its input variable.

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Answer:

X=

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−84=108x

Step 1: Subtract 108x from both sides.

2x−84−108x=108x−108x

−106x−84=0

Step 2: Add 84 to both sides.

−106x−84+84=0+84

−106x=84

Step 3: Divide both sides by -106.

−106x

−106

=

84/−106x=−42/53

The x-intercept is 1 if the function is f(x) =  (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The function is:

f(x) =  (x-1)²/x²-1

To find the x-intercept where y = 0

or f(x) = 0

0 =  (x-1)²/x²-1

x ≠ ±1

x - 1 = 0

x = 1

Thus, the x-intercept is 1 if the function is f(x) =  (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.

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The final balance is $97,920.

Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.

Given this, The principal is $3000.

Interest rate = 4.8%

Time = 2 years We must find the final balance.

The end balance formula is

C = P[ 〖(1+r)〗^n – 1]

C = 3000[ 〖(1+4.8)〗^2 – 1]

C = 3000 [ 〖(5.8)〗^2 – 1]

C = 3000 [ 33.64 – 1]

C = 3000 ( 32.64)

C = 97,920

Therefore the ending balance is $97,920

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The correct option A, 266. 9 cm²;  total surface area of the cone given in figure is found as 266.9 sq cm.

For the given question.

Put values -

Total surface area = πr (h + r)

Total surface area = 3.14 x 5 (12 + 5)

Total surface area = 3.14 x 5 x 17

Total surface area = 266.9 sq cm.

Thus, total surface area of the cone given in figure is found as 266.9 sq cm.

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Answer:

2 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

2 + [tex]\frac{3}{4}[/tex]

= 2 [tex]\frac{3}{4}[/tex] ← as a mixed number

Answer:

  2.4

Step-by-step explanation:

You want the average rate of change on the interval [-9, -4] for the graphed function.

The average rate of change (m) is the slope of the line between the points at the ends of the interval. For function f(x) on interval [a, b], this is ...

  m = (f(b) -f(a))/(b -a)

For the function f(x) on the interval [-9, -4], the average rate of change is ...

  m = (f(-4) -f(-9))/(-4 -(-9)) = (-4 -(-16))/5 = 12/5 = 2.4

The average rate of change of f(x) on [-9, -4] is 2.4.

In linear equation, 22.5 kilometer  is Shaq from his original starting point.

What is linear equation?

Shaq is he climbs up on the side of a mountain = 4 1/2 = 9/2

  then he climbs down = 5 kilometer

Shaq from his original starting point = 9/2 * 5

                                                          = 45/2 = 22.5 kilometer

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All the improper fractions in mixed or whole numbers are as follows:

So, the given improper fractions in the mixed or whole numbers are:

Therefore, all the improper fractions in mixed or whole numbers are as follows:

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