find the area of this circle use 3 for pi

The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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The answer after performing mathematical operation is 8.97998 .

What is mathematical operations?

  In order to add, subtract, multiply, or divide two or more quantities, one must perform a series of four fundamental operations known as mathematical operations. They involve the study of numbers and the order of operations, which are important in all other areas of mathematics like algebra, data processing, and geometry. Without employing mathematical operation rules, we are unable to solve the issue. The addition, subtraction, multiplication, and division operations all follow the same four fundamental rules.

Here the given ,

=> 5.87998 + 3.100

=>  5.87998

  + 3.10000

--------------------

    8.97998

=> 5.87998+3.100=[8.97998]

Hence after performing mathematical operations the answer is 8.97998.

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Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Answer:

this would be 4x

Step-by-step explanation:

this is because when you carry over the dividend you have to divide it by 2 and assuming y is 8 the answer would be 4x

Answer:

0.550

Step-by-step explanation:

The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).

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As a result, the model's representation of the division problem is 7/4 * 1/2 = 3 1/2 as the Circled portion .

In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.

given

Circled portion of the shaded partition is 7/4 of the total.

Take 1/2's reciprocal and switch the sign to multiply. 7/4 * 1/2 = 3 1/2

As a result, the model's representation of the division problem is 7/4 * 1/2 = 3 1/2 as the Circled portion .

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Answer:

14

Step-by-step explanation:

In 70/5 the dividend is 70 and the divisor is 5 .

First draw a number line from zero to the dividend.

Next, starting from 70 skip count by the divisor backwards till you reach 0.

The numbers of skips taken to reach zero is the result, also called, the quotient. In this case there are 14 skips .

The possible values for the discriminant include the following:

A. -1

D. -18

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.

Discriminant, D = b² - 4ac

In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.

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Complete Question:

The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.

A. -1

B. 3

C. 0

D. -18

Answer:

Hi, 3/8 as a decimal by division. Divide 8 into 3 and you get 0.375 not 1.375.

Answer:

0.375

Step-by-step explanation:

use a calculator

The sum of the geometric progression is the sum S₃ = 32

The sum of terms of a geometric progression is given by

Sₙ = a(rⁿ - 1)/(r - 1) where

Given the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then

Now, we desire S₃, that is Sₙ when n = 3.

So, S₃ = a(r³ - 1)/(r - 1)

= 4(2³ - 1)/(2 - 1)

= 4(8 - 1)/1

= 4(8)

= 32

So, the sum S₃ = 32

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Renee’s layaway fee is $15.95, her down payment is $31.90, and her weekly payments are $7.98 each.

We are given that;

Combined price of the items = $318.95

Layaway fee=5%

Down payment=10%

Now,

A percentage is a minimum number or ratio that is measured by a fraction of 100.

The layaway fee by multiplying the item price by 5%. The formula is: layaway fee=item price×0.05

The down payment by multiplying the item price by 10%. The formula is: down payment=item price×0.1

Calculate the weekly payment by multiplying the item price by 15% and dividing it by 6. The formula is: weekly payment=6item price×0.15​

Plugging in the given values and simplify the expressions. Here are the calculations:

layaway fee=318.95×0.05=15.95

down payment=318.95×0.1=31.90

weekly payment=6318.95×0.15​=7.98

Therefore, by percentage the answer will be $15.95, $31.90, and $7.98

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The equation of the line is y = (3/2)x - 1/2.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Let's say you need to know the answer about the equation of a line that passes through points (3, 4) and (5, 7).

Now,

The equation of a line.

y = mx + c

The line passes through points (3, 4) and (5, 7).

m = (7 - 4) / (5 - 3)

m = 3/2

Slope = 3/2 _____(1)

Now,

(3, 4) = (x, y)

4 = 3/2 x 3 + c

4 = 9/2 + c

c = 4 - 9/2

c = (8 - 9) / 2

c = -1/2

y-intercept = -1/2 ____(2)

Now,

y = mx + c

From (1) and (2),

y = (3/2)x - 1/2

Thus,

The equation of the line is y = (3/2)x - 1/2.

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The complete question.

Find the equation of a line that [passes through the point (2, 4), and (5, 7).

The maximum profit the company can make given these constraints is; $1360

We are given that;

Its dealers demand at least 30 skateboards per day and 20 pairs of in-line skates per day. The factory can make at most 60 skateboards and 40 pairs of in-line skates per day. The total number of skateboards and pairs of in-line skates cannot exceed 90. The profit of each skateboard is $12 and the profit on each pair of in-line skates is $19

Thus, the inequalities are as follows;

Let x represent number of skateboards

Let y represent in-line skates

Thus;

x ≥ 30

y ≥ 20

x ≤ 60

y ≤ 40

x + y ≤ 90

y ≤  -x + 90

f(x, y) = 12x + 19y

At (30, 20), f(30, 20) = 12(30) + 19(20) = $740

At (30, 40), f(30, 40) = 12(30) + 19(40) = $1120

At (50, 40), f(50, 40) = 12(50) + 19(40) = $1360

At (60, 20), f(60, 20) = 12(60) + 19(20) = $1100

At (60, 30), f(60,30) =  12(60) + 19(30) = $1290

Thus, the maximum profit the company can make given these constraints is; $1360

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Answer:

Step-by-step explanation:

You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.

The point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.

The tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...

  m = y/x = -4/4 = -1

The tangent line's slope is the opposite reciprocal of this:

  m = -1/(-1) = 1

The point-slope form of the equation for the tangent line is ...

  y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)

  y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)

  x -y = 8 . . . . . . . . . . add 4-y to put in standard form

The equation of the tangent line is x - y = 8.

In the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...

  y -0 = -1(x -0)

  y = -x

The equation of the normal line is y = -x.

__

Additional comment

The normal line can also be written as x + y = 0.

The tangent line can also be written as y = x -8.

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The time taken for the trip will be 12.7 hours.

It should be noted that time taken is calculated as:

Time = Distance / Speed

Distance = 700 miles

Speed = 55 mph

Time = 700/55

Time = 12.7 hours.

Therefore, the time taken for the trip will be 12.7 hours.

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The shaded area under the standard normal curve is 2.58%.

According to z-score table,

Area for < 2.23 = 0.9871

Area for >2.23 = 1 - 0.9871

                        = 0.0129

Area for < 2.23 = 0.0129

Total area = 0.0129 + 0.0129

                 = 0.0258

Area percent = 0.0258*100

                      = 2.58%

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Answer:

  a) f(x) = 12x +11

  b) f(x) = 12(x +11)

  c) f(x) = x/2 -6

  d) f(x) = (x -6)/2

Step-by-step explanation:

The "and then ..." operation applies to the entire result of the first operation.

  "multiplies input by 12" = 12x

  "and then adds 11" = 12x +11

  f(x) = 12x +11

__

  "adds 11 to the input" = x +11

  "and then multiplies by 12" = (x +11)×12 = 12(x +11)

  f(x) = 12(x +11)

__

  f(x) = x/2 -6

__

  f(x) = (x -6)/2

_____

Additional comment

When you write division expressions in plain text using a slash (/) or "divided by" symbol (÷), you need to be careful to identify what the numerator and denominator are. If either one is other than a single token (variable or constant), then parentheses must be used to indicate what is part of the group.

In typeset text, the answer to (d) looks like ...

  \(f(x)=\dfrac{x-6}{2}\)

If you write this in plain text as ...

  f(x) = x -6/2

the Order of Operations requires that you do the division first, giving 6/2 = 3, then the subtraction: x -3. Of course, this result is something entirely different from the f(x) described in part (d). In short, the fraction bar in the typeset expression serves as a grouping symbol, so (x -6) is treated as a single unit. In plain text, the only grouping symbol available is parentheses, so the expression must be written as ...

  f(x) = (x -6)/2

__

The same sort of logic applies to other typeset symbols that do grouping. A radical is another one of these:

  \(g(x)=\sqrt{x-6}\)

is not the same as g(x) = √x -6. However, it is the same as g(x) = √(x -6).

Answer:

Oldest to newest:

10^-35, 10 ^-10, 0

Step-by-step explanation:

Scientific notation

To figure out the power of 10 think "how many places do I move the decimal point?"

When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.

When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.

Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.

So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided

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Answer:

B) the age of a car vs. the value of a car.

Step-by-step explanation:

It is the only one with a negative correlation when displayed on a scatter plot. :)

Answer:

32year

Step-by-step explanation:

let Ahmed be x years then sheriff will be x+8

in 7years time

sheriff will be x+8+7=x+15

Then Ahmed will be x+7

sum of their ages will be 7\10×100=70years

x+15+x+7=70

collect like terms

2x+22=70

2x=70-22

2x/2=48/2

x=24years

Sheriff=24+8

32years

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Option B is the correct answer

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

See below.

Step-by-step explanation:

We know that Sunshine City was formed with a starting population of 100 people.

The city grew exponentially over the years, which can be modeled by the equation:

\(P=100\cdot1.03^t\)

Where P represents the population and t represent the time in years.

Part 1)

The theoretical domain is simply the domain of our equation without any context.

In other words, we just need to find our domain like normally.

Our equation is:

\(P=100\cdot1.03^t\)

Since this is an exponential function, our domain will be all real numbers.

Therefore, our theoretical domain is all real numbers.

Part 2)

Similarly, our theoretical range is simply the range of our equation without any context.

We have the equation:

\(P=100\cdot 1.03^t\)

To find our range, we can graph our function. Refer to the graph below.

We can see that our range is all real numbers greater than 0.

However, note that we have a horizontal asymptote at y=0, so our y will never be exactly 0.

So, our theoretical range is all numbers greater than 0.

Part 3)

To find the amount of people living in Sunshine City after 20 years, we simply need to use our equation:

\(P=100\cdot 1.03^t\)

To find the population after 20 years, substitute 20 for t. So:

\(P=100\cdot 1.03^{20}\)

Use a calculator:

\(P\approx180.6\)

So, there will be about 180 people in Sunshine City after 20 years.

Part 4)

First, let's determine the practical range of our function.

Our theoretical range is all numbers greater than 0 because that's what the graph can output for any input.

However, our practical range will take into account the context.

Since our initial population was 100 and it grew each year, our range should never go below 100.

Therefore, our practical range is all values greater than or equal to 100.

We acquired approximately 180.6. Our answer is within our practical range, so we can indeed use our answer.

The main difference between theoretical range and practical range is that theoretical range doesn't take into account context while the practical range does. We know that we started with 100 people, so our range should be greater than that. This is our practical range. Our practical range will be based upon our practical domain, which in this case will be all numbers greater than 0 since we can't have negative years.

By using the formula for amount of money in a compound interest, it can be calculated that

Amount received after 7 years is $13675.08

What is a compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, then the interest earned is called compound interest.

If p is the principal, r is the rate and n is the time in years, then

amount = \(p(1+\frac{r}{100})^n\)

Difference between amount and principal gives the compound interest.

Principal = $8800

Rate = 6.5 %

Time = 7 years

Amount received = \(8800(1 + \frac{6.5}{100})^7\)

                                 $13675.08

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