the radius of a circle is 1 what is the length of an arc that subtends an angle of pi/4 radians.

When sin R and sin q are equal to 1/4 and PR is equal to 5 cm, the length of PQ in centimeters is 1.875.

Therefore,

PQ/Sin (<PRQ) = PR/Sin (<PQR)

Substitute PR = 5 cm

Sin (<PRQ) = 1/4 , Sin (<PQR) =2/3

PQ/Sin (<PRQ) = PR/Sin (<PQR)

PQ/1/4 = 5/ 2×1/3

PQ = 1.875 cm

To learn more about Pythagorean theorem refer to:

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The correct answer is d. $263

Eric worked 40 hours, gaining $3.20 per hour. Then:

40 hours * $3.2 = $128

Also he made tips for $25, $20, $40, $30 and $20. To get the total from tips, we add all them up:

25 + 20 + 40 + 30 + 20 = $135

The toal earning is

$128 + $135 = $263

Given:

Capacity of the car's fuel tank = 16 gallons

Gas mileage of car = 30 miles per gallon

Given that the driver filled the tank and got on a highway, let's solve for the following:

• (a) How many miles has the car traveled if it has the following amounts of gas left in the tank:

Use the expression:

Where g reresents the amount of gas left.

• 15 gallons:

If the car has 15 gallons left, to calculate the distance traveled, we have:

If the car has 15 gallons left, it has traveled for 30 miles.

• 10 gallons:

For 10 gallons, we have:

If the car has 10 gallons left, it has traveled for 180 miles.

• 2.5 gallons:

If the car has 2.5 gallons left, it has traveled for 405 miles.

• Part b.

Let's write an equation that shows the relationship between the distance traveled (d), and the amount of gas left in the tank in gallons(x).

To write the equation, we have:

• Part C.

Let's find the amount of gallons left in the tank when the car has traveled the following distances:

• 90 miles:

If the car has traveled 90 miles, it will have 13 gallons left in the tank.

• 246 miles:

If the car has traveled for 246 miles, it will have 7.8 gallons left in the tank.

• Part d.

To write the equation, we have:

Answer:

Step-by-step explanation:

For 90 :

90/x = 30

x=90/30

x=3 gallons

For 246 :

246/x=30

x=246/30

x=8.2 gallons

7x +2=58

7x = 58-2

7x = 56

x = 56/7

x = 8

Explanation

Step 1

Given; The graph of the absolute value parent function, f(x) = Ixl, is stretched

horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?

Step 2

Graph f(x)

If f(x) is stretched horizontally by a factor of 3 we have;

Thus, the answer is

The given equation is

Remember that the value which satisfies an equation must give the same equality. For example, in this case, we have to get 25 on both sides of the equation.

Observe that x = 11 will satisfy the equation

EXPLANATION

We can represent the states in the following picture:

We can apply a Trigonometric ratio in order to get the value of the third side, assuming that it is called x:

Multiplying both sides by 8:

Switching sides:

Multiplying terms:

In conclusion, the measure of the third side is approximately equivalent to 4√2 or 5.65

Let x be the total invested in at the 7% account and y the total invested at the 8% account.

Since he has $150 more than the 8% account, it implies that x + y = y + 150 and, therefore, x = $150

Since the total interest is $51, we have:

0.07x + 0.08y = 51

0.07*150 + 0.08y = 51

10.5 + 0.08y = 51

0.08y = 40.5

y = 40.5/0.08 = $506.25

Kevin has $150 at the 7% account and 506.25 at the 8% account.

Substituting x=-9 in the given equation we get:

Simplifying the above result, we get:

Adding 2 to both sides of the equation, we get:

Therefore, the coordinates of the point with x=-9 are:

Answer:

There are a number of transformations that can be used to alter the size and position of a shape. These include dilation, translation, reflection, and rotation.

Dilation can be either an enlargement, which results in an image that is larger than the original figure, or a reduction, which results in an image that is smaller than the original figure. If a dilation operation is performed on a shape, we will have a change in the lengths of the shape or the area covered. However, the angles of the shape remain the same since all the sides change by the same factor.

A reflection is a transformation that preserves both size and shape of a polygon or object. All that happens in a reflection is a change in the position and orientation of the shape.

If triangle ABC is dilated and reflected, any change in the side lengths is from the dilation. The angles are preserved, however, both by dilation and reflection.

The correct option is OPTION C.

Answer:

Step-by-step explanation:

If you have one apple and you buy another one, you will have 2 apples. Therefore,

1) The equation we used today to represent a line is called :

The slope-intercept form

In this form, y=mx +b

2) For the equation y=mx+b, m is the slope

It measures how steep is the line.

3) For the equation y=mx+b, b is the line coefficient

This is the point where the line intercepts the y coordinate.

In order to find the value of x, we need to replace y by 1.8 in the given expression:

Now, we can use the quadratic formula to find x:

Therefore, x can have two different values, which are, approximately,

-0.68 foot and 12.34 feet.

We are asked to find which value makes the equation true.

Let the value be denoted by x.

Let us re-arrange the given equation to find the value of x.

Subtract 0.34 from b

Given the following sequence

We want to know if this sequence is arithmetic. The general term of an arithmetic sequence is given by

Where d represents the common ratio. An arithmetic sequence increases by the same value every term(this value is the common ratio). If the difference between neighbor terms is the same for all of our terms, this sequence can be written as an arithmetic sequence.

Let's calculate the difference between the terms

Since the difference is the same, this sequence is Arithmetic.

We were told that you have from 9:30 pm to 11 pm to do a project. This means that you have an hor and 30 minutes to do the project. Recall,

1 hour = 60 minutes

1 hour and 30 minutes would be 60 + 30 = 90 minutes

A) At 10pm, the amount of time that you have left is 1 hour(between 10pm and 11 pm)

This is equal to 60 minutes. The fraction of time left would be

time left/total number of hours

fraction of time that is remaining = 60/90 = 2/3

B) At 10:50 pm, the number of minutes left before 11 pm is 10 minutes. Thus,

Fraction of time that is remaining = 10/90 = 1/9

2⁵ >5²

Since,

2⁵=32

and

5²=25

The Volume of the box = Length (L) x Width(B) x Height(H)

L= 12cm , B = 6cm and H =9cm

V= LBH

V= 12 x 6 x 9

V = 648 cm^3

First let's start with the graph of y = x:

Then, let's apply the "absolute value" operator: y = |x|

Then, we have an horizontal translation of 2 units to the left: y = |x + 2|:

Then, a vertical stretch by a factor of 1/2: y = (1/2)|x + 2|:

Finally, a vertical translation of 1 unit down: y = (1/2)|x + 2| - 1:

There is one solution to the equation

Here, we want to check the nature of the solution to the equation

We can start this by evaluating the equation;

As we can see, only a single solution exists for the equation

4ac = 60

Explanation:

a=3

c =5

multiply 4 by value of a and value of c

4ac = 4 * 3 *5

4ac = 60

B)272

Explanation

An arithmetic sequence is defined as a series of numbers, in which each term (number) is obtained by adding a fixed number to its preceding term.

where 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the number of terms.so

Step 1

Let

replace,

therefore, the answer is

B)272

I hope this helps you

From the statement, we know that:

• P(A) = 0.4,

• P(A and B) = 0.2.

Because A and B are independent events, the probability of A and B is the product of the individual probabilities:

Replacing the data of the problem, we get:

P(B) = 0.5

ANSWER

The value of x is 4

EXPLANATIONS;

Given that

Re-write the quadratic function

Recall, that the general form of quadratic function is given as

Relating the two functions together

a = -1

b = 8

c = - 16

Determine the number of solutions first using the discriminant

Since D = 0 , then , the quadratic function has one real solution

Solve the equation using the general quadratic formula

Hence, the value of x is 4

Simplify the number to obtain the value in decimal.

The value 3.464 lies between 3 and 4, which are also consecutive whole number.

So answer is 3 and 4.

The formula to find the simple interest is the following:

Where P is the principal amount, r is the interest rate, t is the time and A is the Future value

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

BB' = 6

B'A = 2

Step 02:

scale factor:

The answer is:

scale factor = 3

Trigonometry and Triangles

To solve the problem, we need to recall the following:

* The sum of the interior angles in a triangle is 180°

* The sum of two supplementary angles is 180°

* The tangent of an acute angle in a right triangle is defined as:

We included a new variable z to help solve the problem. Details below:

Angle 59° and angle z° are supplementary because they are a linear pair, thus:

z + 59 = 180

Solving for z:

z = 121

Now we focus on the left triangle with interior angles of 45°, z°, and x°. The sum of all three must be 180°, thus:

45 + 121 + x = 180

Solving for x:

x = 180 - 45 - 121

x = 14

Now focus on the bigger triangle (the one that contains two smaller triangles).

This triangle is right (it has one interior angle of 90°) and it's also an isosceles triangle because it also has one interior angle of 45°.

Any right triangle

To solve this problem, we will use the following property of exponents:

Now, notice that:

Therefore, we can rewrite the given expression as follows:

Recall that:

Therefore, we can split the root as follows:

Simplifying we get:

Multiplying like terms, we get:

Answer:

Example:

Simplify

First, we notice that:

Therefore, we can rewrite the expression as:

Simplifying we get:

Step 1

2n = 70

divide both sides by 2

Step 2

Make a conclusion based on step 1

If n = 3.5

Then substituting for n = 3.5 in the equation

Therefore n = 3.5 is not a solution of the equation 2n = 70