The radius of a circle is 14 yards. What is the circle's circumference?
Use 3.14 for ​.

pls help

Step-by-step explanation:

The 'solution ' is the point where the two lines intersect :    ( 0,-1)

Answer:

AA sim post

Step-by-step explanation:

They DO have equal (similar) angles.....but they do not have equal sides

The circle equation x² + 8x + y² -10y - 32 = 0​ can be graphed using (x + 4)² + (y - 5)² = 73

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

x² + 8x + y² -10y - 32 = 0​

Add 32 to both sides of the equation

This gives

x² + 8x + y² -10y = 32

Group the terms in two's

So, we have

(x² + 8x) + (y² -10y) = 32

When we complete the square on each group, we have

(x + 4)² + (y - 5)² = 16 + 25 + 32

Evaluate the like terms

(x + 4)² + (y - 5)² = 73

Hence, the circle equation can be graphed using (x + 4)² + (y - 5)² = 73

See attachment for the graph

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The volume of the rectangular pyramid is 144.48 cubic feet.

A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.

The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.

The volume of a rectangular pyramid is given as:

[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]

[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]

[tex]\sf V = \dfrac{433.44 }{3}[/tex]

[tex]\sf V = 144.48 \ cubic \ feet[/tex].

Hence, the volume of the rectangular pyramid is 144.48 cubic feet.

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The two men will charge the same amount to complete the job after 3.5 hours.

Let's start with Charles' fee, which is a combination of an upfront fee and an hourly fee. We can represent this as:

C(x) = 115 + 30x

where x is the number of hours Charles works.

For Peter, his fee is a combination of an upfront fee for paint and an hourly fee. We can represent this as:

P(x) = 80 + 40x

where x is the number of hours Peter works.

To find out when the two men will charge the same amount to complete the job, we need to set the two equations equal to each other and solve for x:

115 + 30x = 80 + 40x

Subtracting 30x from both sides: 115 = 80 + 10x

Subtracting 80 from both sides: 35 = 10x

Dividing both sides by 10:

x = 3.5

So, the two men will charge the same amount to complete the job after 3.5 hours.

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Diego is correct as the number of groups result to 6/5 or 1 1/5.

We have to find the number of groups of 5/6 in 1.

So, we need to perform the division as

= 1/ (5/6)

= 1 x 6/5

= 6/5

= 1 1/5

Thus, Diego is correct as the number of groups result to 6/5 or 1 1/5.

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The correct matrix representation is;  [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,

Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)

Given here the points are P₁(1, 3) and P₂(5, 2)

Thus, by the coordinates of the two vectors, we can represent the matrix  ;

[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Hence, Option A) is the correct answer.

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The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

We have,

To factor x² + 12 using the difference of squares formula, we need to express it as the difference between two squares:

x² + 12 = x² + (2√3)²

Now we can use the difference of squares formula, which states that:

a² - b² = (a + b)(a - b)

In this case, we have a = x and b = 2√3. So we can write:

= x² + 12

= x² + (2√3)²

= (x + 2√3)(x - 2√3)

Therefore,

The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

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The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.

We can use the conservation of momentum equation:

(mboat + mperson) * vboat = mperson * vperson

(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)

230 kg * vboat = 56 kg * (0.80 m/s + vperson)

vboat = (56/230) * (0.80 m/s + vperson)

vperson = 0.80 m/s + vboat

vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)

(174/115) * vperson = (504/115) * m/s

Dividing both sides by (174/115), we get:

vperson = 2.896 m/s

vboat = (56/230) * (0.80 m/s + vperson)

Substituting the value of vperson, we get:

vboat = 1.337 m/s

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On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.

1. The equation of the form y = a • bˣ is y = 81 x (¹/₃)ˣ

2. His stamp should be worth approximately $7,851.47 after 6 years.

3. The equation of the form y = a • bˣ is y = (¹/₁₆) x 2²ˣ ⁺ ⁵

1. One will see that y is decreasing by a factor of 3 as x increases by 1. Therefore, we can write the equation as:

y = 81 x (¹/₃)ˣ

2. The increase in value of the stamp can be calculated using the formula:

V = P(1+r)ᵗ

where V is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.

Substituting the given values:

V = 4900(1+0.075)⁶

V ≈ $7,851.47

Therefore, the stamp should be worth approximately $7,851.47 after 6 years.

3. One will see that y is increasing by a factor of 2 as x increases by 1. Therefore, we can write the equation as:

y = (1/16) x 2²ˣ ⁺ ⁵

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The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

The percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.

To solve this problem, we can use the properties of the normal distribution and the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of buyers who paid between 150,000 and 153,300.

According to the empirical rule, given a normal distribution:

approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the  three standard deviations of the mean, the data are contained.

In this case, we want to find the percentage of buyers who paid between 150,000 and 153,300, which is one interval of length 3300 above the mean. To use the empirical rule, we need to standardize this interval by subtracting the mean and dividing by the standard deviation:

z1 = (150,000 - 150,000) / 1100 = 0

z2 = (153,300 - 150,000) / 1100 = 3

Here, z1 represents the number of standard deviations between 150,000 and the mean, and z2 represents the number of standard deviations between 153,300 and the mean.

Since the interval we are interested in is within three standard deviations of the mean (z2 <= 3), we can use the empirical rule to estimate the percentage of buyers who paid between 150,000 and 153,300:

Approximately 68% of the buyers paid within one standard deviation of the mean, which is between 149,000 and 151,000 (using z-scores of -1 and 1).

Approximately 95% of the buyers paid within two standard deviations of the mean, which is between 148,000 and 152,000 (using z-scores of -2 and 2).

Therefore, the remaining percentage of buyers who paid between 152,000 and 153,300 is approximately (100% - 95%) / 2 = 2.5%.

So, the percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.

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144.) The value of X if the two angles of the triangle are congruent would be = 4. That is option D.

145.) The equation that should be used to find the value of X would be = 13x -15 = 22x + 9. That is option H.

For question 144.)

Two triangles are congruent means that the angles are equal to each other. That is;

2.3x +25 = 5.8x + 11

Bring like terms together;

5.8x-2.3x = 25-11

3.5x = 14

X = 14/3.5

= 4.

For question 145.)

When two parallel lines are being cut across by a diagonal line a relationship exists between the angles that are formed.

The two given angles are congruent;

That is;

13x -15 = 22x + 9

Therefore the expression that can be used to calculate X would be = 13x -15 = 22x + 9

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Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

Answer:

Center: (-3, 2)

Radius: 4

Step-by-step explanation:

x2 + 6x + y2 - 4y = 3​

x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4

(x + 3)² + (y - 2)² = 16

(x + 3)² + (y - 2)² = 4²

Center: (-3, 2)

Radius: 4

The condition that will prove the two triangles similar is

side JL = 8 * side ZX

angle L = angle Z

Similar triangles are  triangles which have the  similar shape however not necessarily the equal size. More officially, two triangles are comparable if their corresponding angles are congruent and their corresponding aspects are in proportion.

This means that if we had been to scale one triangle up or down uniformly, the ensuing triangle could be much like the original triangle.

In the figure, the scale is 8

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Answer:

B. More streetlights are installed on one street and people are then asked if they like the change.

Step-by-step explanation:

An experiment is a type of research method that involves manipulating one or more variables and measuring their effects on other variables. In this case, the experiment is to change the color of the product packaging and see how many people like the change. This is because the outcome of the experiment (the number of people who like the change) depends on chance and can be measured using numerical data. The other options are not experiments, but surveys or observations. Surveys involve asking people questions and collecting their opinions or preferences. Observations involve watching and recording people's behavior or reactions without interfering with them.

[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]

is the equation of the given system.

Equation of the line using the coordinates (-3, 0) and (0, 3), we get:

slope = (3 - 0) / (0 - (-3)) = 1

Now we have the slope of the line. Next, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Using the point (-3, 0) and the slope we just found (which is also the slope of the line passing through the point (0, 3)), we get:

y - 0 = 1(x - (-3))

Simplifying, we get:

y = x + 3

Therefore, the equation of the line passing through (-3, 0) and (0, 3) is y=x+3.

Similarly, the equation of the line passing through (1, -1) and (0, -4) is y = -3x + 2.

Thus, from the graph the equation of the system is,

[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]

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Answer:

20

Step-by-step explanation:

She biked an equal amount each day for 8 days to a total of 32 miles. We can write that as 8x = 32. 32/8 = 4 so x = 4. To find how much shell bike in 5 days, we multiply it by x(4). 5*4 = 20.

Answer:

34

Step-by-step explanation:

1. Plug in the week's salary into the formula

S=400+35v

1590=400+35v

2. Solve for v.

1590=400+35v

Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.

1190=35v

Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.

34=v

The coordinates in the solution to the systems of inequalities is (12, 1)

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

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

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The slope field for the differential equation would be D . Graph D .

A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .

The length of line segments represents the magnitude, while the direction indicates the sign of the slope.

The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.

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The amount of poster board left over will be 1275 square inches, the equation used is  A = (b₁ + b₂)h/2.

To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,

we need to find the area of the trapezoid window and subtract it from the area of the poster board.

The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.

Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.

Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.

To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.

Finally, we subtract the area of the window from the area of the poster board using the equation:

1500 - 225 = 1275 square inches.

Therefore, the amount of poster board left over will be 1275 square inches.

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The complete question is

Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?

The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.

The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.

Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.

Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.

Hence, the correct option is {−4, −2, 0, 3, 5}.

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The graph will look like a circle centered at (2, 1) with radius 3.

To graph the equation [tex]x^2 - 4x + y^2 - 2y - 4 = 0[/tex]  by completing the square, we need to rearrange the terms as follows:

[tex](x^2 - 4x + 4) + (y^2 - 2y + 1) = 9[/tex]

This can be simplified to:

[tex](x - 2)^2 + (y - 1)^2 = 3^2[/tex]

So the equation represents a circle with a center at (2, 1) and a radius 3. To graph the circle, we can plot the center point (2, 1) and then draw a circle with radius 3 around that point.

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The measurement of DE is 10 inches.

If we know that E is the point where the diagonals of the rectangle intersect, then we know that DE is equal to half the length of the diagonal BD.

Using the Pythagorean theorem, we can relate the length of the diagonal BD to the sides of the rectangle.

Let's assume that the length of the rectangle is L and the width of the rectangle is W. Then, the length of the diagonal BD is given by:

BD = √(L^2 + W^2)

Since we know that the diagonals of a rectangle are equal, we have:

AC = BD

BD = 20

Therefore, DE = 1/2 BD = 1/2 (20) = 10 inches.

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Okay, let's break this down step-by-step:

* The telephone pole is 54 feet tall

* The guy wire runs 83 feet from point A (top of pole) to point B (ground)

* So the hypotenuse (AB) of the right triangle is 83 feet

* The opposite side (AC) is 54 feet (height of pole)

To find the adjacent side (BC), we use the Pythagorean theorem:

a^2 + b^2 = c^2

54^2 + BC^2 = 83^2

Solving for BC gives:

BC = sqrt(83^2 - 54^2) = sqrt(1296 - 2916) = sqrt(1620) = 40 feet

So the guy wire is secured 40 feet from the base of the telephone pole.

Rounded to the nearest tenth is 40.0 feet.

Therefore, the final answer is:

40.0

Let me know if you have any other questions!

Answer:

3



Step-by-step explanation:

Area = 7pi/5

56/360 × pi r² = 7pi/5

Pi is canceled on both sides.

r² = 7/5 ÷ 56/360 = 9

r = root 9 = 3

According to the information, there are thousands of different lunch options in this restaurant.

To calculate the number of different lunches in the restaurant we must carry out the following mathematical procedure. We must multiply the different options as shown below:

4 green options x 5 protein options x 8 vegetable options x 4 extra options x 6 topping options = 4 x 5 x 8 x 4 x 6 = 4,800 different lunch options.

Based on the above, we can infer that 4,800 different lunch options can be created with the available ingredients.

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The sample proportion who said they pray is approximately 0.84, or 84%.

The sample proportion of college students who said they pray can be calculated by dividing the number of students who said they pray (105) by the total number of students in the sample (125).

Sample proportion = Number of students who said they pray / Total number of students in the sample

Sample proportion = 105 / 125

Sample proportion = 0.84

Therefore, the sample proportion who said they pray is approximately 0.84, or 84%.

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