Suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left.

Brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor.

Does Brian's dart land on the dartboard?

The **equation** of the **circle** that represents the dartboard is (x - 12)² + (y - 17/3)² = 9/16, where the origin is the lower left corner of the room and the unit of the **radius** is feet.

The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.

What is the equation of a circle?Mathematically, the standard form of the **equation** of a **circle** is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

h and k represents the coordinates at the center.r represents theFrom the question, we have the following information:

The height of this standard dartboard, k = 5 feet, 8 inches.

The diameter of this standard dartboard = 18 inches.

The bull's eye, h = 12 feet.

Next, we would convert the all of the units in inches to feet as follows:

Height, k = 5 + 8/12

Height, k = 5 + 2/3

Height, k = 17/3 feet.

For the diameter, we have:

Diameter = 18/12

Diameter = 3/2 feet.

Also, we would determine the **radius** as follows:

Radius, r = diameter/2

Radius, r = (3/2)/2

**Radius**, r = 3/4 feet.

Substituting the parameters into the standard **equation**, we have;

(x - 12)² + (y - 17/3)² = (3/4)²

(x - 12)² + (y - 17/3)² = 9/16

Next, we would determine whether Brian's dart land on the dartboard:

(x - 12)² + (y - 17/3)² < 9/16

(x - 12)² + (y - 17/3)² < 9/16

(11.5 - 12)² + (5.5 - 5.67)² < 0.5625

0.25 + 0.0289 < 0.5625

0.2789 < 0.5625 (Yes, it does land because it's within the circumference of this standard dartboard).

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How many solutions does -14 + 6b + 7 - 2b = 1 + 5b have

The number of **solutions** that -14 + 6b + 7 - 2b = 1 + 5b has is 1 solution.

It should be noted a equation is important to illustrate the relationship between the variables. In this case, the equation **given** is illustrated as:

-14 + 6b + 7 - 2b = 1 + 5b

Collect like **terms**

-8 + 6b - 2b = 5b

b = -8

Therefore, it has only one **solution**.

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Choose all the correct answers using the diagram below.

What is the length of the diagonal?

2

√2

1

√3

No answer text provided.

We want to find the diagonal length of the square given in the question.

[tex]x=?[/tex]Since this shape is a **square**, all four sides are of **equal length**. Therefore, each side of the square must be [tex]1[/tex] unit.

Next, we will use the** Pythagorean Theorem** to find the length of the hypotenuse of a right triangle. This value is also equal to the length of our diagonal. We can find the length of the diagonal using the formula below;

Therefore, the correct answer to our question is the following equality;

[tex]x^2=1^2+1^2[/tex][tex]x^2=2[/tex][tex]\sqrt{x^2} =\sqrt{2}[/tex][tex]x=\sqrt{2}[/tex]**Second option** should be the answer.

Solve quickly!3(x+10)=4(x-2)

**ANSWER**

**x = 38**

**EXPLANATION**

To solve this equation, first, we have to apply the distributive property of multiplication over addition to eliminate the parenthesis,

[tex]\begin{gathered} 3\cdot x+3\cdot10=4\cdot x-4\cdot2 \\ \\ 3x+30=4x-8 \end{gathered}[/tex]Subtract 3x from both sides of the equation,

[tex]\begin{gathered} 3x-3x+30=4x-3x-8 \\ \\ 30=x-8 \end{gathered}[/tex]And add 8 to both sides,

[tex]\begin{gathered} 30+8=x-8+8 \\ \\ 38=x \end{gathered}[/tex]Hence, the **solution is x = 38**.

There were 18,652 geese on a lake. What is this number rounded to the tenthousands place?A20,000B19.600C19.000D18.600car mechanic rounds a car's weight to the nearest thousand. He says theweight is 4,000 pounds. What is the least and the greatest amounts the carcould actually weigh? Explain.

Step 1

There are 18,652 geese on a lake

Required: To round this off to the ten thousand place

Step 2

Hence, we will approximate the thousands and add its value to the ten thousand.

[tex]=\text{ 20,000}[/tex]Step 3

The mechanic rounds the weight of the car to the nearest thousand and gets 4000 lb.

Using the rule below;

[tex]\begin{gathered} (4000\text{ - 500)lb - least} \\ or \\ (4000\text{ + 49}9)lb-\text{ greatest} \\ \end{gathered}[/tex]Therefore,

[tex]\begin{gathered} \text{If we subtract 500 from 4000 we get 3500lb} \\ 3500lb\text{ is the least weight of the car} \\ \text{Notice that 3500 rounded off to the nearest thousand = 4000} \\ \text{Any number less than that say 3499 rounded off to the nearest thousand}=3000 \end{gathered}[/tex][tex]\begin{gathered} \text{If we add 499 to 4000, we get 4499 pounds} \\ 4499\text{ pounds is the greatest weight of the car} \\ \text{Notice if you round off 4499 to the nearest thousand = 4000} \\ \text{Any number more than this say 4500 rounded to the nearest thousand=5}000lb \\ \text{Hence the greatest weight of the car= 4499} \end{gathered}[/tex]Therefore,

[tex]\begin{gathered} \text{Least weight of the car = 3500}lb \\ \text{Greatest weight of the car = }4499lb \end{gathered}[/tex]The circumference of a circle is 12.56 miles. What is the circle's diameter?

**Answer:**

d= 4 miles

**Step-by-step explanation:**

C=2πr

d=2r

d=C

π=12.56

π≈3.99797mi

The measures of the angles of a triangle are shown in the figure below. Solve

for x.

62⁰

82⁰

(x+12)

**Answer: 24**

**Step-by-step explanation:**

The angles of a triangle add to 180 degrees, so:

[tex]62+82+x+12=180\\\\156+x=180\\\\x=24[/tex]

You are catering at a ceremony and have a budget of R1 200 to spend on meat. You

want to serve chicken and steak. Chicken costs R30 per kilogram and steak costs R120

per kilogram.

3.1.1 In the problem description in 3.1 above, state what changes and what remains

the same. In other words, mention the variables for the problem.

Answer:

Step-by-step explanation:

Help with this problem

I₃** indifference curve **represents the highest utility

What is an indifference curve?

An** indifference curve **is a graph that illustrates numerous pairings of two goods or commodities that leave the customer equally well off or satisfied—hence indifferent—when it comes to owning any pairing of the two items that is represented along the** curve**.

A consumer must give up more of one good in order to buy more of another, hence an indifference curve will always have a negative slope.

The given** indifference map **is a fast food meals per week vs movie tickets per week graph .

In which I₃ yields more than I₂ .

And I₂ yields more than I₁.

Thus, I₃ curve represents the highest utility.

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Determine whether the point (4,2) is in the solution set of the system of inequalities below. 4x + y < 2, y > -2

The point (4,2) is not in the solution set as it do not satisfy the first **inequality **4x+y<2.

To be in the solution set of the system of **inequalities** the point (4.2) must satisfy both the given linear inequalities.

So, 4x + y < 2

when x = 4, y = 2

4(4) + 2 = 18 which is not less than 2

So, point do not satisfies this linear inequality

Now, for y>-2,

y = 2 which satisfies the inequality

Therefore, we say that the point (4,2) is not in the solution set of the system of **inequalities**.

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write an equivalent expression for (925x to the 3rd times y to the negative 4th times z to the second) 0

**Answer:**

1

**Step-by-step explanation:**

Anything to the power of 0 is 1.

Ex:

[tex]x^{0} =1\\3643737737^{0} =1\\[/tex]

3. Compute the derivatives of the following functions. Do not simplify.

a) f(x)=tanx/e^3

b) f(x)= tan -¹(x³)(x^5)(ln x) c) f(x)=^7√x^5+ 5^x d) g(x)=x^sec(x)

**Answer:**

**A** im sure

**E****x****a****m****p****l****e**** **** **

*h**o**p**e** **i**t**z** **h**e**l**p**p**p**p*

Let f(x)=(x−7)(x+6)(x−5). Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0.

2. Find the x-intercept(s). List your answers as points in the form (a,b).

**Answer:**

ez

**Step-by-step explanation:**

ezz

What can be concluded from the statement ∠1+∠2m∠1+m∠2 = 90°?

When two angles add to 90º they are called complementary angles.

Then, if in the given statement the sum of angles 1 and 2 is equal to 90º, angles 1 angle 2 are complementary.

Answer: <1 and <2 and <1and <2 are complementaryb.This interval includes one endpoint but not the other; do you see why?We can express this range of values in inequality notation and in interval notation:• Inequality notation: -4 << 4 (alternatively: z>-4 AND 2 ≤4)• Interval notation: (-4,4)Rewrite each of the following inequalities in interval notation:a.-8 -7-6-8 -7-6 -5 -4-8 -7 -6 -5 -4 -3-8 -7 -6-5 -4-B -7 -6-5C.d.0.-5 -4 -3 -2 -10123as an inequality: -7<< -5in interval notation:-1 0 12 3as an inequality: -6 ≤ ≤6in interval notation:-2 -1 0 1 2 3as an inequality: -7 < x < -1in interval notation:-2 -1 0 12 3as an inequality: 5 ≤ ≤7in interval notation:-3-2 -1 0 1 2 3as an inequality: -2 << -1.in interiell-4-34444455555

Given

To find the interval.

Explanation:

It is given that,

That implies,

**a) The interval notation is, (-7,-5).**

**b) The interval notation is, [-6,6].**

**c) The interval notation is, (-7,-1).**

**d) The interval notation is, [5,7].**

**e) The interval notation is, [-2,-1).**

Albert is taking a 60 item multiple choice test. He knows the correct answers to all,except 1/5 of the items.If he guesses correctly on 3/4 of these questions,how many items correctly?

57 **items** are correct.

**What is an item?**

Items are a fundamental component of an OracleAS Portal page. **Item** types are used to categorize **items**. **Item **types determine the contents of an item as well as the information kept about it. Users with the necessary permissions can add an item or create an **item** type. The properties of an object type define the information stored about it. The **item** types that you can add to a page differ depending on whatever **item** types the page group administrator has included in the page group. If the built-in **item** types are insufficiently flexible, users with proper access can develop new custom **item** kinds to fulfill their needs.

1/5 of 60 **items **= 60/5 = 12 **items**

3/4 of 12 **items **= 12x3/4 = 9 **items**

Total no. of correct **items** = 60 - 12 + 9 = 57 **items**

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Which statement is true of the graphed function? (PICTURE OF GRAPH BELOW)a) More information is needed to determine whether the graphed function is even, odd, or neither.b)The function is neither an even nor an odd function.c) The function is an even function.d) the function is an odd function

To determine if a function is even or odd, we start from its definition.

While for an **EVEN FUNCTION** we have: **F(x) = F(-X)**, for an **ODD FUNCTION** we have **F(-X) = -F(X)**

Now, from this, we can check that all the values the function achiever for any X value, the -X has same height. The function presents a symmetry over the Y-axis, and this implies in a function to be **an EVEN FUNCTION.**

And from the solution developed above, the only statement that is true is the

**C) The function is an even function.**

Identify the zeros of the funtion using a graphing calculator.

2

f(x)=x(squared) - 9

enter your answer in {brackets} from least to greatest

The **zeros **of the **function **are x = 3 and x = -3

The **equation **of the **function **is given as

f(x) = x(squared) - 9

Rewrite the **equation **properly

So, we have the following equation

f(x) = x^2 - 9

Express the equation as a **difference **of two squares

So, we have the following equation

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

Set the equation to 0

(x - 3)(x + 3) = 0

Split

x - 3 = 0 and x + 3 = 0

Solve for x

x = 3 and x = -3

Hence, the **solutions **are -3 and 3

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Evaluate using order of operations: (8 + 7) + (3.5)

**Answer:**

**Step-by-step explanation:**

18.5

Answer:

18.5

Step-by-step explanation:

PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)

(8+7)+(3.5)

(15)+(3.5)

18.5

Geometry help for A and B. Answer B approximate volume?

The **volume** of the silo with given height and diameter is 4374π ft or 13734.36 ft. (approximately).

**What is volume?**

**Volume **is a measurement of 3-D space that is occupied. Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). **Volume **and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up.

Given in the question,

The **diameter **of the **cylindrical **silo is 18 ft,

and its height is 54 ft.

**Volume** of a **cylinder **can be calculated using the formula:

[tex]V = \pi r^2 h[/tex]

Here, V = **volume**, r = radius, h = height,

We know that, radius is half of **diameter**. So, radius = 18/2 = 9 ft

Putting the given value in the formula:

[tex]V = \pi 9^2 \times 54[/tex]

[tex]V = \pi \times 81 \times 54[/tex]

**V = 4374π ft.**

Putting the value of π as 3.14 (approximately)

So, **volume** of the silo becomes 13734.36 ft.

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The surface area S of a cylinder is

S

=

2

π

r

2

+

2

π

r

h

where r is the base radius and h is the height. What is h, in inches, when S is 175 square inches and r is 6 inches?

The **value **of **height **(h) will be 1.35 inches.

**What is Surface area?**

The space occupied by a plat surface is called **Surface area.**

Given that;

**Surface area **(S) = 2πr² + 2πrh

Where, r is the base radius and h is the height.

Now, When **Surface area** = 175 square inches

**Radius **(r) = 6 inches.

Then, We can calculate **height **as;

Since,

**Surface area** (S) = 2πr² + 2πrh

175 = 2 × 3.14 × (6)² + 2 × 3.14 × 6 h

175 = 226.08 + 37.68h

175 - 226.08 = 37.68 h

- 51.08 = 37.68 h

h = - 51.08 / 37.68

h = - 1.35

Thus, The **value **of **height **(h) will be 1.35 inches.

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There are 500 fish in a pond, to 1sf. What is the least possible number of fish that could be taken from

the pond so that there are 400 fish in the pond to 1sf

**Answer:**

one

**Step-by-step explanation:**

The least number of fish COULD be 450 ....this would be 500 to 1 S.F.

if you take **ONE** fish away there are then 449 which would be 400 to 1 S.F

Question:

Find all critical points of the function g(x)=sin^2(11x). Express your answer in terms of pi.

(Use symbolic notation and fractions where needed. Use n for all integer values.)

**Critical points **are the points where the **slope **of the function is **zero **thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of **function **g(θ) = sin²(11θ).

A **slope **is a **tangent **or angle at a point and a slope is the **intensity **of **inclination **of any geometrical lines.

Slope = Tanx where x will be the **angle **from the positive x-axis at that point.

As per the given **function**,g(θ) = sin²(11θ).

The **critical** **points **are the points where the **slope **of the **tangent **of the function is **zero**.

The **slope **of the tangent of a function is the **first derivative **thus,

g'(θ) = 0 ⇒ 2× 11 sin(11θ)cos(11θ) = 0

Sin(11θ) = 0 ⇒ θ = 0

Cos(11θ) = 0 ⇒ 11θ = π/2

θ = π/22

Since, **sinusoidal **functions are **repeating **thus,

**Next critical **point = π/22 + π/22 = π/11 and so on.

Hence "**Critical points **are the points where the **slope **of the function is **zero **thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of **function **g(θ) = sin²(11θ)".

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Mei and Dennis compare the numbers graphed on the number line below. Mei writes theinequality -9 <-3. Dennis writes the inequality -3 <-9. Which statement is true?FILE-10 -9 -8 -7 -6 -5 -4 -3 -2 -10A)Mei is correct because -9 is greater than 3.B)Mei is correct because -9 is to the left of -3 onthe number line.C)Dennis is correct because 3 is less than 9.D)Dennis is correct because -3 is to the right of--9 on the number line.

**The correct answer is:**

Mei statement that the inequality** **is** -9 < -3 **is** True.**

Mei is correct because -9 is to the left of -3 on the number line. ( first option in the picture).

I need help

There are 3 consecutive even integers with a sum of 72. Which equation can be used to find such integers?

x + 2 = 24

x + 2 = 12

x + 1 = 12

x + 1 = 24

The **equation** used to find the 3 consecutive **even integers** with a sum of 72 is x + 2 = 24.

For the given data in question.

Let the first** even integer** be 'x'.

Second even integer will be 'x + 2'.

Thirst even integer will be 'x + 4'.

The** sum** is 72

x + x + 2 + x + 4 = 72

Simplifying;

3x + 6 = 72

Divide whole equation by 3.

x + 2 = 24

Thus, the **equation** used to find the** 3 consecutive **even integers with a sum of 72 is x + 2 = 24.

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Find the area of the circle A) 12.56 mm^2B) 25.12 mm^2C) 37.17 mm^2D) 50.24 mm^2

The formula in getting the area of the circle is:

[tex]A=\pi r^2[/tex]where r = the radius of the circle and the value of π = 3.14

In the diagram, the radius of the circle is 4 mm. Let's replace the "r" in the formula with 4 mm and "π" with 3.14

[tex]A=(3.14)(4mm)^2[/tex]Then, simplify.

[tex]\begin{gathered} A=(3.14)(16mm^2) \\ A=50.24\text{ }mm^2 \end{gathered}[/tex]**Therefore, the area of the circle is 50.24 mm². (Option D)**

*We have* **π = 3.14** *and the* **radius is 4 mm**. **Therefore we apply the following formula:**

**Replacing values in the equation.**

**We calculate potentiation.**

**We multiply**

**A = 50.24 mm²**

**Answer: **The circle area is 50.24 mm^2 **(option D)✅ .**

Solve the inequality.16-x^=0

**Inequalities**

Solve:

[tex]16-x^2\le0[/tex]For a better understanding, we first multiply the inequality by -1. Recall by doing so, the sign must be flipped:

[tex]x^2-16\ge0[/tex]Factor the binomial:

[tex](x-4)(x+4)\ge0[/tex]We have a product of two variable expressions and it must be positive or zero. That can only be possible if:

* Both factors are positive or zero

* Both factors are negative or zero

The answer can come from any of the conditions stated above, so the solution is the OR combination of the individual solutions.

The first condition states:

x - 4 ≥ 0 AND x + 4 ≥ 0

This leads to the solution:

x ≥ 4 AND x ≥ -4

If x must be greater or equal to 4 and greater or equal to -4, then the AND combination gives the solution: **x ≥ 4**

The second condition states:

x - 4 ≤ 0 AND x + 4 ≤ 0

This leads to:

x ≤ 4 AND x ≤ -4

The AND combination gives the second solution **x ≤ -4**

The final solution is the first solution OR the second solution, that is:

**x ≤ -4 or x ≥ 4**

Representing the solution in the number line, we get the graph below:

Expressed in interval form: (-∞ , -4] U [4, +∞)

whats 1 plus 1 in mathmaticals

**Answer:**

2

**Step-by-step explanation:**

If you have 1 cookie and someone gives you another cookie you now have 2.

Diego's current ago is five times Martina's age ten years ago. If Martina is currently m years old, what is Diego's current age in terms of m?

Given that Diego's current age is five times Martina's age ten years ago.

Martin is currently m years old.

Ten years ago, Martin's age was (m-10) yers.

Since, Diego's current age is five times Martina's age ten years ago., therefore, Diego's current age is

5(m-10).

**So, Diego's current age is 5(m-10). **

Mary sold 192 worth of greeting cards if she received 25% Commission on all sales how much commission did she receive

25% of 192 = 192 * 25/100 = 192 * 0.25 = 48

**Answer:**

**Mary received $48**

A baker has a bag with 20 cups of flour. The baker plans to use the flour to make 4 loaves of bread. Each loaf of

bread uses 3 cups of flour.

How many cups of flour will remain in the bag when the baker has finished making the bread?

Enter your answer in the space provided.

Answer: 8

Explanation:

4 x 3 is = 12

20 - 12 = 8

8 cups of flour will remain in the bag.

Explanation:

4 x 3 is = 12

20 - 12 = 8

8 cups of flour will remain in the bag.

please help me solve this
NAMEDATEPERICLesson 3: More about Constant of ProportionalityCool Down: Fish TankMai is filling her fish tank. Water flows into the tank at a constant rate. Complete the tableas you answer the questions.1.How many gallons of water will be in the fish tank after 3 minutes? Explain yourreasoning.2.How long will it take to fill the tank with 40 gallons of water? Explain your reasoning3. What is the constant of proportionality?
Please see attachment below Is the following an example of theoretical probability or empirical probability? A fisherman notes that eight out of ten times that he uses a certain lure to catch a fish within an hour. He concludes that the probability that the lure wil catch a fish on his next fishing trip is about 80%. Is it empirical or theoretical?
Using Lincoln's "A House Divided" speech, Walt Whitman's *O Captain! My Captaln!" poem, and Jane Addams's"Influence of Lincoln" memoir chapter, you are going to write an expository essay of at least 750 words to answer thequestion: "What American ideal(s) does Abraham Lincoln embody?" Identify the American ideals and Lincoln'sembodiment of them.Your answer is your interpretation. It should be stated as a thesis following your introduction and leading Into the bodyparagraphs. Use excerpts from the readings to support your response. Don't forget to edit your essay for spelling,grammar, and clarity. Use MLA guidelines for in-text citations and a works cited page.
"-2+8" > "-2" heeeeelpp
If 4(x 4) = 1 over 16 what is the value of x? (2 points)2662
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the delcaration opens with a rational statement of its purpose in a document with such radical intent it is not sure prising that supporting details often use emotionally laden language. find at least five details often use loaded words to cite factual support. what emotions are revealed in the use of charged language.
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