Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36

Answer:

no

Step-by-step explanation:

-5/3x+10=5

-5/3x=5-10=-5

3x=-5/-5=1

=>x=1/3

For the functions, f(x) = −x+2, and g(x)=5x²,

a) f∘g(x) =  5x² + 2

b) g(f(x)) = 5x² -20x + 20

c) f∘(g(x))² = 25x⁴

d) g(x - 1)    = 5x² - 10x + 5

Here, the functions are: f(x) = −x+2, and g(x)=5x²

a) f∘g(x)

We know that composite function f∘g(x) means f(g(x))

For function f(x) substitute x = g(x)

i.e., f(g(x)) = -(g(x)) + 2

                = -(5x²)  +2

                = 5x² + 2

b) g(f(x))

For function g(x) substitute x = f(x)

i.e., g(f(x)) = 5x²

                = 5(-x + 2)²

                = 5(x² -4x + 4)

                 = 5x² -20x + 20

c) f∘(g(x))²

First we find the (g(x))²= (5x²)²

                                     = 25x⁴

Now the composite function  f∘(g(x))² would be,

 f∘(g(x))² = f((g(x))²)

              = -(g(x))²+ 2

              = -(g(x))² + 2

d) g(x - 1)

Substitute x = x -1 in function g(x)

g(x - 1) = 5(x - 1)²

           = 5(x² - 2x + 1)

           = 5x² - 10x + 5

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Answer:

Circumference/Diameter = π

If the diameter is 2, then the circumference is 2π.

If the diameter is 6, then the circumference is 6π.

To find all possible answers, we can start by listing all the numbers between 10 and 20, and all the numbers between 20 and 40, and then check which pairs of numbers have a highest common factor of 4.

Numbers between 10 and 20: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

Numbers between 20 and 40: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40

To have a highest common factor of 4, both numbers must be divisible by 4. Therefore, we can eliminate any numbers in these lists that are not divisible by 4.

Numbers between 10 and 20 that are divisible by 4: 12, 16, 20

Numbers between 20 and 40 that are divisible by 4: 20, 24, 28, 32, 36, 40

Now we can check which pairs of these numbers have a highest common factor of 4.

some possible answers are:

12 and 20

12 and 24

12 and 28

12 and 32

12 and 40

16 and 20

16 and 24

16 and 28

16 and 32

16 and 40

20 and 24

20 and 28

20 and 32

20 and 36

20 and 40

there are more answers, all you have to do is to pair 2 numbers.

if you do not want to include 20 and 40 make sure to not chose them.

Hope this could help.

The expressions are solved to give;

1.n = 1

2. h = 1

3. x = -5

4. n = 1/4

5. x = 7/2

6. p = 2/3

7. x = -12

8. n = 3

9. c = -1

10. x = 6

These are expressions that are made up of term, variables, constants, factors and coefficients.

They are also made up of mathematical operations.

From the information given, we have;

1. 5n + n = 2n + 4

collect and add the like terms

4n = 4

Make n subject

n = 1

2. 5h + 2 = h - 2

collect and add the like terms

4h = 4

h = 1

3. 2x - 1 = 3x + 4

collect and add or subtract the like terms

-x = 5

x = -5

4. n = n + 1/5

cross multiply

4n = 1, n = 1/4

5. x + 5 = 3x - 2

collect like terms

-2x = -7

x = 7/2

6. p = p + 2/4

cross multiply

3p = 2

p = 2/3

7. 4(2 + x) = 3x - 4

expand the bracket

8 + 4x = 3x - 4

collect like term

x = -12

8. 5n + 2 = 3n + 4

collect like terms

n = 3

9. 3c - 2 = -3c - 8

collect like terms

6c = - 6

c = -1

10. 3x + 1 = 2x - 5

collect the like terms

x = 6

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Answer: The first choice.

Step-by-step explanation:

As you can see in the diagram, the line passes through the points[tex](x, y) = (4, -4)[/tex] and [tex](x, y) = (-4, 8)[/tex] . Thus, the slope of the line is [tex]\frac{8-(-4)}{-4-(4)} = \frac{12}{-8} = -\frac{3}{2}.[/tex] Thus, the correct answer is the first choice, as that line has a slope of [tex]-\frac64=-\frac32.[/tex]

Answer:

To calculate the value of Hassim's Fireworks & Cycles today, we can use the formula for the present value of a growing perpetuity:

PV = FCF / (r - g)

where PV is the present value, FCF is the free cash flow, r is the weighted average cost of capital, and g is the growth rate.

Substituting the given values, we get:

PV = 129550 / (0.08 - 0.03)

PV = 2591000

Therefore, the value of Hassim's Fireworks & Cycles today is R2,591,000.

Programme 2 in Los Angeles will be well received by 22 out of 25 people.

Given that the chances of a positive response from Los Angeles residents to two government programmes are 78.4% for Programme 1 and 88.1% for Programme 2, the likelihood of a positive response for Programme 2 given that the person is from Los Angeles must be calculated as follows:

88.1 / 100 = X 44.05 / 50 = X 22,025 / 25 = X

Therefore, Programme 2 will be well-received by 22 out of 25 people in Los Angeles.

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a. On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.

b. On a 33 rpm record (12-inch diameter), the fly would travel 1,245.6 inches in 1 minute.

c. On a 78 rpm record (10-inch diameter), the fly would travel 2,430 inches in 1 minute.

Radius of 45 rpm record = 3.5 inches (7/2)

Circumference = 2 * π * r = 2 * π * 3.5 ≈ 22 inches

Distance in 1 minute = Circumference * rpm = 22 * 45 = 990 inches

Thus, it can be seen that On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.

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Answer:-by-step explanation:

the function has the x-intercept of (-2, 0)

the function has the y-intercept of (0, -8)

the function has the x-intercept of (4, 0)

Answer:

Billy has £20, Liam has £40, and Nicola has £120. The total amount of money they have is £180, as given in the problem.

Step-by-step explanation:

Let's start by defining the variables:

Billy's money: x pounds

Liam's money: 2x pounds (twice as much as Billy)

Nicola's money: 3(2x) = 6x pounds (three times as much as Liam)

The total amount of money they have is £180, so we can write an equation:

x + 2x + 6x = 180

Simplifying the left side of the equation:

9x = 180

Solving for x:

x = 20

Now we can find out how much money each person has:

Billy: x = 20 pounds

Liam: 2x = 2(20) = 40 pounds

Nicola: 6x = 6(20) = 120 pounds

It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.

We have,

Let's start by assigning variables to unknown quantities.

Let m be the time it takes for Mike to wash the car alone (in minutes).

We know that Stephanie takes 17 minutes to wash the car alone, so her rate of work is 1/17 car per minute.

Working together, their combined rate of work is 1/8.24 car per minute.

Using the formula:

(rate of work) = (amount of work) / (time)

we can set up the following equation to represent the work they do together:

1/8.24 = (1 car) / t

where t is the time it takes them to wash the car together.

We can also set up a similar equation for Stephanie's work alone:

1/17 = (1 car) / (t + x)

where x is the extra time it takes Mike to wash the car alone.

Since they are working on the same car, the amount of work done in both cases is the same, so we can set the two equations equal to each other and solve for x:

1/8.24 = 1/(t + x) + 1/17

Multiplying both sides by the least common multiple of the denominators (8.2417(t+x)).

17*(t+x) + 8.24*(t+x) = 8.24*17

Simplifying.

25.24t + 17x = 139.68

We also know that Mike's rate of work is 1/m car per minute.

Since we know the combined rate of work when they work together, we can set up another equation:

1/m + 1/17 = 1/8.24

Multiplying both sides by the least common multiple of the denominators (8.2417m).

178.24m + 8.2417m = 8.2417m + m8.24m

Simplifying.

141.08m = 139.68

Solving for m.

m = 0.989

Therefore,

It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.

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The probability that either event will occur is given as follows:

P(A or B) = 0.83.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The "or probability" is defined as follows:

P(A or B)=P(A) + P(B) - P(A and B).

From the Venn Diagram, the probabilities of each event are given as follows:

Hence the or probability is given as follows:

P(A or B) = 0.5 + 0.3333 + 0

P(A or B) = 0.83. (rounded to the nearest hundredth).

The Venn diagram is given by the image presented at the end of the answer.

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Answer:

When we have a set of points, we can find the distance between them using the formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where d is the distance, x1 and x2 are one point and y1 and y2 are another point.

OB:

Thus, for OB, we can allow O(6, 6) to be our x1 and x2 point and we can allow B(9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(6-9)^2+(6-6)^2} \\d=\sqrt{(-3)^2+(0)^2} \\d=\sqrt{(-9)} \\d=3[/tex]

Thus, the first part/step in the equation is your subtraction expression to find the length of OB.

AB:

For AB, we can allow A(9, 10) to be our x1 and x2 point and we can allow B (9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(9-9)^2+(10-6)^2}\\ d=\sqrt{(0)^2+(4)^2}\\ d=\sqrt{16}\\ d=4[/tex]

The first part/step is your subtraction expression for the length of AB.

The value of (a) in given triangle is approximately 7.44 cm.

A triangle is a three-sided polygon consisting of three sides and three vertices. The most important property of a triangle is that the sum of its interior angles  is  180 degrees.

Let ΔABC is a triangle

Given ∠ B = 75°

∠ C = 31.8°

AB = 12cm

AC = 22cm

find BC = ?

We can use the law of cosines to solve for BC:

BC² = AB² + AC² – 2(AB)(AC)cos(B)

We know that angle B = 75 degrees, so we can substitute:

BC² = 12² + 22² - 2(12)(22)cos(75)

Evaluating cos(75) with a calculator, we get:

BC² ≈ 144 + 484 - 572.59

BC² ≈ 55.41

Taking the square root of both sides gives us:

BC ≈ 7.44

Therefore, BC is approximately 7.44 cm.

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The factors in this algebraic expression are:

14 And (18 - 3x)

An algebraic expression can also be written as a list of its constituent parts. Variables, constants, and operators are the components of an algebraic expression. Terms are separated from one another in an algebraic equation by the addition operation.

Algebraic Expressions can be factorized using many methods. The most common methods used for factorization of algebraic expressions are:

Factorization using common factors

Factorization by regrouping terms

Factorization using identities

The algebraic expression written by Aaron to represent the product of 14 and the difference of 18 and 3x is:

14 * (18 - 3x)

The factors in this expression are:

14

(18 - 3x)

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The system has the following solution: [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals can be used to represent the answer.

A statement in mathematics demonstrating the equality of two expressions is called an equation. Two phrases with the same value are normally separated by the equals sign (=). Finding the area of a circle and predicting planetary motion are only two examples of the many practical issues that equations are used to address.

The linear system's augmented matrix, which is determined by the matrix equation A x = b is given by:

Aequals

[tex]\left[\begin{array}{ccc}1&-3&4\\2&-3&2\\-3&3&4\\-7&15&-4\end{array}\right][/tex]

Part 2:

Aequals

Write the system's solution as a vector after solving it.

We can use Gaussian Elimination to solve this system.

Step 1:

[tex]\left[\begin{array}{ccc}1&1&0\\2&-1&1\\-3&0&1\\-7&8&3\end{array}\right][/tex]

Step 2:

Aequals

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\3&1&0\\-4&3&1\end{array}\right][/tex]

The system's solution is [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals represents the answer.

The matrix is,

[tex]\left[\begin{array}{ccc}-4\\3\\1\end{array}\right][/tex]

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Answer:

We can use trigonometry to find AB.

First, we can use the fact that the sum of the angles in a triangle is 180° to find angle A:

A + B + C = 180°

A + 90° + 30° = 180°

A = 60°

Now, we can use the sine function to find AB:

sin A = opposite/hypotenuse

sin 60° = AB/96

AB = 96 * sin 60°

AB = 96 * √3/2

AB = 48√3

Therefore, AB is approximately 83.14 cm (rounded to two decimal places).

The equation that represents a quadratic function is option b: [tex]y=3x^2-5x+9[/tex]

What is a quadratic function ?

A quadratic function is a function that can be written in the form of f(x) = [tex]ax^2 + bx + c[/tex] , where a, b, and c are constants, and a is not equal to 0. The graph of a quadratic function is a parabola, which can open upwards or downwards, depending on the sign of the coefficient a.

In option b, we can see that the equation is in the form of [tex]f(x) = 3x^2 - 5x + 9[/tex] , which is a quadratic function. The coefficient of [tex]x^2[/tex] is a non-zero constant (a=3), which means that the graph of this function is a parabola.

Option a is not a quadratic function, as it is in the form of [tex]x=y^2-2y+4[/tex], which is a quadratic equation in terms of y, but not in terms of x.

Option c is a little more complicated, as it contains a radical term. However, if we simplify it, we can see that it is also a quadratic function, in terms of x.

Option d is a linear equation, not a quadratic function, because it does not have an [tex]x^2[/tex] term.

Therefore, the quadratic function is [tex]y=3x^2-5x+9[/tex], option b.

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Answer:

Her rate of mowing lawns per hour is 4 lawns to one hour

Step-by-step explanation:so on a table you divide 4÷4=1 then you do the same thing for the 16÷4=4. So Oliva can mow 4 lawns per hour

Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Maxwell's filing status can be described as: b. Married filing jointly.

A filing status is a category that defines your tax-filing status based on your marital status and family situation. The filing status determines tax rate and standard deduction, as well as the eligibility for certain credits, deductions, and exemptions.

Maxwell can be described as married filing jointly because he and his spouse combined their income, deductions, and credits on one tax return. This status generally results in lower tax rates and a larger standard deduction compared to filing separately.

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Answer: 28.27m^2

Step-by-step explanation:

Area of a circle: [tex]A = \pi r^{2} \\[/tex]

Given the diameter of 6m, we can divide that by 2 to get the radius and plug that into the formula.

6/2 = 3m

[tex]A = \pi (3)^2\\A= 28.27m^{2}[/tex]

The answer is Option 2: The measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.

An angle that, when combined with another angle, creates a straight angle (measuring 180 degrees), is known as a supplementary angle. In other words, if the sum of the measurements of two angles is 180 degrees, they are supplementary. Contrarily, a complimentary angle is one that, when combined with another angle, creates a right angle (which has a 90-degree angle). In other words, if the sum of the measurements of two angles is 90 degrees, they are complimentary. A straight angle and a right angle are not the same thing, hence it is crucial to understand that one angle cannot be both supplementary and complimentary at the same time.

From the given figure we see that the measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.

Hence, option 2 is correct.

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The complete question is:

g°f = -9 So, the correct answer is (B) -9.To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

what is function ?

In mathematics, a function is a relation between two sets, called the domain and the range, that assigns to each element of the domain exactly one element of the range.

In the given question,

To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

Step 1: Apply f to -3

f(x) = 3x + 7

f(-3) = 3(-3) + 7 = -2

Step 2: Apply g to the result of f(-3)

g(x) = 2x - 5

g(-2) = 2(-2) - 5 = -9

Therefore, g°f = -9.

So, the correct answer is (B) -9.

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There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.

The dimensions and shape of the object are taken into account while calculating surface area. The volume of water of a cube, for instance, can be computed by adding the areas of the all six of its equal-sized faces. The surface temperature of something like a sphere, while on the other hand, must be calculated using mathematical methods that take into consideration its radius. The concept of surface area is crucial to many branches of mathematics, science, & engineering.

given

The area of each of the two triangles is [tex](1/2) * 3 * 8 = 12[/tex] square units since each triangle has a base of 3 and a height of 8, respectively.

The trapezium features an 8-inch height, a 6-inch top base, a 12-inch bottom base, and a 10-inch slant height.

two rectangles, each measuring 72 square units: 144 square units (2 x 72)

Four trapezoidal sides, each with a surface area of 12 + 72 = 84 square units 336 square units (4 x 84)

There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.

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The selling prices of the sculpture, painting, and photograph were 166.5 million, 107.0 million, and 57.6 million respectively.

Let's call the selling prices of the sculpture, painting, and photograph as S, P, and Ph respectively.

From the first sentence, we know that:

S + P + Ph = 308.0 million

From the second sentence, we know that:

P = Ph + 49.4 million

And from the third sentence, we know that:

P + Ph = S + 24.4 million

Now we can substitute the second equation into the third equation:

(Ph + 49.4 million) + Ph = S + 24.4 million

Simplifying:

2Ph + 49.4 million = S + 24.4 million

2Ph = S - 25 million

Substituting this into the first equation:

S + P + Ph = 308.0 million

S + (Ph + 49.4 million) + Ph = 308.0 million

2Ph + S = 258.6 million

Now we can substitute the equation we derived earlier:

S + 2Ph - 49.4 million = 258.6 million

S + 2Ph = 308.0 million

Substituting 2Ph = S - 25 million:

S + S - 25 million = 308.0 million

2S = 333.0 million

S = 166.5 million

Now we can use this value to find P and Ph:

P = Ph + 49.4 million

P + Ph = S + 24.4 million

Substituting S = 166.5 million in both equations:

P + Ph = 190.9 million

P = Ph + 49.4 million

Solving these two equations simultaneously:

Ph = 57.6 million

P = 107.0 million

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