Write an equation of the line that passes through each pair of points (9,2) (-2,6)

Answer:

16x+4y=2

Step by step explanation

The classification , symmetry , maximum r-values and the zeroes of the function are solved

Given data ,

a)

Let the function be represented as A

Now , the value of A is

r² = 25 sin( 2θ )

The equation represents a cardioid

It is symmetric about the polar axis.

The maximum values of r occur at θ = (π/4) + kπ/2, and the maximum value of r is 5.

The equation has zeroes at θ = kπ/2, and the corresponding values of r are given by r = 0

b)

The equation represents a limaçon.

It is symmetric about the polar axis.

The maximum value of r is 7.

The equation has zeroes at θ = arccos(1/3) + 2kπ or θ = -arccos(1/3) + 2kπ, and the corresponding values of r can be found by substituting into the equation r = 4 - 3cos(θ).

c)

The equation represents an Archimedean spiral.

It does not possess any symmetry.

There is no maximum r value.

The equation has a zero at θ = 1/2.

Hence , the zeroes of the function are solved

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Using the centimeter ruler:

For the quotients:

2.a. To find 1 ÷ 1/10, divide 1 by the fraction 1/10. Dividing by a fraction is the same as multiplying by its reciprocal, rewrite the problem as 1 × 10/1, which simplifies to 10. Therefore, 1 ÷ 1/10 = 10.

To find 4 ÷ 1/10, divide 4 by the fraction 1/10. Again, rewrite the problem as 4 × 10/1, which simplifies to 40. Therefore, 4 ÷ 1/10 = 40.

b. To find each quotient, we used the fact that dividing by a fraction is the same as multiplying by its reciprocal.

c. Following the same pattern, find 18 ÷ 1/10 by dividing 18 by 1/10. This is the same as multiplying 18 by the reciprocal of 1/10, which is 10/1. Therefore, 18 ÷ 1/10 = 180.

d. To find 4 ÷ 2/10, divide 4 by 2/10. Rewrite the problem as 4 × 10/2, which simplifies to 20. Therefore, 4 ÷ 2/10 = 20.

To find 4 ÷ 8/10, divide 4 by 8/10. Rewrite the problem as 4 × 10/8, which simplifies to 5. Therefore, 4 ÷ 8/10 = 5.

3. a. To divide 5 by 1/10, Rewrite the problem as 5 × 10/1, which simplifies to 50. Therefore, 5 ÷ 1/10 = 50.

b. To divide 5 by 3/10, Rewrite the problem as 5 × 10/3, which simplifies to 16 2/3. Therefore, 5 ÷ 3/10 = 16²/₃.

c. To divide 5 by 9/10, Rewrite the problem as 5 × 10/9, which simplifies to 5 5/9. Therefore, 5 ÷ 9/10 = 5⁵/₉.

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The graph of the inequality y ≤ 1/3x + 1 is added as an attachment and it is represented with option (c)

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

y ≤ 1/3x + 1

The above expression is an inequality that implies that

Next, we plot the graph

See attachment for the graph of the inequality

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For the function y = 3sin[2(θ-90°)] + 2, the amplitude is 3, the period is π, the phase shift is -45° and the vertical shift is 2 units up.

The amplitude of a sine function represents the maximum displacement from the midline.

The coefficient in front of the sine function is 3, so the amplitude is 3.

The period of a sine function is the length of one complete cycle. It can be calculated using the formula T = 2π/b, where b is the coefficient of θ inside the sine function brackets.

Here, b = 2, so the period is T = 2π/2 = π.

The phase shift of a sine function indicates a horizontal shift to the left or right.

In this case, c = 90°, so the phase shift is θ = 0° - 90°/2 = -45°.

The vertical shift indicates a shift up or down on the y-axis.

The constant term outside the sine function is 2, so the vertical shift is 2 units up.

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Answer:

The correct statements are:

A) There are no zeroes

D) The vertex is (1, 14)

H) The axis of symmetry is x = 1

J) The "a" of the parabola is positive

M) The parabola has a minimum

Therefore, the options B, C, E, F, G, I, K, N, O, P, Q, and R are all false.

Step-by-step explanation:

Step-by-step explanation:

Remember that, this is quadratic function graph.

Let's analyze fact the graph. We get :

There are two roots/zeroes

Two roots are x1 = -2 , x2 = 6

Vertex is maximum value of parabola (2,14)

Symmetry function is x = 2 (you can show that, x-axis from vertex)

"a" parabola indicated negative

The parabola with "a" negative, thus have maximum value (show that vertex is (2,14))

Conclusion :

The true statements are C,F,I,K,N,O (6 statements are shown)

Subject : Mathematics

Level : JHS

Chapter : Quadratic Functions

The surface area of the square pyramid is 224 square centimeters.

Since the base of the square pyramid is a square, all sides are equal in length.

Let's call the length of one side of the square base "s".

Then the surface area of the pyramid can be found using the formula:

Surface area = Area of base + Area of four triangles

The area of the base is just s², and the height of each triangle can be found using the Pythagorean theorem.

Let's call the height "h". Then:

h² = 14² - (s/2)² (using the longer side of the triangle as the hypotenuse)

h² = 196 - (s²/4)

Now, we need to find the surface area in terms of "s" and simplify:

Surface area = s² + 4(1/2)(s)(h)

Surface area = s² + 2sh

Surface area = s² + 2s√196 - s²/4))

Surface area = s²+ 2s√(784 - s²))/2

Surface area = s² + s√(784 - s²))

We are given that one side of the square base is 8cm, so:

Surface area = 8² + 8√784 - 8²

Surface area = 64 + 8√400

Surface area = 64 + 8(20)

Surface area = 224

Therefore, the surface area of the square pyramid is 224 square centimeters.

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Answer:

$450

Step-by-step explanation:

995/2 = 497.5

95/2 = 47.5

497.5 + 47.5 = 545

495 - 95 = 450

The function h(x) = (2ˣ) + 1 does not have an x intercept.

A function has an x-intercept when the value of the function is equal to zero at some point on the x-axis.

(a) f(x) = -x + 2 is a linear function with a negative slope (-1) and a y-intercept of 2.

To find the x-intercept, we set f(x) equal to zero and solve for x:

0 = -x + 2

x = 2

Therefore, the function f(x) has an x-intercept at (2, 0).

(b) g(x) = -(x²) is a quadratic function that opens downward and has a vertex at (0, 0).

To find the x-intercept, we set g(x) equal to zero and solve for x:

0 = -(x²)

x²= 0

x = 0

Therefore, the function g(x) has an x-intercept at (0, 0).

(c) h(x) = (2ˣ) + 1 is an exponential function

To find the x-intercept, we set h(x) equal to zero and solve for x:

0 = (2ˣ) + 1

-1 = 2ˣ

However, there is no real value of x that satisfies this equation.

h(x) = (2ˣ) + 1 has no x intercept.

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Answer:

The answer is 33°

Yes you are correct

Step-by-step explanation:

angles on a straight line equal 180°

57+90+x=180

x+147=180

x=180-147

x=33°

Hi, I can't tell if there's a little square drawn in red to indicate that there's a right angle in the middle. There's some squiggly lines and so it's kind of hard to tell.

I am going to assume that there is. Let me know if there isn't.

The sum of these 3 angles would be 180 degrees.

As an equation, 57 + 90 + x = 180

Solve for x.

147 + x = 180

x = 33 degrees.

So this would be correct ASSUMING that there's a little red square drawn indicating that there's a right angle.

The resultant of the force that acts in opposite directions is 7 N.

We have,

We know that the resultant force is the force that has the same effect in magnitude and direction as two or more forces that is acting together. We have to note that the force that is actinmg on an object is a vector quantity. The implication of this is that the magnitude and the direction of the forces that are acting on the body is very important.

By the use of the law of vectors we can be able to write in the case of the question that we have here, we can see that the forces are acting in the opposite directions. The implication of this is that we would have to subtract the forces so as obtain the resultant force.

We have to note that when we have opposite forces, one is said to be positive and the other negative and the resultant force can be found by subtraction. As such the resultant force can be obtained from;

Let the +B force be 12 N

Let the -B force be 5N

12 N - 5 N = 7 N

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The first term of a geometric sequence is 2 and the common ratio is 3.  The general term formula for the nth term of a geometric sequence is given by: an = a₁ × rⁿ⁻¹ Where, an is the nth term of the sequence, a₁ is the first term of the sequence, and r is the common ratio of the sequence. The 15th term of the sequence is 86,093,442.

To find the 15th term of the sequence, we need to use the above formula to find a₁ and r.The sequence is: 2, 6, 18, 54, ...Since the first term is 2, then a₁ = 2.The common ratio can be found by dividing any term by its preceding term. We will use the second and first term:6 / 2 = 318 / 6 = 3Again, the common ratio is 3. Now, we can use the formula to find the 15th term of the sequence: an = a₁ × rⁿ⁻¹a15 = 2 × 3¹⁵⁻¹a15 = 2 × 3¹⁴a15 = 2 × 43,046,721a15 = 86,093,442 The 15th term of the sequence is 86,093,442.

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The surface areas of the solids are listed below:

Case I: A = 216 ft²

Case O: A = 204 mm²

Case H: A = 216 ft²

Case L: A = 284.6 cm²

Case E: A = 25.657 yd

Case N: A = 356 yd²

Case S: A = 361.88 ft²

Case T: A = 150 cm²

In this problem we find eight solids, whose surface areas, that is, the sum of the areas of all faces of the solid, must be found. Each face can be represented by the following area formula:

Rectangle

A = w · h

Triangle

A = 0.5 · w · h

Where:

Now we proceed to determine the surface areas:

Case I:

A = 6 · (6 ft)²

A = 216 ft²

Case O:

A = 4 · 0.5 · (6 mm) · (14 mm) + (6 mm)²

A = 204 mm²

Case H:

A = 2 · (8 ft) · (6 ft) + (8 ft) · (5 ft) + (6 ft) · (5 ft) + (10 ft) · (5 ft)

A = 216 ft²

Case L:

A = 2 · 0.5 · (7 cm) · (5 cm) + 2 · (6.1 cm) · (13 cm) + (7 cm) · (13 cm)

A = 284.6 cm²

Case E:

A = 2 · 0.5 · (2 yd)² + 2 · (2 yd) · (4 yd) + (√2 yd) · (4 yd)

A = 25.657 yd

Case N:

A = 2 · (3 yd) · (8 yd) + 2 · (8 yd) · (14 yd) + 2 · (14 yd) · (3 yd)

A = 356 yd²

Case S:

A = 2 · 0.5 · (8 ft) · (6 ft) + 2 · (14 ft) · (7.21 ft) + (14 ft) · (8 ft)

A = 361.88 ft²

Case T:

A = 6 · (5 cm)²

A = 150 cm²

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Answer:

The correct answer:

(B) SAS Similarity

The value of a scalar does not depend on the orientation.

The magnitude of a vector does not depend on the orientation of the axes.

(a) The value of a scalar does not depend on the orientation of the axes. Scalar is a quantity that has only magnitude and no direction, so it is independent of the coordinate system. Examples of scalars include temperature, mass, and time.

(b) Component of a vector depends on the orientation of the axes. If the coordinate axes are rotated or shifted, the components of a vector will change accordingly.

(c) A vector depends on the orientation of the axes. A vector has both magnitude and direction and changes when the orientation of the axes is changed.

(d) The magnitude of a vector does not depend on the orientation of the axes. The magnitude of a vector is defined as the length of the vector, which is independent of the coordinate system. For example, the magnitude of a velocity vector is the speed, which is the same regardless of the orientation of the axes.

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The height of domino #7 is approximately 6.89 cm tall.

The formula for the nth term of a geometric progression is:

[tex]a_n = a * r^(^n^-^1^)[/tex]

where:

a is the first term (the height of the smallest domino, 4.00 cm),

r is the common ratio (the growth rate, 1.12), and

n is the term number (for domino #7, n = 7 + 1 = 8, because the sequence starts with domino #0).

Let's plug these values into the formula:

[tex]a_8 = 4.00 cm * (1.12)^7[/tex]

(Note that we're using 7, not 8, because the first domino is #0, not #1.)

Now, compute the value:

[tex]a_8 = 4.00 cm * (1.12)^7[/tex]

=  6.89 cm

So, domino #7 is approximately 6.89 cm tall.

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You would add the sales tax amount to the cost of the meal to get the total cost. In this case, the sales tax amount is $1, so the total cost would be $26.

One situation that would fit into this scenario is calculating the total cost of a meal at a restaurant that costs $25. Firstly, to calculate the sales tax, you would need to convert the percentage of sales tax into a decimal.

In this case, the sales tax rate is 5%, so you would convert it to 0.05.Next, you would multiply the cost of the meal by the sales tax rate to calculate the sales tax amount.

To do this calculation without a calculator, you can use mental math or estimation techniques.For example, you could estimate 5% of $25 by breaking the 5% into a 1% and 4% calculation.

To calculate 1%, you would simply move the decimal point two places to the left, which gives you $0.25. Then, to calculate 4%, you could multiply $0.25 by 4, which equals $1.

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The sum of the 24 terms of the arithmetic series is 900

How to solve:

To find the sum of an arithmetic series, we can use the formular:

Sn = (n/2)(2a + (n-1)d)

Where;

Sn is the series sum, n is the number of terms, a is the first term, and d is the common difference.

The first term (a) in this scenario is 3, and the common difference (d) is 3. With n equal to 24, we want to find the sum of the first 24 terms.

When the values are entered into the formula, we get:

The sum of the first 24 terms of the arithmetic series is 900 because;

S24 = (24/2)(2(3) + (24-1)(3))

= 12(6 + 23(3))

= 12(6 + 69)

= 12(75)

= 900.

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The minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.

On the basis of the quantity of checks written, we can compare the overall costs of the two accounts.

Let's calculate the total cost for each account based on the given information:

First Account:

Monthly fee: $12

Per-check fee: $0.10

Total cost = Monthly fee + (Per-check fee * Number of checks)

Second Account:

Monthly fee: $9

Per-check fee: $0.25

Total cost = Monthly fee + (Per-check fee * Number of checks)

We must determine the point at which the first account's total cost is less than the second account's total cost. Let's construct the formula:

$12 + ($0.10 * Number of checks) < $9 + ($0.25 * Number of checks)

Simplifying the equation

$12 - $9 < ($0.25 - $0.10) * Number of checks

$3 < $0.15 * Number of checks

Dividing both sides by $0.15:

$3 / $0.15 < Number of checks

20 < Number of checks

Therefore, the minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.

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Answer:

(c):53

Step-by-step explanation:

Let's start with the equation:

3x+5y

Since we already have the values of x and y, we can just solve the equation.

3(11)+5(4)

33+20=53

The answer is (c)53

Measure of angle 1 is,

Angler ACB = 36 degree

We have to given that;

In a parallelogram we get;

Angler CAD = 36 degree

Now, We know that;

Opposite sides are parallel to each other in a parallelogram.

Hence, We get;

Angler CAD = Angle ACB

Since, Angler CAD = 36 degree

Hence, We get;

Measure of angle 1 is,

Angler ACB = 36 degree

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Answer: 4th one is the correct one

Step-by-step explanation:

The sine function with a midline of y=4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2sin(2(x - π/4)) + 4.

To write a sine function with the given properties, we can use the general form of a sine function: y = A * sin(B(x - C)) + D, where A represents the amplitude, B represents the frequency (or inverse of the period), C represents the horizontal shift, and D represents the vertical shift (or midline).

In this case:

The midline is y = 4, so D = 4.

The amplitude is 2, so A = 2.

The period is π, so the frequency is B = 2π/π = 2.

The horizontal shift is π/4 to the right, so C = -π/4.

Plugging these values into the general form, we get the sine function:

y = 2 * sin(2(x - (-π/4))) + 4

Simplifying further:

y = 2 * sin(2(x + π/4)) + 4

Therefore, the sine function with a midline of y = 4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2 * sin(2(x + π/4)) + 4.

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Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than Twice the number of years Mrs. Bright has worked.

The number of years Mrs. Bright has worked for the company. We know that Mr. Oswald has been in the company for 24 years, which is three times the number of years Mrs. Bright has worked.

So, Mrs. Bright has worked for 24 / 3 = 8 years in the company.

Now, let's find the number of years Mr. Oswald needs to work for the company to make it twice the number of years Mrs. Bright has worked.

Twice the number of years Mrs. Bright has worked is 2 * 8 = 16 years.

Since Mr. Oswald is already employed for 24 years, we need to find the additional years he needs to work to reach 16 more years.

16 more years - 24 years = -8 years.

The result of -8 years indicates that Mr. Oswald has already worked for more than twice the number of years Mrs. Bright has worked. Therefore, it is not possible for Mr. Oswald to work for more years in order to make it twice the number of years Mrs. Bright has worked.

Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than twice the number of years Mrs. Bright has worked.

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Using vertical method, the multiplication of (2x² −3x+5). by x + 4 is determined as 10x² - 15x + 25.

In vertical multiplication, the numbers to be multiplied are placed vertically over one another with their least significant digits aligned.

The top number is named the multiplicand and the lower number is the multiplier. The result of the multiplication is the product.

The given expressions;

(x+4)(2x² −3x+5).

We will multiply as follows;

      2x² - 3x + 5

   ×    x + 4

_________________

     2x² - 3x + 5    (Multiply by x)

+   8x² - 12x + 20  (Multiply by 4)

_________________

    10x² - 15x + 25

Thus, using vertical method, the multiplication of (2x² −3x+5). by x + 4 is determined as 10x² - 15x + 25.

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Answer:

Step-by-step explanation:

It's c

-4 1/6

Plug in the number for a and you get -2 1/3 - 11/6

make the first number into a fraction, so -7/3

-7/3 - 11/6

common denominator, so, -14/6 - 11/6, which equals -25/6

simplify: -4 1/6

Hope that helps!

Answer:

The answer is

[tex] \frac{ - 25}{6} [/tex]

-4⅙

Step-by-step explanation:

[tex]a - \frac{ - 11}{6} [/tex]

[tex]a = - 2 \times \frac{1}{3} [/tex]

[tex] \frac{ - 7}{3} - \frac{ - 11}{6} [/tex]

[tex] = \frac{ - 25}{6} [/tex]

Answer:

653.3 bacteria

Step-by-step explanation:

A continuously growing population of bacteria is modeled by the function:

[tex]P(t) = P_0 \cdot e^{rt}[/tex]

where:

In this problem, we are given the following values:

We can plug these into the function to solve for [tex]P(2)[/tex].

[tex]P(t) = P_0 \cdot e^{rt}[/tex]

[tex]P(2) = 484 \cdot e^{(0.15 \, \cdot \, 2)}[/tex]

[tex]P(2) = 484 \cdot e^{0.3}[/tex]

Finally, the right side of this equation can be evaluated using a calculator to solve for the population of the bacteria after 2 hours.

[tex]\huge{\text{P(2) = 653.3 bacteria}}[/tex]