Puzzle #2
2: Find an equation that is
perpendicular to:
1: Find an equation
that is parallel to:
answer choices
A: B: 1 C:
y=-3x. 5 Yax.2 y --4x7
D:
E:
Y = 2x - 5y = 5x • 2
Y***.21
G:
H:
I:
y = 4x - 7 y = 3x - 2y = -2xl
F:-
-4x + 2y = 8
3: Find an equation that
is parallello: +
4: Find an equation that
is perpendicular to:
Type the 4-
letter code into
the answer
box. All CAPS,
no spaces.
3x • y: 1
O2020 Sete Mathie
Your answer

f(x) = 4.1/(42.4x-10(x-2)), x-intercept = -4.878, y-intercept = (0,-2.05), asymptotes: vertical at x=2, horizontal at y=0, and slant at y=4.1/8x.

Given: f(x) = 4.1/(42.4x-10(x-2))

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

0 = 4.1/(42.4x-10(x-2))

0 = 4.1/(32.4x+20)

0 = 4.1/4.08(x+4.878)

So, the x-intercept is x = -4.878.

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

f(0) = 4.1/(42.4(0)-10(0-2))

f(0) = -2.05

So, the y-intercept is (0,-2.05).

To write f(x) in the form f(x) = -1/(ax + b) + q, we can simplify the expression as follows:

f(x) = 4.1/(42.4x-10(x-2))

f(x) = 4.1/(32.4x+20)

f(x) = 4.1/4.08(8x+5)

So, a = 8, b = 5, and q = 4.1/4.08.

To draw the graph of f, we plot the x- and y-intercepts and the vertical asymptote x = 2.

We can find the horizontal asymptote by noting that as x becomes very large or very small, the term 10(x-2) dominates the expression, so f(x) approaches 4.1/-10x. Thus, the horizontal asymptote is y = 0.

To find the equations of the slant asymptotes, we divide the numerator by the denominator using long division:

4.1

8x + 5 | 4.1

- 4.1

0

So, the slant asymptote is y = 4.1/8x.

Therefore, the intercepts of f are x = -4.878 and (0,-2.05), and the equation of f(x) in the form f(x) = -1/(ax + b) + q is f(x) = -1/(8x + 5) + 1.0039.

The graph of f has intercepts with the x-axis at x = -4.878 and the y-axis at (0,-2.05), a vertical asymptote at x = 2, a horizontal asymptote at y = 0, and a slant asymptote at y = 4.1/8x.

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Answer: the other three angles are 83° each

Step-by-step explanation:

The Total of all the angles of a pentagon is 540° Subtract the 150 and 141.

540- 291 = 249. Divide by 3

249/3 = 83

Answer:

14

Step-by-step explanation:

let the number be x

3x=42

x=42/3

=14

The Area of the two circle is 14.13 cm square. and  area of the blue section is 14.13 cm square.

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the shape is the sum of the area of the two smaller circle.

The circles have diameter of 3 unit.

Area of a circle = πr²

where: π = 3.14 = pi

D = diameter

r = radius

1. Radius = 3 cm

Now the area of the big circle =  πr²

Area = 3.14 x 3² = 28.26 cm square

2. Radius = 3/2

Area = 3.14 x 3/2² = 7.06 cm square

Area of the two circle = 7.06 + 7.06 = 14.13 cm square

3.  the area of the blue section = the area of the big circle - Area of the two circle

= 28.26  - 14.13

= 14.13

Therefore, the area of the blue section is 14.13 cm square.

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The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

m = 2/3

Step-by-step explanation:

Answer:

\( \frac{2}{3} \)

Step-by-step explanation:

slope is

\( m = \frac{rise}{run} = \frac{y 2 - y1}{x2 - x1} \)

(0,0) & (3,2)

\( m = \frac{2 - 0}{3 - 0} = \frac{2}{3} \)

Answer:

1.2n=0.45n+1.5

Step-by-step explanation:

Answer:

m∠14 = 80°

Step-by-step explanation:

Angles m∠13 and m∠14 lies on a straight line. Angles on a straight line sums up to 180°.

Hence we can say that,

m∠13 + m∠14 = 180

100 + m∠14 = 180

m∠14 = 180 - 100

m∠14 = 80

The probability that a student has a dog given that they have a cat is 2/15.

Using the data in the table, we see that there are 2 students who have both a cat and a dog, and a total of 18 students who have a dog (whether or not they also have a cat).

So, P(A and B)

= 2/30

= 1/15 represents the probability of a student having both a cat and a dog.

Also, P(B) = 5/30 = 1/6 represents the probability of a student having a cat.

Now we can use the conditional probability formula:

P(A|B) = P(A and B) / P(B)

P(A|B) = (1/15) / (1/6) = 2/15

Therefore, the probability that a student has a dog given that they have a cat is 2/15.

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Answer:

C

Step-by-step explanation:

The area of the octagon is 1395 square units option (A) 1395 square units is correct.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have:

Octagon showed in the picture:

The area of the octagon = 2(1 + √2)a²

a is the side length.

a = 17 units

The area of the octagon = 2(1 + √2)(17)²

The area of the octagon = 1395.4 ≈ 1395 square units

Thus, the area of the octagon is 1395 square units option (A) 1395 square units is correct.

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The equation −12x+y=10 in slope-intercept form is y = 12x + 10

The general equation showing the slope-intercept form of a graph is represented as;

y = mx+ c

Given that;

From the information given, we have the equation as;

−12x+y=10

Now, let's make 'y' the subject of formula by

-12x + y = 10

Take '12x' to the other side of the equality sign

y = 10 + 12x

Make into slope-intercept form, we have

y = 12x + 10

Hence, the formula is y = 12x + 10

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The slope-intercept form of the equation of line −12x + y = 10 is y = 12x + 10.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the line;

−12x + y = 10

To rewrite in slope intercept form ( y = mx + b ), bring terms containing y to the left and x or constant terms to the write side of the equation.

−12x + y = 10

Add 12x to both sides

−12x  + 12x + y = 10 + 12x

y = 10 + 12x

Reorder in slope intercept form

y = 12x + 10

Therefore, the slope intercept form is y = 12x + 10.

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To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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The angles of triangle ABC, from least to greatest, are A ≈ 7.17 degrees, C ≈ 48.86 degrees, and B ≈ 79.61 degrees.

To find the angles of triangle ABC, we'll first solve for the value of x using the given information. Then we'll calculate the side lengths AB, BC, and AC. Finally, we'll use the Law of Cosines to find the angles.

Given:

AB = 6x - 35

BC = 4x + 11

AC = x + 29

Perimeter (P) = 192

Find the value of x

We know that AB + BC + AC = P, so we can substitute the given side lengths and solve for x:

(6x - 35) + (4x + 11) + (x + 29) = 192

Combine like terms:11x + 5 = 192

Subtract 5 from both sides:

11x = 187

Divide both sides by 11:

x = 17

Find the side lengths

Substituting x = 17 into the given expressions for AB, BC, and AC, we can calculate the side lengths:

AB = 6x - 35 = 6(17) - 35 = 102 - 35 = 67

BC = 4x + 11 = 4(17) + 11 = 68 + 11 = 79

AC = x + 29 = 17 + 29 = 46

So, AB = 67, BC = 79, and AC = 46.

Find the angles

We can use the Law of Cosines to find the angles of the triangle. Recall the formula:

\(cos(A) = (b^2 + c^2 - a^2) / (2 \times b \times c)\)

Angle A (opposite side AB):

\(cos(A) = (BC^2 + AC^2 - AB^2) / (2 \times BC \times AC)\\cos(A) = (79^2 + 46^2 - 67^2) / (2 \times 79 \times 46)\\cos(A) = (6241 + 2116 - 4489) / (2 \times 79 \times 46)\\cos(A) = 3878 / (2 \times 79 \times 46)\)

cos(A) ≈ 0.993

A ≈ arccos(0.993) ≈ 7.17 degrees

Angle B (opposite side BC):

\(cos(B) = (AB^2 + AC^2 - BC^2) / (2 \times AB \times AC)\\cos(B) = (67^2 + 46^2 - 79^2) / (2 \times 67 \times 46)\\cos(B) = (4489 + 2116 - 6241) / (2 \times 67 \times 46)\\cos(B) = 364 / (2 \times 67 \times 46)\)

cos(B) ≈ 0.173

B ≈ arccos(0.173) ≈ 79.61 degrees

Angle C (opposite side AC):

\(cos(C) = (AB^2 + BC^2 - AC^2) / (2 \times AB \times BC)\\cos(C) = (67^2 + 79^2 - 46^2) / (2 \times 67 \times 79)\\cos(C) = (4489 + 6241 - 2116) / (2 \times 67 \times 79)\\cos(C) = 8614 / (2 \times 67 \times 79)\\cos(C) = 0.648\)

C ≈ arccos(0.648) ≈ 48.86 degrees

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Answer:

18/11 do no form a proportion

Step-by-step explanation:

2x9 = 18

1x11 = 11

Proportions have to be equal

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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The value of x in the direct and indirect varoation is calculated as: x = 2.

If k is the constant of proportionality among two or more variables (x, y, z), a combined equation of direct and indirect variation is, z = kx/y, if z varies directly with x and indirectly with y.

With the information stated, we would have the following:

z = kx/y³

Find k, by plugging in the values of x, y, and z:

12 = k(8/2³)

12 = k(8/8)

12 = k

k = 12

Find x when y = 1 and z = 24:

24 = 12(x)/1³

24 = 12x

24/12 = x

x = 2.

Therefore, the value of x in the direct and indirect varoation is calculated as: x = 2.

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It is proved that m = √n.

To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:

m^2 ≤ n < (m + 1)^2.

So, after taking the square root, it will be:

m ≤ √n < m + 1

From that we can see m = √n is the unique m.

A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.

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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Answer:

41.86 is the right answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The ratio is given:

Let each equal part be x, then we have:

Total number of counters:

Step-by-step explanation:

Let,

Blue counter = 9x

Red counter = 6x

Yellow counter = 3x

Given,

9x = 6x + 6

9x - 6x = 6

3x = 6

x = 6/3

x = 2

Now,

Total number of counter = 2(9) + 2(6) + 2(3)

=> 18 + 12 + 6

=> 36

Answer: -2x

Step-by-step explanation:

4x+(-6x)

When there is a + in front of an expression in a parentheses, the expression remains the same.

4x-6x

Collect like terms

-2x

10 units is the distance between point A and point C on the number line.

A number system is defined as a system of writing to express numbers.

We need to find the  distance between point A and point C on the number line.

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

The length along a line or line segment between two points on the line or line segment is known as distance.

The point A is at -3.

The point C is at 7

Now the distance between A and C is AC.

AC=OC-OA

=7-(-3)

=7+3

=10

Hence, 10 units is the distance between point A and point C on the number line.

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The equation in term of p that models the above experience is:
2p + 10 = 0.8p + 20.

Any statement that models or captures the factors of a problem where in an equal sign is present to equate two of the factors or expressions therein is called an equation.

Total cost of baking p pizzas with brick oven = A =  p(cost of one pizza) + cost of baking = p(2) + 10 (in dollars).

Total cost of  baking p pizzas with electric oven = B =  p(cost of one pizza) + cost of baking = p(0.8) + 20 (in dollars).

B = A - 1 (as using electric oven saves $1 per day, as given)

Thus, we get:

2p + 10 = 0.8p + 20

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The gas company would charge $154.48 for using 200 hundred cubic feet of natural gas during the month.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division.

The equation that represents the gas company's monthly charges in dollars for using x hundred cubic feet of natural gas is:

y = 0.6924x + 16

Where:

x is the number of hundred cubic feet of natural gas used during the month

0.6924 is the cost per hundred cubic feet of natural gas used

16 is the fixed monthly service fee charged by the gas company.

To calculate the monthly charges for a given amount of natural gas used, we can substitute the value of x into this equation and simplify. For example, if x = 200, then:

y = 0.6924(200) + 16

y = 138.48 + 16

y = 154.48

Therefore, the gas company would charge $154.48 for using 200 hundred cubic feet of natural gas during the month.

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