Tripp is training for a half marathon. He runs 3
miles his first week of training. Each week after, he runs
2 more miles than he did the week before. Which equation represents the total number of miles,
, he runs after
weeks?

Answer:(1,−7π/4)

Step-by-step explanation:

Note that the point is on the circle whose radius is labeled 1, so r=1 or −1. Of the choices available, only an angle of −7π4, drawn from the positive x axis plots at the point A. So θ=−7π4, and r must be positive, as the angle is measured from the positive x axis. Thus, the polar coordinates are (1,−7π4).

The equation of line is,

⇒ y = 1/2x + 2

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 4, 0) and (0, 2).

Now,

Since, The equation of line passes through the points (- 4, 0) and (0, 2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 0) / (0 + 4)

m = 2 / 4

m = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - 0 = 1/2 (x + 4)

⇒ y = 1/2x + 2

Therefore, The equation of line is,

⇒ y = 1/2x + 2

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Answer:

65000 metres

Step-by-step explanation:

65*1000=65000

The set of ordered pairs which represents a function among the given answer choices is; {(1, 2), (-6, 2), (3,9), (5,3)}.

By definition, a function is a special kind of relation in which case, each input value is assigned not more than one output value.

On this note, by evaluation of the given sets of ordered pairs; the set {(1, 2), (-6, 2), (3,9), (5,3)} represents the relation which is a function.

Ultimately, the answer choice which represents a set of ordered pairs that represents a function is; {(1, 2), (-6, 2), (3,9), (5,3)}.

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The new mean annual wage is; $ 43,149.82.

Given that the initial mean weekly wage is $ 2.117.

The growth rate is 4.75%.

We need to find a new annual wage.

Consider the equation, A be the new annual wage.

Here R is the growth rate and P is the initial mean weekly wage and T is the number of weeks in a year.

The number of weeks in a year = 52 weeks.

Substitute P= 2,117, R =4.75% = 0.0475and T =52 in the equation.

A = 2.117 x 52(1 + 0.0475)

A = 43,149.82

The new mean annual wage is; $ 43,149.82.

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The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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Answer: 4m^5-3m^2+2m+21

Step-by-step explanation: you just have to put the exponents int he right order which we always put the highest first so you put 4m^5-3m^2+2m+21 which is the answer

The percentage of saline solution in brand B is 3%.

Let x be Percentage of saline solution in brand B

We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.

Then the equation is given as,

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

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The inverse function of the function f(x) is [tex]g(y) = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]

To find the inverse of the given function f(x) = -(1/2) - log₃√(9-x)

we need to solve for x in terms of y, where y = f(x).

Replace f(x) with y

Function y = -(1/2) - log₃√(9-x)

Solve for x

First, isolate the logarithmic term on one side of the equation.

y + (1/2) = -log₃√(9-x)

[tex]3^-^(^y^ +^ 1^/^2^) = 9-x[/tex]

[tex]x = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]

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a.) The value of each angle when 5 is substituted for X would be ;

Y = 55°

Y = 55°W = 75°

Y = 55°W = 75°Z = 45°

b). Chelsea is wrong in her calculation because the total internal angle of a triangle should be 180° and not 175°.

For angle Y;

11x = 11(5) = 55°

For angle W;

15x = 15(5) = 75°

For angle Z;

(8x+5) = 8(5) +5

= 45°

The total angles = 55+75+45 = 175°

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Answer:

y = 2

Step-by-step explanation:

substitute x = [tex]\frac{4}{5}[/tex] ( = 0.8) into the formula

y = [tex]\frac{4}{0.8}[/tex] + [tex]\sqrt{0.8+0.2}[/tex] - 5(0.8)

 = 5 + [tex]\sqrt{1}[/tex] - 4

 = 5 + 1 - 4

 = 6 - 4

 = 2

Answer:

142ft^2

Step-by-step explanation:

I hope this picture helps, but if you have any questions about the steps let me know

Answer: The relationship between the area of rectangle and area of parallelogram is that they both are equal in area.

Step-by-step explanation:

parallelogram is formed when two parallel lines intersects other two parallel lines and rectangle is a type of parallelogram in which the intersecting lines intersects at right angle.

rectangle and parallelogram shares the same property and If we consider same base and same parallel lines then the area of parallelograms formed is always equal and as I mentioned above rectangle is also a parallelogram.

hence area of rectangle is equal to the area of parallelogram in same base and same parallel lines.

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Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;

f(x) = √x

g(x) = -√9(x - 1) + 2

[tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]

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We raise the fraction to the power of 4/3.

To evaluate the expression:

\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3},

we can simplify each term within the parentheses before multiplying them together.

Let's simplify each term step by step:

\left( \frac{16}{9} \right)^{2/3}:

To simplify this term, we raise the fraction to the power of 2/3.

\left( \frac{16}{9} \right)^{2/3} = \left( \left( \frac{2^4}{3^2} \right)^{1/3} \right)^2 = \left( \frac{2^{4 \cdot 1}}{3^{2 \cdot 1}} \right)^2 = \left( \frac{2^4}{3^2} \right)^2 = \left( \frac{16}{9} \right)^2 = \frac{16^2}{9^2} = \frac{256}{81}

\left( \frac{4}{3} \right)^{4/3}:

Similarly, we raise the fraction to the power of 4/3.

\left( \frac{4}{3} \right)^{4/3} = \left( \left( \frac{2^2}{3^1} \right)^{1/3} \right)^4 = \left( \frac{2^{2 \cdot 1}}{3^{1 \cdot 1}} \right)^4 = \left( \frac{2^2}{3^1} \right)^4 = \left( \frac{4}{3} \right)^4 = \frac{4^4}{3^4} = \frac{256}{81}

\left( \frac{9}{16} \right)^{2/3}:

We raise the fraction to the power of 2/3.

\left( \frac{9}{16} \right)^{2/3} = \left( \left( \frac{3^2}{2^4} \right)^{1/3} \right)^2 = \left( \frac{3^{2 \cdot 1}}{2^{4 \cdot 1}} \right)^2 = \left( \frac{3^2}{2^4} \right)^2 = \left( \frac{9}{16} \right)^2 = \frac{9^2}{16^2} = \frac{81}{256}

\left( \frac{3}{4} \right)^{4/3}:

We raise the fraction to the power of 4/3.

\left( \frac{3}{4} \right)^{4/3} = \left( \left( \frac{3^1}{2^2} \right)^{1/3} \right)^4 = \left( \frac{3^{1 \cdot 1}}{2^{2 \cdot 1}} \right)^4 = \left( \frac{3^1}{2^2} \right)^4 = \left( \frac{3}{4} \right)^4 = \frac{3^4}{4^4} = \frac{81}{256

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The exponential function model is y = (0.85[tex])^{t/12[/tex].

We know, The form of the function should be

y= a bˣ

Where, A should be the initial amount and b decrease rate.

Now, y = [tex]b^{t/12}[/tex]

So, the value of base be

= (100 - 15) / 100

= 0.85

Then, the function should be y = (0.85[tex])^{t/12[/tex]

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The equivalent radian to 300 degree is 5π/3.

The given angle measures 300 degree.

We know that, formula used to convert degrees is Radians = Degrees × π / 180

Here, Radians = 300×π/180

= 30 ×π/18

= 10π/6

= 5π/3

Therefore, the equivalent radian to 300 degree is 5π/3.

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Direct Materials Purchases Budget  is given by,

Rubber Steel

Expected production 3,718,000 lb. 590,000 lb.

Desired ending inventory 62,000 lb. 13,000 lb.

Total required 3,780,000 lb. 603,000 lb.

Less: Beginning inventory (73,000 lb.) (11,000 lb.)

Total to be purchased 3,707,000 lb. 592,000 lb.

Unit price $2.90/lb. $3.80/lb.

Total cost $10,749,300 $2,249,600

To prepare a direct materials purchases budget for Solid Grip Company,

The amount of rubber and steel belts needed for the production of 66,000 passenger car tires and 20,000 truck tires.

The desired ending inventories and estimated beginning inventories for each material.

First, let us calculate the amount of rubber and steel belts required for the production of passenger car and truck tires.

Passenger car tires,

Rubber,

66,000 tires x 33 lb. per unit = 2,178,000 lb.

Steel belts,

66,000 tires x 5 lb. per unit = 330,000 lb.

Truck tires,

Rubber,

20,000 tires x 77 lb. per unit = 1,540,000 lb.

Steel belts,

20,000 tires x 13 lb. per unit = 260,000 lb.

Next, let us calculate the total amount of rubber and steel belts needed for production.

Rubber,

2,178,000 lb. + 1,540,000 lb. = 3,718,000 lb.

Steel belts,

330,000 lb. + 260,000 lb. = 590,000 lb.

To calculate the total amount of rubber and steel belts required for purchase,

Add the desired ending inventories and subtract the estimated beginning inventories,

Rubber,

3,718,000 lb. + 62,000 lb. - 73,000 lb. = 3,707,000 lb.

Steel belts,

590,000 lb. + 13,000 lb. - 11,000 lb. = 592,000 lb.

Finally, calculate the total cost of rubber and steel belt purchases.

Rubber,

3,707,000 lb. x $2.90 per pound = $10,749,300

Steel belts,

592,000 lb. x $3.80 per pound = $2,249,600

Therefore, the direct materials purchases budget for Solid Grip Company for the year ended December 31, 20Y8 is as follows,

Direct Materials Purchases Budget

Rubber Steel

Expected production 3,718,000 lb. 590,000 lb.

Desired ending inventory 62,000 lb. 13,000 lb.

Total required 3,780,000 lb. 603,000 lb.

Less: Beginning inventory (73,000 lb.) (11,000 lb.)

Total to be purchased 3,707,000 lb. 592,000 lb.

Unit price $2.90/lb. $3.80/lb.

Total cost $10,749,300 $2,249,600

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The solution to the given expression by using distributive law is 114

The distributive property posits that an expression that is provided in the form of A (B + C) can be further expressed as A × (B + C) = AB + AC. This distributive law is also useful for subtraction and is expressed as, A (B - C) = AB - AC. This implies that operand A is distributed between the other two operands.

From the given information, we are to expand 19 × 6 using the distributive law. The first step would be to expand 19 into two integers.

Let the two integers be 10 and 9.

So, we can have can express this by using the addition distributive law: A(B+ C)

Mathematically, we have:

= 6(10 + 9)

= 6(19)

= 114

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10 times will the smaller gear turn.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Since the smaller gear has 10 teeth and the bigger gear 20, the smaller gear will turn twice for every rotation of the larger gear (20/10=2).

Therefore, if the larger gear rotates five times, the smaller gear will rotate two times five times, or ten times. The smaller gear will thus rotate 10 times.

So, if the bigger gear turns around 5 times, the smaller gear will turn around 5 x 2 = 10 times.

Therefore, the smaller gear will turn 10 times.

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Robert can make a maximum of 8 milkshakes with the remaining chocolate syrup.

Converting the mixed number 2 2/5 to an improper fraction: 2 2/5 = 12/5

Subtracting the amount of chocolate syrup used per milkshake from the total amount of chocolate syrup:

12/5 - 1/4 = (48 - 5) / 20 = 43/20

Therefore, Robert has 43/20 cups of chocolate syrup left, which is the maximum amount he can use to make milkshakes.

For maximum number of milkshakes:

(43/20) / (1/4) = (43/20) x (4/1) = 172/20 = 8.6

Since Robert cannot make a fraction of a milkshake, he can make a maximum of 8 milkshakes with the remaining chocolate syrup.

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6a7

Step-by-step explanation:

To simplify the expression (2a³) (3a4), you can use the laws of exponents. First, you can multiply the coefficients 2 and 3 to get 6. Then, you can add the exponents of 'a' which gives you a total of 3+4=7. Therefore, the simplified expression is 6a7. It does not have any negative exponents, and it represents the product of two expressions with the same base 'a' and coefficient multiplication.

Answer: 6a7

Step-by-step explanation: Got this right b4.

The order of steps of constructing an inscribed circle of a triangle:

Commence the process by sketching a line that cuts one angle of the triangle in two and intersects the opposing side at some point. Through this action, a pair of miniature triangles with congruent figures materialize.

Subsequently, draft an additional bisector for another angle of the triangle. The second dividing line needs to meet the side opposite to the situated angle at a specific location.

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Compared to Monday, Gordon ran for an additional 15 minutes on Wednesday.

Let x be the number of additional minutes Gordon ran on Wednesday compared to Monday. Then, we can write an equation based on the given information:

43 minutes (Wednesday) = 28 minutes (Monday) + x minutes (additional time on Wednesday)

To solve for x, we can isolate it on one side of the equation:

43 minutes - 28 minutes = x minutes

15 minutes = x

Therefore, Gordon ran 15 more minutes on Wednesday compared to Monday.

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Answer:D

Step-by-step explanation:

got it right

35 16 oz jars and 47 28 oz jars of peanut butter were donated to the food bank by solving equation

Let x be the number of 16 oz jars of peanut butter collected, and y be the number of 28 oz jars of peanut butter collected.

The system of equations that represents the constraints in this situation is:

x + y = 82 (total number of jars collected)

16x + 28y = 1876 (total amount of peanut butter collected in ounces)

b. To solve for the number of 16 oz jars and 28 oz jars of peanut butter donated to the food bank

we need to solve the system of equations from part (a). One way to do this is to use elimination:

Multiplying the first equation by 16, we get:

16x + 16y = 1312

Subtracting this equation from the second equation, we get:

12y = 564

Dividing both sides by 12, we get:

y = 47

Substituting this value of y into the first equation, we get:

x + 47 = 82

Subtracting 47 from both sides, we get:

x = 35

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