A rancher is filling a trough for her horses. The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. How long will it take for the trough to have 80 gallons of water?

Four conditions of congruency are: SSS, ASA, SAS, RHS

Using SSS congruency,

Side: PS = PQ (by the rule, all sides of rhombus are equal)

Side: ST = TQ (by the rule, diagonals bisect each other)

Side: PT = PT (common)

Therefore, Area(PQT) = Area(PST) by SSS congruency

Using ASA congruency,

Angle: ∠TPS = ∠TPQ (diagonals bisect the angles)

Side: PS = PQ (by the rule, all sides of rhombus are equal)

Angle: ∠PST = ∠PQT (opposite angles are equal, and diagonals bisect the angles)

Therefore, Area(PQT) = Area(PST) by ASA congruency

Using SAS congruency,

Side: ST = TQ (by the rule, diagonals bisect each other)

Angle: ∠PTS = ∠PTQ (by the rule, diagonals bisect each other at 90°)

Side: PT = PT (common)

Therefore, Area(PQT) = Area(PST) by SAS congruency.

Using RHS congruency,

Right angle: ∠PTS = ∠PTQ (diagonals bisect each other at 90°)

Hypotenuse: PS = PQ (all sides of rhombus are equal)

Corresponding Side: ST = TQ (by the rule, diagonals bisect each other)

Therefore, Area(PQT) = Area(PST) by RHS congruency

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The equation of the line perpendicular to the given line will be equal to 5y = x - 3.

A line may be defined as a straight figure which is drawn and has no end points. The equation of line in slope intercept form may be written as y = mx + c where m is the slope and c is the y intercept. The equation of line passing through a point (x₁, y₂) will be given as (y - y₁) = m(x - x₁). The slope of line perpendicular to a line having slope m is given by -1/m. The equation of line in the question is y = -5x + 1. The slope of the line is -5. The slope of line perpendicular to this line is 1/5. Equation of line passing through (2, -1) and slope 1/5 is given by

(y + 1) = 1/5(x - 2)

5y + 1 = x -2

5y = x - 3 which is the required equation.

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Answer:

15

Step-by-step explanation:

Supposing:

Coloured marbles = x

Glass marbles = y

According to Question

x = 3y

As,

x + y = 60

3y + y = 60 (putting value of x = 3y)

4y = 60

y = 60/4

y = 15

Hence, Leo has 15 Clear-glass marbles

To paint the circular table top Beth need to buy 2 cans of paint .

In the question ,

it is given that ,

the radius of the circular table top is = 3 feet

So , the area of the circular table top is = π*r² = π*(3)²

= 9π

= 28.26

also given that

area covered by 1 small can of paint = 15 sq. feet

So , the number of cans needed to paint the table top is = (area of table top)/(area covered by 1 small can of paint)

On substituting the values , we get

number of cans needed to paint the table top is = 28.26/15

= 1.884

≈ 2

Therefore , To paint the circular table top Beth need to buy 2 cans of paint  .

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The speed for maximum car mileage will be 48 mph. The maximum gas mileage will be 29.5 mpg.

We are provided with an equation for mileage of car as

m(x) =  -0.028x² + 2.688x  -35.012

here , variable 'x' is the speed of the car.

Now

for the maximum speed of the car we have to first take the derivative of m(x) and then for the boundary value condition by  putting the derivative equal to zero.

comparing to the equation  ax² + bx + c , if the value of

'a' is positive, then we have minimum value at 1st derivative = 0

'a' is negative we have maximum value .

in this case a = -0.028 ( -ve) so we will have a maxima at 1st derivative.

so, dm/dx = -0.056x + 2.688

putting the 1st derivative = 0 , we have

x = 48

therefore , car gets maximum gas mileage at speed of 48 mph.

Also , putting this value in equation (1) we will get max. mileage.

so max. mileage = -0.028 (48)² + 2.688 x 48 - 35.012

                           = -64.512 + 129.024 - 35.012

                           = 29.5

so the maximum gas mileage will be 29.5 mpg .

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Answer:

Hope the picture will help you

Answer:

2.718

Step-by-step explanation:

let x = .027^2/3

x=.027^.67

applying natural log on both sides

lnx = ln.027^.67

lnx = .67ln.027

lnx = 2.42004

applying antilog on both sides

x = e^2.42004

x = 2.718

thus, .027^2/3 = 2.718

The difference between the areas of the posters is 56 in².

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square, all angles are 90° and all sides present the same value.

The area of a square is given by: A= a², where  a=the length of the side.

         A=(13 in)²

         A= 169 in²

         A=(15 in)²

         A= 225 in²

Therefore, the difference in square inches between the area of Latrice's poster and the area of Nura's poster is 225 - 169=56 in²

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Kelly gets 38.59 miles per gallon of gasoline

Miles drove by Kelly = 238 miles

Gasoline used by the car = 6 1/6 gallons

Gasoline used in the car in improper fraction = 37/6 gallons

Average fuel economy: Average fuel economy of a car gives the distance covered by the car in one gallon of gasoline. This is an important factor to consider while buying or using a car as it is a major source of expenditure for the car.

To calculate miles per gallon we use the following formula:

Miles per gallon = Miles driven/ Gasoline used in the car

= 238/(37/6)

= 238*6/37

= 38.59

Miles per gallon = 38.59

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The exponential function y = 60(1.2)7 yields the number of patents in 1998.

The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis. Let y be the number of nanotechnology-related patents issued in the US in year x following 1991.

There were 60 patents on nanotechnology in 1991, and since then there has been a factor of 1.2 increase.

y = 60(1.2)ˣ

y = 60 in 1998 (7 years ago) (1.2)⁷

The exponential function is used to calculate the number of patents in 1998.

y=60(1.2)⁷

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Answer:

-2/5

Step-by-step explanation:

m = (10 - 8)/(31 - 36) = 2/(-5) = -2/5

Answer:

22.5

Step-by-step explanation:

we can use the ratios to turn x+y+z=180 to x+4x+3x= 180

then solve for 180

x = 22.5

Answer: D.) 22.5°

Have a nice day!

Answer:

f(x) = 1/7 * (x + 7)^2 - 2

axis of symmetry: x = -7

vertex: (-7 | -2)

Step-by-step explanation:

f(x) = 1/7 * (x^2 + 14x + 35)

f(x) = 1/7 * (x^2 + 14x) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 7^2) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 49) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2) + 5 - 7

f(x) = 1/7 * (x + 7)^2 + 5 - 7

f(x) = 1/7 * (x + 7)^2 - 2

Answer:

Slope = 1/2 or 0.5

Step-by-step explanation:

Picking two integer points on the line, (any)

(-3, 2) and (-1, 3)

We can find the slope

(3-2)/(-1-(-3)

=1/2

:]

Answer:

Step-by-step explanation:

Student A:

Mean 80.8

Median: 85.5

The Median is a higher score.

Student B:

Mean 82.7

Median: 79.5

Mean is a higher score

Answer:

Student A's median and Student B's mean would result in the highest grade.

Step-by-step explanation:

How to find the mean:

The mean is the average.

Therefore, you must add all numbers listed, then divide the added numbers by the amount of numbers you added together. Lastly, as instructed round to the nearest whole number.

- Student A : Mean = 81

Step 1 : 25+78+80+82+85+86+88+89+96+99 = 808

Step 2: 808 ÷ 10 = 80.8

Step 3: 80.8 ---> 81

- Student B: Mean = 83

Step 1: 71+77+77+79+79+80+88+89+91+96 = 827

Step 2: 827 ÷ 10 = 82.7

Step 3: 82.7 ---> 83

How to find the median:

The median is the middle number in a sorted list of numbers.

Therefore, you list all of the numbers from least to greatest. Then, you get rid of a number from each side until you finally get to the center number. If there are two numbers left in the center you then find the mean(average) of those numbers.

- Student A: Median = 86

Step 1: Knock off a number from each side until you reach the center number(s)

25, 78, 80, 82, 85, 86, 88, 89, 96, 99 ---> 85, 86

Step 2: Find the mean(average) of the two central numbers

85 + 86 = 171 ---> 171 ÷ 2 = 85.5

Step 3: Round your answer

85.5 ---> 86

- Student B: Median = 80

Step1: Knock off a number from each side until you reach the center number(s)

71, 77, 77, 79, 79, 80, 88, 89, 91, 96 ---> 79, 80

Step 2: Find the mean(average) of the two central numbers

79 + 80 ---> 159 ÷ 2 = 79.5

Step 3: Round your answer

79.5 ---> 80

Answer: have you tried m a t h w a y

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

each term inside the parenthesis is raised to the exponent outsie, that is

(2xy)³

= 2³ × x³ × y³ ← 2³ = 2 × 2 × 2 = 4 × 2 = 8

= 8x³y³

Answer:

-1/420

Step-by-step explanation:

-4/7/12/20

= -1/21/20

= -1/420

Answer: 1 1/2 in a hour

Step-by-step explanation:

1/2 every 1/3 so if we add one more half it is 1 and 2/3 the last one is 1 1/2 is 1 full hour.

Answer:

I'm thinking it's 22, but I could be wrong.

Step-by-step explanation:

Answer:

k=3/10

Step-by-step explanation:

8y=12x+6 >>>>(÷8) both sides

y= (3/2)x+(3/4)

if x=0, y=3/4

4y=k(3x+10) >>> plug in (0, 3/4)

4(3/4)= k(0+10)

3= 10k >>> (÷10) both sides

k=3/10

Answer:

Yes! The painting is similar.

Step-by-step explanation:

The sides of the original painting are 30 and 21. If you divide this by 3, it equals 10 and 7 which are the sides of the print. This means that the ratio is right so the paintings are similar.

The type of pay which is modeled in the image attached below is: D) piece rate.

Money or something paid for a purpose and especially as a salary or wage

The types of pay.

In Mathematics, there are four 5) different types of pay and these include:

The different types of compensation include:

Salary.

Hourly Wages.

Sales Commission.

Tips.

Stock Options.

Bonuses.

Incentive Pay.

Other Variable Pay.

Salary

Commission

Bonuses

Piece rate

Method of wage payment that remunerates the employees on the basis of quantity they produced is known as piece rate.

Plucking tea

The number of tee-shirts produced.

Pruning fruit trees

Sorting second-hand clothes (garments)

Hence the graph of a piece rate model is characterized by a straight line with the slope upwards as represented in the image attached.

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Answer:

4.5

Step-by-step explanation:

The answer is

x = 7, -7, √2, -√2

Add the two equations to get

x2 + y2 = 74

Eliminate y from the first by solving for y and using that result:

(x2 − 14) = x√74 - x2

square both sides, then condense:

x4 − 51x2 + 98 = 0

These ready factors:

(x−7)(x+7)(x−√2)(x+√2)=0

I'll let you handle it from there, but keep in mind that if we square all sides, we might find roots that need to be pulled out afterward.

Therefore,

x = 7, -7, √2, -√2

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Scaled copy of the polygon with scale factor 3 is given below.

A polygon is a closed polygonal chain made up of a finite number of straight line segments and is a type of planar figure in geometry. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.

A polygonal circuit's segments are referred to as its edges or sides. A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end.

Polygons include shapes like triangles, quadrilaterals, pentagons, and hexagons. The shape's number of sides is indicated by the name. A quadrilateral has four sides, whereas a triangle has three.

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The integers that are closest to the number in the middle will be 89 < 90 < 91.

It should be noted that an integer simply means a whole number that can be positive, negative, or zero.

It should be noted that on this case, we have to look for the numbers that are closest to 90 one has to be less than 90 and the other one should be greater than it.

Therefore, the numbers that fits the information will be 89 and 91.

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Answer:

(2x + 5)/(x + 4) = 1

and

6x - 19 = 3x - 10

Step-by-step explanation

Linear euqations are the equation for the straight line. When graphed both equations will be straight lines.

Hope this helps you!

The smallest number of kilometers that each must run is 6 kilometers.

From the information, Jim runs 6 kilometers at a time while Maureen prefers to run in blocks of 3 kilometers and at the end of the month, they realize that they have run the same total number of kilometers.

It should be noted that the question simony had to do with finding the least common multiple. This will be:

Multiple of 3 = 3, 6, 9, 12

Multiple of 6 = 6, 12

The least common multiple is 6.

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