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25x - 5y= 30

- 25x + 10y=15

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-5y-(+10y)=30-15

-5y-10y =15

-15y= 15

divide both sides by -15

y= -1

finding the value of x by subs. y=-1

into equation 1

5x-(-1)=6

5x +1=6

5x=6-1

5x=5

divide both sides by 5

x= 1

The length of the rectangular table cloth  is [tex]\mathbf{ 3\dfrac{1}{3} m}[/tex]

A rectangle is a plane figure that has an equal size of the opposite side. These sides are called the length and the width.

Mathematically;

The area of the rectangle = Length × width

From the parameters given:

Using the formula for the area of a rectangle, we have:

[tex]\mathbf{4 \dfrac{1}{6} m^2 =length \times 1 \dfrac{1}{4} \ m }[/tex]

[tex]\mathbf{ \dfrac{25}{6} m^2 =length \times \dfrac{5}{4} \ m }[/tex]

Multiply both sides by [tex]\mathbf{\dfrac{4}{5}\times \dfrac{1} {m}}[/tex]; we have:

[tex]\mathbf{ \dfrac{25}{6} m^2 \times \mathbf{\dfrac{4}{5}\times \dfrac{1} {m}} =length \times \dfrac{5}{4} \ m \times \mathbf{\dfrac{4}{5}\times \dfrac{1} {m}}}[/tex]

[tex]\mathbf{ length = \dfrac{25}{6} m \times \mathbf{\dfrac{4}{5}} }[/tex]

[tex]\mathbf{ length = \dfrac{5}{3} m \times \mathbf{\dfrac{2}{1}} }[/tex]

[tex]\mathbf{ length = \dfrac{10}{3} m}[/tex]

[tex]\mathbf{ length = 3\dfrac{1}{3} m}[/tex]

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Step-by-step explanation:

let the given ages be 2x , 4x and 5x.

Here,

2x + 4x +5x =33

or,x = 33/ 11

or,x =3

Hence,

2x =2 (3)=6years

4x=4(3)=12years

5x=5(3)=15years

Answer:

6,12,15

Step-by-step explanation:

Let the ages be 2x,4x,5x

Given

2x+4x+5x=33

11x=33

x=3.

2x=2×3=6

4x=4×3=12

5x=5×3=15

The elevator travels 4/3 levels per second, or floors per second.

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.

Given, an elevator traveled from the 10th floor to the 2nd floor in 6 seconds.

Elevator cover total distance = 10 -2 = 8 floors

since it took elevator 6 seconds

thus

elevator travels in 6 seconds = 8 floor

elevator travels in 1 seconds = 8/6 =4/3  floor

Therefore, the rate of the elevator in floors per second is 4/3 floor per seconds

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Percent means per 100 so 40% 40 per 100, or simply 40/100

When we divide 40 by 100 we get 0.4 which is a decimal number.

to convert from percent to decimal you have to divide by 100, and then remove the % sign.

3 gallons cost 10.50

20 gallons / 3 = 6 2/3

6 2/3 * 10.50 = 70

 they need $70 for the trip

To compare the rates of travel of a race car and a small jet, divide the distance traveled by the time taken for each. The small jet travels at a faster rate than the race car.

To determine which travels at a faster rate, we need to compare their rates of travel. The rate of travel is found by dividing the distance traveled by the time taken. Let's denote the rate of the race car as 'r1' and the rate of the small jet as 'r2'.

For the race car, we have r1 = 615 miles / 3 hours = 205 miles per hour.

For the small jet, we have r2 = 575 miles / 2.5 hours = 230 miles per hour.

Comparing the rates, we see that the small jet travels at a faster rate than the race car.

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125 three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters.

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected.

We need to find  three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters.

The given letters are FGHIJ.

As we need to find three letter words.

This can be done by using 5³ as the repetitions are allowed.

Five power cube number of three words can be formed.

5×5×5

One hundred twenty five.

125

Hence, 125 three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters.

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Answer:

△NPK≅△HBG; and △KNP≅△GHB

Explanation:

Using the given congruence statement, we can determine corresponding pieces of the triangles:

P corresponds to B; K corresponds to G; and N corresponds to H.

This means that △NKP≅△HGB, not HBG.

△KPN≅△GBH, not BHG.

△NPK≅△HBG; this is correct.

△KNP≅△GHB; this is correct.

Answer: k12 answers have a nice day!!!

Step-by-step explanation:

Answer:

The factors of the expression are 6/7, c and d.

Step-by-step explanation:

The given expression is

[tex]\frac{6}{7}cd[/tex]

We need to find the factors of the expression.

Factors: Numbers and variables multiplied to get an expression, then these numbers and variables are known as factors.

The factor form of given expression is

[tex]\frac{6}{7}cd=\frac{6}{7}\times c\times d[/tex]

Therefore, the factors of the expression are 6/7, c and d.

Answer:

The total distance is 41/9 = 4 5/9 miles

Step-by-step explanation:

Total time is 2 1/2 hours.  

First hour, he walks 1 2/3 = 5/3 miles.

Second hour, he walks 1 3/4 = 7/4 miles.

The last half hour he walks 1/4 of total distance. If we call total distance x.

[tex]\frac{5}{3} + \frac{7}{4} +\frac{x}{4} = x[/tex]

Now, we can eliminate the denominator, multiplying by four and by three.  

[tex]5*4 + 7*3 + 3*x = 4*3*x\\20 + 21 + 3x = 12 x\\41 +3x = 12x \\41 = 12x - 3x\\41 = 9x\\x = 41/9\\x = 4 \frac{5}{9}[/tex]

Total distance is 4 5/9 miles