five number are in the ratio 1:2:3:4:5 and the sum is 585.find the numbers​

Answer:

Length is 5, width is 3.

Step-by-step explanation:

The formula for the perimeter of a rectangle is:

[tex]P=2l+2w[/tex]

Where P is the perimeter, l is the length, and w is the width.

With the original length and width, the perimeter is 16, thus:

[tex]16=2l+2w[/tex]

Now, if we double the length, the 2l will become 4l. Also, the perimeter will change to 26. Thus:

[tex]26=4l+2w[/tex]

Now, we have a system of equations. We can solve it using elimination. Multiply everything by -1 in the first equation:

[tex]16=2l+2w\\-16=-2l-2w[/tex]

Now, add the equations:

[tex]-16=-2l-2w\\26=4l+2w[/tex]

-16 plus 26 is 10. -2l plus 4l is 2l. The 2w cancel. Thus:

[tex]10=2l[/tex]

Divide both sides by 2:

[tex]l=5[/tex]

So, the original length was 5.

To find the original width, substitute 5 back into the first equation:

[tex]16=2(5)+2w[/tex]

Multiply:

[tex]16=10+2w[/tex]

Subtract 10 from both sides:

[tex]2w=6[/tex]

Divide both sides by 2:

[tex]w=3[/tex]

So, the original width was 3.

And we're done!

Checking:

Originally, our length was 5 and 3. This means that the perimeter is 2(5+3)=2(8)=16 which is correct.

After we double our length, our length will be 10. This means that the new perimeter is 2(10+3)=2(13)=26. So, our answers are correct!

Let's assume that length be L and width be B.

Perimeter of rectangle is given by,

Perimeter = 2( L + B)

So,

⇒ 16 cm = 2 ( L + B )

⇒ 8cm = L + B _______( Say equation 1)

Now, we are given that when length is doubled perimeter is 26.

So,

⇒ 26 cm = 2 ( 2 L + B )

⇒ 13 cm = 2 L + B

⇒ 13 cm = L + L + B

Now use equation-1

⇒13 cm = L + 8cm

⇒13 cm - 8 cm = L

⇒5 cm = L

Therefore length is 5cm.

Now substitute this value in equation 1

⇒L + B = 8 cm

⇒5cm + B = 8 cm

⇒B = 8 cm - 5 cm

⇒B = 3 cm

Therefore breadth is 3 cm.

Answer:

55

Step-by-step explanation:

The required solution is 40 and after 40days  $10 left for each of the gift card.

It is required to find the solution.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The first equation is 130 - 3x because you start with $130 and subtract 3 for each 30 day period.

The second equation is 110-2.50x

Set them equal to each other:  130 - 3x = 110 - 2.50x

Solve for x:

130 - 3x = 110 - 2.50x

130-110=3x-2.50x

20=0.50x

40 = x

After 30-40 day periods (1200 days), both cards should have equal value.

Card 1 after 40 periods,

=130 - 3(40) = $10 left

Card 2 after 40 periods

=110 - 2.5(40) = $10 left

Therefore, the required solution is 40 and after 40days  $10 left for each of the gift card.

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Answer:

i. $26

ii. $(8 + 3t)

Step-by-step explanation:

Given that: automatic fee is $8, and fee per hour is $3. Then;

i. If he left his car in the lot for 6 hours, amount to be paid can be calculated as thus;

since fee per hour is $3, then for 6 hours; the fee = 6 x $3

                                                                                   = $18

Total amount to be paid after 6 hours = automatic fee + $18

                                                               = $8 + $18

                                                               = $26

For parking his car for 6 hours, he would pay $26

ii. Amount paid for t hours = automatic fee + $ 3 x t

                                                          = $(8 + 3t)

Answer/Step-by-step explanation:

Given the function, [tex] g(z) = 5z + 2.1 [/tex], the table can be completed by substituting the given value of z as follows:

Question 2: z = -7

[tex] g(-7) = 5(-7) + 2.1 [/tex]

[tex] g(-7) = -35 + 2.1 [/tex]

[tex] g(-7) = 32.9 [/tex]

Question 3: z = -8

[tex] g(-7) = 5(-8) + 2.1 [/tex]

[tex] g(-7) = -40 + 2.1 [/tex]

[tex] g(-7) = 37.9 [/tex]

Answer:

t=-3.7

Step-by-step explanation:

5 (t+3)=-3.5

solving the bracket we have;

5t+15=-3.5

collect like terms

5t=-3.5-15

5t=-18.5

divide both sides by 5;

t=-3.7

The value of t in the given algebraic expression is; t = -2.3

We are given the equation;

5(t + 3) = 3.5

Using distributive property on the left hand side, we have;

5t + (5 × 3) = 3.5

5t + 15 = 3.5

Using subtractive property of equality, subtract 15 from both sides to get;

5t + 15 - 15 = 3.5 - 15

5t = -11.5

Divide both sides by 5 to get;

5t/5 = -11.5/5

t = -2.3

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Answer: 11 stickers each

Step-by-step explanation:

given data:

packs of stickers bought by mark = 12 ( 5 ) = 60 stickers

no of stickers left with mark = 27

= Total no of stickers – stickers remaining with mark

= 60 – 27

= 33 stickers

he gave his 3 friends equal number of stickers.

3x = 33

x = 11

number of stickers received by each friend is 11

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

B (4, 6) and K (–6, –2)

The distance is

[tex] |BK| = \sqrt{ ({4 + 6})^{2} + ({6 + 2})^{2} } \\ = \sqrt{ {10}^{2} + {8}^{2} } \: \: \: \: \: \: \: \: \: \\ = \sqrt{100 + 64} \: \: \: \: \: \: \: \: \: \\ = \sqrt{164} \\ = 2 \sqrt{41} \\ = 12.80[/tex]

We have the final answer as

Hope this helps you

GCF = 38

38 = 2×19

76 = 4×19 = 2²×19

114 = 2×3×19

GCF = 2×19 = 38

Answer:

3 divided by 4

Step-by-step explanation:

the slash mark means divided.

Answer:12

Step-by-step explanation:6+(5+1)

5+1=6

6+(6)=12

Answer:

K

Step-by-step explanation:

As per diagram, the intersection of the line JL and plane R is the point K

Correct option is the last one

Answer:

15

Step-by-step explanation:

Answer:

59

Step-by-step explanation:

1. -35

2. +9

3. -23

4. +3

5. +5

6. -7

7. +125

8. -18

Add them all up in a calculator and you get 59

Step-by-step explanation:

for a perpendicular,

make x the subject.

8x=11-3y

x=11/8 +3/8

for a perpendicular, the gradient

x= -1/m

x= (-1/11/8) - (-1/3y/8)

x= 8/3y -8/11.

therefore the gradient (m) = 8/3y -8/11.

Answer:

The opposite of a number is its additive inverse. The sum of a number and its opposite is zero

Step-by-step explanation:

Answer:

- x, 0

Step-by-step explanation:

The opposite of x is - x because they cancel each other out. It doesn't matter what x is because - x and x are the same amount of distance from each other.

The sume of x and its opposite is 0.

Hope This Helps :)

Answer:

See Below

Step-by-step explanation:

[tex]\frac{2}{5} -7[/tex]

First, let's make 7 into an improper fraction

7x5 =35

2/5 - 35/5 = -33/5

Answer:

-3=a

Step-by-step explanation:

-a+4a-9=8a+6

3a-9=8a+6

3a-9-6=8a+6-6

3a-15=8a

3a-3a-15=8a-3a

-15=5a

-15/5=5a/5

-3=a

Answer:

105 cm squared

Step-by-step explanation:

15×6 to get the rectangle =90

then we have a triangle left so you do 15- 9 for the base =6 and multiply that by hight (6×5=30) and since it's a triangle and not a square we have to divide that answer by 2 and we get 15. Add those together, we get 105. Hope that helped!

The area of the shape below is 105 cm².

The area of a rectangle is calculated by multiplying the length and width of the rectangle.

The area of a triangle is equal to half of the product of the triangle's base and height.

Cut the shape given into a triangle and a rectangle as given in the following figure. Then the area of the shape is the sum of the area of the triangle and the area of the rectangle. In the shape, we can clearly specify that the base of the triangle is (15-9) cm=6cm and the height is

(11-6)cm=5cm.

Thus,

The area of the rectangle in the figure is (6×15) cm²=90 cm², and

the area of the triangle in the figure is (1/2)(6×5) cm²=15 cm².

Hence, the area of the shape is 90+15 cm² = 105 cm².

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Answer:

Surface Area would be 200² inches.

Step-by-step explanation:

SA=2(12*9)+2(9*2)+2(12*2)

SA=2(108)+2(18)+2(24)

SA=216+36+48

SA=200² in.

Answer:

0.0045

Step-by-step explanation:

:)

Answer:

i think underroot 29 is a midpoint of this two unit

Answer:

B(-6,7)

mid point (1,5)

Step-by-step explanation:

A=-2,-3  M (-4,2) is the midpoint between A and B

x of M=(xA+xB)/2

-4=-2+xB/2

-4(2)=-2+xB

yM=(yA+yB)/2

2=(-3+yB)/2

2(2)=-3+yB

yB=4+3

midpoint (xa+xb/2 , ya+yb/2)

(-1+3/2 ,4+6/2)

(1,5)

Answer:

-2x^2

Explanation:

=-2*x^2

=-2*(x*x)

=-2x^2

Answer:5 12/25

Step-by-step explanation:

48-24-12

over

100-50-25

Answer:

D'(1, - 1 )

Step-by-step explanation:

Assuming the dilatation is centred at the origin, then multiply the coordinates of D by [tex]\frac{1}{2}[/tex] , that is

D(2, - 2 ) → D'([tex]\frac{1}{2}[/tex] (2) , [tex]\frac{1}{2}[/tex] (- 2) ) → D'(1, - 1 )

Answer:

9:16

Step-by-step explanation:

In a similar rectangle , the ratio of lengths should be equal to ratio of widths.

Ratio of lengths =

[tex] \frac{length \: of \: rectangle \: 1}{length \: of \: rectangle \: 2} = \frac{3}{4} [/tex]

Hence , Ratio of widths =

[tex] \frac{width \: of \: rectangle \: 1}{width \: of \: rectangle \: 2} = \frac{3}{4} [/tex]

Area of rectangle 1 = Length 1 × Width 1 = 3×3 = 9

Area of rectangle 2= Length 2 × Width 2= 4×4= 16

Ratio of areas of both rectangles =

[tex] \frac{area \: of \: rectangle \: 1}{area \: of \: rectangle \: 2 \: } = \: \frac{9}{16} [/tex]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Amount Noah borrowed from his mother = $17

Amount paid = $8

Change in the amount of money Noah's mother has :

Let initial amount her mother has = x

Hence, the amount she has after Noah paid $8 to her will be :

Initial amount - amount borrowed + amount paid

= x - $17 + $8.

The simplified amount = x - $9

The amount Noah still owes :

Total amount owed - amount paid

$17 - $8 = $9

The change in the amount of money that Noah's mother will be $ 9.

Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.

Noah borrowed $17 from his mother. He then paid back $8 of the amount he owed.

Then the amount owed will be given as the difference between the initial amount and paid amount.

→ $ 17 - $ 8

→ $ 9

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