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4 years ago

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"Find four numbers proportional to the numbers 2, 4, 5, and 6 if the difference between the sum of the two last numbers and the

sum of the first two numbers is equal to 4.8."

2 answers:

Liono4ka [1.6K]4 years ago

5 0

Answer:

1.92, 3.84, 4.8, 5.76

Step-by-step explanation:

In the given set, the sum of the last two numbers is 5+6 = 11; the sum of the first two numbers is 2+4 = 6. The difference between these sums is 11-6 = 5.

You want to scale all the numbers by a factor of 4.8/5 = 0.96 so that the difference computed the same way is 4.8 instead of 5.

Then the numbers are ...

0.96{2, 4, 5, 6} = {1.92, 3.84, 4.8, 5.76}

Lana71 [14]4 years ago

5 0

Answer:

$\boxed{\text{1.92, 3.84, 4.80, and 5.76}}$

Step-by-step explanation:

The numbers must be in the ratio 2:4:5:6.

Let's call them 2x, 4x, 5x, and 6x. Then

5x + 6x = 11x = sum of last two numbers

2x + 4x = 6x = sum of first two numbers

According to the condition,

11x – 6x = 4.8

5x = 4.8

x = 0.96

2x = 1.92; 4x = 3.84; 5x = 4.80; 6x = 5.76

The numbers are $\boxed{\textbf{1.92, 3.84, 4.80, and 5.76}}$

Check:

(4.80 + 5.76) – (1.92 + 3.84) = 4.8

10.56 – 5.76 = 4.8

4.8 = 4.8

OK.

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x+10=0

Solve.

x-3=0

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3 years ago

A rectangle has a width of 6 inches and a perimeter of 26 inches. What is the length of the rectangle?

labwork [276]

Answer:

Length = 7 inches

Step-by-step explanation:

Perimeter = 2L+2W

Perimeter = 26

W = 6

Plug these in: 26=2L + 2*6 ; 26 = 2L + 12

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3 years ago

If Benito is selecting samples of five values from the table, which row will result in the greatest mean? Population Data Row 1

castortr0y [4]

Row 4

Explanation

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Row 2 - 3+3+4+3+2 = 15 / 5 = 3
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6 0

3 years ago

Read 2 more answers

Two times Antonio’s age plus three times Sarah’s age equals 34. Sarah’s age is also five times Antonio’s age. How old is Sarah?

sergejj [24]

Let Sarah's age be s and Antonio's age be a.

According to your question,

2a + 3s = 34
s = 5a

substituting the value of s in eq. 1,

2a + 3(5a) = 34

= 2a + 15 a = 34

17a = 34

thus, a = 34/17 = 2

substituting the value of a is s,

s = 5(2)
= 10

Thus, Sarah's age is 10 years and Antonio's age is 2 years.

5 0

3 years ago

Katen [24]

Answer:

Q2. (16,8)

Q3. $k=\frac{2}{3}$ , ratio=5:1

Q4. Ratio=2:1

Q5. Ratio=1:1

Step-by-step explanation:

Q2. Let (2a,a) be the coordinates of P.

Since P is equidistant from Q (2,-5) and R (-3, 6), we have

$|PQ|=|PR|$

This gives us:

$\sqrt{(2a-2)^2+(a+5)^2}=\sqrt{(2a+3)^2+(6-a)^2}$

$\implies (2a-2)^2+(a+5)^2=(2a+3)^2+(6-a)^2$

Expand:

$4a^2-8a+4+a^2+10a+25=4a^2+12a+9+a^2 -12a+36$

$2a=16$

$a=8$

The coordinates of P are $(16,8)$

Q.3 The equation of the line segment joining the points

A (5.-6) and B (-1,-4) is $x+3y=-13$ .

The x-coordinate of the point that divides AB in the ratio m:n is

$x=\frac{mx_2+nx_1}{m+n}$

The y-axis meets this line at $(0,-\frac{13}{3})$

We substitute $x_2=-1,x_1=5,x=0$ into this equation and solve for m and n.

$0=\frac{-m+5n}{m+n}$

$m=5n$

$\frac{m}{n}=\frac{5}{1}$

Therefore the ratio is m:n=5:1

Q.4 The equation of the line segment joining

the points (-5,-4) and (-2,3) is $-7x+3y=23$ .

The point (-3, k) must satisfy this line because it lies on it.

$-7(-3)+3k=23$ .

$\implies k=\frac{2}{3}$

We again use the equation $x=\frac{mx_2+nx_1}{m+n}$ to find the given ratio.

Substitute: $x_2=-2,x_1=-5$

$4=\frac{-2m+-5n}{m+n}$

$\implies m=2n$

$\frac{m}{n}= \frac{2}{1}$

The ratio is m:n=2:1

Q. 5 The equation of the line joining A (2,3) and B(6,-3) is $3x+2y=12$ .

We substitute (4,m) to get:

12+4m=12

4m=0

m=0

It is obvious that: (4,0) is the midpoint of A(2,3) and B(6,-3).

Hence the ratio is 1:1

5 0

3 years ago