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2 years ago

If the sum of a number and four is tripled the result is eight less than twice the number

Mathematics

2 answers:

Drupady [299]2 years ago

5 0

Answer:

The number is -20.

Step-by-step explanation:

If x is the number, then 3(x+4)=2x-8.

3x+12=2x-8

x=-20

kiruha [24]2 years ago

4 0

Answer:

- 20

Step-by-step explanation:

if the number if x then 3(X+y 4= 2X-8: 3X+12= 2x-8

x = -20

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A community is building a square garden with a walkway around the perimeter with the design shown at the right. Find the side le

castortr0y [4]

Answer:

x = 17 ft ... ( nearest 10th of a foot )

Step-by-step explanation:

Given:-

- The side length of inner square = x ft

- The side length of outer square = 20 ft

Find:-

Find the side length of the inner square that would make the area of the inner square equal to 75% of the total area of the garden.

Solution:-

- Compute the area of the inner square (A_i) using side length (x):

A_i = side length ^2

A_i = x^2 ft^2

- The area of the entire garden is the area (A_o) of the outer square with side length equal to 20 ft.

A_o = side length ^2

A_o = 20^2

A_o = 400 ft^2

- The 75% of the entire garden is :

(75 / 100)*A_o

(75 / 100)*400

300 ft^2

- The area of the inner square is 75% of the entire garden the mathematical expression for it is:

A_i = 300 ft^2

x^2 = 300 ft^2

- The side length required for the inner square is the solution to the quadratic equation above:

x = √300

x = 17.320508ft.

x = 17 ft ... ( nearest 10th of a foot )

3 0

3 years ago

Read 2 more answers

HELP QUICK 10 POINTS!!!!!!

padilas [110]

$\frac{x}{5}$ = 10 Multiply both sides by 5 to cancel out the fraction
x = 50

5 0

3 years ago

So far this season, Shawn has averaged 4 out of 11 free throws per game. Based on his previous performance, how many free throws

yulyashka [42]

Answer:

Step-by-step explanation:

Multiply 11 by 2 to get to 22; do the same to 4

5 0

2 years ago

The vector (a) is a multiple of the vector (2i +3j) and (b) is a multiple of (2i+5j) The sum (a+b) is a multiple of the vector (

kow [346]

Answer:

$\|a\| = 5\sqrt{13}$ .

$\|b\| = 3\sqrt{29}$ .

Step-by-step explanation:

Let $m$ , $n$ , and $k$ be scalars such that:

$\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}$ .

$\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}$ .

$\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}$ .

The question states that $\| a + b \| = 34$ . In other words:

$k\, \sqrt{8^{2} + 15^{2}} = 34$ .

$k^{2} \, (8^{2} + 15^{2}) = 34^{2}$ .

$289\, k^{2} = 34^{2}$ .

Make use of the fact that $289 = 17^{2}$ whereas $34 = 2 \times 17$ .

$\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}$ .

$k^{2} = 2^{2}$ .

The question also states that the scalar multiple here is positive. Hence, $k = 2$ .

Therefore:

$\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}$ .

$(a + b)$ could also be expressed in terms of $m$ and $n$ :

$\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}$ .

$\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}$ .

Equate the two expressions and solve for $m$ and $n$ :

$\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}$ .

$\begin{cases}m = 5 \\ n = 3\end{cases}$ .

Hence:

$\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}$ .

$\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}$ .

6 0

2 years ago

What is the fraction and decimal of 95%

zhuklara [117]

.95 in decimal form and 95/100 as a fraction or 19/20

7 0

3 years ago

Read 2 more answers