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2 years ago

If x is located at -2 and y is located at -5, find Z such that XY is divided into a 2:1 ratio

Mathematics

1 answer:

DIA [1.3K]2 years ago

5 0

Answer:

z = -4

Step-by-step explanation:

Given :

x = -2
y = -5
z divides xy in the ratio 2 : 1 (m : n)

Solving :

Take the section formula
z = [my + nx] / [m + n]
z = [2 x -5 + 1 x -2] / [2 + 1]
z = -10 - 2 / 3
z = -12 / 3
z = -4

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The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).

garri49 [273]

Answer:

(-1,-6)

Step-by-step explanation:

$f(x)=x^2+6x+3$

$g(x)=f(x-2)$

$g(x)=(x-2)^2+6(x-2)+3$ (Replaced x in f with (x-2))

$g(x)=x^2-4x+4+6x-12+3$ (Used $(x+b)^2=x^2+2bx+b^2$ and distributive property)

$g(x)=x^2-4x+6x+4-12+3$ (Gathered like terms)

$g(x)=x^2+2x-5$ (Simplified)

The vertex of a parabola occurs at $(\frac{-b}{2a},g(\frac{-b}{2a})$ .

Let's find $\frac{-b}{2a}$ first.

$\frac{-2}{2(1)}=-1$

Now we can obtain $g(\frac{-b}{2a})$ which is $g(-1)$ in this case:

$g(x)=x^2+2x-5$

$g(-1)=(-1)^2+2(-1)-5$

$g(-1)=1-2-5$

$g(-1)=-1-5$

$g(-1)=-6$ .

The vertex is (-1,-6).

6 0

3 years ago

The formula for finding the area of a triangle is A = 1/2bh. A triangle has height 12 in. and area 54in^2. What is the length of

KatRina [158]

Answer:

9in

Step-by-step explanation:

54 = 1/2(12*x)

54 = 6*x

x = 9

Check

12 x 9 = 108

108/2 = 54

8 0

2 years ago

What is the least significant place in 0.1030

olchik [2.2K]

<h3>Least Significant Digit Place (LSD)</h3>

The Least Significant Digit Place, or LSD, is the digit with the least value in a string of numbers.

In 0.1030, there are 4 different significant places. 0.1030

For 0.1030, the least valuable digit place is the 0.1030. This is because this numeral appears at the end of the string, and is the least valuable.

5 0

2 years ago

Read 2 more answers

A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $28.75 , with a standard

bulgar [2K]

Answer:

Following are the solution to the given choices:

Step-by-step explanation:

Using chebyshev's theorem :

$\to P(|(x-\mu)|\leq k \sigma)\geq 1- \frac{1}{k^2}\\\\here \\ \to \mu=28.75\\\\ \to \sigma=4.44$

In point a)

$\to |(x-\mu)|= |20.17-28.75|=8.58 and \sigma=4.44 \\\\so, \\k= \frac{ |(x-\mu)| }{\sigma}$

$= \frac{8.58}{4.44} \\\\ =1.9 \\\\ =2$

$value= (1- \frac{1}{k^2}) \times 100 \% =75\%$

In point b)

$\to (1- \frac{1}{k^2}) \times 100 \% =84\% \\\\\to (1- \frac{1}{k^2})=0.84 \\\\\to \frac{1}{k^2} =0.16 \\\\\to \frac{1}{k}=0.4\\\\ \to k=2.5 \\\\\to |(x-\mu)| \leq k \sigma \\\\= |(x-\mu)|\leq 2.5 \times 4.44 \\\\ = |(x-\mu)|\leq 1.11 \\\\ = (28.75\pm 11.1) \\\\\to \text{fares lies between}(17.65,39.85)$