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4 years ago

Use the substitution to solve the system of equations y= -2xx-3y=21

Mathematics

1 answer:

vovikov84 [41]4 years ago

3 0

<span>y= -2x
x-3y=21

x - 3(-2x) = 21
x + 6x = 21
7x = 21
x = 21/7
x = 3

</span>y= -2x
y = -2*3
y = -6

(3, -6)

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Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the

LiRa [457]

Answer:

option d.

Step-by-step explanation:

We have the following set of data:

x 0 1 2 3 4

f (x) 18 14 10 6 2

Let's assume the function is linear, then, the equation of the line would ne:

(y - y0) = m(x-x0)

where m= (y1-y0) / (x1-x0)

And (x1, y1) = (1, 14)

(x0, y0) = (0, 18)

You can choose any of the points given in the set of data.

Then,

m = (14-18)/(1-0) = -4.

Then the equation of the line is:

(y - 18) = -4x

y = -4x + 18.

If the function is linear, then all the points given in the set of data will satisfy the function. Let's try:

(2, 10):

10 = -4(2) + 18.

10 = 10

SATISFIES THE EQUATION

(3, 6):

6 = -4(3) + 18.

6 = 6

SATISFIES THE EQUATION

(4, 2)

2 = -4(4) + 18.

6 = 6

SATISFIES THE EQUATION

So, the function is linear. And the correct option is option d.

5 0

3 years ago

An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartr

Basile [38]

Answer / Step-by-step explanation:

In this exercise, we know that the agency collected 1,829 bullets which according to the agency, all came from different source.

The number of pair of bullet is :

(1,829) = 1, 829 ! / 2! ( 1,829 - 2 ) = 1, 829 x 1,828 x 1827 ! / 2 x 1 x 1,827

( 2 )

= 6, 108,413,724 / 3654

= 1671,706.

Also, we know that the agency found 658 matches. According to this, the chance of false positive ( that is, the agencies find a match but the bullets are from two different source ) is

P (False positive ) = 658 / 671,706

= 0.000979.

The probability is small to an extent, therefore, we should have confidence in the agency forensic report and evidence

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4 years ago

2 and 2/5 divided by 1 and 1/2 =

storchak [24]

Answer:

1.6 2 and 2/5 divided by 1 and 1/2 =1.6

Step-by-step explanation:

6 0

3 years ago

Simplify the expression.<br> 3 (15- 3)² - 4 ]

Jet001 [13]

Answer:

428.

Step-by-step explanation:

Work is in picture

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3 years ago

HELP ASAP<br> PLZ ITS URGENT

Radda [10]

Answer:

It landed at a height of 14 feet

Step-by-step explanation:

Given

$y = -\frac{1}{8}x^2 +4x$ --- Path of a t-shirt

$3y = 2x - 14$ --- height of bleachers

Required

Height when t-shirts land in bleachers

$3y = 2x - 14$

Make y the subject

$y = \frac{2}{3}x - \frac{14}{3}$

Substitute $y = \frac{2}{3}x - \frac{14}{3}$ in $y = -\frac{1}{8}x^2 +4x$

$\frac{2}{3}x - \frac{14}{3} = -\frac{1}{8}x^2 +4x$

Multiply through by 24

$16x- 112 = -3x^2 +96x$

Express as:

$3x^2 + 16x -96x- 112 = 0$

$3x^2 -80x- 112 = 0$

Using a calculator:

$x = 28$ or $x = -\frac{4}{3}$

x can not be negative:

So:

$x = 28$

Substitute $x = 28$ in $y = -\frac{1}{8}x^2 +4x$ to calculate the height it landed

$y = -\frac{1}{8} * 28^2 + 4 * 28$

$y = 14$

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3 years ago