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1 year ago

Solve by completing the square: x^2+18x+45=0

Mathematics

1 answer:

MrRa [10]1 year ago

5 0

Answer:

x = -3 , - 15

Step-by-step explanation:

Given:

x² + 18x + 45 = 0

Solve:

$x_{1,\:2}=\frac{-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45}}{2\cdot \:1}$

Simplify

$-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45=12$

$x_{1,\:2}=\frac{-18\pm \:12}{2\cdot \:1}$

Separate the solution

$x_1=\frac{-18+12}{2\cdot \:1},\:x_2=\frac{-18-12}{2\cdot \:1}$

$x_1=\frac{-18+12}{2\cdot \:1}=-3$

$x_2=\frac{-18-12}{2\cdot \:1}=-15$

Thus, the answer are:

$x=-3,\:x=-15$

Kavinsky

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Harlamova29_29 [7]

For this case we have:

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3 years ago

A certain ferry moves up and down a river between Town A and

Blizzard [7]

Answer: 60 miles

Step-by-step explanation:

Given

It takes ferry 2 hours to travel to town A and only $1.5\ hr$ to travel back to town B.

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Suppose the speed of the ferry is $v$ mph

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$\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph$

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2 years ago

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The experimental research has two key advantages over correlational studies.

1. The possibility of random assignment

2. Causal connections can be assumed.

<h3>What benefit does experimental research have over correlational research?</h3>

Correlational studies merely examine the data that already exists, whereas experimental studies give the researcher the opportunity to influence the study's factors. Researchers can make inferences about how changes in one variable affect changes in another through the use of experimental investigations.

The factors in a correlation study are out of the control of the researcher or research team. The researcher merely measures the information she discovers in the outside world. She can then determine whether changes in one are related to changes in the other, or if the two variables are correlated. In such a study, experimenters gather existing data and use statistical methods to examine it, such as economic statistics from governments. The findings of correlation studies can lead to hypotheses that can be verified through a more focused experimental one.

To learn more about correlational research visit:

brainly.com/question/14375687

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1 year ago

The line AB has midpoint (2,5). A has coordinates (1, 2). Find the coordinates of B.

Gekata [30.6K]

Answer:

$X_m = \frac{A_x +B_x}{2}= \frac{1+B_x}{2}= 2$

And we can solve for $B_x$ and we got:

$1+B_x = 4$

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And we can solve for $B_x$ and we got:

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$B_y = 8$

So then the coordinates for B are (3,8)

Step-by-step explanation:

For this case we know that the midpoint for the segment AB is (2,5)

And we know that the coordinates of A are (1,2)

We know that for a given segment the formulas in order to find the midpoint are given by:

$X_m = \frac{A_x +B_x}{2}= \frac{1+B_x}{2}= 2$

And we can solve for $B_x$ and we got:

$1+B_x = 4$

$B_x = 3$

$Y_m = \frac{A_y +B_y}{2}= \frac{2+B_y}{2}= 5$

And we can solve for $B_x$ and we got:

$2+B_y = 10$

$B_y = 8$

So then the coordinates for B are (3,8)

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