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3 years ago

Find the product and sum of the roots of the equation: 2x^2-9x-10=0

Mathematics

1 answer:

BabaBlast [244]3 years ago

3 0

Answer:

<h3> sum of the roots: $x_1+x_2=4\frac12$ </h3><h3> product of the roots: $x_1x_2=-5$ </h3><h3> Step-by-step explanation:</h3>

$2x^2-9x-10=0\quad\implies\quad a=2\,,\ b=-9\,,\ c=-10$

$b^2-4ac=(-9)^2-4(2)(-10)=81+80=161>0$

From Vieta's formulas applied to quadratic polynomial we have:

if $b^2-4ac\geqslant0$ then

sum of roots: $x_1+x_2=-\dfrac ba=-\dfrac{-9}2=4\frac12$

product of the roots: $x_1x_2=\dfrac ca=\dfrac{-10}2=-5$

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There are 15 rolls of film in a box and 3 are defective. Two rolls are to be selected, one after the other. What is the probabil

dem82 [27]

<h2>Answer:</h2><h2>The probability of selecting a defective roll followed by another defective roll = $\frac{1}{35}$ </h2>

Step-by-step explanation:

The total number of rolls in a box = 15

The number of defective items = 3

Two rolls are to be selected, one after the other. The probability of selecting a defective roll followed by another defective roll = ?

The probability that the first roll is detective = $\frac{3}{15}$

The probability that the second roll is detective = $\frac{2}{14}$

Required probability = $(\frac{3}{15} ) (\frac{2}{14} )$

= $\frac{1}{35}$

7 0

2 years ago

A home is purchased for $60,000 in 2001 and sold for $225,000 in 2021. Plot this on a graph. Then draw 2 lines, 1 mapping a line

astraxan [27]

Answer:

a. 3.6

b Linear

c. 2.13333

Plot a graph going up vertically by amounts 30,000 would be = 1

60,.000 would be = 2, 90,000 would be = 3 etc.

225,000 would show between 7 and 8. where marks of 15/30 = 1/2 would be counted back from 240,000 to 225,000 and between 210,000 to 240,000

After mapping the x rate must be 1 for both linear and for exponential.

The average rate of change is found when 60k = 2 and 225k = 7.5 is increasing and years shown 2001 to 2021 are shown on x axis.

= 20 years

Therefore linear shows 2 when x = 1 then shows 7.5 when x = 20

20/7.5 = 2.6

Therefore, this relationship is linear because each yyy-value is 7.5/20 more than the value before it. The x value goes up by 1 each value of 0.37 for y

When the value is exponential the y value should go up by 1 and as it is 30,000 each 1 value and x =1 goes up 2 2/3 = 2.6667 for every 30.000k to every x value.

A. 2 -2 2/3 = 2.31555.. average rate of change.for exponential and between 3.5 and 3.7 = 3.6 average rate of change for linear.

B linear

C 2008 = 8 YEARS 8/20 X 2 = 0.8

0.8 X 2 2/3= 2.13333333 is the app value of the linear model 2008.

6 0

3 years ago

If 25% of a number is 20, what is 60% of the number

Iteru [2.4K]

Set up a proportion, 20 over 25% and x over 60% and the answer is 48

7 0

3 years ago

Read 2 more answers

Only the function represented by graph has an inverse function.

Arlecino [84]

Answer:

Only the function represented by graph 2 has an inverse function

Step-by-step explanation:

* Lets explain the inverse of the function

- The Function is a relation between x-coordinates and the y-

coordinates of the order pairs under the condition every

x-coordinate has only one y-coordinate

- Ex: R = {(2 , 3) , (1 , 5) , (-2 , -3)} is a function because every x-

coordinate has only one y-coordinate and R = {(2 , 3) , (-1 , 4) ,

(2 , 5)} not a function because the x-coordinate 2 has two y-

coordinates 3 and 5

- We use the vertical line to test the graph is function or not, if

the vertical line intersects the graph in one point then the

graph is function if intersects it in more than one point then the

graph is not function

- We have two types of function one-to-one function and

many-to-one function

# one-to-one function means every x-coordinate has only 1 y-coordinate

# many-to-one function means some x-coordinates have only 1

y-coordinate

- We find the inverse function by switching x and y, then one-to-

one function has inverse but many-to-one has not inverse

because when we switched x and y it will be one-to-many

means one x-coordinate has many y-coordinates and this is not

a function

- We use the horizontal line to test the graph of the function has

inverse or not, if the horizontal line intersects the graph in one

point then the function of the graph has inverse if it intersects

the graph in more than one point ,then the function of the

graph has no inverse

* Now lets test all the graphs by using the horizontal line

# graph 1

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 1 has no inverse

# graph 2

∵ The horizontal line cuts the graph in just 1 point

∴ The function of graph 2 has inverse

# graph 3

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 3 has no inverse

# graph 4

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 4 has no inverse

* Only the function represented by graph 2 has an inverse function

4 0

3 years ago

What is the slope of a line that is parallel to the line represented by the equation 3x+4y=12?

mash [69]

Slope-intercept form is:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0)

(there is probably another way to do this, but I will be doing it this way)

Isolate the "y" in the equation

3x + 4y = 12 Subtract 3x on both sides

4y = 12 - 3x Divide 4 on both sides

$y=3-\frac{3}{4}x$ or $y=-\frac{3}{4} x+3$ The slope is -3/4

For lines to be parallel, they have to have the SAME slope. The given line's slope is -3/4, so the slope of the parallel line is also $-\frac{3}{4}$

8 0

3 years ago