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2 years ago

Write a quadratic equation given the solutions -4,-6

Mathematics

1 answer:

BigorU [14]2 years ago

3 0

$x^{2} +6x+24$ is the quadratic equation with the solutions -4 and -6

Given that -4 and -6 are solutions of a quadratic equation and asked to find out the quadratic equation

If "a" and "b" are the roots of the quadratic equation then,

sum of roots = a+b

product of roots = ab

There the required quadratic equation is $x^{2} -(a+b)x+ab$

Given that a= -4 and b= -6

sum of roots = a+b = -4 +(-6) = -10

product of roots = ab =( -4 )( -6 ) = 24

There the required quadratic equation is $x^{2} +10x+24$

Hence, $x^{2} +6x+24$ is the quadratic equation with the solutions -4 and -6

Learn more about quadratic equation here:

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2. A surveyor measures the distance across a river that flows straight north by the following method. Starting directly across f

IgorLugansk [536]

Answer:

The wide is 70.02 m.

Step-by-step explanation:

First you need to draw a triangle with only one 90 degrees angle.

The opposite side to the 90 degrees angle will be the hypotenuse.

We will call the remaining sides ''Baseline'' and ''River wide''.

The angle between hypotenuse and baseline is 35 degrees.

The triangle has one 90 degrees angle so we can apply the tangent equation

in the angles that are no 90 degrees.

Tangent (angle) = Opposite side/adjacent

Tan(35°)= River wide/100m

River wide = 100m.Tan(35°)

River wide = 70.02 m

6 0

3 years ago

please use a peice of paper to write down your work and take a picture of it and put it here, I need to show my work there is 2

mihalych1998 [28]

The answer to question 1 is n=-17, and the answer to question 2 is y=-5.8 (<u>could also be seen as -29/8</u>)

Work is shown in the pictures below

4 0

3 years ago

1. What is the circumference of the circle<br> below?<br> 11 cm

Ket [755]

11^2 x pi that is the formula now find the answer

3 0

3 years ago

Wilma earns $9 per hour at her job. Then she spent $15 on a birthday gift for her best friend. Write an expression to represent

frozen [14]

Answer:

Wilma has $12.

Step-by-step explanation:

Since we don't know how many hours she worked, we know that Wilma earned 9x dollars at her job. Then she spends $15, so we can just subtract 15 from 9x.

$9x-15$

We can just replace the x with 3 to get:

$27-15\\12$

Hence, Wilma has $12.

3 0

3 years ago

Read 2 more answers

HELPPPP!!!!!!!! 100 points!!!! I need help on 37-39 thanks!

____ [38]

Answer:

Part 37)

a) Point-slope form $y-5=(1)(x-3)$

b) Slope intercept form $y=x+2$

c) Standard form $x-y=-2$

Part 38)

a) Point-slope form $y-2=0.25(x+4)$

b) Slope intercept form $y=0.25x+3$

c) Standard form $x-4y=-12$

Part 39)

a) Point-slope form $y-3=2(x-1)$

b) Slope intercept form $y=2x+1$

c) Standard form $2x-y=-1$

Step-by-step explanation:

Part 37) Line passing through point (3,5) and slope of 1

Part a) Equation of the line in point slope form

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute the given values

$y-5=(1)(x-3)$

$y-5=(x-3)$ -----> equation of the line in point slope form

Part b) Equation of the line into slope intercept form

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

Substitute the given values in the equation and solve for b

$5=(1)(3)+b$

$5=3+b$

$b=5-3$

$b=2$

substitute

$y=x+2$ -----> equation of the line in slope intercept form

Part c) Equation of the line in standard form

The equation of the line in standard form is equal to

$Ax+By=C$

where

A is a positive integer

B and C are integers

we have

$y=x+2$

Convert to standard form

Subtract y both sides

$y-y=x+2-y$

$0=x+2-y$

Subtract 2 both sides

$-2=x+2-y-2$

$-2=x-y$

Rewrite

$x-y=-2$ ----> equation in standard form

Part 38) Line passing through points (-4,2) and (0,3)

Part a) Equation of the line in point slope form

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

Find the slope m

$m=(3-2)/(0+4)=1/4=0.25$

with the slope m=0.25 and point (-4,2)

substitute the given values

$y-2=0.25(x+4)$ -----> equation of the line in point slope form

Part b) Equation of the line into slope intercept form

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$m=0.25$

$b=3$ -----> the y-intercept is the point (0,3)

Substitute the given values in the equation

$y=0.25x+3$ -----> equation of the line in slope intercept form

Part c) Equation of the line in standard form

The equation of the line in standard form is equal to

$Ax+By=C$

where

A is a positive integer

B and C are integers

we have

$y=0.25x+3$

Convert to standard form

Multiply by 4 both sides to remove the decimal number

$4y=x+12$

Subtract 4y both sides

$4y-4y=x+12-4y$

$0=x+12-4y$

Subtract 12 both sides

$-12=x+12-4y-12$

$-12=x-4y$

Rewrite

$x-4y=-12$ ----> equation in standard form

Part 39) Line passing through points (1,3) and (2,5)

Part a) Equation of the line in point slope form

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

Find the slope m

$m=(5-3)/(2-1)=2/1=2$

with the slope m=2 and point (1,3)

substitute the given values

$y-3=2(x-1)$ -----> equation of the line in point slope form

Part b) Equation of the line into slope intercept form

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

with the slope m=2 and point (1,3)

Substitute the given values and solve for b

$3=(2)(1)+b$

$3=2+b$

$b=3-2=1$

substitute

$y=2x+1$ -----> equation of the line in slope intercept form

Part c) Equation of the line in standard form

The equation of the line in standard form is equal to

$Ax+By=C$

where

A is a positive integer

B and C are integers

we have

$y=2x+1$

Convert to standard form

Subtract y both sides

$y-y=2x+1-y$

$0=2x+1-y$

Subtract 1 both sides

$-1=2x+1-y-1$

$-1=2x-y$

Rewrite

$2x-y=-1$ ----> equation in standard form

8 0

4 years ago