The 1st positive and the 1st negative coterminal angles to angle (- 446°)

Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

Answer Check

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

Answer

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

8 0

3 years ago

Hector, Sam, Ted, and Gina are comparing their savings. Hector saved twice as much money as Sam. Ted saved $100 more than Hector

lutik1710 [3]

Answer:

$2x+50$

Step-by-step explanation:

Given: Hector saved twice as much money as Sam.

Ted saved $100 more than Hector.

Gina saved $50 less than Ted.

As given, lets assume the amount of money Sam has in saving be "x".

Now, finding saving of each person given.

Writing the algebric expression of each´s saving amount.

we know, Hector saved twice as much money as Sam.

∴ Hector saving= $\$2x$

Also, Ted saved $100 more than Hector.

∴ Ted´s saving= $\$(2x+100)$

Next finding Gina´s saving

As given, Gina saved $50 less than Ted.

∴ Gina´s saving= $\$ (2x+100)-\$ 50$

Opening parenthesis and solving it.

⇒ Gina´s saving= $\$ 2x+\$50$

Algebric expression of Gina´s saving= $2x+50$

5 0

3 years ago

If the interest rate is 10% a month what is the annual rate? 213.8?

Hatshy [7]

On month -------- 10%
12 month ---------- x %
-------------------------------
x = 12*10/1 = 12*10 = 120%

3 0

3 years ago

Michael's dad is 30 years of age. He is 2 years more than four times Michaels age m. Write and solve a two-step equation to dete

Ksenya-84 [330]

Answer:

The two step equation that we can use to find michael's age is x = (f-2)/4 where f = 30. So Michael is 7 years old.

Step-by-step explanation:

In order to solve this problem we will attribute variables to the ages of Michael and his father. For his father age we will attribute a variable called "f" and for Michael's age we will attribute a variable called "x". The first information that the problem gives us is that Michael's dad is 30 years of age, so we have:

f = 30

Then the problem states that the age of the father is 2 years "more" than four "times" Michaels age. The "more" implies a sum and the "times" implies a product, so we have:

f = 2 + 4*x

We can now find Michael's age, for that we need to isolate the "x" variable. We have:

f - 2 = 4*x

4*x = f - 2

x = (f-2)/4

x = (30 - 2)/4 = 7 years

The two step equation that we can use to find michael's age is x = (f-2)/4 where f = 30. So Michael is 7 years old.

7 0

3 years ago

Read 2 more answers

You have to find the slope and y intercept of the table.

stepladder [879]

Answer:

slope=-1.1/500

y-intercept=212.0

Step-by-step explanation:

the y-intercept is always the number next to x, on the y side.

the boiling point is going down by 1.1

8 0

3 years ago