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3 years ago

Write a recursive rule for the sequence. 3, 8, 13, 18, 23, ...

Mathematics

1 answer:

adoni [48]3 years ago

3 0

Answer:

Step-by-step explanation:

c.d. d=8-3=5

$a_{n}=a_{n-1}+5$

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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

2 years ago

Will give brainliest and 5stars and thank you if youre answer is right

slega [8]

Step-by-step explanation:

since

25⁰= 1 minute

x⁰ = 11 minutes

cross multiply

25 x 11= x

x= 275⁰

temperature after being turned on=275⁰

temperature after 11 minutes= 275⁰ + 75⁰= 350⁰

temperature(x) after being turned on

25tt=x

temperature (x) after minutes

x= 25tt + 75⁰

8 0

2 years ago

If a 25 ft rope is cut into two sections with one section 4 times as long as the other section, how long is the shorter piece?

DaniilM [7]

X = short section of rope
4x = longer section of rope

x + 4x = 25
5x = 25
x = 5

…or in other words the shorter piece of rope is 5 feet long

7 0

2 years ago

Harry is saving for a vacation. He kept track of how much he saved each month over the last six months in the following table. W

Alexandra [31]

The correct answer is A $152.50 if you add up all of the numbers then divide by the total amount of numbers then you have your answer also known as the mean of the data

8 0

3 years ago

Read 2 more answers

Which equation represents a line that passes through (4,1/3) and has a slope of 3/4?

scoray [572]

Step-by-step explanation:

With this kind of problem, we're looking at an equation in the form

y - y1 = m(x - x1)

(m = slope)

so we can substitute m, y1, and x1 with the values we're given.

y - y1 = m(x - x1)

y - 1/3 = 3/4(x - 4)

Answer:

y - 1/3 = 3/4(x - 4)

6 0

3 years ago