All categories

3 years ago

Given the function f(x)=(x+3)^2 and g(x)=3x+13 determine the x values of the point intersection

Mathematics

1 answer:

charle [14.2K]3 years ago

3 0

Answer:

x = - 4, x = 1

Step-by-step explanation:

At the point of intersection

f(x) = g(x) , that is

(x + 3)² = 3x + 13 ← expand left side using FOIL

x² + 6x + 9 = 3x + 13 ( subtract 3x + 13 from both sides )

x² + 3x - 4 = 0 ← in standard form

(x + 4)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 1 = 0 ⇒ x = 1

You might be interested in

Dwight can run four times faster than Jim. If Jim runs a mile in 3 minutes, which equation would allow you to solve for Dwight's

Shalnov [3]

Answer:

the office

Step-by-step explanation:

5 0

3 years ago

Find the points of intersection between x^2+y^2=45 and -3x+y=15

MatroZZZ [7]

Step-by-step answer:

Given:

Circle C1: x^2+y^2 = 45

Line L1: -3x+y=15

Need to find the points of intersection.

Solution:

basically we need to solve for the roots of equations C1 and L1.

Here, we can use substitution of L1 into C1.

Rewrite L1 as : y=3x+15

substitute into C1:

x^2+(3x+15)^2 = 45

Expand

x^2 + 9x^2+90x+225 = 45

Rearrange terms:

10x^2+90x+180 = 0

Simplify

x^2+9x+18 = 0

Factor

(x+6)(x+3) = 0

x=-6 or x=-3

Back-substitute x into L1 to calculate y:

x=-6, y=3*x+15 = 3(-6)+15 = -3 => (-6,-3)

x=-3, y=3*x+15 = 3(-3) + 15 = 6 => (-3, 6)

Therefore the intersection points are (-6,-3) and (-3,6)

Check using equation C1:

(-6)^2+(-3)^2 = 36+9 = 45 ok

(-3)^2+(6)^2 = 9 + 36 = 45 ok

Check using equation L1:

Point (-6,-3) : y = 3x+15 = 3(-6) +15 = -3 ok

Point (-3,6) : y = 3x+15 = 3(-3)+15 = 6 ok.

4 0

4 years ago

4th grade work help my brotherrr please!!

exis [7]

4 x 20 and that is 160

3 0

3 years ago

Read 2 more answers

33. The standard deviation divided by the square root of the sample size n is equal to the _______________ of the mean. Sample e

kupik [55]

Answer:

Standard error

Step-by-step explanation:

Standard error: In statistics, the term standard error is also denoted as SE, and is reffered to as the estimate of a particular parameter.

It is defined as the standard deviation in statistics related to its sampling distribution or else the the standard deviation's estimate.

Therefore, if a particular parameter or statistic is considered as a mean then it would be denoted as the standard error of that mean.

The standard error of an estimate may also be defined as the square root of the estimated error variance √ $\sigma^{2}$ of the quantity,

$S_{e}$ =√ $\sigma^{2}$

In the given question, the appropriate answer would be standard error.

4 0

3 years ago

What would 6×6×6 equal with an exponent

Anastaziya [24]

Answer:

6³

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers