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lawyer [7]
2 years ago
6

First-person to answer correctly gets brainiest Find an equation for each line.

Mathematics
2 answers:
seropon [69]2 years ago
3 0
Green = -1x - 1
Black = -2x
Orange = Y = 4
Blue = X = -4
LUCKY_DIMON [66]2 years ago
3 0
Black: -2x
Green: -x -1
Blue: X=-4
Orange: Y=4
You might be interested in
List 3 values that would make this inequality true. 65<15x
Romashka-Z-Leto [24]
Anything 5 and up, because when you multiply the by 15, they equal more than 65, making the inequality true.
5 0
3 years ago
I dont understand how to do this precalc question
Alexeev081 [22]

Answer:

  • x-intercept:  (-0.1, 0)
  • Horizontal Asymptote: y = -3
  • Exponential <u>growth</u>

(First answer option)

Step-by-step explanation:

<u>General form of an exponential function</u>

y=ab^x+c

where:

  • a is the initial value (y-intercept).
  • b is the base (growth/decay factor) in decimal form:
    If b > 1 then it is an increasing function.
    If 0 < b < 1 then it is a decreasing function.
  • y=c is the horizontal asymptote.
  • x is the independent variable.
  • y is the dependent variable.

Given <u>exponential function</u>:

y=4(10)^x-3

<h3><u>x-intercept</u></h3>

The x-intercept is the point at which the curve crosses the x-axis, so when y = 0.  To find the x-intercept, substitute y = 0 into the given equation and solve for x:

\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}

Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.

<h3><u>Asymptote</u></h3>

An <u>asymptote</u> is a line that the curve gets infinitely close to, but never touches.

The <u>parent function</u> of an <u>exponential function</u> is:

f(x)=b^x

As<em> </em>x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.

Therefore, there is a horizontal asymptote at y = 0.

This means that a function in the form  f(x) = ab^x+c always has a horizontal asymptote at y = c.  

Therefore, the horizontal asymptote of the given function is y = -3.

<h3><u>Exponential Growth and Decay</u></h3>

A graph representing exponential growth will have a curve that shows an <u>increase</u> in y as x increases.

A graph representing exponential decay will have a curve that shows a <u>decrease</u> in y as x increases.

The part of an exponential function that shows the growth/decay factor is the base (b).  

  • If b > 1 then it is an increasing function.
  • If 0 < b < 1 then it is a decreasing function.

The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.

Learn more about exponential functions here:

brainly.com/question/27466089

brainly.com/question/27955470

6 0
2 years ago
What will be the new function g(x) if f(x)=2x is translated 2 units down and 3 units left?
Fed [463]

2 units down means y is decreased by 2

3 units left mean x is decreased by 3

So

for

  • f(x)=2x

The translation is

  • f(x)=2(x+3)-2
6 0
2 years ago
The ratio of dogs to cats in a veterinarian’s office is 9:7. What is the ratio of the number of dogs to the total number of dogs
lara31 [8.8K]
The answer is 9:16 just add 9+7=16 and then we know out of the 16 nine were dogs so 9:16
3 0
3 years ago
John bought an odd shaped lot that was 100 feet deep, but the front footage was 160 feet and the length of the back side of the
Snowcat [4.5K]

This lot has the shape of a trapezoid. Regard the 2 different lengths as 160' and 80' and the width 100'


Applying the formula for the area of a trapezoid:


80' + 160'

A = ----------------- * 100' = 24000 ft^3

2

4 0
3 years ago
Read 2 more answers
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