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disa [49]
3 years ago
6

Pls help pls someone

Mathematics
1 answer:
suter [353]3 years ago
5 0

Answer:

(2x-1)(x + 4) = 0

=> x=1/2or, x=-4

smaller x = -4

larger x = 1/2

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5.7 as a mixed number in simplist form
Sveta_85 [38]
5.7 is 5 7/10 and it cannot be simplified
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Common Core - how many thousands are in 440,000? and explain the answer
Sedbober [7]
440 thousands. You take out the three zeros and you'll get your answer. Hope it helps! :)
6 0
3 years ago
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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
A vegetable garden has 3 tomato plants for every 5 lettuce plants. How many tomato plants are there if there are 45 lettuce plan
adelina 88 [10]

Answer:

the answer is 27

Step-by-step explanation:

because 45 divided by 5 equals 9

and 9 times 3 equals 27

6 0
2 years ago
The admission fee at an amusement park is $2.00 for children and $6.80 for adults. On a certain day, 388 people entered the park
san4es73 [151]

Answer: 188 children and 200 adults were admitted

Step-by-step explanation:

Let x represent the number of children that were admitted.

Let y represent the number of adults that were admitted.

On a certain day, 388 people entered the park. It means that

x + y = 388

The admission fee at the amusement park is $2.00 for children and $6.80 for adults. The admission fees collected on that day totaled $1736. It means that

2x + 6.8y = 1736- - - - - - - - - - 1

Substituting x = 388 - y into equation 1, it becomes

2x + 6.8y = 1736

2(388 - y) + 6.8y = 1736

776 - 2y + 6.8y = 1736

- 2y + 6.8y = 1736 - 776

4.8y = 960

y = 960/4.8

y = 200

x = 388 - y = 388 - 200

x = 188

4 0
3 years ago
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