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marissa [1.9K]
3 years ago
15

Please show me step by step on how to solve this.

Mathematics
1 answer:
Readme [11.4K]3 years ago
7 0
Well, you have to be given an interval. That is not an interval.

You should be given something like 1 \leq x \leq 2

If you add those fractions up you'll just get a point on the number line.

Find the LCD for all of them which is 9/6 - 4/6 + 3/6 = 8/6 = 2/3

You'll end up with a point on 2/3 
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The "middle" term of a trinomial form of (3x+1)(x-4) is:
Zarrin [17]

Answer:

Expand the following expression

(3x+1)(x-4) = 3x^2-12x+x-4

middle term = -11x

3 0
2 years ago
X^2-14x+49 as a graph
Vaselesa [24]
<span> -x^2 + -14x = 49
-(x^2 +14) = 49
-[(x+7)^2 -49] = 49
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5 0
3 years ago
A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
IgorC [24]

Answer:

a = 2

Step-by-step explanation:

Let's find the equation of the line using the 2 points given.

Let's call -1 as x_1 and -5 as y_1

also, 4 as x_2 and 5 as y_2

The equation of line is :

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)

<em>Let's plug the points and get the equation of the line:</em>

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y+5=\frac{5+5}{4+1}(x+1)\\y+5=2(x+1)\\y+5=2x+2\\y=2x-3

Now, to find a, we substitute a in x and 1 in y of the equation of the line we just got:

y=2x-3\\1=2(a)-3\\1=2a-3\\2a=4\\a=\frac{4}{2}=2

4 0
3 years ago
Read 2 more answers
Which expression is equivalent to 16x4 – 64? and explain the answer plzz​
GuDViN [60]

Answer:

4(4x1-16)

Hope this helps

Have a good day :)

PS I disibuted 4 to 4x1 to get 16 and 4 to -16 to get -64

Step-by-step explanation:

3 0
3 years ago
Uninhibited growth can be modeled by exponential functions other than​ A(t) ​=Upper A 0 e Superscript kt. For ​ example, if an i
laila [671]

The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than A(t)=A_{0}e^{kt}. for example, if an initial population P₀ requires n units of time to triple, then the function P(t)=P_{0}(3)^{\frac{t}{n} } models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

a) If the population triples in 30 days, and 50 insects are present initially, write an exponential function of the form P(t)=P_{0}(3)^{\frac{t}{n} } that models the population.

b) What will the population be in 47 days?

c) When wil the population reach 750?

d) Express the model from part (a) in the form A(t)=A_{0}e^{kt}.

Answer: a) P(t)=50(3)^{\frac{t}{30} }

              b) P(t) = 280 insects

              c) t = 74 days

             d) A(t)=50e^{0.037t}

Step-by-step explanation:

a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is

P(t)=50(3)^{\frac{t}{30} }

b) In t = 47 days:

P(t)=50(3)^{\frac{t}{30} }

P(47)=50(3)^{\frac{47}{30} }

P(47)=50(3)^{1.567}

P(47) = 280

In 47 days, population of insects will be 280

c) P(t) = 750

750=50(3)^{\frac{t}{30} }

\frac{750}{50}=(3)^{\frac{t}{30} }

(3)^{\frac{t}{n} }=15

Using the property <u>Power</u> <u>Rule</u> of logarithm:

log(3)^{\frac{t}{30} }=log15

\frac{t}{30}log(3)=log15

t=\frac{log15}{log3} .30

t = 74

To reach a population of 750 insects, it will take 74 days

d) To express the population growth into the described form, determine the constant k, using the following:

A(t) = 3A₀ and t = 30

A(t)=A_{0}e^{kt}

3A_{0}=A_{0}e^{30k}

3=e^{30k}

Use Power Rule again:

ln3=ln(e^{30k})

ln3=30k

k=\frac{ln3}{30}

k = 0.037

Equation for exponential growth will be:

A(t)=50e^{0.037t}

3 0
2 years ago
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