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2 years ago

Alexa says that the pattern with the expression 5n+3 will not contain the term 82. Is she right? Explain your answer.

Mathematics

1 answer:

kolbaska11 [484]2 years ago

6 0

Answer:

correct

Step-by-step explanation:

She is correct.

For any integer, n, 5n is a multiple of 5.

5n + 3 is 3 more than a multiple of 5.

Start with 82. Subtract 3. Now you have 79.

79 is not a multiple of 5, so 5n + 3 will not contain the term 82.

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Which number has the same value as 20 tens

barxatty [35]

200 has the same value as 20 tens beucase 20*10=200

4 0

3 years ago

Based on a study of population projections for 2000 to 2050, the projected population of a group of people (in millions) can b

Olegator [25]

Answer:

(a) 0.107 million per year

(b) 0.114 million per year

Step-by-step explanation:

$A(t) = 11.19(1.009)^t$

(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, $t=0$ and in 2014, $t=14$ . Mathematically,

$\text{Rate}=\dfrac{A(2014) - A(2000)}{2014-2000}=\dfrac{11.19(1.009)^14-11.19(1.009)^0} {14}$

$A(0)=\dfrac{12.69-11.19}{14}=\dfrac{1.5}{14}=0.107$

(b) The instantaneous rate of change is determined by finding the differential derivative at that year.

The result of differentiating functions of the firm $y=a^x$ (where $a$ is a constant) is $\dfrac{dy}{dx}=a^x\ln a$ . Let's use in this in finding the derivative of $A(t)$ .

$A\prime(t) = \dfrac{A}{t}=11.19\cdot1.009^t\ln1.009$

In the year 2014, $t=14$ .

$A\prime(14) =11.19\cdot1.009^14\ln1.009=0.114$

6 0

3 years ago

to support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. t

Leokris [45]

Choice given:
<span>33.6°
39.8°
50.2°
56.4°

I drew the figure.
I got 12 ft as the hypotenuse, 10 ft as the opposite.

Sin</span>Θ = opposite / hypotenuse
SinΘ = 10/12
SinΘ = 0.83

I used the calculator to get the value of each angle using the sine function
sin(33.6°) = 0.55
sin(39.8°) = 0.64
sin(50.2°) = 0.77
sin(56.4°) = 0.83

The angle where the wire meets the ground is approximately 56.4°

8 0

3 years ago

Read 2 more answers

Taille LHRISTINE

BartSMP [9]

Answer:

$-5 = x$

Step-by-step explanation:

$7(4x + 9) - 10 = -87 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \: 10 \: \: \: \: + 10 \\ \\ \frac{7(4x + 9)}{7} = -\frac{77}{7} \\ \\ 4x + 9 = -11 \\ \: \: \: \: \: \: -\: 9 \: \: \: \: \: - \: 9 \\ \\ \frac{4x}{4} = -\frac{20}{4} \\ \\ x = -5$

** The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

5 0

3 years ago

How to solve this substitution

Lena [83]

-5x+4y=11
substitute for x which is 5
(-5)(5)+4y=11

simplify :
4y-25=11

add 25 on both sides
4y-25=11
+25 +25
the 25 cancels out

so it would be 4y=36
and you divide both sides by 4

4/4 =36/4

which gives you (5,9)
x= 5 , y =9

6 0

2 years ago