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3 years ago

Find 3 consecutive even numbers where the product of the smaller two numbers is 40 less than the square of the largest number.

1 answer:

5 0

$3\ consecutive\ even\ numbers:\ 2x,2x+2,2x+4\\\\2x(2x+2)+40=(2x+4)^2\\\\
4x^2+4x+40=4x^2+16x+16\\\\
4x^2-4x^2+4x-16x=16-40\\\\-12x=-24\ \ |:(-12)\\\\x=\frac{24}{12}=2\\\\2x=2=4\\\\2x+2=6\\\\2x+4=8\\\\Numbers\ are\ 4,6,8.$

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In Δ,∠=70°,∠=50° ∠ . <br> ℎ ∠.

AveGali [126]

Answer:

100°

Step-by-step explanation:

A triangle is a polygon shape with three sides. Triangles are of different types such as obtuse, scalene, equilateral, isosceles etc.

In triangle ABC:

70° + 50° + ∠C = 180° (sum of angles in a triangle)

120 + ∠C = 180

∠C = 180 - 120

∠C = 60°

Since ∠C is bisected into ∠ACD and ∠BCD, hence:

∠ACD = ∠BCD = ∠C / 2

∠ACD = ∠BCD = 60 / 2

∠ACD = ∠BCD = 30°

In triangle ACD:

∠A + ∠ACD + ∠ADC = 180° (sum of angles in a triangle)

50 + 30 + ∠ADC = 180

∠ADC + 80 = 180

∠ADC = 100°

6 0

3 years ago

Please Help me! Algebra 1

dem82 [27]

Option a: The number of bacteria at time x is 0.

Option b: An exponential function that represents the population is $y=200(1.5)^x$

Option c: The population after 10 minutes is 11534(app)

Explanation:

It is given that the coordinates of the graph are (0,200), (1,300) and (2, 450)

Option a: To determine the number of bacteria x when y = 200

From the graph, we can see that the line meets y = 200 when x = 0

Thus, the coordinates are (0,200)

Hence, the number of bacteria at time x is 0 when y = 200.

Option b: Now, we shall determine the exponential function of the population.

The general formula for exponential function is $y=a \cdot b^{x}$

Where a is the starting point and $a=200$

b is the common difference.

To determine the common difference, let us divide,

$\frac{300}{200} =1.5$

Also, $\frac{450}{300} =1.5$

Hence, the common difference is $b=1.5$

Thus, substituting the values $a=200$ and $b=1.5$ in the formula $y=a \cdot b^{x}$ ,

we have, $y=200(1.5)^x$

Hence, An exponential function that represents the population is $y=200(1.5)^x$

Option c: To determine the population after 10 minutes, let us substitute $x=10$ in $y=200(1.5)^x$ , since the x represents the population of the bacteria in minutes.

Thus, we have,

$\begin{aligned}y &=200(1.5)^{x} \\&=200(1.5)^{10} \\&=200(57.67) \\&=11534\end{aligned}$

Hence, the population after 10 minutes is 11534(app)

7 0

4 years ago

Select the adjective(s) in the following sentence.

horsena [70]

Answer: Clean

Explanation:
Adjectives are words that describes nouns. Therefore, clean is an adjective.

5 0

3 years ago

A team of researchers published an article on the study of how vehicles are dispatched based on an airport-based taxi service. T

nikklg [1K]

Answer:

a. The mean would be 0.067

The standard deviation would be 0.285

b. Would be of 1-e∧-375

c. The probability that both of them will be gone for more than 25 minutes is 1-e∧-187.5

d. The likelihood of at least of one of the taxis returning within 25 is 1-e∧-375

Step-by-step explanation:

a. According to the given data the mean and the standard deviation would be as follows:

mean=1/β=1/15=0.0666=0.067

standard deviation=√1/15=√0.067=0.285

b. To calculate How likely is it for a particular trip to take more than 25 minutes we would calculate the following:

p(x>25)=1-p(x≤25)

since f(x)=p(x≤x)=1-e∧-βx

p(x>25)=1-p(x≤25)=1-e∧-15x25=1-e∧-375

c. p(x>25/2)=1-p(x≤25/2)=1-e∧-15x25/2=1-e∧-187.5

d. p(x≥25)=1-e∧-15x25=1-e∧-375

3 0

3 years ago

How do you find x and y

andriy [413]

To find X and Y X is horizontal Y is vertical, so that means SCP is horizontal and EF or a B is oops sorry all the way around

5 0

3 years ago