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3 years ago

If the sum of five consecutive even integers is 90, what is the smallest of the five integers?

1 answer:

5 0

So the pattern of even integers is: 2, 4, 6, 8, etc. They are always 2 more than the prior even integer. Using this knowledge, our 5 consecutive even numbers are (let x = smallest even number): x, x + 2, x + 4, x + 6, and x + 8.

Now that we have the numbers, we can form our equation as such: $x+x+2+x+4+x+6+x+8=90$ . From here we can solve for x.

Firstly, combine like terms: $5x+20=90$

Next, subtract 20 onto both sides of the equation: $5x=70$

Lastly, divide both sides by 5 and <u>your smallest integer is $x=14$ </u>

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In a lab experiment, 1900 bacteria are placed in a petri dish. The conditions are such

GREYUIT [131]

Answer:

393 bacteria

Step-by-step explanation:

First find how much it would increase per hours :

1900 / 29 = 65.5172414

Then take this and multiply it by 6 to get :

393.103448

Round it to the nearest whole number to get:

393 bacteria

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3 years ago

Given: x+2y=-6. Solve for y. y=x-6/2

Snowcat [4.5K]

$x+2y=-6\\\\2y=-6-x\quad|:2\\\\y=\dfrac{-6-x}{2}\\\\\\\boxed{y=-3-\frac{x}{2}}$

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2 years ago

Hey can you please help me posted picture of question

dmitriy555 [2]

From the graph we can observe that G(x) is obtained by shifting F(x) 3 units to the left and 1 unit upwards.

Thus, both horizontal and vertical translations are involved. Horizontal translation of 3 units to left can be obtained by adding 3 to x in the equation and vertical translation of 1 can be obtained by adding 1 to the entire function.

So,

G(x) = F(x+3) + 1

G(x) = (x+3)² + 1

Thus the correct answer is option C

5 0

3 years ago

How can you write 1,360/200 as a repeating decimal?

Alisiya [41]

1360/200

13.6/2

6.8

It is a finite decimal, but if you want repeating, there are zeroes that follow, like so:

6.8000000000000 . . . (and on to infinity)

6 0

3 years ago

Steven is moving to another city next weekend and wants to rent a moving truck. The rental rates for two companies in his area a

ASHA 777 [7]

Answer:

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Company (2) is $7.4 cheaper.

Step-by-step explanation:

From the tables given in the picture,

Let the equation representing the rental 'y' and distance traveled 'x' is represented by,

y = mx + b

For company (1),

Here m = per mile rental charges = Slope of the graph

b = Initial charges

Since slope of the line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

m = $\frac{y_2-y_1}{x_2-x_1}$

Therefore, slope of the line passing through (30, 53.55) and (60, 87.15) will be,

m = $\frac{87.15-53.55}{60-30}$ = $1.12 per mile

So the equation will be,

y = 1.12x + b

Since this line passes through (30, 53.55),

53.55 = 1.12(30) + b

b = 53.55 - 33.6

b = 19.95

So the expression representing charges for the company (1) will be,

y = 1.12x + 19.95

For company (2),

Per mile charges = slope of the line

m = $\frac{78-56.75}{50-25}$

m = $0.85 per mile

Equation for the charges will be,

y = 0.85x + b

Since this line passes through (25, 56.75),

56.75 = 0.85(25) + b

b = 56.75 - 21.25

b = 35.5

Therefore, equation representing total charges for company (2) will be,

y = 0.85x + 35.5

By comparing per mile charges,

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Steven plans to drive 85 km in rental truck.

Charges for company (1),

y = 1.12x + 19.95

y = 1.12(85) + 19.95

y = $115.15

Charges for company (2),

y = 0.85x + 35.5

y = 0.85(85) + 35.5

y = $107.75

Difference in charges of both the companies = 115.15 - 107.75 = $7.4

Therefore, company (2) is $7.4 cheaper.

6 0

3 years ago