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3 years ago

Rewrite the equation in Ax+By=C form. Use integers for A, B, and C. y-2 = -2(x+6)

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

6 0

Answer:

6x + -2y or 2y = 4

Step-by-step explanation:

I think

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Andrea bought 1 2/5 pounds of avocados at $4.20 per pound and 2 1/

guapka [62]

Answer:

$14.43¢

Step-by-step explanation:

We are given; $1\frac{2}{5}$ pounds, 1 pound = $4.20 and $2\frac{1}{4}$ pounds,1 pound = $3.80 that Andrea bought.

Now we need to find her total cost. To do that, we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert $1\frac{2}{5}$ to a decimal. It is 1.4. Now we can set up a graph.

Avocados

$\frac{4.2}{1}=\frac{x}{1.4}$

Switch sides

$\frac{x}{1.4}=\frac{4.2}{1}$

Apply rule: $\frac{a}{1}=a$

$\frac{x}{1.4}=4.2$

Multiply both sides by 1.4

$\frac{1.4x}{1.4}=4.2\cdot \:1.4$

Simplify

$x=5.88$

So, her cost for avocados is $5.88¢

Now we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert $2\frac{1}{4}$ to a decimal. It is 2.25. Now we can set up a graph.

Asparagus

$\frac{3.8}{1}=\frac{x}{2.25}$

Switch sides

$\frac{x}{2.25}=\frac{3.8}{1}$

Apply rule : $\frac{a}{1}=a$

$\frac{x}{2.25}=3.8$

Multiply both sides by 2.25

$\frac{2.25x}{2.25}=3.8\cdot \:2.25$

Simplify

$x=8.55$

So, her cost for asparagus is $8.55¢

Total cost

Now that we have found out how much both of the fruits Andrea bought costs, we need to sum it up (meaning add it) to find the total cost:

$5.88¢ + 8.55¢ =

5.88 + 8.55 = 14.43

Therefore, Andrea's total cost of the fruits is $14.43¢

8 0

3 years ago

6 painters can paint the fence in 15 hours. How long would it take 5 workers to do the same job?

SOVA2 [1]

Answer:

12.5 hours

Step-by-step explanation:

15/6 is 2.5. 2.5 is how many hours per worker. 5 times 2.5 is 12.5 hours

8 0

3 years ago

Read 2 more answers

Suppose that 5 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 39 cm.

vesna_86 [32]

Answer

given,

work = 5 J

spring stretch form 30 cm to 39 cm

$W = \dfrac{1}{2}kx^2$

x = 0.39 - 0.30 = 0.09 m

$5 = \dfrac{1}{2}k\times 0.09^2$

$k = \dfrac{5\times 2}{0.09^2}$

k = 1234.568 N/m

a) work when spring is stretched from 32 cm to 34 cm

x₂= 0.34 -0.30 = 0.04 m

x₁ = 0.32 - 0.30 = 0.02

$W = \dfrac{1}{2}k(x_2^2-x_1^2)^2$

$W = \dfrac{1}{2}\times 1234.568 \times (0.04^2-0.02^2)^2$

W = 0.741 J

b) F = k x

25 = 1234.568 × x

x = 0.0205 m

x = 2.05 cm

3 0

3 years ago

Lamaj is rides his bike over a piece of gum and continues riding his bike at a constant rate time = 1.25 seconds the game is at

Hitman42 [59]

Lamaj rides his bike over a piece of gum and continues riding his bike at a constant rate. At time = 1.25 seconds, the gum is at a maximum height above the ground and 1 second later the gum is on the ground again.

a. If the diameter of the wheel is 68 cm, write an equation that models the height of the gum in centimeters above the ground at any time, t, in seconds.

b. What is the height of the gum when Lamaj gets to the end of the block at t = 15.6 seconds?

c. When are the first and second times the gum reaches a height of 12 cm?

Answer:

Step-by-step explanation:

We are being told that:

Lamaj rides his bike over a piece of gum and continues riding his bike at a constant rate. This keeps the wheel of his bike in Simple Harmonic Motion and the Trigonometric equation that models the height of the gum in centimeters above the ground at any time, t, in seconds. can be written as:

$\mathbf {y = 34cos (\pi (t-1.25))+34}$

where;

y = is the height of the gum at a given time (t) seconds

34 = amplitude of the motion

the amplitude of the motion was obtained by finding the middle between the highest and lowest point on the cosine graph.

$\mathbf{ \pi}$ = the period of the graph

1.25 = maximum vertical height stretched by 1.25 m to the horizontal

b) From the equation derived above;

if we replace t with 1.56 seconds ; we can determine the height of the gum when Lamaj gets to the end of the block .

So;

$\mathbf {y = 34cos (\pi (15.6-1.25))+34}$

$\mathbf {y = 34cos (\pi (14.35))+34}$

$\mathbf {y = 34cos (45.08)+34}$

$\mathbf{y = 58.01}$

Thus, the gum is at 58.01 cm from the ground at t = 15.6 seconds.

When are the first and second times the gum reaches a height of 12 cm

This indicates the position of y; so y = 12 cm

From the same equation from (a); we have :

$\mathbf {y = 34 cos(\pi (t-1.25))+34}$

$\mathbf{12 = 34 cos ( \pi(t-1.25))+34}$

$\dfrac {12-34}{34} = cos (\pi(t-1.25))$

$\dfrac {-22}{34} = cos(\pi(t-1.25))$

$2.27 = (\pi (t-1.25)$

t = 2.72 seconds

Similarly, replacing cosine in the above equation with sine; we have:

$\mathbf {y = 34 sin (\pi (t-1.25))+34}$

$\mathbf{12 = 34 sin ( \pi(t-1.25))+34}$

$\dfrac {12-34}{34} = sin (\pi(t-1.25))$

$\dfrac {-22}{34} = sin (\pi(t-1.25))$

$-0.703 = (\pi(t-1.25))$

t = 2.527 seconds

Hence, the gum will reach 12 cm first at 2.527 sec and second time at 2.72 sec.

7 0

3 years ago

................. plz let only deltaalex answer:) don’t trust anyone on here but them!

nevsk [136]

Answer:

Step-by-step explanation:

oh law of sines soo sin(A) / a = Sin(B) / b

2a)

here DE = side f then let's find that side with law of sines and plug side f in as 'a' in law of sines , so

Sin(28) / a = Sin(54) / 31 ( where a = f = DE )

can you do the algebra here Emily? or do you want me to show that?

Sin(28) *31 / Sin(54) = a

17.989 =a

18.0 =a (rounded to nearest 10th)

DE = 18.0 m

2b)

find RT where RT = side a

since they give use 2 of the other sides of the triangle we can quickly figure out the S angle. 180 = 71+62+S so S = 47° ( I'm going kinda fast b/c I don't know how much time you have :? )

then Sin(A) /a = Sin(B) / b

Sin(47) / a = Sin(62) / 29

Sin(47) *29 / Sin(62) = a

24.020 = a

RT = 24.0 meters ( rounded to nearest 10th )

2c)

they want us to find ∠X with law of sines soo

I'll just use the letter they give us for variables

Sin(X) / x = Sin(Y ) / y

Sin(X) = x* Sin(y) / y

X = arcSin [ 14 * Sin(108) / 34 ]

X = arcSin [ 0.3916115]

X = 23.0548°

X= 23° ( rounded to nearest degree )

2d)

they ask us to find ∠E

I'll , again, use the letter they give us for variables

Sin(E) / e = Sin( F ) / f

Sin(E) / 18 = Sin(78) / 30

E = arcSin[ 18 * Sin(78) / 30 ]

E = arcSin [ 0.5868856 ]

E = 35.936 °

E = 36 ° ( rounded to nearest degree )

3 0

3 years ago