A given line has the equation 10x + 2y = −2.

What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?

Answer:

y = sin(4x) + 3

Step-by-step explanation:

y = Asin(Bx + C) + D

A is amplitude = 1

B = 2pi/period = 2pi / (pi/2) = 4

C does not mention.

D: shift up or down = 3

=> y = sin(4x) + 3

In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.

In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.

For example, in the point (3, 5), the x-coordinate is 3 and the y-coordinate is 5.

Together, the x and y coordinates specify the precise location of a point in the xy-plane.

when you have 2 negative numbers you actually add the 2nd number to the first one

 example:

-4 - -2 =  becomes -4 + 2 = -2

Answer:

.227

Step-by-step explanation:

Answer:

0.227

Step-by-step explanation:

Answer:

Im working on it right now and its 1

Step-by-step explanation:

Answer: The speed of the plane with no wind is 440 miles per hour.

Step-by-step explanation:

Let the maximum speed of the plane be 'x'.

Let the maximum speed of the wind be 'y'.

Since we have given that an airplane travels 2400 miles against the wind in 6 hours.

As we know that

Downstream is given by

[tex]x+y=\dfrac{2400}{6}=400--------------(1)[/tex]

Since we have also given that flying with the wind, the plane can travel the same distance in 5 hours.

As we know tha t

Upstream is given by

[tex]x-y=\dfrac{2400}{5}=480-------------------(2)[/tex]

We just need to find the speed of the plane with no wind.

Using the elimination method,

[tex]x+y=400\\\\x-y=480\\\\-----------------------------\\\\2x=880\\\\x=\dfrac{880}{2}\\\\x=440[/tex]

Hence, the speed of the plane with no wind is 440 miles per hour.

The functions representing the areas of the square and circle as functions of the length of one side of the square x are [tex]\[ A_s(x) = x^2 \][/tex] and [tex]\[ A_c(x) = \frac{(10 - x)^2}{4\pi} \][/tex] respectively.

Let's denote:

- [tex]\( x \)[/tex] as the length of one side of the square (in feet).

- [tex]\( 10 - x \)[/tex] as the length of the rope used to form the circle.

1. Area of the Square [tex](\( A_s \))[/tex]:

The area of a square is given by the formula: [tex]\( A_s = x^2 \)[/tex].

2. Area of the Circle [tex](\( A_c \))[/tex]:

The circumference of the circle, formed by the rope, is used to find the radius [tex]\( r \)[/tex] of the circle:

[tex]\[ \text{Circumference} = 2\pi r = 10 - x \][/tex]

Solving for [tex]\( r \)[/tex], we get: [tex]\( r = \frac{10 - x}{2\pi} \)[/tex]

The area of the circle is then given by the formula: [tex]\( A_c = \pi r^2 \)[/tex].

Substituting the value of [tex]\( r \)[/tex], we get:

[tex]\[ A_c = \pi \left(\frac{10 - x}{2\pi}\right)^2 \][/tex]

[tex]\[ A_c = \frac{(10 - x)^2}{4\pi} \][/tex]

Downpayment is the percent amount paid from a sum  of money. The amount left after the downpayment is  $904.80

Downpayment is the percent amount paid from a sum  of money. If Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price, the amount he have left is;

Amount left = (100 - 13)% * 1040

Amount left .= 87% of 1040

Amount left = 0.87 * 1040

Amount left =  $904.80

Hence the amount left after the downpayment is  $904.80

Learn more on downpayment here: https://brainly.com/question/26173748

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Final answer:

To find out the distance a bat will fly in 15 minutes at an average speed of 32 kilometers per hour, you multiply the speed by the time in hours (15 minutes is 0.25 hours). The bat will fly 8 kilometers.

Explanation:

To calculate how far a bat flies in 15 minutes at an average speed of 32 kilometers per hour, we need to convert the time into hours since the speed is given in kilometers per hour (km/h). 15 minutes is equal to 0.25 hours (since there are 60 minutes in 1 hour, so 15 minutes divided by 60 minutes per hour equals 0.25 hours).

We can then use the formula for distance which is:

Distance = Speed × Time

The average speed of the bat is 32 km/h, and the time is 0.25 hours.

Distance = 32 km/h × 0.25 h = 8 km

So, the bat will fly 8 kilometers in 15 minutes.

distance = Sqrt((x2-x1)^2 +(y2-y1)^2)

15-3 =12

16-7=9

12^2 = 144

9^2 = 81

144+81 = 225

square root of 225 = 15

 the distance is 15

The circumference of an object is the total length of the line that forms the object. For a circle, the formula is:

C = 2 π r

We can see that in the formula, what is multiplied by 2 π is the radius (r).

Therefore the answer to this is

B. Radius

Answer:

The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.

Step-by-step explanation:

Given  : The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

To find : The four angles of the quadrilateral are °, °, °, and °, respectively.

Solution : We have given that  The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

Let the angle of the quadrilateral is x

Then all the  angles are  x  , 2x , 5x ,4x

Complete angle formed by circle is 360 °

Sum of all the angle are 360

x + 2x + 5x + 4x = 360 .

12 x = 360 .

On dividing both sids by 12.

x = 30 .

Then

2x =  60

5x = 5 * 30 = 150 .

4x = 4 *30 = 120 .

Therefore, The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.

Answer:

for plato users the answers are 45,75,135,105

Step-by-step explanation:

Final answer:

Compound interest plays a crucial role in determining the final amount of an investment over time, showcasing the power of compounding. In this scenario, with an initial amount of $1,000, an interest rate of 10.1%, and 47 years of compounding annually, the total interest earned would be $91,045.80.

Explanation:

Compound interest is calculated on the principal amount plus the interest earned over time. In this case, with an initial amount of $1,000, an interest rate of 10.1% compounded annually, and an end amount of $92,045.80 after 47 years, compound interest plays a significant role in determining the final amount.

To calculate the total interest earned over the 47 years, you subtract the initial principal amount of $1,000 from the end amount of $92,045.80. This gives you the total interest earned. In this scenario, the total interest earned would be $92,045.80 - $1,000 = $91,045.80.

Compound interest is crucial in understanding how investments grow over time, and it showcases the power of compounding when money is invested wisely and for a long period.

i = [tex]p(0) = \frac {3} {8} x \frac {2} {7} = \frac {3} {28} ; p (1) = \frac {3} {8} x \frac {5} {7} + \frac {5} {8} x \frac {3} {7} = \frac {15} {28}; p (2) = \frac {5} {8} x \frac {4} {7} = \frac {5} {14} [/tex]

(a)  i. The probability mass function of X is 5 / 14

Hypergeometric Distribution is the probability distribution of a hypergeometric random variable.

The hypergeometric distribution is used to calculate the statistical importance of having drawn a specific k successes (out of n total draws) from the aforementioned population in the hypergeometric test uses.

ii. Please see attached image for the answer.

To find the probability distribution for x, consider the possible values of x and calculate the probability of each value. When 2 marbles are drawn without replacement, there are two possible outcomes. The probability distribution for x is P(x = 0) = 3/28, P(x = 1) = 15/56, and P(x = 2) = 5/14.

To find the probability distribution for x, we need to consider the possible values of x and calculate the probability of each value.

Since there are 5 white marbles and 3 black marbles in the urn, the total number of marbles is 8.

When 2 marbles are drawn without replacement, there are two possible outcomes: (1) both marbles are white and (2) one marble is white and one marble is black.

Let's calculate the probabilities:

P(x = 0) = P(both marbles are black) = (3/8) * (2/7) = 6/56 = 3/28

P(x = 1) = P(one marble is white and one marble is black) = (5/8) * (3/7) = 15/56

P(x = 2) = P(both marbles are white) = (5/8) * (4/7) = 20/56 = 5/14

Therefore, the probability distribution for x is:

P(x = 0) = 3/28

P(x = 1) = 15/56

P(x = 2) = 5/14

Answer:

Well if you still need the answer around 4 years later LOL its √32

Step-by-step explanation:

Answer:

√32

Step-by-step explanation:

Because this is totally helpful 4 years later