Alex house is 15 blocks from school. Carlene lives 7 blocks from Alex's house. Which equation represents the location of Carlene's house in relation to the school?

|x+7|=15
|x-7|=15
|x+15|=7
|x-15|=7​

Given,

\(h(x) = {6x}^{2} + {4x}^{4} + 7x\)

\(g( x) = {6x}^{2} - 4x + {3x}^{4} \)

Therefore,

\(h(x) + g(x)\)

\(( {6x}^{2} + {4x}^{4} + 7x) + ({6x}^{2} - 4x + {3x}^{4})\)

\( {6x}^{2} + {4x}^{4} + 7x + {6x}^{2} - 4x + {3x}^{4}\)

\((4 {x}^{4} + 3 {x}^{4} ) + ( {6x}^{2} + {6x}^{2} ) + (7x - 4x)\)

\( {7x}^{4} + {12x}^{2} + 3x\)

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

C. The solution t = 5 is the only valid solution to this system since time cannot be negative.

Step-by-step explanation:

Given

\(h(t) = -16t^2 + 48t + 210\)

\(h(t) = 50\)

Required

Determine which of the options is true

After solving

\(h(t) = -16t^2 + 48t + 210\)

for

\(h(t) = 50\)

We have that

\(t = -2\) and \(t = 5\)

Because time can't be negative, we have to eliminate \(t = -2\)

So, we're left with

\(t = 5\)

Because of this singular reason, we can conclude that option c answers the question

Answer: To find the distance of a chord from the center of a circle, we need to use the following formula:

Distance from center = sqrt(r^2 - (c/2)^2)

Where r is the radius of the circle and c is the length of the chord.

In this case, the radius of the circle is 3.7cm and the length of the chord is 7cm.

So, substituting these values in the formula, we get:

Distance from center = sqrt(3.7^2 - (7/2)^2)

= sqrt(13.69 - 12.25)

= sqrt(1.44)

= 1.2 cm

Therefore, the distance of the chord from the center of the circle is 1.2 cm.

Step-by-step explanation:

Answer:

(0, -6) is the y-intercept.

a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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Answer:

vertex:(−4,−4)

y-intercept:(0,12)

roots x=−2

and x= -6

AOS:-4

Step-by-step explanation:

if the question is 2y+3y=a and z+6z=b

then i could solve it otherwise sry

Answer:

a. P(A∪B)=0.85

b. P(A∩C)=0

c. P(A/B)=0

d. P(B∪C)= 0.70

Step-by-step explanation:

Events are said to be mutually exclusive when both cannot occur simultaneously in the result of experimentation. They are also known as incompatible events.

Being P(A)=0.30,  P(B)= 0.55 and P(C)= 0.15

Let A and B be any two events, P (A) and P (B) the probability of occurrence of events A or B, is known as the probability of union [denoted as P (A U B)]:

P(A∪B)=P(A) + P(B) - P(A∩B)

Mutually exclusive events are results of an event that cannot occur at the same time. So:

P(A∩B)=0 That is, there is no chance that both events will occur.

So: P(A∪B)=P(A) + P(B)

In this case: P(A∪B)=P(A) + P(B)= 0.30 + 0.55 → P(A∪B)=0.85

As mentioned, if two events are mutually exclusive, there is no chance that both events will occur. Being the intersection an operation whose result is made up of the non-repeated and common events of two or more sets, that is, given two events A and B, their intersection is made up of the elementary events that they have in common, then: P(A∩C)=0

The probability that event A will occur if event B has occurred is called the conditional probability and is defined:

P(A/B)=P(A∩B)÷P(B) being P(B)≠0

Since A and B are mutually exclusive, P (A∩B) = 0. So:

P(A/B)=P(A∩B)÷P(B)=0÷0.55 → P(A/B)=0

Finally, P(B∪C)=P(B) + P(C) - P(B∩C)

Since A and B are mutually exclusive, P (B∩C) = 0. So:

P(B∪C)=P(B) + P(C)= 0.55 + 0.15 → P(B∪C)= 0.70

The money each person owed is $10.853725 if the cost of the meal without tax or tip is $105.89.

Percentage is defined as the parts of a number per fraction of 100. It is denoted by the symbol '%'.

We can calculate percentage of a number by dividing a number with it's whole and then multiply with 100.

Given,

Cost of the meal before tax or tip = $105.89

Amount of tip = 18% of $105.89

                       = 18% × 105.89

                       = 0.18 × 105.89

                       = $19.0602

Amount of tax = 5% of $105.89

                       = 5% × 105.89

                       = 0.05 × 105.89

                       = $5.2945

Total cost for the meal = $105.89 + $19.0602 + $5.2945

                                      = $130.2447

Total number of friends = 12

Money owed by each friend = $130.2447 / 12

                                               = $10.853725

Hence the money owed by each is $10.853725.

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Answer:

i dont know have an amazing day

Step-by-step explanation:

be kind ppl

Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Answer:

-8(-x-5)-2 = -2 (x+1)

8x + 40 -2 = -2x -2

8x + 2x = -2 -40 +2

10x = -40

x = -40/10

x = -4

The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

Answer:

Hahahahahahahahahahhahahahahaha

Answer:

$0.0756 for 18 oz

$0.0634 for 32 oz

Step-by-step explanation:

(a) The closed form for ∑2 is 2.

(b) The closed form expression for ∑3 is 24.

(c) The closed form for the sum ∑n = 0(― 1)² ― 1 is n(1 - n) / 2.

(d) The value of -3 matches the manual computation of the four terms.

Our closed form solution is correct.

To find the closed form for ∑2, we can use the formula for the sum of the first n terms of an arithmetic series:

∑2 = n(a + l) / 2

In this case, a = 2 (the first term) and l = 2 (the last term) since we are summing a series of 2's.

We also know that there is only one term, so n = 1.

Substituting these values into the formula, we have:

∑2 = 1(2 + 2) / 2

= 4 / 2

= 2

The formula for the sum of the first n terms of an arithmetic series is:

∑n = n(a + l) / 2

In this case, we have a = 3 (the first term), l = 13 (the last term), and n = 3 (the number of terms).

Substituting these values into the formula, we get:

∑3 = 3(3 + 13) / 2

= 3(16) / 2

= 48 / 2

= 24

The formula we developed in class is:

∑n = n(a + a + (n - 1)d) / 2

In this case, we have a = 0 (the first term) and d = -1 (the common difference).

Substituting these values into the formula, we get:

∑n = n(0 + 0 + (n - 1)(-1)) / 2

= n(0 - n + 1) / 2

= n(1 - n) / 2

To test the closed form solution for ∑3 = 0(― 1)² ― 1, we substitute n = 3 into the closed form expression we derived in part (c):

∑3 = 3(1 - 3) / 2

= 3(-2) / 2

= -6 / 2

= -3

Now, let's manually compute the sum of the first four terms of ∑3 = 0(― 1)² ― 1:

0(― 1)² ― 1 + 1(― 1)² ― 1 + 2(― 1)² ― 1 + 3(― 1)² ― 1

= 0 - 1 - 2 - 3

= -6

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Answer:

B

Step-by-step explanation:

Because they took the correct steps to answer the equation.They also got the right answer (-2).

At the begining they added 4 to both sides (to cancel out the 4)

C would be wrong because they subtracted 4 from a negative four and this does NOT cancel it out.

Have a Supercalifragilisticexpialidocious day, I hope you like my explination. If you do please give rating or brainliest :)

Answer:

\( \boxed{D. \: 40\degree} \)

Step-by-step explanation:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°

So,

\( = > 2y \degree + (y + 10)\degree + 50\degree = 180\degree \\ \\ = > 2y\degree + y\degree + 10\degree + 50\degree = 180\degree \\ \\ = > 3y\degree + 60\degree = 180\degree \\ \\ = > 3y\degree = 180\degree - 60\degree \\ \\ = > 3y\degree = 120\degree \\ \\ = > y = \frac{120\degree}{3\degree} \\ \\ = > y = 40\degree \)

Answer:

Step-by-step explanation:

the formula is

follow this

Answer:

radius

Step-by-step explanation:

Answer:

-0.366666666667

Step-by-step explanation:

that's what you get when you divide -22/5 (-4 2/5) by 4/3 (1 1/3)

Answer:

-24/5 is the correct answer.

Steps:

1) -4 x 2/5 = -8/5

2) 1 x 1/3 = 1/3

3) -8/5 : 1/3 = -24/5

Answer:

German

Step-by-step explanation:

Given :

Number of people who spoke French as first language in 2000 = 7.7 * 10^7 ; in standard form ;

7.7 * 10^7 = 7.7 * (10 * 10* 10 * 10* 10* 10 * 10) = 77,000,000 = 77 million

Number of people who spoke German as first language in 2000 = 1 * 10^8 ; in standard form ;

1 * 10^8 = 1 * (10 * 10* 10 * 10* 10* 10 * 10 * 10) = 100,000,000 = 100 million

German had more speakers

Answer:

1/16

if u need an explanation just ask in the comments!

For the given quadratic equation we only have a maximum at y = 18.

Here we have:

\(f(x) = -2x^2 - 4x + 16\)

Notice that this is a quadratic equation of negative leading coefficient.

Then we have a maximum at the vertex, and both arms tend to negative infinity as x tends to infinity or negative infinity.

The vertex is at:

x = -(-4)/(2*(-2)) = -1

The maximum is:

\(f(-1) = -2*(-1)^2 - 4*(-1) + 16 = -2 + 4 + 16 = 18\)

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