Two cars, a Porsche Boxster and a Toyota Scion XB, are traveling in the same direction, although the Boxster is 115.0 m behind the Scion. The speed of the Boxster is 26.0 m/s and the speed of the Scion is 18.9 m/s. How much time does it take for the Boxster to catch the Scion? [Hint: What must be true about the displacement of the two cars when they meet?]

See the attached picture:

Answer:

if you put the trigangle diagnal then do a box the a square

hope that helps

if not tell me I will change the answer with the right answers

Answer:

The answer to your question is: length = 14 ft; width = 3 ft

Step-by-step explanation:

Data

Area = 42 ft²

length = 8 + 2w

w = width = ?

length = ?

Formula

Area = length x width = l x w

Substitution

                     42 = (2w + 8)w

                     42 = 2w² + 8w

                     2w² + 8w - 42 = 0

                                                                  Dividing by 2

                      w² + 4w - 21 = 0                 Factorize

                     (w + 7) (w - 3) = 0

                     w1 = -7                      w2 = 3

     It's not possible to have negative widths

So the answer is w = 3 ft

      length = 2(3) + 8

      length = 6 + 8

      length = 14 ft

The length and width of the rectangle barn are 14 feet and 3 feet, respectively.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Let the width of the rectangle be represented by x. Therefore, the dimension of the barn is,

Width = x

Length = 2x + 8

The area of a rectangular wall of a barn is 42 square feet.

Area = Width × Length

Area = x × (2x+8)

42 square feet = x(2x + 8)

42 = 2x² + 8x

2x² + 8x - 42 = 0

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x(x + 7) - 3(x + 7) = 0

(x + 7)(x - 3) = 0

x = -7, 3

Since width can not be negative, therefore, the length and the width of the wall of the barn are,

Width = x = 3

Length = 2x+8 = 2(3)+8 = 14

Hence, the length and width of the rectangle barn are 14 feet and 3 feet, respectively.

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Let , a, b and c be the length of three sides of triangle, represented in terms of vectors as [tex]\vec{a},\vec{b},\vec{c}[/tex].

Now, vector of same Magnitude acts as normal vector to each side.

So, equation of any vector p having normal q is given by

      [tex]\vec{p} \times\vec{q}[/tex]

Now sum of three vector and it's normal is given as

    [tex]=\vec{a} \times\vec{a}+\vec{b} \times\vec{b}+\vec{c} \times\vec{c}\\\\=0+0+0\\\\=0[/tex]

Cross product of two identical vectors is Zero.

[tex]\rightarrow \vec{i} \times\vec{i}=0[/tex]

The sum of the outward normal vectors of a triangle's sides is always 0 due to vector closure around the triangle.

Let us denote the vertices of the triangle as A, B, and C. The sides of the triangle are AB, BC, and CA. We need to show that the sum of the outward normal vectors of these sides is zero.

Let u be the outward normal vector of side AB.

Let v be the outward normal vector of side BC.

Let w be the outward normal vector of side CA.

These normal vectors are each associated with a side of the triangle and have the same length as the corresponding side.

For any triangle, the vector from one vertex to another can be expressed as the difference of position vectors:

AB = B - A

BC = C - B

CA = A - C

The normal vector u to side AB can be aligned such that u is perpendicular to AB and has magnitude equal to the length of AB.

Similarly, v is perpendicular to BC and has magnitude equal to the length of BC.

Similarly, w is perpendicular to CA and has magnitude equal to the length of CA.

To show that the sum of these vectors is zero, consider that the sum of vectors around a closed polygon (in this case, the triangle) is zero. The outward normal vectors form a closed system since each side’s normal vector effectively cancels out with the adjacent ones due to their perpendicularity and length.

Thus:

u + v + w = 0.

Answer:

correct 0.25

Step-by-step explanation:

The questions relate to solving mathematical expressions involving radicals and imaginary numbers. Errors in the original expressions were corrected for accurate solutions. For example, the corrected calculation (6) - sqrt(25)/4 results in 4.75. x= (5) + sqrt(-49)/6 simplifies to 5 + 7/6i.

This question pertains to the field of Mathematics, specifically the area dealing with radicals and complex numbers. The original queries from the student need a bit of clarification since in a few cases the operations mentioned are mathematically invalid. For instance, in the question

(6) - sqrt(25)/4

, we are subtracting a square root from a number without any operator between them. Assuming we need to subtract the result of sqrt(25) divided by 4 from 6, we simplify sqrt(25) to 5 because the square root of 25 is 5. We then divide this by 4 to get 1.25. Subtracting 1.25 from 6 answers the first question as 4.75 Similarly, for the problem

x= (5) + sqrt(-49)/6

dealing with negative radicands, we know that the square root of a negative number results in an imaginary number. The sqrt(-49) simplifies to 7i (because the square root of 49 is 7 and the negative sign makes it imaginary). We then divide this by 6 to get 7/6i. Adding it to 5 we obtained the answer

5 + 7/6i

.

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Answer:

The lady is on the second door

Step-by-step explanation:

we have that

The sign on the first door reads "In this room there is a lady, and in the other one there is a tiger"

The sign on the second door reads "In one of these rooms, there is a lady, and in one of them there is a tiger."

so

The sign on the second door is true

The sign on the first door is true or false

Since one of these signs is true and the other is false, the sign in the first door must be false

therefore

The lady is on the second door

If the first sign is true, the lady is behind the first door, if the second sign is true, the lady is behind the second door.

Let's consider the first sign first. If the sign on the first door is true, then there must be a lady in that room and a tiger in the other room. This means that the sign on the second door is false, and there is no lady in the second room. Therefore, the lady must be behind the first door. If the sign on the first door is false, then the lady cannot be in the first room. This means that the second sign is true, and there must be a lady in the second room. So, the lady is behind the second door.

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Concetta initially had 2kg of flour. After using 180g to make biscotti, she was left with 1820g of flour. This equates to 1.82kg when converted back from grams to kilograms.

At the beginning, Concetta had a bag of flour weighing 2kg. We need to convert kilograms to grams first to make the units the same, and we know that 1kg is equal to 1000g. Therefore, she initially had 2000g of flour.

After making biscotti, she used 180g of flour. So, to find out how much she has left, we subtract the amount used (180g) from the total amount (2000g), which results in 1820g of flour remaining.

Finally, we need to convert this back to kilograms. Because there are 1000g in 1kg, we divide 1820 by 1000, which gives us that Concetta has 1.82kg of leftover flour.

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Answer:

  3w + 8 – w = 4w – 2(w – 4)

Step-by-step explanation:

The simplified forms of each of these equations are ...

Answer:

the answer is 5

Step-by-step explanation:

if you have any questions or a more detailed explanation feel free to ask in the comments.

Answer:

$5.75

Step-by-step explanation:

First we will make an equation. We will put child tickets as x, and adult tickets as x+3.50. =

2x+7+3x=35.75=

5x=28.75

x=5.75

Answer:

662.64

Step-by-step explanation:

i got it wrong on apex and it told me the right answer. you're welcome.

Answer:

$662.63

Step-by-step explanation:

Cost of mortgage = $120,000

Interest rate of first period = 5.25%

The loan was amortized over 30 years.

The interest rate at the end of the initial loan period = 6.75%

Margin = 1.5%

The loan was amortized for over (30*12) months

= 360 months

The interest rate of the first period per month = 5.25% / 12

= 0.0525/12

= 0.004375

Payment for monthly mortgage =

(120000(0.004375)) / 1 - (1 + 0.004375)^-360

= 525 / 1 - (1.004375)^-360

= 525 / (1 - 0.2077)

= 525 /0.7923

= 662.63

= $662.63

Answer:

D) [tex]y = 10 * 4^{x}[/tex]

Step-by-step explanation:

Replace each function with x = 0

A) [tex]y = 1*4^{x} \\y = 1*4^{0} \\y = 1[/tex]

B) [tex]y = 3*10^{x} \\y= 3* 10^{0} \\y = 3 \\[/tex]

C) [tex]y = 2*4^{x} \\y = 2*4^{0} \\y = 2[/tex]

D) [tex]y = 10*4^{x} \\y= 10*4^{0} \\y = 10[/tex]

If you check the graph with x = 0, the value of y is between 8 and 12 so the only probably answer acoording to the alternatives is D) which gives y = 10 when x = 0

Answer:

Step-by-step explanation:

y = -2x^5 - 1

Desired reflection would be f'(x) = -2x⁵ -1

The reflection over the x-axis equation's basic guidelines The reflection equation of the new reflected graph will be y=f(x) y = f (x) given an equation, y=f(x) y = f (x). Simply multiplying the function by 1 will result in a curve that is mirrored across the x-axis.

Given the equation f(x) = x⁵, From reflection rile, the reflection of this graph would be f'(x) = - x⁵.

asked to stretch the graph by 2 and shift down 1 unit.

Therefore, the function results after applying the sequence of transformation are f'(x) = -2x⁵ -1. for better understanding a graph is attached below.

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Answer:

Slope and y-intercept

Step-by-step explanation:

The complete question is shown in the image attached with.

For each trip an initial fee of $ 25 is charged and $ 0.10 is charged for each vertical meter descended.

Since, for each vertical meter the charge is $ 0.10, for x meters the charges will be $ 0.10x. So,

Total charges of the trip would be:

Total charges/fee = Initial Fee + Fee for x meters

y = 25 + 0.10x

y = 0.10x + 25

The general slope intercept form of the equation of the line is:

y = mx + c

Where,

m = slope of the line

c = y-intercept

Compairing both the equations given above we, get:

Slope of line = m = 0.10

y-intercept = c = 25

So, the given statements gives us the slope and the y-intercept of the graph.

Answer:

Slope and y-intercept

Step-by-step explanation:

There are 3,628,800 possible codes that can be entered into the 10-letter keypad.

The number of codes that can be formed using the 10-letter keypad is calculated using the concept of permutations. Since each key can only be used once, we need to find the number of ways we can arrange 10 letters without repetition. This can be calculated as:

P(10, 10) = 10!

Therefore, there are 3,628,800 possible codes that can be entered into the keypad.

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The number of possible ten-letter codes using the keys labeled A to J, are 3,628,800 possible codes.

The number of different codes can be found by calculating the permutations of 10 unique keys, or 10!.

The factorial of a number n (written as n!) is the product of all positive integers from 1 to n.

So, the calculation for 10 keys is:

Computing this gives:

Therefore, there are 3,628,800 possible codes for opening the garage door.

Step by step:A prediction is basically an educated guess and if you are looking for the exact word to describe that you would find that hypothesis is the correct way to tell what is a prediction.

Answer:B

Final answer:

The maximum length of the playground is 38 meters, given that the perimeter cannot exceed 120 meters and the width cannot exceed 22 meters. The possible lengths are therefore from 0 to 38 meters.

Explanation:

Possible Lengths of the Playground

Given that the maximum width (w) is 22 meters and the maximum perimeter is 120 meters, we can substitute these values to find the maximum length:

The maximum length of the playground is 38 meters. However, the length can be any value less than or equal to 38 meters, so the possible lengths of the playground are from 0 meters to 38 meters.

Answer:

kn

Step-by-step explanation:

qoierh2rhfjfwjfjj2jnfcdfejghitu43o4ip

9514 1404 393

Answer:

  Adam

Step-by-step explanation:

It is pretty easy to make comparisons to 10 ft/s.

If Liz ran 10 ft/s, she would run 460 ft in 46 s. Since she runs 420 ft, she runs slower than that.

If Emily ran 10 ft/s, she would run 600 ft in 1 minute, so Emily runs faster than that.

If Adam ran 10 ft/s, he would only run 4270 ft in 427 seconds. Since he runs 5280 ft in that time, his speed is definitely greater than 10 ft/s.

__

At this point, we know that Adam and Emily run faster than Liz and Stephanie. So we need to compare Adam and Emily's rates.

Adam's time for 1 mile is about 7 minutes. If Emily ran for 7 minutes, her distance would be less than 7×700 ft = 4900 ft, substantially less than 1 mile (5280 ft).

Adam runs the fastest.

_____

Comment on straightforward solution

Each rate can be computed by dividing distance by time:

  Liz: (420 ft)/(46 s) = 9.13 ft/s

  Adam: (5280 ft)/(427 s) = 12.37 ft/s

  Emily: (667 ft)/60 s) = 11.12 ft/s

Adam's is the highest, well above Stephanie's 10 ft/s.

These calculations require a calculator. The solution above was done without a calculator.

Final answer:

To determine the fastest runner, we calculated each runner's speed in feet per second. Adam was found to be the fastest with a speed of 12.37 feet per second.

Explanation:

To find out who the fastest runner is, we need to calculate the speed of each runner in feet per second and then compare. Stephanie's speed is already given as 10 feet per second. Next, we calculate Liz's speed by dividing the distance she runs by the time it takes her: 420 feet / 46 seconds = 9.13 feet per second. Now, we convert Adam's mile into feet, knowing that 1 mile = 5280 feet. Adam's speed is 5280 feet / 427 seconds = 12.37 feet per second. Lastly, we need to convert Emily's time into seconds since she runs for 1 minute (which is 60 seconds). So, Emily's speed is 667 feet / 60 seconds = 11.12 feet per second. Comparing all speeds, Adam runs the fastest at 12.37 feet per second.

Answer:

Part 1) The converse is "If one of the two angles is acute then two angles are supplementary"

Part 2) The inverse is " If two angles are not supplementary, then one of the two angles is not acute"

Part 3) The contrapositive is "If one of the two angles is not acute then two angles are not supplementary"

Step-by-step explanation:

we  have

The following conditional statement " If two angles are supplementary, then one of the two angles is acute"

The hypothesis is "If two angles are supplementary"

The conclusion is " one of the two angles is acute"

Part 1) Rewrite the conditional statement as a converse

we know that

To form the converse of the conditional statement, interchange the hypothesis and the conclusion

therefore

The converse of " If two angles are supplementary, then one of the two angles is acute"  is "If one of the two angles is acute then two angles are supplementary"

Part 2) Rewrite the conditional statement as a inverse

we know that

To form the inverse of the conditional statement, negating both the hypothesis and conclusion of a conditional statement.

therefore

The inverse of " If two angles are supplementary, then one of the two angles is acute"  is " If two angles are not supplementary, then one of the two angles is not acute"

Part 3) Rewrite the conditional statement as contrapositive

we know that

To form the contrapositive, switching the hypothesis and conclusion of a conditional statement and negating both

therefore

The contrapositive of "If two angles are supplementary, then one of the two angles is acute" is "If one of the two angles is not acute then two angles are not supplementary"

Answer:

  $32.67

Step-by-step explanation:

Her purchase total was ...

  (1.4 lb)($12.00/lb) +(4.5 lb)($0.35/lb) = $17.33

Her change from $50 will be ...

  $50 - 17.33 = $32.67

Answer:

  3

Step-by-step explanation:

Let "a" represent Alondra's number. Then the math she performs on it is ...

  2a-6 . . . .double my number and subtract 6

  | 2a-6 | < 2 . . . . . the result is less than 2 units from zero

This absolute value expression can be "unfolded" to two of them ...

  -2 < 2a -6 < 2

Dividing by 2 gives ...

  -1 < a -3 < 1

Adding 3, we get ...

  2 < a < 4

The only whole number in this range is ...

  a = 3

Alondra is thinking of the number 3.

Answer:

being financially responsible

Step-by-step explanation:

Answer:

a misconception

Step-by-step explanation:

I think it's a misconception because she just assumed, which means she dousn't really know.

Answer:

- p ⇒ - q

Step-by-step explanation:

p : Drive over 65 miles

q : You get a speeding ticket.

So then we get the negations.

- p : You do not drive over 65 miles

- q : You don't get a speeding ticket.

So, we need to connect the sentences. For that we use ⇒.

⇒ : then.

So, the sentence, If you do not drive over 65 miles per hour, then you will not get a speeding ticket

Can be written as : -p ⇒ -q

The expression representing the proposition using the variables p and q is ¬p → ¬q, which follows the logical rule of Modus Tollens.

The proposition "If you do not drive over 65 miles per hour, then you will not get a speeding ticket" can be represented using the variables p for "You drive over 65 miles per hour" and q for "You get a speeding ticket". The logical expression for the given proposition, using logical connectives and negations, is ¬p → ¬q, which means "not p implies not q".

This is an example of the logical rule known as Modus Tollens, which can be expressed as ((p→q) ∧ ¬q) → ¬p. If the implication p→q is true, and the consequent q is false (¬q), then it must follow that the antecedent p is also false (¬p).

Answer:

We can form a triangle if none of the resulting pieces is at least 1/2, i.e. if no ... It is not hard to show that if you choose a point randomly in this triangle, the distances to the three ... of lengths that you obtain by breaking a stick at two random points. ..... we get line segments joining the midpoints of the edges of the triangle.

Step-by-step explanation:

The probability that three pieces from breaking a unit length stick can form a triangle, based on the triangle inequality theorem and geometric probability principles, is 1/4.

The question belongs to the area of Mathematics called geometric probability. Here, we are asked to find the probability that three stick pieces formed from a unit length stick can form a triangle.

The rule which applies to this situation is the triangle inequality theorem. This theorem states that for any triangle, the length of any side (say c) must be less than the sum of the lengths of the other two sides (say a and b). In mathematical terms, a + b > c.

Considering the above theorem, since we break the stick into three pieces simultaneously, the break points must be such that each piece is less than 0.5 units to be able to form a triangle. In this case, the length of the longest piece (c) will be less than the sum of the lengths of the other two pieces.

So, to form a triangle, each piece must be less than 0.5 in length. The region where this condition is satisfied forms a triangle in a unit square, thus giving a geometric probability of 1/4. Hence, the probability that the three pieces can form a triangle is 1/4.

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Answer:

$4083.21

Step-by-step explanation:

Compound interest is an interest rate that stacks on top of each other

So basically I did 3600 × 1.065 for the first year

=3834

then i did 3834 × 1.065 again to calculate the second year

=4083.21

Hope this helps! If you have any questions ask! :)

Answer:

D. $4083.21

Step-by-step explanation:

Answer:

[tex]u+v =8.323717394km[/tex]

Ф=[tex]64.86489406[/tex]°

Step-by-step explanation:

[tex]u=4km[/tex]

[tex]v=5km[/tex]

For easy calculations let's decompose the vector in its rectangular components:

[tex]u_x=u*cos(\alpha )=4000*cos(90)=4000*0=0[/tex]

[tex]u_y=u*sin(\alpha )=5000*sin(90)=4000*1=4000[/tex]

[tex]v_x=v*cos(\beta )=5000*cos(45)=3535.533906[/tex]

[tex]v_y=v*sin(\beta )=5000*sin(45)=3535.533906[/tex]

Now lets calculate the resultant vector:

[tex]u+v=R[/tex]

[tex]R=R_x+R_y[/tex]

[tex]R_x=u_x+v_x=0+3535.533906=3535.533906[/tex]

[tex]R_x=u_y+v_y=4000+3535.533906=7535.533906[/tex]

Finally let´s calculate the magnitude and direction of R:

║[tex]R[/tex]║=[tex]\sqrt{(R_x)^{2}+(R_y)^{2}  }=\sqrt{(3535.533906)^{2}+(7535.533906)^{2}  }  =8.323717394km[/tex]

Ф=[tex]arctan(\frac{R_y}{R_x})=arctan(\frac{7535.533906}{3535.533906})=64.86489406[/tex]°

Answer:

1) 6840

2) 4845

3) 1050

Step-by-step explanation:

1) How many different ways are there to choose a chairman, assistant chairman, and a treasurer department of 20 people?

As it ordered:

C   AC   TD  

20    19      18   = 20.19.18 = 6840

2) How many ways are there to choose a committee of 4 people from this same committee?

Not ordered:

C₂₀,₄ = 20!   = 20.19.18.17.16! = 20.19.18.17 = 4845

         16! 4!        16! 4.3.2.1             4.3.2.1

3) If the committee is required to be comprised of 2 women and 2 men, and there are 5 women in the department, how many different committees are possible?

5 women and 15 men

committee: 2 w and 2 m

C₁₅,₂*C₅,₂ = 105*10=1050

C₁₅,₂ = 15!   = 15.14.13! = 15.14 = 105

         13! 2!     13! 2.1           2

C₅,₂ = 5!   = 5.4.3! = 5.4 = 10

         3! 2!   3! 2.1      2

Answer: Hi!

Let's start, you have 3 boxes and 3 types off eggs inside of each. The fact that they each box is labelled incorrectly means that inside the box labelled Large, only can be the set of small or mixed eggs.

So, let's suppose we open this Box labelled LARGE and inside of it we find the small eggs.

now we have two remaining boxes, the labeled SMALL and the labelled MIXED.

the MIXED can only contain the set of large eggs or the set of small, because you know that is wrong labelled, and also you know that the small eggs are in the first box that you oppened, so here are the large eggs, and now in the last box is the last set of eggs, the mixed one.

So you only will need to open one box to know which eggs are in what box.

Answer:

A. The selection is a combination.

Step-by-step explanation:

A combination is a selection of all or part of a set of objects, without regard to the order in which they were selected.  

Then, a permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

For example, the student scans the novels to be checked out in no particular order hence it is a combinations problem. Scanning novels with titles A, B, C, D and E in the order B, C, D, E and then A produces the same result. When it comes to library books, the order in which we scan the novels for check out is of no importance since in the end the same novels are carried out the door by the library patron.

Answer:

  6.44×10⁷ g

Step-by-step explanation:

The scenario seems unlikely, as a brachiosaurus weighs about 6.9 times as much as a tyrannosaur. The sum of the two weights is ...

  8.16×10³ kg + 1.24×10⁵ lb

  = 8.16×10³ kg + (1.24×10⁵ lb)/(2.2046 lb/kg)

  = 8.16×10³ kg + 5.62×10⁴ kg

  = 6.44×10⁴ kg . . . . . rounded to 3 significant figures

  = 6.44×10⁷ g . . . . . . weight of not-so-hungry tyrannosaur

_____

1 kg = 10³ g