Two buses leave a station at the same time and travel in opposite directions. One bus travels 18 miles per hour faster than the other. If the two buses are 744 miles apart after 6 hours, what is the rate of each bus?

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \: - 2( {b}^{2} - 5c)[/tex]

( put the values )

[tex] \qquad❖ \: \sf \: - 2 \{( - 3) {}^{2} - 5( - 1) \}[/tex]

[tex] \qquad❖ \: \sf \: - 2(9 - (- 5))[/tex]

[tex] \qquad❖ \: \sf \: - 2(9 + 5)[/tex]

[tex] \qquad❖ \: \sf \: - 2 \times 14[/tex]

[tex] \qquad❖ \: \sf \: - 28[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

The inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]x=g(y)=-\frac{y}{3}+1[/tex].

Here, the given function is [tex]f(x)=-3x+3[/tex].

Then we get:

[tex]y=-3x+3\\\Longrightarrow x=-\frac{y}{3}+1[/tex]

Thus, the inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]g(x)=-\frac{x}{3}+1[/tex].

The graph representing this inverse function is given as follows:

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Answer:

2

Step-by-step explanation:

Substitute:

2(1)(3)+2 / 2(1)(3)-2 =

6 + 2 / 6 - 2 =

8 / 4 =

2.

Hey there!

2ab + 2 / 2ab - 2

= 2(1)(3) + 2 / 2(1)(3) - 2

= 2(3) + 2 / 2(3) - 2

= 6 + 2 / 6 - 2

= 8 / 4

= 2

Therefore, your answer should be: 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The line segment that has the same measure as TQ is TR

The figure that completes the question is added as an attachment

From the figure, we have the following properties:

The above implies that the line segment that has the same measure as TQ is TR

Hence,  the line segment that has the same measure as TQ is TR

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Answer:

It's TR

Step-by-step explanation:

did it on edgenuidy

(a) We want to find a scalar function [tex]f(x,y,z)[/tex] such that [tex]\mathbf F = \nabla f[/tex]. This means

[tex]\dfrac{\partial f}{\partial x} = 2xy + 24[/tex]

[tex]\dfrac{\partial f}{\partial y} = x^2 + 16[/tex]

Looking at the first equation, integrating both sides with respect to [tex]x[/tex] gives

[tex]f(x,y) = x^2y + 24x + g(y)[/tex]

Differentiating both sides of this with respect to [tex]y[/tex] gives

[tex]\dfrac{\partial f}{\partial y} = x^2 + 16 = x^2 + \dfrac{dg}{dy} \implies \dfrac{dg}{dy} = 16 \implies g(y) = 16y + C[/tex]

Then the potential function is

[tex]f(x,y) = \boxed{x^2y + 24x + 16y + C}[/tex]

(b) By the FTCoLI, we have

[tex]\displaystyle \int_{(1,1)}^{(-1,2)} \mathbf F \cdot d\mathbf r = f(-1,2) - f(1,1) = 10-41 = \boxed{-31}[/tex]

[tex]\displaystyle \int_{(-1,2)}^{(0,4)} \mathbf F \cdot d\mathbf r = f(0,4) - f(-1,2) = 64 - 41 = \boxed{23}[/tex]

[tex]\displaystyle \int_{(0,4)}^{(2,3)} \mathbf F \cdot d\mathbf r = f(2,3) - f(0,4) = 108 - 64 = \boxed{44}[/tex]

Answer:

1/7

Step-by-step explanation:

Lets start with the probability of flipping tails, 1/2.

Then the probability of the day starting with the letter s, 2/7.

Calculate the final probability by multiplying the two together.

[tex]\frac{1}{2}*\frac{2}{7}=\frac{2}{14}[/tex]

You can simplify 2/14 down to 1/7

Answer:

x² + 6x + 9

Step-by-step explanation:

(x + 3)²

= (x + 3)(x + 3)

each term in the second factor is multiplied by each term in the first factor , that is

x(x + 3) + 3(x + 3) ← distribute parenthesis

= x² + 3x + 3x + 9 ← collect like terms

= x² + 6x + 9 ← in standard form

Answer:

5

Step-by-step explanation:

46/9.2 = 5

Answer:

gradient = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope/gradient and c the y- intercept )

given

3y = 5x - 6 ( divide through by 3 )

y = [tex]\frac{5}{3}[/tex] x - 2 ← in slope- intercept form

with gradient = [tex]\frac{5}{3}[/tex]

According to the data, it can be inferred that Lin is faster than Andre because she is going at 0.3 km/min speed while he is going at 0.25 km/min speed.

To calculate who goes faster we must divide the time into the distance traveled by each character as shown below:

According to the above, the point K of each would be equal to the distance that each of them travels in one minute. As shown in the graph, after 5min (Lin) and 8min (Andre), each one reaches their respective destination located 1.5km and 2km away, respectively, taking the point (0,0) as the starting point.

The graph is attached.

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Step-by-step explanation:

Let's solve for the first one,

[tex]R.H.S. = Cos²A + cos²A.cot²A[/tex]

Step 1- Take Cos²A common,

[tex] = Cos²A( 1+ cot²A)[/tex]

[tex] \small \sf \: Now \: we \: know \: that \\ \small (1 + Cot^{2} \theta = Cosec^{2} \theta)[/tex]

Step 2 - Substituting above value in step 1,

[tex] = Cos^{2} A(Cosec^2A)[/tex]

[tex] \small \sf \: We \: know \: that \: Cosec \theta= \frac{1}{Sin \theta} [/tex]

Step 3 - Substitute Cosec²A with 1/Sin²A

[tex] = \frac{Cos^2A}{Sin^2A} [/tex]

[tex] \small \sf \: Now \: the \: basic \: trigonometric \: function \: is \\ \small \frac{Cos\theta}{Sin \theta} = Cot\theta[/tex]

Step 4 - Replacing the product of step 3 with above function,

[tex] = {Cot}^{2} A[/tex]

Hence proved,

[tex]R.H.S = L.H.S[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Now let's prove the second relation,

[tex](1-sin²A)(1+cot²A)=cot²A[/tex]

Let's solve for R.H.S.,

[tex]R.H.S.= (1-sin^{2} A)(1+cot^{2} A)[/tex]

As I told above,

[tex]\small(1+cot^{2} \theta) = cosec^{2} \theta[/tex]

Another important relation is,

[tex] \small sin^2\theta + cos^2\theta= 1 \: or \: \\ \small cos^2\theta = 1 - sin^2\theta[/tex]

Replacing both the above brackets with this relation we get,

[tex] = Cos^2A \cdot Cosec^2A [/tex]

Now follow the step 3 and step 4 of first question and you will get,

[tex]R.H.S. = L.H.S.[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Some important trigonometric relations that you must learn,

[tex]Sin^2\theta + Cos^2\theta = 1 \\ 1 + Cot^2\theta = Cosec^2\theta \\ 1+Tan^2\theta = Sec^2\theta[/tex]

[tex] \small\sf \: Thanks \: for \: joining \: brainly \: community! [/tex]

Answer:

below

Step-by-step explanation:

-14y = 28 - 10x

10x - 14y - 28 = 0.

a = 10

b = -14

c = -28

Answer:

a = 10

b = -14

c = 28

Step-by-step explanation:

Goal form: Standard form

ax + by = c

Given form: linear form (not fully simplified)

-14y = 28 - 10x

Add 10x on both sides (to move the x-value to the left-hand side of the equation)

-14y + 10x = 28 - 10x + 10x

-14y + 10x = 28

10x - 14y = 28

Determine [ a ], [ b ], [ c ]

ax + by = c

10x - 14y = 28

[tex]\Large\boxed{a=10}[/tex]

[tex]\Large\boxed{b=-14}[/tex]

[tex]\Large\boxed{c=28}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

67.5 - 67.5 - 45 °

Step-by-step explanation:

Sum of INTERIOR angles of a polygon

  (n-2) * 180      <====ya just have to remember/know this !

n is the number of sides     n = 8 in this case

(8-2)*180 = 1080 °     < === this is the SUM of the 8 interior angles

        EACH interior angle is then   1080 / 8 = 135 °

  you can see from the picture that each of the two outside angles of the green triangle are 1/2 of this = 67.5° each

   so the triangle measurements are

              67.5 - 67.5 - 45     ( they have to sum to 180 for triangle)

Answer:

x = -7

x = 5

Step-by-step explanation:

The standard form of quadratic equations is

Ax^2 + Bx + C = 0

The factors need to multiply together to be C and add together to be B.

The two numbers that will multiply together to be -35 and add together to be 2 are -5 & 7.

The factor pairs are (x+7)(x-5). Zero product property means we set each of those factor pairs = 0 and solve.

x + 7 = 0

-7 -7 Subtract 7 from each side to solve

x = -7

x - 5 = 0

+5 +5 Add 5 to each side to solve

x = 5

To solve the equation, factor x²+2x−35 use the formula x² +(a + b) x + ab = (x + a)(x + b). To find a and b, set up a system to be solved.

a + b = 2

ab = −35

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.

Calculate the sum of each pair.

The solution is the pair that gives sum 2.

Rewrite the factored expression (x + a)(x + b) with the values obtained.

To find solutions to equations, solve x−5=0 and x+7=0.

ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

Answer:

Step-by-step explanation:

.11x = 55

11x = 5500

x = 500

Check the picture below.

now hmmm let's observe, hmmmm 11 has two digits, and low and behold, the 2 is right in the middle, then 1 and 1 on flanking it.

let's check 111 hmmmm has three digits and has a 3 right in the middle as well, and low and behold, is flanked by a regressing count, namely an "outwards" count.

let's check 1111 and 11111, same happens, one has a digit of 4 in the middle and the other 5, and yes, the "outwards" count on each, outwards count towards 1 each time btw.

so, if we were to take that pattern, we can say that eight 1's, namely 11111111 x 11111111, will have an 8 in the middle, and will look like 1234567   8   7654321.

The probability of obtaining a success is 0.010935.

Given that the probability of obtaining success is P(X>=5),n=6,p=0.3.

We are required to find the probability of obtaining a success if the probability is P(X>=5).

Probability is basically likeliness of happening an event among all the events possible.

Binomial distribution is basically the discrete probability distribution of the number of successes in a sequence of n independent experiments.

[tex](a+b)^{n} =nC_{0}p^{0} (1-p)^{n-0}+-----------nC_{n} p^{n} (1-p)^{0}[/tex]

We have to just put n=6 anr r=6 and 5 one by one to get the probability.

P(X>=5)=[tex]6C_{5}(0.3)^{5} (0.7)^{1} +6C_{6}(0.3)^{6} (0.7)^{0}[/tex]

=6!/5!1!8*0.00243*0.7+0.000729

=6*0.00243*0.7+0.000729

=0.010206+0.000729

=0.010935

Hence the probability of obtaining a success if the probability is P(X>=5) is 0.010935.

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The statement that demonstrates the correct calculation for simple interest is " A principal balance of $10,000 at 5% interest earns $500 each year as interest.

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

Simple interest does not compound interest on an interval basis. For instance quarterly, semi annually, annually etc. This are carried out in the case of compound interest.

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

Hence base don the explanation above, the statement that demonstrates the correct calculation for simple interest is " A principal balance of $10,000 at 5% interest earns $500 each year as interest.

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Answer:

472.19

Step-by-step explanation:

$472.19 weekly

Thus the required weekly installment is $402.30 for 25 years.

Given,
The family borrowed $400,000 from the bank to purchase a new home.
the bank charges 3.8% interest per year, compounded weekly, it will take 25 years to pay off the loan. How much will each weekly payment to be determined?

Statistics is the study of mathematics that deals with relations between comprehensive data.

The principle amount to refund = 400,000
Let the principle amount for weekly = P
Rate per year = 3.8%
Tenure = 25 year
For weekly installments,
52 Weeks in a year
Tenure = 25/52

Now,
[tex]Amount = P(1-(1+r)^{-tn})/i\\400000 = P (1-(1+0.038/52)^{-25*52}) / (0.038/52)\\400000 * 0.038/52 = P(1-(52.038)^{-25*52})\\292.30 = P(1-(1.001)^{-1300})\\292.30 = P(1-0.273)\\292.30=P * 0.727\\P = 402.30[/tex]

Thus the required weekly installment is $402.30 for 25 years.

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[tex]\textbf{Answer:\ \ \large\boxed{\frac{12}{25} }\ or\ 0.4800}[/tex]

Step-by-step explanation:

[tex]\large\boxed{13\ green\ marbles\ and\ 13\ white\ marbles}[/tex]

After a white marble is chosen:

[tex]\large\boxed{13\ green\ marbles\ and\ 12\ white\ marbles}[/tex]

Now there are 25 (13 + 12) total marbles.

Without replacing the white marble we chose already, what is the probability of choosing another white marble?

Well, now there are 12 white marbles to choose from, out of a total of 25 marbles. This means our probability is:

[tex]\large\boxed{\frac{12}{25} }[/tex]

This in decimal form is:

0.4800

Answer:

the answer will be 6 centimeter

Answer:

8.64 hours, so

8 hours, 38 mins, 24 seconds

Just find that 27% you have left, then find how much that 27% is in terms of time.

It might be wrong so double check it please.

Answer:

8.64 hours

which is 8hrs 38mins and 24secs

Step-by-step explanation:

If you've completed 73% then you have 27% left to go still. (100-73 = 27)

27% of 32

= .27×32

= 8.64 hours left

That is 8hrs and .64 of an hour .64×60=38.4 mins

which is 38 mins and .4 of a minute.

.4×60 = 24secs

Probably you will just round this answer.

Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.

From the Rule of Sine;

sinA/a = sinB/b = sinC/c

Where A,B and C are the angles of the triangle and a, b and c are the corresponding opposing sides.

Given that;

Using the rule of sine.

sinB/b = sinC/c

We substitute the given values into the equation

sin( 18° )/9 = sinC/20

We solve for C.

sin( 18° ) × 20 = sinC × 9

0.309016994 × 20 = sinC × 9

6.18033988 = sinC × 9

Divide both sides by 9

6.18033988/9 = (sinC × 9)/9

sinC = 0.686704431

C = sin⁻¹( 0.686704431 )

C = 43.3697°

C = 43°

Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.

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The number of license plates is 11232000

The given parameters are:

Characters = 6 i.e. 3 letters and 3 digits

Letters = 3 different letters

Digits = 3 different digits

There are 10 different digits and 26 different letters.

Since each character is different from the other, then we have:

Digits = 10, 9 and 8

Characters = 26, 25 and 24

The number of license plates is then calculated as:

n = 10 * 9 * 8 * 26 * 25 * 24

Evaluate the product

n = 11232000

Hence, the number of license plates is 11232000

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The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].

The explicit rule for this sequence:

The obvious rule for an arithmetic sequence is given as follows:

[tex]a_{n}=a_{1} +(n-1)d[/tex]

The first term = [tex]a_{1}[/tex].

The number of terms = n.

The common difference for two consecutive terms = d.

A recursive rule for an arithmetic sequence: [tex]a_{1} =4[/tex].

[tex]a_{n} =a_{n-1}-3[/tex]

The arithmetic sequence is given by:

[tex]a_{n} =a_{n-1}+d[/tex]

We get: d = -3

Substitute the given values:

[tex]a_{n} =4+(n-1)(-3)[/tex]

[tex]a_{n} =4-3n+3[/tex]

=7-3n

The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].

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The explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].

Given the recursive formula for an arithmetic sequence: [tex]a_1=4, a_n=a_{n-1}-3[/tex].

Thus, the first term of the arithmetic sequence is [tex]a=a_1=4[/tex]. using the recursive formula, we can get the 2nd term by putting [tex]n=2[/tex], [tex]a_2=a_1-3=4-3=1[/tex].

So, the common difference of the given arithmetic sequence is [tex]d=a_2-a_1=1-4=-3[/tex].

Thus, the nth term of the arithmetic sequence is given by [tex]a_n=a+(n-1)d\\\Longrightarrow a_n=4+(n-1)\times(-3)\\\Longrightarrow a_n=7-3n[/tex]

Therefore, the explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].

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