Two trains going in opposite directions leave at the same time. Train B travels 5 mph faster than train A. In 3 hours the trains are 315 miles apart. Find the speed of each train

Another way to write the equation is 7x + 54 = 0

Given the equation;

[tex]\frac{7}{8}x + \frac{3}{4} = -6[/tex]

Find the LCM on the left side, which is 8

[tex]\frac{7x + 6}{8} = -6[/tex]

Cross multiply

[tex]7x + 6 = -6[/tex] × [tex]8[/tex]

[tex]7x + 6 = -48[/tex]

Collect like terms

[tex]7x = -48 - 6[/tex]

[tex]7x = -54[/tex]

Take all to one side

[tex]7x + 54 = 0[/tex]

Thus, another way to write the equation is 7x + 54 = 0

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Answer:

I think it's 80%

Step-by-step explanation:

Method 1: (40/50)*100 = 80%

Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%

Answer:

6.871 decimeters

Step-by-step explanation:

687.1 square centimeters = 6.871 square decimeters

1 dm² = 100 cm²

Answer:

6.871

Step-by-step explanation:

calculator

Answer: B. (2,2)

Step-by-step explanation:

The vertex of the parabola in the form [tex](x-h)^2 = 4p(y-k)[/tex] is (h, k).

Only Set B  is a partition of set N of natural numbers .

Numbers starting from 1 to infinity comes under Natural Numbers.

It is asked in the question that to determine whether or not each of the following is a partition of set N of natural numbers

A  ) {{n | n > 5}, {n | n < 5}]

It is not a set of natural numbers as it does not include 5.

B  )  [{n | n ≥ 6}, {1, 3,5} , {2, 4}]

{1,3,5} {2,4}and {n|n≥6} include all the natural numbers

Therefore , it forms a partition of N.

C ) {{n | n^2 > 11}, {n | n^2 < 11}

Every natural number n must satisfy either n^2 > 11 or n^2 < 11

This cannot be possible , therefore it is not the partition of Natural Numbers.

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Answer:

ANSWER IS B

Step-by-step explanation:

NEXT TIME USE any graph website online

Answer: A. -3.65

Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.

[tex](+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\[/tex]

Knowing this, we can input it into the calculator and find the answer's sign.

[tex]-27.375/7.5=-3.65[/tex]

Therefore, the answer is A. -3.65.

I hope this helps! Pls mark brainliest!! :)

Answer:

21

Step-by-step explanation:

[tex]3t-7=5t[/tex]

subtract 3t from both sides

[tex]-7 = 2t[/tex]

multiply both sides by 3

[tex]-21 = 6t[/tex]

so 6t = -21

Answer:

$800

Step-by-step explanation:

per hour $40×10hours=$400

$400÷$50=8 times initial fee

8×$50=$400 total initial fee

$400hours fee+$400 initial fee=$800 total payment

Answer:

10

Step-by-step explanation:

24/30 = 0.8

24+x/30+x =0.85

10=x

If you want more clarification just ask

Total games Chase has to win in a row to achieve an 85% win percentage would be 10.

We can write the total number game won by Chase as -

w = 80% of 30

w = 80/100 x 30

w = 4/5 x 30

w = 24

Assume that he wins {x} games after winning 24 games to achieve 85% win percentage. Now, we can write that out of (30 + x) number of games played, Chase won (24 + x) games to achieve 85% win percentage. So, we can write that -

(24 + x)/(30 + x) = 85/100

(24 + x)/(30 + x) = 0.85

(24 + x) = 0.85(30 + x)

24 + x = 25.5 + 0.85x

0.15x = 1.5

x = 10

Total games Chase has to win in a row to achieve an 85% win percentage would be 10.

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Answer:

sure how can I help you? please tell me

The value of m∠G = 48.6° .

A triangle is a polygon with three sides , angles and vertices.

It is given that

In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°

m∠G = ?

well, using the law of cosines,

GH ² = 9² + 11² - 2(9)(11) cos65°

f = 10.88 ft

now, using the law of sines,

sinG/9 = sin65°/10.88

m∠G = 48.6°

Therefore the value of m∠G = 48.6° .

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Answer: (1+2a)^2 or (1+2a)(1+2a)

Step-by-step explanation:

Answer:

[tex](2a +1)( 2a + 1)[/tex]

Step-by-step explanation:

Answer:

68.5% seats filled

76% points earned

Step-by-step explanation:

Percentages are formed when one finds a ratio of two related quantities, usually comparing the first partial quantity to the amount that "should" be there.

[tex]\text{ratio}=\dfrac {\text{the "part"}}{\text{the whole}}[/tex]

For instance, if you have a pie, and you eat half of the pie, you're in effect imagining the original pie (the whole pie) cut into two equal pieces, and you ate one of them (the "part" of a pie that you ate).  To find the ratio of pie that you ate compared to the whole pie, we compare the part and the whole:

[tex]\text{ratio}=\dfrac {\text{the number of "parts" eaten}}{\text{the number of parts of the whole pie}}[/tex]

[tex]\text{ratio}=\dfrac {1}{2}[/tex]

If you had instead eaten three-quarters of the pie, you're in effect imagining the original pie cut into 4 equal pieces, and you ate 3 of them.

[tex]\text{ratio}=\dfrac {\text{the number of "parts" eaten}}{\text{the number of parts of the whole pie}}[/tex]

[tex]\text{ratio}=\dfrac {3}{4}[/tex]

There can be cases where the "part" is bigger than the whole.  Suppose that you are baking pies and we want to find the ratio of the pies baked to the number that were needed, the number of pies you baked is the "part", and the number of pies needed is the whole.  This could be thought of as the ratio of project completion.

If we need to bake 100 pies, and so far you have only baked 75, then our ratio is:

[tex]\text{ratio}=\dfrac {\text{the number of "parts" made}}{\text{the number of parts of the whole order}}[/tex]

[tex]\text{ratio}=\dfrac {75}{100}[/tex]

But, suppose you keep baking pies and later you have accidentally made more than the 100 total pies.... you've actually made 125 pies.  Even though it's the bigger number, the number of pies you baked is still the "part" (even though it's bigger), and the number of pies needed is the whole.

[tex]\text{ratio}=\dfrac {\text{the number of "parts" made}}{\text{the number of parts of the whole order}}[/tex]

[tex]\text{ratio}=\dfrac {125}{100}[/tex]

To find a percentage from a ratio, there are two small steps:

Going back to the pies:

When you ate half of the pie, your ratio of pie eaten was [tex]\frac{1}{2}[/tex]

Dividing the two numbers, the result is [tex]0.5[/tex]

Multiplying by 100 gives 50.  So, the percentage of pie that you ate (if you ate half of the pie) is 50%

When you ate three-quarters of the pie, the ratio was [tex]\frac{3}{4}[/tex]

Dividing the two numbers, the result is 0.75

Multiplying by 100 gives 75.  So, the percentage of pie that you ate (if you ate three-quarters of the pie) is 75%.

When you were making pies, and 100 pies were needed, but so far you'd only baked 75 pies, the ratio was [tex]\frac{75}{100}[/tex]

Dividing the two numbers, the result is 0.75

Multiplying by 100 gives 75.  So, the percentage of the project that you've completed at that point is 75%.

Later, when you had made 125 pies, but only 100 pies were needed, the ratio was [tex]\frac{125}{100}[/tex]

Dividing the two numbers, the result is 1.25

Multiplying by 100 gives 125%.  So, the percentage of pies you've made to complete the project at that point is 125%.... the number of pies that you've made is more than what you needed, so the baking project is more than 100% complete.

1.   27400 spectators n a 40000 seat stadium percentage.

Here, it seems that the question is asking what percentage of the stadium is full, so the whole is the 40000 seats available, and the "part" is the 27400 spectators that have come to fill those seats.

[tex]\text{ratio}=\dfrac {\text{the number of spectators filling seats}}{\text{the total number of seats in the stadium}}[/tex]

[tex]\text{ratio}=\dfrac {27400}{40000}[/tex]

Dividing gives 0.685.  Multiplying by 100 gives 68.5.  So, 68.5% of the seats have been filled.

2.   an archer scores 95 points out of a possible 125 points percentage

Here, it seems that the question is asking what percentage of the points possible were earned, so the whole is the 125 points possible, and the "part" is the 95 points that were earned.

[tex]\text{ratio}=\dfrac {\text{the number of points earned}}{\text{the total number of points possible}}[/tex]

[tex]\text{ratio}=\dfrac {95}{125}[/tex]

Dividing gives 0.76.  Multiplying by 100 gives 76.  So, 76% of points possible were earned.

The values of x and y at t=3 are -4.95 and 0.423 respectively.

The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.

The value of the tangent slope at t=3 is 4.21.

The speed at t=3 is 3.05 units/sec.

Given the equation of x as the function of t is

x= 5 cos t

similarly, the equation of y as the function of t is

y= 3 sin t

At t=3 the value of x will be

x (at t=3) = 5 cos 3= 5(-0.989)= -4.95

At t=3 the value of y will be

y (at t=3) = 3 sin 3= 3(0.141)= 0.423

The derivative of the function of x with respect to t will be

dx/dt= d(5 cos t)/dt= 5d(cos t)/dt= -5 sin t

at t=3 the value of dx/dt will be

dx/dt (at t=3) = -5 sin 3= -5(0.141)= 0.71

The derivative of the function of y with respect to t will be

dy/dt= d(3 sin t)/dt= 3d(sin t)/dt= 3 cos t

at t=3 the value of dy/dt will be

dy/dt (at t=3) = 3 cos t= 3(-0.989)= -2.97

The tangent slope is dy/dx which can be calculated by

dy/dx= (dy/dt)(dt/dx)= (dy/dt)/(dx/dt)= 3 cos t/ -5 sin t=  (-3/5) cot t

at t=3 the value of tangent slope will be

dy/dx (at t=3) = (-3/5) cot 3= 4.21

The speed at t=3 will be

speed v= [tex]\sqrt{v_{x} ^{2} + v_{y} ^{2} }[/tex]

= √(dx/dt)²+(dy/dt)²

at t=3

= √(0.71)²+(-2.97)²

= √9.325

= 3.05 unit/sec

Therefore the values of x and y at t=3 are -4.95 and 0.423 respectively.

The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.

The value of the tangent slope at t=3 is 4.21.

The speed at t=3 is 3.05 units/sec.

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Answer:

Solution:

Here,

[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}[/tex]

Weight of 13 m of rod=23.4 kg

Weight of 1 m of rod=23.4/13 kg

[less length,less weight]

Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg

[more length,more weight]

Thus,the weight of 6 m of rod is 10.8 kg.

Alternative method:

Let,the required weight be x kg.

Then,

[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}[/tex]

We know that,

More length of iron rod([tex]\red{\uparrow}[/tex]) will have the more weight([tex]\red{\uparrow}[/tex]).

So,using the rule of direct proportion;

i.e. Ratio of length=Ratio of weight

[tex] \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }[/tex]

[tex] \rm{13x = 6 \times 23.4}[/tex]

[tex] \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}[/tex]

[tex] \therefore{x = 10.8}[/tex]

Thus,the weight of 6 m long iron rod is 10.8 kg.

Jaira is completing the construction of a regular hexagon inscribed in a circle, as shown below: The next step in her construction should be:

A closed polygon with six equal sides and six equal angles is called a regular hexagon.

Thus, the steps highlighted above will help Jaira complete her construction.

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b. Total fixed cost are $49885

Sometimes production of a product may increase or decrease, but the cost which do not change with the change of output is called fixed cost of the product.

Highest monthly total cost = $83800

Highest monthly production units = 3500 desks

Lowest monthly total cost = $61900

Lowset monthly production units = 1240 desks

So, variable cost per unit = (Highest cost-lower cost)/(highest production units-lowest production units)

= ($83800-$61900)/(3500-1240)

= $21900/2260

= $9.7

∴ Total fixed costs=Highest monthly total cost-(highest production units×variable cost per unit)

= $83800-(3500×$9.7)

= $83800-$33950

= $49850

Nearest value is $49885, whch is the correct one.

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Answer:

See below

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

In the sentence "15 is 25% of 60.", 25% is the percentage.

15 is the partial amount and 60 is the total amount.

15/60 = .25

convert a decimal to a percentage by multiplying by 100

.25 × 100 = 25

Some people use a shortcut of moving the decimal two places to the right. This is the same as multiplying by 100.

15/60 is 25%

Answer:

f=- 6, x=-1

f = - 6, x=-3

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Step-by-step explanation:

please attach a picture for us to see the choices

The question is asking you to understand that a population which is raised by a common ratio over a certain time period follows an exponential pattern. See:

After 1 hour, the population is 3*10

After 2 hours, the population is 3*3*10

After 3 hours, the population is 3*3*3*10

.....

This can be generalised as a function of t, the time in hours:

f(t) = (3^t) * 10

Since the function determines the population at a given time, it is more prudent to replace f(t) with P, the population after time t:

P = (3^t) * 10

Since 20 minutes is equal to (1/3) hours, t can be substituted for (1/3) in order to calculate the population size after 20 minutes:

P = (3^(1/3)) * 10 = 14.4224957031 ≈ 14

Therefore the population after 20 minutes is 14.

Answer:

True, True, False

Step-by-step explanation:

The function has a local minima at  ( 20 , -7 )

Function is a mathematical statement formed when two algebraic expression are equated by an equal sign.

The expression given is

y = -2 +5sin ( (π/12) (x-2))

the minima of the given expression will be when

the sine term = -1

as the lowest value sin can have is -1

y = -2 +5 * (-1)

y = -7

The sin ( (π/12) (x-2)) = -1

(π/12) (x-2) = 3π /2

On solving this

x = 20

Therefore the function has a local minima at  ( 20 , -7 )

It can also be confirmed form the graph attached with the answer.

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Answer:

Step-by-step explanation:

It represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.

Here, number of hours represents input value and minutes represents the output value,

Now, By the given table,

The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),

Also,

⇒  The rate of change output value with respect to input value remains constant,

Hence, It represents a linear function because there is a constant rate of change.