Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 18 miles per hour slower than the westbound train. If the two trains are 570 miles apart after 3 hours, what is the rate of the eastbound train?

well, let's take a look at the graph hmmmm as "x" is moving further towards the right, the line is going down, or namely "y" is lessening and lessening, which is another way to say that "y" is inversely proportional to "x".

well, we know a few points on the line hmmm let's use say hmm (10 , 8) to get the constant of proportionality.  Any point will do btw, we're just using this one.

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\stackrel{\textit{"H" varies inversely with "w"}}{H=\cfrac{k}{w}}\qquad \textit{we know that} \begin{cases} H=8\\ w=10 \end{cases} \\\\\\ 8=\cfrac{k}{10}\implies \boxed{80=k}[/tex]

Answer:

No.  Steven is not correct.

Step-by-step explanation:

The area of shape A is 15 (either multiply 5 x 3 or just count squares).  The area of shape B is 9.

15 is not double 9.

Answer:

C

Step-by-step explanation:

You just need to convert some of the mixed numbers so that they have a denominator (of the fraction part) as 8:

10 4/8 = 10 1/2

10 6/8 = 10 3/4

11 2/8 = 11 1/4

Answer:

I believe it should be

4 : 1 : 200

Step-by-step explanation:

Answer:

25/10 ,30/12,10/4

Step-by-step explanation:

1) 5/2*5/5

2)5/2*6/6

3)5/2*2/2

Answer:

The choice first

[tex] \tan(x) = \frac{12}{5} [/tex]

Answer:

x = 15°

Step-by-step explanation:

If you use Vertical Angles, you can move the two algebraic expressions next to each other and totaling 90° (because m and n are perpendicular)

x + 21 + 3x + 9 = 90°

combine like terms.

4x + 30 = 90

subtract 30 from both sides.

4x = 60

divide by 4.

x = 60/4

x = 15

Answer:

Club 1: 16 would be 120

Club 2: 15 would be 120

Answer:

I think its D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer: True

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

Answer:

True

Step-by-step explanation:

Using the vertical line test since it only passes through the graph once it is a function

Answer:

He overspent 8.61% as a percentage of his monthly salary.

Step-by-step explanation:

Answer:

8.61% (2 dp)

Step-by-step explanation:

Salary = 1850

Food = 690

Other = 940

Rent = 20.5% = 20.5/100 = 0.205

Therefore, 20.5% of the salary = 0.205 x 1850 = 379.25

Total spent = 690 + 940 + 379.25 = 2009.25

Percent change = [ (difference between initial and final value) ÷ initial value] x 100

=[(2009.25 - 1850) ÷ 1850] x 100 = 8.61% (2 dp)

Step-by-step Explanation:

First find out what is the price after 30% off.

250 · 0.3 = 75

250 - 75 = 175

Then find the tax and add it on. Remember to calculate the tax AFTER  the discount.

175 · 0.06 = 10.50

175 + 10.50 = 185.50

Answer:

The number 0.7 is plotted on the number line.

Answer:

Step-by-step explanation:

Count up 0 to 1.

Stop at the point.

If you stop at the point, you should know what the point is.

The point is graphed at 0.7.

The area of Krista’s mom new pan is 11 1/4 ft² and two possible dimensions are (5 , 4 1/2) and (4 1/2 , 2 1/2)

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

[tex]A=a\times b[/tex]

Here, (a)is the length of the rectangle and (b) is the width of the rectangle

The dimensions of pan which, Krista’s mom, had planned is 5 feet long by 4 1/2 feet wide. Therefore, the length of the pen is 5 feet and the width of the pan is 4 1/2 feet.

Thus, the area of this rectangular pan is,

[tex]A=5\times4\dfrac{1}{2}\\A=5\times\dfrac{9}{2}\\A=22\dfrac{1}{2}\rm ft^2[/tex]

The area of the pan is 22 1/2 ft².

Now, Krista’s mom has told her she needs to make the pen 1/2 the size. Thus the area of new pan is,

[tex]A=\dfrac{22\dfrac{1}{2}}{2}\\A=\dfrac{\dfrac{45}{2}}{2}\\A=\dfrac{45}{4}}\\A=11\dfrac{1}{4}}\\[/tex]

For this area, possible dimensions are 4 1/2 and 2 1/2.

Hence, the area of Krista’s mom new pan is 11 1/4 ft² and two possible dimensions are (5 , 4 1/2) and (4 1/2 , 2 1/2)

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Answer:

equation;

[tex](x + 4) {}^{2} + (y - 2) {}^{2} = 27[/tex]

Center (-4,2)

Radius is

[tex]3 \sqrt{3} [/tex]

Step-by-step explanation:

Since the x^2 and y^2 have the same coeffiecent this will be a circle in a form of

[tex](x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]

Where (h,k) is center

r is the radius

So first we group like Terms together

[tex] {x}^{2} + 8x + {y}^{2} - 4y - 7 = 0[/tex]

Add 7 to both sides

[tex] {x}^{2} + 8x + {y}^{2} - 4y = 7[/tex]

[tex]( {x}^{2} + 8x) +( {y}^{2} - 4y) = 7[/tex]

Since the orginal form of the equation of the circle has a perfect square we need to complete the square for each problem

[tex] (\frac{8}{2} ) {}^{2} = 16[/tex]

and

[tex]( - \frac{4}{2} ) {}^{2} = 4[/tex]

so we have

[tex] {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 7 + 16 + 4[/tex]

[tex] {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 27[/tex]

[tex](x + 4) {}^{2} + (y - 2) {}^{2} = 27[/tex]

To find our center, h is -4 and k is 2

so the center is (-4,2)

The radius is

[tex] \sqrt{27} = 3 \sqrt{3} [/tex]

So the radius is 3 times sqr root of 3.

Answer:

i) 134

ii) Number of bottles sold on Tuesday:   [tex]\dfrac{x}{45}[/tex]

iii) Number of bottles sold on Wednesday:  [tex]\dfrac{(x-75)}{48}[/tex]

iv) [tex]x=3915[/tex]

Therefore, 87 bottles were sold on Tuesday and 80 bottles were sold on Wednesday

Step-by-step explanation:

i) You need to ensure that the values are both in the same format (either both in dollars, or both in cents).

45 cents = 45/100 dollars = 0.45 dollars

60.30 ÷ 0.45 = 134

ii) both values are in cents, so no need to convert one of them.

Let n be the number of bottles sold.

So 45n = x

Therefore, n = x/45

ii)

Let n be the number of bottles sold.

So 48n = (x - 75)

Therefore, n = [tex]\dfrac{(x-75)}{48}[/tex]

iv)

Number of bottles sold on Tuesday:   [tex]\dfrac{x}{45}[/tex]

Number of bottles sold on Wednesday:  [tex]\dfrac{(x-75)}{48}[/tex]

If the number of bottles sold on Tuesday was 7 more than those sold on Wednesday:

[tex]\implies \dfrac{x}{45}-7=\dfrac{(x-75)}{48}[/tex]

multiply both sides by 48:  

[tex]\implies \dfrac{48x}{45}-336=x-75[/tex]

multiply both sides by 45:

[tex]\implies 48x-15120=45x-3375[/tex]

[tex]\implies 3x=11745[/tex]

[tex]\implies x=3915[/tex]

Therefore, 87 bottles were sold on Tuesday and 80 bottles were sold on Wednesday

Answer:

.25

Step-by-step explanation:

Answer:

if there are 4 people and she pours 1/4 of a 1-liter coke bottle equally, it means that she gave each member 25% or 0.25 of a liter or bottle of coke

Answer:

14 = 15 - x

Step-by-step explanation:

14 = 15 - x

14 = 15 -1

14 = 14

Hope this helps!

Answer:

5-4x

Step-by-step explanation:

8 - 4x - 3

5 - 4x

Answer:

I think your answer is 5.25% or it could be 5.3 or 5

5.26 percent of the summer camp registration decreased in 2021

The ratio of two numbers that has no dimensions is what is known as a percentage. It may be used to determine how much one number exceeds another when comparing two figures, or it is used to compare the two statistics to a uniform grid.

In 2020, there was a $285 membership fee for summer camp.

It is stated that the membership cost for summer camp increased by $15 in 2020 compared to 2021. We can calculate the summer camp registration cost for 2021 using the data given.

In 2021, there was a $285-$15 membership fee for summer camps.

there was a $270 membership fee for summer camps.

The gradual decrease in the summer enrichment registration price must be determined = (Drop/Initial Value)*100 represents the proportion decrease.

= (15/285)*100 represents the percentage decline.

The membership price for summer camps has decreased by 5.26 percent.

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Answer:

y = 10.5

Step-by-step explanation:

Δ MOP and Δ MNQ are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{OP}{NQ}[/tex] = [tex]\frac{MO}{MN}[/tex] ( substitute values )

[tex]\frac{y}{7}[/tex] = [tex]\frac{8+4}{8}[/tex] = [tex]\frac{12}{8}[/tex] ( cross- multiply )

8y = 84 ( divide both sides by 8 )

y = 10.5

Rs. 92.59 is each article's CP

Step-by-step Explanation:-

As per conditions given,

[tex]1500 \div 15 \div (1 + 8[/tex]%)

[tex] = > 100 \div 1.08[/tex]

[tex] = > approx. \: 92.59[/tex]

Hence, the CP of each article is Rs. 92.59

Answer:

x = [tex]\sqrt{48}[/tex]

Angle B = 60 degrees

Step-by-step explanation:

Since the triangle is equilateral, we know that all sides will be 8 units long. Side CB is split in half so each half (CD and DB) are 4 units long. Side CA is 8 units long and is the hypotenuse for triangle ACD. To find the unknown side (AD aka x):

4^2 + x^2 = 8^2.     use the pythagorean theorem

16 + x^2 = 64.     subtract 16 from both sides

x^2 = 48.     take the square root of both sides

x = [tex]\sqrt{48}[/tex]

For angle B, we know that all the angles in triangle ABC will be the same since it is an equilateral triangle.

180/3 = 60.     total sum of all angles in a triangle will be 180 so divide that by total angles (3)

Angle B = 60 degrees

The value of x is 6.92 units.

The measure of angle B is 60 degree.

The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

Given:

Since the triangle is equilateral all sides will be 8 units long.

and, CD or DB  = 1/2 (CB)

                          = 4 units long.

Now, In ΔACD using Pythagoras theorem

4² + x² = 8²

16 + x² = 64

x² = 48

x = 6.92 unit.

and, We know all three angles of Equilateral triangle are Equal in measure.

So, 180/3 = 60.  

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Answer:

If you don't add decimals a 63.

Step-by-step explanation:

because 55 out of 87 correct on a test would be a 63%

Answer:

x = 9/2

Step-by-step explanation:

The outside triangle is also a right triangle, with hypotenuse 8 and side 6.

The missing side can be calculated with pythagoras as:

[tex]\sqrt{8^2-6^2} = \sqrt{28}[/tex]

Now for the vertical line, lets call it y, which is a side for two "back to back" triangles, you can do pythagoras twice:

left triangle: [tex]y^2 + (8-x)^2 = 28[/tex]

right triangle: [tex]y^2 + x^2 = 6^2[/tex]

Eliminating y², you can solve:

[tex]28 - (8-x)^2 = 36 - x^2[/tex]

[tex]28 -x^2 + 16x - 64 = 36 - x^2[/tex]

[tex]16x = 36 + 64 - 28[/tex]

[tex]x = \frac92[/tex]

Answer:

Step-by-step explanation:

Find the area of the rectangle. A = length * width

Find the area of each circle.   A = π*radius*radius

Subtract the area of each circle from the area of the rectangle.

A = length * width

A = (3+6+9+12) * 18

A = 30 * 18

A = 540 square inches

Bottom circle

A = π * radius * radius.  (radius is 1/2 of the diameter)

A = 3.14 * 6 * 6

A = 133.04 square inches

Middle circle

A = π * radius * radius

A = 3.14 * 4.5 * 4.5

A = 63.59 square inches

Top circle

A = π * radius * radius

A = 3.14 * 3 * 3

A = 28.26 square inches

Subtract the circles from the rectangle.

540 - 133.04 - 63.59 - 28.26 = 315.11 square inches is the area of the shaded part.

For the given geometric series the value of the common ratio(r) is 3, while the value of a₁  is 1.

A series of numbers whose any two consecutive numbers are always in a common ratio of that series.

Given to us

Series,  1 3 9 27 81

To find the value of the common ratio(r), we will simply find the ratio of any two consecutive numbers, therefore,

[tex]r = ratio = \dfrac{3}{1} = 3[/tex]

As we can see the common ratio of the given series is 3, therefore, every next number will be thrice the number before.

We need to find the value of a₁ for the given  series, and as we know that a₁ is the first number of the series with which the series is starting, therefore,

a₁  = 1

Hence, for the given geometric series the value of the common ratio(r) is 3, while the value of a₁  is 1.

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