Ports M and N are 162 mi apart. A ship left port M for port N
at a speed of 45 mph. Forty-five minutes later, a second ship left
port N and steamed toward the first ship at a speed of 36 mph.
How long after the departure of the first ship will the two ships
meet?

The coordinates of the vertices of the new triangle are A'(8,-12), B'(-16,20), C'(-20,0). The area of the new triangle will be 4 times the original triangle.

The scale factor is defined as the ratio of the new image's size to the old image's size. The dilation center is a fixed point in the plane. The dilation transformation is defined based on the scale factor and the center of dilation. If the scale factor is greater than one, the image will stretch.

Given that ABC is a triangle. The vertices of the triangle are A(2,-3), B(-4,5), C(-5,0).

The triangle is dilated by a scale factor of 4.

To find the coordinate of the new triangle multiply 4 with x-coordiante and y-coordiante of the vertices of the triangle ABC.

The new coordinate of A is (2×4,-3×4) → A'(8,-12).

The new coordinate of B is (-4×4,5×4) → B'(-16,20).

The new coordinate of C is (-5×4,0×4) → B'(-20,0).

To learn more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

The Answer is A

Step-by-step explanation:

Trust me I just did the Assignment.

The correct function which has a constant additive rate of change of -1/4 is shown in figure 1.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable.

Given that;

To find the correct function which has a constant additive rate of change of -1/4.

Now, From figure 1;

Two points are (2,1) and (- 2, 2).

Hence, We get;

Rate of change = (2 - 1) / (- 2 - 2)

                        = - 1/4

Thus, The correct function which has a constant additive rate of change of -1/4 is shown in figure 1.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ7

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer:

08 runners finished the race.

Step-by-step explanation:

Given that:

Number of runners at the race = 60

Number of runners dropped in first half = 1/3 of 60

Number of runners dropped in first half = \(\frac{1}{3}*60 = 20\)

Remaining runners = 60 - 20 = 40

Number of runners dropped in second half = 4/5 of 40

Number of runners dropped = \(\frac{4}{5}*40 = 32\)

Runners left = 40 - 32 = 08

Hence,

08 runners finished the race.

Answer:

  25 yards long, 5 yards wide

Step-by-step explanation:

The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.

The length and width can be represented by x and y. The formulas for area and perimeter give two equations relating these two variables:

  A = LW   ⇒   125 = xy

  P = 2(L+W)   ⇒ 60 = 2(x +y)

Using the second equation to write an expression for y, we have ...

  y = 30 -x

Substituting into the first equation gives ...

  125 = x(30 -x)

This suggests we can find x by looking for factors of 125 that total 30.

  125 = 1(125) = 5(25)

Factor totals are 126 and 30. This means we have ...

  x = 5, y = 30-5 = 25

or

  x = 25, y = 30 -25 = 5

The rectangle dimensions are 5 yards by 25 yards.

__

Additional comment

The two equations can also be solved graphically, as in the attachment.

The rectangle will be 25 yards long, and 5 yards wide.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.

The length and width can be represented by x and y. The formulas for area and perimeter give two equations relating to these two variables:

 A = LW   ⇒   125 = xy

 P = 2(L+W)   ⇒ 60 = 2(x +y)

Using the second equation to write an expression for y, we have ...

y = 30 -x

Substituting into the first equation gives ...

125 = x(30 -x)

This suggests we can find x by looking for factors of 125 that total 30.

125 = 1(125) = 5(25)

Factor totals are 126 and 30. This means we have.

x = 5, y = 30-5 = 25

x = 25, y = 30 -25 = 5

Therefore, the rectangle will be 25 yards long, and 5 yards wide.

To know more about the area follow

https://brainly.com/question/25073211

#SPJ1

If Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint

A word problem in mathematics is a maths question written as one sentence or more that requires the application of mathematics knowledge to a 'real-life' scenario.

Given that 6 gallons of light green paint use 3/8 gallon of white paint, this can be expressed as:

3/8 gallons of white paint = 6 gallons of light green

We are to determine if 9/16 gallons will be enough to make 8 gallons of light green paint. This can be expressed as

9/16 gallons of white paint = x

Divide both expressions

3/8 x 16/9 = 6/x

2/3 = 6/x

By cross multiplying

2x = 3 x 6

2x = 18

x = 18/2

x = 9

This shows that if Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint

Learn more about word problem on:https://brainly.com/question/21405634

#SPJ1

Answer:

Ab^2 = CA^2 + BC^2

8^2 = 6^2 + a^2

64 = 36 + a^2

64-36 = a^2

28 = a^2

square root of 28 = square root of a^2

5 ,29 = a

5 = a

The dollar value of total revenue at each price is $\(0\), $\(10\), $\(12\), $\(12\), $\(10\), and $\(6\). Total revenue will be the greatest at a price of $\(4\), with \(3\) units sold.

To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:

Price: $\(6\)

Quantity: \(0\)

Total Revenue: $\(6 \times 0\) = $\(0\)

Price: $\(5\)

Quantity: \(2\)

Total Revenue: $\(5 \times 2\) = $\(10\)

Price: $\(4\)

Quantity: \(3\)

Total Revenue: $\(4 \times 3\) = $\(12\)

Price: $\(3\)

Quantity: \(4\)

Total Revenue: $\(3 \times 4\) = $\(12\)

Price: $\(2\)

Quantity: \(5\)

Total Revenue: $\(2 \times 5\) = $\(10\)

Price: $\(1\)

Quantity: \(6\)

Total Revenue: $\(1 \times 6\) = $\(6\)

To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $\(3\), and the corresponding quantity sold is \(4\) units.

Therefore, at a price of $\(3\), the total revenue will be the greatest, with \(4\) units sold.

For more such questions on revenue:

https://brainly.com/question/25102079

#SPJ8

Answer:

Each friend gets 3 cards

Step-by-step explanation:

Divide 15 by 5 since he is splitting 15 cards with 5 friends.

:D

Answer:

Simplifying

6x + 32 = 180

Reorder the terms:

32 + 6x = 180

Solving

32 + 6x = 180

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-32' to each side of the equation.

32 + -32 + 6x = 180 + -32

Combine like terms: 32 + -32 = 0

0 + 6x = 180 + -32

6x = 180 + -32

Combine like terms: 180 + -32 = 148

6x = 148

Divide each side by '6'.

x = 24.66666667

Simplifying

x = 24.66666667

6x + 32> -4

6x > -4 - 32

6x > -36

x > -6

Answer:

A

Step-by-step explanation:

The equation of line is y= -4x -23

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. 

The slope of the line is the ratio of the rise to the run, or the rise divided by the run, therefore the change in y coordinate with regard to the change in x coordinate may be expressed as follows. In the coordinate plane, it describes the slope of the line.

Given:

We can take the coordinates from the given graph as (0, 3) and (2, -5)

Now, the slope = (-5 - 3)/ (2 - 0)

slope= -8/ 2

slope= -4

Now, using the point- slope form

(y - \(y_1\)) = m(x - \(x_1\))

(y- (-3))= -4( x- (-5))

y+3 = -4(x+5)

y+ 3= -4x - 20

y= -4x -23

Hence, the equation of line is y= -4x -23.

Learn more about equation of line here:

https://brainly.com/question/21511618

#SPJ2

The surface region of the cylinder will be 301.44 square inches.

Let r be the radius and h be the altitude of the cylinder. Then the surface region of the cylinder will be given as,

SA = 2πrh + 2πr² square units

The radius of the cylinder is 4 inches and the height of the cylinder is 8 inches.

Then the surface area of the cylinder is calculated as,

SA = 2πrh + 2πr²

SA = 2 x 3.14 x 4 x 8 + 2 x 3.14 x 4²

SA = 200.96 + 100.48

SA = 301.44 square inches

The surface region of the cylinder will be 301.44 square inches.

More about the surface area of the cylinder link is given below.

https://brainly.com/question/22074027

#SPJ9

Answer:

A , B and C

Step-by-step explanation:

evaluate the expressions following the order of operations as set out in PEMDAS

initial expression

note that • indicates multiplication

3 (2 + 6) + 4 × 5 ← evaluate parenthesis

= 3(8) + 20 = 24 + 20 = 44

A

5 × 4 + 3 × (6 + 2) ← evaluate parenthesis

= 5 × 4 + 3 × 8 ← perform multiplication

= 20 + 24 ← perform addition

= 44

B

(6 + 2) × 3 + 4 × 5 ← evaluate parenthesis

= 8 × 3 + 4 × 5 ← perform multiplication

= 24 + 20 ← perform addition

= 44

C

3 × 2 + 3 × 6 + 4 × 5 ← perform multiplications

= 6 + 18 + 20 ← perform addition

= 44

D

3 × 2 + (6 + 4) × 5 ← evaluate parenthesis

= 3 × 2 + 10 × 5 ← perform multiplication

= 6 + 50 ← perform addition

= 56

the expressions equivalent to the initial expression are A , B and C

Answer:

48 ounces.

Step-by-step explanation:

Steps:

Combine the weight of the cats.

12 (assuming it is a typo, 1212 pounds is a pretty big cat!) + 17 = 30 pounds

Convert to ounces.

33 pounds = 528 ounces

30 pounds = 480 ounces

Subtract the two/find the difference.

528 - 480 = 48.

The difference in ounces between Audrey's dog and the combined weights of Drew's cats is 48 ounces.

Answer:

100 pounds

Step-by-Step Explanation:

20+100=120

cat weighs 20

dog weighs 100

dog weighs 80 pounds more than the cat (20) = 100

Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

For more such questions on quadrilaterals

https://brainly.com/question/27991573

#SPJ8

The expression for the total cost of Sal's purchases is 7x + 5y cents.

We know that Sal paid (x + 2y) cents for a quart of milk and (2x + y) cents each for three cartons of orange juice.To find the total cost of Sal's purchases we need to add the cost of the milk and the cost of the three cartons of orange juice and simplify the expression.The cost of the milk is given as (x + 2y) cents. The cost of three cartons of orange juice is (2x + y) cents each.

Therefore, the cost of three cartons of orange juice is (3 × (2x + y)) cents. To find the total cost of Sal's purchases, we add the cost of the milk and the cost of the three cartons of orange juice.(x + 2y) + (3 × (2x + y)) cents = x + 2y + 6x + 3y cents= 7x + 5y cents.

For more questions on cost

https://brainly.com/question/2292799

#SPJ8

The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

Read more about volume at

brainly.com/question/463363

#SPJ1

Answer:

i think its 3 im not sure

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30/30

→ [ x = -1 ]

Hence, the value of x is -1.

Solution :

a). \($\text{Set up hypothesis}$\)

    \($\text{Null hypothesis}$\) : There is no significance between them.

                                  \($H_0:\mu_1=\mu_2$\)

    \($\text{Alternate hypothesis}$\) : There is significance between them.

                                 \($H_1:\mu_1!=\mu_2$\)

b). Test statics

    \($X(\text{mean}) = 2.214$\)

    Standard deviation \($(s.d1)=1.718; \text{Number}(n_1)=20$\)

    \($Y(\text{mean})=2.0115$\)

     Standard deviation \($(s.d2)=1.8917; \text{Number}(n_2)=20$\)

     We use the test statics :

  \($t=\frac{X-Y}{\sqrt{\frac{s.d1^2}{n_1}+\frac{s.d2^2}{n_2}}}$\)

 \($t_0=\frac{2.214-2.0115}{\sqrt{\frac{2.95152}{20}+\frac{3.57853}{20}}}$\)

 \($t_0=0.35$\)

\($|t_0|=0.35$\)

c. The critical value of |t| with minimum \($(n_1-1)$\) , i.e. 19 d.f is \($2.093$\)

   We got \($|t_0|$\) = 0.35439 and |t| = 2.093

Answer:

\(If \: d \: represents \: the \: distance \: Moby \: travels, \: one \: way \: to \: write \: a \: proportion \: for \: this \: situation \: is \: \\ \frac{240}{4} = \frac{d}{10} \)

\(Using \: cross \: multiplication \: gives \: us \: a \: new \: equation: \\ 2400 = 4d\)

\(The \: final \: step \: is \: to \: divide \: by \: 4, \: which \: tells \: us \: that \: Moby \: can \: travel \: 600 \: miles \: in \: 10 \: hours\)

Explanation:

Solve.

\( \frac{240}{4} = \frac{d}{10} \\ \\ \frac{4d}{4} = \frac{2400}{4} \\ \\ d = 600 \)

Answer:

It is -4/7

Step-by-step explanation:

\( \frac{168}{ - 294} \\ \\ = - \frac{4}{7} \)

Answer:

168/-294 × 5/5 = 840/1470

= - 840/ 1470

= 1470

Answer:

\(f'(-1) = \pm 2\sqrt{2}\)

Step-by-step explanation:

For \(f: \mathbb{R} \rightarrow \mathbb{R}\) such that \(f(x) = 7-x^2\), find \(f'(-1)\)

Recall that

\(f'(y)=x \text{ whenever } f(x) = y, \forall y \in \mathbb{R}\)

Therefore,

\(f(x) = 7-x^2 \implies y = 7-x^2 \implies x = 7-y^2 \implies y = \pm \sqrt{ 7-x}\)

\(\therefore f'(x) = \pm \sqrt{ 7-x}\)

\(f'(-1) = \pm \sqrt{ 7-(-1)} = \pm \sqrt{8} = \pm \sqrt{2^3 } = \pm 2\sqrt{2}\)

Answer:

------------------------------------------

The number is n.

The equation we can set:

Solve it:

For the given number 4 x 5³/₈. The whole part is 4 and the fraction part is 5³/₈. Both are added together to form a fraction of 43/8.

An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that.

For the given number 4 x 5³/₈.

The whole part is 4.

The fraction part is 5³/₈.

Solving the mixed fraction:

= 5³/₈.

= (5*8 + 3) /8

Both are added together to form a fraction:

= 43/8

The final number becomes:

= 4 x 5³/₈

= 4 x 43/8

= 43/2

Thus, the result of the final number obtained is 43/2.

know more about the conversion of mixed fraction

https://brainly.com/question/19318336

#SPJ1

Answer:

40% as a fraction is 40/100 which is narrowed down to 4/10 then 2/5

Hope this helps!

Answer:

40/100=4/10=2/5-------------------- By the way- I do RSM to! I don't like it-I hate it! I go to class 6_2-6th grade advanced :( No offense

Step-by-step explanation: