What is the y-coordinate of the point that divides the
directed line segment from J to k into a ratio of 2:3?

Answer:

12x484=5808

Take 484x12 should be answer

Miss Tate travels a total of 5,808 miles each year making round trip journeys from St. Louis to Indianapolis and back 12 times.

Miss Tate travels from St. Louis to Indianapolis and back, comprising a distance of 484 miles for each round trip. She does these trips 12 times a year. To find the total number of miles Miss Tate travels each year, we simply multiply the round-trip distance by the number of trips she makes. Therefore, when calculated, the total number of miles traveled by Miss Tate from St. Louis to Indianapolis and back each year is 484 miles * 12 = 5,808 miles.

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Answer:

The answer is 27,493 Puerto Rico Trench Depth Deepest Point In the Atlantic Ocean

Step-by-step explanation:

Answer:

38.6 m/s

Step-by-step explanation:

The motion of the ball is a projectile motion, which consists of two independent motions:  

- A uniform motion (constant velocity) along the horizontal direction  

- A uniformly accelerated motion, with constant acceleration (acceleration of gravity) in the downward direction  

Therefore we have to analyze the horizontal and vertical motion separately.

Along the horizontal direction, the velocity is constant during the motion, since there are no forces acting in this direction. So the horizontal velocity 3 seconds after the launch will be the same as the velocity at the launch:

[tex]v_x = v_0 = 25 m/s[/tex]

The vertical velocity instead changes according to the suvat equation:

[tex]v_y = u_y - gt[/tex]

where

[tex]u_y=0[/tex] is the initial vertical velocity

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

t is the time

Therefore, after t = 3 s,

[tex]v_y=0-(9.8)(3)=-29.4 m/s[/tex]

So the velocity after 3 seconds is < 25, -29.4 > m/s. The magnitude of the velocity is

[tex]v=\sqrt{v_x^2+v_y^2}=\sqrt{25^2+(-29.4)^2}=38.6 m/s[/tex]

The statement is true regarding the horizontal component but contains a typo in the vertical component. A ball thrown horizontally from a 150m building will maintain its horizontal velocity but the vertical velocity will be -29.4 m/s after 3 seconds. The total speed will be 38.6 m/s, not 46.493 m/s.

The statement is True. To analyze the velocity and speed of a ball thrown horizontally, we will consider two components of the motion separately: the horizontal component, which remains constant due to the absence of horizontal forces when air resistance is ignored, and the vertical component, which changes due to gravity.

Horizontally, the velocity remains at the initial value of 25 m/s because no horizontal forces are acting on the ball (assuming air resistance is negligible).

Vertically, the acceleration due to gravity (g) is 9.8 m/s2. The vertical velocity (Vy) at a time t after release can be calculated using the equation Vy = g × t, which after 3 seconds gives us Vy = 9.8 m/s² × 3 s = 29.4 m/s.

Since the question states a vertical velocity of -39.2 m/s, there might be a typo, as the correct vertical velocity should be -29.4 m/s (negative sign indicates downward direction).

Now, to find the overall speed, we use the Pythagorean theorem: speed = \/(Vx² + Vy²). Substituting Vx = 25 m/s and Vy = -29.4 m/s, we get the speed as 38.6 m/s (approximately).

Therefore, the provided velocity and speed are incorrect; the corrected velocity after 3 seconds is <25, -29.4> and the speed is approximately 38.6 m/s.

Answer:

-4 and -3

Step-by-step explanation:

-4 + -3 = -7

-4 times -3 = 12

The circumference of a circle with a radius of 9 meters, using pi as 3.142, is calculated as 56.6 meters when rounded to one decimal place.

The circumference of a circle can be calculated using the formula C = 2πr, where r is the radius of the circle.

In this case, the radius of the circle is 9m. Let's substitute this value into the formula:

C = 2 × 3.142 × 9

C = 56.556m

Therefore, the circumference of the circle is 56.6 meters (rounded to 1 decimal place).Calculating the Circumference of a Circle

To calculate the circumference of a circle with a radius (r) of 9 meters and using π (pi) as 3.142, we use the formula C = 2πr. By plugging in the given values, we get C = 2 × 3.142 × 9m. Performing the multiplication, we find that the circumference is 56.556 meters. Since we need to give our answer with one decimal place, we round to 56.6 meters.

The step-by-step calculation involves:

Answer: he invested $8600 in bonds.

Step-by-step explanation:

Let x represent the part of his money that he invested in stocks.

Let y represent the part of his money that he invested in bonds.

Ben invested part of his $15,000 savings in stocks paying 4.25% simple interest annually. He invested the rest in bonds paying 3.75% simple interest annually. It means that

x + y = 15000

The interest that he would earn on the amount invested in stocks after 1 year is

4.25/100 × x = 0.0425x

The interest that he would earn on the amount invested in bonds after 1 year is

3.75/100 × y = 0.0375y

If Ben earned $594.50 in interest after one year, it means that

0.0425x + 0.0375y = 594.5- - - - - - 1

Substituting x = 15000 - y into equation 1, it becomes

0.0425(15000 - y) + 0.0375y = 594.5

637.5 - 0.0425y + 0.0375y = 594.5

- 0.0425y + 0.0375y = 594.5 - 637.5

- 0.005y = - 43

y = - 43/- 0.005

y = $8600

x = 15000 - 8600

x = $6400

Answer:

14.137

Step-by-step explanation:

volume of a circle is 4/3pie(radius to the 3rd power)

Answer: 14 in cubed

Step-by-step explanation:

Answer:

Part a) The railroad ties are parallel

Part b) One railroad tie is perpendicular to both rails

Step-by-step explanation:

Part a) The railroad ties are each perpendicular to one rail

we know that

if one line is perpendicular to several other lines, then the other lines are parallel

Conclusion:

If the railroad ties are each perpendicular to one rail then the railroad ties are parallel

That means----> The slopes of the railroad ties are equal and they are opposite reciprocal to the slope of the rail

Part b) The rails are parallel. One railroad tie is perpendicular to one rail

we know that

if two lines are parallel and another line is perpendicular to one of them, then this line is perpendicular to both lines

Conclusion:

If One railroad tie is perpendicular to one rail, then one railroad tie is perpendicular to both rails

That means ---> The slopes of the railroad ties are opposite reciprocal to the slope of the rail

Final answer:

The railroad ties are perpendicular to both rails, and the rails are parallel to each other, reflecting principles of linear perspective in geometry.

Explanation:

The student's questions relate to geometry, specifically the properties of lines and angles about railroad tracks and railroad ties. When analyzing these geometric structures, we draw on concepts such as parallel lines, and perpendicular lines, and the characteristics of their interaction.

Analysis of Statements

Therefore, we can conclude that the railroad ties are perpendicular to both rails and that the rails are parallel to each other. This aligns with linear perspective and the visual effect of perpendicular lines (orthogonal) converging at a vanishing point as they recede into the distance.

Answer:

B.  A = (x + 20)(x + 10) - 12

Step-by-step explanation:

please kindly check the attached file for explanation

The problem involves finding the surface area and volume of a cylinder with a height of 18 ft and a diameter of 11 ft. Using the formulas for a cylinder's surface area and volume, appropriate calculations can be performed to determine the cylinder's surface area and volume.

To find the surface area and volume of a given figure, we need to identify the shape of the object. The question does not specify the shape, but the provided formulas suggest that we might be dealing with a cylinder. For a cylinder:

If the cylinder has a height (h) of 18 ft and a diameter of 11 ft (radius is half of the diameter, so r = 5.5 ft), we can calculate its surface area and volume using the following formulas:

Plugging in the values:

Now, you can substitute π with approximately 3.1416 to find the numeric answers. Remember to use the unit ft² for surface area and ft³ for volume.

Answer:

A; The approximate area of the shaded sector is 283[tex]cm^{2}[/tex]

Step-by-step explanation:

In this question, we are tasked with calculating the area of the sector of a circle that subtends a particular angle at the center of the circle

To calculate this, we use the formula for the area of a sector.

Mathematically,

Area of the shaded sector = θ/360 × π × [tex]r^{2}[/tex]

In this question, The angle subtended by the sector ;θ = 100° and radius of the circle r = 18 cm

Area = 100/360 × 22/7 × [tex]18^{2}[/tex] = 712,800/2520 = 282.86 which is approximately 283[tex]cm^{2}[/tex]

Answer:

[tex]A \approx 282.743\,cm^{2}[/tex]

Step-by-step explanation:

The approximate area of the shaded sector is:

[tex]A = \frac{100}{360}\cdot \pi\cdot (18\,cm)^{2}[/tex]

[tex]A \approx 282.743\,cm^{2}[/tex]

Answer: f(x) = (x+6)^2 -25

vertex is (-6, -25)

Step-by-step explanation: complete the square, than use the binomial formula, then simplify and expand

Answer:

equation is y = (x+1)(x+11)

vertex: (-1,-11)

Step-by-step explanation:

y = x^2 + 12x + 11. The last value, the value 11 is how we can determine our values in the equation. First we need to find the factors of positive 11 which are: -11 * -1 and 1*11. now we will look at the second portion the 12x. As we can see the value is positive. Now we will add the two factors together and see which one gives us positive 12. The factors 1 and 11 make positive 12. Now we simply just need to add those values to x. When this is factored down or in other words vertex form, the equation is y = (x+1)(x+11). The vertex is what value would make the equation equal 0.  Since -1 + 1 equals 0 then that is one of the vertex and since -11 + 11 equal 0 that also makes that a vertex. This makes the vertex -1,-11.

Answer:

314

Step-by-step explanation:

Answer:

314

Step-by-step explanation:

I got it right.

Answer:

The thickness of the walls is 0.5 feet.

Step-by-step explanation:

Let's call the thickness of each all by T.

The external dimensions of the room are 12 feet by 17 feet, and these values include thickness of 2 walls each, so the internal dimensions are (12-2T) and (17-2T).

If the internal area is 176, we have the equation:

(12-2T) * (17-2T) = 176

204 - 58T + 4T2 = 176

4T2 - 58T + 28 = 0

2T2 - 29T + 14 = 0

Using Bhaskara, we have:

Delta = (-29)^2 - 4*2*14 = 729

sqrt(D) = 27

T1 = (29 + 27)/4 = 14 feet

T2 = (29 - 27)/4 = 0.5 feet

As the first value is too big and would generate a negative side for the room, we have that the thickness of the walls is 0.5 feet.

Answer:

D

Step-by-step explanation:

C = 2pir

Divide both sides by 2pi

C/(2pi) = 2pi/2pi r -->

C/(2pi) = r

That's D

The required solution of given formula is r = C/(2π). which is the correct answer would be option (D)

What is the Circumference of a circle?

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have been given that formula as:

⇒ C = 2πr

We have to formula solve for r

⇒ C = 2πr

Divide both sides by 22π

⇒ C/(2π) = r2π/2π

⇒ C/(2π) = r or

⇒ r = C/(2π)

Hence, the correct answer would be option (D)

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Answer:

1/2

Step-by-step explanation:

The first thing you want to do is get y by itself. Subtract 7 from both sides:

2x-4y=-7

and then subtract 2x ( the goal is to make your equation look like this: y=mx+b):

-4y= -2x-7

Now, y is mostly isolated, all you have to do now is divide both sides by -4 in order for y to be completely by itself:

y=-2/-4x -7/-4

Simplify completely:

y=1/2x+7/4

Now you have your equation you can easily read it as y=mx+b.

** m is slope & b is the y-intercept**

So your slope would be: 1/2

Answer:

X+5

X = -5

-5 plus 5 equals 0

2x-3

X= 3/2

-3/2 plus 3/2 equals 0

The solutions to the equation (x+5) (2x-3) = 0 are x = -5 and x = 3/2.

Given that an equation (x+5) (2x-3) = 0, we need to find the solution of the equation,

To find the solutions to the equation (x+5) (2x-3) = 0, we set each factor equal to zero and solve for x,

Seetting x + 5 equal to 0:

x + 5 = 0

x = -5

Seetting 2x-3 equal to 0:

2x - 3 = 0

2x = 3

x = 3/2

Therefore, the solutions to the equation (x+5) (2x-3) = 0 are x = -5 and x = 3/2.

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Answer:

1.2^n

Step-by-step explanation:

since a single dot brings about an increment by 20%, the total magnification becomes 120% after the click. The common ratio = 120 / 100 = 1.2

the formula  becomes 1.2^n  

The formula for the nth term of the geometric sequence that represents the magnification of each zoom level is an = (1.2)n-1.

In this problem, you are looking at a geometric sequence that represents the magnification of each zoom level on a map. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

In this case, the common ratio is 1 + 0.2 = 1.2 because the magnification increases by 20% (or 0.2 in decimal form) each time. We can denote the nth termed 'an'. The general formula for the nth term in a geometric sequence is: an = a1 * rn-1.

Since the initial magnification doesn't specify a specific value, we will take a1 as 1 for this case. Substituting these values into the formula yields: an = 1 * (1.2)n-1, or just an = (1.2)n-1.

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Answer:

 52

Step-by-step explanation:

Let x represent the smallest of the three numbers. Then the other two are (x+2) and (x+4). Their sum is ...

  x + (x+2) +(x+4) = 162

  3x = 156 . . . . . . . . . . . .subtract 6

  x = 156/3 = 52

The smallest of the three numbers is 52.

___

I like to work problems like this by considering the average number. Here, the average of the three numbers is 162/3 = 54, the middle number of the three. Then the smallest of the three consecutive even numbers is 2 less, or 52.

Answer:

The answer is:

The domain consists of all the x-values

Step-by-step explanation:

The domain is the set of possible input values

The domain is the set of all possible values of the independent variable

In any ordered pair (x , y), x is the input (independent)

The domain is all values of x which make the function defined

The range is the set of possible output values

The range is the complete set of all possible resulting values of the dependent variable

In any ordered pair (x , y), y is the out put (dependent)

The range is all values of y which corresponding to x

The answer is:

The domain consists of all the x-values

Answer: 2

Turn 2 1/7 into an Improper Fraction

Multiply 2×7 and get 14. Now add 1 and get 15.

2 1/7 = 15/7

Turn 1 1/14 into an Improper Fraction

Multiply 1×14 and get 14. Now add 1 and get 15.

1 1/14 = 15/14

Your New Problem: 15/7×15/14

Multiply

15/7×15/14=225/98

Simplify

225/98=2.29591836735

Round (Nearest ones)

2.29591836735 rounded equals 2

Final Answer: 2

Answer:

[tex]2[/tex]

Step-by-step explanation:

[tex]2 \frac{1}{7} \div 1 \frac{1}{14} \\ \frac{15}{7} \div \frac{15}{14} \\ \frac{15}{7} \times \frac{14}{15} \\ = \frac{2}{1} = 2[/tex]

Answer:

Step-by-step explanation:

on the number line your starting point is  6 then go back 9 and you will get -3

Answer:

Step-by-step explanation:

let n be the total number of notebooks.

let p be the total number of pens.

according to the question total number of pen and notebook is 8.

Therefore mathematically

n+p = 8 ---------------------equation A

______________________________________________

cost of one notebook = $2.50

number of notebook = n

therefore total cost of n notebook = n* 2.50 = 2.5n

cost of one pen = $2.00

number of pen = p

therefore total cost of p pen = p* 2.00 = 2p

according to the question total c cost of pen and notebook is $19.00.

Therefore mathematically

2.5n + 2p = 19 ---------------------equation B

______________________________________________

Set of equation as required by question are

Answer:

6,2

Step-by-step explanation:

(looked at in desmos)

Answer:

The volume is 58.64.

I hope this helps you out :)

Answer:

7. A = 40.8 deg; B = 60.6 deg; C = 78.6 deg

8. A = 20.7 deg; B = 127.2 deg; C = 32.1 deg

Step-by-step explanation:

Law of Cosines

[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]

You know the lengths of the sides, so you know a, b, and c. You can use the law of cosines to find C, the measure of angle C.

Then you can use the law of cosines again for each of the other angles. An easier way to solve for angles A and B is, after solving for C with the law of cosines, solve for either A or B with the law of sines and solve for the last angle by the fact that the sum of the measures of the angles of a triangle is 180 deg.

7.

We use the law of cosines to find C.

[tex] 18^2 = 12^2 + 16^2 - 2(12)(16) \cos C [/tex]

[tex] 324 = 144 + 256 - 384 \cos C [/tex]

[tex]-384 \cos C = -76[/tex]

[tex]\cos C = 0.2[/tex]

[tex] C = \cos^{-1} 0.2 [/tex]

[tex] C = 78.6^\circ [/tex]

Now we use the law of sines to find angle A.

Law of Sines

[tex] \dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C} [/tex]

We know c and C. We can solve for a.

[tex] \dfrac{a}{\sin A} = \dfrac{c}{\sin C} [/tex]

[tex] \dfrac{12}{\sin A} = \dfrac{18}{\sin 78.6^\circ} [/tex]

Cross multiply.

[tex] 18 \sin A = 12 \sin 78.6^\circ [/tex]

[tex] \sin A = \dfrac{12 \sin 78.6^\circ}{18} [/tex]

[tex] \sin A = 0.6535 [/tex]

[tex] A = \sin^{-1} 0.6535 [/tex]

[tex] A = 40.8^\circ [/tex]

To find B, we use

m<A + m<B + m<C = 180

40.8 + m<B + 78.6 = 180

m<B = 60.6 deg

8.

I'll use the law of cosines 3 times here to solve for all the angles.

Law of Cosines

[tex] a^2 = b^2 + c^2 - 2bc \cos A [/tex]

[tex] b^2 = a^2 + c^2 - 2ac \cos B [/tex]

[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]

Find angle A:

[tex] a^2 = b^2 + c^2 - 2bc \cos A [/tex]

[tex] 8^2 = 18^2 + 12^2 - 2(18)(12) \cos A [/tex]

[tex] 64 = 468 - 432 \cos A [/tex]

[tex] \cos A = 0.9352 [/tex]

[tex] A = 20.7^\circ [/tex]

Find angle B:

[tex] b^2 = a^2 + c^2 - 2ac \cos B [/tex]

[tex] 18^2 = 8^2 + 12^2 - 2(8)(12) \cos B [/tex]

[tex] 324 = 208 - 192 \cos A [/tex]

[tex] \cos B = -0.6042 [/tex]

[tex] B = 127.2^\circ [/tex]

Find angle C:

[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]

[tex] 12^2 = 8^2 + 18^2 - 2(8)(18) \cos B [/tex]

[tex] 144 = 388 - 288 \cos A [/tex]

[tex] \cos C = 0.8472 [/tex]

[tex] C = 32.1^\circ [/tex]

Answer:

I think It would be C or B

Step-by-step explanation:

Depending on the value of the car at first purchase.

Answer:

C

Step-by-step explanation:

23,490/29000=0.81

0.81*23,490=19026.90

Answer:

the probability of P given K is 0.86

Step-by-step explanation:

Conditional probability is defined as the probability that an event would happen based on the occurrence of an event that has already happened. It is calculated by multiplying the probability of the both the preceding event and the succeeding event together. It is given by the formula:

[tex]P(B/A)=\frac{P(A nB)}{P(A)}[/tex]

Given that:

Probability of members in the key club P(K) = 7.8% = 0.078

Probability of members enrolled in AP physics P(P)  = 8.6% = 0.086

Probability of members in both P(P n K) = 6.7% = 0.067

Therefore:

[tex]P(P/K)=\frac{P(PnK)}{P(K)} =\frac{0.067}{0.078} = 0. 86[/tex]

the probability of P given K is 0.86

Answer:

100 seconds or 1 minute 40 seconds

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

20,000 divided by 200

=100

Answer:

Branliest appreciated

3. x = 14 degrees

4. x = 17.5 degrees

Step-by-step explanation:

SO, The first question:

6x - 21 = 105

6x = 105 -21

6x = 84

x = 14

SO, The second question:

55 + 85 = 8x

140 = 8x

17.5 = x