Do you think there are any ordered pairs that are solutions to BOTH y = x + 5 and y = –2x – 1? Explain.

Answer:

El tren tardo 0.82 minutos .

To calculate the travel time of the train, we subtract the departure time (07:34) from the arrival time (08:16), which equals 42 minutes. Thus, the duration of the train's journey is 42 minutes.

Calculating Travel Time:

The given problem is a straightforward task of subtracting the time the train left from the time it arrived at its destination. The train leaves at 07:34 and arrives at 08:16. To find out how long the journey took, we simply calculate the difference in time.

To perform the calculation, convert the times into a 24-hour format if they are not already. Since both times are in the morning, we just need to calculate the minutes. From 34 minutes past the hour to 60 minutes past the hour is 26 minutes. Then, there are an additional 16 minutes from 08:00 to 08:16. Add these two segments together to find the total duration of the trip.

The total duration is 26 minutes + 16 minutes = 42 minutes.

Therefore, it took the train 42 minutes to reach its destination.

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:

314

Step-by-step explanation:

Answer:

314

Step-by-step explanation:

I got it right.

Answer:

The volume is 58.64.

I hope this helps you out :)

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: 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:

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:

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

The graph of y - 2g(x) - 1 is obtained by applying vertical stretching, reflection, and vertical translation to the original function g(x). The transformed points are (0, -1), (-2, -9), and (4, -5).

To draw the graph of y - 2g(x) - 1, we first need to understand the transformations applied to the original function g(x). The given coordinates (0, 0), (-2, -4), and (4, -2) correspond to points on the graph of g(x).

Now, consider the expression y - 2g(x) - 1. This involves subtracting twice the values of g(x) from y and then subtracting 1. This process suggests vertical stretching, reflection, and vertical translation.

Starting with the points on g(x), let's apply these transformations:

Vertical Stretching: The factor of 2 before g(x) indicates vertical stretching by a factor of 2.

Reflection: The subtraction of 2g(x) reflects the graph over the x-axis.

Vertical Translation: Finally, subtracting 1 shifts the graph downward by 1 unit.

Applying these transformations to the given points, we get the transformed coordinates: (0, -1), (-2, -9), and (4, -5).

Now, plot these transformed points on the graph. Connect the points smoothly to represent the new function y - 2g(x) - 1.

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.

The length of minor arc AC is calculated by finding the proportion of the total circumference that the arc's angle represents. In this case, the length of minor arc AC is 3π units.

In circle geometry, the length of an arc (minor arc AC in this case) is proportional to the measure of its central angle. By knowing the central angle and the circumference of the circle, we can calculate the length of the arc. The formula for the circumference of a circle is 2πr, where r is the radius. In this case, AB is the radius, which equals to 15 units. So the circumference of the circle would be 2π * 15 = 30π units.

Now, the measure of the entire circle in terms of degrees is 360º. The measure of AC is given as 36º. Hence, minor arc AC is 36º out of the total 360º, which is (36/360) = 1/10. Therefore, the length of minor arc AC would be 1/10 of the total circumference.

Calculating the length of minor arc AC would be = 1/10 * 30π =  3π units.

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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:

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:

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:

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:

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:

B.  A = (x + 20)(x + 10) - 12

Step-by-step explanation:

please kindly check the attached file for explanation

Answer:

Step-by-step explanation:

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

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

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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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:

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

Part A

Sue

A = P*(1+r/n)^(n*t) is the compound interest formula

A = 2300*(1+0.024/1)^(1*3)

A = 2469.6061952

A = 2469.61

A - P = 2469.61-2300 = 169.61

-----------

Bill

A = P*(1+r/n)^(n*t)

A = 1800*(1+0.034/1)^(1*3)

A = 1989.9131472

A = 1989.91

A-P = 1989.91-1800 = 189.91

Bill has earned more in interest.

=====================================================

Part B

By year 2, Bill has 1924.48 pounds in his account based on the work shown below

A = P*(1+r/n)^(n*t)

A = 1800*(1+0.034/1)^(1*2)

A = 1924.4808

A = 1924.48

This amount is the new deposit, so to speak, when we change the interest rate. Now r = 0.034 changes to r = 0.04. We only go for one year so t = 1

A = P*(1+r/n)^(n*t)

A = 1924.48*(1+0.04/1)^(1*1)

A = 2001.4592

A = 2001.46

Bill has 2001.46 pounds in his account after 3 years if the interest rate for the 1234 account changes to 4% in the third year.

Now subtract off the original amount Bill deposited to get

2001.46-1800 = 201.46

For this scenario, Bill earns 201.46 pounds in interest.

Therefore, Bill has earned the most interest for both cases of the interest rate staying at 3.4% or changing to 4% for that third year.

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:

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:

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:

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:

There is a 1/2 chance of getting tails on the coin and there is 3/8 chance of the spinner landing on red. hope this helps

Final answer:

To find the probability of "tails" on the coin, and the spinner landing on red, you should multiply the probability of getting tails (0.5) by the probability of landing on red (0.375), resulting in 0.1875 or 18.75%

Explanation:

The probability of a particular outcome in a compound event (two or more independent events happening together) is the product of the probabilities of the individual events. Tossing a coin has two possible outcomes: heads or tails, each with a probability of 0.5. Spinning a spinner with 8 equal regions, where 3 are red, gives a probability of landing on red as 3 out of 8, which simplifies to 0.375.

Therefore, the probability of getting "tails" on the coin and the spinner landing on red can be calculated by multiplying the probability of getting tails on the coin (0.5) by the probability of the spinner landing on red (0.375):

Probability(Tails and Red) = Probability(Tails) × Probability(Red)

Probability(Tails and Red) = 0.5 × 0.375

Probability(Tails and Red) = 0.1875 or 18.75%

Answer:

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

Step-by-step explanation: