The position of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function y = 14t2. A second train that is 1,200 feet ahead of the first train is traveling at a constant speed of 130 feet per second and can be modeled by the function y = 130t + 1200. Solve the system of equations. Which solution represents a viable time that the trains are side by side?

A. 14 sec
B. 15 sec
C. 16 sec
D. 17 sec

Answer:

15

Step-by-step explanation:

[tex]since \: \: \frac{5}{8} \times 40 \\ = 25[/tex]

[tex]those \: that \: did \: not \: sprout \: would \: be \\ \: equals \: to \: 40 - 25 \\ = 15[/tex]

Answer:

Step-by-step explanation:

2⁵ = 2*2*2*2*2

     = 32

Answer:

3x=2y
Explanation:

There is a proportional relationship between the number of apples and  teaspoons of cinnamon that is 3x = 2y.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Given that Devon’s favorite apple sauce recipe calls for 2 teaspoons of cinnamon for every 3 apples.

Now, let x be the number of apple and y be the teaspoons of cinnamon

the proportion are;

x/2 = y/3

Therefore, the proportional relationship between the number of apples and  teaspoons of cinnamon is

3x=2y

More can be learned about proportions at;

brainly.com/question/24372153

#SPJ2

Hey there!
In order to multiply fractions, all we should do is multiply the numerator of the first fraction times the numerator and the denominator of the first fraction times the denominator of the second one:

[tex]\bold{\displaystyle\frac{2}{7} x\frac{1}{3} }[/tex]

Multiply 2 times 1 and 7 times 3:

[tex]\boxed{\boxed{\bold{\displaystyle\frac{2}{21} }}}[/tex] (Final Answer)

Hope everything is clear.

Let me know if you have any questions; if so, please comment.

#LearningDoesn'tEnd

#LearningIsFun

[tex]\rule{200}{2}[/tex]

Answer:

.0214

Step-by-step explanation:

2.14 * .01 = .0214

to check:

.0214 * 100 = 2.14

Answer:

22.50

Step-by-step explanation:

25% of 30 is 7.50

30-7.50 is 22.50

Answer: A: $22.50

Step-by-step explanation:

The original price of the game, $30, is 100%.

If the game if 25% off, then it will be, (100 - 25), 75% of its original price.

All we need to do is 75% x 30:

0.75 x 30 = 7.5 x 3 = $22.50

So your answer is A: $22.50

Answer:

60

Step-by-step explanation:

By the triangle midsegment theorem, 2(SU)=RV.

2(w-30)=w, meaning w=60.

So, RV=60 as well

The statement that describes the content of the two boxes is that the box on the top contains a pure substance, while the one on the bottom contains a mixture.

A pure substance often refers to a specific element such as nitrogen, helium, etc. that has not been modified or mixed with others.

On the other hand, a mixture includes two or more elements mixed.

The first box contains only nitrogen, which is a pure substance.

Different from the first box, this box contains two types of substances carbon and oxygen, which is why particles have two different colors. This means the content is a mixture.

Learn more about substances in: https://brainly.com/question/24372098

Answer: 0.45  and -2.74

Step-by-step explanation:

You're going to want to use the Quadratic Formula, so (-b±√(b^2-4ac))/2a.

When you plug in you should get -16 ± √16^2-4(7)(-8)/2(7)

-16± √(256+224) all divided by 2 x 7 or 14

(-16 ± 22.3607)/14

0.45  and -2.74 are your answers

Answer:

Formula for volume of hemisphere;

V = 2/3 * π * [tex]r^{3}[/tex]

π - pi, which is 3.14 or 22/7

r = radius (half of the diameter/ 1/2 x diameter)

Since we are given the diameter, we find 1/2 of the diameter to find the radius.

1/2 x 8.9(diameter)

8.9/2 = 4.45 is our radi.

So now, we plug in this value into our equation.

V = 2/3 * π * [tex]r^{3}[/tex]

V = 2/3 * 22/7 * 4.45^3

V = 2/3 * 22/7 * 88.12

V = 2/3 * 276.95

V = 184.63 cubic centimetres.

Answer:

the one you click is correct.

Step-by-step explanation:

The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series

The sigma notation of the series is: [tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

The series is given as:

7 + 16 + 25 +34 +43 +52 + 61

The above series is an arithmetic series, with the following parameters

Start by calculating the nth term using:

a(n) = a + (n - 1) * d

This gives

a(n) = 7 + (n - 1) * 9

Evaluate the product

a(n) = 7  - 9 + 9n

Evaluate the difference

a(n) = 9n - 2

So, the sigma notation is:

[tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

Read more about arithmetic series at:

https://brainly.com/question/6561461

Answer:

x = 26.3

Step-by-step explanation:

There are three trigonometric rules that this question will apply to, they are:

[tex]Sin\theta\frac{opp}{hyp} Cos\theta\frac{adj}{hyp} Tan\theta\frac{opp}{adj}[/tex]

Where opp is the length of the side opposite to angle Φ, hyp is the hypotenuse of the triangle and adj is the length of a side adjacent to angle Φ.

In the provided picture, angle Φ has been provided alongside the hypotenuse with the opposite side length needing to be calculated. A trig function that includes all three of these must be used. The only one that does have all three is sin, ergo it is what we will use.

In the current equation form, the subject is incorrect and need to be changed so that it becomes the opposite side.

[tex]Sin\theta = \frac{opp}{hyp}\\ opp = sin\theta \cdot hyp[/tex]

Plug the known values in:

[tex]x = Sin(18\textdegree) \cdot 85\\x = 0.3090169 \cdot 85\\x = 26.266\\x = 26.3[/tex]

Hope this helps!

Answer:

no they dont form a Pythagorean triple

Step-by-step explanation:

a2 + b2 = c2

3 gallons => 54 miles

so

1 gallon => 54 : 3 = 18 miles

then

8 gallons => 18x 8= 144 miles

Answer:

X = 2.8

Step-by-step explanation:

5x+2=16

5x=16-2

5x=14

x=14÷5

x=2.8

Hope that helps!

Answer:

Option 1 and 4

Step-by-step explanation:

Answer:

A represents -2.5.......

Answer:

-2.5

Step-by-step explanation:

<------3, -2.5, -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2, 2.5, 3 ---->

When it's negative on the number line the value of a number gets smaller. When it's positive the value gets bigger.

I hope this helps!

The correct statement about the data set is the mean would be the best measure of central tendency for Mr Cochran's class because the data is symetrical.

A measure of central tendency attempts to describe a data set by determining the central value of the data set. Measures of central tendency are mean, median and mode.

Mean is the average of a data set. Median is the number at the center of the data set. Mode is the number that occurs most in the data set.  A data set is negatively skewed if the mean is less than the mode. If the mean is equal to the mode, the data is symmetric.

Mean of Mrs culpepper’s class = (1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3) / 10 = 1.9

Mode of Mrs culpepper’s class = 1

Mean of mr Cochran's class  = (1+ 1 + 2 + 3 + 3 + 3 + 3 + 4 + 9 + 9) / 10 = 3.8

Mode of mr Cochran s class = 3

To learn more about median, please check: https://brainly.com/question/20434777

Answer:

a=0.7

A Area

0.49

Using the formula

A=a2

Solving fora

a=A=0.49=0.7

Answer:

[A] (4 ÷ 2)+(0.8 ÷ 2)

Step-by-step explanation:

Divide the 2 into each digit, which must be in the same spot it was before:

Knowing that 8 in 4.8 ⇒ 0.8

Thus, you can infer that [B] is wrong

You also infer that [D]  and [C] is wrong because 4 is a whole number.

Thus, that left us with [A] 4 ÷ 2+0.8 ÷ 2 which shows the quotient of 4.8 ÷ 2

Hence, [A] 4 ÷ 2+0.8 ÷ 2 is the answer.

~Learn with Lenvy~

Answer:

Option A

Simplification:

[tex]\rightarrow (4 + 0.8) \div 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{4.8 can also be written as 4 + 0.8}][/tex]

[tex]\rightarrow \dfrac{(4 + 0.8)}{2} = \dfrac{4 + 0.8}{2}[/tex]

[tex]\rightarrow \dfrac{4}{2} + \dfrac{0.8}{2}[/tex]

[tex]\rightarrow (4 \div 2) + (0.8 \div 2) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\large{[Option A}}][/tex]

Step-by-step explanation:

1.7

1.8

2.2

2.4

The other person got no 1 wrong take note

Answer:

Mariah's investement is growing faster

Step-by-step explanation:

Here to find the rate at which the savings are growing at, we have to observe the slope of the line which describes the line representing the savings of each as a function of time.

The slope of a line is given by the relation;

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Where m is the slope.

(x1,y1) is any point on the curve.

(x2,y2) is any other point on the curve.

Let's start of with Mariah by picking any 2 points from the table.

(0,150)

(1,159)

[tex]m(mar) = \frac{159 - 150}{1 - 0} = \frac{9}{1} = 9[/tex]

Let's move on to Mauricio's line and choose 2 points that lie on that line.

(0,190)

(1,195.7)

[tex]m(mau) = \frac{195.7 - 190}{1 - 0} = \frac{5.7}{1} = 5.7[/tex]

By looking at both slopes, we see that Mariah's growth rate (slope) 9>Mauricio's growth rate (slope) which is 5.7

needless to say that the conversion from miles to kilometers uses a constant value, and therefore, they're directly proportional.

now, I could write the direct proportional relation blah blah but there's no need, we can simply squeeze it out of the table by simply checking how many kilometers there are in 1 mile.

well, we know that 11.0 miles give us 17.699 km, ok hmmm if we divide 17.699 ÷ 11 = 1.609.

if we do the same on table for 26 and 41.834, so 41.834 ÷ 26 = 1.609, and the next pair 54.706 ÷ 34 = 1.609, the value of 1.609 is consistent or constant, or namely that there are 1.609 kilometers in 1 mile.

(Assuming all these lines are parallel to each other)

Angle x = 70, because it is corresponding to the 70 angle.

Angle y = 70, because it is corresponding to x

Angle z = 70, because angle z and angle y are alternate angles

(corresponding angles and alternate angles are equal to each other with the condition of parallel lines)

Answer: 4 cups

Step-by-step explanation:

First, convert the 6 cups of water to fluid ounces:

6 cups (8 fluid ounces / 1 cup) = 48 fluid ounces.

Then, since each bowl took 4 fluid ounces, and there are 4 bowls, the total fluid ounces used must be 16.

Thus, if there was 48, and 16 were used, 32 fluid ounces must be left. Convert this to cups by dividing by 8 and getting 4 cups.

Answer:

4 quarters

Step-by-step explanation:

4 quarters = $1

14 nickels = $0.70