A train travels along a straight piece of track between 2 stations
A and B. The train starts from rest at A and accelerates at
1.25m/s² until it reaches a speed of 20m/s. Find the distance
from A to B.

The slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.

Slope, also called as gradient of a line is a value or number that describes both of the directions x and y. It basically tells the steepness of the line.

To find the slope of line, formula given below is used

[tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex] = slope

Here, y2 = 9

          y1 = 7

          x2 = 6

          x1 = 3

Thus, 9 - 7/6 - 3

= 2/3

Therefore, we can conclude that the  slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.

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Answer:

t > -2/3

Step-by-step explanation:

−8>−3t−10

Step 1: Flip the equation.

−3t−10<−8

Step 2: Add 10 to both sides.

−3t−10+10<−8+10

−3t<2

Step 3: Divide both sides by -3.

−3t/−3 < 2/−3

t > −2/3

The pairs of angles that are alternate interior angles will be angle 6 and angle 8.

When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.

Angles that are exterior to the lines, have different vertices, and sit on different sides of the transversal are referred to as alternate exterior angles. In other words, eight angles are created when a transversal intersects two parallel lines.

These van be illustrated in angle 6 and 8

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Lines l and m are parallel. Which of the following pairs of angles are alternate interior angles? ∠1 and ∠4 ∠2 and ∠3 ∠6 and ∠8

Answer:1,600

Step-by-step explanation:C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

you already have the answer :)

Answer:

all the number to the left of -12 on a number line.  -12 is not a solution.  If we were graphing this, we would have an open circle above -12 on a number line and the dark ray points to the left of -12

Step-by-step explanation:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

angle = 26 degress

complement angle = ?

Step 02:

26 + x = 90

x = 90 - 26

x = 64

The answer is:

The complement angle is 64 degrees

Answer:

d) division property of =

Step-by-step explanation:

by step 3, the variable x is still being multiplied by 3. In order to isolate x, you must divide by 3 on both sides.

we have the expression

Rewrite as equivalent rational expressions with denominator (3x-8)(x-5)(x-3)

In this problem

3x^2-23x+40=3(x-5)(3x-8)

so

Multiply by (x-3)/(x-3)

Part 2

we have the expression

we have that

3x^2-17x+24=3(3x-8)(x-3)

so

Multiply the expression by (x-5)/(x-5)

We are asked to find the simple interest associated with a principal of 5480 , an annual rate of 0.04 (4%) and at the end of 7 years:

We use the simple interest formula:

I = P r t

in our case: I = (5480) (0.04) (7) = 1534.4

So the interest is: 1534.40

We answer using two decimal places because this is refering to cents of a dollar.

The speed from City A to City B is 352 miles/hour.

Given:

Distance for trip = 1600 miles

Distance for return trip = 1600 miles

The round-trip took 8 h 20 min.

Total time taken for both trips = 8 hours 20 minutes = 8 + (1/3) hours = 25/3 hours

It is mentioned that on the return trip, the average speed was 20% faster than the outbound speed.

Let's assume x is the speed for an outbound trip.

So, x + 20% of x is the average speed of the return trip

x + 20% of x = x + 0.2x = 1.2x

Speed for the return trip = 1.2x

Total time = (distance/speed of outbound trip) + (distance/speed of return trip)

⇒ [tex]\frac{25}{3} =\frac{1600}{x} +\frac{1600}{1.2x}[/tex]

⇒ [tex]\frac{25x}{3} =\frac{1600*1.2 +1600}{1.2}[/tex]

⇒ [tex]10x = 3520[/tex]

⇒ [tex]x = 352[/tex]

Therefore, the speed from City A to City B is 352 miles/hour.

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Minh can use unitary method to determine how many cans he will need in all to paint the 12 rooms, which will give a total of 8 cans as requirement. The tools he'll need for the same are : counters, pencil and paper.

In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple.

How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units.

This is typically how the concepts of ratio and proportion are used. The unitary method entails calculating the value of a single unit before calculating the value of the required number of units.

Given, He requires 2 paint cans to paint 3 rooms.

Once more, he will require 2/3 of a can of paint to paint 1 room.

He will thus require cans of paint to paint 12 rooms, which equals (2/3)*23 = 8.

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The value of x coordinate be 0 or -2.

Given,

Vertex of the graph, f(x) = x² + 2x + 2

We have to find the x coordinate.

Here,

f(x) = x² + 2x + 2 is in the form of quadratic equation.

So, we can find x coordinate by using quadratic formula.

Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Here,

a = 1, b = 2 and c = 2

So,

[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

= [tex]\frac{-2(+-)\sqrt{2^{2}-4(1)(2) } }{2(1)}[/tex]

= [tex]\frac{-2(+-)\sqrt{4-8} }{2}[/tex]

= (-2±(-√4)) ÷ 2

= (-2±(-2)) ÷ 2

Solve for.

-2 + (-2) / 2 = -2 -2 / 2 = -4/2 = -2

Solve for,

-2 - (-2) / 2 = -2 + 2 / 2 = 0

That is,

The value of x coordinate be 0 or -2.

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Since we see that P is a point on the perpendicular bisector, l, of MN, we have proven the required PM = PN by the definition of reflection, we can conclude that point P is the image of itself , while point N is the image of M .

We are given :

P is a point on the perpendicular bisector, l, of MN.

Now, we want to prove the assertion that PM = PN

A Reflection is defined as a transformation in which a given figure is the mirror image of the other. This means that every point on the new image is a mirror reflection of itself .

From the question, we can say that by the definition of reflection, we can conclude that point P is the image of itself , while point N is the image of M .

The perpendicular bisector, l is acting as a Line of symmetry which is also called axis of reflection.

Now, due to the fact that reflections preserve lengths in transformation,  it means that we have; PM = PN.

Therefore, we see that point N is the image of M .

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Answer:

Point M

Step-by-step explanation:

Division is opposite of multiplication. If 3 groups of 4 make 12 in the multiplication, 12 divided into the 3 equal groups give 4 in each group in division. The main goal of dividing is to see how many equal groups are formed or how many are in the each group when sharing fairly.

In divisions involving fractions, numerator is called the dividend while the denominator is called the divisor while the answer is called the quotient.

Now, when Dividing decimal by a whole number, it means the decimal is the numerator while the whole number is the denominator.

The first step is to estimate quotient by approximating the dividend and divisor to the nearest compatible numbers. For example; 6.5/9

The nearest compatible number for numerator is 6 while for the denominator it is 10. Thus, we have;

7/10 = 0.7

Second step is to perform division with original numbers. This gives us;

6.5/9 = 0.722

Third step is to compare the both answers to see if our estimate makes sense.

Using compatible numbers gave us quotient of 0.7 while the normal division gave us a quotient of 0.722

Since both the quotient are very close, then it means our estimated quotient is okay.

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Assuming that the scores on the first exam are a representation for the ones in the second exam, we will see that the probabilities are:

First we want to get the probability that a randomly selected student gets better than a C on the second test.

We assume the percentages for the first test can be applied for the second, so, the ones that got better than a C on the first exam are:

A: 12%

B: 28%

Then the probability is:

P( more than a C) = 12% + 28% = 40% (or 0.40 in actual probability notation)

b) Now we want to find the probability of fail.

The percentage that failed the first test is:

100% - 12% - 28% - 41% - 11% = 8%

So 8% of the students failed the first exam, this means that the probability that a randomly selected student fails the second exam is:

P = 8% or 0.8 in decimal notation.

C) 12% of the students tgot an A, so the probability that a randomly selected student does not get an A is:

P = 100% - 12%  =88%

or 0.88 in decimal notation.

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The definition of the slope can be interpreted by the following formula.

selcect two points from the graph

(0,-2)

(0,-4)

replace the points into the formula

Since any number divided by 0 is indetermined, the slope of the line is undefined.

The parabolic equation that passes through the points is y = 29/7x^2 + -27/7x - 342/7

Parabolic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The given parameters are

x-intercepts (-3,0) and (4,0)

Point = (2,-40)

From the definition above, we have the form to be

y = ax^2 + bx + c

Substitute (-3,0) and (4,0)  in the above equation

So, we have

0 = a(-3)^2 + b(-3) + c

0 = a(4)^2 + b(4) + c

This gives

9a -3b + c = 0

16a + 4b + c = 0

Substitute (2,-40) in the above equation y = ax^2 + bx + c

a(2)^2 + b(2) + c = -40

So, we have

4a + 2b + c = -40

The equations become

9a -3b + c = 0

16a + 4b + c = 0

4a + 2b + c = -40

Using a graphing tool, we have

a = 29/7, b = -27/7 and c = -342/7

So, we have

y = ax^2 + bx + c

This gives

y = 29/7x^2 + -27/7x - 342/7

Hence, the equation is y = 29/7x^2 + -27/7x - 342/7

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Answer:

3:7

Step-by-step explanation:

Given:

To Find:

Formula used:

Using the formula, we have

No. of boys = 28 - 16 = 12

Proportion of boys = 12/28 = 3/7

So, proportion of boys = 3:7.

Answer:

6 and 2

Step-by-step explanation:

Let the first and second numbers be x and y respectively.

x = 4 + y..... (1)

2x = 4 + 4y...... (2)

Using the substitution method from Eqn(1) into (2)

Anywhere we see x in Eqn(2) we substitute it with 4 + y

I. E. 2(4 + y) = 4 + 4y

8 + 2y = 4 + 4y

Collect like terms.

8 - 4 = 4y - 2y

4 = 2y

.: y = 2

Put y = 2 in Eqn(1), and we have;

x = 4 + 2

x = 6.

.: the first number is 6 and the second number is 2.

Option C is correct.

Using proportions, it is found that due to the higher proportion of successful trials, Treatment A had the better success rate

A proportion is a fraction of a total amount, and hence it is represented by the sum of the desired amounts divided by the sum of the total amounts.

For Treatment A, we have that:

Hence the proportion of successful trials for Treatment A is given by:

315/357 = 0.8824.

For Treatment B, we have that:

Hence the proportion of successful trials for Treatment B is given by:

289/350 = 0.8257.

The proportion for Treatment A is higher, as 0.8824 > 0.8257, hence it had the better success rate.

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Answer:

  see attached

Step-by-step explanation:

You want to finish filling the given 2-way table.

Any single missing value in a row or column will be the value that makes the total correct for that row or column. Filling the single missing values will fill enough of a row or column with two or more missing values so that the remaining missing values can be filled the same way.

It is basically a series of subtraction problems.

For example, the upper left cell is filled with 20 -4 = 16, so the total on that row is 16+4=20.

The required quotient is 6.5625 when -5 2/8 is divided by (-4)/5.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

The quotient is given in the question:

-5 2/8 ÷ (-4)/5

-(42/8) / (-4)/5

Reciprocal the term in the denominator

-(42/8) × -(5)/4

210/32

6.5625

Therefore, the required quotient is -5 2/8 ÷ (-4)/5 = 6.5625.

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Given the information, we have the following:

Now, since AC=15, we have the following expression:

Solving for x we get:

Therefore, x=-6

(a) The percentage of discounts for manufacturers A and B is 32.92% and 31%, respectively.

(b) The Home Depot should buy from manufacturer A.

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[tex] = x \times 2 + 15 \\ = 2x + 15[/tex]

DOUBLING IT MEANS MULTIPLYING IT BY 2

THEN ADD 15 AS SHOWN ABOVE.

HOPE THIS HELPS

The values are as follows:

center:  y²/25-x²/25 = 1

transverse axis : b = 5

Vertices:  (0,5) and (0,-5)

Foci: (0,5√2) and (0,-5√2)

Asymptotes: y = x and y = -x

An asymptote is a line being approached by a curve but never touching the curve. i.e., an asymptote is a line to which the graph of a function converges. We usually do not need to draw asymptotes while graphing functions.

Types of Asymptotes:

1) Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k.

2) Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k.

3) Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b.

y² -x² =25 up down hyperbola with (h,k) = (0,0) a = 5 and b = 5

(y-k)²/a²-(x-h)²/b² = 1 is the standard equation of up-down hyperbola.

With semi-axis is a and semi-conjugate axis is b.

and centre (h,k).

Center = (y-0)²/5²-(y-0)²/5² = 1

= y²/25-x²/25 = 1

The axes are a = 5 and b = 5

transverse axis is b = 5

The foci are given by (h, k+c) and (h, k-c), where c = √a²+b²

c = √5²+5² = 5√2

therefore, the foci are (0,5√2) and (0,-5√2).

The vertices are (h, k+a) and (h, k-a)

(h,k) = (0,0) and a = 5 and b = 5

vertices are (0,5) and (0,-5)

Asymptotes are y = x and y = -x.

Therefore, the summary is as follows:

center:  y²/25-x²/25 = 1

transverse axis : b = 5

Vertices:  (0,5) and (0,-5)

Foci: (0,5√2) and (0,-5√2)

Asymptotes: y = x and y = -x

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[tex](5x - 23) + (7x - 1) = 180 \\ 5x + 7x - 23 - 1 = 180 \\ 12x - 24 = 180 \\ 12x = 180 + 24 \\ 12x = 204 \\ \frac{12x}{12} = \frac{204}{12} \\ x = 17[/tex]

x=17°