Two trains leave towns 1152km apart at the same time and travel toward each other. One train travels 14km/h slower than the other. If they meet in 4 hours, what is the rate of each train?

[tex]\bf \stackrel{mixed}{-3\frac{3}{8}}\implies -\cfrac{3\cdot 8+3}{8}\implies \stackrel{improper}{-\cfrac{27}{8}}~\hfill \stackrel{mixed}{-1\frac{3}{4}}\implies -\cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{-\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{from left to right}}{-\cfrac{\stackrel{9}{~~\begin{matrix} 27 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\times -\cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\div -\cfrac{7}{4}}\implies \cfrac{9}{4}\div -\cfrac{7}{4}[/tex]

[tex]\bf \cfrac{9}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\times-\cfrac{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{7}\implies -\cfrac{9}{7}[/tex]

Answer:

C. [tex]y=(x-3)^2[/tex] and [tex]y=x^2-6x+9[/tex]

Step-by-step explanation:

before answering the problem let us remind the formula for square of sum and differences

[tex](a+b)^2=a^2+2 \times a \times b + b^2[/tex]

[tex](a-b)^2=a^2-2 \times a \times b + b^2[/tex]

We are going to use the above two formulas to solve each part and come to an answer

A. [tex]y = (x + 3)^2[/tex]

[tex](x + 3)^2=x^2+2 \times x \times 3 + 3^2[/tex]

[tex](x + 3)^2=x^2+6x+9[/tex]

Hence this option is not correct pair

B. [tex]y = (x-5)^2[/tex]

[tex](x - 5)^2=x^2-2 \times x \times 5 + 5^2[/tex]

[tex](x -5)^2=x^2-10x+25[/tex]

Hence this option is also not correct pair

C. [tex]y = (x -3)^2[/tex]

[tex](x - 3)^2=x^2-2 \times x \times 3 + 3^2[/tex]

[tex](x -3)^2=x^2-6x+9[/tex]

Hence this option is correct as it have equivalent pair

D. [tex]y = (x + 5)^2[/tex]

[tex](x + 5)^2=x^2+2 \times x \times 5 + 5^2[/tex]

[tex](x + 5)^2=x^2+10x+25[/tex]

Hence this option is also not correct pair

Answer:

A

Step-by-step explanation:

Lets say x=1

y: 3(1)+1=4

x: 4(1)-1=3

Final answer:

The correct option is (D) (2,7). To solve the system of equations, set them equal to each other and solve for x, which is 2, and then substitute x back into either equation to find y, which is 7. Hence, the intersection point is (2, 7).

Explanation:

To find the solution to a system of equations when graphed, you look for the point where the two lines intersect. The given equations are y=3x+1 and y=4x-1.

Since both equations equal y, you can set them equal to each other to find the point of intersection:

3x + 1 = 4x - 1.

To solve for x, subtract 3x from both sides:

1 = x - 1.

Then, add 1 to both sides to isolate x:

x = 2.

To find the corresponding y value, substitute x into one of the original equations, let's use the first one:

y = 3(2) + 1,

which simplifies to y = 6 + 1 = 7.

Therefore, the solution to the system of equations and the point of intersection is (2, 7).

Answer:

87.88 ft^2.

Step-by-step explanation:

Area = 1/2 * base * height

= 1/2 * 16.9 * 10.4

= 87.88 ft^2.

Answer:

87.88 ft²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 16. 9 and h = 10.4, so

A = 0.5 × 16.9 × 10.4 = 87.88 ft²

Answer:

The correct answer would be option A, 21.37

Step-by-step explanation:

In order to find out the percentage change of price of a product, either increase of decrease, that is found by finding the change in the price and then divide it by the base price and then finding the percentage of that price. The whole process is as follows:

Original price of iPod: $210.95

New Price of iPod: $165.88

Decrease in the price of iPod: 210.95-165.88= 45.07

Now dividing decreased price with the original price we get:

45.07/210.95=0.213652

Now to find the percentage, we need to multiply it with 100

0.213652*100=21.3652% which is approximately 21.37%

Answer:

420 minutes

Step-by-step explanation:

1 hour = 60 minutes

7 * 1 hour = 7 * 60 minutes

7 hours = 420 minutes

We know that 1 hour = 60 minutes

To find how many minutes is in seven hours, we can multiply 60 by 7 and we will get a product of 420.

1 hour = 60 minutes

2 hours = 120 minutes

3 hours = 180 minutes

4 hours = 240 minutes

5 hours = 300 minutes

6 hours = 360 minutes

7 hours = 420 minutes

The answer is:

The fraction is equivalent to 80%.

To solve the problem, we need to remember that if we want to convert from numbers to percentual values, we need to multiply the given number by 100.

So, if we have the fraction four-fifths which is:

[tex]\frac{4}{5}=0.8[/tex]

If we need to convert it to percent, we need to multiply it by 100:

[tex]0.8*100=80(percent)[/tex]

Hence, we have that the fraction is equivalent to 80%.

Have a nice day!

Answer:

80%

Step-by-step explanation:

We know 4/5 is the same as 4 divided by 5 then using long division for 4 divided by 5 gives us 0.8 converting our number to a percent

0.8 x 100 = 80%

Answer:

A=1512

Step-by-step explanation:

The area of a rectangle with a length of 27 and a height of 56 is 1512.

Formula: A=wl

A=wl=56·27=1512

Answer: 1,512 units^2

Step-by-step explanation: To find the area of a rectangle, multiply the length by the width. 27 x 56 =1512. Since you are finding the area, the answer would be squared.

Answer:

10) Exact Answer: 36

Estimate: 36

11) Exact Answer: 2001

Estimate: 1900

Step-by-step explanation:

10a) To find the exact answer, simply divide the given numbers.

10b) To find the estimated answer, use compatible numbers. We know that any "hundred" number is easily divisible by 5. Therefore, 900/5 = 36.

It is possible for the estimate to be the same as the exact answer.

10a) To find the exact answer, simply divide the given numbers.

10b) To find the estimated answer, use compatible numbers. There is no pattern we can look for, so round to the nearest whole number.

We know that if we rounded .38 to 0 or 1, the answer would not be nearly as close as if we rounded .38 to .4.

Therefore, 760/.4 = 1900

Please mark as Brainliest, hope this helps!

Answer:

5.

Step-by-step explanation:

1 1/3 * 3 3/4

= 4/3 * 15/4

= 60/12

= 5.

First we simplify,

[tex]1\dfrac{1}{3}\cdot3\dfrac{3}{4}[/tex]

to

[tex]\dfrac{4}{3}\cdot\dfrac{15}{4}[/tex]

Then we continue simplifying,

[tex]

\dfrac{4\cdot15}{4\cdot3}=\dfrac{15}{3}=\boxed{5}

[/tex]

Hope this helps.

r3t40

Answer:

x=[tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

4x-6=10x-3 (add 6 to both sides)

4x=10x+3 (subtract 10x from both sides)

-6x=3 (divide both sides by -6)

x=[tex]\frac{-1}{2}[/tex]

Answer: X = -1/2

Step-by-step explanation: Your goal is to isolate x. First, subtract 4x from each side.

-6 = 6x - 3

Add 3 on both sides.

-3 = 6x

Divide by 6 on each side.

X = -1/2

Answer:

14, 18, 20, and 24 are not perfect squares.

The numbers that are not perfect squares are:

1. 20

2. 18

3. 14

4. 24

These numbers do not have integer square roots, which means they are not perfect squares.

A perfect square is a number that can be expressed as the product of an integer multiplied by itself. For example, 25 is a perfect square because [tex]\(5 \times 5 = 25\).[/tex]

Let's examine each number:

1. 25 - This is a perfect square because  [tex]\(5 \times 5 = 25\).[/tex]

2. 20 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

3. 18 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

4. 36 - This is a perfect square because [tex]\(6 \times 6 = 36\).[/tex]

5. 16 - This is a perfect square because [tex]\(4 \times 4 = 16\).[/tex]

6. 14 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

7. 24 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

Therefore, the numbers that are not perfect squares are 20, 18, 14, and 24. They cannot be represented as the square of an integer. The other numbers, 25, 36, and 16, are perfect squares as they can be expressed as the square of an integer.

The complete question is here.

Which numbers are not perfect squares? 25 20 18 36 16 14 24

Answer:

54

Step-by-step explanation:

Answer:

54 square units

Step-by-step explanation:

In order to calculate the surface area of the prism you have to calculate the area of each face of the prism, and you have to remember the different formulas to calculate the areas:

[tex]Rectangle=Length*Width[/tex]

[tex]Triangle=\frac{Base*Height}{2}[/tex]

So you just have to insert the values into the formulas:

[tex]Rectangle1=4*3.5[/tex]

[tex]Rectangle1=14[/tex]

[tex]Rectangle2=5*3.5[/tex]

[tex]Rectangle2=17.5[/tex]

[tex]Rectangle3=3*3.5[/tex]

[tex]Rectangle3=10.5[/tex]

[tex]Triangle1=\frac{4*3}{2}[/tex]

[tex]Triangle1=6[/tex]

[tex]Triangle2=\frac{4*3}{2}[/tex]

[tex]Triangle2=6[/tex]

If you add up all the faces, you get the surface area of the prism:

14+17.5+10.5+6+6=54

If there was an illustration, I would be happy to assist you.

Answer:

Option C: (x − 3)(x + 3)(2x + 1)

Step-by-step explanation:

Answer:

  F ≥ 45

Step-by-step explanation:

"No less than" means "greater than or equal to", so you can write the expression as ...

  F ≥ 45 . . . . . miles per gallon

Answer:

s(x) = f(x) + g(x) = (5x + 2) + (7x + 4) = 12x + 6

p(x) = 6*g(x) = 6(7x + 4) = 42x + 24

Step-by-step explanation:

Answer:

-1½ = b

Step-by-step explanation:

Combining all like-terms on the right side of the equivalence symbol will give you this:

4b + 6 = 0

- 6 -6

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

4b = -6 [Divide by 4]

b = -1½ [OR -1,5]

I am joyous to assist you anytime.

Answer:

Explanation:

You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.

1. Determine the expression that relates the variables.

a) The name of the variables is given:

b) Point rules:

In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.

2) Building the graph

In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.

        x ≥ 0 and y ≥ 0

The resulting graph is attached.

Answer:

D

Thank me later!! Just did the test on edge

It is not A. because 8 is not a prime number.

It is not B. because 12 is not a prime number.

C. 2 x 2 x 2 x 2 x 2 x 3 = 4*4*6= 96

D. 2 x 2 x 2 x 2 x 2 x 3 x 3= 4*4*6*3=16*18= 288

Answer is C. -2 x 2 x 2 x 2 x 2 x 3 : 96 ( not D. = 298 , 298 is greater than 96)

The prime factorization of the number 96 is 2 x 2 x 2 x 2 x 2 x 3. The correct option is C.

A number can be expressed as a product of its prime factors through the process of prime factorization. Prime factorization is the process of factorizing the bigger numbers in a way that all the numbers are prime.

Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is any natural number greater than one that is not prime.

The given number is 96. The factorization of the number 96 will be done as below:-

96 = 2 x 2 x 2 x 2 x 2 x 3

Therefore, the prime factorization of the number 96 is 2 x 2 x 2 x 2 x 2 x 3. The correct option is C.

To know more about prime factorization follow

https://brainly.com/question/18187355

#SPJ2

Answer:

C 90

Step-by-step explanation:

Answer: OPTION B.

Step-by-step explanation:

You can observe in the figure provided that the angle 3 and the angle that measures 70° , share the same vertex, therefore, you can conclude that they are Vertical angles and they are congruent. Then:

[tex]m\angle 3=70\°[/tex]

You can notice that the angle 1 and the angle that measures 70° are Complementary angles (They add up to 90°), then you can find the measure of the angle 1:

[tex]m\angle 1+70\°=90\°\\\\m\angle 1=90\°-70\°\\\\m\angle 1=20\°[/tex]

Then:

[tex]m\angle 3-m\angle 1=70\°-20\°\\\\m\angle 3-m\angle 1=50\°[/tex]

Answer:

4

Step-by-step explanation:

Start by multiplying both sides by 4.

[tex]\frac{1}{4} x-\frac{1}{8} =\frac{7}{8} +\frac{1}{2} x\\x-\frac{1}{2} =\frac{7}{2}+2x[/tex]

Next, combine like terms.

[tex]x-\frac{1}{2} =\frac{7}{2}+2x\\-\frac{1}{2} =\frac{7}{2} +x\\x=\frac{8}{2} \\x=4[/tex]

Answer:

2.4 years

Step-by-step explanation:

you have to first convert the trees' heights into inches. three feet is equivalent to 36 inches and four feet is equivalent to 48 inches. Since three A grows at 15 inches a year it'll become a the expression 15x+36 and the expression for tree B will be 10x+48. You set them up to each other and simplify it.

15x+36=10x+48

 -10x        -10x

5x+36=48

   -36        -36

5x=12

/5    /5

x=2.4

So it'll be 2.4 years

Answer:

x=0

Step-by-step explanation:

(x-5)=4x-5

Subtract x from each side

x-5-x=4x-x-5

-5 = 3x-5

Add 5 to each side

-5+5 = 3x-5+5

0 = 3x

Divide by 3

0/3 = 3x/3

0 =x

x=0

Answer:

964.62

Step-by-step explanation:

Let x = the original price

35% less than means we pay 65% of  the original price

627 = 65% x

Changing to decimal form

627 = .65x

Divide each side by .65

627/.65 = .65x/.65

964.6153846 =x

Rounding to the near cent

964.62

Answer:

corresponding angles

Step-by-step explanation:

Corresponding angles are in matching corners .

Both 5 and 6 are in the lower left corner

Answer:

-2a²

Step-by-step explanation:

The question is  2a × -a

This means 2a(-a)

= -2×(a×a)

=-2(a²)

=-2a²

Answer:

8y³ + 6y² - 29y + 15

Step-by-step explanation:

Take each separate term in the second set of parentheses and multiply it by the terms in the first set of parentheses. Put them altogether, and you will arrive at the above answer.

I am joyous to assist you anytime.

Hence, the product is [tex]8y^3+6y^2-29y+15[/tex]

The product of two numbers is the result you get when you multiply them together. So 12 is the product of 3 and 4, 20 is the product of 4 and 5, and so on.

multiplying corresponding terms,

[tex](4y-3)(2y^2+3y-5)\\8y^3+12y^2-20y-6y^2-9y+15\\8y^3+6y^2-29y+15[/tex]

Hence, the product is [tex]8y^3+6y^2-29y+15[/tex]

to learn more about product: https://brainly.com/question/1755985

#SPJ2

Answer:

A. 3x^2+19x-14

Step-by-step explanation:

Applying the distributive property the given expression is equal to 3x²+19x-14 (Letter A).

The properties of multiplication are:

For evaluating the given question, you should apply the distributive property.

The question gives the expression (x+7)(3x-2). Thus, from the distributive property, you have:

3x²-2x+21x-14

3x²+19x-14

From the given options of the question, 3x²+19x-14 is shown in option A.

Read more about the distributive property  here:

brainly.com/question/4077386

#SPJ6