Monster Mike's truck decelerates from 72 m/s to 0 m/s in 6 seconds. What is his rate of deceleration?

Answer:

54 words  does Rachel type per minute

Step-by-step explanation:

Unit rate defined as the rates are expressed as a quantity as 1 such as 4 meter per seconds or 5 km per hour

As per the statement:

Rachel types 162 words in 3 minutes Rachel types at a constant rate.

We have to find  how many words does Rachel type per minute.

By definition of unit rate:

[tex]\text{Unit rate per minute} = \frac{162}{3}[/tex]

Simplify:

[tex]\text{Unit rate per minute} =54[/tex] words

Therefore, 54 words  does Rachel type per minute

The number of words typed by Rachael in one minute at a constant rate is 54 words

The parameters given :

Step-by-step explanation:

Since, the typing rate is constant ; the typing rate per minute can be calculated thus :

Therefore, Rachael types at a constant rate of 54 words per minute.

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we know that

The hallway is painted using equal amounts of white and black paint

so

To know the amount of white paint------> calculate the area of white paint

[tex]A=5x*6=30x\ ft^{2}[/tex]

To know the amount of black paint------> calculate the area of black paint

[tex]A=(x+1)*4*6=(24+24x)\ ft^{2}[/tex]

equate the areas

[tex]30x=(24+24x)\\30x-24x=24\\6x=24\\x=4\ ft[/tex]

Find the length of the hallway

[tex]5x+(4x+4)=9x+4=9*4+4=40\ ft[/tex]

therefore

the answer part a) is

The hallway is [tex]40\ ft[/tex] long

Part b) Can this same hallway be painted with the same pattern, but using twice as much black paint as white paint?

we know that

the amount of white paint is [tex]30x\ ft^{2}[/tex]

if the black paint is twice that the white paint

then

amount of black paint is [tex]2*30x=60x\ ft^{2}[/tex]

amount of black paint with the same pattern is [tex](24+24x)\ ft^{2}[/tex]

equate

(24+24x)\ ft^{2}=(60x)\ ft^{2}

solve for the new value of x

[tex]24x+24=60x\\ 60x-24x=24\\ x=24/36\\x= 2/3\ ft[/tex]

Find the new length of the hallway

[tex]5x+(4x+4)=9x+4=9*(2/3)+4=10\ ft[/tex]

therefore

the answer is

Yes, the same hallway can be painted with the same pattern, using twice as much black paint as white paint, but the hallway decreases in length

Answer:

Thank you so much callculista

Step-by-step explanation:

If money you earn at your job varies directly with the number of hours you work. Then 20 hours will you need to work to earn $145 if you earn $21.75 for 3 hours

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

Amount or money you earn at your job varies directly with the number of hours you work

One can earn  $21.75 for 3 hours

We need to find how many hours taken to earn $145.

To find this we form an equation.

Let x be the number of hours to earn 145

21.75/3=145/x

Apply cross multiplication

21.75x=3×145

21.75x=435

Divide both sides by 21.75

x=20

Hence, it took 20 hours to earn $145.

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RS and RT are both segments on the same line. Therefore their equation can be added together and set equal to the equation that is given representing the entire length of segment ST.:

4x+10+ -2x+24=4x+12

Now that you have created one larger equation to solve for x you can now go ahead and combine like terms, (all the x's with the x's and the regular numbers with the regular numbers)

2x+34=4x+12

Now you must move the variables and constants to the opposite sides of the equation. This is called isolating the variable:

2x= 22

Now you can solve for x by dividing by 2 and your answer is x = 11

Now that you have solved for the value of x you can take that value and plug it into the equation that is given for the length of segment RS.

-2X+24 NOW BECOMESSS......

-2(11)+24= -22+24= 2

The length of segment RS is 2

The business bought a total of 2,048 pens over two months. In the first month, they purchased 1,152 pens, and in the second month, they purchased 896 pens.

The problem involves simple multiplication and addition operations. First, we need to find out how many pens the business bought in total for each month. In the first month, the business bought 9 bags of pens, and each bag contains 128 pens. So, we multiply 9 (number of bags) by 128 (number of pens per bag) to get 1,152 pens for the first month.

For the second month, the business bought 7 bags of pens. Again, we multiply 7 (number of bags) by 128 (number of pens per bag) to get 896 pens.

Finally, we add together the totals for the two months: 1,152 pens (for the first month) plus 896 pens (for the second month) gives us a total of 2,048 pens bought by the business over the two months. So, the correct answer is B. 2,048 pens.

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Answer: -11, -9, -7

the smallest:   2x+1 = -11

Step-by-step explanation:

{z - some integer}

2z+1  - the smallest number

7(2z+1)  - seven times the smallest number

2z+1+2=2z+3  - the middle number

2z+3+2 = 2z+5 - the largest number

2(2z+5) - twice the largest number

7(2z+1) + 2(2z+5)  - the sum of 7 times the smallest and twice the largest

7(2z+1) + 2(2z+5)   = -91

14z + 7 + 4z + 10 = -91

             -17              -17

     18z   = -108

      ÷18        ÷18

       z = -6

2z+1 = 2(-6)+1 = -12 + 1 = -11  

2z+3 = 2(-6)+3 = -12 + 3 = -9

2z+5 = 2(-6)+5 = -12 + 5 = -7        

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# SPJ 5

Answer: +5

Explanation: When a problem is asking us to find the absolute value of a number, it's really asking us how far is that number from zero.

So the absolute value of -5 is really asking us

how far is -5 away from zero on a number line.

I have drawn a number line below and you can see that -5

is 5 units to the left of zero which means its 5 units from zero.

So the absolute value of -5 is +5.

The expression (3x - 2) is a factor of the given expression 18x² - 12x - 3x + 2. The correct answer would be an option (A).

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

18x² - 12x - 3x + 2

We have to determine the factor of the given expression.

As per the question, we have

18x² - 12x - 3x + 2

Factor out the above expression, and we get

6x(3x - 2) - 1(3x - 2)

(6x - 1)(3x - 2)

Thus, the expression (3x - 2) is a factor of the given expression.

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divide the yearly pay by 12 ( 12 months in a year)

45650 / 12 = 3804.17 per month

6 Glasses Ryan can made.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Ryan made 3/4 of a gallon of lemonade.

Each glass holds 1/8 of a gallon of lemonade.

so, the number of glasses of Ryan made

= (3/4)/ (1/8)

= 3/4 x 8

= 3 x 2

= 6

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By using a distributive property the expression 48 + 30 will be written as 6(8+5).

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

Given expression of addition is 48 + 30. The expression by using distributive property will be written as:-

E = 48 + 30

Take 6 commons from the above equation.

E = 48 + 30 = 6 ( 8 + 5 )

48 + 30 = 6( 8 + 5 ) ( Distributive property )

Therefore, by using a distributive property the expression 48 + 30 will be written as 6(8+5).

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