A cyclist rides her bike at a rate of 21 kilometers per hour. What is this rate in kilometers per minute? How many kilometers
will the cyclist travel in 2 minutes? Do not round your answers.

Final answer:

Both lawn care services, Green Lawn and Grass Team, will cost the same after 3 months, with each service costing a total of $136 at that point.

Explanation:

The student asked at how many months will both lawn care services, Green Lawn and Grass Team, cost the same and what will be that cost. To solve this, we set up an equation with Green Lawn's cost model: $49 (startup fee) + $29 per month (monthly fee) and Grass Team's cost model: $25 (startup fee) + $37 per month (monthly fee). Let m represent the number of months.

The equation will look like this:
49 + 29m = 25 + 37m

To find the number of months where the costs are the same, we will solve for m:

Therefore, both services will cost the same after 3 months. The total cost at this point will be calculated by substituting m back into either cost model (we will use Green Lawn's model):

Answer:

[tex]50+5x\le 100[/tex]

[tex]x\le 10[/tex]

You can visit at most 10 swim classes.

Step-by-step explanation:

Let x be the number of swim classes you can attend with.

At your local pool, it costs $50 to join the swim association and $5 for each swim class. then x classes cost $5x and the total cost is $(50 + 5x).

You have budgeted $100 to improve your swimming over the summer. Hence,

[tex]50+5x\le 100[/tex]

Solve this inequality:

[tex]50+5x-50\le 100-50\\ \\5x\le 50\\ \\x\le 10[/tex]

You can visit at most 10 swim classes.

The student can join the swim association and attend up to 10 swim classes within the $100 budget.

This question is asking for the creation and solution of an inequality based on a budgeting scenario. The student has budgeted $100 and needs to spend $50 to join the swim association, leaving $50 for swim classes at $5 each. The problem can be represented by the inequality 5c ≤ 50, where c is the number of swim classes.

To solve the inequality, you would divide both sides by 5. The solution of this inequality is c ≤ 10. So, the student can attend up to 10 swim classes within the budget.

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Answer:

No Solution.

Step-by-step explanation:

2 - 3(x + 4) = 3(3 - x)

2 - 3x - 12 = 9 - 3x

Move the terms in x to one side and the numbers to the other

-3x + 3x = 9 - 2 + 12

0 = 19.

This is absurd so there is No Solution.

Lily has saved $ 7

Solution:

Given that bracelet costs $30

The bracelet Lily would like to buy costs $5 less than 5 times the amount she has saved

Cost of bracelet = $ 30

From given statement,

Cost of bracelet = 5 times the amount she has saved - 5

Let "x" be the amount saved by lily

Cost of bracelet = 5 times x - 5

Here "times" represents multiplication

30 = 5(x) - 5

30 = 5x - 5

30 + 5 = 5x

5x = 35

On dividing 35 by 5 we get 7

x = 7

Thus Lily saved $ 7

Answer:

1.  Start with the cost of the bracelet: 30.

2. Add 5: 30 + 5 = 35.

3. Divide by 5: 35 / 5 = 7

So, Lily has $7 saved

Step-by-step explanation:

Hope it helpss ! :D

Answer:

Step-by-step explanation:

Sum all the angles of triangle =  180

One angle is 90 as it is a right angle.Take the unknown angle as X.

90 + 20 + x = 180

110 + x = 180

x = 180 - 110

x = 70

47 / 14 ≈ 3.36

Firstly, let's covert the fraction 47 / 14 to a decimal. The decimal format of 47 / 14 will be

Finally, let's approximate the decimal to the nearest hundredth

Always remember to use the approximate symbol when you approximate an answer.

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Final answer:

To round 47/14 to the nearest hundredth as a decimal, divide 47 by 14 to get 3.3571..., and then round this to 3.36 since the third decimal place is 7.

Explanation:

To convert the fraction 47/14 to a decimal rounded to the nearest hundredth, you first divide 47 by 14. This gives you the decimal form. After obtaining the decimal, you look at the third decimal place. If it's 5 or more, you round the second decimal place up. If it's less than 5, you leave the second decimal place as is.

Dividing 47 by 14 gives us 3.3571... To round it to the nearest hundredth, we look at the third decimal place, which is a 7, so we round up the second decimal place from 5 to 6, thus the answer is 3.36.

Solving for x...

22+0.50x=37+0.35x

22+0.15x=37

0.15x=15

x=100

Answer:

An odd number is an integer which is not a multiple of two; A number that when divided by two, leaves a remainder. If it is divided by two the result is a fraction. One is the first odd positive number. ... Some sequential odd numbers are: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35}, and so on.

Step-by-step explanation:

Answer:

I cant see the numbers, but I will tell you the definiton of an odd number:

An odd number is a number that leaves a remainder or a fraction when divided by 2.

Answer: 41/100

Step-by-step explanation: First, we can change .41 to 0.41 by putting a zero in front of the decimal point.

Using the place value chart, we can see that 0.41 means 0 units, 4 tenths a 1 hundreth. Think of 4 tenths and 1 hundredth as 41/100 so we have 41/100.

Since the fraction 41/100 is in lowest terms, this is our final answer.

Answer:

Ans => 45

Step-by-step explanation:

3(d+1) = 4(d-2)

Expanding the brackets we have:

3d + 3 = 4d - 8

our aim now is to solve for d

3d - 4d = -8 - 3

-d = -11

=> d = 11

we can now get 5(d-2)

substituting d = 11

5(11-2)

5(9)

= 45

The value of 5(d-2) is 45.

3(d+1)=4(d–2)

3d + 3 = 4d - 8.

3d - 4d = -8 - 3.

-d = -11

d = 11

Substitute d = 11 into 5(d–2):

5(d-2)=5(11-2)

= 5(9)

= 45.

Answer:

21

Step-by-step explanation:

32-25<1/3x

7*3=x

21=x

Answer:

171

Step-by-step explanation:

Carl’s age, 32 + 25 = 57

57 x 3 = 171

Answer:

x=7

Step-by-step explanation:

The function is:

f(x)=3x-21.

The zero(s) is/are any value(s) that make(s) the function equal(s) to zero.

This implies that, to find the zero(s), we equate the function to 0 and solve for x

This implies that:

3x-21=0

3x=21

Dividing through by 3, we obtain

x=7

Answer:

y=80x+50 for the one time service fee.

Anytime after that would be y=80x

Step-by-step explanation:

Y is how much the total is and 80 is how much it is an hour. X is the number of hours worked. With the first time fee of $50, your equation would be y=80x+50. Anytime after that, excluding the “one time fee,” the equation would be y=80x.

For this case we must resolve the following inequality:

[tex]750x + 150 <1000[/tex]

Subtracting 150 from both sides of the inequality we have:

[tex]750x <1000-150\\750x <850[/tex]

We divide between 750 on both sides of the equation:

[tex]x <\frac {850} {750}[/tex]

We simplify, dividing by 5 numerator and denominator:

[tex]x <\frac {170} {150}[/tex]

We simplify, dividing by 5 numerator and denominator:

[tex]x <\frac {34} {30}[/tex]

We simplify, dividing by 2 numerator and denominator:

[tex]x <\frac {17} {15}[/tex]

Thus, the solution is given by all values of x less strict than[tex]\frac {17} {15}[/tex]

Answer:

[tex]x <\frac {17} {15}[/tex]

Answer:

The length of the carpet = l = 5 meter  

The cost of carpeting the room is Rs 6300  .

Step-by-step explanation:

Given as :

The area of the room = 45 m²

The width of the carpet = w = 9 m

Let The length of the carpet = l meter

The cost of the carpet per meter = Rs 225

Let The cost of carpeting the room = Rs x

Now, According to question

The Area of room = length × breadth

Or, 45 m² = l m × b m

Or,  45 m² = l m × 9 m

∴  l = [tex]\dfrac{45}{9}[/tex]

i.e l = 5 m

So, The length of the carpet = l = 5 meter

Again

Perimeter of carpet = 2 × length + 2 × width

Or, Perimeter of carpet = 2 × 5 m + 2 × 9 m

Or, Perimeter of carpet = 28 meters

∵ The cost of carpet per meter = Rs 225

∴ The cost of carpeting the room = Rs 225 × 28

i.e The cost of carpeting the room = Rs 6300

Hence, The length of the carpet = l = 5 meter and The cost of carpeting the room is Rs 6300  . Answer

Answer:

(2, 1).

Step-by-step explanation:

f(x)=2x^2-8x+9

Find -b/2a first, it's -(-8)/2(2)=8/4=2.

Then find the y-coordinate of the vertex.

2(2)^2-8(2)+9=2(4)-16+9=8-16+9=-8+9=1

Answer:

B. [tex]x=-210[/tex]

D. [tex]x=-201[/tex]

Step-by-step explanation:

Given:

The inequality for 'x' is given as:

[tex]x<-200[/tex]

The above inequality tells us that, the value of the variable 'x' is less than -200.

-200 is a negative number. So, for a negative number, the larger the value of the number, the smaller the number is.

Example: -2 is less than -1 although 2 has a greater magnitude than 1.

Therefore, the numbers that are less than -200 are -210 and -201.

So, the values of 'x' that satisfy the given inequality are -201 and -210

Thus, the correct options are (B) and (D).

Answer:

20/3

Step-by-step explanation:

Answer:

hence small rolls 60 and large rolls 70

Step-by-step explanation:

let club sold s small rolls

hence club sold s+10 large  rolls

earning from small roll 3s

earning from large rolls 4.5(s+10)

hence

4.5(s+10) - 3s  = 135

or  4.5(s+10) = 3s +135

3s +135 = 4.5(s+10)

3s +135 = 4.5s +45

4.5s +45 = 3s +135

4.5s -3s = 135-45

1.5s = 90

s = 90/1.5

s= 60

s+10 = 70

hence small rolls 60 and large rolls 70

The history club sold 60 small rolls of wrapping paper according to the given equation.

The subject here is Mathematics, specifically algebra. The equation given by the problem, 3S + 135 = 4.5(S + 10), can be solved to find 'S', which represents the number of small rolls sold by the history club. Start by distributing the 4.5 across the (S + 10) on the right side of the equation. This gives 3S + 135 = 4.5S + 45. Subtract 3S from both sides of the equation to get 135 = 1.5S + 45. Subtracting 45 from both sides then gives 90 = 1.5S. Finally, divide each side of the equation by 1.5 to get S = 60. So, the history club sold 60 small rolls.

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Answer:

Step-by-step explanation:

Sam has sold 63 pizzas, because the problem is asking what is the half of 126 basically, which is 63 and is also saying that sam sold HALF as many pizzas.

Answer:

4/3

Step-by-step explanation:

(1/3)/(1/4)

(1/3)(4/1)

4/3

The ratio 1/3:1/4 is simplified to 4:3 by finding a common denominator. In the given proportion with a scale factor, cross-multiplication is used to find the actual dimension which results in x=8 when the scale dimension is 4.

To express the ratio 1/3:1/4 in its simplest form, find a common denominator for the two fractions, which in this case is 12. The fraction 1/3 is equivalent to 4/12, and 1/4 is equivalent to 3/12. Therefore, the ratio 1/3:1/4 becomes 4/12:3/12. Since both denominators are the same, they can be canceled out, leaving us with the simplified ratio 4:3.

Now, let's apply this to a problem with a scale factor. For the proportion 1:2=4:x, to find the value of x, you can cross-multiply. This gives us 1*x = 2*4 which simplifies to x=8. Therefore, if the scale dimension is 4, the actual dimension is 8.

Answer:

A & B Not Similar B & C Not Similar A & C Similar

Step-by-step explanation:

i just took the test and these are the correct answers that they gave on review of test, Youre welcome :)

Answer: At [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.

Step-by-step explanation:

Since we have given that

Distance at which Selena is standing on a rock cliff = 52 feet

Height of boulder above a rock cliff = 12 foot

So, the given quadratic equation would be

[tex]p(t)=-16t^2+12t+52[/tex]

First we derivative it w.r.t  t,

[tex]p'(t)=-32t+12[/tex]

Now, we will find the critical value,

[tex]-32t+12=0\\\\-32t=-12\\\\t=\dfrac{12}{32}=\dfrac{6}{16}=\dfrac{3}{8}[/tex]

Now, we will check whether it is maximum or not.

[tex]p''(t)=-32<0[/tex]

So, we get that it is maximum.

Hence, at [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.

Answer:

The answer is t=3/8

Answer:

10%

Step-by-step explanation:

Good morning,

Answer:

Step-by-step explanation:

Let x be the cost price and

     y the final sell price

     p gain percent

the gain precent p = (20/100)-(10/100)-[(20×10)/(100×100)]

                               = (20-10)/100 - 2/100

                               = 10/100 - 2/100

                               = 8/100

example : x=20

x(1+20/100)(1-10/100) = 20(1+20/100)(1-10/100) = 20(120/100×90/100)

                                                                           = 20(10 800÷10 000)

                                                                           = 21.6

20+20p% =21.6 then 20p%=1.6 then p%=1.6/20=16/200=8/100 then p=8.

for more details look at the photo below.

:)

Answer:

Option 1 and 2.

Step-by-step explanation:

Consider he given inequality is

[tex]x^2 + 12 x+35\ge0[/tex]

Splitting the middle term we get

[tex]x^2 +7x+5x+35\ge0[/tex]

[tex]x(x+7)+5(x+7)\ge0[/tex]

[tex](x+5)(x+7)\ge0[/tex]

The related equation is

[tex](x+5)(x+7)=0[/tex]

Using zero product property we get

[tex]x+5=0\Rightarrow x=-5[/tex]

[tex]x+7=0\Rightarrow x=-7[/tex]

Draw number line and mark -5 and -7 on it.

Now the three intervals are (-∞ , -7], [-7,-5] and [-5,∞).

The set of possible test points for

⇒ (-∞ , -7] → -8,  -10

⇒ [-7,-5] → -6

⇒ [-5,∞) → -4, 0, 4, 6

-8,-6,-4 and -10,-6,0 satisfies the given condition.

Therefore, the correct options are 1 and 2.

Answer:

the line 1 has negative slope of -1/4 and line 2 has positive slope of 1/4.

Step-by-step explanation:

let the line 1 be y = -1/4x + 2 and line 2 be 2y = 1/2x - 4

these lines are in the form of y = mx + c

where m is the slope of the line and c is the  intercept made with y axis.

dividing the line 2 by 2 we get [tex]y = \frac{1}{4}x -2[/tex]

line 1 meets x axis when y = 0 applying y = 0 in equation 1 we get x = 8

line 2 meets x axis when y=0 applying y = 0 in equation 2 we get x = 8

line 1 meets y axis when x = 0 applying x= 0in equation 1 we get y = 2

line 2 meets y axis when x = 0 applying x= 0in equation 2 we get y = -2

therefore line 1 passes through (8,0)and (0,2) with negative slope of -1/4

and line 2 passes through (8,0) and (0,-2) with positive slope of 1/4.

Answer:

20

Step-by-step explanation:

Line m and n are parallel lines cut by the transversal (without name). So, angles with measures [tex]65^{\circ}[/tex] and [tex](3x+5)^{\circ}[/tex] are corresponding angles.

The Corresponding Angles Theorem states if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Hence,

[tex]3x+5=65\\ \\3x+5-5=65-5\\ \\3x=60\\ \\x=\dfrac{60}{3}\\ \\x=20[/tex]

Answer:

Step-by-step explanation:

Answer:

Full bottle can fill 34 ounces water and 27.2 ounces left in the bottle

Step-by-step explanation:

Full bottle : 100%

6.8 ounces: 20%

100% / 20% = 5

Full bottle = 6.8 x 5 = 34 ounces

water remain in bottle = 34 -6.8 = 27.2 ounces

There is 34 ounces of water in the bottle initially and this can be determined by using the unitary method.

Given :

The following steps can be used in order to determine the total amount of water in the full bottle:

Step 1 - The unitary method can be used in order to determine the total amount of water in the full bottle.

Step 2 - According to the given data, Diego pours 6.8 ounces of water from a full bottle which is the 20% of the water in the bottle.

Step 3 - If 20% is 6.8 ounces of water than the 100% is given by:

[tex]=\dfrac{6.8}{20}\times 100[/tex]

Multiply 6.8 by 100 in the above expression.

[tex]=\dfrac{680}{20}[/tex]

Divide 680 by 20 in the above expression.

= 34 ounces

So, there is 34 ounces of water in the bottle initially.

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The number of miles William run from his house to school is 0.167 miles

let

x = number of miles run in 75 seconds

Ratio of miles to time

8 miles : 3600 seconds = x miles : 75 seconds

8/3600 = x/75

8 × 75 = 3600 × x

600 = 3600x

x = 600/3600

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