Two runners start 30 kilometers apart and run toward each other. They meet after 3 hours. One runner runs 2 kilometers per hour faster than the other runner. What rate do they run?
2 km/hr and 4 km/hr
3 km/hr and 5 km/hr
5 km/hr and 7 km/hr
4 km/hr and 6 km/hr

Answer:

b = 26.97 or b = 0.03

Step-by-step explanation:

[tex]\frac{\frac{4}{5} }{b} +b=27[/tex]

[tex]\frac{4}{5b} +b=27[/tex]

[tex]\frac{4+5b^{2} }{5b} =27[/tex]

[tex]4+5b^{2} =135b[/tex]

[tex]5b^{2} -135b+4=0[/tex]

[tex]b=\frac{135+\sqrt{18225-80} }{10}[/tex] or

[tex]b=\frac{135-\sqrt{18225-80} }{10}[/tex]

b = 26.97 or b = 0.03

Answer:

$800 is the answer because you subtract 7200 from 8000 and you get 800

Final answer:

To earn an $8,000 commission at a rate of 4%, the car dealer needs to increase his total sales by $20,000, from $180,000 last month to $200,000 this month.

Explanation:

The car dealer wishes to increase his commission from $7,200 to $8,000. Since he earns a 4% commission on all cars sold, we first need to determine how much his sales were last month. To do this, we divide his commission for the last month by the commission rate:

Last month's sales = Commission / Commission rate = $7,200 / 0.04 = $180,000

To earn $8,000 this month, we need to find the total sales required:

This month's sales = Desired commission / Commission rate = $8,000 / 0.04 = $200,000

To find the increase in total sales needed, we subtract last month's sales from this month's sales target:

Required increase in sales = This month's sales - Last month's sales = $200,000 - $180,000 = $20,000

Answer: $20.5

Step-by-step explanation:

Let x  denotes the amount for total bill.

We are given that ,  Sierra left $4.50 as a tip for a waiter.

This was 18% of the bill before the tip.

We can write 18% = 0.18. [To convert percent into decimal we divide it by 100.]

Then, the tip amount = 0.18 x Total bill

[tex]\Rightarrow\ 4.5=0.18x\\\\\Rightarrow\ x=\dfrac{4.5}{0.18}=25[/tex]

So, the total bill amount = $25

Hence, her total bill before the tip= Total bill amount - Tip amount

= $25- $4.50=$20.5

Thus ,her total bill before the tip= $20.5

To find Sierra's total bill before the tip, an equation can be created where the tip amount ($4.50) is 18% of the total bill. Solving the equation provides that Sierra's total bill before the tip was $25.

To solve this problem, you want to figure out the original bill amount before the tip was added. We know that the tip amount, $4.50, represents 18% of the original bill. Therefore, we can set up an equation to find the total bill before the tip was included.

The equation is as follows: 0.18x = $4.50, where 'x' stands for the total bill before the tip. By dividing both sides of the equation by 0.18, we can find 'x' which represents the initial bill.

So, x = $4.50 / 0.18 and calculating this gives us x = $25. Therefore, Sierra's total bill before the tip was $25.

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Answer: 59,000

Step-by-step explanation:

(2.5 * 10^4) + (3.4 * 10^4)

(2.5 * 10,000) + (3.4 * 10,000)

25,000 + 34,000

59,000

10 • 10 • 10 • 10 = 10,000

(2.5 • 10,000) + (3.4 • 10,000)

    25,000             34000

25,000 + 34,000 = 59,000

Answer:

The cost of the bench is 425 dollars.

Step-by-step explanation:

Let x represent the garden table.

Let y represent the bench.

x + y = 804

x = y - 46

Use the substitution method.

y - 46 + y = 804

2y - 46 = 804

Add 46 to both sides.

2y = 850

Divide both sides by 2.

y = 425

Answer:

The cost of the bench is 425 dollars.

Answer:

The correct option is A.

Step-by-step explanation:

From the given table it is noticed that the line is passing through the points (-1,1), (1,2), (3,3), (5,4) and (7,5).

Slope of a line is calculated as

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Choose any two pair of coordinates from the given points.

Let the line is passing through (5,4) and (7,5).

[tex]m=\frac{5-4}{7-5}[/tex]

[tex]m=\frac{1}{2}[/tex]

Therefore the slope of line is [tex]\frac{1}{2}[/tex] and option A is correct.

Answer:

The actual answer is C

Step-by-step explanation:

Answer:

Statement                                            Reason

1. <R=<Q, AS=AT                                  Given

2. <5=<6                                               Base <'s of isosceles triangles are =

3. <4, <5 are supplementary               Exterior sides in opposite rays

   and <6, <7 are supplementary

4. <4=<7                                                Two <'s supplementary to equal <'s are =

5. Triangle RAS congruent to              AAS

   Triangle QAT

6. RS=QT                                              CPCTE

Step-by-step explanation:

Statement

1. <R=<Q, AS=AT. This is given.

2. <5=<6, because base angles of isosceles triangles are congruent.

3. <4, <5 are supplementary and <6, <7 are supplementary, because they have exterior sides in opposite rays.

4. <4=<7, because two angles supplementary to equal angles are congruent

5. Triangle RAS congruent to Triangle QAT because Angle Angle Side (AAS)    

6. RS=QT, because Congruent Parts in Congruent Triangles are equal (CPCTE)

Answer:

Answer is: 5^ -8  *  5^4 =  5^-4

Step-by-step explanation:

To simplify : 5^ -8  *  5^4

This can also be written as :

5^ -8  *  5^4 = 1/5^8 * 5^4

or 5^ -8  *  5^4 = 5^4 / 5^8

or 5^ -8  *  5^4 = 5^(4 - 8)

or 5^ -8  *  5^4 = 5^-4

Hence we got 5^ -8  *  5^4 =  5^-4

Answer:

3 1/13 hours

Step-by-step explanation:

Lets create a variable:

Samantha and Kylee together (NOT the answers) = [tex]T_{SK}[/tex]

Now lets create an equation:

[tex]1/T_{SK} = 1/T_{S} +1/T_{K}[/tex]

Let's look at the time Samantha and Kylee takes to decorate the cake by themselves:

Samantha: 5 hours

Kylee: 8 hours

Let's create an equation to find the answer now:

[tex]1/T_{SK} = 1/5 + 1/8[/tex]

Note that now that's its basically algebra, change the variable to [tex]x[/tex] like this:

[tex]1/x = 1/5 +1/8[/tex]

Now let's find the LCM (Lowest Common Multiple) of 5, 8, and [tex]x[/tex] which is 40[tex]x[/tex].

[tex]40 = 8x + 5x[/tex]

[tex]40 = 13x[/tex]

[tex]13x = 40[/tex]

[tex]x = 40/13[/tex]

[tex]x[/tex] = 3 1/13 hours

Please note that the step where it swapped 13[tex]x[/tex] and 40 is only my way, it is not necessary, it's just my own comfort.

Answer:

1. 1:2

2. 2:2

3. 2:5

4. 2:10

5. 4:10

Step-by-step explanation:

Answer:

Area = 2x^2 -5x-12

Step-by-step explanation:

Area = length * width

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

We will use the FOIL technique  to multiply the terms.

First:  2x*x = 2x^2

Outer:  2x* -4 = -8x

Inner:  3*x = 3x

Last = 3* -4  = -12

Add the 4 terms together:  2x^2 -8x+3x -12   = 2x^2 -5x-12

Area = 2x^2 -5x-12

Answer: 2x^2 - 5x - 12

Step-by-step explanation: The correct answer is 2x^2 - 5x - 12. To find the area of a rectangle you multiply the length by the width. So you multiply (2x + 3)(x - 4) using the FOIL method.

Answer:

well you would need to look at how much he gets a weekend, and then worry anout the tips.

Step-by-step explanation:

He gets paid $80 each weekend, and a 15% with tips.

you would need to figure out the tips, by taking the $725 and timesing it by .15 for the percent.

which would be 108.75

you would now take 108.75 and add 80 to get what he made that weekend.

108.75+80 = 188.75 dollars

Answer:

20 years

Step-by-step explanation:

Simple interest is only interest on the original principal amount. Every year, you earn the same interest amount.

At 5% simple interest, you earn 5% of the principal each year.

In any year, you earn

5% of $500 = 5% * 500 = 0.05 * 500 = $25

Each year, you earn $25 in interest.

How many years will it take to earn a full $500 by earning $25 per year?

$500/$25 = 20

It takes 20 years to double the $500.

Answer:

Your range is (1,2,4,8)

Answer:

93.5 in^2

Step-by-step explanation:

we know that

Jodi is cutting out pieces of paper that measure  inches by  inches

The area of each piece that jodi is cutting out is equal to the area of a rectangle

Answer:

C. about 17 feet

Step-by-step explanation:

Since, we know that,

The area of a square is,

[tex]A=s^2[/tex]

Where,

s = side length,

If A = 290 square feet,

[tex]\implies 290 = s^2[/tex]

[tex]\implies s = \sqrt{290}=17.0294\approx 17[/tex]

Hence, the side length of the patio would be about 17 ft,

OPTION C is correct.

[tex]\dfrac{5+2\sqrt3}{7+4\sqrt3}=\dfrac{5+2\sqrt3}{7+4\sqrt3}\cdot\dfrac{7-4\sqrt3}{7-4\sqrt3}\\\\\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{(5+2\sqrt3)(7-4\sqrt3)}{7^2-(4\sqrt3)^2}\\\\\text{use distributive property}\\\\=\dfrac{(5)(7)+(5)(-4\sqrt3)+(2\sqrt3)(7)+(2\sqrt3)(-4\sqrt3)}{49-4^2(\sqrt3)^2}\\\\=\dfrac{35-20\sqrt3+14\sqrt3-8(3)}{49-16(3)}=\dfrac{35-6\sqrt3-24}{49-48}=\dfrac{11-6\sqrt3}{1}\\\\=11-6\sqrt3\\\\11-6\sqrt3=a+b\sqrt3\to\boxed{a=11\ and\ b=-6}[/tex]

Answer:

u ≤ 4

Step-by-step explanation:

The given inequality

15 ≤ 39 - 6u

Subtract 39 from both sides, we get

15 - 39 ≤ 39 - 6u - 39

-24 ≤ -6u

Dividing both sides by -6, we get

4 ≥ u                      [Remember, when we divide by negative, the direction of    

                              the inequality changes]

Which is u ≤ 4.

Thank you.

Answer:

U is greater than or equal to 4

Step-by-step explanation:

(pretend theres a line under the <)

15 < 39 - 6u

subtract both sides by 39 to get -6u by itself

-24 < -6u

divide both sides by -6 and get u completely by itself

4 < u

u is greater than or equal to 4.

Answer:

(A) y= -1.026x^2 + 1016.402x - 162075

Step-by-step explanation:

Given is the data 'x' -Items produced. The equation that satisfies the given data can be found by simply substituting the values of x in the given equations. For example:

Substituting the value of x= 100 in the given equations,

A) y= -1.026(100)^2 + 1016.402(100)-162075= -70,500

Similarly you can check the values on the rest of the equations and if they satisfy the equation, then the given is the required equation.

Answer:

(A)

Step-by-step explanation:

WE are given the data which represents the company's profit based on number of items produced.

The equation which best represents the data can be found out by substituting the values of x in the given equations.

So,substituting x=100 in first equation, we have:

[tex]y=-1.026x^{2} +1016.402x-162075[/tex]

[tex]y=-1.026(100^{2})+1016.402(100)-162075[/tex]

[tex]y=-10260+101640.2-162075[/tex]

[tex]y=-70500[/tex]

which satisfies the equation. Hence, option A satisfies.

We can also substitute the different values of x in the equations to check whether it satisfies or not.

Answer:

2000>= 637+ x

1363>= x

He can spend no more than $1363 on everything else

Step-by-step explanation:

If he has 2000 dollars to spend in total, that will go on one side of the inequality.  Everything he spends goes on the other.  2000 is the maximum he can spend.  He is going to sped 637 on an airline ticket plus x on other expenses.

2000>= 637+ x

Subtract 637 from each side

2000-637 >= 637-637 +x

1363>= x

To find out how much your brother can spend for everything else, subtract the cost of the airplane ticket from his total savings. Your brother can spend up to $1,363 for everything else.

To find out how much your brother can spend for everything else, we need to subtract the cost of the airplane ticket from his total savings. Let's say his total savings is $2,000 and the cost of the airplane ticket is $637. We can write the inequality as:

2000 - 637 ≤ x

Simplifying the inequality, we have:

1363 ≤ x

Therefore, your brother can spend up to $1,363 for everything else.

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[tex]Use:\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\(a^n)^m=a^{nm}\\\\\left(5^{\frac{3}{4}}\right)^{\frac{2}{3}}=5^{\frac{3}{4}\cdot\frac{2}{3}}=5^{\frac{1}{2}\cdot\frac{1}{1}}=5^{\frac{1}{2}}=\sqrt[2]{5}=\boxed{\sqrt5}[/tex]

Answer:

5v

Step-by-step explanation:

First you convert all the subtraction to addition: 2v+8v+(-5v)

Then you combine like terms: 2v+3v:

5v

2v + 8v - 5v    combine like terms

= (2 + 8 - 5)v

= (10 - 5)v

= 5v

Answer:

As shown, both terms are equal to 192. To add two or more monomials that are like terms, add the coefficients; keep the variables and exponents on the variables the same. To subtract two or more monomials that are like terms, subtract the coefficients; keep the variables and exponents on the variables the same.

Step-by-step explanation:

Answer:

The radius of the circle is 3 unit.

Step-by-step explanation:

Given : The diameter of a circle is 6 units.

To find : What is the radius of the circle?

Solution :

The radius of the circle is [tex]r=\frac{d}{2}[/tex]

Where, d is the diameter d=6 units

Substitute the value,

[tex]r=\frac{6}{2}[/tex]

[tex]r=3[/tex]

Therefore, the radius of the circle is 3 unit.

[tex]\sqrt[n]{a}=a^{\frac{1}{n}}\\\\\text{Therefore}\\\\\sqrt3=3^\frac{1}{2}\\\\\sqrt[5]{3}=3^\frac{1}{5}\\\\\text{We have}\\\\(\sqrt3)(\sqrt[5]3)=3^\frac{1}{2}\cdot3^\frac{1}{5}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=3^{\frac{1}{2}+\frac{1}{5}}=3^{\frac{5}{10}+\frac{2}{10}}=3^{\frac{7}{10}}\\\\Answer:\ \boxed{D.\ 3^{\frac{7}{10}}}[/tex]

Answer: y=1/7am -1/7

Step-by-step explanation:

First: 3y+4y+z =am - z

Second: 7y=am - z

Third: y=1/7am -1/7z

Finally: y=1/7am -1/7

Answer:

$4.10

Step-by-step explanation:

Subtotal = (3 pairs of socks) x (price of socks):  

Subtotal = (3 x $1.29) = $3.87  

To get the overall total, you add tax, which is 6% of the subtotal:  

6% of the subtotal = 0.06 x subtotal = 0.06 x $3.87 = $0.23  

Subtotal + tax = $3.87 + $0.23 = $4.10

Answer:

slope is easy it is rise over run

Step-by-step explanation:

rise/run

rise means up

run means move sideways

Answer:

Slope = rise/run

Step-by-step explanation:

Example: (6,3) (2, 2)

Add the x's and divide by two and then add the y's and divide by two.

6 + 2 = 8

8/2 = 4

3 + 2 = 5

5/2 = 2.5

So, the slope would be 4/2.5

Answer:

a.  He started with $50 in the the account.

b.  The account grow by $10 dollars each week

c see graph

Step-by-step explanation:

y = 50 + 10x

We can rewrite this as

y = 10x+50

This is in the form y = mx+b

where m = 10 which is the slope and b =50 which is the y intercept

The y intercept = 50 is the starting value or the value when x = 0

a.  He started with $50 in the the account.

The slope is how much it grows by as x grows.  As x increase by 1 , y will grow by the slope or 10, so  the account will grow by 10 each week.

b.  The account grow by $10 dollars each week

c see graph

Answer:

$156.35

Step-by-step explanation:

we know that

A group of friends went to lunch, and their bill was $132.50

In this problem

$132.50 represent the 100%

100%+18%=118%

so

using proportion

Find out the total amount that represent 118%

Let

x ----> the total amount of the bill

[tex]\frac{\$132.50}{100\%}=\frac{x}{118\%}\\\\x=132.50(118)/100\\\\x=\$156.35[/tex]

Answer:

Step-by-step explanation:

The answer is $156.35