This is a copy of the worksheet my son was given from school, can anybody look at this and tell if this is being done correctly, because it doesn’t look right to me....

Let x = distance traveled (not round trip)

x/10 + x/3 = 6.5

13/30x = 6.5

x = 15 miles

answer: 15 miles

Answer:

15 miles

Step-by-step explanation:

Find out the  how far into the country does he go.  

To proof

Let us assume that the total diatance travelled into the country be x .

Formula

As given

A cyclist rides into the country at an average speed of 10 miles per hour. When his bicycle gets a flat tire,

he walks it back at an average speed of 3 miles per hour.

If he returns home 6 and a half hours after he starts i.e the total time including the bike time and walk time of the cyclist be 6.5 hours.

Than the equation becomes

L.C.M of (10,3) = 30

Than the equation becomes

3x +10x = 195

solving

13x = 195

x = 15 miles into the country

Hence proved

Answer:

20

Explanation:

PEMDAS

Answer:

0.45 45%

Step-by-step explanation:

Answer: it has no solution

Step-by-step explanation:

8x - 2y = 1 ..................... equation 1

-4x + y = 3 ...................... equation 2

solving the system of linear equation by substitution method . From equation 2 , make y the subject of the formula.

y = 3 + 4x .......................... equation 3

substitute equation 3 into equation 1 .

8x - 2(3 + 4x ) = 1

8x - 6 - 8x = 1

8x- 8x - 6 = 1

-6 = 1

this means that the equation has no solution

Answer:

12

Step-by-step explanation:

4(2+1)

4*3

12

Answer:

substitute n in bigger equation with 2.

4(2+1)

4×3=12

Answer:

4x - 8 = -(8 - 4x)

Step-by-step explanation:

Answer: -32

First you would have to multiply 4x8 which is 32 and then just add the dash before the 32.

Answer:

720°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 ( number of sides of a hexagon ), thus

sum = 180° × 4 = 720°

The sum of the measures of the interior angles of a hexagon is [tex]720^{\circ}[/tex]

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain. The bounded plane region, the bounding circuit, or the two together, may be called a polygon. A hexagon is a six-sided polygon or [tex]6-[/tex]gon. Interior angles are those that lie inside a polygon.

The total of the internal angles of any simple hexagon is [tex]\boldsymbol{720^{\circ}}[/tex]

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Sally gave 30 shells to Jason

Solution:

Given that, Sally found 58 seashells on the beach, she gave Jason some of her seashells

She has 28 left

To find: Number of sea shells she gave to Jason

From given,

Total number of shells she found = 58

Remaining shells = 28

Therefore,

Number of sea shells she gave to Jason = Total number of shells she found - Remaining shells

Number of sea shells she gave to Jason = 58 - 28 = 30

Thus Sally gave 30 shells to Jason

Answer:

10

Step-by-step explanation:

You are doing:

(2/5) * 25

You can do it two ways, first divide, then multiply, OR multiply, then divide.

In this case, I will multiply, then divide:

First, multiply:

(2 * 25)/5 = (50)/5

Next, divide:

50/5 = 10

10 is your answer.

~

Answer:

Job B

Step-by-step explanation:

Job A:

Job A pays $28.59 per hour.

Lauren expects to work 2,000 hours during the year, so Lauren can expect to be paid

[tex]\$28.59\times 2,000=\$57,180[/tex]

Job B:

Job B pays $25.71 per hour.

Lauren expects to work 2,000 hours during the year, so Lauren can expect to be paid

[tex]\$25.71\times 2,000=\$51,420[/tex]

Health insurance costs $6,650. Add health insurance to job B payment:

[tex]\$51,420+\$6,650=\$58,070[/tex]

Since [tex]\$58,070>\$57,180,[/tex] Lauren should take job B

Answer:

-10

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

Answer:

Step-by-step explanation:

|x-4|<13.

The above equation means, whatever the actual value of x is, the value of (x - 4) must be greater than - 13 and less than 13.

Hence, -13 < x - 4 < 13 or, -9 < x < 17. The value of x will be in between -9 and 17. The value of x can not be -9 or 17.

Answer:

The correct answer is A. x = 2 +/- √42

Step-by-step explanation:

Let's solve for x the quadratic equation, this way:

x² - 4x - 9 = 29

x² - 4x - 38 = 0

Using the quadratic formula, we have:

x = [- (-4) +/- √ -4² - 4 * -38]/2

x = 4 +/- √ 16 + 152/2

x = 4 +/- √ 168/2

x = 4 +/- √ 4 * 42/2

x = 4 +/- 2 √42/2

x = 2 +/- √42

The correct answer is A. x = 2 +/- √42

Answer:

the answer is A on edg2020

Step-by-step explanation:

Final answer:

To find the final cost of an Apple iPod after a mail-in rebate and the cost of mailing the rebate (envelope and stamp), subtract the rebate amount from the original price and add the mailing costs. The total cost after these calculations is $726.82.

Explanation:

Let's tackle the Apple iPod rebate calculation problem. An Apple iPod sells for $781.29 and has a mail-in rebate for $55.00. To calculate the cost after the rebate, you must also consider the costs of an envelope and a stamp, which are $0.13 and $0.40, respectively. The formula for the final cost after applying the mail-in rebate, including the expenses for an envelope and a stamp, is as follows:

Calculate the rebate price by subtracting the rebate amount from the original price: $781.29 - $55.00 = $726.29.

Add the costs of the envelope and stamp to the price after rebate: $726.29 + $0.13 + $0.40 = $726.82.

The final cost of the iPod after the rebate and additional costs is $726.82.

Answer:

Step-by-step explanation:

[tex]m+3m+6=4m-9+15\qquad\text{combine like terms}\\\\(m+3m)+6=4m+(-9+15)\\\\4m+6=4m+6\qquad\text{subtract}\ 4m\ \text{from both sides}\\\\4m-4m+6=4m-4m+6\\\\6=6\qquad\bold{TRUE}\\\\\bold{CONCLUSION:}\ \text{infinitely many solutions}[/tex]

Answer:

Step-by-step explanation:

(14)

Given :

y = [tex]\frac{1}{2}[/tex][tex](x-3)^{2}[/tex] - 6

comparing with the standard form :

y = a[tex](x-h)^{2}[/tex] + k

vertex = ( h , k )

Focus = (h , k+14a )

Directrix = y = k

comparing the equation and the standard form ;

Vertex = ( 3 , -6 )

Focus = ( 3 , -6+14{1/2} )

Focus = ( 3 , 1)

Directrix ⇒ y = -6

(19)

[tex]x^{2}[/tex] + [tex]4y^{2}[/tex] = 13 .............. equation 1

[tex]x^{2}[/tex] - [tex]4y^{2}[/tex] = 5  ..................... equation 2

add equation 1 and 2

2[tex]x^{2}[/tex] = 18

divide through by 2

[tex]x^{2}[/tex] = 9

x = ±3

substitute x = 3 into equation 1

[tex]3^{2}[/tex] + 4[tex]y^{2}[/tex] = 13

9 +4[tex]y^{2}[/tex] = 13

4[tex]y^{2}[/tex] = 13 - 9

4[tex]y^{2}[/tex] = 4

[tex]y^{2}[/tex] = 1

y = ±1

Therefore , the solution is ( 3 , 1 ) or (-3 , -1 )

Answer:

  14) vertex: (3, -6); focus: (3, -5.5); directrix: y = -6.5

  17) see below for a graph

  19) (±3, ±1) — four points

  20) see below for the work

Step-by-step explanation:

14) The vertex form of a quadratic equation can be written as ...

  [tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex]

This parabola will have its vertex at (h, k), its focus at (h, k+p), and its directrix at y=k-p.

The given equation is ...

  y = 1/2(x -3)² -6

Comparing this to the form above, we see that ...

  4p = 2, h = 3, k = -6

From this, we can find the value of p to be ...

  p = 2/4 = 1/2 . . . . divide the above equation by 4

Now, we know the parameters of the parabola are ...

_____

17) The equation of the parabola is given as ...

  y = 1/4(x -1)² +5

Comparing the given equation to the form shown in the above problem, we see that ...

So the parameters of the parabola are ...

The graph is shown below.

_____

20) It is convenient to show the solution steps before showing the solution. Hence we show problem 20 (steps) before problem 19 (solution).

The given system of equations is ...

The two equations can be added to give ...

  (x² +4y²) +(x² -4y²) = (13) +(5)

  2x² = 18 . . . . . . eliminate parentheses, collect terms

  x² = 9 . . . . . . . . divide by 2

  x = ±3 . . . . . . . . take the square root

__

The second equation can be subtracted from the first to give ...

  (x² +4y²) -(x² -4y²) = (13) -(5)

  8y² = 8 . . . . . . . eliminate parentheses, collect terms

  y² = 1 . . . . . . . . . divide by 8

  y = ±1 . . . . . . . . . take the square root

_____

19) Based on the above, the four solutions to the given system of equations are ...

  (3, 1), (3, -1), (-3, 1), (-3, -1)

__

A graph is shown in the second attachment.

Answer:

(- 2, - 3 )

Step-by-step explanation:

Given the endpoints of a segment (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[0.5(x₁ + x₂), 0.5(y₁ + y₂ ) ]

Here (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (x, y) and the midpoint = (0, 0), thus

0.5(2 + x) = 0 , that is

2 + x = 0 ( subtract 2 from both sides )

x = - 2

0.5(3 + y) = 0, that is

3 + y = 0 ( subtract 3 from both sides )

y = - 3

Thus (x, y) = (- 2, - 3 )

Answer:

Yes it is 15

Step-by-step explanation:

30/2 =15

Answer:

Yes, you are right! The answer is 15!  :)

Step-by-step explanation:

2y = 30

Divide by two to get y on it's own.

y = 15

The value of function f (x) at x = 3 is,

⇒ f (3) = - 22

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = - 2x² - 4

Now, Put x = 3 in above function we get;

⇒ f (x) = - 2x² - 4

Put x = 3;

⇒ f (3) = - 2 (3)² - 4

⇒ f (3) = - 2 x 9 - 4

⇒ f (3) = - 18 - 4

⇒ f (3) = - 22

Thus, The value of function f (x) at x = 3 is,

⇒ f (3) = - 22

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Answer:

The number is 50.

Step-by-step explanation:

0.6x=30

x=30/0.6

x=50

There are 2100 cups in the package.

Step-by-step explanation:

Given,

Number of green cups in package = 630

This represent 30% of the total package.

Let,

x represent the total number of cups in package.

30% of x = 630

[tex]\frac{30}{100}*x=630\\0.30x=630[/tex]

Dividing both sides by 0.30

[tex]\frac{0.30x}{0.30}=\frac{630}{0.30}\\x=2100[/tex]

There are 2100 cups in the package.

Keywords: percentage, division

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The larger number is 97 and smaller number is 22.

Step-by-step explanation:

Let,

The two numbers are x and y.

According to given statement;

x+y=119      Eqn 1

y-4x=9       Eqn 2

Subtracting Eqn 2 from Eqn 1

[tex](x+y)-(y-4x)=119-9\\x+y-y+4x=110\\5x=110[/tex]

Dividing both sides by 5

[tex]\frac{5x}{5}=\frac{110}{5}\\x=22[/tex]

Putting x=22 in Eqn 1

[tex]22+y=119\\y=119-22\\y=97[/tex]

The larger number is 97 and smaller number is 22.

Keywords: linear equation, elimination method

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Answer:

Step-by-step explanation:

The LCM of 5,4,3 is 5×4×3=60

Answer:

Step-by-step explanation:

Integers with a product of 567 are ...

  567 = 1·567 = 3·189 = 7·81 = 9·63 = 21·27

The last of these pairs of factors have a difference of 6, so they are the answers.

Jackie's number is 27; Adrian's number is 21.

_____

You could let "a" represent Adrian's number and write the equation ...

  a(a +6) = 567

  a^2 +6a +9 = 576 . . . . . complete the square

  (a +3)^2 = 24^2 . . . . . . . write as squares

  a = -3 +24 = 21 . . . . . . . . take the positive square root; subtract 3

Adrian's number is 21; Jackie's number is 27.

Answer:

54.

Step-by-step explanation:

Start at 60 and subtract 6. That leaves you with 54.

The 60th term in the arithmetic sequence -6, -3, 0, 3, ... can be determined using the formula of an arithmetic sequence, which results in a value of 171.

An arithmetic sequence, also known as an , is a sequence of numbers in which each term is obtained by adding a fixed constant to the previous term. In simpler terms, it's a sequence where the difference between any two consecutive terms is always the same.

The given sequence is an arithmetic progression where each term differs from the previous term by a constant value. In this case, the common difference[tex](\(d\))[/tex]between consecutive terms is 3.

To find the 60th term of this sequence, we can use the formula for the nth term of an arithmetic sequence:

[tex]\[a_n = a_1 + (n - 1) \cdot d\][/tex]

Here,[tex]\(a_n\)[/tex]represents the nth term, \(a_1\) is the first term, \(n\) is the term number we want to find, and \(d\) is the common difference.

In this sequence:

- The first term [tex](\(a_1\)) is -6.[/tex]

- The common difference [tex](\(d\)) is 3.[/tex]

- We want to find the 60th term, so [tex]\(n = 60\).\\[/tex]

Now, we can substitute these values into the formula:

[tex]\[a_{60} = -6 + (60 - 1) \cdot 3\][/tex]

[tex]\[a_{60} = -6 + 59 \cdot 3\][/tex]

[tex]\[a_{60} = -6 + 177\][/tex]

[tex]\[a_{60} = 171\][/tex]

Therefore, the 60th term in this arithmetic sequence is 171. This means that if you continued the sequence, the 60th term would be 171 units greater than the first term (-6), following the pattern of adding 3 at each step.

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Answer:

I believe that it would just be 20% of the $45 which would mean that you would have to pay $36 a month.

Hope this is helpful!

The cost to you per month, after the landlord's contribution, is $36.

If you buy both Liability and Contents insurance, and take advantage of the landlord's offer to pay 20% of the cost, the cost to you per month can be calculated as follows:

Let's assume the cost of Liability insurance is represented by 'L' and the cost of Contents insurance is represented by 'C'.

According to the information given, if you buy both insurances at the same time, the cost is $45 per month.

This means: L + C = $45

The landlord is willing to pay 20% of the cost, which is equal to 20% of ($45). To calculate this amount:

20% of $45 = (20/100) x $45 = $9

So, the landlord will pay $9 towards the cost of both insurances.

Now, if you subtract the landlord's contribution from the total cost, you'll get the amount you have to pay:

(L + C) - $9 = $45 - $9 = $36

Therefore, the cost to you per month, after the landlord's contribution, is $36.

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