Marty's class collected $16.00 in a school-wide penny collection contest.If Tommy's class collected,x, and then multiplied the difference by 2,they would have the same amount of money as Marty's class.How much money did Tommy's class collect?
A.$23.00
B.$13.00
C.$18.00
D.$5.00

Answer:

File is given in attachements .

Step-by-step explanation:

[tex]y = \sqrt[3]{x}  + 2[/tex] will pass through (0,2) and (-8,0) . Its shape will be as shown in the graph.

Answer:

Graph C

Step-by-step explanation:

The value of n is [tex]1\frac{4}{5}[/tex].

Step-by-step explanation:

Given,

[tex](2\frac{2}{3}-n)/-2\frac{1}{5}=\frac{-13}{33}[/tex]

Writing the fractions in simplified form;

[tex](\frac{8}{3}-n)/\frac{-11}{5}=\frac{-13}{33}[/tex]

Taking LCM on left hand side;

[tex](\frac{8-3n}{3})/\frac{-11}{5}=\frac{-13}{33}\\[/tex]

[tex]\frac{8-3n}{3}*\frac{-5}{11}=\frac{-13}{33}\\\\\frac{-40+15n}{33}=\frac{-13}{33}\\\\[/tex]

Multiplying both sides by 33

[tex]33*(\frac{-40+15n}{33})=\frac{-13}{33}*33\\-40+15n=-13\\15n=-13+40\\15n=27[/tex]

Dividing both sides by 15

[tex]\frac{15n}{15}=\frac{27}{15}\\n=\frac{9}{5}\\n=1\frac{4}{5}[/tex]

The value of n is [tex]1\frac{4}{5}[/tex].

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Answer:

[tex]x^{6}[/tex] - 8

Step-by-step explanation:

A difference of cubes has the form

a³ - b³

Note that [tex]x^{6}[/tex] is a perfect cube, that is [tex](x^2)^{3}[/tex], but

[tex]x^{8}[/tex] is not

8 is a perfect cube, that is 2³ , but 6 is not

Thus

[tex]x^{6}[/tex] - 8 ← is a difference of cubes

= [tex](x^2)^{3}[/tex] - 2³

The expression which is a difference of cubes is B. x⁶ - 8.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Difference of cubes is termed for those expressions which can be written as the difference of terms which are cubes of some numbers or expressions.

Here,

From, x⁶ - 6, we cannot write 6 as a cube of any number.

So this is not the option.

From x⁶ - 8,

x⁶ can be written as (x²)³ using power of a power rule.

x⁶ - 8 = (x²)³ - (2)³

Hence the expression is x⁶ - 8.

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The equation in standard form is x + 2y = 8

Solution:

Given that we have to write the given equation in standard form

The equation given is:

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

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers. When we shift the variable terms to the left side of the equation and everything else to the right side, we get the standard form.

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

Keep the variables on one side and constant term on other side

x + 2y = 8

Thus the above equation is in standard form of Ax + By = C

Answer:

x+2y=8

Step-by-step explanation:

Answer:

Therefore the equation of the line through ( -7 , 5 ) and ( -5 , 9) is

Linear Relationship i.e [tex]y-5=2(x+7)[/tex]

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( -7, 5 )  

point B( x₂ , y₂) ≡ (-5, 9)  

To Find:

Equation of Line AB =?

Solution:

Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula

[tex](y - y_{1} )=(\frac{y_{2}-y_{1} }{x_{2}-x_{1} })\times(x-x_{1}) \\[/tex]

Substituting the given values in a above equation we get

[tex](y-(5))=(\frac{9-(5)}{-5--7})\times (x--7)\\ \\(y-5)=\frac{4}{2}(x+7)\\\\y-5=2(x+7)...............\textrm{which is the required equation of the line AB}[/tex]

Therefore the equation of the line through ( -7 , 5 ) and ( -5 , 9 ) is

Linear Relationship i.e [tex]y-5=2(x+7)[/tex]

Answer:

ok??? whats the question?

Step-by-step explanation:

Answer:

question???

Step-by-step explanation:

Answer:10

Step-by-step explanation:

Adds 7 each time

31 - 3 = 28

Going from first term to fifth term is 4 increases.

28 ÷ 4 = 7

This means we have a common difference of 7.

Sequence is 3, 10, 17, 24, 31

Answer:

The interest that is obtained from that investment is $55.2

Step-by-step explanation:

If the balance at the end of eight years on an investment of $230 that has been invested at a rate of 3% is $285.20, so the principal of investment is $230 and the matured sum is $285.20.

Now, we know that Principal + Interest = Matured sum.

Hence, the interest that is obtained from that investment is $(285.2 - 230) = $55.2 (Answer)

Answer:

The interest credited after investment is $55.2

Step-by-step explanation:

Given as :

The investment principal amount = p = $230

The Amount after 8 years of investment = A = $285.20

The Time period for investment = 8 years

The rate of interest applied = r = 3%

Let The interest credited after investment = I

Now, According to question

From Compound Interest

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

And Interest = Amount - Principal

Or, I = A - p

Or, I = $285.20 - $230

∴   I = $55.2

So, The interest credited after investment = I = $55.2

Hence, The interest credited after investment is $55.2 Answer

The measure of the third angle is 65°

Step-by-step explanation:

Each lapel on a suit jacket is in the shape of a triangle

In a triangle:

∵ The sum of the measures of the interior angles = 180°

∵ The measure of one angle = 47°

∵ The measure of other angle = 68°

- Substitute the measures of the two angles in the rule above

∴ 47 + 68 + measure 3rd angle = 180°

- Add the like terms

∴ 115 + measure 3rd angle = 180°

- Subtract 115 from both sides

∴ measure 3rd angle = 65°

The measure of the third angle is 65°

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Answer:

1875 arrangements

Step-by-step explanation:

Break-Even is the point when costs are equal to profit.

The cost is 15,000

We need to cover this up with the profit we get from sales.

Each arrangement is 17 (cost) and is sold for 25, so the profit from each arrangement is:

25 - 17 = 8

So, with each arrangement sale, we make profit of $8. How many of these we need to sell in order to break even (in order to make 15,000)??

We simply divide this amount (15,000) by the profit we make from each arrangement ($8), so that would be:

Number of Arrangements Needed to Break-Even = 15,000/8 = 1875

After 1875 arrangements, the boutique breaks even.

Answer:   Hence the dimension of triangle are 15, 15 and 23.

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram attached.

Suppose two congruent sides of triangle are : x

Suppose the base of the triangle : y

As per question, the base of the triangle is seven less than two times the congruent sides lengths.

So,

[tex]y = 2x-7[/tex]  .......................(1)

Now the perimeter of triangle is given as : 53

It means

[tex]x+x+y=53[/tex]

[tex]2x+y=53[/tex]  .......................(2)

Plugging the value of y from equation (1) in equation (2)

[tex]2x+2x-7=53[/tex]

[tex]4x-7=53[/tex]

[tex]4x=60[/tex]

[tex]x=15[/tex]

Plugging the value of x in equation (1)

[tex]y=2\times (15)-7[/tex]

[tex]y=23[/tex]

Hence the dimension of triangle are 15, 15 and 23.    :   Answer

Hope it will help :)

Answer:D

Step-by-step explanation:

From the inequality, y= -75 or Less, the next whole number less than -75 is -76

Answer:

Y=74

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/3 = 8/x+6

2 * ( x+6) = 8 * 3

2x + 2 * 6 = 24

2x + 12 = 24

2x = 24 -12

2x = 12

x = 12/2

x = 6

Answer:

I took the test and its B

Step-by-step explanation:

Also the person above me has got it covered so im gonna avoid confusion and not explain

Answer:

1. f(2) = 6

2. Slope, m = [tex]$ \frac{7}{2} $[/tex]

Step-by-step explanation:

Problem 1:

Given f(x) = |3x|

To find f(2), substitute x = 2.

⇒ f(2) = |3(2)|

= |6|

= 6

Problem 2:

The given equation is: 2y = 7x + 8

The general equation of the line is: y = mx + c, where m is the slope of the line.

Therefore, we reduce the given equation to the general form of the line.

Dividing the given equation by 2, we get:

y = [tex]$ \frac{7}{2}x + \frac{8}{2} $[/tex]

[tex]$ \implies y = \frac{7}{2}x + 4 $[/tex]

Thus, slope, m = [tex]$ \frac{7}{2} $[/tex] which is the answer.

Problem 3:

Given with 14 gallons of gas, we can drive 392 miles.

The capacity of the tank if 14 gallons.

If 14 gallons can take us 392 miles, then 1 gallon of gas should take us: [tex]$ \frac{392}{14} $[/tex] miles.

= 28 miles/gallon of gas

Therefore, with 3.7 gallons of gas, we can travel 3.7 X 28 miles

= 103. 6 miles

Answer: Im assuming this is a true or false question anyways the answer would be false if it is

Step-by-step explanation:

Answer:

(-4 1/8)

Step-by-step explanation:

-6 1/4 - (-2 1/8)          The subtraction cancels out the subtraction.

-6 1/4 + 2 1/8            

-6 + 2 = -4                 The whole numbers are independent in this case.

1/4 + 1/8                     Find the least common multiple

Multiples:

4| 4_8_12

8| 8_16

8 is the least common multiple

4 goes into 8 twice so multiply the top and bottom by 2

4 * 2 = 8              1 * 2 = 2

-2/8 + 1/8 = -1/8

add that to -4

Answer:

Therefore the value of 'x' is 7.

Step-by-step explanation:

Given:

[] ABCD is a Parallelogram

AB = 4x+ 7

BC = 8x - 12

CD = 7x - 14

To Find:

x = ?

Solution:

[] ABCD is a Parallelogram ..............Given:

Opposite sides of a Parallelogram are Equal

side AB and CD are the opposite sides of the parallelogram.

∴ AB = CD

On substituting the values we get

[tex]4x+7=7x-14\\\\7x-4x=7+14\\\\3x=21\\\\x=\dfrac{21}{3} =7\\\\\therefore x =7[/tex]

Therefore the value of 'x' is 7.

Answer:

y=3/4x-5

Step-by-step explanation:

3x-4y=20

4y=3x-20

y=3/4x-20/4

y=3/4x-5

If you're talking the equation [tex]\frac{5x-2}{3} =6[/tex], then:

[tex]\frac{5x-2}{3} =6[/tex]

[tex]5x-2=18[/tex]

[tex]5x=20[/tex]

[tex]x=4[/tex]

If you're talking about the equation [tex]5x-\frac{2}{3} =6[/tex], then:

[tex]5x-\frac{2}{3} =6[/tex]

[tex]5x = 6+\frac{2}{3}[/tex]

[tex]x=\frac{6}{5} +\frac{2}{15}[/tex]

[tex]x=\frac{18}{15} +\frac{2}{15}[/tex]

[tex]x=\frac{20}{15} = \frac{4}{3} = 1\frac{1}{3}[/tex]

There are 13 triangles will be in the 7th term.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sequence is,

Δ, ΔΔΔ, ΔΔΔΔΔ..

Now,

Number of triangles in sequence are;

⇒ 1 , 3 , 5, ...

Clearly, The sequence is in arithmetic sequence, with common difference = 3 - 1 = 2 and first term is 1.

Hence, The 7th term is find as;

⇒ T ₇ = a + (n - 1) d

⇒ T ₇ = 1 + (7 - 1) (2)

⇒ T ₇ = 1 + 6 x 2

⇒ T ₇ = 1 + 12

⇒ T ₇ = 13

Thus,  There are 13 triangles will be in the 7th term.

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Rahul gets 12 paper clips.

Step-by-step explanation:

Given,

Paper clips Tian have = 56

He gives 3/4 of them to joe.

Joe gets = [tex]\frac{3}{4}*56=\frac{168}{4}[/tex]

Joe gets = 42 paper clips

He given 2/7 of received to Rahul.

Rahul gets = [tex]\frac{2}{7}*42=\frac{84}{7}[/tex]

Rahul gets = 12 paper clips

Rahul gets 12 paper clips.

Keywords: fraction, division

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Answer:

The maximum value of function is 81 .

Step-by-step explanation:

Given function as :

y = 4 (x + 7) (2 - x)

Now, The function can be written as

y = 4 (2 x - x² + 14 - 7 x)

y = 4 ( - x² - 5 x + 14)

y = - 4 x² - 20 x + 56

Now, For maximum value of function , differentiation of y with respect to x

[tex]\frac{\partial y}{\partial x}[/tex] = 0

Or, [tex]\frac{\partial ( - 4x^{2} - 20 x +56)}{\partial x}[/tex] = 0

Or, - 8 x - 20 = 0

Or, - 8 x = 20

∴  x = [tex]\dfrac{-20}{8}[/tex]

i.e  x = [tex]\dfrac{-5}{2}[/tex]

Now, Putting the value of x in the given equation

y = - 4 ( [tex]\dfrac{-5}{2}[/tex])² - 20 ( [tex]\dfrac{-5}{2}[/tex]) + 56

Or, y = - 4 ([tex]\dfrac{25}{4}[/tex]) + 50 + 56

Or, y = - 25 + 50 + 56

∴    y = 81

So, The maximum value of function is 81

Hence,The maximum value of function is 81 . Answer

Answer: 4 pancakes

Step-by-step explanation: because 30min÷6pancakes=5

So, 20min÷5=4

Answer:

The numbers between -5 and 5

Step-by-step explanation:

Intersection of Intervals

Given the intervals A,B,C,etc. The intersection of them all is the set of all values that are common to all the intervals.

We must find

[tex]\{x | x > -5\} \bigcap \ \{x | x < 5\}[/tex]

which is the intersection between the intervals x > -5 and x < 5. The intersection represents all the numbers greater than -5 and less than 5. It can also be said The numbers between -5 and 5 (non inclusive), third option

Answer: The answer is D all real numbers

Answer:

it is less than and equal to

Step-by-step explanation:

its > with a line under it

Answer:

y = 4/7x + 2 ( slop-intercept form)

Step-by-step explanation:

Answer:

The slope-intercept form of the given equation is,

[tex]y = \frac{4x}{7}-2[/tex]

Step-by-step explanation:

The given equation of the line is,

- 4x + 7y = - 14

Adding '4x' on both sides of the above equation, we get

   - 4x + 7y + 4x = - 14 + 4x

⇒ 7y = 4x - 14

Now, dividing both sides of the above equation by '7', we get

       7y ÷ 7 = (4x - 14) ÷ 7

[tex]\implies y = \frac{4x}{7}-\frac{14}{7}[/tex]

[tex]\implies y = \frac{4x}{7} - 2[/tex]

This is the required equation of the line in slope-intercept form.

Answer:

13 pencils.

Step-by-step explanation:

Let x be the pens and y be the pencils

Given:

Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95.

Total pens and pencils is 22

So, [tex]x+y=22[/tex]----------------(1)

And he bought all utensils for $11.95. and each pen for 75 cents and pencils for 40 cents.

[tex]0.75x+0.40y=11.95[/tex]------------(2)

solve equation 1 and equation 2 for x and y.

From equation 1.

[tex]x+y=22[/tex]

[tex]y=22-x[/tex]----------------(3)

put y value in equation 2.

[tex]0.75x+0.4(22-x)=11.95[/tex]

[tex]0.75x+0.4\times 22-0.4x=11.95[/tex]

[tex]0.75x+8.8-0.4x=11.95[/tex]

[tex]0.75x-0.4x=11.95-8.8[/tex]

[tex]0.35x=3.15[/tex]

[tex]x=\frac{3.15}{0.35}[/tex]

[tex]x=9[/tex]

Now substitute x value in equation 3.

[tex]y=22-9[/tex]

[tex]y=13[/tex]

So, he buy 13 pencils.

Answer:

Step-by-step explanation:

(2/7)^3=8/343

Answer:

(2/7)^3

8/343

Step-by-step explanation:

(2/7)^3=2^3/7^3

=8/343

Answer:

1) The slope of the line is [tex]m=\frac{5}{2}[/tex]  or  [tex]m=2.5[/tex]

2) The equation of the line is [tex]y=2.5x-4[/tex]

Step-by-step explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

take any two points from the values in the table

(2,1) and (4,6)

substitute the values in the formula

[tex]m=\frac{6-1}{4-2}[/tex]

[tex]m=\frac{5}{2}[/tex]

[tex]m=2.5[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=2.5[/tex]

[tex]point\ (2,1)[/tex]

substitute

[tex]y-1=2.5(x-2)[/tex]

Convert to slope intercept form

isolate the variable y

[tex]y-1=2.5x-5[/tex]

[tex]y=2.5x-5+1[/tex]

[tex]y=2.5x-4[/tex]

Answer:

Step-by-step explanation: