You have budgeted $100 to improve your swimming over the summer. At your local pool, it costs $50 to join the swim association and $5 for each swim class. Write and solve an inequality to find the possible numbers of swim classes you can attend with

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.

To find the product for 2(2n + 3), use the distributive property to multiply 2 with each term inside the parentheses, resulting in 4n + 6.

The question asks to find the product for 2(2n + 3). To solve this, we need to use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Applying this rule to the given expression, we multiply 2 with each term inside the parentheses.

First, multiply 2 by 2n to get 4n. Next, multiply 2 by 3 to get 6. Therefore, the expression simplifies to 4n + 6.

We have successfully used the distributive property to find that the product of 2(2n + 3) is 4n + 6.

Answer: 7c ≤ 63

Ivan will buy at most 9 pounds of candy, which means that multiplying 9 by 7, the cost of the candy, will get your answer: 63. Plug these values into an inequality with a less than or equal to sign (≤) facing away from 63 and you're done!

The possible amounts Ivan will spend on candy can be represented as c ≤ 7.

Let's denote the amount Ivan will spend on candy as c. The cost of candy is $7 per pound, and Ivan will buy at most 9 pounds of candy. Therefore, the maximum amount he could spend on candy is 9 pounds multiplied by $7 per pound, which is 9c ≤ 63.

Since we are looking for possible amounts, we can rewrite this inequality as c ≤ 63/9, which simplifies to c ≤ 7.

So, the possible amounts Ivan will spend on candy are values less than or equal to $7.

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Answer:

y=3/4x-5

Step-by-step explanation:

3x-4y=20

4y=3x-20

y=3/4x-20/4

y=3/4x-5

Answer:

n=6

Step-by-step explanation:

4(n+2)=2(n+10)

4n+8=2n+20

4n-2n+8=20

2n+8=20

2n=20-8

2n=12

n=12/2

n=6

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:

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

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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x=-3

9x+2(3x+7)= -31

multiply the "3x" and the "7" by two (distributive property)

[="6x" and "7"]

add the "9x" and the "6x" [="15x"]

subtract "14" from"-31" [= "-45"]

divide "15x" from "-45"

="-3"

put the "-3" in for "x"

multiply 9(-3) [=-27]

multiply 3(-3) [=-9]

distribute the 2 to the "-9" and the "7" [="-18" and "14"]

add the "-18" and "14" [=-4]

add the "-27" and the "-4"

=-31 ✓

9x+2(3x)+2(7)= -31

9x+6x+14= -31

15x+14= -31

-14 -14

15x= -45

/15= /15

x= -3

9x+2(3x+7)= -31

9(-3)+2(3(-3)+7= -31

-27+2(-9+7)= -31

-27+(2(-9)+2(7))= -31

-27+(-18+14)= -31

-27+ (-4)= -31

-31= -31✓

Answer:

ok??? whats the question?

Step-by-step explanation:

Answer:

question???

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

There are 48 cards numbered from 1 to 48.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48

Multiples of 8: 8, 16, 24, 32, 40, 48

Multiples of 6 and 8: 24, 48.

Hence,

Total number of cards = 48,

Number of cards which are multiples of 6 and 8 = 2

The probability that the number card is a multiple of both 6 and 8 is

[tex]P=\dfrac{2}{48}=\dfrac{1}{24}[/tex]

Answer:

it is less than and equal to

Step-by-step explanation:

its > with a line under it

Answer:

125

Step-by-step explanation:

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:

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:

(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:

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:

G

Step-by-step explanation:

G = -2

-2 is greater than -4, yet, less than 0

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]

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: 4 pancakes

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

So, 20min÷5=4

Answer:

50m

Step-by-step explanation:

Information from the question:

The length is 15m

The width is 10m

Length is represented by "l"

Width is represented by "w"

The perimeter is the total of its side lengths. A rectangle has four sides that are two lengths and two widths.

Use the formula for perimeter:

P = 2(l + w)            Put in the length and width measurements

P = 2(15m + 10m)    Add inside the brackets

P = 2(25m)        Multiply

P = 50m           Answer

Therefore the perimeter of the rectangular swimming pool is 50 meters.

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

Step-by-step explanation:

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:

3:5

Step-by-step explanation:

Please see attached picture for full solution. ( Unit method)

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].

Keywords: fraction, division

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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:

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: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 graph is plotted below.

One ordered pair as solution is (0, 0).

Step-by-step explanation:

Given:

The inequality is given as:

[tex]y\geq x-5[/tex]

In order to plot it, we first replace '≥' by '=' sign. This gives,

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

Now, we plot the above line. For that, we need the x and y intercepts.

At x-intercept, y = 0. So,

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

The point is (5, 0)

At y-intercept, x = 0. So,

[tex]y=0-5\\y=-5[/tex]

The point is (0, -5)

Now, plot these two points and draw a line passing through these two points. The graph is shown below.

Now, replace '=' by '≥' sign. Since, 'y' is greater than equal to 'x - 5'. So, the solution region is above the given including the values on the line.

Therefore, any ordered pair in the solution region is a solution of the given inequality. From the graph, one such ordered pair is (0, 0).

This can be verified from the inequality also.

[tex]0\geq 0-5\\0\geq -5(True)[/tex]

So, one ordered pair is (0, 0).