Manuel needs to save more than $75 for a class trip. He already has $24 and
will save an equal amount each week for the next 6 weeks. Which inequality
can be used to determine how much money Manuel should save each week?

Answer:

a. y = 0.012x²

b. 4.80 m

c. 25 m/s

Step-by-step explanation:

a. First, we need to determine what kind of function this is (linear, quadratic, etc.).

Logically, the function must pass through the origin, so we can compare the ratios between points.

Let's look at (5.00, 0.30) and (10.00, 1.20).  When we double the speed, the depth quadruples.  That tells us this must be a quadratic equation.

y = kx²

Plug in a point to find k:

0.30 = k (5.00)²

k = 0.012

Therefore, the equation is:

y = 0.012x²

We can check our answer by plugging in more points.

1.20 = 0.012 (10.00)²

2.70 = 0.012 (15.00)²

b. Find y when x = 20.00.

y = 0.012 (20.00)²

y = 4.80

c. Find x when y = 7.50.

7.50 = 0.012 x²

x = 25

Answer: 8 1/3 yards per second

500 yards/60 seconds=8 1/3 yards per second

Check Work:

8 1/3 yards per second*60 seconds=500 yards per minute.

Hope this helps!

Answer:

2!

Step-by-step explanation:

To find out what fraction of 2 1/2 is 4/5, convert 2 1/2 to a fraction (5/2), then multiply 4/5 by the reciprocal of 5/2 which gives 8/25. So, 4/5 is 8/25 of 2 1/2.

The question is asking about what fraction of 2 1/2 is 4/5. In order to solve this, we should firstly convert the mixed number 2 1/2 to a fraction, which is 5/2. Then we have to divide 4/5 by 5/2 to find out the fraction. To divide fractions, we multiply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

So, the problem becomes 4/5 * 2/5, and the solution is 8/25. Therefore, 4/5 is 8/25 of 2 1/2.

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Answer:

The first step in evaluating {[(−)]}÷ is operating the brackets

Step-by-step explanation:

To find the first step in evaluating {[(−)]}÷ :

In general we may use BODMAS operation to evaluate the expression and is stands for

BODMAS- B for Brackets in the expression

                 O for operations in brackets for the expression

                 D for  doing division operation in the  expression

                M for doing multiplication operation in the expression

                 A for  doing addition operation in the expression

                 S for doing subtraction operation in the expression

Applying all the operations and finally weget the evaluated expression or values.

Therefore the first step in evaluating {[(−)]}÷ is operating the brackets

Answer:

The sixteenth term is (7.5y - 6.5x).

Step-by-step explanation:

The first term of the A.P. is given to be x and the common difference is assumed to be d.

So, the third term = y = x + (3 - 1)d {Given that the third term is y}

Then, 2d = y - x

⇒ [tex]d = \frac{y - x}{2}[/tex]

Therefore, the sixteenth term of the A.P. will be = x + (16 - 1)d

= [tex]x + 15 \times \frac{y - x}{2}[/tex]

= x + 7.5y - 7.5x

= 7.5y - 6.5x (Answer)

Answer:

The sixteenth term is [tex]x+\frac{15(y-x)}{2}[/tex].

Step-by-step explanation:

Given,

[tex]a_1=x[/tex]

[tex]a_3=y[/tex]

And also given, [tex]T_n=a+(n-1)d[/tex]

We have to find out the 16th term of given A.P.

Firstly, we will find out the common difference(d).

Common difference(d) is calculated by given formula.

[tex]T_3=a+(n-1)d[/tex]

On putting the values, we get;

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

Now the value of 'd' is calculated, so we can find out the 16th term by using the formula.

[tex]T_{16}=x+(16-1)\frac{y-x}{2}\\\\T_{16}=x+15\times\frac{y-x}{2}\\\\ T_{16}=x+\frac{15(y-x)}{2}[/tex]

Hence The sixteenth term is [tex]x+\frac{15(y-x)}{2}[/tex].

Answer:

c ≈ 4.2 ft

Step-by-step explanation:

Using the cosine rule with a = 7, b = 8 and C = 32°, then

c² = 7² + 8² - (2 × 7 × 8 × cos32°)

   = 49 + 64 - (112 × cos32°)

   = 113 - 94.98

c = [tex]\sqrt{113-94.98}[/tex] ≈ 4.2 ft ( to the nearest tenth )

Answer:

x=√67 or x=−√67

Step-by-step explanation:

Step 1: Add 7 to both sides.

x2−7+7=60+7

x2=67

Step 2: Take square root.

x=±√67

x=√67 or x=−√67

Answer:

25%

Step-by-step explanation:

Draw a Venn diagram.  One circle is 95%, and the other circle is 30%.  Let's say x is the overlap.  The total is 100%.  If you add the 95 and 30 together, you'll be counting the overlap twice, so subtract one x.

95 + 30 − x = 100

x = 25

Answer:

$ 140.55 ≤ $ 7.59x + 0.89$ y

$ 140.55 ≤ $ 9.37x   where 0≤ x ≤ 15.

Step-by-step explanation:

$ 140.55 ≤ $ 7.59x + 0.89$ y

Let x be the number of sweatshirts and y be the number of bags where y= 2x

and 0≤ x ≤ 15.

$ 140.55 ≤ $ 7.59x + 0.89$ (2x)   Putting y= 2x

$ 140.55 ≤ $ 7.59x + $ 1.78x

$ 140.55 ≤ $ 9.37x  where 0≤ x ≤ 15.

Answer:

$ 140.55 ≤ $ 7.59x + 0.89$ y

$ 140.55 ≤ $ 9.37x   where 0≤ x ≤ 15.

Step-by-step explanation:

$ 140.55 ≤ $ 7.59x + 0.89$ y

Let x be the number of sweatshirts and y be the number of bags where y= 2x

and 0≤ x ≤ 15.

$ 140.55 ≤ $ 7.59x + 0.89$ (2x)   Putting y= 2x

$ 140.55 ≤ $ 7.59x + $ 1.78x

$ 140.55 ≤ $ 9.37x  where 0≤ x ≤ 15.

Step-by-step explanation:

Answer:

y=-1/3x+2/7

Step-by-step explanation:

y=-3x+6/7

x=-3y+6/7

-3y=x-6/7

y=-1/3x+(6/7)/3

y=-1/3x+(6/7)(1/3)

y=-1/3x+6/21

y=-1/3x+2/7

Answer:

60

Step-by-step explanation:

87/29=3

3$ for each pound.

20*3= 60.

answer is 60.

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf \stackrel{\textit{x-intercept}}{(\stackrel{x_1}{6}~,~\stackrel{y_1}{0})}\qquad \stackrel{\textit{y-intercept}}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{5})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{6}}}\implies -\cfrac{5}{6}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{-\cfrac{5}{6}}(x-\stackrel{x_1}{6}) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6(y-0)=6\left(-\cfrac{5}{6}(x-6) \right)}\implies 6y=-5(x-6) \\\\\\ 6y=-5x+30 \implies 5x+6y=30[/tex]

The standard form of the line with an x-intercept of 6 and a y-intercept of 5 is -5x + 6y = 30.

The standard form of a linear equation is given by the equation Ax + By = C, where A, B, and C are real numbers and A and B are not both zero. To find the standard form of the line with an x-intercept of 6 and a y-intercept of 5, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope using the two intercepts. The slope is (y-intercept - x-intercept) / (0 - 6) = (5 - 0) / -6 = -5/6.

Now, we can substitute the slope and the y-intercept into the standard form equation to get: (-5/6)x + y = 5. Multiplying through by 6, we get -5x + 6y = 30. Therefore, the standard form of the line is -5x + 6y = 30.

Answer:

The slope intercept is y=mx+b

y=-1x (you go down one over one from your y-intercept)

y=-1x-1 (It would be minus one because that is where it crosses the y-axis)

Step-by-step explanation:

Answer:

1 11/20m

Step-by-step explanation:

4 times 5 is 20

3/4(5) 4/5(4) =

15/20m + 16/20m =

31/20m = 1 11/20m

Complete Question:

As you missed to add the area and length value. So, after a little research I was able to find the complete question. I will answer the question based on this complete question I am mentioning, but hopefully it would clear your concept anyways. So, here is the complete question.

The Area of a rectangular patio is 5 5/8 square yards, and it's length is 1 1/2 yards.What is the patio's width,in yards?

Answer:

The width of patios is [tex]w = \frac{15}{4} yards[/tex].

Step-by-step explanation:

As the area of a rectangular patio is [tex]A = 5\frac{5}{8}[/tex] square yards.

⇒ [tex]A = 5\frac{5}{8}[/tex]

⇒ [tex]A = 5\frac{5}{8}[/tex] can be written as : [tex]A = \frac{45}{8}[/tex]

The length of a rectangular patio is [tex]l = 1\frac{1}{2}[/tex] square yards.

⇒[tex]l = 1\frac{1}{2}[/tex]

⇒[tex]l = 1\frac{1}{2}[/tex]  can be written as : [tex]l = \frac{3}{2}[/tex]

As the area of rectangular patio can be computed by multiplying the length and width. So, width [tex](w)[/tex] can be computed by dividing the Area by length.

[tex]A = lw[/tex]

[tex]w = \frac{A}{l}[/tex]

So, [tex]w = \frac{\frac{45}{8}}{\frac{3}{2} }[/tex]

[tex]w = (\frac{45}{8}) (\frac{2}{3} )[/tex]

[tex]w = \frac{90}{24}[/tex]

[tex]w = \frac{15}{4}[/tex] or [tex]w = 3\frac{3}{4}[/tex]

Hence, the width of patios is [tex]w = \frac{15}{4} yards[/tex].

Keywords: area of rectangle, width, length

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Answer:

2 y for every 1 x

Step-by-step explanation:

2 and 1 is the answer

Answer:

22.18 = x

Step-by-step explanation:

a^2 + (b)^2 = (x/2)^2

a = sqrt(74)

b = 7

x/2 = ?

(74)[^1/2]^2 = 74            

b^2 = 7^2 = 49

74 + 49 = (x/2)^2       Substitute into a^2 + b^2 = c^2

123 = (x/2)^2              Combine like terms

(123^0.5) = x/2           Take the square root of both sides.

11.09 = x/2                  Multiply both sides by 2

11.09*2 = x

22.18 = x                     The full length of the base of the triangle is 22.18

Answer:

10

Step-by-step explanation:

Trust me

The equation is simplified to -x = 5, yet a negative x value indicates that the identity is not true. Hence, there is no solution to this equation.

To solve this equation, we should first try to simplify both sides of the equation.

On the left side, combine like terms. This gives us -6x - 7.

On the right side, we already have -5x - 12.

Setting these expressions equal to each other yields: -6x - 7 = -5x - 12.

Adding 5x to both sides gives us -x - 7 = -12.

Then adding 7 to both sides gives us -x = 5.

However, a negative x value would indicate that the identity is not true, thus the equation has no solution.

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Answer:

The required points of the given line segment  are ( - 7, - 4 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( - 2, 3 ) and point A is ( 3, 10), then we have to find point B of the line segment AB -

As we know that-

If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and  ( [tex]x_{2}, y_{2}[/tex]  )then the mid points M are-  

M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex]  , [tex]\frac{ y_{1} + y_{2} }{2}[/tex]  )

Here,

Let A ( 3, 10 ), B ( x, y ) with midpoint M ( - 2, 3 ) -

then by the midpoint formula M are-

( - 2, 3 )  = ( [tex]\frac{ 3 + x}{2}[/tex] , [tex]\frac{ 10 + y}{2}[/tex] )

On comparing x coordinate and y coordinate -

We get,

( [tex]\frac{ 3 + x}{2}[/tex] = - 2  , [tex]\frac{ 10 + y}{2}[/tex] = 3)

( 3 + x = - 4, 10 + y = 6 )

( x = - 4 - 3, y = 6 - 10 )

( x = - 7, y = -4 )

Hence the required points  A are ( - 7, - 4 ).

We can also verify by putting these points into Midpoint formula.

Final answer:

To find the other endpoint of a line segment with a known endpoint (3, 10) and midpoint (-2, 3), use the midpoint formula in reverse to calculate the coordinates, resulting in the other endpoint being (-7, -4).

Explanation:

To find the other endpoint of a line segment when given one endpoint and the midpoint, you can use the midpoint formula in reverse. The midpoint formula in two dimensions is
( (x1+x2)/2, (y1+y2)/2 ), where (x1, y1) and (x2, y2) are the endpoints of the line segment. Given that (3, 10) is one endpoint and (-2, 3) is the midpoint, we can set up equations to find the coordinates of the unknown endpoint (x2, y2).

To find x2, we use the formula for x-coordinate of the midpoint: (-2 + 3)/2 = (x2 + 3)/2. Solving for x2 gives us x2 = -2 - 3 = -7.

To find y2, we use the formula for y-coordinate of the midpoint: (3 + 10)/2 = (y2 + 10)/2. Solving for y2 gives us y2 = 2*3 - 10 = 6 - 10 = -4.

Therefore, the other endpoint of the line segment is (-7, -4).

Answer:

[tex]3n^3(2-n^2)[/tex]

Step-by-step explanation:

Given expression:

[tex]6n^3-3n^5[/tex]

To factor out the expression completely.

Solution:

In order to factor out the expression, we will find the greatest common factor of each term.

To find the G.C.F. of the two terms, we will list down their factors and then find the common ones.

The factors of the terms can be given as:

[tex]6n^3=2\times 3\times n\times n\times n[/tex]

[tex]3n^5=3\times n\times n\times n \times n\times n[/tex]

The G.C.F. = [tex]3\times n\times n\times n=3n^3[/tex]

So, we factor out the G.C.F. and write the remaining factors inside the parenthesis.

The expression will be given using distributive property as:

⇒ [tex]3n^3(2-n^2)[/tex] (Answer)

Final answer:

To factor out [tex]6n^3 - 3n^5,[/tex] find the greatest common factor and simplify the expression.

Explanation:

A factor, in mathematics, refers to a number or algebraic expression that divides another number or expression evenly, meaning without leaving a remainder. When we say that one number is a factor of another, it means that when you divide the larger number by the factor, the result is an integer. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these numbers divides 12 without leaving a remainder.

Factoring out [tex]6n^3 - 3n^5[/tex] involves finding the greatest common factor of the terms.

Step 1: Factor out [tex]n^3[/tex] from both terms to get [tex]n^3(6 - 3n^2).[/tex]

Step 2: Further simplify to [tex]n^3(2)(3 - n^2[/tex]) for the final factored form.

Answer:

x = 7

Step-by-step explanation:

The inscribed angle (5x - 3) is equal to half the measure of the intercepted arc

5x - 3 = 0.5(9x + 1) ← multiply both sides by 2

10x - 6 = 9x + 1 ( subtract 9x from both sides )

x - 6 = 1 ( add 6 to both sides )

x = 7

33.3...% = 1/3.

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Answer: 33.3 or 1/3

Step-by-step explanation:

i really good at math so if you need help message me

Answer:

Step-by-step explanation:

first we need to find the slope using the slope formula :

slope = (y2 - y1) / (x2 - x1)

(-9,7)...x1 = -9 and y1 = 7

(-6,-3)....x2 = -6 and y2 = -3

now we sub

slope = (-3 - 7) / (-6 - (-9) = -10 / (-6 + 9) = -10 / 3

so our slope is -10/3

now we use y = mx + b....with m representing the slope

slope(m) = -10/3

use either of ur points....I will use (-9,7)...x = -9 and y = 7

we are solving for b, the y intercept

now we sub

7 = -10/3(-9) + b

7 = 30 + b

7 - 30 = b

- 23 = b

so ur equation is : y = -10/3x - 23

Final answer:

To find the equation of the line through (-9, 7) and (-6, -3), calculate the slope, which is -10/3, and then use the point-slope form to derive the equation y = -10/3 x + 23.

Explanation:

To complete the equation of the line through the points (-9, 7) and (-6, -3), we need to find the slope (m) and use one of the points to find the y-intercept (b) in the slope-intercept form y = mx + b.

Step 1: Find the slope (m):

Step 2: Use point-slope form to find equation:

The completed equation of the line is y = -10/3 x + 23.

Answer:

The closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]

Step-by-step explanation:

Given that the first term [tex]a_{1}=0.3[/tex] and [tex]a_{n+1}=a_{n}+0.75[/tex]

To find the closed linear form for the given sequence

The formula for arithmetic sequence is

[tex]a_{n}=a_{1}+(n - 1)d[/tex]  (where d is the common difference)

The above equation is of the given form  [tex]a_{n+1}=a_{n}+0.75[/tex]

Comparing this we get d=0.75

With [tex]a_{1}=0.3[/tex] and d=0.75

We can substitute these values in [tex]a_{n}=a_{1}+(n - 1)d[/tex]

[tex]a_{n}=a_{1}+(n - 1)d[/tex]

[tex]=0.3+(n-1)(0.75)[/tex]

[tex]=0.3+0.75n-0.75[/tex]

[tex]=-0.45+0.75n[/tex]

Rewritting as below

[tex]=0.75n-0.45[/tex]

Therefore [tex]a_{n}=0.75n-0.45[/tex]

Therefore the closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]

Answer:

-216 has three real cube roots.

Step-by-step explanation:

To calculate the area of a carpet square with sides of 9 inches, you multiply the side length by itself, resulting in an area of 81 square inches.

The question is asking for the area of a carpet square whose sides are 9 inches long. To find the area of a square, you multiply the length of one side by itself, because the formula for the area of a square is Area = side × side. In this case, each side of the carpet square is 9 inches long.

So, the area of the carpet square would be calculated as follows:

Therefore, the area of the carpet square is 81 square inches.

Answer:

slope: 2/3

y intercept: - 2

x-0,3

y - 3 0

Answer:

graph C

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

f(n) = 7n - 3

f(8) = 7*8 - 3 = 56 - 3 = 53

Final answer:

To find the 8th term of the arithmetic sequence given by f(n) = 7n - 3, substitute n with 8 and calculate the result to get 53.

Explanation:

The question is about finding the 8th term of an arithmetic sequence. The function for the sequence is given as f(n) = 7n - 3. To find the 8th term, we substitute n with 8 in the function. So, f(8) = 7(8) - 3. Calculating the value, we get f(8) = 56 - 3 = 53.

So, the 8th term of the sequence is 53. This result is obtained by applying the formula for the general term of an arithmetic sequence, where f(n) represents the term at position n. In this sequence, each term is obtained by adding 7 to the previous term.

The constant difference between successive terms (7 in this case) is a characteristic feature of an arithmetic sequence. Therefore, the 8th term of the sequence is 53.

Evaluate.

Follow PEMDAS.

7+(10-4)²÷4×(1/2)³

parentheses and exponents first

7+36÷4×(1/8)

multiplication next

7+9×(1/8) ----> 7+(9/8)

addition

8 1/8

answer: third choice