joseph had started saving quarters,dimes,nickel and penny but is unable to give the
exact change for a hamburger costing $3.50.What the greatest amount of money he could have in coins.

2(5x+4)+3(2x-1)

Use the distributive property for both sets of parenthesis:

2(5x+4) = 2*5x + 2*4 = 10x+8

3(2x-1) = 3*2x - 3*1 = 6x-3

Now you have:

10x+8 + 6x-3

Now combine like terms:

10x + 6x = 16x

8-3 = 5

The final answer is 16x+5

Algebraic expression includes at least one unknown variable and at least one mathematics operation. The simplified way to represent the given equation is [tex]16x+5[/tex].

The given algebraic expression is,

[tex]2(5x+4)+3(2x-1)[/tex]

An algebraic expression is the mathematical expression of variable which is the combination of variables, coefficients of variables and constants.Algebraic expression includes at least one unknown variable and at least one mathematics operation.

Let [tex]f(x)[/tex] is equal to the given expression. Thus,

[tex]f(x) =2(5x+4)+3(2x-1)[/tex]

The above equation consist one unknown variable x.

Solve the equation using the BODMOS rule. According to the BODMOS to solve a equation first open its bracket. Thus,

[tex]f(x) =2(5x+4)+3(2x-1)[/tex]

[tex]f(x) =10x+8+6x-3[/tex]

Arrange the equation with same power of the variables,

[tex]f(x) =10x+6x+8-3[/tex]

[tex]f(x) =16x+5[/tex]

Hence the simplified way to represent the given equation is [tex]16x+5[/tex].

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Answer:

28.57142857% decrease

Step-by-step explanation:

To find the percentage decrease in speed, take the original speed minus the new speed over the original speed.  Then multiply by 100%

original speed = 70   new speed =50

percent decrease = (70-50)/70 *100%

                              = 20/70 *100%

                              =28.57142857%

Step-by-step explanation:

The answer is attached.

Probability helps us to know the chances of an event occurring. The given symbols can be matched with their description as shown below.

Probability helps us to know the chances of an event occurring.

The given symbols can be matched with their description as shown below, therefore,

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Answer:

a. The approximated salary cap in 2009 is $136.0 millions

b. The salary cap reached 65 million dollars in 2000

Step-by-step explanation:

* Lets explain how to solve the problem

- The quadratic model of the salary cap in million is

 y = 0.2313 x² + 2.600 x + 35.17

- The approximation of this cap in millions of dollars for the years

  1993-2013 where x = 0 represents 1993, x = 1 represents 1994,

  and so on

a. Lets calculate the approximated sports league salary cap in 2009

∵ x at 2009 = 2009 - 1993 = 16

∵ y = 0.2313 x² + 2.600 x + 35.17

∴ y = 0.2313 (16)² + 2.600 (16) + 35.17

∴ y = 135.98 ≅ 136.0 millions

* The approximated salary cap in 2009 is $136.0 millions

b. Lets calculate in what year did the salary cap reach 65 million dollars

∵ y = 65

∵ y = 0.2313 x² + 2.600 x + 35.17

∴ 65 = 0.2313 x² + 2.600 x + 35.17

- Subtract 65 from both sides

∴ 0.2313 x² + 2.600 x - 29.83 = 0

- Use the calculator to find the value of x by solving the quadratic

 equation

∴ x = 7.05 and x = -18.29 (we will reject this value)

∴ x ≅ 7 years

∴ The salary cap reached 65 million dollars in (1993 + 7) = 2000

* The salary cap reached 65 million dollars in 2000

Final answer:

To approximate the sports league salary cap in 2009, plug in 2009 for x in the given quadratic model equation. The salary cap in 2009 is approximately $942.9 million. If we set the salary cap to $65 million and solve for x using the quadratic model, we find that the cap reached $65 million in the year 2004.

Explanation:

To approximate the sports league salary cap in 2009, plug in 2009 for x in the quadratic model given. The equation becomes:

y = 0.2313(2009)^2 + 2.600(2009) + 35.17

Simplifying the equation gives:

y ≈ 942.85

Therefore, the approximate sports league salary cap in 2009 is $942.9 million (rounded to the nearest tenth).

To determine the year when the salary cap reached $65 million, set y = 65 in the quadratic model and solve for x:

65 = 0.2313x^2 + 2.600x + 35.17

By rearranging the equation and solving for x using the quadratic formula, we find that:

x ≈ 4.56

Rounding down to the nearest year, we can conclude that the salary cap reached $65 million in the year 2004.

Answer:

=22%

Step-by-step explanation:

Since we have given two conditions simultaneously that is windy and not sunny. So we will use the concept of conditional probability.

The probability of sunny day= P(sunny)=10%

P(sunny)=10%=0.1

The probability of windy and not sunny=P(windy|not sun)=20%

P(windy|not sun)=20% = 0.2

Now divide the both probabilities:

P(windy|not sun)/P(sunny)

=0.2/[1-0.1]              

{Hence there are 10% chances of sun tomorrow than there are (1 - 0.1) chances of no sun}

If we subtract 1 from 0.1 than it becomes:

=0.2/0.9

=2/9

=0.2222222222

=22%

Hence the probability that it is windy = 22% ....

The probability that it is windy given that it is not sunny is approximately 22% when rounded to the nearest percent.

To find the probability that it is windy given that it is not sunny, you apply the concept of conditional probability. There's a 10% chance of sun, hence, there is a 90% chance of no sun (100% - 10%). Among this 90%, there is a 20% chance that it's windy without sun. To find the probability of windiness given no sun, you would take the chance of wind and no sun (20%) and divide it by the probability of no sun (90%).

The calculation would be as follows:

(20% chance of wind and no sun) / (90% chance of no sun) = (0.20) / (0.90)
= approximately 0.222

When expressed as a percentage and rounded to the nearest percent, this is approximately 22%.

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]hypotenuse^2=leg^2+leg^2[/tex]

We have

[tex]leg=AC=36,\ leg=AB=15, hypotenuse=BC[/tex]

Substitute:

[tex]BC^2=36^2+15^2\\\\BC^2=1296+225\\\\BC^2=1521\to BC=\sqrt{1521}\\\\BC=39[/tex]

Answer:

39

Step-by-step explanation:

3.1.3

let's firstly convert the mixed fractions to improper fractions and then simply get their difference, our denominators will be 8 and 2, so our LCD will be 8.

[tex]\bf \stackrel{mixed}{27\frac{3}{8}}\implies \cfrac{27\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{219}{8}}~\hfill \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{219}{8}-\cfrac{5}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)219~~-~~(4)5}{8}}\implies \cfrac{219-20}{8}\implies \cfrac{199}{8}\implies 24\frac{7}{8}[/tex]

Answer:

  x = {-8/3, 7/2}

Step-by-step explanation:

To use the zero product property, you need the equation in the form of a product that is equal to zero. We can get that by subtracting 56 and factoring the resulting equation.

  6x^2 -5x -56 = 0

  (3x +8)(2x -7) = 0

The zero product property tells us this product is zero only when the factors are zero:

  3x +8 = 0   ⇒   x = -8/3

  2x -7 = 0   ⇒   x = 7/2

The solution is x = {-8/3, 7/2}.

_____

Comment on factoring

Consider the product ...

  (ax +b)(cx +d) = (ac)x^2 +(ad +bc)x +(bd)

Now consider the product of first and last term coefficients compared to the coefficient of the middle term:

  acbd = (ad)(bc)  vs.  ad+bc

We see that the coefficient of the middle term is the sum of two of the factors of the first·last product. This means we want factors of 6·(-56) that have a sum of -5.

  6(-56) = -(2^4)(3)(7) . . . . has 20 divisors.

We're looking for factors that are nearly equal. The clue is given by simplifying the above factoring:

  = -(16)(21) = (16)(-21) . . . . the sum of these factors is -5, as we need.

Again considering the first-last product and the middle coefficient, we see that we can choose ...

  ad = -21, bc = 16; ac = 6, so a=3, c=2, and ...

  (a, b, c, d) = (3, 8, 2, -7)

These values give us the factors we used above.

Note this process gets easier with practice and familiarity with multiplication tables.

Answer:

Mary has 72 breads and Sue has 72 breads....Total they have 144 breads.

Step-by-step explanation:

Let the bread of Sue be x and Mary be y.

y=x

Later , Sue has x- 54 breads and Mary has y+ 54 breads.

As per question,

y+54=7(x-54)

y+54= 7x-378

y+54=7y- 378

6y= 378+54

y=432/6

y=72

Answer:

2313

Step-by-step explanation:

A = P(1+r)^t

where A is the final amount, P is the initial amount, r is the rate, and t is time.

Here, P = 1000, r = 0.15, and t = 6.

A = 1000(1.15)^6

A ≈ 2313

Step-by-step explanation:

Population after n days is given by

              [tex]P_n=P_0(1+r)^n[/tex]

Initial population, P₀ = 1000

Increase rate, r = 15 % = 0.15

Number of days, n = 6

Substituting

             [tex]P_n=P_0(1+r)^n\\\\P_6=1000(1+0.15)^6\\\\P_6=1000(1.15)^6\\\\P_6=1000\times 2.313\\\\P_6=2313[/tex]

Number of bacteria after 6 days = 2313

Answer:

that is really confusing.

Step-by-step explanation:

Answer:  [tex]\bold{B)\quad x = \dfrac{8}{3}}[/tex]

Step-by-step explanation:

[tex]log_2(9x)-log_2(3)=3\\\\\\log_2\bigg(\dfrac{9x}{3}\bigg)=3\qquad\qquad \rightarrow \text{used rule for condensing logs}\\\\\\log_2(3x)=3\qquad\qquad \rightarrow \text{simplified}\\\\\\3x=2^3\qquad\qquad \rightarrow \text{used rule for eliminating log}\\\\\\3x=8\qquad\qquad \rightarrow \text{simplified}\\\\\\\large\boxed{x=\dfrac{8}{3}}[/tex]

The equation of the word problem is ( x - 5 ) × 2 = 26 and the value of the unknown number is 18.

Given that;

A number is decreased by five and then the result is multiplied by two.

The result is 26.

Let x represent the unknown know number.

Hence,

The equation is ( x - 5 ) × 2 = 26

We can go further and solve for the value of the unknown number.

( x - 5 ) × 2 = 26

2x - 10 = 26

2x = 26 + 10

2x = 36

x = 36 ÷ 2

x = 18

The equation of the word problem is ( x - 5 ) × 2 = 26 and the value of the unknown number is 18.

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Final answer:

The equation based on the given statement is 2(x - 5) = 26. By following the order of operations and solving for the unknown number x, we find that x = 18.

Explanation:

To write an equation for the statement "If a number is decreased by five and then the result is multiplied by two, the result is 26," we start by letting x represent the unknown number. First, we decrease x by five, which is represented mathematically as x - 5. Following this, we then multiply the result by two, which gives us 2(x - 5). The statement concludes by saying that this expression is equal to 26, giving us the final equation:

2(x - 5) = 26

To solve for x, we can follow these steps:

Therefore, the number we are looking for is 18.

Answer:

7 boxes

Step-by-step explanation:

Simply divide 42 by 6 to get your answer.

I am joyous to assist you anytime.

Answer:

f(x) = -5x + 250

Step-by-step explanation:

* Lets  explain how to solve the problem

- In week 10 the manufacturer fixed 200 cars

- In week 15, the manufacturer fixed 175 cars

- the reduction in the number of cars each week is linear

- The form of the linear equation is y = mx + c, where m is the slope of

 the line which represent the equation and c is the y-intercept

- The slope of the line m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

  where (x1 , y1) and (x2 , y2) are two points on the line

* Lets solve the problem

- Assume that the weeks' number is x and the cars' number is y

∴ (10 , 200) and (15 , 175) are two points on the line which represent

  the linear equation between the cars' numbers and the weeks

  numbers

∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)

∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175

- Use the rule of the slope above to find m

∴ [tex]m=\frac{175-200}{15-10}=\frac{-25}{5}=-5[/tex]

- Substitute the value of x in the form of the linear equation above

∴ y = -5x + c

- To find c substitute x and y by one the coordinates of one of the

  two points

∵ x = 10 when y = 200

∴ 200 = -5(10) + c

∴ 200 = -50 + c

- Add 50 to both sides

∴ 250 = c

- Substitute the value of c by 250

∴ y = -5x + 250, where the number of cars seen each week is y and

  x is the number of the week

∵ f(x) = y

∴ f(x) = -5x + 250

Answer:

B f(x) = −5x + 250

Step-by-step explanation:

Answer:

Step-by-step explanation:

Look at the picture.

Mark points (0, 2) and (8, -4) in the coordinate system.

Plot the line going through these points.

Read the coordinates of the intersection of the line (solution).

The solution of the system of linear equation is (4,-1) and this can be determined by using the arithmetic operations.

Given :

Equations  ---  y = x - 5   --- (1)

                       [tex]\rm y = -\dfrac{3}{4}x+2[/tex]    --- (2)

The system of linear equations can be determined by substituting the value of y in terms of x in another equation in order to determine the value of 'x' and by finding the value of 'x', the value of 'y' can also be determined.

Substitute the value of 'y' in equation (2) that is:

[tex]\rm x-5 = -\dfrac{3}{4}x+2[/tex]

Further, simplify the above equation.

[tex]4x - 20 = -3x +8[/tex]

7x = 28

x = 4

Now, substitute the value of 'x' in equation (1) that is:

y = 4 - 5

y = -1

So, the solution of the system of linear equation is (4,-1).

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Answer:

the answer is 15

Step-by-step explanation:

Step-by-step explanation:

recall in a linear equation expressed in the form

y = mx + b,

m represents the slope or the rate of change in the value of y for a unit change in the value of x

b represents the y-intercept (i.e the value of y when x = 0)

If you compare these definitions to what was given in the question, the rate of  change in snowfall is given as 1/2 inches per hour. This is equivalent to the m value in our general equation above. Hence we can say that the rate of change in snowfall is equal to the slope of the graph.

The question also states that before the snow even started to fall (i.e when x=0 hours), there was already 8 inches on the ground. This is equivalent to the value of b in our general equation above. Hence we can say that the y-intercept is representative of the 8 inches that was already on the ground when the snow started falling.

Answer:

800 basic 200 accent tiles

Step-by-step explanation:

The required square feet of basic tile and accent tile is 800 and 200 square feet respectively.

As the data available, 1,000 square feet of tile. He will do most of the floor with a basic tile that costs $1.50 per square foot, but he also wants to use an accent tile that costs $9.00 per square foot.

In mathematics, it deals with numbers of operations according to the statements.

Here,
Let the number of basic tiles be x and the number of accent tiles be y,
According to the question,
x + y = 1000
x = 1000 - y  - - - - - -- - - - - - - (1)
1.5x + 9y = 3000  - - - - -  - -- - - (2)
Put the value of x in equation 2
1.5 (1000 - y ) + 9y = 3000
1500 - 1.5y + 9y = 3000
7.5y = 1500
y = 1500 / 7.5
y = 200
Now, put y in equation 1
x = 800

Thus, the required square feet of basic tile and accent tile is 800 and 200 square feet respectively.

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Answer:

The 5 all the way to the left

325,251.58

Step-by-step explanation:

The 8 is in the hundredths place

The 5 is in the tenths place

The 1 is in the ones place

The 5 is in the tens place

The 2 is in the hundreds place

The 5 is in the thousands place

The 2 is in the ten-thousands place

The 3 is in the hundred-thousands place

Hope This Helped :}

Neither of the given numbers (325,25 and 1.58) have a thousands place. This would typically be represented by the digit to the left of the hundreds place.

The student has asked about the thousands place in a pair of numbers. Looking at the numbers provided (325,25 and 1.58), neither of these numbers actually have a thousand place digit. In a number, the thousands place digit is the digit to the left of the hundreds place. For example, in the number 6528, which is from an arithmetic operation given in the reference information (6527.23 + 2 = 6528.23), the 6 represents 6 thousands, or 6000.

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Answer: 72

Step-by-step explanation:

The value of x will be equal to 3.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

We know that the  exterior angles are equal to the opposite interior angles

So the equation would be:

25x  +  57  +  x   =   45x

26x  +  57   =   45x

57  =   19x

x    =    3

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[tex]\large\boxed{\$4}[/tex]

In this question, we're trying to find how much Voldemort had to pay for the ice cream.

To answer this question, we need to gather some important information that was provided in the question.

Important information:

With the information above, we can solve the problem.

The easiest way to solve this problem is to multiply. We would multiply 6.6 and 0.60 in order to see how much did Voldemort had to pay.

[tex]6.6*0.60=3.96[/tex]

When you multiply, you should get 3.96

This means that Voldemort payed $3.96 for the ice cream.

But we need to round it to the nearest dollar.

When you round it, you should get $4

Answer:

4

Step-by-step explanation:

Answer:

-12x+54

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{In order for you to simplify, you need to}[/tex] [tex]\huge\text{ distribute}[/tex]

[tex]\huge\text{The formula is: a(b + c) = a(b) + a(c) = ab + ac}[/tex]

[tex]\huge\text{Simplify: -6(2x - 9)}[/tex]

[tex]\huge\text{-6(2x) = -12x}\\\huge\text{-6(-9) = 54}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: -12x + 54}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

x=15

y=5

Step-by-step explanation:

The small looking triangle has 3 angles that are congruent to each other. We know this because they all share that same single marker. That means each of those angles ate 60 degrees. That triangle is known as both a equilateral and equilangular. All that means is all of it's 3 sides are congruent and all of it's 3 angles are congruent.

So that angle that measures 8x forms a linear pair with the angle right next to it in the other triangle. All that means is that is supplementary to and adjacent to that angle that measures 60 degrees.

So we have 8x+60=180.

We need to solve this equation for x:

8x+60=180

Subtract 60 on both sides:

8x. =120

Divide both sides by 8

x. =120/8

x. =15

Now to find y.

The bigger looking triangle is an isosceles. We know this because its two base angles are congruent (they have the same double marker). This means 5y+1=26.

Solving:

5y+1=26

Subtracting 1 on both sides:

5y. =25

Dividing 5 on both sides:

y. =5

The values of [tex]x[/tex] and [tex]y[/tex] are required.

[tex]x=15,y=5[/tex]

In the figure

[tex]\angle BAD=\angle BDA[/tex]

This means the sides opposite to the angles will also be equal.

So, [tex]AB=BD=26[/tex]

In [tex]\Delta BDC[/tex] all angles are equal, so it is an equilateral triangle.

So, all angles are [tex]60^{\circ}[/tex]

[tex]\angle ABD+\angle DBC=180\\\Rightarrow 8x+60=180\\\Rightarrow x=\dfrac{180-60}{8}\\\Rightarrow x=15[/tex]

All sides are equal in [tex]\Delta BDC[/tex]

[tex]26=5y+1\\\Rightarrow y=\dfrac{26-1}{5}\\\Rightarrow y=5[/tex]

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Answer:

Part 1)  [tex]x=11[/tex]

Part 2)  [tex]k=57.2[/tex]  

Part 3)  [tex]y=9.2[/tex]

Part 4)  [tex]x=2.375[/tex]

Part 5) [tex]y=3.3[/tex]

Part 6)  [tex]k=6.7[/tex]

Part 7)  [tex]k=115.2[/tex]

Part 8)  [tex]y=1.4[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Part 1) y varies inversely with x. If y = 3 and k (the constant of variation) = 33, what is x?

we have

[tex]y*x=k[/tex]

[tex]y=3[/tex]

[tex]k=33[/tex]

substitute and solve for x

[tex]3*x=33[/tex]

Divide by 3 both sides

[tex]x=33/3[/tex]

[tex]x=11[/tex]

Part 2) y varies inversely with x. When y = 11, x = 5.2. What is the value of k, the constant of inverse variation?

we have

[tex]y*x=k[/tex]

[tex]y=11[/tex]

[tex]x=5.2[/tex]

substitute and solve for k

[tex]11*5.2=k[/tex]

[tex]k=57.2[/tex]  

Part 3) y varies inversely with x, and k (the constant of variation) = 72. What is the value of y when x = 7.8?

we have

[tex]y*x=k[/tex]

[tex]x=7.8[/tex]

[tex]k=72[/tex]

substitute and solve for y

[tex]y*7.8=72[/tex]

Divide by 7.8 both sides

[tex]y=72/7.8[/tex]

[tex]y=9.2[/tex]

Part 4) y varies inversely with x. If y = 8 and k (the constant of variation) = 19, what is x?

we have

[tex]y*x=k[/tex]

[tex]y=8[/tex]

[tex]k=19[/tex]

substitute and solve for x

[tex]8*x=19[/tex]

Divide by 8 both sides

[tex]x=19/8[/tex]

[tex]x=2.375[/tex]

Part 5) y varies inversely with x, and k (the constant of variation) = 23. What is the value of y when x = 7?

we have

[tex]y*x=k[/tex]

[tex]x=7[/tex]

[tex]k=23[/tex]

substitute and solve for y

[tex]y*7=23[/tex]

Divide by 7 both sides

[tex]y=23/7[/tex]

[tex]y=3.3[/tex]

Part 6) y varies inversely with x. When y = 6.7, x = 1. What is the value of k, the constant of inverse variation?

we have

[tex]y*x=k[/tex]

[tex]y=6.7[/tex]

[tex]x=1[/tex]

substitute and solve for k

[tex]6.7*1=k[/tex]

[tex]k=6.7[/tex]

Part 7) y varies inversely with x. When y = 9.6, x = 12. What is the value of k, the constant of inverse variation?

we have

[tex]y*x=k[/tex]

[tex]y=9.6[/tex]

[tex]x=12[/tex]

substitute and solve for k

[tex]9.6*12=k[/tex]

[tex]k=115.2[/tex]

Part 8) y varies inversely with x, and k (the constant of variation) = 5.6. What is the value of y when x = 4?

we have

[tex]y*x=k[/tex]

[tex]x=4[/tex]

[tex]k=5.6[/tex]

substitute and solve for y

[tex]y*4=5.6[/tex]

Divide by 4 both sides

[tex]y=5.6/4[/tex]

[tex]y=1.4[/tex]

Answer:

7y - 4x

Step-by-step explanation:

Given

- 3(2x - y) + 2y + 2(x + y) ← distribute both parenthesis

= - 6x + 3y + 2y + 2x + 2y ← collect like terms

= - 4x + 7y

= 7y - 4x

Replace x in the equation with -5 and solve.

5(-5) +40 = -25 + 40 = 15

The value of f(x) when x = -5 is f(-5) = 15 by substitution.

Given that a function is defined as:

f(x) = 5x + 40

It is required to find the value of f(x) when the value of x = -5.

Substitute the value of x = -5 in the expression for f(x).

So,

f(-5) = 5(-5) + 40

       = -25 + 40

       = 15

So, the value of f(x) when x = -5 is 15.

Hence f(x) = 15 when x = -5.

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[tex]\huge{\boxed{1}}[/tex]

This statement can be represented as [tex]2*\frac{3}{6}[/tex], since the quotient is the answer to a division problem.

Divide. [tex]2*\frac{1}{2}[/tex]

Multiply. [tex]2*\frac{1}{2}=\frac{2}{1}*\frac{1}{2}=\frac{2*1}{1*2}=\frac{2}{2}[/tex]

Simplify.  When the numerator and denominator are the same, the fraction is equal to 1. [tex]\frac{2}{2}=1[/tex]