all numbers are divisible by​

Answer:

x ≤ 11

Step-by-step explanation:

Simplify the equation, then isolate "x" by using reverse operations in reverse BEDMAS order.

3x + 2 ≤ 5(x-4)     Distribute over the bracket by multiplying.

= 3x + 2 ≤ 5x - 20     Start isolating "x" on the left side.

= 3x + 2 - 2 ≤ 5x - 20 - 2     Subtract 2 from both sides.

= 3x ≤ 5x - 22    

= 3x - 5x ≤ 5x - 22 - 5x     Subtract 5x from both sides to move x to left side

= -2x ≤ -22

= -2x/-2 ≤ -22/-2     Divide both sides by -2 to isolate x

= x ≤ 11     Final answer

Answer:

Step-by-step explanation:

a₂ = 14

a₃ = 18

d = a₃ -a₂ = 18 - 14 = 4

a₁ = 14 - 4 = 10

nth term = a + (n-1)d

a₅₁ = 10 +  50 * 4

  = 10 + 200

 = 210

Answer:

Therefore the equation dor nth term is,

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

[tex]a_{30} =-18[/tex]

Step-by-step explanation:

Given:

Arithmetic Sequence as

11 , 10 , 9 , 8 , ..........

∴   First term     = a₁ = 11

   Second term = a₂ = 10

∴ Common Difference = d =  a₂ - a₁ = 10 - 11 = -1

∴ d = -1

To Find:

[tex]a_{n} = ?\\and\\a_{30} = ?[/tex]

Solution:

An equation for the nth term of the arithmetic sequence is given by

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

Substitute n= 30 for [tex]a_{30}[/tex] and a₁ and d we get

[tex]a_{30} =11 + (30-1)\times -1\\\\a_{30} =11+29\times -1\\\\a_{30} =11-29\\\\a_{30} =-18\\\\\therefore a_{30} =-18\ \textrm{as required}[/tex]

Therefore,

[tex]a_{30} =-18[/tex]

The nth term of the given arithmetic sequence can be represented by the equation an = 12 - n. The 30th term of this sequence is -18.

In order to write an equation for the nth term of an arithmetic sequence, we need to know the first term (a1) and the common difference (d). In the given arithmetic sequence 11, 10, 9, 8, ..., the first term a1 is 11 and the common difference d is -1 (because each term reduces by 1).

The general formula for the nth term (an) of an arithmetic sequence is: an = a1 + (n-1) * d. Substituting the values of a1 and d in the equation, we get: an = 11 + (n-1) * -1 = 12 - n.

To find a30, substitute n = 30 in the equation, we get a30 = 12 - 30 = -18.

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Graphing is a very useful tool to solve a system of equations but the only major disadvantage is that it is very time-consuming. So, we can solve the system of equations quickly by isolation one variable in one equation and then we get the answer by substituting the resulting expression for the variable in the other equation.

Step-by-step explanation :

Step 1:

Consider the system of equations:

5x + y =13  

3x=15 - 3y

Step 2 :  

y is the easiest variable to isolate in the first equation, because it has no coefficient:

y = 13 - 5x

Step 3 :

In the second equation, substituting for y :

3x = 15 - 3(13 - 5x)

Step 4 :

Solve the equation:

3x = 15 - 39 + 15x

3x = 15x - 24

-12x = - 24

x = 2

substituting this x-value into the "isolated equation" to find y:

y = 13 - 5x = 13 - 5(2) = 13 - 10 = 3

The solution to the system is (2, 3).  This point is used to check for solutions in both equations.

Interpreting the solution of a system of equations involves determining the type of solution (unique, infinitely many, or no solution) and understanding how it relates to the problem being solved. It allows us to find the specific values for the variables that satisfy all the equations and provides insights into the relationships between the variables.

Interpreting the solution of a system of equations is a crucial step in solving a problem. It allows us to understand the relationship between the variables and determine the values that satisfy all the equations in the system. Here's how you can interpret the solution:

1. Determine the type of solution: A system of equations can have three types of solutions: a unique solution, infinitely many solutions, or no solution. To determine the type of solution, solve the system of equations using methods such as substitution, elimination, or matrices.

2. Unique solution: If the system of equations has a unique solution, it means that there is only one set of values for the variables that satisfies all the equations. This solution represents the point where all the equations intersect. In practical terms, this means that there is a specific answer to the problem being solved.

3. Infinitely many solutions: If the system of equations has infinitely many solutions, it means that there are multiple sets of values for the variables that satisfy all the equations. This usually occurs when the equations represent the same line or planes that overlap. In practical terms, this may indicate that there are multiple valid solutions to the problem.

4. No solution: If the system of equations has no solution, it means that there are no values for the variables that satisfy all the equations simultaneously. This usually occurs when the equations represent parallel lines or planes that do not intersect. In practical terms, this may indicate that the problem being solved is not feasible or does not have a valid solution.

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To divide the given polynomial by a binomial, use polynomial long division, resulting in a quotient of -2x² - 10x - 30 and a remainder of 92.

Dividing a Polynomial by a Binomial

To divide the polynomial -2x³ – 4x² + 3x + 2 by the binomial x - 3, we will use polynomial long division, which is a process similar to long division with numbers. It involves subtracting multiples of the divisor from the dividend to get a quotient and possibly a remainder.

First, divide the first term of the dividend, -2x³, by the first term of the divisor, x, to get -2x².

Multiply the divisor x - 3 by the first term of the quotient, -2x², to get -2x³ + 6x².

Subtract this result from the dividend to obtain the new dividend -4x2 (adjusting the original terms), which becomes -10x².

Repeat this process with the remaining terms of the new dividend.

Continue until all terms of the dividend have been divided.

This process results in the quotient -2x² - 10x - 30 and a remainder of 92. The complete division statement is -2x³ – 4x² + 3x + 2 = (x - 3)(-2x² - 10x - 30) + 92.

Answer:

1377 minutes

Step-by-step explanation:

645 + 732 = 1377 min

Answer:

0.0555555556

Step-by-step explanation:

Answer:

1/18 or 0.055...

Step-by-step explanation:

2/36=1/18

Answer:

8.9 thats rounded if it wasnt rounded it'll be 8.944

Step-by-step explanation

AB = 14.42

If you plot these points on a graph, they will not be in a straight line, so we'll need to do a little more math here. Draw a diagonal line connecting both points, and use this line as the hypotenuse, so you can draw a right triangle. Count the lengths of each side (except the long, diagonal line called the hypotenuse). Use the equation a^2 + b^2 = c^2 to find the length of side c.

Since side a is 8 units long, square it to get 64.

And side b is 12 units long, and if we square it we get 144.

64 + 144 = 208.

One last step. Now we need to find the square root of 208.

It is 14.42.

So, the distance between points a and b is 14.42 units.

Answer:

Step-by-step explanation:

reduced amount  = 70 - 40 = $30

Percent of reduction =  [tex]\frac{30}{70}*100\\=\frac{300}{7} \\=42\frac{6}{7}[/tex]%

0r 42.86%

Answer:

Step-by-step explanation:

percent decrease = (original number - new number) / (original number) * 100

                              = (70 - 40) / 70 * 100

                             = 30/70 * 100

                             = 0.42857 * 100

                             = 42.857 % decrease....if u need it rounded, 42.86%....or if u

                               need it rounded to the nearest whole percent, its 43%

Answer:

Dave:

$20 + 8% of 20 = $21.6

Dave payed a total of $21.6 for the basketball.

Mel

$28 + 8% of 28 = $30.2

Mel payed a total of $30.2 for the football.

$30.2 - $21.6 = $8.6

The difference is $8.6.

Answer:

A = (90°, 1)

B = (270°,-1)

Step-by-step explanation:

if we don't use a calculator, we can explain by reasoning.

Observation 1:

recall y=sin x and y=cos x take values between -1 ≤ y ≤ 1, hence we know that the largest possible value for both functions is 1 and the smallest possible value is -1.

Observation 2:

we also know that both sin and cos functions are cyclic, which means that at some point, the function repeats itself every 360 degrees.

in question 1, we see that point A is located at the top most part of the curve, by observation 1, we can conclude that the y-value must be the maximum value of 1.

We also see that point A is 1/4 of the distance between the starting point of the curve at x=0 and to the end of the curve at x=360 before the curve begins to repeat itself,

hence the x - value is 1/4 of 360 = 90 degrees

Similarly, for point B, we see that B is at the lowest point of the curve, hence by observation 1, we can say that at B, y = -1.

B is also 3/4 of the distance between the start point and the end of the curve before it repeats itself,

hence the x-value of B is 3/4 x 360 = 270 degrees

Asa has 15 dimes and 32 quarters.

Step-by-step explanation:

Given,

Total coins = 47

Worth of coins = $9.50 = 9.50*100 = 950 cents

1 dime = 10 cents

1 quarter = 25 cents

Let,

Number of dimes = x

Number of quarters = y

According to given statement;

x+y=47      Eqn 1

10x+25y=950   Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=47)\\10x+10y=470\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](10x+25y)-(10x+10y)=950-470\\10x+25y-10x-10y=480\\15y=480[/tex]

Dividing both sides by 15

[tex]\frac{15y}{15}=\frac{480}{15}\\y=32[/tex]

Putting y=32 in Eqn 1

[tex]x+32=47\\x=47-32\\x=15[/tex]

Asa has 15 dimes and 32 quarters.

Keywords: linear equation, elimination method

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The question involves setting up and solving a system of linear equations based on the total number and value of the coins. It's a high school level mathematics question about algebra.

The subject of this question falls into the field of Mathematics, specifically algebra. We need to find the number of dimes (let's denote it as D) and quarters (Q) Asa has saved, knowing their total amount and value. We can set up a system of equations based on the information provided:

Solving this system of equations will give us the precise numbers of each coin that Asa has saved.

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Answer:

53.702

Step-by-step explanation:

You split the two numbers into two.

24, 0.41, 2, and 0,2

Then multiply each one by each other

2 x 24

2 x 0.41

0.2 x 24

0.2 x 24

24 x 2

24 x 0.2

0.41 x 2

then add all of them together and you get your answer

Answer:

606 and 612

Step-by-step explanation:

A number is a multiple of 6 if:

1. the sum of its integers can be divided by 3

2. The number is even (ending in 0, 2, 4, 6, 8

With this rule in mind, you have to play around with the numbers. Of course, all odd numbers are out.

606:

6 is even

6 + 6 = 12

12 divided by 4 is 3

612:

2 is even

6 + 1 +  2=  9

9 divided by 3 is 3

Step-by-step explanation:Given that Carter lives on a street where all the house numbers are multiples of 6. We are given to name any two possible house numbers between 601 and 650.The numbers lying between 601 and 650 are602, 603, 604, 605, . . . ,648, 649.And the numbers among these which are multiples of 6 are606, 612, 618, 624, 630, 636, 642, 648.So, any two of these eight numbers can be possible.Thus, the numbers are 606 and 650.

Density of wooden block is 850 kilogram per cubic meter

Solution:

Given that wooden block immersed partially into water

There were 15% of the total volume of the block  exposed and 85% of the total volume immersed in water

To find: density of the wooden block

The upward force exerted by any fluid upon a body placed in it is called buoyant force

Buoyant force is balanced by weight force of block

Buoyant force is weight of water displaced by block

Buoyant force = [tex]\rho_{w} V_{2} g[/tex]

Density of water = [tex]\rho_w[/tex] = 1000 kg/m3

[tex]V_2[/tex] = volume of block in water = 0.85 V

[tex]V_1[/tex] = Volume of block in air = 0.15 V

Weight of block = [tex]\rho V g[/tex]

Therefore,

[tex]\rho V g = \rho_{w} V_{2} g\\\\\rho V = \rho_{w} V_{2}\\\\ \rho V = 1000 \times 0.85V\\\\\rho = 1000 \times 0.85\\\\\rho = 850[/tex]

Thus density of wooden block is 850 kilogram per cubic meter

Answer:

Step-by-step explanation:

When you add the numbers of students with A's in history and math, you get  8+15 = 23. However, this counts the 3 kids who got A's in both subject two times! So, there are 23-3=20 (20 students) different students who got an A in at least one of the courses. That gives us 35-20=15 who didn't get an A in either.

So, the answer is 15!!

Hope this helped, have a great day! :D

Answer:

x = -4 , y = 3

Step-by-step explanation:

5x - 7y = -41 ... (i)

-3x - 5y = -3 ... (ii)

Multiplying (i) by -3 and (ii) by 5 ;

-15x + 21y = 123 ... (i)

-15x - 25y = -15 ... (ii)

Subtracting (i) by (ii) ;

0 + 46y = 138

46y = 138

y = 138 ÷ 46 = 3

Returning to equation (ii) ;

-3x - 5(3) = -3

-3x = -3 + 15

-3x = 12

x = -4

Answer: The values of x and y in the given equations are [tex]x=-4[/tex] and [tex]y=3[/tex]

Step by step explanation:

Given system of equations are

[tex]5x-7y=-41\hfill (1)[/tex]

[tex]-3x-5y=-3\hfill (2)[/tex]

To find the values of x and y :

by using Elimination method

Now multiplying the equation (1) into 3 we get

[tex]15x-21y=-123[/tex]

Now multiplying the equation (2) into 5 we get

[tex]-15x-25y=-15[/tex]

Adding the above two equations

[tex]15x-21y=-123[/tex]

[tex]-15x-25y=-15[/tex]

_________________

[tex]-46y=-138[/tex]

_________________

[tex]46y=138[/tex]

[tex]y=\frac{138}{46}[/tex]

[tex]y=3[/tex]

Therefore [tex]y=3[/tex]

Substitute y value in equation (1)

[tex]5x-7y=-41[/tex]

[tex]5x-(7\times 3)=-41[/tex]

[tex]5x-21=-41[/tex]

[tex]5x=21-41[/tex]

[tex]5x=-20[/tex]

[tex]x=-\frac{20}{5}[/tex]

[tex]x=-4[/tex]

Therefore [tex]x=-4[/tex]

The values of x and y are [tex]x=-4[/tex] and [tex]y=3[/tex]

Answer:

4

Step-by-step explanation:

Answer:

[tex]x^2-4x+4[/tex]

Step-by-step explanation:

In order to complete the square, we need to half b and then square it. This allows us to find c.

In this case, the coefficient of x is b and the unknown term is c

From this, we can see that b = -4

First, we need to half it

[tex]-\frac{4}{2} \\\\-2[/tex]

Next we need to square it

[tex](-2)^2\\\\4[/tex]

This gives us our answer of 4.

To complete the square, we want to form a perfect square trinomial from the given quadratic expression, x^2 - 4x + _____.
A perfect square trinomial is an expression that can be factored into (x - p)^2, which when expanded, is x^2 - 2px + p^2.
This means we're looking for a value that will allow us to write our given expression in the form of (x - p)^2 where -2p will be the coefficient of x, which in our case is -4.
Now, go through the steps to find the value needed to complete the square:
1. We start with the coefficient of x, which is -4.
2. To find p, we divide this coefficient by 2: -4 / 2 = -2.
3. Finally, we square this result to find the number that completes the square: (-2)^2 = 4.
Therefore, the number needed to complete the square in the expression x^2 - 4x + _____ is 4.
When you add 4, the expression becomes x^2 - 4x + 4, which is equivalent to (x - 2)^2, thus completing the square.

Answer:

5

Step-by-step explanation:

Answer:

y = 2x - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation

To fid c substitute (5, - 4) into the partial equation

- 4 = 10 + c ⇒ c = - 4 - 10 = - 14

y = 2x - 14 ← equation of parallel line

Janice earns $12.50 per hour. If her tours last 1 hour each, that's also her rate per tour. She needs to give 40 tours to reach her goal of $500.

First, we need to find out how much Janice earns per hour. She earns $62.50 for 5 hours of work, so we divide $62.50 by 5 to find her hourly rate. This gives us $12.50 per hour. If Janice's goal is to earn $500 by the end of the summer, we divide $500 by her hourly rate of $12.50 to find out how many hours she needs to work. This equals 40 hours total.

However, to fully answer this question, we also need to know the duration of a single tour. Without knowing how long each tour lasts, it's impossible to calculate how many tours Janice needs to give. Let's imagine each tour lasts 1 hour for simplicity. In that case, Janice would need to give 40 tours to reach her goal of $500.

So, Janice's unit rate per tour (assuming each tour is 1 hour long) is $12.50, and she needs to give 40 tours to reach her summer earnings goal of $500.

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Answer:

2.58

Step-by-step explanation:

47 1/2=95/2

122.55/(95/2)=(122.55/1)(2/95)=245.1/95=2.58

Answer:

[tex]361\dfrac{1}{9}[/tex] tons of high steel and [tex]138\dfrac{8}{9}[/tex] tons of low steel

Step-by-step explanation:

Let x be the number of tons of high grade steel and y be the number of tons ow low grade steel needed.

In x tons of high grade steel there are

[tex]0.85x[/tex] tons of iron

[tex]0.15x[/tex] tons of magnese

In y tons of low grade steel there are

[tex]0.67y[/tex] tons of iron

[tex]0.33y[/tex] tons of magnese

NASA orders 500 tons of steel, so

[tex]x+y=500[/tex]

and specifies that it must be in the proportion 80% iron and 20% magnese, so

[tex]0.85x+0.67y=500\cdot 0.8\\ \\0.85x+0.67y=400[/tex]

From the first equation,

[tex]x=500-y[/tex]

Substitute it into the second equation:

[tex]0.85(500-y)+0.67y=400\\ \\425-0.85y+0.67y=400\\ \\-0.18y=-25\\ \\y=\dfrac{2,500}{18}=138\dfrac{8}{9}\ tons\\ \\x=361\dfrac{1}{9}\ tons[/tex]

Answer:

B. [tex]y=8x[/tex]

Step-by-step explanation:

A proportional relationship in 'x' and 'y' is given as:

[tex]y=kx[/tex]

Where, 'k' is called as the constant of proportionality.

So, the graph of a proportional relationship always crosses the origin.

This means that the 'x' and 'y' intercepts of a proportional relationship is always at the origin (0, 0).

From among all the options, the option that matches the definition of a proportional relationship is option B. [tex]y=8x[/tex]

Here, [tex]k=8[/tex].

Therefore, the correct option is option B.

Answer:

A.

The cruise ship will travel 8 nautical miles in 152 minutes.

Step-by-step explanation:

Distance covered by the cruise ship in 342 minutes = 18 nautical miles

Distance covered in 1 minute = [tex]\frac{18}{342}[/tex] nautical miles

                                                = [tex]\frac{1}{19}[/tex] nautical miles

Distance covered in 152 minutes = [tex]\frac{1}{19}\times152[/tex] nautical miles

                                                       = 8 nautical miles

So, distance covered by cruise ship in 152 minutes is 8 nautical miles.

∴ The correct answer is option A.

Answer:

Step-by-step explanation:

the only way I knew this was division was because of the word quotient. Before u post, please check ur question to see if it is worded correctly....equals does not mean division.

197.6 / 5.48.....estimate

197.6 rounds to 200

5.48 rounds to 5

so the best way would be : C. 200 / 5 = 40 <===

the real answer is : 197.6 / 5.48 = 36.058.......so an estimate is not exact...but it can be close

The best way for Elena to estimate the quotient of 197.6 divided by 5.48 is to round 197.6 to 200 and 5.48 to 5, and then calculate 200 divided by 5, which gives 40 as the estimated result. This corresponds to Option C: 200 ÷ 5 = 40.

Elena wants to estimate the quotient of 197.6 divided by 5.48. Estimation involves rounding numbers to make calculations easier while still getting a number that is close enough to the actual answer for practical purposes. The ideal way to estimate is to round each number to a convenient figure that is easy to divide mentally.

In our case, 197.6 can be rounded to 200 since it is very close to it, and 5.48 can be rounded to 5 or 10. The options provided suggest rounding to the nearest whole number or to the nearest ten. Thus:

Option C (200 ÷ 5 = 40) uses rounding to the nearest fifth, which provides an estimate that is most accurate.

Option D (200 ÷ 10 = 20) also provides a reasonable estimate, but it rounds the divisor to the nearest ten, which might lead to a less accurate estimate.

Therefore, the number sentence that shows the best way to estimate this quotient is Option C: 200 ÷ 5 = 40.

Answer:

the first one is "perpendicular"

the second one is also  "perpendicular"

Step-by-step explanation:

Answer:

1. Perpendicular; 2, perpendicular  

Step-by-step explanation:

1. Segments JK and LM

(a) Calculate the slopes of the segments

(i) Segment JK

[tex]m_{1} = \dfrac{4 - 9 }{7 - 1} = -\dfrac{5}{6}[/tex]

(ii) Segment LM

[tex]m_{2} = \dfrac{13 - 1 }{8 - (-2)} = \dfrac{12}{8 + 2} = \dfrac{12}{10 } = \dfrac{6}{5}[/tex]

(b) Compare their slopes

[tex]m_{2} =\dfrac{6}{5} = -\dfrac{1}{m_{1}}[/tex]

The two segments are perpendicular.

Their graphs are shown in Figure 1.

2. Equations

(a) Calculate the slopes of the segments

(i) First equation

4x + 5y = 10

5y = 10 - 4x

y = 2 - ⅘x

m₁ = -⅘

(ii) Second equation

5x - 4y = -28

-4y = -28 - 5x

y = 7 + ⁵/₄x

m₂ = ⁵/₄

(b) Compare the slopes

m₂ = ⁵/₄ = -1/m₁

[tex]m_{2} =\dfrac{5}{4} = -\dfrac{1}{m_{1}}[/tex]

The two lines are perpendicular.

The graphs are shown in Figure 2.

Answer:

The cost of 1 hat = $2.24

The coat of 1 pair of oven mitten = $2.06

Step-by-step explanation:

Let us assume the cost of 1 hat = $ x

The cost of 1 pair of oven mitten = $y

Case 1:   5 hat and 4 pairs of mittens for $30

Cost of 5 hats  =5 x ( cost of 1 hat) = 5 x    = $ (5 x)

Cost of 4 mittens  =4 x ( cost of 1 mittens) = 4 (y)    = $ (4 y)

Total cost of 5 hats + 4 mittens  = 5x  + 4 y

⇒ 5 x + 4 y = $30 ....... (1)

Case 2:   2 hat and 5 pairs of mittens for $30

Cost of 2 hats  =2 x ( cost of 1 hat) = 2 x    = $ (2 x)

Cost of 5 mittens  =5 x ( cost of 1 mittens) = 5 (y)    = $ (5 y)

Total cost of 2 hats + 5 mittens  = 2 x  + 5 y

⇒2 x + 5 y = $19 ....... (2)

Now, solving (1) and (2) , we get:

5 x + 4 y = $30     (multiply by -2)

2 x + 5 y = $19      (multiply by 5)

Add both equations, we get:

-10 x  - 8 y + 10 x + 25 y = -60 + 95

or, 17 y =  35

or, y =  35/17 =  2.05

or, y  = $2.06

Now, 5 x +  4y = 30

⇒ 5 x + 4 (2.06) = 30

or, 5 x = 30 - 8.24 =  21.76

so, x =  21.76/5 = 2.24

or, x =  $2.24

Hence, the cost of 1 hat = $2.24

And the coat of 1 pair of oven mitten = $2.06